polya's problem solving app

• Jul 5, 2021

Problem-Solving Steps that Actually Work

Updated: Mar 6, 2023

Whenever our students encounter problems, it can be a tricky situation. On one hand, I get super excited about the idea of my students THINKING about everything they know to solve the problem. I love watching their brains work while they access that filing cabinet in their brain of math information and pull out the information to solve a challenging problem.

On the other hand, that same process can become a brick wall when it becomes too overwhelming. Students can shut down and refuse to move. They can cry and become frustrated. These same students can then begin believing they are just not good at math from this point forward.

That's a lot of pressure from a simple math problem.

If you haven't read Jo Boaler's Mathematical Mindsets, I strongly suggest it as a way to begin helping our students see math learning with a growth mindset. It's a helpful guide in teaching our students and ourselves that knowledge is something that grows and is not fixed. It is based on Carol Dweck's work with Growth Mindsets from Mindset: The New Psychology of Success . (Another great read in helping children as a parent, teacher or coach.)

So what do we do? Instead of bombarding our students with several strategies to make problem-solving easier, I think it's important to boil it down to the basics. What strategies can I give my students that help them with all problems? What's something that's easy for them to remember and recall? What's something that would give them confidence moving forward?

Enter in Polya's Problem-Solving Method by George Polya who was known as the father of problem solving. These four steps sum up everything our students need to solve problems successfully. They are easy to remember and easy to implement.

(This post does contain affiliate links.)

Understand the Problem: This is the focus on comprehension. What is the problem asking me to do? What do I know from reading the problem? What can I comprehend?

Plan: This is the time where students think about how they want to move forward. Before solving with mathematics, we want our students to determine what steps they should take.

Solve : This is where students do the math. They follow the steps in their plan and work out the problem.

Look Back: Now we want students to look back and see that their answer makes sense. We want them to check the answer using estimation or even by trying to solve it in another way.

Four steps...that's totally manageable right? I love the simplicity of it all and even find that it carries over to all aspects of our life when solving real-life problems.

Now that students have a way to solve problems, it's time to give them the tools to make a plan that will work. I've been talking about Singapore's heuristics in my Member's Facebook group, and I wanted to share some of those with you. Stay tuned in the next few weeks to learn about the heuristics and how these strategies help students determine a meaningful plan to solve problems.

In the meantime, be sure to grab your problem-solving poster by clicking below!

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Polya’s Problem-Solving Process

Emma Moore, Teaching Excellence Program Master Teacher 

Problem-solving skills are crucial for students to navigate challenges, think critically, and find innovative solutions. In PISA, problem-solving competence is defined as “an individual’s capacity to engage in cognitive processing to understand and resolve problem situations where a method of solution is not immediately obvious” (OECD, 2014, p. 30). Returning to the classroom post-COVID, I found that students had lost their ‘grit’ for these deep-thinking tasks. They either struggled to start, gave up easily, or stopped at their first ‘answer’ without considering if it answered the problem or was the only possible solution.

To re-invigorate these skills, I investigated the impact of explicitly teaching Polya's problem-solving process in my Year Six class. This framework developed student agency and supported them to manage their feelings if they felt challenged by the work.

Here, I will share the impact of this initiative and how it empowered students to become effective and resilient problem solvers.  

Understanding Polya's Problem-Solving Process

Polya's problem-solving process, developed by mathematician George Polya, provides a structured approach to problem-solving that can be applied across various domains. This four-step process consists of understanding the problem, devising a plan, trying the plan, and revisiting the solution. (Polya, 1947)

In order to focus on the skills and knowledge of the problem-solving process, I began by using tasks where the mathematical processes were obvious. This allowed me to focus on the problem-solving process explicitly.

The question shown in Figure 2 is taken from Peter Sullivan and Pat Lilburn's Open-Ended Maths Activities book. This task was used to establish a baseline assessment for each stage of the process. I planned the prompts in dot points and revealed them one by one through the PowerPoint. After launching the task and giving the students time to think, they recorded all their possible answers in their workbook.

The student sample shown in Figure 3 demonstrates that the student followed a pattern and stuck to it but did not revisit their work. On line two, their response (1 half and 1 half is 2 quarters) is unreasonable.

Figure 3 is a sample gathered from a small group of students. This group required support to start. They used paper folding and paper strips to model their thinking.

Over half of the class could give at least one correct answer, but only four students showed signs of checking to see if their plans addressed the problem and yielded correct answers. Understanding the problem and revisiting the solutions became the focus of my inquiry.

The following series of lessons covering operations with fractions and decimals focused on the stages of Polya’s process.  

Step 1: Understanding the Problem

The first step of Polya's problem-solving process emphasises the importance of ensuring you thoroughly comprehend the problem. In this step, students learn to read and analyse the problem statement, identify the key information, and clarify any uncertainties. This process encourages critical thinking (Bicer et al., 2020) as students develop the ability to break down complex problems into manageable parts. I facilitated this process by engaging students in discussions and guiding them to identify the essential components of the problem. By fostering a collaborative learning environment, students shared their perspectives and learned to refine their questions when they were unsure. Figure 6 shares an example of a prompt I use for Step 1.

