steps of problem solving method in education

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Problem solving.

• Richard E. Mayer Richard E. Mayer University of California, Santa Barbara
• https://doi.org/10.1093/acrefore/9780190264093.013.860
• Published online: 30 October 2019

Problem solving refers to cognitive processing directed at achieving a goal when the problem solver does not initially know a solution method. A problem exists when someone has a goal but does not know how to achieve it. Problems can be classified as routine or non-routine, and as well-defined or ill-defined. The major cognitive processes in problem solving are representing, planning, executing, and monitoring. The major kinds of knowledge required for problem solving are facts, concepts, procedures, strategies, and beliefs. The theoretical approaches that have developed over the history of research on problem are associationism, Gestalt, and information processing. Each of these approaches involves fundamental issues in problem solving such as the nature of transfer, insight, and goal-directed heuristics, respectively. Some current research topics in problem solving include decision making, intelligence and creativity, teaching of thinking skills, expert problem solving, analogical reasoning, mathematical and scientific thinking, everyday thinking, and the cognitive neuroscience of problem solving. Common theme concerns the domain specificity of problem solving and a focus on problem solving in authentic contexts.

• problem solving
• decision making
• intelligence
• expert problem solving
• analogical reasoning
• mathematical thinking
• scientific thinking
• everyday thinking

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6 Tips for Teaching Math Problem-Solving Skills

Solving word problems is tougher than computing with numbers, but elementary teachers can guide students to do the deep thinking involved.

A growing concern with students is the ability to problem-solve, especially with complex, multistep problems. Data shows that students struggle more when solving word problems than they do with computation , and so problem-solving should be considered separately from computation. Why?

Consider this. When we’re on the way to a new destination and we plug in our location to a map on our phone, it tells us what lane to be in and takes us around any detours or collisions, sometimes even buzzing our watch to remind us to turn. When I experience this as a driver, I don’t have to do the thinking. I can think about what I’m going to cook for dinner, not paying much attention to my surroundings other than to follow those directions. If I were to be asked to go there again, I wouldn’t be able to remember, and I would again seek help.

If we can switch to giving students strategies that require them to think instead of giving them too much support throughout the journey to the answer, we may be able to give them the ability to learn the skills to read a map and have several ways to get there.

Here are six ways we can start letting students do this thinking so that they can go through rigorous problem-solving again and again, paving their own way to the solution. 

1. Link problem-solving to reading

When we can remind students that they already have many comprehension skills and strategies they can easily use in math problem-solving, it can ease the anxiety surrounding the math problem. For example, providing them with strategies to practice, such as visualizing, acting out the problem with math tools like counters or base 10 blocks, drawing a quick sketch of the problem, retelling the story in their own words, etc., can really help them to utilize the skills they already have to make the task less daunting.

We can break these skills into specific short lessons so students have a bank of strategies to try on their own. Here's an example of an anchor chart that they can use for visualizing . Breaking up comprehension into specific skills can increase student independence and help teachers to be much more targeted in their problem-solving instruction. This allows students to build confidence and break down the barriers between reading and math to see they already have so many strengths that are transferable to all problems.

2. Avoid boxing students into choosing a specific operation

It can be so tempting to tell students to look for certain words that might mean a certain operation. This might even be thoroughly successful in kindergarten and first grade, but just like when our map tells us where to go, that limits students from becoming deep thinkers. It also expires once they get into the upper grades, where those words could be in a problem multiple times, creating more confusion when students are trying to follow a rule that may not exist in every problem.

We can encourage a variety of ways to solve problems instead of choosing the operation first. In first grade, a problem might say, “Joceline has 13 stuffed animals and Jordan has 17. How many more does Jordan have?” Some students might choose to subtract, but a lot of students might just count to find the amount in between. If we tell them that “how many more” means to subtract, we’re taking the thinking out of the problem altogether, allowing them to go on autopilot without truly solving the problem or using their comprehension skills to visualize it. 

3. Revisit ‘representation’

The word “representation” can be misleading. It seems like something to do after the process of solving. When students think they have to go straight to solving, they may not realize that they need a step in between to be able to support their understanding of what’s actually happening in the problem first.

Using an anchor chart like one of these ( lower grade , upper grade ) can help students to choose a representation that most closely matches what they’re visualizing in their mind. Once they sketch it out, it can give them a clearer picture of different ways they could solve the problem.

Think about this problem: “Varush went on a trip with his family to his grandmother’s house. It was 710 miles away. On the way there, three people took turns driving. His mom drove 214 miles. His dad drove 358 miles. His older sister drove the rest. How many miles did his sister drive?”

If we were to show this student the anchor chart, they would probably choose a number line or a strip diagram to help them understand what’s happening.

If we tell students they must always draw base 10 blocks in a place value chart, that doesn’t necessarily match the concept of this problem. When we ask students to match our way of thinking, we rob them of critical thinking practice and sometimes confuse them in the process. 

4. Give time to process

Sometimes as educators, we can feel rushed to get to everyone and everything that’s required. When solving a complex problem, students need time to just sit with a problem and wrestle with it, maybe even leaving it and coming back to it after a period of time.

This might mean we need to give them fewer problems but go deeper with those problems we give them. We can also speed up processing time when we allow for collaboration and talk time with peers on problem-solving tasks. 

5. Ask questions that let Students do the thinking

Questions or prompts during problem-solving should be very open-ended to promote thinking. Telling a student to reread the problem or to think about what tools or resources would help them solve it is a way to get them to try something new but not take over their thinking.

These skills are also transferable across content, and students will be reminded, “Good readers and mathematicians reread.” 

6. Spiral concepts so students frequently use problem-solving skills

When students don’t have to switch gears in between concepts, they’re not truly using deep problem-solving skills. They already kind of know what operation it might be or that it’s something they have at the forefront of their mind from recent learning. Being intentional within their learning stations and assessments about having a variety of rigorous problem-solving skills will refine their critical thinking abilities while building more and more resilience throughout the school year as they retain content learning in the process. 

Problem-solving skills are so abstract, and it can be tough to pinpoint exactly what students need. Sometimes we have to go slow to go fast. Slowing down and helping students have tools when they get stuck and enabling them to be critical thinkers will prepare them for life and allow them multiple ways to get to their own destination.

• Intervention

Understanding the MTSS Problem-Solving Process: What You Need to Know

The terms MTSS (Multi-Tier System of Supports) and RTI (Response to Intervention) are often used interchangeably among educators, but the truth is these two frameworks are NOT one in the same. MTSS is a set of evidence-based practices implemented across a system to meet the needs of all learners (Kansas Multi-Tier System of Supports [MTSS]: Academic Structuring Guide, 2011). The MTSS framework is broader than Response to Intervention or a problem-solving process alone. It establishes a paradigm of support service delivery focused on leadership, professional development, and empowering culture within the context of assessment, curriculum, and instruction.

