4 step math problem solving model

Weekly dose of self-improvement

The easy 4 step problem-solving process (+ examples)

This is the 4 step problem-solving process that I taught to my students for math problems, but it works for academic and social problems as well.

Every problem may be different, but effective problem solving asks the same four questions and follows the same method.

• What’s the problem? If you don’t know exactly what the problem is, you can’t come up with possible solutions. Something is wrong. What are we going to do about this? This is the foundation and the motivation.
• What do you need to know? This is the most important part of the problem. If you don’t know exactly what the problem is, you can’t come up with possible solutions.
• What do you already know? You already know something related to the problem that will help you solve the problem. It’s not always obvious (especially in the real world), but you know (or can research) something that will help.
• What’s the relationship between the two? Here is where the heavy brainstorming happens. This is where your skills and abilities come into play. The previous steps set you up to find many potential solutions to your problem, regardless of its type.

When I used to tutor kids in math and physics , I would drill this problem-solving process into their heads. This methodology works for any problem, regardless of its complexity or difficulty. In fact, if you look at the various advances in society, you’ll see they all follow some variation of this problem-solving technique.

“The gap between understanding and misunderstanding can best be bridged by thought!” ― Ernest Agyemang Yeboah

Generally speaking, if you can’t solve the problem then your issue is step 3 or step 4; you either don’t know enough or you’re missing the connection.

Good problem solvers always believe step 3 is the issue. In this case, it’s a simple matter of learning more. Less skilled problem solvers believe step 4 is the root cause of their difficulties. In this instance, they simply believe they have limited problem-solving skills.

This is a fixed versus growth mindset and it makes a huge difference in the effort you put forth and the belief you have in yourself to make use of this step-by-step process. These two mindsets make a big difference in your learning because, at its core, learning is problem-solving.

Let’s dig deeper into the 4 steps. In this way, you can better see how to apply them to your learning journey.

Step 1: What’s the problem?

The ability to recognize a specific problem is extremely valuable.

Most people only focus on finding solutions. While a “solutions-oriented” mindset is a good thing, sometimes it pays to focus on the problem. When you focus on the problem, you often make it easier to find a viable solution to it.

When you know the exact nature of the problem, you shorten the time frame needed to find a solution. This reminds me of a story I was once told.

When does the problem-solving process start?

The process starts after you’ve identified the exact nature of the problem.

Homeowners love a well-kept lawn but hate mowing the grass.

Many companies and inventors raced to figure out a more time-efficient way to mow the lawn. Some even tried to design robots that would do the mowing. They all were chasing the solution, but only one inventor took the time to understand the root cause of the problem.

Most people figured that the problem was the labor required to maintain a lawn. The actual problem was just the opposite: maintaining a lawn was labor-intensive. The rearrangement seems trivial, but it reveals the true desire: a well-maintained lawn.

The best solution? Remove maintenance from the equation. A lawn made of artificial grass solved the problem . Hence, an application of Astroturf was discovered.

This way, the law always looked its best. Taking a few moments to apply critical thinking identified the true nature of the problem and yielded a powerful solution.

An example of choosing the right problem to work the problem-solving process on

One thing I’ve learned from tutoring high school students in math : they hate word problems.

This is because they make the student figure out the problem. Finding the solution to a math problem is already stressful. Forcing the student to also figure out what problem needs solving is another level of hell.

Word problems are not always clear about what needs to be solved. They also have the annoying habit of adding extraneous information. An ordinary math problem does not do this. For example, compare the following two problems:

What’s the height of h?

A radio station tower was built in two sections. From a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25º, and the angle of elevation of the top of the second section is 40º. To the nearest foot, what is the height of the top section of the tower?

The first is a simple problem. The second is a complex problem. The end goal in both is the same.

The questions require the same knowledge (trigonometric functions), but the second is more difficult for students. Why? The second problem does not make it clear what the exact problem is. Before mathematics can even begin, you must know the problem, or else you risk solving the wrong one.

If you understand the problem, finding the solution is much easier. Understanding this, ironically, is the biggest problem for people.

Problem-solving is a universal language

Speaking of people, this method also helps settle disagreements.

When we disagree, we rarely take the time to figure out the exact issue. This happens for many reasons, but it always results in a misunderstanding. When each party is clear with their intentions, they can generate the best response.