Figure 4: Example prompt for Step 1.

Initially, students who were stuck provided the classic ‘white flag’ responses.

Student: I just don’t get it.

Teacher: What part don’t you get?

Student: All of it!

As a starting point, the students and I co-created a classroom display of helpful questions the students could use to develop their understanding.

These questions supported me to develop a deeper understanding of what students didn’t understand when they expressed uncertainty. This could range from not understanding specific terminology (often easy to explain) to where numbers came from and why their classmates interpreted the problem differently. I found engaging in this step made triaging their misunderstandings easier.  

Step 2: Devising a Plan

Once students had grasped the problem, the next step was to formulate a plan of action. In this step, students explored different strategies and selected the most appropriate approach. I prompted students to brainstorm possible solutions, draw diagrams, make tables, and create algorithms, all the time fostering creativity and diverse thinking.

This step had been a strength during the baseline assessment data, and a wide range of strategies were explored. Polya’s strategies were displayed in the classroom as the mathematician’s strategy tool kit, so students were comfortable acknowledging the many ways to solve the problem.

Students developed critical thinking and decision-making skills by keeping this step in problem-solving. They become adept at evaluating multiple approaches and selecting the most effective strategy to solve a problem, thus promoting the development of mathematical reasoning abilities (Barnes, 2021). Figure 7 shows a slide used in Step 2.

Figure 5: Example prompt for Step 2.

Step 3: Try

The students implemented their selected strategy, performed calculations, made models, drew diagrams, created tables, and found patterns. This stage encouraged students to persevere and take ownership of their problem-solving process.

At Cowes Primary School, we have developed whole-school expectations around providing opportunities for hands-on learning, allowing students to engage in practical activities that support the development of ideas, expecting students to represent their work visually (pictures, materials and manipulatives), using language and numbers/symbols. This approach enhances students' problem-solving skills and fosters a sense of autonomy and confidence in their capabilities and ability to talk about their work (Roche et al., 2023). Figure 9 shows the slide used for Step 3.

Figure 6: Example prompt for Step 3.

Step 4. Re-visiting the solution

The last step in Polya's problem-solving process is re-visit. After finding a solution, students critically analyse and evaluate their approach after finding a solution. They consider the effectiveness of their chosen strategy, identify strengths and weaknesses, and reflect on how they could improve their problem-solving techniques. This step was missing from most students’ work during the baseline assessment.

As a class, we added to the display questions to facilitate better reflective practice and developed a more critical approach to looking at our work. This process encouraged students to refine their answers, not go too far down the wrong path, fostered resilience, embrace challenge and normalise uncertainty (Buckley & Sullivan, 2023).

Figure 7: Class display showing our questions.

  Figure 8: Student samples from the task.

Impact and Benefits:

Figure 9 shows four tasks, including the initial baseline assessment. The blue series shows the percentage of students who arrived at least one correct solution. The green series shows evidence that students were revisiting their initial solutions using other strategies to check they were correct or checking in with other groups and adjusting. There was a steady increase in both skills over the course of these four tasks.

By explicitly teaching Polya's problem-solving process, the students cultivated valuable skills that extend beyond maths problems. Some of the key benefits observed were:

Mathematical Reasoning: Polya's process promotes the development of mathematical reasoning skills. Students analysed problems, explored different strategies, and apply logical thinking to arrive at solutions. These skills can enhance their overall mathematical proficiency.

Self-efficacy: Through problem-solving, students gained confidence in their ability to tackle problems. They become more self-reliant, taking ownership of their learning, and seeking solutions proactively.

Collaboration and Communication: The process encouraged collaboration and communication among students. They discussed problems, shared ideas, and considered multiple perspectives, students developed effective teamwork and interpersonal skills.

Metacognition: The reflective aspect of Polya's process fostered metacognitive skills, enabling students to monitor and regulate their thinking processes. They learned to identify their strengths and weaknesses, supporting continuous improvement and growth.  

Overall using the 4 steps was a really effective and an explicit way to focus on developing the problem-solving skills of my Year 6 students.

This article was originally published for the Mathematical Association of Victoria's Prime Number.    

References:

Barnes, A. (2021). Enjoyment in learning mathematics: Its role as a potential barrier to children’s perseverance in mathematical reasoning. Educational Studies in Mathematics , 106(1), 45–63. https://doi.org/10.1007/s10649-020-09992-x

Bicer, Ali, Yujin Lee, Celal Perihan, Mary M. Capraro, and Robert M. Capraro. ‘Considering Mathematical Creative Self-Efficacy with Problem Posing as a Measure of Mathematical Creativity’. Educational Studies in Mathematics 105, no. 3 (November 2020): 457–85. https://doi.org/10.1007/s10649-020-09995-8

Buckley, S., & Sullivan, P. (2023). Reframing anxiety and uncertainty in the mathematics classroom. Mathematics Education Research Journal , 35(S1), 157–170. https://doi.org/10.1007/s13394-021-00393-8

OECD (Ed.). (2014). Creative problem solving: Students’ skills in tackling real-life problems. OECD.