Within this system, there are typically three tiers of supports where students receive instruction and interventions to help them on their path to achievement. Determining the appropriate interventions for each student is vital to the success of this system, and MTSS utilizes a data-driven decision-making process to aid in those determinations.

The MTSS problem-solving process consists of four important steps:

Define the problem or goal

Analyze the problem and relevant data

Implement an intervention plan

Evaluate the intervention for effectiveness

1.  Define the problem

The first step in the decision-making process determines the goal and direction of the rest of the process. A team must identify what problem needs to be solved—such as lack of adequate academic progress or a non-academic situation such as poor attendance or behavior. Teams may look at the difference between the desired outcome in an area and the actual performance of a student in order to select the appropriate problem to highlight.

2.  Analyze the data

MTSS is a system driven by data. After a problem has been defined, it is necessary to review the data to determine the cause. The cause could be a specific skill deficit or various gaps in a particular domain of learning, or, alternatively, it could be based on a non-academic factor. In the second step of the problem-solving process, team members gather relevant information and data and then analyze it to not only determine the problem, but also pinpoint what barriers may exist to successfully achieving the goal.

The ICEL/RIOT matrix is a useful tool for identifying the proper type of data needed for decision-making.  

ICEL stands for four domains of learning to be assessed during the problem-solving process:

I  - Instruction

C - Curriculum

E - Environment

L - Learner  

RIOT includes four potential sources of data:

R - Review of records

I - Interviews of key stakeholders who are familiar with the student

O - Observation of student in a regular setting

T - Test student using various methods of measurement

The data collected provides a good overview of the student’s needs and is helpful in explaining the occurrence of a problem. It also serves as a foundation for designing an appropriate intervention plan in the next step of the process.

3.  Implement an intervention plan

Having focused on the process of defining the problem and analyzing the data, the problem-solving team is then ready to design and implement an intervention plan that is appropriate for a student’s specific needs as shown by the data.

The Florida Department of Education identifies specific criteria for interventions in “A Teacher’s Guide to Problem Solving Within the MTSS Framework.” These specific criteria indicate that interventions should:

Consist of evidence-based programs, strategies, and techniques

Be delivered with integrity and fidelity

Allow for intensified instruction

Be implemented for a sufficient time and an evaluated frequently, and be integrated across the tiers

Using the problem-solving process for decision-making allows for interventions to be designed to address the unique needs and situation of each student, and provides for flexibility in both intensity and implementation of a plan. Frequent progress-monitoring during implementation is important for proper execution of the last step of the process—evaluating the intervention.

4.  Evaluate the intervention

After spending time to create and implement an intervention, it is essential for teams to spend time evaluating. In this step, the decision-making team must determine if the intervention was considered successful and whether the student responded well to the intervention strategy.

If the data is showing adequate progress, the team can decide if continuing the intervention is necessary. If the data is not showing as much progress as expected, team members can make changes to the intervention plan. If evaluation shows that the intervention was not successful, the team can re-engage in the problem-solving process to complete further analysis of both the problem and the data to ensure that proper interventions are put in place.  

The MTSS problem-solving process allows teams to determine the appropriate interventions within a multi-tiered structure to provide for the academic and non-academic needs of all students. Each step of the process is necessary for ensuring that students are given the right interventions at the right time, allowing for the best possible path to achievement.

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Think-Alouds

Effective teachers think out loud on a regular basis

Download for free.

What Are Think-Alouds?

Think-alouds are a strategy in which students verbalize their thoughts while reading or answering questions. By saying what they're thinking, students can externalize and process their thoughts.

Effective teachers think out loud regularly to model this process for students. In this way, they demonstrate practical ways of approaching difficult problems while bringing to the surface the complex thinking processes that underlie reading comprehension, problem solving, and other cognitively demanding tasks.

Why Use Think-Alouds?

Key takeaways:

• The think-aloud strategy is used to model comprehension processes such as making predictions, creating images, and linking information to prior knowledge.
• Teachers model expert problem-solving by verbalizing their thought processes, aiding students in developing their own problem-solving skills, and fostering independent learning.
• Teachers can assess students' strengths and weaknesses by listening to their verbalized thoughts.
• Getting students into the habit of thinking out loud enriches classroom discourse and gives teachers an important assessment and diagnostic tool.
• Research has demonstrated that the think-aloud strategy is effective for fostering comprehension skills from an early age.

Summary of the research

Think-alouds, where teachers vocalize their problem-solving process, serve as a model for students to develop their inner dialogue, a critical tool in problem-solving (Tinzmann et al. 1990). This interactive approach fosters reflective, metacognitive, independent learning. It helps students understand that learning requires effort and often involves difficulty, assuring them they are not alone in navigating problem-solving processes (Tinzmann et al. 1990).

Think-alouds are used to model comprehension processes such as making predictions, creating images, linking information in text with  prior knowledge , monitoring comprehension, and overcoming problems with word recognition or comprehension (Gunning 1996).

By listening in as students think aloud, teachers can diagnose students' strengths and weaknesses. "When teachers use assessment techniques such as observations, conversations and interviews with students, or interactive journals, students are likely to learn through the process of articulating their ideas and answering the teacher's questions" (National Council of Teachers of Mathematics 2000).

Research into the impact of using the think-aloud strategy to enhance reading comprehension of science concepts found that implementing think-alouds as a during-reading activity significantly improved the comprehension of science concepts in Kindergarten students (Ortleib & Norris, 2012). This finding underscores the effectiveness of the think-aloud strategy in fostering comprehension skills from an early age.

How To Use Think-Alouds

Think-alouds are versatile teaching tools that can be applied in various ways. For instance, in math, teachers can model the strategy by vocalizing their problem-solving process as they work through a problem. In reading, the think-aloud strategy enhances comprehension by allowing students to actively engage with the text, verbalizing their thought processes, questions, and connections.

Another approach is the use of reciprocal think-alouds, which fosters collaboration and helps students understand different ways of thinking. Think-alouds can also be used as an assessment tool to pinpoint individual student needs, shaping instruction to better suit each learner.

Think-alouds can be used in a number of ways across different subject areas, including:

• Reading/English: The think-aloud process can be used during all stages of reading, from accessing prior knowledge and making predictions to understanding text structure and supporting opinions.
• Writing: Think-alouds can be used to model the writing process, including pre-writing strategies, drafting, revision, and editing.
• Math: Use think-alouds to model the use of new math processes or strategies, and assess student understanding.
• Social Studies: During discussions on complex topics, have students use think-alouds to explain their reasoning and opinions.
• Science: Think-alouds can be used to model the scientific inquiry process, and students can reflect on this process in their journals or learning logs.