Education systems fail when they don’t consider the problem they’re supposed to solve. Foreign language education in America is one of the best examples.

The problem is that students can’t speak the target language. It seems obvious that the solution is to have students spend most of their time speaking. Unfortunately, language classes spend a ridiculous amount of time learning grammar rules and memorizing vocabulary.

The problem is not that the students don’t know the imperfect past tense verb conjugations in Spanish. The problem is that they can’t use the language to accomplish anything. Every year, kids graduate from American high schools without the ability to speak another language, despite studying one for 4 years.

Well begun is half done

Before you begin to learn something, be sure that you understand the exact nature of the problem. This will make clear what you need to know and what you can discard. When you know the exact problem you’re tasked with solving, you save precious time and energy. Doing this increases the likelihood that you’ll succeed.

Step 2: What do you need to know?

All problems are the result of insufficient knowledge. To solve the problem, you must identify what you need to know. You must understand the cause of the problem. If you get this wrong, you won’t arrive at the correct solution.

Either you’ll solve what you thought was the problem, only to find out this wasn’t the real issue and now you’ve still got trouble or you won’t and you still have trouble. Either way, the problem persists.

If you solve a different problem than the correct one, you’ll get a solution that you can’t use. The only thing that wastes more time than an unsolved problem is solving the wrong one.

Imagine that your car won’t start. You replace the alternator, the starter, and the ignition switch. The car still doesn’t start. You’ve explored all the main solutions, so now you consider some different solutions.

Now you replace the engine, but you still can’t get it to start. Your replacements and repairs solved other problems, but not the main one: the car won’t start.

Then it turns out that all you needed was gas.

This example is a little extreme, but I hope it makes the point. For something more relatable, let’s return to the problem with language learning.

You need basic communication to navigate a foreign country you’re visiting; let’s say Mexico. When you enroll in a Spanish course, they teach you a bunch of unimportant words and phrases. You stick with it, believing it will eventually click.

When you land, you can tell everyone your name and ask for the location of the bathroom. This does not help when you need to ask for directions or tell the driver which airport terminal to drop you off at.

Finding the solution to chess problems works the same way

The book “The Amateur Mind” by IM Jeremy Silman improved my chess by teaching me how to analyze the board.

It’s only with a proper analysis of imbalances that you can make the best move. Though you may not always choose the correct line of play, the book teaches you how to recognize what you need to know . It teaches you how to identify the problem—before you create an action plan to solve it.

The problem-solving method always starts with identifying the problem or asking “What do you need to know?”. It’s only after you brainstorm this that you can move on to the next step.

Learn the method I used to earn a physics degree, learn Spanish, and win a national boxing title

• I was a terrible math student in high school who wrote off mathematics. I eventually overcame my difficulties and went on to earn a B.A. Physics with a minor in math
• I pieced together the best works on the internet to teach myself Spanish as an adult
• *I didn’t start boxing until the very old age of 22, yet I went on to win a national championship, get a high-paying amateur sponsorship, and get signed by Roc Nation Sports as a profession.

I’ve used this method to progress in mentally and physically demanding domains.

While the specifics may differ, I believe that the general methods for learning are the same in all domains.

This free e-book breaks down the most important techniques I’ve used for learning.

Step 3: What do you already know?

The only way to know if you lack knowledge is by gaining some in the first place. All advances and solutions arise from the accumulation and implementation of prior information. You must first consider what it is that you already know in the context of the problem at hand.

Isaac Newton once said, “If I have seen further, it is by standing on the shoulders of giants.” This is Newton’s way of explaining that his advancements in physics and mathematics would be impossible if it were not for previous discoveries.

Mathematics is a great place to see this idea at work. Consider the following problem:

What is the domain and range of y=(x^2)+6?

This simple algebra problem relies on you knowing a few things already. You must know:

• The definition of “domain” and “range”
• That you can never square any real number and get a negative

Once you know those things, this becomes easy to solve. This is also how we learn languages.

An example of the problem-solving process with a foreign language

Anyone interested in serious foreign language study (as opposed to a “crash course” or “survival course”) should learn the infinitive form of verbs in their target language. You can’t make progress without them because they’re the root of all conjugations. It’s only once you have a grasp of the infinitives that you can completely express yourself. Consider the problem-solving steps applied in the following example.

I know that I want to say “I don’t eat eggs” to my Mexican waiter. That’s the problem.

