problem solving in early childhood education

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Problem Solving with Others

Problem solving with others.

The skills needed to solve problems are learned just like academic skills – they don’t develop on their own or overnight

At a Glance

Preschool children are still learning how to effectively resolve disagreements. To do so, they need to take the perspective of another person and understand how their actions impact others. For example, a child is not likely to think about how taking a toy from another child would make that child mad or sad, which stands in the way of finding a safe, fair solution. You can empower children to learn to solve their own problems by helping them to identify the problem, take another child’s perspective, and implement a solution when issues arise.

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What It Looks Like

A quick glance at how you can help preschoolers develop their problem-solving skills, practice solving problems.

Encouraging children to think about and practice problem solving can prepare them to come up with solutions in the moment.

Problem Solving During Center Time

Promote children’s problem solving skills by having them think and talk about the issue. Then work with them as they explore and agree on a resolution.

Use Solutions Cards

Using solution cards prompts children to find and accept solutions. Supports like this work to build children’s ability to problem solve.

CLASSROOM STRATEGIES

Teach, Model, Support

Young children are still learning how to socialize, collaborate, and negotiate with others. With our support, children can learn these valuable skills and work together to find solutions as challenges arise. Learn key strategies you can use to teach social problem solving in advance and support it in the moment.

TRAUMA-INFORMED CARE

The Power of Play

A brief video from the Harvard Center on the Developing Child explores how play in early childhood can reduce stress (including trauma-related stress) and scaffold problem solving.

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FAMILY CONNECTION

Families as a Resource

In this article from the Center for Responsive Schools, Carol Davis shares how educators can have conversations with families about problems that occur in the classroom.

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• Download the Guiding Questions

CONSIDERING EQUITY

Considering Culture

In this NAEYC webinar, Dr. Isik-Ercan offers transformative yet practical tips educators can use to understand children’s cultural backgrounds and to support children as they encounter and solve social problems.

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PROBLEM SOLVING THROUGH BOOKS

Share and Take Turns

Written by Cheri J. Meiners, this book provides many opportunities to talk and think about social situations that young children may encounter in the classroom, such as sharing toys or taking turns.

Activity Cards for Preschool Classrooms

Part of the streamin 3 curriculum, these activity cards provide simple and fun ways you can prompt children to collaborate and solve problems together.

Solve A Problem

Create typical social scenarios that children can use to brainstorm solutions.

Partner Talk

Invite children to turn to a peer and ask them something about their life.

Dance Party

You and children will work together to create a new dance.

People Sort!

Challenge children to sort themselves by patterns or colors on their clothing.

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Includes questions and activities to guide your use of the videos, book suggestions, and activity cards featured for each of the Core Skills

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Introduction

Nature of learning and play, categories of play, object play, physical, locomotor, or rough-and-tumble play, outdoor play, social or pretend play alone or with others, development of play, effects on brain structure and functioning, benefits of play, benefits to adults of playing with children, implications for preschool education, modern challenges, role of media in children’s play, barriers to play, role of pediatricians, conclusions, lead authors, contributor, committee on psychosocial aspects of child and family health, 2017–2018, council on communications and media, 2017–2018, the power of play: a pediatric role in enhancing development in young children.

POTENTIAL CONFLICT OF INTEREST: The authors have indicated they have no potential conflicts of interest to disclose.

FINANCIAL DISCLOSURE: The authors have indicated they have no financial relationships relevant to this article to disclose.

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Michael Yogman , Andrew Garner , Jeffrey Hutchinson , Kathy Hirsh-Pasek , Roberta Michnick Golinkoff , COMMITTEE ON PSYCHOSOCIAL ASPECTS OF CHILD AND FAMILY HEALTH , COUNCIL ON COMMUNICATIONS AND MEDIA , Rebecca Baum , Thresia Gambon , Arthur Lavin , Gerri Mattson , Lawrence Wissow , David L. Hill , Nusheen Ameenuddin , Yolanda (Linda) Reid Chassiakos , Corinn Cross , Rhea Boyd , Robert Mendelson , Megan A. Moreno , MSEd , Jenny Radesky , Wendy Sue Swanson , MBE , Jeffrey Hutchinson , Justin Smith; The Power of Play: A Pediatric Role in Enhancing Development in Young Children. Pediatrics September 2018; 142 (3): e20182058. 10.1542/peds.2018-2058

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Children need to develop a variety of skill sets to optimize their development and manage toxic stress. Research demonstrates that developmentally appropriate play with parents and peers is a singular opportunity to promote the social-emotional, cognitive, language, and self-regulation skills that build executive function and a prosocial brain. Furthermore, play supports the formation of the safe, stable, and nurturing relationships with all caregivers that children need to thrive.

Play is not frivolous: it enhances brain structure and function and promotes executive function (ie, the process of learning, rather than the content), which allow us to pursue goals and ignore distractions.

When play and safe, stable, nurturing relationships are missing in a child’s life, toxic stress can disrupt the development of executive function and the learning of prosocial behavior; in the presence of childhood adversity, play becomes even more important. The mutual joy and shared communication and attunement (harmonious serve and return interactions) that parents and children can experience during play regulate the body’s stress response. This clinical report provides pediatric providers with the information they need to promote the benefits of play and and to write a prescription for play at well visits to complement reach out and read. At a time when early childhood programs are pressured to add more didactic components and less playful learning, pediatricians can play an important role in emphasizing the role of a balanced curriculum that includes the importance of playful learning for the promotion of healthy child development.

Since the publication of the American Academy of Pediatrics (AAP) Clinical Reports on the importance of play in 2007, 1 , 2 newer research has provided additional evidence of the critical importance of play in facilitating parent engagement; promoting safe, stable, and nurturing relationships; encouraging the development of numerous competencies, including executive functioning skills; and improving life course trajectories. 3 , – 5 An increasing societal focus on academic readiness (promulgated by the No Child Left Behind Act of 2001) has led to a focus on structured activities that are designed to promote academic results as early as preschool, with a corresponding decrease in playful learning. Social skills, which are part of playful learning, enable children to listen to directions, pay attention, solve disputes with words, and focus on tasks without constant supervision. 6 By contrast, a recent trial of an early mathematics intervention in preschool showed almost no gains in math achievement in later elementary school. 7 Despite criticism from early childhood experts, the 2003 Head Start Act reauthorization ended the program evaluation of social emotional skills and was focused almost exclusively on preliteracy and premath skills. 8 The AAP report on school readiness includes an emphasis on the importance of whole child readiness (including social–emotional, attentional, and cognitive skills). 9 Without that emphasis, children’s ability to pay attention and behave appropriately in the classroom is disadvantaged.

The definition of play is elusive. However, there is a growing consensus that it is an activity that is intrinsically motivated, entails active engagement, and results in joyful discovery. Play is voluntary and often has no extrinsic goals; it is fun and often spontaneous. Children are often seen actively engaged in and passionately engrossed in play; this builds executive functioning skills and contributes to school readiness (bored children will not learn well). 10 Play often creates an imaginative private reality, contains elements of make believe, and is nonliteral.

Depending on the culture of the adults in their world, children learn different skills through play. Sociodramatic play is when children act out the roles of adulthood from having observed the activities of their elders. Extensive studies of animal play suggest that the function of play is to build a prosocial brain that can interact effectively with others. 11  

Play is fundamentally important for learning 21st century skills, such as problem solving, collaboration, and creativity, which require the executive functioning skills that are critical for adult success. The United Nations Convention on the Rights of the Child has enshrined the right to engage in play that is appropriate to the age of the child in Article 21. 12 In its 2012 exhibit “The Century of the Child: 1900–2000,” the Museum of Modern Art noted, “Play is to the 21st century what work was to industrialization. It demonstrates a way of knowing, doing, and creating value.” 13 Resnick 14 has described 4 guiding principles to support creative learning in children: projects, passion, peers, and play. Play is not just about having fun but about taking risks, experimenting, and testing boundaries. Pediatricians can be influential advocates by encouraging parents and child care providers to play with children and to allow children to have unstructured time to play as well as by encouraging educators to recognize playful learning as an important complement to didactic learning. Some studies 15 , – 18 note that the new information economy, as opposed to the older industrial 1, demands more innovation and less imitation, more creativity and less conformity. Research on children’s learning indicates that learning thrives when children are given some agency (control of their own actions) to play a role in their own learning. 19 The demands of today’s world require that the teaching methods of the past 2 centuries, such as memorization, be replaced by innovation, application, and transfer. 18  

Bruner et al 20 stressed the fact that play is typically buffered from real-life consequences. Play is part of our evolutionary heritage, occurs in a wide spectrum of species, is fundamental to health, and gives us opportunities to practice and hone the skills needed to live in a complex world. 21 Although play is present in a large swath of species within the animal kingdom, from invertebrates (such as the octopus, lizard, turtle, and honey bee) to mammals (such as rats, monkeys, and humans), 22 social play is more prominent in animals with a large neocortex. 23 Studies of animal behavior suggests that play provides animals and humans with skills that will help them with survival and reproduction. 24 Locomotor skills learned through rough-and-tumble play enables escape from predators. However, animals play even when it puts them at risk of predation. 25 It is also suggested that play teaches young animals what they can and cannot do at times when they are relatively free from the survival pressures of adult life. 26 Play and learning are inextricably linked. 27 A Russian psychologist recognized that learning occurs when children actively engage in practical activities within a supportive social context. The accumulation of new knowledge is built on previous learning, but the acquisition of new skills is facilitated by social and often playful interactions. He was interested in what he called the “zone of proximal development,” which consists of mastering skills that a child could not do alone but could be developed with minimal assistance. 28 Within the zone of proximal development, the “how” of learning occurs through a reiterative process called scaffolding, in which new skills are built on previous skills and are facilitated by a supportive social environment. The construct of scaffolding has been extrapolated to younger children. Consider how a social smile at 6 to 8 weeks of age invites cooing conversations, which leads to the reciprocal dance of social communication even before language emerges, followed by social referencing (the reading of a parent’s face for nonverbal emotional content). The balance between facilitating unstructured playtime for children and encouraging adult scaffolding of play will vary depending on the competing needs in individual families, but the “serve-and-return” aspect of play requires caregiver engagement. 29  

Early learning and play are fundamentally social activities 30 and fuel the development of language and thought. Early learning also combines playful discovery with the development of social–emotional skills. It has been demonstrated that children playing with toys act like scientists and learn by looking and listening to those around them. 15 , – 17 However, explicit instructions limit a child’s creativity; it is argued that we should let children learn through observation and active engagement rather than passive memorization or direct instruction. Preschool children do benefit from learning content, but programs have many more didactic components than they did 20 years ago. 31 Successful programs are those that encourage playful learning in which children are actively engaged in meaningful discovery. 32 To encourage learning, we need to talk to children, let them play, and let them watch what we do as we go about our everyday lives. These opportunities foster the development of executive functioning skills that are critically important for the development of 21st century skills, such as collaboration, problem solving, and creativity, according to the 2010 IBM’s Global CEO Study. 33  

Play has been categorized in a variety of ways, each with its own developmental sequence. 32 , 34  

This type of play occurs when an infant or child explores an object and learns about its properties. Object play progresses from early sensorimotor explorations, including the use of the mouth, to the use of symbolic objects (eg, when a child uses a banana as a telephone) for communication, language, and abstract thought.

This type of play progresses from pat-a-cake games in infants to the acquisition of foundational motor skills in toddlers 35 and the free play seen at school recess. The development of foundational motor skills in childhood is essential to promoting an active lifestyle and the prevention of obesity. 36 , – 39 Learning to cooperate and negotiate promotes critical social skills. Extrapolation from animal data suggests that guided competition in the guise of rough-and-tumble play allows all participants to occasionally win and learn how to lose graciously. 40 Rough-and-tumble play, which is akin to the play seen in animals, enables children to take risks in a relatively safe environment, which fosters the acquisition of skills needed for communication, negotiation, and emotional balance and encourages the development of emotional intelligence. It enables risk taking and encourages the development of empathy because children are guided not to inflict harm on others. 25 , 30 , 40 The United Kingdom has modified its guidelines on play, arguing that the culture has gone too far by leaching healthy risks out of childhood: new guidelines on play by the national commission state, “The goal is not to eliminate risk.” 41  

Outdoor play provides the opportunity to improve sensory integration skills. 36 , 37 , 39 These activities involve the child as an active participant and address motor, cognitive, social, and linguistic domains. Viewed in this light, school recess becomes an essential part of a child’s day. 42 It is not surprising that countries that offer more recess to young children see greater academic success among the children as they mature. 42 , 43 Supporting and implementing recess not only sends a message that exercise is fundamentally important for physical health but likely brings together children from diverse backgrounds to develop friendships as they learn and grow. 42  

This type of play occurs when children experiment with different social roles in a nonliteral fashion. Play with other children enables them to negotiate “the rules” and learn to cooperate. Play with adults often involves scaffolding, as when an adult rotates a puzzle to help the child place a piece. Smiling and vocal attunement, in which infants learn turn taking, is the earliest example of social play. Older children can develop games and activities through which they negotiate relationships and guidelines with other players. Dress up, make believe, and imaginary play encourage the use of more sophisticated language to communicate with playmates and develop common rule-bound scenarios (eg, “You be the teacher, and I will be the student”).

Play has also been grouped as self-directed versus adult guided. Self-directed play, or free play, is crucial to children’s exploration of the world and understanding of their preferences and interests. 19 , 32 , 44 Guided play retains the child agency, such that the child initiates the play, but it occurs either in a setting that an adult carefully constructs with a learning goal in mind (eg, a children’s museum exhibit or a Montessori task) or in an environment where adults supplement the child-led exploration with questions or comments that subtly guide the child toward a goal. Board games that have well-defined goals also fit into this category. 45 For example, if teachers want children to improve executive functioning skills (see the “Tools of the Mind” curriculum), 46 they could create drum-circle games, in which children coregulate their behavior. Familiar games such as “Simon Says” or “Head, Shoulders, Knees, and Toes” ask children to control their individual actions or impulses and have been shown to improve executive functioning skills. 47 Guided play has been defined as a child-led, joyful activity in which adults craft the environment to optimize learning. 4 , 48 This approach harkens back to Vygotsky 28 and the zone of proximal development, which represents the skills that children are unable to master on their own but are able to master in the context of a safe, stable, and nurturing relationship with an adult. The guidance and dialogue provided by the adult allow the child to master skills that would take longer to master alone and help children focus on the elements of the activity to guide learning. One way to think about guided play is as “constrained tinkering.” 14 , 48 This logic also characterizes Italy’s Emilio Reggio approach, which emphasizes the importance of teaching children to listen and look.