Modeling Thinking-Alouds

Modeling think-alouds is a method where a teacher vocalizes their problem-solving process, serving as a guide for students. This strategy allows learners to see the internal mechanisms of problem-solving, demonstrating that learning is an active process. It helps students develop their metacognitive skills, promoting independent learning.

What does this look like in the classroom?

Before proceeding with the actual think-aloud, first, explain the concept and its significance. For instance, "Today, we're going to use the think-aloud strategy as we work through this problem. The think-aloud strategy helps us to vocalize our inner thoughts and reasoning as we solve a problem. It's a useful tool because it allows us to better understand our own thought processes and identify areas where we might be struggling."

Modeling the Think-Aloud Strategy for Math

The think-aloud strategy is instrumental in developing problem-solving skills as it promotes metacognition, enabling students to understand and evaluate their thought processes while tackling a problem.

For example, suppose during math class you'd like students to estimate the number of pencils in a school. Introduce the strategy by saying, "The strategy I am going to use today is estimation. We use it to . . . It is useful because . . . When we estimate, we . . ."

Next say, "I am going to think aloud as I estimate the number of pencils in our school. I want you to listen and jot down my ideas and actions." Then, think aloud as you perform the task.

Your think-aloud might go something like this:

"Hmmmmmm. So, let me start by estimating the number of students in the building. Let's see. There are 5 grades; first grade, second grade, third grade, fourth grade, fifth grade, plus kindergarten. So, that makes 6 grades because 5 plus 1 equals 6. And there are 2 classes at each grade level, right? So, that makes 12 classes in all because 6 times 2 is 12. Okay, now I have to figure out how many students in all. Well, how many in this class? [Counts.] Fifteen, right? Okay, I'm going to assume that 15 is average. So, if there are 12 classes with 15 students in each class, that makes, let's see, if it were 10 classes it would be 150 because 10 times 15 is 150. Then 2 more classes would be 2 times 15, and 2 times 15 is 30, so I add 30 to 150 and get 180. So, there are about 180 students in the school. I also have to add 12 to 180 because the school has 12 teachers, and teachers use pencils, too. So that is 192 people with pencils."

Continue in this way.

Modeling the Think-Aloud Strategy for Reading

The think-aloud strategy enhances reading comprehension by promoting metacognitive understanding of the reading process. It allows students to actively engage with the text, verbalizing their thought processes, questions, and connections, which leads to deeper understanding and retention of material.

When reading aloud, you can stop from time to time and orally complete sentences like these:

• So far, I've learned...
• This made me think of...
• That didn't make sense.
• I think ___ will happen next.
• I reread that part because...
• I was confused by...
• I think the most important part was...
• That is interesting because...
• I wonder why...
• I just thought of...

More Ways to Model Think-Alouds

Another option is to video the part of a lesson that models thinking aloud. Students can watch the video and figure out what the teacher did and why. Stop the video periodically to discuss what they notice, what strategies were tried, and why, and whether they worked. As students discuss the process, jot down any important observations.

Once students are familiar with the strategy, include them in a think-aloud process. For example:

Teacher: "For science class, we need to figure out how much snow is going to fall this year. How can we do that?"

Student: "We could estimate."

Teacher: "That sounds like it might work. How do we start? What do we do next? How do we know if our estimate is close? How do we check it?"

In schools where teachers work collaboratively in grade-level teams or learning communities, teachers can plan and rehearse using the think-aloud strategy with a partner before introducing it to students. It is often more effective when the whole school focuses on the same strategy and approaches to integrate it into learning.

Reciprocal Think-Alouds

In reciprocal think-alouds, students are paired with a partner. Students take turns thinking aloud as they read a difficult text, form a  hypothesis in science , or compare opposing points of view in  social studies . While the first student thinks aloud, the second student listens and records what the first student says. Then students change roles so each partner can think aloud and observe the process. Next, students reflect on the process together, sharing what they tried and discussing what worked well for them and what didn't. As they write about their findings, they can start a mutual learning log that they refer back to.

Think-Alouds as an Assessment Tool

After students are comfortable with the think-aloud process you can use it as an assessment tool. As students think out loud through a problem-solving process, such as reflecting on the steps used to solve a problem in math, write what they say. This allows you to observe the strategies students use. Analyzing the results will allow to pinpoint the individual student's needs and provide appropriate instruction.

Assign a task, such as solving a specific problem or reading a passage of text. Introduce the task to students by saying, "I want you to think aloud as you complete the task: say everything that is going on in your mind." As students complete the task, listen carefully and write down what students say. It may be helpful to use a tape recorder. If students forget to think aloud, ask open-ended questions: "What are you thinking now?" and "Why do you think that?"

After the think-alouds, informally interview students to clarify any confusion that might have arisen during the think-aloud. For example, "When you were thinking aloud, you said . . . Can you explain what you meant?"

Lastly, use a  rubric  as an aid to analyze each student's think-aloud, and use the results to shape instruction.

For state-mandated tests, determine if students need to think aloud during the actual testing situation. When people are asked to solve difficult problems or to perform difficult tasks, inner speech goes external (Tinzmann et al. 1990). When faced with a problem-solving situation, some students need to think aloud. For these students, if the state testing protocol permits it, arrange for testing situations that allow students to use think-alouds. This will give a more complete picture of what these students can do as independent learners.

See the research that supports this strategy

Tinzmann, M B. et. al. (1996) What Is the Collaborative Classroom? Journal: NCREL. Oak Brook.

Gunning, Thomas G. (1996). Creating Reading Instruction for All Children. Chapter 6, 192-236.

The National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc .

Wilhelm, J. D. (2001). Improving Comprehension with Think-Aloud Strategies. New York: Scholastic Inc.

Ortlieb, E., & Norris, M. (2012). Using the Think-Aloud Strategy to Bolster Reading Comprehension of Science Concepts. Current Issues in Education , 15 (1)

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The Role of the Teacher Changes in a Problem-Solving Classroom

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How can teachers help students develop problem-solving skills when they themselves, even though confronted with an array of problems every day, may need to become better problem solvers? Our experience leads us to conclude that there is an expertise in a certain kind of problem-solving that teachers possess but that broader problem-solving skills are sometimes wanting.There are a few reasons why this happens. One reason may be that teacher preparation programs remain focused on how to teach subjects and behavior management techniques. Another reason may be that professional development opportunities offered in schools are focused elsewhere. And, another reason could be that leaders still often fail to engage their faculties in solving substantive problems within the school community.