Pólya, G. (1988). How to solve it: A new aspect of mathematical method (2nd ed). Princeton university press.

Roche, A., Gervasoni, A., & Kalogeropoulos, P. (2023). Factors that promote interest and engagement in learning mathematics for low-achieving primary students across three learning settings. Mathematics Education Research Journal , 35(3), 525–556. https://doi.org/10.1007/s13394-021-00402-w

Four Steps of Polya's Problem Solving Techniques

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In the world of mathematics and algorithms, problem-solving is an art which follows well-defined steps. Such steps do not follow some strict rules and each individual can come up with their steps of solving the problem. But there are some guidelines which can help to solve systematically.

In this direction, mathematician George Polya crafted a legacy that has guided countless individuals through the maze of problem-solving. In his book “ How To Solve It ,” Polya provided four fundamental steps that serve as a compass for handling mathematical challenges. 

• Understand the problem
• Devise a Plan
• Carry out the Plan
• Look Back and Reflect

Let’s look at each one of these steps in detail.

Polya’s First Principle: Understand the Problem

Before starting the journey of problem-solving, a critical step is to understand every critical detail in the problem. According to Polya, this initial phase serves as the foundation for successful solutions.

At first sight, understanding a problem may seem a trivial task for us, but it is often the root cause of failure in problem-solving. The reason is simple: We often understand the problem in a hurry and miss some important details or make some unnecessary assumptions. So, we need to clearly understand the problem by asking these essential questions:

• Do we understand all the words used in the problem statement? 
• What are we asked to find or show? What is the unknown? What is the information given? Is there enough information to enable you to find a solution?
• What is the condition or constraints given in the problem? Separate the various parts of the condition: Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
• Can you write down the problem in your own words? If required, use suitable notations, symbols, equations, or expressions to convey ideas and encapsulate critical details. This can work as our compass, which can guide us through calculations to reach the solution.
• After knowing relevant details, visualization becomes a powerful tool. Can you think of a diagram that might help you understand the problem? This can serve as a bridge between the abstract and tangible details and reveal patterns that might not be visible after looking at the problem description.

Just as a painter understands the canvas before using the brush, understanding the problem is the first step towards the correct solution.

Polya’s Second Principle: Devise a Plan

Polya mentions that there are many reasonable ways to solve problems. If we want to learn how to choose the best problem-solving strategy, the most effective way is to solve a variety of problems and observe different steps involved in the thought process and implementation techniques.

During this practice, we can try these strategies:

• Guess and check
• Identification of patterns
• Construction of orderly lists
• Creation of visual diagrams
• Elimination of possibilities
• Solving simplified versions of the problem
• Using symmetry and models
• Considering special cases
• Working backwards
• Using direct reasoning
• Using formulas and equations

Here are some critical questions at this stage:

• Can you solve a portion of the problem? Consider retaining only a segment of conditions and discarding the rest.
• Have you encountered this problem before? Have you encountered a similar problem in a slightly different form with the same or a similar unknown? Look closely at the unknown.
• If the proposed problem proves challenging, try to solve related problems first. Can you imagine a more approachable related problem? A more general or specialized version? Could you utilize their solutions, results, or methods?
• Can you derive useful insights from the data? Can you think of other data that would help determine the unknown? Did you utilize all the given data? Did you incorporate the entire set of conditions? Have you considered all essential concepts related to the problem?

Polya’s Third Principle: Carry out the Plan

This is the execution phase where we transform the blueprint of our devised strategy into a correct solution. As we proceed, our goal is to put each step into action and move towards the solution.

In general, after identifying the strategy, we need to move forward and persist with the chosen strategy. If it is not working, then we should not hesitate to discard it and try another strategy. All we need is care and patience. Don’t be misled, this is how mathematics is done, even by professionals. There is one important thing: We need to verify the correctness of each step or prove the correctness of the entire solution.

Polya’s Fourth Principle: Look Back and Reflect

In the rush to solve a problem, we often ignore learning from the completed solutions. So according to Polya, we can gain a lot of new insights by taking the time to reflect and look back at what we have done, what worked, and what didn’t. Doing this will enable us to predict what strategy to use to solve future problems.

• Can you check the result? 
• Can you check the concepts and theorems used? 
• Can you derive the solution differently?
• Can you use the result, or the method, for some other problem?

By consistently following the steps, you can observe a lot of interesting insights on your own.

George Polya's problem-solving methods give us a clear way of thinking to get better at math. These methods change the experience of dealing with math problems from something hard to something exciting. By following Polya's ideas, we not only learn how to approach math problems but also learn how to handle the difficult parts of math problems.

Shubham Gautam

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Polya's Problem Solving

George Polya was a famous Hungarian mathematician who developed a framework for problem-solving in mathematics in 1957. His problem-solving approach is still used widely today and can be applied to any problem-solving discipline (i.e. chemistry, statistics, computer science). Below you will find a description of each step along with strategies to help you accomplish each step. Having a specific strategy like this one may help to reduce anxiety around math tests.