According to Vygotsky, 28 the most efficient learning occurs in a social context, where learning is scaffolded by the teacher into meaningful contexts that resonate with children’s active engagement and previous experiences. Scaffolding is a part of guided play; caregivers are needed to provide the appropriate amount of input and guidance for children to develop optimal skills.

How does play develop? Play progresses from social smiling to reciprocal serve-and-return interactions; the development of babbling; games, such as “peek-a-boo”; hopping, jumping, skipping, and running; and fantasy or rough-and-tumble play. The human infant is born immature compared with infants of other species, with substantial brain development occurring after birth. Infants are entirely dependent on parents to regulate sleep–wake rhythms, feeding cycles, and many social interactions. Play facilitates the progression from dependence to independence and from parental regulation to self-regulation. It promotes a sense of agency in the child. This evolution begins in the first 3 months of life, when parents (both mothers and fathers) interact reciprocally with their infants by reading their nonverbal cues in a responsive, contingent manner. 49 Caregiver–infant interaction is the earliest form of play, known as attunement, 50 but it is quickly followed by other activities that also involve the taking of turns. These serve-and-return behaviors promote self-regulation and impulse control in children and form a strong foundation for understanding their interaction with adults. The back-and-forth episodes also feed into the development of language.

Reciprocal games occur with both mothers and fathers 51 and often begin in earnest with the emergence of social smiles at 6 weeks of age. Parents mimic their infant’s “ooh” and “ah” in back-and-forth verbal games, which progress into conversations in which the parents utter pleasantries (“Oh, you had a good lunch!”), and the child responds by vocalizing back. Uncontrollable crying as a response to stress in a 1-year-old is replaced as the child reaches 2 to 3 years of age with the use of words to self-soothe, building on caregivers scaffolding their emotional responses. Already by 6 months of age, the introduction of solid foods requires the giving and receiving of reciprocal signals and communicative cues. During these activities, analyses of physiologic heart rate rhythms of infants with both their mothers and fathers have shown synchrony. 49 , 52  

By 9 months of age, mutual regulation is manifested in the way infants use their parents for social referencing. 53 , 54 In the classic visual cliff experiment, it was demonstrated that an infant will crawl across a Plexiglas dropoff to explore if the mother encourages the infant but not if she frowns. Nonverbal communication slowly leads to formal verbal language skills through which emotions such as happiness, sadness, and anger are identified for the child via words. Uncontrollable crying in the 1-year-old then becomes whining in the 2-year-old and verbal requests for assistance in the 3-year-old as parents scaffold the child’s emotional responses and help him or her develop alternative, more adaptive behaviors. Repetitive games, such as peek-a-boo and “this little piggy,” offer children the joy of being able to predict what is about to happen, and these games also enhance the infants’ ability to solicit social stimulation.

By 12 months of age, a child’s experiences are helping to lay the foundation for the ongoing development of social skills. The expression of true joy and mastery on children’s faces when they take their first step is truly a magical moment that all parents remember. Infant memory, in Piagetian terms, develops as infants develop object permanence through visible and invisible displacements, such as repetitive games like peek-a-boo. With the advent of locomotor skills, rough-and-tumble play becomes increasingly available. During the second year, toddlers learn to explore their world, develop the beginnings of self-awareness, and use their parents as a home base (secure attachment), frequently checking to be sure that the world they are exploring is safe. 55 As children become independent, their ability to socially self-regulate becomes apparent: they can focus their attention and solve problems efficiently, they are less impulsive, and they can better manage the stress of strong emotions. 56 With increased executive functioning skills, they can begin to reflect on how they should respond to a situation rather than reacting impulsively. With the development of language and symbolic functioning, pretend play now becomes more prominent. 57 Fantasy play, dress up, and fort building now join the emotional and social repertoire of older children just as playground activities, tag, and hide and seek develop motor skills. In play, children are also solving problems and learning to focus attention, all of which promote the growth of executive functioning skills.

Play is not frivolous; it is brain building. Play has been shown to have both direct and indirect effects on brain structure and functioning. Play leads to changes at the molecular (epigenetic), cellular (neuronal connectivity), and behavioral levels (socioemotional and executive functioning skills) that promote learning and adaptive and/or prosocial behavior. Most of this research on brain structure and functioning has been done with rats and cannot be directly extrapolated to humans.

Jaak Panksepp, 11 a neuroscientist and psychologist who has extensively studied the neurologic basis of emotion in animals, suggests that play is 1 of 7 innate emotional systems in the midbrain. 58 Rats love rough-and-tumble play and produce a distinctive sound that Panksepp labeled “rat laughter.” 42 , 59 , – 64 When rats are young, play appears to initiate lasting changes in areas of the brain that are used for thinking and processing social interaction.

The dendritic length, complexity, and spine density of the medial prefrontal cortex (PFC) are refined by play. 64 , – 67 The brain-derived neurotrophic factor ( BDNF ) is a member of the neurotrophin family of growth factors that acts to support the survival of existing neurons and encourage the growth and differentiation of new neurons and synapses. It is known to be important for long-term memory and social learning. Play stimulates the production of BDNF in RNA in the amygdala, dorsolateral frontal cortex, hippocampus, and pons. 65 , 68 , – 70 Gene expression analyses indicate that the activities of approximately one-third of the 1200 genes in the frontal and posterior cortical regions were significantly modified by play within an hour after a 30-minute play session. 69 , 70 The gene that showed the largest effect was BDNF . Conversely, rat pup adversity, depression, and stress appear to result in the methylation and downregulation of the BDNF gene in the PFC. 71  

Two hours per day of play with objects predicted changes in brain weight and efficiency in experimental animals. 11 , 66 Rats that were deprived of play as pups (kept in sparse cages devoid of toys) not only were less competent at problem solving later on (negotiating mazes) but the medial PFC of the play-deprived rats was significantly more immature, suggesting that play deprivation interfered with the process of synaptogenesis and pruning. 72 Rat pups that were isolated during peak play periods after birth (weeks 4 and 5) are much less socially active when they encounter other rats later in life. 73 , 74  

Play-deprived rats also showed impaired problem-solving skills, suggesting that through play, animals learn to try new things and develop behavioral flexibility. 73 Socially reared rats with damage to their PFC mimic the social deficiencies of rats with intact brains but who were deprived of play as juveniles. 66 The absence of the play experience leads to anatomically measurable changes in the neurons of the PFC. By refining the functional organization of the PFC, play enhances the executive functioning skills derived from this part of the brain. 66 Whether these effects are specific to play deprivation or merely reflect the generic effect of a lack of stimulation requires further study. Rats that were raised in experimental toy-filled cages had bigger brains and thicker cerebral cortices and completed mazes more quickly. 67 , 75  

Brain neurotransmitters, such as dopamine made by cells in the substantia nigra and ventral tegmentum, are also related to the reward quality of play: drugs that activate dopamine receptors increase play behavior in rats. 76  

Play and stress are closely linked. High amounts of play are associated with low levels of cortisol, suggesting either that play reduces stress or that unstressed animals play more. 23 Play also activates norepinephrine, which facilitates learning at synapses and improves brain plasticity. Play, especially when accompanied by nurturing caregiving, may indirectly affect brain functioning by modulating or buffering adversity and by reducing toxic stress to levels that are more compatible with coping and resilience. 77 , 78  

In human children, play usually enhances curiosity, which facilitates memory and learning. During states of high curiosity, functional MRI results showed enhanced activity in healthy humans in their early 20s in the midbrain and nucleus accumbens and functional connectivity to the hippocampus, which solidifies connections between intrinsic motivation and hippocampus-dependent learning. 79 Play helps children deal with stress, such as life transitions. When 3- to 4-year-old children who were anxious about entering preschool were randomly assigned to play with toys or peers for 15 minutes compared with listening to a teacher reading a story, the play group showed a twofold decrease in anxiety after the intervention. 24 , 80 In another study, preschool children with disruptive behavior who engaged with teachers in a yearlong 1-to-1 play session designed to foster warm, caring relationships (allowing children to lead, narrating the children’s behavior out loud, and discussing the children’s emotions as they played) showed reduced salivary cortisol stress levels during the day and improved behavior compared with children in the control group. 81 The notable exception is with increased stress experienced by children with autism spectrum disorders in new or social circumstances. 82 Animal studies suggest the role of play as a social buffer. Rats that were previously induced to be anxious became relaxed and calm after rough-and-tumble play with a nonanxious playful rat. 83 Extrapolating from these animal studies, one can suggest that play may serve as an effective buffer for toxic stress.

The benefits of play are extensive and well documented and include improvements in executive functioning, language, early math skills (numerosity and spatial concepts), social development, peer relations, physical development and health, and enhanced sense of agency. 13 , 32 , 56 , 57 , 84 , – 88 The opposite is also likely true; Panksepp 89 suggested that play deprivation is associated with the increasing prevalence of attention-deficit/hyperactivity disorder. 90  

Executive functioning, which is described as the process of how we learn over the content of what we learn, is a core benefit of play and can be characterized by 3 dimensions: cognitive flexibility, inhibitory control, and working memory. Collectively, these dimensions allow for sustained attention, the filtering of distracting details, improved self-regulation and self-control, better problem solving, and mental flexibility. Executive functioning helps children switch gears and transition from drawing with crayons to getting dressed for school. The development of the PFC and executive functioning balances and moderates the impulsiveness, emotionality, and aggression of the amygdala. In the presence of childhood adversity, the role of play becomes even more important in that the mutual joy and shared attunement that parents and children can experience during play downregulates the body’s stress response. 91 , – 94 Hence, play may be an effective antidote to the changes in amygdala size, impulsivity, aggression, and uncontrolled emotion that result from significant childhood adversity and toxic stress. Future research is needed to clarify this association.

Opportunities for peer engagement through play cultivate the ability to negotiate. Peer play usually involves problem solving about the rules of the game, which requires negotiation and cooperation. Through these encounters, children learn to use more sophisticated language when playing with peers. 95 , 96  

Play in a variety of forms (active physical play, pretend play, and play with traditional toys and shape sorters [rather than digital toys]) improves children’s skills. When children were given blocks to play with at home with minimal adult direction, preschool children showed improvements in language acquisition at a 6-month follow-up, particularly low-income children. The authors suggest that the benefits of Reach Out and Play may promote development just as Reach Out and Read does. 97 When playing with objects under minimal adult direction, preschool children named an average of 3 times as many nonstandard uses for an object compared with children who were given specific instructions. 98 In Jamaica, toddlers with growth retardation who were given weekly play sessions to improve mother–child interactions for 2 years were followed to adulthood and showed better educational attainment, less depression, and less violent behavior. 3  

Children who were in active play for 1 hour per day were better able to think creatively and multitask. 22 Randomized trials of physical play in 7- to 9-year-olds revealed enhanced attentional inhibition, cognitive flexibility, and brain functioning that were indicative of enhanced executive control. 99 Play with traditional toys was associated with an increased quality and quantity of language compared with play with electronic toys, 100 particularly if the video toys did not encourage interaction. 101 Indeed, it has been shown that play with digital shape sorters rather than traditional shape sorters stunted the parent’s use of spatial language. 102 Pretend play encourages self-regulation because children must collaborate on the imaginary environment and agree about pretending and conforming to roles, which improves their ability to reason about hypothetical events. 56 , 57 , 103 , – 105 Social–emotional skills are increasingly viewed as related to academic and economic success. 106 Third-grade prosocial behavior correlated with eighth-grade reading and math better than with third-grade reading and math. 17 , 107  

The health benefits of play involving physical activity are many. Exercise not only promotes healthy weight and cardiovascular fitness but also can enhance the efficacy of the immune, endocrine, and cardiovascular systems. 37 Outdoor playtime for children in Head Start programs has been associated with decreased BMI. 39 Physical activity is associated with decreases in concurrent depressive symptoms. 108 Play decreases stress, fatigue, injury, and depression and increases range of motion, agility, coordination, balance, and flexibility. 109 Children pay more attention to class lessons after free play at recess than they do after physical education programs, which are more structured. 43 Perhaps they are more active during free play.

Play also reflects and transmits cultural values. In fact, recess began in the United States as a way to socially integrate immigrant children. Parents in the United States encourage children to play with toys and/or objects alone, which is typical of communities that emphasize the development of independence. Conversely, in Japan, peer social play with dolls is encouraged, which is typical of cultures that emphasize interdependence. 110  

Playing with children adds value not only for children but also for adult caregivers, who can reexperience or reawaken the joy of their own childhood and rejuvenate themselves. Through play and rereading their favorite childhood books, parents learn to see the world from their child’s perspective and are likely to communicate more effectively with their child, even appreciating and sharing their child’s sense of humor and individuality. Play enables children and adults to be passionately and totally immersed in an activity of their choice and to experience intense joy, much as athletes do when they are engaging in their optimal performance. Discovering their true passions is another critical strategy for helping both children and adults cope with adversity. One study documented that positive parenting activities, such as playing and shared reading, result in decreases in parental experiences of stress and enhancement in the parent–child relationship, and these effects mediate relations between the activities and social–emotional development. 111 , – 113  

Most importantly, play is an opportunity for parents to engage with their children by observing and understanding nonverbal behavior in young infants, participating in serve-andreturn exchanges, or sharing the joy and witnessing the blossoming of the passions in each of their children.

Play not only provides opportunities for fostering children’s curiosity, 14 self-regulation skills, 46 language development, and imagination but also promotes the dyadic reciprocal interactions between children and parents, which is a crucial element of healthy relationships. 114 Through the buffering capacity of caregivers, play can serve as an antidote to toxic stress, allowing the physiologic stress response to return to baseline. 77 Adult success in later life can be related to the experience of childhood play that cultivated creativity, problem solving, teamwork, flexibility, and innovations. 18 , 52 , 115  

Successful scaffolding (new skills built on previous skills facilitated by a supportive social environment) can be contrasted with interactions in which adults direct children’s play. It has been shown that if a caregiver instructs a child in how a toy works, the child is less likely to discover other attributes of the toy in contrast to a child being left to explore the toy without direct input. 38 , 116 , – 118 Adults who facilitate a child’s play without being intrusive can encourage the child’s independent exploration and learning.