A recent issue of Education Leadership was dedicated to the topic, “Unleashing Problem Solvers”. One theme that ran through several of the articles was the changing role of the teacher. In a positive but traditional classroom, information is shared by the teacher and the students are asked to demonstrate application of that information. A problem-solving classroom is different. A problem-solving classroom requires extraordinary planning on the part of the teacher. For problems to have relevance, students are engaged in the identification of the problem. Teachers have to become experts at creating questions that require students to reach back to information and skills already attained, while figuring out what they need to learn next in order to solve the problem. Some of us are really good at asking these kinds of questions. Others are not.

Students have to become experts at reflecting on these questions as guides resulting in a gathering of new information and skills, and answers. Teachers have to be prepared to offer lessons that bridge the gaps between the skills and information already attained and those the performance of the students demonstrate remain needed. Often it involves teams of students and they are simultaneously learning collaboration and communication skills.

Problem-Based Classrooms Require Letting Go

Opportunities for teachers to work with each other, to learn from experts, to receive feedback from observers of their work, all allow for skill development. But at the same time, there is a more challenging effort required of the teacher. Problem-based classrooms require teachers to dare to let go of control of the learning and to take hold of the role of questioner, coach, supporter, and diagnostician. In addition to the lack of training teachers have in these skills, the leaders in charge of evaluating their work also have to know what problem-solving classrooms look like and how to capture that environment in an observation, how to give feedback on the teachers’ efforts. Of course, if problem- solving is a collaborative school community process, how does that change the leader’s role? Are leaders, themselves, ready to become facilitators of the process rather than the sole problem solver? Many talk about wanting that but most get rewarded for being the problem solver.

Questions are Essential

There is a place to begin and that place is the shared understanding of what problem-based learning actually is. Because teachers traditionally plan for a time for Q and A within classes, they and their leaders may think of questions as having a correct answer. In moving into a problem-based learning design, the questions also have to be more overarching, create cognitive dissonance, and provoke the learner to search for answers. Here is why it is important to come to an understanding about the types of questions to be asked and shifting the teaching and learning practices to be one of expecting more from the learner.

Students Need Problem-Solving Skills

Problem-based learning skills are skills that prepare for a changing environment in all fields. Current educators cannot imagine some of the careers our students will have over their lifetimes. We do know that change will be part of everyone’s work. Flexibility and problem-solving are key skills. Problem- solving involves collaboration, communication, critical thinking, empathy, and integrity. If we listen to the business world, we will hear that design thinking is the way of the future.

Tim Brown, CEO of IDEO says,

Design thinking is a human-centered approach to innovation that draws from the designer’s toolkit to integrate the needs of people, the possibilities of technology, and the requirements for business success.

The only way for educators to develop these skills in students is to build lessons and units that are interdisciplinary and demand these skills. If we begin from the earliest of grades and expect more as they ascend through the grades, students will have mastered not only their subjects, but the skills that will prepare them for the world of work. How do we best prepare our students? We think problem solving is key.

A nn Myers and Jill Berkowicz are the authors of The STEM Shift (2015, Corwin) a book about leading the shift into 21st century schools. Ann and Jill welcome connecting through Twitter & Email .

Photo courtesy of Pixabay

The opinions expressed in Leadership 360 are strictly those of the author(s) and do not reflect the opinions or endorsement of Editorial Projects in Education, or any of its publications.

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 Integrated Scientific Method 

by Craig Rusbult, PhD .  

Before you explore this page — which is a condensed overview for the first half of my PhD dissertation that will help you understand the complexity of science — you can focus on the simplicity of science in my Introduction to Scientific Method .  It begins with a summary:

what it is :   Integrated Scientific Method ( ISM ) is a model for scientific thinking-and-actions.  It's a synthesis of ideas — mainly from scientists and philosophers, but also from psychologists, sociologists, historians, educators, and myself — that describes the activities of scientists: what they think about and what they do.  It shows how the mutually supportive skills of creativity and critical thinking are intimately integrated in the problem-solving methods used by scientists.

Scientific Method in Education  

Practical Applications in Science Education In all schools — public, private, and home, from K-12 through college — teachers are wondering whether "scientific method" exists and how scientific thinking skills can be taught in the classroom.  Teachers want to offer a quality education that includes science concepts and also thinking skills , so students will be motivated to think and will learn how to think more often and more effectively, with enthusiasm and skill.  A variety of questions — about scientific method and much more — are explored in the area for thinking skills education, and you can see what's available in an overview-sitemap for pages that include An Introduction to Design Method for Problem Solving in Education & Life and Developing an Education Curriculum for Thinking Skills and Problem Solving and pages by other authors about problem solving by using design method & scientific method .

      An Integrative Model      My model of Integrated Scientific Method (ISM) has two kinds of integration, in its sources and function.      sources:  I developed the model by combining ideas from scientists and philosophers, plus psychologists, sociologists, historians, educators, and myself.      function:  This model describes the thinking & actions of scientists who are trying to understand (by using evidence-and-logic) how the world works, are being influenced by a combination of factors (empirical, conceptual, cultural-personal), using thinking that is creative-and-critical, with creativity and critical thinking intimately integrated in their problem-solving methods.     { what the model is & isn't and what it's for  }

     an update — After developing this model during my PhD work, I generalized it to construct a model for Problem-Solving Process that combines Science Process with Design Process.  This model (and how we can use it) is described in my website about Education for Problem Solving .

      Here is a quick summary of ISM (a model for Integrated Scientific Method), focusing on the symbolism for the shapes and colors you see above :       In the eight ovals are major activities of science:  generate and evaluate actions , generate and evaluate theories , generate and evaluate experiments , do thought-experiments and physical experiments .       Comparing the results of a mental experiment and physical experiment produces Hypothetico-Deductive logic (combining yellow-and-green information, predictions and observations ) in the two H-D boxes.       Three types of evaluation criteria ( light blue boxes) influence theory evaluation ( blue oval).       The intimate connections between generation (red) and evaluation (blue) are symbolized by purple (red plus blue makes purple*) as a reminder of the continual interplay between creative thinking and critical thinking to make productive thinking.    {*with pigments}       The activities of scientists are motivated-and-guided by goals (gold).

an integrative model of Scientific Method

Most of this page was written in 1997.  In 2006, I said, in a section about "Designing of Scientific Theories" in An Introduction to Scientific Method ,       In their daily work, scientists rarely design large-scale generalized mega-theories, such as the theories of gravity, invariance, or evolution developed by Newton, Einstein, or Darwin.  Instead, they typically are applying generalized theories that already are accepted, in their study of particular experimental systems for which they are designing small-scale specialized sub-theories.       Even more commonly, scientists design experiments ( Part 6 ) based on mega-theories and sub-theories that already are accepted, with the goal of simply making observations so they can learn more about nature.