Understand the Problem  

Understanding the problem is a crucial first step as this will help you identify what the question is asking and what you need to calculate. Strategies to help include: 

• Identify (i.e. highlight or circle) the unknowns in the problem or question.
• Draw or visualize a picture that can help you understand the problem. 

Devise a Plan  

Devising a plan is a process in which you find the connection between the data/information you are given and the unknown. However, you may not have been given enough data/information to find a connection immediately, so this process may involve calculating/finding additional variables before the final unknown can be solved. Strategies to help you devise a plan include:  

• List the unknowns and knowns. 
• Identify if a theorem would help you calculate the unknown (i.e. a2 + b2 = c2). 
• Decide what variables you need to know the value of to solve for the unknown. 
• Select which variable you will solve for first.

Carry Out the Plan  

This step involves calculating the steps identified in the “Devise a Plan” stage. Strategies to help you carry out the plan include:  

• Focus on solving one part of the problem at a time.
• Clearly write out each step. 
• Double check each variable or step as you solve.
• Repeat this process until you solve for the final unknown. 

Look Back 

This step involves reviewing your answer and steps to confirm that your final calculation is correct. Strategies to help you review your work include:  

• Recalculate each step to see if you get the same answer.
• Check if your final calculation has the appropriate units (i.e. m/s, N/m2). 
• Repeat steps to correct any errors found.

Polya's Problem Solving Canvas

The Polya's Problem-Solving Canvas is about guiding individuals or teams through a structured approach to solving problems methodically. It provides a systematic process for breaking down complex problems into 4 manageable steps.

This template helps you achieve effective problem-solving by providing a clear, step-by-step approach. It assists in understanding the problem, planning a solution, solving it, and reviewing the results.

By following the template, you are more likely to arrive at a well-thought-out and efficient solution.

The Polya's Problem-Solving Technique template is beneficial for individuals or teams facing a wide range of problems in various domains, such as mathematics, engineering, computer science, and general decision-making.

Students, professionals, and anyone encountering complex problems can benefit from this structured approach.

How to Use It

To use the Polya's Problem-Solving Technique template:

Start by clearly understanding the problem or task at hand.

Plan a strategy or approach to solve the problem. This might involve breaking it down into smaller steps.

Execute the plan by following the steps you've outlined.

Review the results to ensure they make sense and address the problem adequately. If necessary, iterate through the process.

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• Ks2 Maths Polya Problem Solving

KS2 maths – Polya’s problem-solving

From groans and panic to calm and curiosity – how Claire Coolin made systematic maths lessons less scary…

Are you met with groans when you utter the term ‘problem-solving’ to your class?

We all agree that it’s is an important aspect of the curriculum and indeed a life skill, but yet remains a divisive topic of conversation with pupils, parents and colleagues.

So, what is the problem with problem-solving? 

My Year 5 class were high-achieving. In general, they enjoyed maths but when it came to problem-solving many of them froze.

They showed disinterest, nervousness and confusion, saying things like, “The information is hard to process,” and “I couldn’t understand the information as it was just a block of words”.

Interestingly, pupils found the lessons boring when the problems that they solved followed the same routine and pattern, and didn’t provide a level of challenge, interest or excitement.

These routine problems ‘took the fun’ out of maths for them, and while using skills such as addition, subtraction , and so on are all part and parcel of problem-solving, is this what we are trying to achieve here? 

Routine and non-routine problems

Problem-solving can show an in-depth understanding of mathematical concepts where pupils are required to manipulate numbers in order to get to an answer.

However, while routine problems might be easier for the children to solve, they are not aligned to maths in real life .

We don’t live our adult lives practising budgeting for the weekly supermarket shop from Monday to Thursday, with the real deal happening on Friday. Rather, real-life problems can often be spontaneous, unexpected and at first have no obvious solution.

Should we therefore be teaching pupils what to do with the unexpected? Should we be equipping them with the skills to solve non-routine problems? I think the answer is, yes, most definitely. 

Polya’s problem-solving

So what can be done? Is it enough to tell the children in your class to highlight the important words in the problem ?

While this might have helped a few of my pupils to see a way forward, for many this just became a colouring exercise with an impressive array of fancy highlighters on show.

And so I began an action research project to find answers. After poring over many academic articles, I came across Polya’s problem-solving cycle : a cyclical four-step process that could be used to solve any problem, in maths or otherwise. The steps are:  

• Understanding the problem 
• Devising a plan 
• Carrying out the plan 
• Looking back and reflecting 

Polya’s process was something I wanted to introduce to my class, and so I taught this way of thinking about a problem over a term. The results were surprising and long-lasting, with four key takeaway points. 

I found that the cycle: 

Developed time management skills and enhanced focus 

Polya’s cycle automatically forced students to work through each phase in turn, slowing them down and therefore helping them explore the problem with a more thoughtful and connected approach.