Scaffolding play activities facilitated by adults enable children to work in groups: to share, negotiate, develop decision-making and problem-solving skills, and discover their own interests. Children learn to resolve conflicts and develop self-advocacy skills and their own sense of agency. The false dichotomy between play versus formal learning is now being challenged by educational reformers who acknowledge the value of playful learning or guided play, which captures the strengths of both approaches and may be essential to improving executive functioning. 18 , 19 , 34 , 119 Hirsh-Pasek et al 34 report a similar finding: children have been shown to discover causal mechanisms more quickly when they drive their learning as opposed to when adults display solutions for them.

Executive functioning skills are foundational for school readiness and academic success, mandating a frame shift with regard to early education. The goal today is to support interventions that cultivate a range of skills, such as executive functioning, in all children so that the children enter preschool and kindergarten curious and knowing how to learn. Kindergarten should provide children with an opportunity for playful collaboration and tinkering, 14 a different approach from the model that promotes more exclusive didactic learning at the expense of playful learning. The emerging alternative model is to prevent toxic stress and build resilience by developing executive functioning skills. Ideally, we want to protect the brain to enable it to learn new skills, and we want to focus on learning those skills that will be used to buffer the brain from any future adversity. 18 The Center on the Developing Child at Harvard University offers an online resource on play and executive functioning with specific activities suggested for parents and children ( http://developingchild.harvard.edu/wp-content/uploads/2015/05/Enhancing-and-Practicing-Executive-Function-Skills-with-Children-from-Infancy-to-Adolescence-1.pdf ). 120  

Specific curricula have now been developed and tested in preschools to help children develop executive functioning skills. Many innovative programs are using either the Reggio Emilia philosophy or curricula such as Tools of the Mind (developed in California) 121 or Promoting Alternative Thinking Strategies–Preschool and/or Kindergarten. 122 Caregivers need to provide the appropriate amount of input and guidance for children to develop optimal problem-solving skills through guided play and scaffolding. Optimal learning can be depicted by a bell-shaped curve, which illustrates the optimal zone of arousal and stress for complex learning. 123  

Scaffolding is extensively used to support skills such as buddy reading, in which children take turns being lips and ears and learn to read and listen to each other as an example of guided play. A growing body of research shows that this curriculum not only improves executive functioning skills but also shows improvement in brain functioning on functional MRI. 6 , 124 , – 126  

Focusing on cultivating executive functioning and other skills through playful learning in these early years is an alternative and innovative way of thinking about early childhood education. Instead of focusing solely on academic skills, such as reciting the alphabet, early literacy, using flash cards, engaging with computer toys, and teaching to tests (which has been overemphasized to promote improved test results), cultivating the joy of learning through play is likely to better encourage long-term academic success. Collaboration, negotiation, conflict resolution, self-advocacy, decision-making, a sense of agency, creativity, leadership, and increased physical activity are just some of the skills and benefits children gain through play.

For many families, there are risks in the current focus only on achievement, after-school enrichment programs, increased homework, concerns about test performance, and college acceptance. The stressful effects of this approach often result in the later development of anxiety and depression and a lack of creativity. Parental guilt has led to competition over who can schedule more “enrichment opportunities” for their children. As a result, there is little time left in the day for children’s free play, for parental reading to children, or for family meal times. Many schools have cut recess, physical education, art, and music to focus on preparing children for tests. Unsafe local neighborhoods and playgrounds have led to nature deficit disorder for many children. 127 A national survey of 8950 preschool children and parents found that only 51% of children went outside to walk or play once per day with either parent. 128 In part, this may reflect the local environment: 94% of parents have expressed safety concerns about outdoor play, and access may be limited. Only 20% of homes are located within a half-mile of a park. 129 , 130 Cultural changes have also jeopardized the opportunities children have to play. From 1981 to 1997, children’s playtime decreased by 25%. Children 3 to 11 years of age have lost 12 hours per week of free time. Because of increased academic pressure, 30% of US kindergarten children no longer have recess. 42 , 129 An innovative program begun in Philadelphia is using cities (on everyday walks and in everyday neighborhoods) as opportunities for creating learning landscapes that provide opportunities for parents and children to spark conversation and playful learning. 131 , 132 For example, Ridge et al 132 have placed conversational prompts throughout supermarkets and laundromats to promote language and lights at bus stops to project designs on the ground, enabling children to play a game of hopscotch that is specifically designed to foster impulse control. By promoting the learning of social and emotional skills, the development of emotional intelligence, and the enjoyment of active learning, protected time for free play and guided play can be used to help children improve their social skills, literacy, and school readiness. Children can then enter school with a stronger foundation for attentional disposition based on the skills and attitudes that are critical for academic success and the long-term enjoyment of learning and love of school.

Media (eg, television, video games, and smartphone and tablet applications) use often encourages passivity and the consumption of others’ creativity rather than active learning and socially interactive play. Most importantly, immersion in electronic media takes away time from real play, either outdoors or indoors. Real learning happens better in person-to-person exchanges rather than machine-to-person interactions. Most parents are eager to do the right thing for their children. However, advertisers and the media can mislead parents about how to best support and encourage their children’s growth and development as well as creativity. Parent surveys have revealed that many parents see media and technology as the best way to help their children learn. 133 However, researchers contradict this. Researchers have compared preschoolers playing with blocks independently with preschoolers watching Baby Einstein tapes and have shown that the children playing with blocks independently developed better language and cognitive skills than their peers watching videos. 34 , 134 Although active engagement with age-appropriate media, especially if supported by cowatching or coplay with peers or parents, may have some benefits, 135 real-time social interactions remain superior to digital media for home learning. 136  

It is important for parents to understand that media use often does not support their goals of encouraging curiosity and learning for their children. 137 , – 141 Despite research that reveals an association between television watching and a sedentary lifestyle and greater risks of obesity, the typical preschooler watches 4.5 hours of television per day, which displaces conversation with parents and the practice of joint attention (focus by the parent and child on a common object) as well as physical activity. For economically challenged families, competing pressures make it harder for parents to find the time to play with children. Encouraging outdoor exercise may be more difficult for such families given unsafe playgrounds. Easy access to electronic media can be difficult for parents to compete with.

In the 2015 symposium, 137 the AAP clarified recommendations acknowledging the ubiquity and transformation of media from primarily television to other modalities, including video chatting. In 2016, the AAP published 2 new policies on digital media affecting young children, school-aged children, and adolescents. These policies included recommendations for parents, pediatricians, and researchers to promote healthy media use. 139 , 140 The AAP has also launched a Family Media Use Plan to help parents and families create healthy guidelines for their children’s media use so as to avoid displacing activities such as active play, and guidelines can also be found on the HealthyChildren.org and Common Sense Media (commonsensemedia.org) Web sites.

There are barriers to encouraging play. Our culture is preoccupied with marketing products to young children. 142 Parents of young children who cannot afford expensive toys may feel left out. 143 Parents who can afford expensive toys and electronic devices may think that allowing their children unfettered access to these objects is healthy and promotes learning. The reality is that children’s creativity and play is enhanced by many inexpensive toys (eg, wooden spoons, blocks, balls, puzzles, crayons, boxes, and simple available household objects) and by parents who engage with their children by reading, watching, playing alongside their children, and talking with and listening to their children. It is parents’ and caregivers’ presence and attention that enrich children, not elaborate electronic gadgets. One-on-one play is a time-tested way of being fully present. Low-income families may have less time to play with their children while working long hours to provide for their families, but a warm caregiver or extended family as well as a dynamic community program can help support parents’ efforts. 144 The importance of playtime with children cannot be overemphasized to parents as well as schools and community organizations. Many children do not have safe places to play. 145 Neighborhood threats, such as violence, guns, drugs, and traffic, pose safety concerns in many neighborhoods, particularly low-income areas. Children in low-income, urban neighborhoods also may have less access to quality public spaces and recreational facilities in their communities. 145 Parents who feel that their neighborhoods are unsafe may also not permit their children to play outdoors or independently.

Public health professionals are increasingly partnering with other sectors, such as parks and recreation, public safety, and community development, to advocate for safe play environments in all communities. This includes efforts to reduce community violence, improve physical neighborhood infrastructure, and support planning and design decisions that foster safe, clean, and accessible public spaces.

Pediatricians can advocate for the importance of all forms of play as well as for the role of play in the development of executive functioning, emotional intelligence, and social skills ( Table 1 ). Pediatricians have a critical role to play in protecting the integrity of childhood by advocating for all children to have the opportunity to express their innate curiosity in the world and their great capacity for imagination. For children with special needs, it is especially important to create safe opportunities for play. A children’s museum may offer special mornings when it is open only to children with special needs. Extra staffing enables these children and their siblings to play in a safe environment because they may not be able to participate during crowded routine hours.

Recommendations From Pediatricians to Parents

Adapted from pathways.org ( https://pathways.org/wp-content/uploads/2019/07/PlayBrochure_English_LEGAL_FOR-PRINT_2022.pdf ).

The AAP recommends that pediatricians:

Encourage parents to observe and respond to the nonverbal behavior of infants during their first few months of life (eg, responding to their children’s emerging social smile) to help them better understand this unique form of communication. For example, encouraging parents to recognize their children’s emerging social smile and to respond with a smile of their own is a form of play that also teaches the infants a critical social–emotional skill: “You can get my attention and a smile from me anytime you want just by smiling yourself.” By encouraging parents to observe the behavior of their children, pediatricians create opportunities to engage parents in discussions that are nonjudgmental and free from criticism (because they are grounded in the parents’ own observations and interpretations of how to promote early learning);

Advocate for the protection of children’s unstructured playtime because of its numerous benefits, including the development of foundational motor skills that may have lifelong benefits for the prevention of obesity, hypertension, and type 2 diabetes;

Advocate with preschool educators to do the following: focus on playful rather than didactic learning by letting children take the lead and follow their own curiosity; put a premium on building social–emotional and executive functioning skills throughout the school year; and protect time for recess and physical activity;

Emphasize the importance of playful learning in preschool curricula for fostering stronger caregiver–infant relationships and promoting executive functioning skills. Communicating this message to policy makers, legislators, and educational administrators as well as the broader public is equally important; and

Just as pediatricians support Reach Out and Read, encourage playful learning for parents and infants by writing a “prescription for play” at every well-child visit in the first 2 years of life.

A recent randomized controlled trial of the Video Interaction Project (an enhancement of Reach Out and Read) has demonstrated that the promotion of reading and play during pediatric visits leads to enhancements in social–emotional development. 112 In today’s world, many parents do not appreciate the importance of free play or guided play with their children and have come to think of worksheets and other highly structured activities as play. 146 Although many parents feel that they do not have time to play with their children, pediatricians can help parents understand that playful learning moments are everywhere, and even daily chores alongside parents can be turned into playful opportunities, especially if the children are actively interacting with parents and imitating chores. Young children typically seek more attention from parents. 46 Active play stimulates children’s curiosity and helps them develop the physical and social skills needed for school and later life. 32  

Cultural shifts, including less parent engagement because of parents working full-time, fewer safe places to play, and more digital distractions, have limited the opportunities for children to play. These factors may negatively affect school readiness, children’s healthy adjustment, and the development of important executive functioning skills;

Play is intrinsically motivated and leads to active engagement and joyful discovery. Although free play and recess need to remain integral aspects of a child’s day, the essential components of play can also be learned and adopted by parents, teachers, and other caregivers to promote healthy child development and enhance learning;

The optimal educational model for learning is for the teacher to engage the student in activities that promote skills within that child’s zone of proximal development, which is best accomplished through dialogue and guidance, not via drills and passive rote learning. There is a current debate, particularly about preschool curricula, between an emphasis on content and attempts to build skills by introducing seat work earlier versus seeking to encourage active engagement in learning through play. With our understanding of early brain development, we suggest that learning is better fueled by facilitating the child’s intrinsic motivation through play rather than extrinsic motivations, such as test scores;

An alternative model for learning is for teachers to develop a safe, stable, and nurturing relationship with the child to decrease stress, increase motivation, and ensure receptivity to activities that promote skills within each child’s zone of proximal development. The emphasis in this preventive and developmental model is to promote resilience in the presence of adversity by enhancing executive functioning skills with free play and guided play;

Play provides ample opportunities for adults to scaffold the foundational motor, social–emotional, language, executive functioning, math, and self-regulation skills needed to be successful in an increasingly complex and collaborative world. Play helps to build the skills required for our changing world; and

Play provides a singular opportunity to build the executive functioning that underlies adaptive behaviors at home; improve language and math skills in school; build the safe, stable, and nurturing relationships that buffer against toxic stress; and build social–emotional resilience.

For more information, see Kearney et al’s Using Joyful Activity To Build Resiliency in Children in Response to Toxic Stress . 147  

American Academy of Pediatrics

brain-derived neurotrophic factor

prefrontal cortex

Dr Yogman prepared the first draft of this report and took the lead in reconciling the numerous edits, contributions, and suggestions from the other authors; Drs Garner, Hutchinson, Hirsh-Pasek, and Golinkoff made significant contributions to the manuscript by revising multiple drafts and responding to all reviewer concerns; and all authors approved the final manuscript as submitted.

The opinions and assertions expressed herein are those of the author(s) and do not necessarily reflect the official policy or position of the Uniformed Services University or the Department of Defense.

FUNDING: No external funding.

This document is copyrighted and is property of the American Academy of Pediatrics and its Board of Directors. All authors have filed conflict of interest statements with the American Academy of Pediatrics. Any conflicts have been resolved through a process approved by the Board of Directors. The American Academy of Pediatrics has neither solicited nor accepted any commercial involvement in the development of the content of this publication.

Clinical reports from the American Academy of Pediatrics benefit from expertise and resources of liaisons and internal (AAP) and external reviewers. However, clinical reports from the American Academy of Pediatrics may not reflect the views of the liaisons or the organizations or government agencies that they represent.

The guidance in this report does not indicate an exclusive course of treatment or serve as a standard of medical care. Variations, taking into account individual circumstances, may be appropriate.

All clinical reports from the American Academy of Pediatrics automatically expire 5 years after publication unless reaffirmed, revised, or retired at or before that time.