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How Your Child Learns to Problem-Solve

Your preschooler is figuring out what things are, why things are, and how things work..

In the course of your child's day, dozens of questions like these arise: "What's inside this box?" "How can I get into it?" "How far can I throw this ball?" "What will happen if I spill all of the crayons out of the box?" "I wonder if my teddy bear floats?" "How can I get these pieces of paper to stick to that piece of paper?" "Why does my block tower keep falling over?"

By asking these questions, your child is identifying and figuring out ways to solve them, and trying out her ideas. Every time she experiments with and investigates things in her world, such as how far water will squirt from a sprayer and what's inside a seedpod, for example, she is building her ability to solve problems. This is also true when she selects materials for building or when she learns to resolve an argument with a friend or sibling over a toy.

If we look at this process more closely, we discover that problem solving involves both creative and critical thinking. Both are necessary to figure out the solutions to problems of all kinds.

Creative Thinking

Creative thinking is the heart of problem solving. It is the ability to see a different way to do something, generate new ideas, and use materials in new ways. Central to creative thinking is the willingness to take risks, to experiment, and even to make a mistake. Part of creative thinking is "fluent" thinking, which is the ability to generate or brainstorm ideas. So ask your child "wide-open" questions! For instance, ask him to:

• imagine all the different ways to get to school (walking, flying, driving, swimming!).
• name everything he can think of that's red.
• name everything he can think of that's round.
• imagine all the things he could make out of clay or paper bags or even an empty box.

These are good examples of thinking problems that have many right answers. Research has shown that the ability to think fluently has a high correlation to school success later on. Another part of creative thinking is "flexible" thinking, which is the ability to see many possibilities or to view objects or situations in different ways. The next time your child pretends a pot is a hat or a spoon is a microphone or speculates on all the reasons that a child in a picture might feel sad, he is practicing his flexible thinking.

Critical Thinking

Critical, or logical, thinking is the ability to break an idea into its parts and analyze them. The math skills of sorting and classifying, comparing similarities and differences, are all parts of critical thinking. Whenever your child looks at, say, two glasses of juice and tries to figure out which one holds more, he is practicing this kind of thinking. To encourage it, ask your child:

• how many different ways he can sort his blocks.
• how many different ways he can make a building out of the blocks.
• how the building would be different if he used blocks of only one size.
• how a bottle of juice and his lunch box are alike and how they are different.
• how family members' shoes are alike and how they are different.

Asking questions about things that don't seem to make sense is another way children think critically. Questions such as "Why do I have a shadow on the playground but not inside?" or "Why can't I see the wind?" are examples of critical thinking. You don't need to have one right answer, but do encourage your child to express his ideas. There's one other thing to remember about problem solving: It's fun! So make room for spontaneity and prepare yourself to be surprised and delighted as you discover your child's unique way of thinking.

Resources >

Mckinsey approach to problem solving, a guide to the 7-step mckinsey problem solving process.

McKinsey and Company is recognized for its rigorous approach to problem solving. They train their consultants on their seven-step process that anyone can learn.

This resource guides you through that process, largely informed by the McKinsey Staff Paper 66. It also includes a PowerPoint Toolkit with slide templates of each step of the process that you can download and customize for your own use.

In this guide you'll learn:

Overview of the mckinsey approach to problem solving, problem solving process, problem definition.

• Problem Statement

Stakeholder Analysis Worksheet

Structure the problem, hypothesis trees, issue trees, analyses and workplan, synthesize findings, craft recommendations, communicate, distinctiveness practices, harness the power of collaboration, sources and additional reading, request the mckinsey approach to problem solving.

Problem solving — finding the optimal solution to a given business opportunity or challenge — is the very heart of how consultants create client impact, and considered the most important skill for success at McKinsey.

The characteristic “McKinsey method” of problem solving is a structured, inductive approach that can be used to solve any problem. Using this standardized process saves us from reinventing the problem-solving wheel, and allows for greater focus on distinctiveness in the solution. Every new McKinsey associate must learn this method on his or her first day with the firm.

There are four fundamental disciplines of the McKinsey method:

1. Problem definition

A thorough understanding and crisp definition of the problem.

2. The problem-solving process

Structuring the problem, prioritizing the issues, planning analyses, conducting analyses, synthesizing findings, and developing recommendations.

3. Distinctiveness practices

Constructing alternative perspectives; identifying relationships; distilling the essence of an issue, analysis, or recommendation; and staying ahead of others in the problem-solving process.

4. Collaboratio n

Actively seeking out client, customer, and supplier perspectives, as well as internal and external expert insight and knowledge.

Once the problem has been defined, the problem-solving process proceeds with a series of steps:

• Structure the problem
• Prioritize the issues
• Plan analyses
• Conduct analyses
• Synthesize findings
• Develop recommendations

Not all problems require strict adherence to the process. Some steps may be truncated, such as when specific knowledge or analogies from other industries make it possible to construct hypotheses and associated workplans earlier than their formal place in the process. Nonetheless, it remains important to be capable of executing every step in the basic process.

When confronted with a new and complex problem, this process establishes a path to defining and disaggregating the problem in a way that will allow the team to move to a solution. The process also ensures nothing is missed and concentrates efforts on the highest-impact areas. Adhering to the process gives the client clear steps to follow, building confidence, credibility, and long-term capability.

The most important step in your entire project is to first carefully define the problem. The problem definition will serve the guide all of the team’s work, so it is critical to ensure that all key stakeholders agree that it is the right problem to be solving.

The problem definition will serve the guide all of the team’s work, so it is critical to ensure that all key stakeholders agree that it is the right problem to be solving.

There are often dozens of issues that a team could focus on, and it is often not obvious how to define the problem.

In any real-life situation, there are many possible problem statements. Your choice of problem statement will serve to constrain the range of possible solutions.

Constraints can be a good thing (e.g., limit solutions to actions within the available budget.) And constraints can be a bad thing (e.g., eliminating the possibility of creative ideas.) So choose wisely.

The problem statement may ignore many issues to focus on the priority that should be addressed. The problem statement should be phrased as a question, such that the answer will be the solution.

Example scenario – A family on Friday evening :

A mother, a father, and their two teenage children have all arrived home on a Friday at 6 p.m. The family has not prepared dinner for Friday evening. The daughter has lacrosse practice on Saturday and an essay to write for English class due on Monday. The son has theatre rehearsal on both Saturday and Sunday and will need one parent to drive him to the high school both days, though he can get a ride home with a friend.