Instead of jumping straight into the doing, the children took time to think about their understanding of what was being asked, and would often get out a dictionary to look up a word they didn’t know the meaning of, or on one occasion, a child even dusted off the ‘never-really-used-before-but-every-class-has-one’ maths dictionary to look up the meaning of a mathematical term.  

Equipped all students with a strategy for tackling any maths problem 

When talking to a group of pupils in my class about problem-solving, I recall them saying, “I can’t work out if I should multiply or add or subtract or whatever.”

This is true for many students and can lead to them freezing, or in some cases, frantically adding and subtracting numbers – essentially jumping straight into phase three.

They needed a strategy. Using the problem-solving steps gave my class a framework, allowing them to think in a logical way.

Straight away, students unfroze, the manic scribbling stopped, and they started from a phase one and worked through the problem more systematically.  

Allowed pupils to see the link between maths and the real world  

When I asked my class why they thought we were learning about problem-solving, I was met with answers about becoming better at maths.

But after using Polya’s steps, the children began to see how the skills in solving maths problems are the same ones used in solving real-world problems.

For example, they realised that if a maths problem can be divided into chunks, then so could any problem.

One sunny afternoon, a couple of students came to me to help solve their playground argument. You can imagine my utter surprise when one of the students said, “I think first we need to understand why we have fallen out then we can come up with a plan to put it right.” Real life problem-solving in action! 

Equipped students with the necessary tools to engage with challenge 

Having challenge in any subject is important, but having the right level of challenge is even more so.

Routine problems can remove that challenge for many, and one of my pupils commented that, “You shouldn’t do lots of the same as it gets too easy. You don’t want to spoil it by knowing all the answers.”

Using Polya’s problem-solving steps with non-routine problems gives the more able pupils enhanced scope and freedom to try out and manipulate numbers in different ways, while giving that scaffolding to support the less able in the class. 

So, what now?

What have I learned from this experience? Well, with more than 10 years teaching under my belt, this action research brought me back to my roots.

I started from scratch with something and didn’t rely on my tried-and-tested resources. I had a chance to listen to my pupils and in doing so stumbled onto a way of thinking that works not just for a maths problem, but for all problems.

The steps have since become a classroom philosophy, and I use the vocabulary of the process daily. Trying something new can pay off!  

How to introduce Polya’s process 

• Talk about the cycle and what each phase means. Take note that it’s like a roundabout, which means you can get off at any stop and go back if necessary.  E.g. If you’re carrying out your plan (phase three) but it’s not working, you can go back to phase one: understanding the problem.  
• Use subheadings. I wanted the students to really spend time thinking about each phase, so I made a very simple Performa with each phase sub-headed. The students were required to write within each subheading. 
• Model how to do it. Using different non-routine problems, I modelled how I would use the problem-solving phases. I then built up to working on problems as a class, and finally asked pupils to work in pairs to solve problems using the steps.  
• Make it part of your classroom vocabulary. To embed the process in my class, the language didn’t just come out when doing maths problems, but was used in other subjects and day-to-day school life.   

Claire Coolin conducted this research project while teaching Year 5 at Oxford High Prep School, GDST with the Global Action Research Collaborative, ICGS. From September 2022 she will be a maths specialist teacher and PSHE head of department at Summer Fields School, Oxford.

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Experience the future of communication with Question.AI, the ultimate AI Chatbot app that's revolutionizing the way you gather information, communicate, and stay informed across various facets of life. Whether you're a student, a professional at work, an inquisitive mind, or a business enthusiast, our app is designed to make your life easier, smarter, and more efficient in any context. 【Key Features】 - Simplicity at its Best: Seeking answers has never been easier. Just ask your questions, and our intuitive AI will promptly provide you with accurate responses. No need for complex commands or jargon - it's like having a knowledgeable friend by your side 24/7. - Your Personal Assistant: From quick facts to in-depth research, Question.AI is your personal assistant ready to assist you. Need a definition, explanation, or summary? Count on us to deliver information tailored to your needs. - Global Connectivity: Break language barriers effortlessly. With the ability to translate into 140+ languages, Question.AI ensures you can communicate and connect with individuals from all around the world. Expand your horizons and broaden your perspectives with ease. - Intelligent Writing: Enhance your writing with AI-powered suggestions. Whether you're crafting an email, composing a report, or writing creatively, our app's intelligent writing feature offers insightful recommendations to make your content shine. - Adaptable Across Occasions: Question.AI is your versatile companion across various occasions, whether it's for studying, working, managing your business, or simply enhancing your daily life. We're here to assist you in every scenario. 【Why Choose Question.AI?】 With a commitment to excellence and user satisfaction, Question.AI stands out as the ultimate AI Chatbot app: - User-Friendly: Our user-centric design prioritizes simplicity and accessibility, ensuring a seamless experience for users of all ages. - Instant Insights: Get answers in real-time, allowing you to make informed decisions and impress others with your newfound knowledge. - Trusted Accuracy: Our AI's responses are backed by robust algorithms, ensuring that the information you receive is reliable and up-to-date. - Empowering Communication: Break down language barriers, foster connections, and engage with a global community effortlessly. - Unleash Creativity: Elevate your writing and communication skills with AI-powered suggestions that refine and elevate your content. Ready to embark on a journey of knowledge and connection? Download Question.AI now and experience the future of communication in the palm of your hand. Get started today! 【Contact us】 Email: [email protected] Official Website: www.questionai.com Instagram: @question.ai_app YouTube: @QuestionAI-Official Facebook: bit.ly/QuestionAI_FB TikTok: @question.ai_app Discord: bit.ly/QuestionAI_DC Messenger Group: https://m.me/j/AbaNe6U1Rhv5NAiL/ Privary Policy: https://www.questionai.com/privacy-policy Terms and Conditions: https://www.questionai.com/useTerm