Michael Yogman, MD, FAAP

Andrew Garner, MD, PhD, FAAP

Jeffrey Hutchinson, MD, FAAP

Kathy Hirsh-Pasek, PhD

Roberta Golinkoff, PhD

Virginia Keane, MD, FAAP

Michael Yogman, MD, FAAP, Chairperson

Rebecca Baum, MD, FAAP

Thresia Gambon, MD, FAAP

Arthur Lavin, MD, FAAP

Gerri Mattson, MD, FAAP

Lawrence Wissow, MD, MPH, FAAP

Sharon Berry, PhD, LP – Society of Pediatric Psychology

Amy Starin, PhD, LCSW – National Association of Social Workers

Edward Christophersen, PhD, FAAP – Society of Pediatric Psychology

Norah Johnson, PhD, RN, CPNP-BC – National Association of Pediatric Nurse Practitioners

Abigail Schlesinger, MD – American Academy of Child and Adolescent Psychiatry

Karen S. Smith

David L Hill, MD, FAAP, Chairperson

Nusheen Ameenuddin, MD, MPH, FAAP

Yolanda (Linda) Reid Chassiakos, MD, FAAP

Corinn Cross, MD, FAAP

Rhea Boyd, MD, FAAP

Robert Mendelson, MD, FAAP

Megan A Moreno, MD, MSEd, MPH, FAAP

Jenny Radesky, MD, FAAP

Wendy Sue Swanson, MD, MBE, FAAP

Justin Smith, MD, FAAP

Kristopher Kaliebe, MD – American Academy of Child and Adolescent Psychiatry

Jennifer Pomeranz, JD, MPH – American Public Health Association Health Law Special Interest Group

Brian Wilcox, PhD – American Psychological Association

Thomas McPheron

Competing Interests

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Mathematical Problem Solving in the Early Years: Developing Opportunities, Strategies and Confidence

• familiar contexts
• meaningful purposes
• mathematical complexity.

• which they understand - in familiar contexts,
• where the outcomes matter to them - even if imaginary,
• where they have control of the process,
• involving mathematics with which they are confident.
• taking some from one doll and giving to another, in several moves,
• starting again and dealing, either in ones or twos,
• taking two from each original doll and giving to the new doll,
• collecting the biscuits and crumbling them into a heap, then sharing out handfuls of crumbs.

• brute force: trying to hammer bits so that they fit,
• local correction: adjusting one part, often creating a different problem,
• dismantling: starting all over again,
• holistic review: considering multiple relations or simultaneous adjustments e.g. repairing by insertion and reversal.
• getting a feel for the problem, looking at it holistically, checking they have understood e.g. talking it through or asking questions;
• planning, preparing and predicting outcomes e.g. gathering blocks together before building;
• monitoring progress towards the goal e.g. checking that the bears will fit the houses;
• being systematic, trying possibilities methodically without repetition, rather than at random, e.g. separating shapes tried from those not tried in a puzzle;
• trying alternative approaches and evaluating strategies e.g. trying different positions for shapes;
• refining and improving solutions e.g. solving a puzzle again in fewer moves (Gifford, 2005: 153).
• Getting to grips:     What are we trying to do?    
• Connecting to previous experience:  Have we done anything like this before?
• Planning:      What do we need?
• Considering alternative methods:   Is there another way?
• Monitoring progress:    How does it look so far?
• Evaluating solutions:    Does it work?  How can we check?  Could we make it even better?

• Construction - finding shapes which fit together or balance
• Pattern-making - creating a rule to create a repeating pattern
• Shape pictures - selecting shapes with properties to represent something
• Puzzles - finding ways of fitting shapes to fit a puzzle
• Role-play areas - working out how much to pay in a shop
• Measuring tools - finding out how different kinds of scales work
• Nesting, posting, ordering - especially if they are not obvious
• Robots - e.g. beebots: directing and making routes
• preparing, getting the right number e.g. scissors, paper for creative activities
• sharing equal amounts e.g. at snack time
• tidying up, checking nothing is lost
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• PE: organising in groups, timing and recording

• Decision making - what shall we call the new guinea pig?
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• Design Projects - the role play area, new outdoor gardens or circuits
• Hiding games - feely bags with shapes, the 'Box' game
• Story problems - e.g. unfair sharing, with remainders and fractions, making things to fit giants or fairies

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Research on early childhood mathematics teaching and learning

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• Volume 52 , pages 607–619, ( 2020 )

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• Camilla Björklund   ORCID: orcid.org/0000-0001-5436-537X 1 ,
• Marja van den Heuvel-Panhuizen 2 , 3 &
• Angelika Kullberg 1  

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This paper reports an overview of contemporary research on early childhood mathematics teaching and learning presented at recent mathematics education research conferences and papers included in the special issue (2020–4) of ZDM Mathematics Education . The research covers the broad spectrum of educational research focusing on different content and methods in teaching and learning mathematics among the youngest children in the educational systems. Particular focus in this paper is directed to what lessons can be drawn from teaching interventions in early childhood, what facilitates children’s mathematical learning and development, and what mathematical key concepts can be observed in children. Together, these themes offer a coherent view of the complexity of researching mathematical teaching and learning in early childhood, but the research also brings this field forward by adding new knowledge that extends our understanding of aspects of mathematics education and research in this area, in the dynamic context of early childhood. This knowledge is important for future research and for the development of educational practices.

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1 Introduction

Early childhood mathematics education is a rich field of study and practice that includes the provision of stimulating activities and learning environments, organized and orchestrated by teachers, care-takers and other professionals with the aim of offering young children experiences that extend their knowledge and development of mathematical concepts and skills. Generally, early childhood mathematics education involves children aged 3–6 years, but in many countries even the youngest toddlers go to early childhood centres. Therefore, contemporary research on early mathematics education focuses on children from birth until they enter formal schooling in the first grade. To develop this field of research, a strong foundation of theory and methodology is necessary, along with consideration of the practical settings of young children’s learning as well as the societal needs and relevant educational policy frameworks. Moreover, from a didactical perspective, it also requires consideration of the essence of the mathematics to be taught to young children.

High-quality research grounded in theory is necessary for all areas of mathematics education, in order to move forward and contribute to the generation of new knowledge from which the educational practice can benefit. Since there is much evidence that later development in mathematics is laid in the early years (e.g., Duncan et al. 2007 ; Krajewski and Schneider 2009 ; Levine et al. 2010 ), such high-quality research is especially critical for early childhood mathematics education. Research involving young children entails certain challenges that cannot simply be solved by adopting research designs that are used with older students. The aim of gaining deep knowledge of how young children’s mathematical understanding can be fostered places high demands on research methods. As early as 40 years ago, Donaldson ( 1978 ) stated that children act differently in their everyday situations than they do in experiment situations, and this has been confirmed by many others since then. Thus, gaining knowledge about teaching and learning mathematics in the early years requires research that is conducted in various learning environments and that acknowledges that these learning environments are complex, multifaceted, and dynamic.

Research in mathematics education is a relatively recent scientific discipline beginning in the last century (Kilpatrick 2014 ). Investigating young children’s mathematical learning and teaching became part of this discipline much later. Early childhood mathematics has long been the research field of developmental psychology and cognitive sciences. From the studies of mental abilities and thinking in mathematical problem-solving carried out in these disciplines, we have gained knowledge about the influence of working memory and attention span (e.g., Ashcraft et al. 1992 ; Passolunghi and Costa 2016 ; Stipek and Valentino 2015 ), as well as about the role of innate abilities of numerical awareness in children’s mathematical performance (e.g., Butterworth 2005 ; Wynn 1998 ). Yet, these studies lack a deeper investigation of the mathematics that is performed and how it is developed by children. Neither do such investigations address why certain mathematical competencies are important or why some activities stimulate their development and others do not. Contrary to psychological research, mathematics education research has a didactic perspective, which means that it is linked to the perspective of the learning child, the teaching teacher, and the environment offering learning opportunities in which the teaching and learning take place. Above all, didactic research distinguishes itself from psychological research because it deals explicitly with the question of what the mathematics is in early childhood activities, both within and outside formal education.

2 A brief overview of the current field of early mathematics education research

As shown by the many publications on teaching and learning of mathematics in early childhood that have been released in the past few years, this area of mathematics education research has increasingly become a mature discipline. The same is reflected by the special interest groups, working groups, and research fora dedicated to mathematics education in the early years. No self-respecting conference today can afford not to pay attention to the area of early mathematics, and there are now also communities and conferences that focus exclusively on early childhood mathematics education. All these communities and conferences are the epicentres where the latest developments in this field are brought together. To set the scene for research on early childhood mathematics teaching and learning, without it being complete, we first provide a brief overview of recently presented and discussed early mathematics education research. As an orientation point for this overview, we used what has recently been presented by researchers at three international meetings.

2.1 CERME 11 thematic working group (TWG) on early years mathematics

A conference that already has a considerable track record for including early childhood mathematics as a fixed part of its programme is the biennial conference of the European Society for Research in Mathematics Education (ERME). This conference started in 2009 with a Thematic Working Group (TWG) on Early Years Mathematics. Since then, the number of participants in this group has grown consistently. In 2019, this TWG (that is, TWG13) consisted not only of European researchers but also attracted participants from Canada, Japan, and Malawi. The most dominant theme presented there involved studies of children’s emerging number knowledge. Many of these presentations were traditional in design, including giving children tasks that had to be solved both individually when the children were interviewed and when they worked in groups in a classroom setting. Based on these studies, researchers formulated descriptions of the children’s knowledge. Sometimes, learning trajectories could be generated from these empirical observations. However, within this TWG several examples of studies with more innovative designs and research settings were also presented, including different modes of exploring and expressing numbers, which can extend our knowledge of early childhood mathematics education. An example of such research is Bjørnebye’s ( 2019 ) study, in which a dice game including elements of multiple representations and embodiment of counting strategies opened up the possibility of observing how children’s actions and responses reflect their understanding. Other studies investigated how affordances of manipulatives and applications encouraged children to develop new ways of thinking about numbers either by working in a digital environment (Bakos and Sinclair 2019 ) or by using their fingers to represent numbers (Lüken 2019 ; Björklund and Runesson Kempe 2019 ).

A characteristic of the research community gathered at CERME11 TWG13 is that the participants generally had in common an interest in better understanding the mathematical thinking of the child. Therefore, it was considered crucial that research establish clues for how to recognize mathematical thinking in the early years. For this purpose, Sprenger and Benz ( 2019 ) used eye-tracking data, as this platform was considered to contribute to the analysis of children’s perception of structure in the process of determining quantities. Yet, what Sprenger and Benz discovered is that data from technological devices still need to be interpreted, and that other expressions of children’s perceptions and reasoning are necessary assets for drawing valid conclusions.

A further important issue that was present at CERME11 TWG13 was related to teaching practice. Specifically, several presentations addressed the questions of how mathematics education should be orchestrated in early childhood education and what opportunities to learn should be offered to children. For example, Breive ( 2019 ) investigated the link between inquiry-based education and open-ended problem-solving, and the role of the teacher in orchestrating such conditions for mathematical exploration. In her paper, Breive described the teachers’ behaviour in terms of the degrees of freedom offered to the children with respect to their actions related to the mathematical content and context. Based on the data she collected, Breive concluded that teachers’ ways of acting, and the accompanying learning opportunities, should be given more attention within early mathematics education research. Similarly, Vogler ( 2019 ), who observed teacher–child group interactions, concluded that so-called indirect learning (which can be found as a common approach in many preschool settings) may induce an obstacle to learning mathematics embedded in activities if there is not a mutual understanding of what learning content is the aim of the activity. In line with these two studies, other researchers who focused on teachers’ interactions with children also highlighted critical issues for educational practice and supported further research inquiries.

Another source for learning about the latest developments in early childhood mathematics education research is the POEM conferences (Mathematics education perspective on early mathematics learning between the poles of instruction and construction). The latest conference, POEM4, was held in 2018. The presentations published in the conference proceedings (Carlsen et al. 2020 ) all, in one way or another, reflect the question “In what way—and how much—should children be ‘educated’ in mathematics before entering primary school?” This was also the recurring question in the discussions between the participating scholars. Among the contributions, three themes stood out: children’s mathematical reasoning, early mathematics teaching, and parents’ role in children’s mathematical development. There was a strong interest in children’s reasoning abilities and strategies in problem-solving. For example, Tsamir et al. ( 2020 ) investigated how children express their understanding of patterning. For this purpose, the researchers provided preschoolers with patterns to be copied and compared, while observing their strategies. Children’s strategy use was also observed in relation to play situations. Bjørnebye and Sigurjonsson ( 2020 ) observed them in teacher-led outdoor games, while Lossius and Lundhaug ( 2020 ) observed child-initiated play activities. Some researchers used their observations of children’s encounters with mathematical content for theoretical discussions on how to understand children’s meaning-making, for example by taking the semiotic mediation perspective (e.g., Bartolini Bussi 2020 ) or through the lens of attentional processes (Verschaffel et al. 2020 ).

With respect to early mathematics teaching, at POEM4 it was discussed that teachers’ educational work largely concerns how to empower children in the learning process, assuming that children have agency in their learning (Radford 2020 ). Some of the presented studies (e.g., Palmér and Björklund 2020 ) specifically chose children's perspectives and problematized how seriation was made a content for learning in a children’s story. They showed how different manipulatives and tools used in teaching have different implications for what is made possible for the children to learn. A critical but essential notion was expressed by Tzekaki ( 2020 ), who underlined that whether children act and think mathematically and learn mathematical concepts depends on what is defined to be mathematical thinking and acting. In line with this perspective, Keuch and Brandt ( 2020 ) and Bruns et al. ( 2020 ) also raised the issue that teachers’ and student teachers’ knowledge of mathematics in early childhood education affects their readiness to exploit the content in ways that facilitate children’s mathematical learning.

The issue of the knowledge of mathematics in early childhood was also addressed in papers on the role of parents in children’s learning of mathematics. Parents are recognized as young children’s first educators, contributing to their mathematical understanding and skills. One example of this research focus is Lembrér’s ( 2020 ) study. In order to know what experiences children bring with them into preschool education and thus might inform their encounter with mathematics, she investigated what parents value in the mathematics activities in which their children are engaged at home.