The family dog, a poodle, must be taken to the groomer on Saturday morning. The mother will need to spend time this weekend working on assignments for her finance class she is taking as part of her Executive MBA. The father plans to go on a 100-mile bike ride, which he can do either Saturday or Sunday. The family has two cars, but one is at the body shop. They are trying to save money to pay for an addition to their house.

Potential problem definitions – A family on Friday evening :

The problem definition should not be vague, without clear measures of success. Rather, it should be a SMART definition:

• Action-oriented

Given one set of facts, it is possible to come up with many possible problem statements. The choice of problem statement constrains the range of possible solutions.

Before starting to solve the problem, the family first needs to agree on what problem they want to solve.

• What should the family do for dinner on Friday night?
• How can the family schedule their activities this weekend to accomplish everything planned given that they only have one vehicle available?
• How can the family increase income or reduce expenses to allow them to save $75K over the next 12 months to pay for the planned addition to their house?

Problem Statement Worksheet

This is a helpful tool to use to clearly define the problem. There are often dozens of issues that a team could focus on, and it is often not obvious how to define the problem. In any real-life situation, there are many possible problem statements. Your choice of problem statement will serve to constrain the range of possible solutions.

• Use a question . The problem statement should be phrased as a question, such that the answer will be the solution. Make the question SMART: specific, measurable, action-oriented, relevant, and time-bound. Example: “How can XYZ Bank close the $100 million profitability gap in two years?”
• Context . What are the internal and external situations and complications facing the client, such as industry trends, relative position within the industry, capability gaps, financial flexibility, and so on?
• Success criteria . Understand how the client and the team define success and failure. In addition to any quantitative measures identified in the basic question, identify other important quantitative or qualitative measures of success, including timing of impact, visibility of improvement, client capability building required, necessary mindset shifts, and so on.
• Scope and constraints . Scope most commonly covers the markets or segments of interest, whereas constraints govern restrictions on the nature of solutions within those markets or segments.
• Stakeholders . Explore who really makes the decisions — who decides, who can help, and who can block.
• Key sources of insight . What best-practice expertise, knowledge, and engagement approaches already exist? What knowledge from the client, suppliers, and customers needs to be accessed? Be as specific as possible: who, what, when, how, and why.

In completing the Problem Statement Worksheet, you are prompted to define the key stakeholders.

As you become involved in the problem-solving process, you should expand the question of key stakeholders to include what the team wants from them and what they want from the team, their values and motivations (helpful and unhelpful), and the communications mechanisms that will be most effective for each of them.

Using the Stakeholder Analysis Worksheet allows you to comprehensively identify:

• Stakeholders
• What you need from them
• Where they are
• What they need from you

The two most helpful techniques for rigorously structuring any problem are hypothesis trees and issue trees. Each of these techniques disaggregates the primary question into a cascade of issues or hypotheses that, when addressed, will together answer the primary question.

A hypothesis tree might break down the same question into two or more hypotheses. 

The aim at this stage is to structure the problem into discrete, mutually exclusive pieces that are small enough to yield to analysis and that, taken together, are collectively exhaustive.

Articulating the problem as hypotheses, rather than issues, is the preferred approach because it leads to a more focused analysis of the problem. Questions to ask include:

• Is it testable – can you prove or disprove it?
• It is open to debate? If it cannot be wrong, it is simply a statement of fact and unlikely to produce keen insight.
• If you reversed your hypothesis – literally, hypothesized that the exact opposite were true – would you care about the difference it would make to your overall logic?
• If you shared your hypothesis with the CEO, would it sound naive or obvious?
• Does it point directly to an action or actions that the client might take?

Quickly developing a powerful hypothesis tree enables us to develop solutions more rapidly that will have real impact. This can sometimes seem premature to clients, who might find the “solution” reached too quickly and want to see the analysis behind it.

Take care to explain the approach (most important, that a hypothesis is not an answer) and its benefits (that a good hypothesis is the basis of a proven means of successful problem solving and avoids “boiling the ocean”).

Example: Alpha Manufacturing, Inc.

Problem Statement: How can Alpha increase EBITDA by $13M (to $50M) by 2025?

The hypotheses might be:

• Alpha can add $125M revenues by expanding to new customers, adding $8M of EBITDA
• Alpha can reduce costs to improve EBITDA by $5M

These hypotheses will be further disaggregated into subsidiary hypotheses at the next level of the tree.

Often, the team has insufficient knowledge to build a complete hypothesis tree at the start of an engagement. In these cases, it is best to begin by structuring the problem using an issue tree.

An issue tree is best set out as a series of open questions in sentence form. For example, “How can the client minimize its tax burden?” is more useful than “Tax.” Open questions – those that begin with what, how, or why– produce deeper insights than closed ones. In some cases, an issue tree can be sharpened by toggling between issue and hypothesis – working forward from an issue to identify the hypothesis, and back from the hypothesis to sharpen the relevant open question.

Once the problem has been structured, the next step is to prioritize the issues or hypotheses on which the team will focus its work. When prioritizing, it is common to use a two-by-two matrix – e.g., a matrix featuring “impact” and “ease of impact” as the two axes.

Applying some of these prioritization criteria will knock out portions of the issue tree altogether. Consider testing the issues against them all, albeit quickly, to help drive the prioritization process.

Once the criteria are defined, prioritizing should be straightforward: Simply map the issues to the framework and focus on those that score highest against the criteria.

As the team conducts analysis and learns more about the problem and the potential solution, make sure to revisit the prioritization matrix so as to remain focused on the highest-priority issues.

The issues might be:

• How can Alpha increase revenue?
• How can Alpha reduce cost?

Each of these issues is then further broken down into deeper insights to solutions.

If the prioritization has been carried out effectively, the team will have clarified the key issues or hypotheses that must be subjected to analysis. The aim of these analyses is to prove the hypotheses true or false, or to develop useful perspectives on each key issue. Now the task is to design an effective and efficient workplan for conducting the analyses.

Transforming the prioritized problem structure into a workplan involves two main tasks:

• Define the blocks of work that need to be undertaken. Articulate as clearly as possible the desired end products and the analysis necessary to produce them, and estimate the resources and time required.
• Sequence the work blocks in a way that matches the available resources to the need to deliver against key engagement milestones (e.g., important meetings, progress reviews), as well as to the overall pacing of the engagement (i.e., weekly or twice-weekly meetings, and so on).

A good workplan will detail the following for each issue or hypothesis: analyses, end products, sources, and timing and responsibility. Developing the workplan takes time; doing it well requires working through the definition of each element of the workplan in a rigorous and methodical fashion.

It’s useful to match the workplan to three horizons:

• What is expected at the end of the engagement
• What is expected at key progress reviews
• What is due at daily and/or weekly team meetings

The detail in the workplan will typically be greater for the near term (the next week) than for the long term (the study horizon), especially early in a new engagement when considerable ambiguity about the end state remains.