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19.5K Ratings

Literal LIFE SAVER

Your math teacher don't explain stuff like this and you know it. All you gotta do is just take a picture and it'll explain everything step by step. The app is free, but the pro cost money. Yes, the pro helps, but the app itself without any add-ons is still amazing and literally life-saving. If you are ever in doubt in math just snap a pic. And to make it even better is does others subject if you need any more help. Its just so awesome in general , like whoever came up with this stuff is a genius and so relatable. The videos would be so helpful but I don't pay for pro because my mom won't let me😭 Anywho, the step by step process is really easy to understand as well. Just get this app if you are in need of a math tutor, and tbh I think everyone needs a lil help on math especially, just consider downloading this app. Super easy to use and super easy to understand. THANK YOU DEARLY QUESTION A.I!!!🤗🤗

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We're thrilled to know that you're satisfied with our app! Your positive experience is our greatest reward. Thank you for choosing us!

Love this app!!

I love this app so much usually you have to pay a monthly fee but with this you don’t, I didn’t buy it at first. I thought that we would have to pay monthly and I didn’t feel like getting the app but I gave it out a try. After I gave it a few tries and math questions I realize it really does help and that I love it so much,being in middle school and having tough math helps me so much with this even though I don’t really read the videos on how to do it sure helps with the answers and that is what it’s great about this app because you can help me with with my homework and if I need help it’ll give me. I love this app so much definitely recommended you don’t have to pay any monthly fee and this is the first app. I’ve actually waited five stars and left a comment because usually these apps aren’t good, but this one is amazing. Love it so much. Thanks.

We have always focused on providing high-quality service and user experience. Thank you for your recognition and support!

I’ve never been so greatful towards an app before, usually there was a deal with other apps that you had only a few tries before you had to pay for the full thing or wait your time…which 90% of the time didn’t even give you an answer or help… I’ve never had something this smooth be so dang helpful 😭❤️ Not only did it help me pass my test (88% omg 😍) but it also gave helpful advice and dumbed it down for me so i didn’t have to read through everything. Quite literally gave me the information i wanted and also the answer which is AMAZING 😨❤️Helped me better understand the questions SO THANK YOU 🙏 will definitely be using this on math 🥶 hoping for the same smoothness on math since it’s what i struggle with but overall just from a first time use i’m deeply thankful for this app!! 😭🙏❤️

Thank you for your positive feedback! I'm delighted to hear that you're enjoying the application. Please feel free to share any suggestions you have directly, and I'll do my best to assist or pass them along to the appropriate team for consideration.

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iOS 18’s Big AI Update Could Automatically Solve Math Problems for You

Like predictive text, but for math equations.

WWDC 2024 hype season is upon us! We’re a little over a week away from Apple’s annual developer conference, where the company is expected to announce new versions of all of its platforms, including iOS 18 .

All rumors point to iOS 18 being the biggest update to the iPhone software in years, with generative AI as the headlining act. We’ve already heard of some obvious AI updates, like smart summaries, photo retouching, and automatic replies . However, a new report from AppleInsider suggests there’s even more AI in store. The Apple-focused publication says iOS 18 will get a “Catch Up” feature where Siri can provide an overview of recent notifications, cross-device media controls where you can activate Siri on one device to control another, and even the ability to create and edit images within iMessage using generative AI.

With all these leaked AI features, it might be easy to overlook perhaps the most underrated one: AI that can automatically solve math problems.

The Calculator functionality is going to be integrated into the Notes app.

No Need to Open Up the Calculator App

According to AppleInsider , a new feature called “Keyboard Math Predictions” will detect and automatically solve math equations that are entered as text. Think of this like your iPhone’s predictive text that finishes your sentences for you, but for math problems. On top of that, the Notes app will get a crash course in math, with the ability to recognize math equations and offer solutions with help from the Calculator app’s integration. Apple is also reportedly working on a way to generate graphs within the Notes app.

Apple’s AI isn’t the only one that can handle some math thrown its way. OpenAI previously announced GPT-4o, and the AI chatbot made easy work of an equation looking to solve for x. GPT-4o can even act as more of a personal tutor for more involved problems.

WWDC 2024 will finally reveal all the AI things that Apple has been working on.