2.3 ICME-13 monograph “Contemporary research and perspectives on early childhood mathematics education”

The ICME-13 Monograph “Contemporary research and perspectives on early childhood mathematics education” (Elia et al. 2018 ) is the third source for becoming informed about the state of the art in the field of teaching and learning mathematics in early childhood. This book, which has its foundations in the ICME-13 (International Congress on Mathematical Education) Topic Study Group 1 (TSG1) “Early childhood mathematics education” held in 2016, contains chapters on a broad range of topics grouped into five key themes: pattern and structure, number sense, embodied action and context, technology, and early childhood educators’ professional issues and education.

Within these themes, the domain-overarching theme of pattern and structure played a prominent role. As Mulligan and Mitchelmore ( 2018 ) showed in a series of studies, children’s awareness of mathematical structures turned out to be crucial for acquiring mathematical competence. Particularly children’s structuring skills were found to be critical to developing coherent mathematical concepts and relationships. These findings are in line with Lüken and Kampmann’s ( 2018 ) intervention study with first graders, in which 5 months of explicit teaching of pattern and structure during regular mathematics lessons resulted in significant differences between pre- and post-test arithmetic achievement scores in the intervention group. Moreover, the intervention was most beneficial to the low-achieving children.

The research within the theme number sense examined a large variety of different aspects of number development. For example, there was a study about children’s enumeration skills when making lists for designating and representing collections of objects (Dorier and Coutat 2016 ). Also, attention was paid to the use of numerical finger gestures and other bodily-based communication in order to facilitate the learning process (Rinvold 2016 ), children’s spontaneous focusing on numerosity (SFON) (Rathé et al. 2018 ; Bojorque et al. 2018 ), and the link between writing skills and number development (Adenegan 2016 ). Furthermore, an exploration of children’s ability to operate with numbers revealed that 5-year-olds were able to solve multiplication and division problems when they were presented in familiar contexts (Young-Loveridge and Bicknell 2016 ).

In the theme embodied action and context , Karsli’s ( 2016 ) video-ethnographic research in a pre-kindergarten classroom showed that young children’s hand and body movements hold rich potential for engaging them in mathematics, and underlined the importance of early childhood teachers’ attention to the embodied ways in which children engage with mathematics, with potential for creating teachable moments. Other studies investigated children’s engagement in the context of play. In Henschen’s ( 2016 ) study free play was examined, while Nakken et al. ( 2016 ) compared free with guided play, of which the latter resulted in the children exhibiting deeper mathematical thinking, and engagement with more specific mathematical concepts. Anderson and Anderson ( 2018 ) broadened the scope by investigating children’s learning of mathematics in their home environment. Thom’s ( 2018 ) and Elia’s ( 2018 ) research on geometrical and spatial thinking in early childhood offered further insights into the crucial role of the body and other semiotic resources (language, drawings, and artefacts) by which young children develop and communicate spatial-geometrical thinking. A general conclusion within this theme was that the limited ways in which young children are invited to engage with geometrical, spatial, and measurement concepts undervalue the embodied, gestural, in-context nature of their mathematical thinking.

The theme technology specifically addressed the integration of technology into early childhood mathematics teaching and learning both at school and at home. The focus was mostly on touch-screen tablet-based applications. Because this new technology significantly differs from the traditional physical aid materials, professional development is needed to help educators identify and implement effective uses of these applications. To learn more about the role of the educator (teacher or parent) in the child’s interaction with the software, Baccaglini-Frank ( 2018 ) carried out an analysis of student-software-teacher relations, revealing how the teacher’s goal of helping the children experience success actually limited their development of numerical abilities. The use of technology also opened a window to a new perspective in early childhood mathematics, namely by exposing young children to advanced mathematics such as understanding symmetric transformation (Fletcher and Ginsburg 2016 ) and dealing with large numbers (also in symbolic form) and ordinality (Sinclair 2018 ).

In the theme early childhood educators’ professional issues and education , Cooke and Bruns ( 2018 ) provided a comprehensive overview of the various contributions in TSG1, for which they proposed to distinguish conditions at three levels that influence opportunities for young children to develop mathematical understanding and skills. At the macro level, curricula provide a framework (aims, content to learn, and activities) for mathematics teaching and learning in early childhood, with varying views. Several papers mentioned the tensions regarding new curricula and frameworks that may impose mathematical content rather than allowing the child to develop understanding of mathematical concepts through play. At the meso level, with focus on the teachers’ competence, all involved papers agreed as to the importance that the teacher possess a fundamental understanding of mathematics as the basis for high-quality early mathematics education. However, different studies used different conceptualizations and instruments to measure teachers’ mathematical competence. The micro level refers to the mathematics educational programmes and materials, as well as to the required training for teachers to develop their ability to effectively select and implement such programmes that address children’s mathematical needs (Fritz-Stratmann et al. 2016 ).

In sum, the common themes that stand out from the three international meetings are children’s learning through play, and concerns regarding how to apply content-focused teaching, with or without technology. We found that a great deal of the research is on children’s mathematical thinking and learning, including two main areas concerning children’s emerging number knowledge and children’s learning of patterns. It is noteworthy that in both areas, how children perceive structure or how they manifest structuring abilities were analysed in several of the studies. There were also a number of studies that focused on how finger patterns, gestures, or bodily-based communication may facilitate children’s learning of numbers.

Children’s learning through free or guided play is also a main issue that was discussed. Teachers’ guiding interaction with children in play was shown to contribute more to deeper mathematical thinking and engagement with specific mathematical content. How teaching affects children’s learning opportunities in preschool was furthermore of great concern in several of the studies. A conclusion drawn from this research is that teachers’ ways of acting and the learning opportunities created for children should be given more attention. In what way, and how much, children should be educated before entering primary school remains a central issue.

3 The contributions of this special issue

In this special issue of ZDM Mathematics Education (Issue 2020–4), contemporary research on early childhood mathematics teaching and learning is discussed by researchers from all over the world. The initiative emanated from the 42nd PME conference in Umeå, Sweden (July 2018), where we had the opportunity to organize a Research Forum in which researchers involved in the field of early childhood mathematics education gathered to present and discuss theoretical and methodological challenges and outcomes of studies on learning and teaching arithmetic skills in early years (Björklund et al. 2018 ; Van den Heuvel-Panhuizen 2018 ). The conclusion of the Research Forum was that early childhood mathematics education research is key, but that more efforts are needed to bring together the state of the art within this field as a foundation for moving early childhood mathematics education research forward. This special issue again provides a window into the contemporary field of research on early childhood mathematics teaching and learning. To discuss what this special issue adds to this field and reflect on the challenges that lie ahead for research on early childhood mathematics education, in the next section we synthesize the themes that emerge from the 15 papers included in this special issue. Each theme highlights the papers’ shared knowledge and contributions to research methods. Many papers are related to several themes, but for our discussion we chose those papers that predominantly belong to a particular theme. In total, we identified three recurring themes: the early interventions and their effects, the facilitating factors for learning and development, and the mathematical key concepts that can be observed in children. Together, these themes bring to the fore aspects that are essential for understanding the learning and teaching of mathematics in the early years.

3.1 What lessons can be drawn from interventions?

Research shows that children’s development of mathematical skills and knowledge is often influenced by socio-economic and curricular factors, and by social interaction in both short- and long-term perspectives (Pruden et al. 2011 ). Thus, there is a raised awareness of the impact early childhood education may have on reducing differences in conditions for learning and on increasing and securing equal opportunities for a good foundation in learning for all children. Based on their meta study of early mathematics education research, Duncan et al. ( 2007 ) stated that early intervention counts and numerous references to the same study indicate that this is an important standpoint in research. Why else indulge in the challenging task of researching learning among the youngest in our education systems, if one does not believe that efforts made through teaching are significant for children’s wellbeing and lifelong learning path?

Research on teaching and learning mathematics often shares a common research design in which interventions are implemented (designed, conducted, and the outcomes assessed) with the aim of finding ways to improve teaching practice for the benefit of the learning child, and often to reduce socio-economic inequality. Intervention studies can be objects of research in different ways, focusing on the children’s learning outcomes or the teaching practices. Nevertheless, the goal is to enhance learning through improved teaching. In the papers in this special issue we find efforts to implement well-designed interventions, explicitly focusing on how to teach. Some implement and analyse fine-grained differences in (teaching) actions and the effects on children’s attention to certain content (Paliwal and Baroody 2020 ; Mulligan et al. 2020 ), while others study the effects of attentiveness to children’s experiences and knowledge and the related choices of tasks (Clements et al. 2020 ; Grando and Lopes 2020 ). Nevertheless, essential to studying intervention success or failure is how learning outcomes are measured and interpreted, which is also an important aspect of early childhood mathematics education research (Li et al. 2020 ).

How teaching is framed to present mathematical content to young children, in order for it to be meaningful to them, and in order to be attentive to children’s experiences and knowledge, is investigated and discussed by Grando and Lopes ( 2020 ). Through narratives provided by early childhood teachers, they find insights into how teachers chose to frame the subjects of statistics and probability in ways that engaged children and were responsive to the children’s own experiences, rather than using materials provided by textbooks. Unconventional teaching methods whereby teachers turned their mathematics classroom into a space of creative insubordination are discussed in this paper in relation to the opportunities they offer children to become equipped with critical thinking. The authors argue that the specific content—statistics and probability—demands problematizing activities and experimentation with uncertain outcomes of problems in order to develop probabilistic thinking. This study highlights an essential issue in didactical research: that the content to be taught is not indifferent to how the teaching is designed. The study particularly raises concerns that the design of teaching cannot be random but rather has to be linked to the educational environment and the students attending that particular environment. Consequently, the generalizability of intervention programmes and teaching methods has to be taken into serious consideration if they are to be implemented in different educational settings.

Clements et al. ( 2020 ) set out to investigate the efficacy of implementing an intervention programme in which instructions and progression are grounded in a research-based learning trajectory. Even though the programme itself had previously been found to have positive outcomes for preschool children’s mathematics learning, the goal of the current study was to investigate how to teach in the most successful way. For this purpose, the authors used the same programme but adapted the choices of the tasks’ difficulty level to the children’s current knowledge levels. How to teach was then related to what to teach individual children. Results indicate that skipping difficulty levels to shorten the steps to the learning goals was not successful. This thorough investigation of teaching by adapting the complexity of the content to the child’s ability to learn best what is intended draws attention to the delicate work of teaching in early childhood education. The study supports child-centred approaches that are sensitive to the individual needs and potential of the child, while simultaneously aiming for the learning goals set by the curriculum.

While Clements et al. investigated the effects of an intervention programme covering broader numerical knowledge, Paliwal and Baroody ( 2020 ) aimed to investigate what conditions for learning the cardinality principle are most effective and how subitizing abilities impact on cardinality knowledge achievement. Their efforts were directed towards a fine-grained analysis of how to teach this aspect of the number concept, and what learning processes different approaches elicit in children. What stands out in their study is that they used a highly advanced research design, which allowed them to examine the effects of different ways of directing children’s attention to seeing numbers’ cardinality. In their paper, they point out the importance of directing children’s attention to various ways of seeing numbers’ cardinality, as follows: as a constructing act by adding units to get a number; as an act starting from naming the whole set with a counting word and then differentiating the added units by counting; and a third condition, attending only to single units in a counting act. Thus, their intervention was designed with explicit rigour as to what was made possible for the children to experience, and their investigation concerned the learning outcomes of the different conditions. While this attention in Paliwal and Baroody’s study to the different conditions can at first glance be considered subtle and far from the instruction children encounter in their mathematics education, the study offers insight into the importance of teachers’ awareness of their way of directing children’s attention to certain meanings of the content.

In another paper focusing on the effects of an intervention programme, Mulligan et al. ( 2020 ) analysed children’s written answers to pattern tasks in order to identify differences and changes in their structural awareness. They found a positive effect on the children’s development of awareness of mathematical pattern and structure (AMPS), and showed how the levels changed as an effect of a 37-week intervention programme. Mulligan et al. add to the field of early childhood mathematics knowledge of a particular ability (structural awareness), how it can be identified among young children, and also how the ability changes over a prolonged period of time (during an intervention), which may provide insight into what children actually learn while taking part in an intervention programme.

Children’s learning is of course at the centre of attention in intervention studies, and Li et al. ( 2020 ) pay explicit attention to how to interpret results from a pre- and post-diagnostic test. In their study, Li et al. investigated the development of mathematics problem-solving skills among kindergarteners by analysing their responses to a cognitive diagnostic test. As in most large-scale analyses, it can be shown in quantitative terms how children develop in producing correct answers that indicate growth in knowledge within certain domains that are tested for. However, Li et al. take a step further in their inquiry and illustrate how two children who scored similarly on the cognitive diagnostic test before an intervention had made different progress during the intervention period. Li et al. suggest that the reason for this difference may lie in how children understand and approach tasks, indicating different understanding even though similar answers are produced. Quantitative measures alone do not reveal such differences. The study thus shows the significance of paying attention to how children reason in order to solve a task. Based on their study, Li et al. recommend that children’s learning outcomes from participating in interventions be seen in the light of how the effects of interventions are measured, as it is observed that some developed skills do not endure over time and similar outcomes among children may conceal different learning paths.

3.2 What facilitates children’s learning and development?

Today, it is undisputed that the development of mathematical skills and the teaching of emerging skills in the early years are essential for mathematics education and developmental progress in the long term (Aunio and Niemivirta 2010 ; Duncan et al. 2007 ; Krajewski and Schneider 2009 ). However, in contrast to this perspective, a recent overview of the long-term effects of preschool mathematics education and interventions (Watts et al. 2018 ) challenges this almost taken-for-granted assumption, as most early interventions have a substantial fadeout effect. Thus, there is a need to revisit our current knowledge of teaching and learning, and scrutinize what seems to make a difference. Some of the papers in the special issue particularly consider this issue in their efforts to ascertain what facilitates children’s mathematical learning and development, and focus on influential aspects found in play settings (Reikerås 2020 ; Tirosh et al. 2020 ), verbal communication in teaching practices (Hundeland et al. 2020 ), and the home numeracy environment (Rathé et al. 2020 ).

Hundeland et al. ( 2020 ) raise the question of how children learn to use and understand the canonical language of mathematics, and study this aspect in terms of mathematical discourses taking place in kindergarten teaching sessions. They take a sociocultural stance (see Vygotsky 1987 ), seeing communication as the link between internal communication (thinking) and external communication (interaction). Therefore, children’s opportunities to contribute ideas and arguments are vital for their (mathematical) learning processes. Earlier research has also shown that care-takers’ talk influences not only children’s vocabulary but also, for instance, their spatial problem-solving (Pruden et al. 2011 ). The deeper knowledge that the study by Hundeland et al. ( 2020 ) provides regarding the quantity and quality of mathematical talk in which children are involved, offers us better opportunities also to organize supportive and stimulating conditions for knowledge growth.