Here are three different templates for a workplan:

This is the most difficult element of the problem-solving process. After a period of being immersed in the details, it is crucial to step back and distinguish the important from the merely interesting. Distinctive problem solvers seek the essence of the story that will underpin a crisp recommendation for action.

Although synthesis appears, formally speaking, as the penultimate step in the process, it should happen throughout. Ideally, after you have made almost any analytical progress, you should attempt to articulate the “Day 1” or “Week 1” answer. Continue to synthesize as you go along. This will remind the team of the question you are trying to answer, assist prioritization, highlight the logical links of the emerging solution, and ensure that you have a story ready to articulate at all times during the study.

McKinsey’s primary tool for synthesizing is the pyramid principle. Essentially, this principle asserts that every synthesis should explain a single concept, per the “governing thought.” The supporting ideas in the synthesis form a thought hierarchy proceeding in a logical structure from the most detailed facts to the governing thought, ruthlessly excluding the interesting but irrelevant.

While this hierarchy can be laid out as a tree (like with issue and hypothesis trees), the best problem solvers capture it by creating dot-dash storylines — the Pyramid Structure for Grouping Arguments.

Pyramid Structure for Grouping Arguments

• Focus on action. Articulate the thoughts at each level of the pyramid as declarative sentences, not as topics. For example, “expansion” is a topic; “We need to expand into the European market” is a declarative sentence.
• Use storylines. PowerPoint is poor at highlighting logical connections, therefore is not a good tool for synthesis. A storyline will clarify elements that may be ambiguous in the PowerPoint presentation.
• Keep the emerging storyline visible. Many teams find that posting the storyline or story- board on the team-room wall helps keep the thinking focused. It also helps in bringing the client along.
• Use the situation-complication-resolution structure. The situation is the reason there is action to be taken. The com- plication is why the situation needs thinking through – typically an industry or client challenge. The resolution is the answer.
• Down the pyramid: does each governing thought pose a single question that is answered completely by the group of boxes below it?
• Across: is each level within the pyramid MECE?
• Up: does each group of boxes, taken together, provide one answer – one “so what?” – that is essentially the governing thought above it?
• Test the solution. What would it mean if your hypotheses all came true?

It is at this point that we address the client’s questions: “What do I do, and how do I do it?” This means not offering actionable recommendations, along with a plan and client commitment for implementation.

The essence of this step is to translate the overall solution into the actions required to deliver sustained impact. A pragmatic action plan should include:

• Relevant initiatives, along with a clear sequence, timing, and mapping of activities required
• Clear owners for each initiative
• Key success factors and the challenges involved in delivering on the initiatives

Crucial questions to ask as you build recommendations for organizational change are:

• Does each person who needs to change (from the CEO to the front line) understand what he or she needs to change and why, and is he or she committed to it?
• Are key leaders and role models throughout the organization personally committed to behaving differently?
• Has the client set in place the necessary formal mechanisms to reinforce the desired change?
• Does the client have the skills and confidence to behave in the desired new way?

Once the recommendations have been crafted in the problem-solving process, it’s vital to effectively communicate those findings and recommendations.

An executive summary is a great slide to use for this. See more on executive summary slides, including 30 templates, at our Ultimate Guide to Executive Summary Slides .

Great problem solvers identify unique disruptions and discontinuities, novel insights, and step-out opportunities that lead to truly distinctive impact. This is done by applying a number of practices throughout the problem-solving process to help develop these insights.

Expand: Construct multiple perspectives

Identifying alternative ways of looking at the problem expands the range of possibilities, opens you up to innovative ideas, and allows you to formulate more powerful hypotheses. Questions that help here include:

• What changes if I think from the perspective of a customer, or a supplier, or a frontline employee, or a competitor?
• How have other industries viewed and addressed this same problem?
• What would it mean if the client sought to run the company like a low-cost airline or a cosmetics manufacturer?

Link: Identify relationships

Strong problem solvers discern connections and recognize patterns in two different ways:

• They seek out the ways in which different problem elements – issues, hypotheses, analyses, work elements, findings, answers, and recommendations – relate to one another.
• They use these relationships throughout the basic problem-solving process to identify efficient problem-solving approaches, novel solutions, and more powerful syntheses.

Distill: Find the essence

Cutting through complexity to identify the heart of the problem and its solution is a critical skill.

• Identify the critical problem elements. Are there some issues, approaches, or options that can be eliminated completely because they won’t make a significant difference to the solution?
• Consider how complex the different elements are and how long it will take to complete them. Wherever possible, quickly advance simpler parts of the problem that can inform more complex or time-consuming elements.

Lead: Stay ahead/step back

Without getting ahead of the client, you cannot be distinctive. Paradoxically, to get ahead – and stay ahead – it is often necessary to step back from the problem to validate or revalidate the approach and the solution.

• Spend time thinking one or more steps ahead of the client and team.
• Constantly check and challenge the rigor of the underlying data and analysis.
• Stress-test the whole emerging recommendation
• Challenge the solution against a set of hurdles. Does it satisfy the criteria for success as set out on the Problem Statement Worksheet?

No matter how skilled, knowledgeable, or experienced you are, you will never create the most distinctive solution on your own. The best problem solvers know how to leverage the power of their team, clients, the Firm, and outside parties. Seeking the right expertise at the right time, and leveraging it in the right way, are ultimately how we bring distinctiveness to our work, how we maximize efficiency, and how we learn.

When solving a problem, it is important to ask, “Have I accessed all the sources of insight that are available?” Here are the sources you should consider:

• Your core team
• The client’s suppliers and customers
• Internal experts and knowledge
• External sources of knowledge
• Communications specialists

The key here is to think open, not closed. Opening up to varied sources of data and perspectives furthers our mission to develop truly innovative and distinctive solutions for our clients.

• McKinsey Staff Paper 66 — not published by McKinsey but possibly found through an internet search
• The McKinsey Way , 1999, by Ethan M. Rasiel

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Effective Problem-Solving Techniques in Business

Problem solving is an increasingly important soft skill for those in business. The Future of Jobs Survey by the World Economic Forum drives this point home. According to this report, complex problem solving is identified as one of the top 15 skills that will be sought by employers in 2025, along with other soft skills such as analytical thinking, creativity and leadership.

Dr. Amy David , clinical associate professor of management for supply chain and operations management, spoke about business problem-solving methods and how the Purdue University Online MBA program prepares students to be business decision-makers.

Why Are Problem-Solving Skills Essential in Leadership Roles?

Every business will face challenges at some point. Those that are successful will have people in place who can identify and solve problems before the damage is done.