Big AI Reveal on June 10

Fortunately, we only have to wait until Apple kicks off its WWDC 2024 on June 10 to see what’s in store with iOS 18. The software update won’t officially arrive until the fall, but Apple will share installable developer and public betas shortly after WWDC if you’re willing to deal with bugs and such throughout the summer.

With Apple hopping on the wave, generative AI chatbots are proving that they can handle math just as well as they can understand natural language. You could argue that AI-assisted math could make us all dumber, but that’s also what people said about calculators and computers. Sure, technology has made some people lazier, but it’s also helped save us time and solve even more complex problems. Adding AI that can solve math into the iPhone will only strengthen its purpose as do-it-all device.

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Polya's Problem Solving Professional Lea...

Professional development.

Polya's Problem Solving Professional Learning

10 questions

Introducing new   Paper mode

No student devices needed.   Know more

Who created Polya's Problem Solving Steps?

George Clooney

George Jefferson

George Polya

George Foreman

What problem solving step comes first?

Look Back-Check

Solve the Problem

Devise a Plan

Understand the Problem

What problem solving steps comes second?

Carry Out a Plan-Solve

Which is NOT a strategy to solve a problem?

Draw a picture

Use the inverse operation (work backwards)

Model with manipulatives/tools

What problem solving step comes third?

Look back-Check

What should you do if you are struggling to solve a problem?

Copy from my neighbor

Give up and take a ZERO

Solve a simpler problem

Google the answer

What problem solving step is last?

Carry Out the Plan-Solve

Why should you understand the problem before trying to solve it?

Because I can't solve a problem that I don't understand

Because my teacher said it

Because my friend was talking about it

Because I saw it on YouTube

Which equation is correct? Evan wants a bike that costs $126 and a coat for $51. How much do the two cost?

$51 + B = $126

$126 - $51 = B

$126 + $51 = B

B + $126 = $51

Are you going to implement Polya's Problem Solving Process (UPS Check) in your class to assist your students with solving word problems?

Explore all questions with a free account

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2.1: George Polya's Four Step Problem Solving Process

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Step 1: Understand the Problem

• Do you understand all the words?
• Can you restate the problem in your own words?
• Do you know what is given?
• Do you know what the goal is?
• Is there enough information?
• Is there extraneous information?
• Is this problem similar to another problem you have solved?

Step 2: Devise a Plan: Below are some strategies one might use to solve a problem. Can one (or more) of the following strategies be used? (A strategy is defined as an artful means to an end.)

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You'll Have No Words Seeing This Precious 2-Year-Old Genius Do Multiplication on AGT

Simon Cowell pleads, “Get us a calculator!” and asks Baby Dev to negotiate his next deal in this incredible AGT Season 19 Audition.

While most toddlers are stacking blocks and coloring with crayons, this pint-sized genius does addition, subtraction, and multiplication on national television.

How to Watch

Watch America’s Got Talent Tuesdays at 8/7c on NBC and next day on Peacock . 

Devan is the youngest Act ever to light up the America’s Got Talent stage, and in the Season 19 premiere, we can see why. The sweet boy knocked everyone’s socks off as he sailed through three different math equations that, to be honest, had the Judges stumped .

“We’re all sitting here thinking the same thing: get us a calculator,” said Simon Cowell after the performance, adding, “I now feel really stupid.”

RELATED:  Who Are the America's Got Talent Season 19 Judges?

Baby Dev’s father, Duane, a retired police officer, told NBC Insider he noticed something very special about his son early on: “At 4 months old, we realized his love for numbers.”

Duane explained that when he exposed his son to early learning shows, Baby Dev would suddenly cry when they switched away from math. “And when we turned it back, he would stop. We’re like, all right, he has this love and passion for numbers,” he said.

How old is Baby Devan?

Devan is 2 years old, the youngest-ever contestant on AGT . 

From the moment Baby Dev fist-bumped Terry Crews backstage before his Season 19 debut, AGT fans were charmed. The precious boy laughed, jumped, and squealed with delight after solving equations and politely saying “hello” and “thank you” to the Judges while on stage with his proud dad.

“His first word before mama and dada was seven,” Duane told the Judges. “That’s my lucky number,” exclaimed Simon. And it seemed to be Baby Dev’s, too. Three whiteboards were set up on stage — two for multiplication and one for addition — with Judges calling out random numbers. When Baby Dev quickly solved 7 x 9, there was a stunned silence before the crowd erupted in applause.

How did Devan develop his math skills?

Duane explained to NBC Insider how he nurtured his son’s penchant for math.

“At age 1, we had bought him a writing tablet. We would practice writing numbers with him from 1 to 10… and we would practice writing every day, and by 15 months old, he knew how to write numbers on his own.” After mastering addition, the math prodigy moved on to subtraction and his times tables.

“We can just be in bed, and he’ll be like… ‘Math, please. I wanna do math, please,’ and then he’ll go to his writing board and just do math equations,” said his dad, who noted that the little boy always loved counting everything. “Cars on the street, birds, trees… he has number magnets that he carries with him like it’s a toy.”