What differs in the study by Hundeland et al. compared to most others with similar research questions is their focus on the kind of interaction that the mathematical discourse induces, which, based on the chosen sociocultural theoretical framework, should be crucial for positive learning outcomes. However, what they study and compare is the impact on the mathematical discourse that a certain in-service training has. This places mathematics in the spotlight of mathematics education research. While psychological and cognitive research provides us with important knowledge of mental processes and developmental advancement, studies like the one by Hundeland et al. have a clear direction towards understanding, and not least improving, the conditions for children’s learning and development, either by implementing teachers’ professional development or through curriculum improvements.

It is commonly agreed that young children’s learning is often situated in play. In a large-scale observation study, Reikerås ( 2020 ) conducted a thorough examination of the kind of play in which toddlers engage, for the purpose of learning how play skills may be related to early mathematical skills. It was found that competencies that allow the child to be active in solitary and parallel play, as well as children’s ability to initiate and remain in a play activity, correlated positively with the toddlers’ mathematical skills. The kind of play skills that showed the highest correlation with mathematical skills was their competence to interact in play. General social play skills thus seem to have an impact on mathematical learning, but Reikerås’ study cannot reveal how these are connected or any causal effects. An effort to better understand the interaction going on in toddlers’ play is made by Tirosh et al. ( 2020 ), investigating the challenges toddlers may face as they practise one-to-one correspondence in a playful context, and how different individuals participate in the playful mathematical context. Here, interaction and social skills become one issue with an impact on the learning opportunities arising in the play.

In many cases, the messy context of children’s play is a methodological challenge. It is not possible to control influencing variables to the same extent as in an experimental design. On the other hand, findings from the messy settings are more likely to bring to the fore aspects that were not anticipated, which raises new questions for research and theory development. Design research supports this kind of knowledge contribution, as several cycles are conducted, each developed based on insights from the previous cycle. These cycles adhere to children’s initiatives such as practising one-to-one correspondence in a setting the table task by putting one spoon inside each cup instead of placing one spoon beside each cup (see Tirosh et al. 2020 ); thus, the child is expressing an understanding of the concept, but is expressing it differently than how the task suggests. This highlights the importance of directing attention to instructions used in research studies, and particularly to the language of mathematics and the spatial aspects of props used in a task, related to the possibilities involved as young children interpret and execute a task.

Children take part in cultural life, where today numerical aspects are an inevitable part of the everyday environment. Nevertheless, there are differences in the extent to which children attend to these aspects, and consequently in how they learn the meaning of numbers, graphical representations of numbers, and how to use numbers. A common assumption is that home numeracy environment is a strong factor (LeFevre et al. 2009 ; Skwarchuk et al. 2014 ), which is reflected not least in the abundance of studies regarding socio-cultural background and demographic factors as a pre-cursor for learning progress. Rathé et al. ( 2020 ) put the common assumption to the test—that home environment has an influence on children’s progress in mathematical development—by comparing young children’s tendency to focus spontaneously on numeracy and numerical symbols in their home numeracy environment. Concerning this specific directionality to numbers, which is assumed to have an impact on children’s arithmetic skills in later years (see McMullen et al. 2015 ), based on their study they propose that the home numeracy environment does not seem to have any significant impact.

3.3 What mathematical key concepts can be observed in children?

A great deal of research in the field of early childhood mathematics education studies what mathematics children understand and how this understanding evolves. This knowledge is crucial in designing teaching that contributes to more advanced thinking and problem-solving strategies that support conceptual growth. Therefore, children’s utterances and how they act are the centre of interest for many researchers. Also, in this special issue, much attention is paid to the mathematical key concepts that can be attributed to children’s thinking, resulting in papers addressing children’s understanding of similarity in mathematical objects (Palmér and Van Bommel 2020 ), their understanding and use of structures (Sprenger and Bentz 2020 ; Kullberg and Björklund 2020 ), their understanding of the concept of cardinality and ordinality (Askew and Venkat 2020 ), and the underlying structure of their quantitative competencies (Van den Heuvel-Panhuizen and Elia 2020 ).

Children’s expressions, and how they are allowed to express themselves, are critical for our understanding of the learning of mathematics. Children’s problem posing is one aspect that can tell us about their understanding of mathematics (Cai et al. 2015 ). In the special issue, this is particularly addressed in the paper by Palmér and Van Bommel ( 2020 ), who investigated children’s understanding of similarity in mathematical objects. They analysed how children themselves created tasks in three-dimensional geometry that were similar to a previous problem-solving task they had worked on. It is suggested that this finding sheds light on the children’s interpretation of the specific mathematical features of the original task.

How children perceive structure has been shown to play an important role in how they, for example, determine a number of objects or solve an arithmetic problem (Ellemor-Collins and Wright 2009 ; Resnick 1983 ). In line with these earlier studies, Sprenger and Bentz ( 2020 ) investigated how 5-year-olds perceive structures in visually presented sets. By having the children determine the number of eggs in a 10-egg box while using an eye-tracking device (and recording the children’s utterances and gestures), they were able to analyse the children’s gaze when determining the cardinality of the set, and thereby gain insight into the process of perception. The eye-tracking data showed, for example, that many of the children were able to see structures (e.g. 4 + 1 or 3 + 2) and use them to determine a quantity without having to count all the objects. The authors argue that children’s ability to perceive structures in sets and use them to determine cardinality is central for their further arithmetic learning, as how children perceive sets (e.g., as individual objects, as a composite whole, or in structured part-whole relations) affects the strategies they use for solving arithmetic tasks.

Similar ideas are found in the study by Kullberg and Björklund ( 2020 ), who studied 5-year-olds’ use of finger patterns to structure number relations while solving an arithmetic problem. They identified two major ways of structuring the task: only structuring, and counting and structuring. In the group that both structured using their fingers and counted on some fingers, some ways were found to be more powerful. Children who solved the arithmetic task (3 + _ = 8) by creating a finger pattern of eight raised fingers and simultaneously identifying (‘seeing’) the missing part (5) on two hands (3 + (2 + 3) = 8) were more successful in solving arithmetic tasks, even in a later follow-up assessment. It is suggested that a possible reason for this later success is that these children were able to see numbers as parts included in other numbers, which has been found in earlier research (Resnick 1983 ) to be important for developing arithmetic skills.

Baccaglini-Frank et al. ( 2020 ) also argue that the appropriate use of fingers can contribute to developing children’s number sense. They studied how 4-year-olds interacted (verbally and using finger patterns) when using the application TouchCounts. The app combines multi-touch with audile, visual, and symbolic representation, and several solution strategies are possible, affording the simultaneous experience of, for example, finger patterns on the screen, with the number both seen and spoken. In their paper the authors emphasize how multimodal affordances may encourage children to use different strategies in response to different tasks, and thus experience a broad range of abilities related to number sense, including both cardinality and ordinality.

Askew and Venkat ( 2020 ) examined children’s understanding of the concept of cardinality and ordinality in connection with their awareness of additive and multiplicative number relations. To investigate this topic, first graders (6- and 7-year-olds) in South Africa were asked to position the numerals 1–9 on a bounded 0–10 number line. The children were able to do this in the correct order, with the fewest errors at the upper and lower ends of the number range. Furthermore, evidence was found that awareness of ordinality and that of cardinality develop alongside each other. However, the logarithmic scale, predicted in earlier research, which is considered to indicate a multiplicative structuring of number relationships, was not confirmed in the South African data. Instead, when the numerals grew larger the intervals became more stretched out rather than compressed. In fact, the children’s responses were closer to the linear model, which is considered to indicate an additive structuring of number relationships. Also, the use of unit sizes that did not take into account the length of the number line, together with the underestimation of the position of 5 on the 0–10 line, offered limited evidence of the children’s awareness of the multiplicative structure of the cardinality of numbers. More research is needed to disclose the deep interconnections between children’s understanding of cardinality and ordinality, and their understanding of multiplicative and additive number relations.

Another effort to unravel the complex nature of children’s early number understanding was carried out by Van den Heuvel-Panhuizen and Elia ( 2020 ), investigating the structure of the quantitative competence repertoire of kindergartners. Based on a literature review, they arrived at a model consisting of two constituent parts: quantification (the ability to connect a number to a given collection of objects) and quantitative reasoning (the ability to think and operate with quantities). Quantification was split up into counting and subitizing, and quantitative reasoning into additive and multiplicative reasoning. Although this model is partly in line with models found in earlier research, it also extends previously developed models by including multiplicative reasoning. Data were collected in the Netherlands and Cyprus. A series of confirmatory factor analyses showed that the hypothesized four-factor model fitted the empirical data of the Netherlands, but not those of Cyprus, which clearly challenges the model’s generalizability. A comparison of the component performances in the Dutch sample revealed that, in accordance with other studies, the lowest scores were found for multiplicative reasoning and that the competence of subitizing seems to develop before counting. This was partly confirmed by a statistical implicative analysis at item level. Although this analysis resulted in different implicative chains in the two countries, in both samples the multiplicative reasoning and conceptual subitizing items were found at the top of the chain and the counting and perceptual subitizing items at the end. Also, more research is necessary here, particularly concerning the generalizability of the model to other countries.

4 Future directions for research on early mathematics teaching and learning

After the Research Forum at PME42 we concluded that to move early childhood mathematics education research forward, more efforts are needed to bring together the state of the art within this field. Thus, we proposed a special issue on the theme Research on early childhood mathematics teaching and learning for the purpose of opening up further discussion and inquiry. In this article, the 15 papers included in the special issue are synthesized and discussed in terms of their contribution to the current field of research in early mathematics teaching and learning along with recent research presented at international mathematics education research conferences. Naturally, these do not cover the worldwide field of research, but they at least give a general idea of the current research interests and challenges.

All the papers in this special issue address aspects of early mathematics education and its underlying theories and research methodologies. They share common interests and challenges concerning how to gain knowledge of the youngest children’s mathematical development, and they identify prosperous teaching approaches. Our appeal to researchers participating in the special issue was to cover the broad span of mathematical ideas that are relevant in early childhood education. Nevertheless, we see a strong direction towards research on the learning and teaching of number concepts and basic arithmetic. This is in line with Alpaslan and Erden ( 2015 ) review of early mathematics research published in 2000–2013 in high-ranked scientific journals in the field of mathematics education, in which the most frequently reported research topics were number systems and arithmetic. The same trend is also found in the research addressed in the latest meetings of ICME, ERME, and POEM. We believe further research should widen this scope, and consider and investigate mathematical topics that are currently less highlighted. There is a need for deeper insight into what mathematics means to young children, and also how the foundations can be laid for the domains of spatial and geometric thinking and measurement, as well as for the domains of structures and patterns, data handling, problem-solving and mathematical reasoning.

Moving an educational field forward, however, is not solely based in covering a broad field of content. To strengthen the field, we need to scrutinize the research designs and methods that are used and the knowledge that is generated. Here, new technologies may open up opportunities for designing tools for investigating children’s competencies. However, this initiative goes beyond choosing digital tools or concrete building blocks; it concerns children’s opportunities to express themselves within different environments and make use of tools and manipulatives that may reveal new insights into their competencies and open up for innovative research questions to be posed. What is made available to experience surely has an impact on children’s expressions of knowledge. And expressions in both words and gestures are important keys here to interpreting the youngest children’s knowledge and skills. We can see this in the recent ICME, ERME, and POEM meetings’ presentation of a large variety of research designs and in the papers of this special issue. Many innovative research designs have been developed that allow thorough investigation of children’s mathematical competence and understanding. What we see, for example, is that subtle differences in expression (e.g. gaze, finger use, or ways of posing questions) reveal new and important insights for developing knowledge of children’s mathematical learning. These innovations in methodology allow for the thorough investigation of key features of learning mathematics that go beyond the broad content areas and highlight how mathematical aspects such as cardinality, ordinality, and number structure are experienced by children. Several of the papers in the special issue particularly attend to these aspects, and do so by creating and using new methodologies and technologies.

The consensus in the field of early mathematics education, reflected in the papers and conference presentations, is strong concerning the impact of early interventions on children’s opportunities to thrive as mathematics learners. From longitudinal studies, we know that early knowledge and skills seem to follow through the child’s development; that is, weak mathematical skills in early childhood years are likely to predict weak mathematics performance in later school years (Reikerås and Salomonsen 2019 ; Hannula-Sormunen et al. 2015 ). This means that early intervention and knowledge of how to offer all children a good start for their mathematical learning are essential to the field of early childhood mathematics education. However, it cannot be assumed that simply participating in education, whether it is framed as free or guided play or problem-solving, or stimulating interactive environments, will result in successful learning outcomes, even though most interventions do have a positive impact and most children develop their knowledge to some extent (Wang et al. 2016 ). Common research objectives, therefore, concern intervention implementation, and analyses of children’s learning outcomes from participating in differently designed activities. These studies are of high importance, as they connect the teaching to the learning and provide insights into what seem to be key aspects in the teaching practice. Nevertheless, researching interventions is delicate work, and it is essential to maintain scientific rigor in the design and analysis. Because early childhood education most often takes place in dynamic settings, the conditions under which children learn vary greatly. This diversity is observed in many studies in which children’s engagement in play, both self-initiated and guided, is used as data for analysing their mathematics competencies and learning of mathematics. This phenomenon means that the conditions offered to explore mathematical concepts and principles should be critically examined, along with how learning from interventions is measured and valued. There is a need to determine what works, what seems critical, and what aspects serve as particular challenges. In research, also special attention has to be given to the nature of the teaching practices. What we learn from intervention studies, both those included in the special issue and those in other contemporary research, is the importance of situating research in the current field of knowledge and the context in which the research is conducted. Each study broadens the picture of the teaching–learning relationship, which is by no means one-directional. There are many aspects to consider that potentially influence this relationship, and all of them cannot be included in one study alone.