“The business world is constantly changing, and companies need to be able to adapt well in order to produce good results and meet the needs of their customers,” David says. “They also need to keep in mind the triple bottom line of ‘people, profit and planet.’ And these priorities are constantly evolving.”

To that end, David says people in management or leadership need to be able to handle new situations, something that may be outside the scope of their everyday work.

“The name of the game these days is change—and the speed of change—and that means solving new problems on a daily basis,” she says.

The pace of information and technology has also empowered the customer in a new way that provides challenges—or opportunities—for businesses to respond.

“Our customers have a lot more information and a lot more power,” she says. “If you think about somebody having an unhappy experience and tweeting about it, that’s very different from maybe 15 years ago. Back then, if you had a bad experience with a product, you might grumble about it to one or two people.”

David says that this reality changes how quickly organizations need to react and respond to their customers. And taking prompt and decisive action requires solid problem-solving skills.

What Are Some of the Most Effective Problem-Solving Methods?

David says there are a few things to consider when encountering a challenge in business.

“When faced with a problem, are we talking about something that is broad and affects a lot of people? Or is it something that affects a select few? Depending on the issue and situation, you’ll need to use different types of problem-solving strategies,” she says.

Using Techniques

There are a number of techniques that businesses use to problem solve. These can include:

• Five Whys : This approach is helpful when the problem at hand is clear but the underlying causes are less so. By asking “Why?” five times, the final answer should get at the potential root of the problem and perhaps yield a solution.
• Gap Analysis : Companies use gap analyses to compare current performance with expected or desired performance, which will help a company determine how to use its resources differently or adjust expectations.
• Gemba Walk : The name, which is derived from a Japanese word meaning “the real place,” refers to a commonly used technique that allows managers to see what works (and what doesn’t) from the ground up. This is an opportunity for managers to focus on the fundamental elements of the process, identify where the value stream is and determine areas that could use improvement.
• Porter’s Five Forces : Developed by Harvard Business School professor Michael E. Porter, applying the Five Forces is a way for companies to identify competitors for their business or services, and determine how the organization can adjust to stay ahead of the game.
• Six Thinking Hats : In his book of the same name, Dr. Edward de Bono details this method that encourages parallel thinking and attempting to solve a problem by trying on different “thinking hats.” Each color hat signifies a different approach that can be utilized in the problem-solving process, ranging from logic to feelings to creativity and beyond. This method allows organizations to view problems from different angles and perspectives.
• SWOT Analysis : This common strategic planning and management tool helps businesses identify strengths, weaknesses, opportunities and threats (SWOT).

“We have a lot of these different tools,” David says. “Which one to use when is going to be dependent on the problem itself, the level of the stakeholders, the number of different stakeholder groups and so on.”

Each of the techniques outlined above uses the same core steps of problem solving:

• Identify and define the problem
• Consider possible solutions
• Evaluate options
• Choose the best solution
• Implement the solution
• Evaluate the outcome

Data drives a lot of daily decisions in business and beyond. Analytics have also been deployed to problem solve.

“We have specific classes around storytelling with data and how you convince your audience to understand what the data is,” David says. “Your audience has to trust the data, and only then can you use it for real decision-making.”

Data can be a powerful tool for identifying larger trends and making informed decisions when it’s clearly understood and communicated. It’s also vital for performance monitoring and optimization.

How Is Problem Solving Prioritized in Purdue’s Online MBA?

The courses in the Purdue Online MBA program teach problem-solving methods to students, keeping them up to date with the latest techniques and allowing them to apply their knowledge to business-related scenarios.

“I can give you a model or a tool, but most of the time, a real-world situation is going to be a lot messier and more valuable than what we’ve seen in a textbook,” David says. “Asking students to take what they know and apply it to a case where there’s not one single correct answer is a big part of the learning experience.”

Make Your Own Decision to Further Your Career

An online MBA from Purdue University can help advance your career by teaching you problem-solving skills, decision-making strategies and more. Reach out today to learn more about earning an online MBA with Purdue University .

If you would like to receive more information about pursuing a business master’s at the Mitchell E. Daniels, Jr. School of Business, please fill out the form and a program specialist will be in touch!

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A four-stage strategy for solving AC transmission expansion planning problem in large power system based on differential evolution algorithm and teaching–learning-based optimization algorithm

• Original Paper
• Published: 02 July 2024

Cite this article

• Thanh Long Duong 1 &
• Nguyen Duc Huy Bui 1  

AC transmission expansion planning (ACTEP) is one of the most critical issues in electric power system expansion planning. In existing research on ACTEP, the reduction of power losses is often overlooked due to the significant computational workload associated with ACTEP problem. While in some instances, minimizing power loss is included as an objective function in the TEP problem, this approach may impact the addition of new lines. Consequently, to address this issue, a four-stage strategy is proposed in this paper for resolving ACTEP problem while considering power loss reduction. Specifically, the reduction of power losses is addressed after the deployment of new transmission lines. Moreover, a hybrid approach, referred to as differential evolution (DE) combined with teaching–learning-based optimization (TLBO) algorithms, called (DE-TLBO), is proposed for optimizing reactive power planning and determining the size of thyristor-controlled series compensators (TCSC) to minimize power loss in ACTEP problem. Simulation results conducted on Graver 6 bus, IEEE 24 bus, and modified IEEE 118 bus systems demonstrate the efficacy of the proposed algorithm when compared to conventional methods such as differential evolution (DE), modified artificial bee colony, and real genetic algorithms (RGA). Additionally, the proposed method also illustrates the effectiveness of utilizing TCSC to reduce power loss in the Graver 6 bus and the IEEE 24 bus systems by 3.72% and 11.95%, respectively.

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We acknowledge the support of time and facilities from Industrial University of Ho Chi Minh City for this study.

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Thanh Long Duong & Nguyen Duc Huy Bui

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Conceptualization done by T.L.D; methodology done by T.L.D; software provided by N.D.H.B; validation done by T.L.D and N.D.H.B; formal analysis done by T.L.D; investigation done by N.D.H.B; data curation done by N.D.H.B; writing—original draft preparation done by T.L.D and N.D.H.B; writing—review and editing done by T.L.D; visualization done by N.D.H.B; supervision done by T.L.D.

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Duong, T.L., Bui, N.D.H. A four-stage strategy for solving AC transmission expansion planning problem in large power system based on differential evolution algorithm and teaching–learning-based optimization algorithm. Electr Eng (2024). https://doi.org/10.1007/s00202-024-02566-7

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Received : 15 December 2023

Accepted : 24 June 2024

Published : 02 July 2024

DOI : https://doi.org/10.1007/s00202-024-02566-7

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