Baby Dev does not receive formal tutoring, and as one audience member pointed out, “He’s not even using his fingers” to count. However, he might have one strict requirement when calculating: Not being interrupted. As Baby Dev tackled a math problem and jotted down numbers, Howie Mandel loudly whispered, “We get to see the process.”

We can just be in bed, and he’ll be like… ‘Math, please. I wanna do math, please!’” Duane, Baby Dev's dad

The toddler shot him a look that could freeze water. After a long pause and some shushing directed toward Mandel, Baby Dev continued on and solved the final equation. He was unanimously voted on to the next round — but he may have something extra on his plate, too.

When Simon asked, “Devon, will you help me negotiate my next deal?” the little cutie responded, “Yes!”

Obviously this charming youngster moved on to the next round of the competition where fans are surely eager to see what mathematical wizardry he'll come up with next. 

Watch all-new episodes of  America’s Got Talent , airing Tuesdays at 8/7c on NBC   and streaming the next day on  Peacock .

-  Reporting by McKenzie Jean-Philippe

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GameChanger's AI tech is helping support youth sports and showcase more than 7 million games annually

• GameChanger provides mobile apps and services for capturing content from youth sports.
• It uses AI to recognize video images and automatically detect and track fast-moving sports action.
• This article is part of " CXO AI Playbook " — straight talk from business leaders on how they're testing and using AI.

For "CXO AI Playbook," Business Insider takes a look at mini case studies about AI adoption across industries, company sizes, and technology DNA. We've asked each of the featured companies to tell us about the problems they're trying to solve with AI, who's making these decisions internally, and their vision for using AI in the future.

GameChanger's livestreaming and team-management technology has been used by parents of child athletes and amateur team coaches for more than a decade.

Users capture more than 7 million games annually through the smartphone app, with more than 1 million teams using the platform each year.

GameChanger is based in New York City and owned and operated by Dick's Sporting Goods.

Situation analysis: What problem was the company trying to solve?

The Data Resource Center for Child and Adolescent Health found that in 2022, about 53.8% of children between 6 and 17 years old played on a sports team or took sports lessons after school or on the weekends.

Capturing highlight videos and recording statistics in youth sports can be a big challenge.

"The capture of it is very complicated and very hard to scale," Sameer Ahuja, the president of GameChanger, said. Think of all the moving players in an average basketball game crisscrossing one another and how hard it is to pick out the ball — or your child — from all those bodies.

Traditionally, coaches, parents, or volunteers manually scored games and captured video using their own tools, which could be time-consuming and increase the risk of errors.

GameChanger wanted to use artificial intelligence to automate as much of the process as possible for parents and coaches.

"If you can supplement what they're doing with automation, you can capture all this content," Ahuja said.

Key staff and partners

GameChanger's AI initiative was a collaboration between Ahuja, his fellow senior leaders at the company, and its product and engineering teams. No third-party providers were involved because the company wanted to maintain control over the user experience.

Ahuja told Business Insider that GameChanger's leadership team decided to develop the technology in-house: "We took iterative steps and brought on a couple of people. We didn't want to outsource it."

AI in action

GameChanger used its large, proprietary dataset of footage from youth sports to train AI computer-vision models for various tasks, such as detecting a ball, identifying the players and the areas they occupy, tracking ball motion to detect scoring events, and localizing where on the field the action took place.

GameChanger focuses on sports that its algorithms can easily track, Ahuja said, such as basketball and volleyball, with plans to expand to freer-flowing sports with more players on a field, such as soccer.

The computer-vision program enables GameChanger's apps to automatically capture highlights, track stats, provide radio-style commentary of the game action, and more. According to its website, GameChanger has worked with organizations, including Little League, USA Baseball, and PGC Basketball, to cover more than 35 million games since the launch of its app in 2010.

Did it work, and how did leaders know?

Ahuja said success metrics included more teams creating automated game recordings for entire seasons, high levels of user engagement, and passionate feedback — both positive and constructive.

"Taking that content and delivering it to mom and dad, to grandma and grandpa, is literally a delight," Ahuja said.

What's next?

GameChanger plans to continue expanding its AI-powered automation to sports beyond basketball and volleyball, like football, soccer, and lacrosse.

"I think we'll stay focused on team sports," Ahuja said, adding that he's personally excited about including cricket because he grew up with the sport and wanted to expand to an international audience. 

The company is also planning to expand its engineering and product teams to bolster its AI competency.

Beyond that, Ahuja intends to continue releasing updates to the technology. So far, the company has rolled out updates about every two weeks as it continues to tweak the product based on user feedback.

Eventually, Ahuja said he hoped to reach his ultimate goal for the app: "a set-it-and-forget-it experience."

We want to hear from you. If you are interested in sharing your company's AI journey, email [email protected] .

May 29, 2024 — An earlier version of this story misstated the number of teams that use GameChanger annually. The number of teams that use the platform each year is more than 1 million, not 750,000.

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