Early childhood mathematics education research often attends to the opportunities and conditions that are offered for learning. There is no doubt that children’s activities and interaction with others, already from an early age, offer many opportunities to learn mathematical concepts and basic principles, but our ability to discern what children actually learn from the mathematical learning environments offered to them places high demands on the interpretation process. How to understand the processes going on in play and interaction, and what impacts the children’s learning outcomes—what is made possible to learn—often remains an unsolved issue, as the interaction between teacher and children is dynamic, and particularly as play is multidirectional in nature. Studies of interaction in both formal and informal contexts are nevertheless important, as they are conducted in the complex of social and cultural settings that do influence, through norms and individuals’ experiences, what is possible for children to learn.

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Björklund, C., van den Heuvel-Panhuizen, M. & Kullberg, A. Research on early childhood mathematics teaching and learning. ZDM Mathematics Education 52 , 607–619 (2020). https://doi.org/10.1007/s11858-020-01177-3

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Problem Solving for Preschoolers: 9 Ways to Strengthen Their Skills

By Carrie Mesrobian on 12/20/2021

As an adult, you likely run into dozens of small issues every day that require problem-solving skills. While you might not give much thought to the process of figuring out the best way to put groceries away or how to run errands without backtracking all over town anymore, these basic problem-solving abilities weren’t always so simple. You refined these skills as a child with practice and guidance from adults.

Building problem-solving skills in preschool-age children is a foundational duty of all parents and early childhood educators. But it can be easy to lose sight of how to incorporate these skills, especially when family life gets hectic or classrooms become busy.

For some fresh perspective on how to look at problem solving from a preschooler lens, we asked several experts in the early childhood education (ECE) field how they teach skills in their own classrooms. Read on for some insight on helping the young ones in your life figure out creative and workable solutions.

9 Tried-and-true ways to develop problem-solving skills in preschoolers

1. use everyday moments.

The handy thing about teaching problem-solving skills at this age is that there are no textbooks, worksheets or special equipment involved. Every day, normal situations provide all the materials you’ll need to practice.

“Parents can help their children develop problem-solving skills through ongoing interactions with their children throughout their day,” explains Paula Polito, owner of Beary Cherry Tree Child Development Center. “At home, in the grocery store and in everyday routines, such as mealtime or bath time.”

Rebecah Freeling, parent coach and child behavior expert at Wits’ End Parenting ®, believes household chores are an excellent way to teach problem solving.

“Housework is a matter of solving one problem after another. All these things go wrong when you’re doing housework,” Freeling explains. “Kids get this idea that problems are no big deal. Problems happen all the time and we just solve them.”

That doesn’t necessarily mean making a chore chart, though Freeling says some kids respond well to them. Instead, she encourages parents to try to integrate kids into the everyday maintenance of the home, and when possible, work alongside them.

“Say, ‘What would you like to be in charge of today?’” Freeling advises. “It’s the difference between getting to do something versus having to do it.”

While a grocery store trip can sometimes be a stressful rush, there are infinite opportunities to practice problem solving, says Dr. Elizabeth DeWitt, senior curriculum and implementation specialist at Learning Without Tears . DeWitt suggests using a list or a recipe of ingredients and asking your child to help you find certain items.

“Say, ‘I have this recipe that says we need chicken, rice and soup. I see chicken and soup in our cart. What are we missing? What could we or should we add?’” DeWitt says.

Taking the time to simply talk children through the thought process—no matter how simple it seems—helps reinforce and show them how you came to that conclusion.

2. Ask open-ended questions

As in the grocery store situation, just asking questions is a powerful way to foster both problem solving and creativity in young children.

“When your child comes across a difficult task, like zipping their coat, it can often be faster and easier to stop what you're doing and zip it for them,” says Becky Loftfield, an ECE teacher at Community of Saints Preschool .

If a child says, “I can't do this,” Loftfield advises asking “how come?” This lets them answer in their own words. “Asking ‘how come’ usually works better than ‘why’ for young children,” Loftfield adds.

Pausing to listen to the child’s explanation of the problem in their own words guides what happens next.

“Perhaps they don't know how zippers line up at the bottom for the mechanism to slide,” says Loftfield. “Maybe the zipper itself is too small for them to grip. Encourage your child to explore what the problem actually is beyond ‘I can't zip my coat.’”

Polito also believes in the power of conversational questions to build problem-solving skills.

“For example, parents can ask a child to explain why they did something a certain way,” Polito explains. “Providing hints to children as opposed to giving them the answer is also another way for children to think deeper about a concept.”

“We promote more learning when we allow them to think through the question,” Polito says.

3. Center emotions

All problem solving involves emotions. In the zipping-up-the-coat situation, a child might act frustrated, get angry or start crying. Handling the emotion is often the key to the child sorting out the situation, as well as learning that they are capable of finding solutions.

“We are not born knowing how to solve problems or having the vocabulary to express our feelings,” says Torri Parker, a pre-K instructor at Aspen Academy . “Often I hear a student telling another child ‘You’re not my friend,’ when what the child is meaning is that they are hurt by something their friend did, or they would like some space.”

Parker suggests picture books that focus on emotions and offer multiple ways to express them can be a powerful way to help kids not only problem solve but also identify emotions in their peers and develop greater empathy.

“By providing the words needed to convey those feelings, a child learns what that feeling feels like and can then have the vocabulary in the future to solve a conflict like that,” Parker says.

4. Read books and tell stories

Sometimes, not having to tackle a problem that’s happening in the moment is a good way to practice these skills. This is where reading books and telling stories come into play.

“Books have the opportunity to build incredible social-emotional skills,” DeWitt says. Not only are kids looking for solutions to the characters’ problems, they’re also building vocabulary, narrative skills and critical thinking as well.

Nicole Evert, a pre-K teacher and ECE trainer at Creating Butterflies, recommends the use of “ social stories ” for preschool problem solving.

“A social story introduces a problem, then shows successful ways to solve the problem,” Evert explains. “Sometimes a social story will include silly pages that show how to not solve the problem.”

Social stories can be especially helpful for children with anxiety about certain activities or routines, as well as kids with disabilities.

“Parents and educators can even make their own social stories using pictures of the specific child and their environment, which can be so powerful,” adds Evert.

5. Take advantage of natural curiosities and interests

One approach to helping young children practice problem-solving skills is in the discovery of something they are authentically interested in learning about. Adam Cole, music director at The Willow School , explains his school’s Reggio Emilia -inspired philosophy where a teacher gives students “provocations.”

“Provocations are opportunities for them to encounter something for which they may then express further interest,” Cole explains. “For instance, a teacher may set up a drawing provocation, and the children may draw buildings. The teacher may pick up on this and talk with the children about buildings, asking how they are built and where they can find more. This may lead to research or trips to see buildings and will continue on until the thread plays itself out.”

Because the focus is centered on topics or activities that already capture the child’s interest, the problem-solving aspect is more meaningful and compelling for many children. Because the teacher works alongside the child to problem solve, it offers space for the teacher to ask questions and encourage further creativity.

“This is an organic way to learn to solve problems, bolstered by the intrinsic desire of the child to learn more,” Cole adds.

6. Model problem solving

Preschoolers are always observing our behavior as parents and teachers.

“Given that 90% of brain development occurs between birth and four years of age, we have an opportunity during these preschool years to set our children up for success,” says Polito.

It may seem obvious, but our strategies and methods provide kids with in-the-moment examples of how to handle life with things go wrong.

“From a teaching perspective, you can think, ‘I’m teaching this child how to be who they are, how to live life,’” says Freeling. “A spill derails you a bit. So, stop and ask the child, ‘How should I clean this up?’”

Loftfield agrees. “Parents and educators can act as guides for a child’s experience, demonstrating how they problem solve and modeling what they want to see.”

This doesn’t mean that the adult must do everything perfectly or without emotions, however. Managing feelings is all part of learning to problem solve. “Allow time for mistakes, time for meltdowns and time for celebration,” Loftfield advises.

7. Look to the child for the solution

This last one might seem counter to number six above, but Freeling believes that parents and teachers can help children learn to problem solve by removing themselves from the process.

“Moving past your instincts to fix or smooth over problems helps a lot,” Freeling says. “Project the kid’s age in your mind. Think of a 25-year-old graduating from college. I want them to be able to ask for a higher salary, to vocalize what they want. You’re not just getting kids to be obedient—you’re teaching them how to negotiate the world.”

This is why Freeling advises adults to try coming into a problem-solving situation with children without a ready-made solution. She offers an example: there’s only one red truck, and two children both want to play with it.

“You’re really looking to the child and trusting their thinking and intelligence for solutions you hadn’t thought of,” Freeling says. She recommends repeating questions until the kids come to a decision and as long as no one’s at risk of injury, standing by the children’s solution.

“They might say, ‘We have to paint all the trucks red, since everyone wants a red truck,’” Freeling says. This might seem odd to an adult. But the point is to make the children a vital part of the creative process instead of just getting them to comply with the adult’s idea.

Developing empathy also factors into this scenario, especially in situations where problems stem from hurt feelings or other emotional conflicts. Freeling believes that finding ways to make restitution to others they’ve hurt is a better practice than forcing kids to apologize. She suggests having a child draw a picture of something the upset child likes as a way to make amends and help them recognize the other’s individuality.

“We don’t want kids to feel guilt for hurting someone; we want them to feel compassion,” Freeling says. “And solving problems in a relationship requires empathy.”

Is an early childhood education career right for you?

Enjoying the process of seeing life through a little one’s eyes? Early childhood education is an exciting, dynamic field full of creativity and potential to positively impact the lives of children and their families. If helping kids learn and grow sounds like something you’d be good at, check out our article “9 Signs You Should Be Teaching Preschool.”

Related Articles: 

Working with Defiant Preschoolers: What Educators Should Know

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Making Math Meaningful for Young Children

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Children are natural mathematicians. They push and pull toys, stack blocks, and fill and empty cups of water in the bathtub. All of these activities allow young children to experience math concepts as they experiment with spatial awareness, measurement, and problem solving (ETFO 2010; NAEYC 2010). Young children easily learn as they describe, explain, and consider the ideas from their immediate environment. Am I as tall as Yancey? How can I find out? I know! We can both stand next to each other in front of the mirror.

Early math is not about the rote learning of discrete facts like how much 5 + 7 equals. Rather, it’s about children actively making sense of the world around them. Unlike drills or worksheets with one correct answer, open-ended, playful exploration encourages children to solve problems in real situations. Because the situations are meaningful, children can gain a deeper understanding of number, quantity, size, patterning, and data management (Grossman 2012). For example, it is easier to understand what six means when applied to a real-life task such as finding six beads to string on a necklace or placing one cracker on each of six plates.

Creating a math-rich classroom

Research suggests that preschool classrooms can be the ideal environment for learning about math (ETFO 2010). Children sort materials into corresponding bins at cleanup time, explore patterns and shapes while creating at the art table, tell time while using the visual schedule to predict which activities come next, and measure when they squeeze their bodies through the climber on the playground (ETFO 2010).

Preschool classrooms also celebrate curiosity and risk-taking as children engage in inquiry-based exploration at various learning centers and outdoors. Interesting items in the environment encourage children to find answers to their questions and solve problems across all curricular domains. Children measure as they clap out the beats to music. They repeat rhythmic patterns as they dance. They describe, sort, and count objects in the discovering science center and look for patterns while on a nature walk. They count the rungs while climbing up the ladder to the loft. Many familiar children’s songs, stories, and poems contain mathematical messages that help familiarize children with counting, measuring, and patterning. For example, children can count along with “One, two, buckle my shoe” and “Ten little monkeys jumping on the bed.”

In addition to offering blocks, buttons, and other loose materials to touch and explore, teachers can ask open-ended questions that promote problem solving and probe and challenge children’s mathematical thinking and reasoning (Ontario Ministry of Education 2010). Such questions are not meant to elicit correct answers but rather to engage children in open-ended conversations that promote high-level thinking, such as What do you notice about these objects? How might we sort the toys? One of the foundations of play-based learning is that the teacher is active in the play, asking questions and adding knowledge and insight. The teacher learns together with children throughout the inquiry process.

Every preschool classroom needs to be rich with materials that encourage math exploration and learning. A well-stocked math and manipulatives center includes found objects such as shells, stones, bread tags, and sticks, as well as purchased materials. The center can include photos of completed geoboard creations or of children sorting coins in the dramatic play center. There might be narratives of children’s learning, such as transcripts of children’s comments and conversations, and artwork featuring pattern or shape exploration. Teachers can post documentation of math learning as a way of encouraging children to reflect on past experiences and motivate them to plan and revise future ones. These visuals can inspire even deeper, more connected learning. They help children maintain their focus on a particular topic, refine and expand their ideas, communicate their learning to others, and reflect on their experiences before making new plans.

Encourage children to play mathematically

Young children need to see themselves as capable mathematicians. Child-guided and child-focused explorations and teacher-guided math activities help children practice and consolidate their learning. This helps them feel confident about what they know and can do. Although many preschoolers learn some math concepts on their own, it’s important for teachers to include math in authentic experiences, resulting in a deeper understanding by children (ETFO 2010).

In addition to creating a rich math and manipulatives learning center, teachers can encourage children to use math tools and strategies in all areas of the classroom. Children might use a set of plastic links to measure their buildings in the block center, use play money to pay for a train ticket in the dramatic play center, and use rulers to measure the growth of spring bulbs in the discovering science center. Take a set of scales outdoors so children can figure out who found the heaviest rock. Using math tools for real-life tasks frees both teachers and children to act spontaneously, resulting in richer interactions and a calmer learning environment (Wien 2004).

In addition to the freedom to use materials in authentic ways, children also need freedom of time and space to deeply engage in math. The preschool schedule should include plenty of time for uninterrupted play so children have the time they need to work on sustained tasks of interest. This allows children to explore materials thoroughly, often resulting in more complex and evolved experiences over time. If a child spends all of his time at one learning center, he is not missing out on learning opportunities elsewhere. Instead, his deep connection to the center is often indicative of rich learning. Teachers can model the use of other materials at the center, such as using writing materials to draw plans for a structure to be built, or pose challenges that encourage the child to think beyond her play, such as How tall can you build this tower before it falls?

To support learning, it is important to encourage children to communicate their explorations and findings. Teachers can establish a routine through which children share their experiences at group time. For example, a child might explain how he built a structure with blocks, do a dance with repeating steps, or share a photo of a complex pattern made with colorful buttons. While circulating through the room, a teacher might notice high-quality work and suggest that a child share it with her peers during group time. The child making the presentation grows in confidence and the onlookers may want to try the experience themselves.

Most children enter preschool knowing a lot about math. In a safe and supportive classroom they will feel comfortable taking risks and engaging in self-directed problem solving. Weaving math into all areas of the curriculum will heighten children’s play experiences and allow all learners to experience success. Children will soon see themselves as capable mathematicians who apply their skills in a number of ways. Their growing math skills, confidence, and interests will serve them well in school and life.

Supporting Dual language learners

Children who are DLLs can learn math concepts and skills without being fluent in their second language. Much of the meaning is found in the right materials. If families send to the classroom familiar items from home, the children will know the name and function of the items in their home language. They can use this prior knowledge as a foundation to help them learn math. For example, young children may not understand how to sort plastic shapes, but they already know it is important to sort the baby’s socks and daddy’s socks in separate piles—a math activity that has real-life meaning in any language.

ETFO (Elementary Teachers’ Federation of Ontario). 2010. Thinking It Through: Teaching and Learning in the Kindergarten Classroom . Toronto, ON: ETFO.

Grossman, S. 2012. “The Worksheet Dilemma: Benefits of Play-Based Curricula.” Early Childhood News . www.earlychildhoodnews.com/earlychildhood/article_view.aspx?ArticleID=134 .

NAEYC. 2010. “Early Childhood Mathematics: Promoting Good Beginnings.” A joint position statement of NAEYC and the National Council of Teachers of Mathematics (NCTM). www.naeyc.org/files/naeyc/file/positions/psmath.pdf .

Ontario Ministry of Education. 2010. The Full-Day Early Learning-Kindergarten Program (draft version). Toronto, ON: Queen’s Printer for Ontario. www.edu.gov.on.ca/eng/curriculum/elementary/kindergarten_english_june3.pdf .

Wien, C.A. 2004. “From Policing to Participation: Overturning the Rules and Creating Amiable Classrooms.” Young Children 59 (1): 34–40. www.naeyc.org/files/yc/file/200401/Wien.pdf .

Deanna Pecaski McLennan , PhD, is a kindergarten educator and author in Windsor, Ontario, Canada. She loves exploring mathematics through a play-, inquiry-based approach. She enjoys sharing her classroom practice and connecting with others using social media. @McLennan1977

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Maths problem-solving – Activities for Early Years settings

• Written By: Judith Dancer
• Subject: Maths

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Critical thinking doesn’t have to be a daunting prospect. There are simple, effective and exciting ways to encourage children’s maths problem-solving skills, says Judith Dancer…

Maths is a subject many adults lack confidence in. Having struggled with it at school they often avoid it, wherever possible, when grown up.

But if maths seems scary for some people, then maths problem-solving can cause even more anxiety. There is no ‘safety net’ of knowing the ‘correct answer’ beforehand. This is because maths problem-solving lends itself to investigation and exploration with lots of possible tangents.

Understandably this is often the area of maths where many practitioners feel least confident. However, young children, who are not restrained by right answers, feel the most enthused and animated.

The non-statutory  Development Matters Guidance , as part of ‘creating and thinking critically’ in the Characteristics of Effective Learning, identifies that practitioners need to observe how a child is learning, noting how a child is:

• thinking of ideas;
• finding ways to solve problems;
• finding new ways to do things;
• making links and noticing patterns in their experience;
• making predictions;
• testing their ideas;
• developing ideas of grouping, sequences, cause and effect;
• planning, making decisions about how to approach a task, solve a problem and reach a goal;
• checking how well their activities are going;
• changing strategy as needed;
• reviewing how well the approach worked.

All of these elements are, at one time or another, part of the problem-identifying and solving process – although not at the same time and in the same problem.

Role of the adult

Maths problem-solving for young children involves them understanding and using two kinds of maths:

• Maths knowledge – learning and applying an aspect of maths such as counting, calculating or measuring.
• Maths thinking skills – reasoning, predicting, talking the problem through, making connections, generalising, identifying patterns and finding solutions.

The best maths problems for children are the ones that they identify themselves. They will be enthused, fascinated and more engaged in these ‘real’, meaningful problems.

Children need opportunities to problem-solve together. As they play, they will often find their own mathematical problems.

One of the key roles of practitioners is to provide time, space and support for children. We need to develop situations and provide opportunities in which children can refine their maths problem-solving skills and apply their mathematical knowledge.

Supporting maths problem-solving

You can effectively support children’s developing maths problem-solving strategies through:

• Modelling maths talk and discussion – language is part of maths learning because talking problems through is vital. Children need to hear specific mathematical vocabulary in context. You can promote discussion through the use of comments, enabling statements and open-ended questions.
• Providing hands-on maths problem-solving activities across all areas of the setting. Children learn maths through all their experiences and need frequent opportunities to take part in creative and engaging experiences. Maths doesn’t just happen in the maths learning zone!
• Identifying potential maths learning indoors and outdoors. Provide rich and diverse open-ended resources that children can use in a number of different ways to support their own learning. It is important to include natural and everyday objects and items that have captured children’s imaginations, including popular culture.

Maths problem-solving possibilities

Spell it out.

This experience gives children lots of opportunities to explore calculating, mark making, categorising and decisions about how to approach a task.

What you need to provide:

• Assorted containers filled with natural materials. This includes leaves, pebbles, gravel, conkers, twigs, shells, fir cones, mud and sand. Include some ‘treasure’ – sequins, gold nuggets, jewels and glitter.
• Bottles and jugs of water, large mixing bowls, cups, a ‘cauldron’, small bottles, spoons and ladles.
• Cloaks and wizard hats.
• Laminated ‘spells’ – e.g. “To make a disappearing spell, mix 2 smooth pebbles, 2 gold nuggets, 4 fir cones, a pinch of sparkle dust, 3 cups of water”.
• Writing frameworks for children’s own spell recipes and a shiny ‘Spell Book’ to stick these in.
• Temporary mark-making opportunities such as chalk on slate.

The important thing with open-ended maths problem-solving experiences like this is to observe, wait and listen. Then, if appropriate, join in as a co-player with children, following their play themes.

So if children are mixing potions, note how children sort or categorise the objects. What strategies do they use to solve problems? What happens if they want eight pebbles and they run out? Observe what they do next.

When supporting children’s maths problem-solving, you need to develop a wide range of strategies and ‘dip into’ these appropriately. Rather than asking questions, it is often more effective to make comments about what you can see. For example, say, “Wow, it looks as though there is too much potion for that bottle”.

Acting as a co-player offers lots of opportunities to model mathematical behaviours. This might include reading recipes for potions and spells out loud, focusing on the numbers – one feather, three shells…

Going, going, gone

We all know that children will engage more fully when involved in experiences that fascinate them. If a particular group has a real passion for cars and trucks , consider introducing maths problem-solving opportunities that extend this interest.

This activity offers opportunities for classifying, sorting, counting, adding and subtracting, among many other things.

• Some unfamiliar trucks and cars and some old favourites. Ensure these include metal, plastic and wooden vehicles that can be sorted in different ways.
• Masking tape and scissors.
• Sticky labels and markers.

Mark out some parking lots on a smooth floor, or huge piece of paper using masking tape. Lining paper is great for this. Line the vehicles up around the edge of the floor area.

Encourage one child to select two vehicles that have something the same about them. Ask the child, “What is the same about them?”.

When the children have agreed on what is the same – e.g. size, materials, colour, lorries or racing cars – the child selects a ‘parking lot’ to put the vehicles in. So this first parking lot could be for ‘red vehicles’.

Another child chooses two more vehicles that have something the same. Do they belong in the same ‘parking lot’, or a different parking lot? E.g. these vehicles could both be racing cars.

What happens when a specific vehicle could belong in both lots? E.g. it could belong in the set of red vehicles and also belongs in the set of racing cars.

Support the children as they discuss the vehicle. Make new ‘parking lots’ with masking tape and create labels for the groups, if you choose.

Observe children’s strategies

It’s really important to observe the strategies the children use. Where appropriate, ask the children to explain what they are doing and why.

If necessary, introduce and model the use of the vocabulary ‘the same as’ and ‘different from’. Follow children’s discussions and interests. If they start talking about registration plates, consider making car number plates for all the wheeled toys outdoors.

Do the children know the format of registration plates? Can you take photos of cars you can see in the local environment?

Camping out

Constructing camps and dens outdoors is a good way to give children the opportunity to be involved in lots of maths problem-solving experiences and construction skills learning. This experience offers opportunities for using the language of position, shape and space, and finding solutions to practical problems.

• Materials to construct a tent or den such as sheets, curtains, poles, clips and string.
• Rucksacks, water bottles, compasses and maps.
• Oven shelf and bricks to build a campfire or barbecue.
• Buckets and bowls and water for washing up.

Encourage the children to explore the resources and decide which materials they need to build the camp. Suggest they source extra resources as they are needed.

Talk with the children about the best place to make a den or erect a tent and barbecue. During the discussion, model the use of positional words and phrases.

Follow children’s play themes. This could include going on a scavenger hunt collecting stones, twigs and leaves and going back to the campsite to sort them out.

Encourage children to try different solutions to the practical problems they identify. Use a running commentary on what is happening without providing the solution to the problem.

Look for opportunities to develop children’s mathematical reasoning skills by making comments such as, “I wonder why Rafit chose that box to go on the top of his den.”

If the children are familiar with traditional tales, you could extend this activity by laying a crumb trail round the outdoor area for children to follow. Make sure that there is something exciting at the end of the trail. It could be a large dinosaur sitting in a puddle, or a bear in a ‘cave’.

Children rarely have opportunities to investigate objects that are really heavy. Sometimes they have two objects and are asked the question, “Which one is heavy?” when both objects are actually light.

This experience gives children the chance to explore really heavy things and measures (weight). They also need to cooperate and find new ways to do things.

• A ‘building site’ in the outdoor area. Include hard hats, builders’ buckets, small buckets, shovels, spades, water, sand, pebbles, gravel, guttering, building blocks, huge cardboard boxes and fabric (this could be on a tarpaulin).
• Some distance away, builders’ buckets filled with damp sand and large gravel.
• Bucket balances and bathroom scales.

With an open-ended activity such as this, it is even more important to observe, wait and listen as the children explore the building site and the buckets full of sand and gravel.

Listen to the discussions the children have about moving the sand and the gravel to the building site. What language do they use?

Note the strategies they use when they can’t lift the large buckets. Who empties some of the sand into smaller buckets? Who works together collaboratively to move the full bucket? Does anyone introduce another strategy, for example, finding a wheelbarrow or pull-along truck?

Where and when appropriate, join in the children’s play as a co-player. You could act in role as a customer or new builder. Ask, “How can I get all this sand into my car?”. “How much sand and gravel do we need to make the cement for the foundations?”.

Extend children’s learning by modelling the language of weight:

• heavy/heavier than/heaviest
• light/lighter than/lightest
• about the same weight as/as heavy as
• balance/weigh

Judith Dancer is an author, consultant and trainer specialising in communication and language and mathematics. She is co-author, with Carole Skinner, of  Foundations of Mathematics – An active approach to number, shape and measures in the Early Years .

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Top 10 Challenges to Teaching Math and Science Using Real Problems

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Nine in ten educators believe that using a problem-solving approach to teaching math and science can be motivating for students, according to an EdWeek Research Center survey.

But that doesn’t mean it’s easy.

Teachers perceive lack of time as a big hurdle. In fact, a third of educators—35 percent—worry that teaching math or science through real-world problems—rather than focusing on procedures—eats up too many precious instructional minutes.

Other challenges: About another third of educators said they weren’t given sufficient professional development in how to teach using a real-world problem-solving approach. Nearly a third say reading and writing take priority over STEM, leaving little bandwidth for this kind of instruction. About a quarter say that it’s tough to find instructional materials that embrace a problem-solving perspective.

Nearly one in five cited teachers’ lack of confidence in their own problem solving, the belief that this approach isn’t compatible with standardized tests, low parent support, and the belief that student behavior is so poor that this approach would not be feasible.

The nationally representative survey included 1,183 district leaders, school leaders, and teachers, and was conducted from March 27 to April 14. (Note: The chart below lists 11 challenges because the last two on the list—dealing with teacher preparation and student behavior—received the exact percentage of responses.)

Trying to incorporate a problem-solving approach to tackling math can require rethinking long-held beliefs about how students learn, said Elham Kazemi, a professor in the teacher education program at the University of Washington.

Most teachers were taught math using a procedural perspective when they were in school. While Kazemi believes that approach has merit, she advocates for exposing students to both types of instruction.

Many educators have “grown up around a particular model of thinking of teaching and learning as the teacher in the front of the room, imparting knowledge, showing kids how to do things,” Kazemi said.

To be sure, some teachers have figured out how to incorporate some real-world problem solving alongside more traditional methods. But it can be tough for their colleagues to learn from them because “teachers don’t have a lot of time to collaborate with one another and see each other teach,” Kazemi said.

What’s more, there are limited instructional materials emphasizing problem solving, Kazemi said.

Though that’s changing, many of the resources available have “reinforced the idea that the teacher demonstrates solutions for kids,” Kazemi said.

Molly Daley, a regional math coordinator for Education Service District 112, which serves about 30 districts near Vancouver, Wash., has heard teachers raise concerns that teaching math from a problem-solving perspective takes too long—particularly given the pressure to get through all the material students will need to perform well on state tests.

Daley believes, however, that being taught to think about math in a deeper way will help students tackle math questions on state assessments that may look different from what they’ve seen before.

“It’s myth that it’s possible to cover everything that will be on the test,” as it will appear, she said. “There’s actually no way to make sure that kids have seen every single possible thing the way it will show up. That’s kind of a losing proposition.”

But rushing through the material in a purely procedural way may actually be counterproductive, she said.

Teachers don’t want kids to “sit down at the test and say, ‘I haven’t seen this and therefore I can’t do it,’” Daley said. “I think a lot of times teachers can unintentionally foster that because they’re so urgently trying to cover everything. That’s where the kind of mindless [teaching] approaches come in.”

Teachers may think to themselves: “’OK, I’m gonna make this as simple as possible, make sure everyone knows how to follow the steps and then when they see it, they can follow it,” Daley said.

But that strategy might “take away their students’ confidence that they can figure out what to do when they don’t know what to do, which is really what you want them to be thinking when they go to approach a test,” Daley said.

Data analysis for this article was provided by the EdWeek Research Center. Learn more about the center’s work.

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