I don’t know how to say that, but last night I told my date “No bebo alcohol” (“I don’t drink alcohol”). I also know the infinitive for “eat” in Spanish (comer). This is what I already know.

Now I can execute the final step of problem-solving.

Step 4: What’s the relationship between the two?

I see the connection. I can use all of my problem-solving strategies and methods to solve my particular problem.

I know the infinitive for the Spanish word “drink” is “beber” . Last night, I changed it to “bebo” to express a similar idea. I should be able to do the same thing to the word for “eat”.

“No como huevos” is a pretty accurate guess.

In the math example, the same process occurs. You don’t know the answer to “What is the domain and range of y=(x^2)+6?” You only know what “domain” and “range” mean and that negatives aren’t possible when you square a real number.

A domain of all real numbers and a range of all numbers equal to and greater than six is the answer.

This is relating what you don’t know to what you already do know. The solutions appear simple, but walking through them is an excellent demonstration of the process of problem-solving.

In most cases, the solution won’t be this simple, but the process or finding it is the same. This may seem trivial, but this is a model for thinking that has served the greatest minds in history.

A recap of the 4 steps of the simple problem-solving process

• What’s the problem? There’s something wrong. There’s something amiss.
• What do you need to know? This is how to fix what’s wrong.
• What do you already know? You already know something useful that will help you find an effective solution.
• What’s the relationship between the previous two? When you use what you know to help figure out what you don’t know, there is no problem that won’t yield.

Learning is simply problem-solving. You’ll learn faster if you view it this way.

What was once complicated will become simple.

What was once convoluted will become clear.

Ed Latimore

I’m a writer, competitive chess player, Army veteran, physicist, and former professional heavyweight boxer. My work focuses on self-development, realizing your potential, and sobriety—speaking from personal experience, having overcome both poverty and addiction.

Follow me on Twitter.

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• My Dashboard

• Content: Polya’s Problem-Solving Method

Back to: Helping Students Do Math

The purpose of this tool for the field is to help paraprofessionals become more familiar with, and practice using, Polya’s four-step problem-solving method.

• Read the example below about Mrs. Byer’s class, and then look over the example of how Polya’s method was used to solve the problem.

Every person at a party of 12 people said hello to each of the other people at the party exactly once. How many “hellos” were said at the party?           

A new burger restaurant offers two kinds of buns, three kinds of meats, and two types of condiments. How many different burger combinations are possible that have one type of bun, one type of meat, and one condiment type?

A family has five children. How many different gender combinations are possible, assuming that order matters? (For example, having four boys and then a girl is distinct from having a girl and then four boys.)

Hillary and Marco are both nurses at the city hospital. Hillary has every fifth day off, and Marco has off every Saturday (and only Saturdays). If both Hillary and Marco had today off, how many days will it be until the next day when they both have off?

Reflect on your experience.

• In which types of situations do you think students would find Polya’s method helpful?
• Are there types of problems for which students would find the method more cumbersome than it is helpful?
• Can you think of any students who would particularly benefit from a structured problem-solving approach such as Polya’s?

                           Background Information

Nearly 100 years ago, a man named George Polya designed a four-step method to solve all kinds of problems: Understand the problem, make a plan, execute the plan, and look back and reflect. Because the method is simple and generalizes well, it has become a classic method for solving problems. In fact, the method is applicable to all areas of our lives where we encounter problems—not just math. Although the method appears to be a straightforward method where you start at Step 1, and then go through Steps 2, 3, and 4, the reality is that you will often need to go back and forth through the four steps until you have solved and reflected on a problem.

Polya’s Problem-Solving Chart: An Example

A version of Polya’s problem-solving chart can be found below, complete with descriptions of each step and an illustration of how the method can be used systematically to solve the following problem:

Scenario 

There are 22 students in Mrs. Byer’s third grade class. Every student is required to either play the recorder or sing in the choir, although students have the option of doing both. Eight of Mrs. Byer’s students chose to play the recorder, and 20 students sing in the choir. How many of Mrs. Byer’s students both play the recorder and sing in the choir?

Helping Students Do Math

• Introductory Scenario and Pre-Test
• Content: Does Anyone Know What Math Is?
• Introductory Scenario
• Content: The Fennema-Sherman Attitude Scales
• Content: Past Experience with Math
• Content: Learning About Math
• Content: What is it like to teach math?
• Content: Using a Frayer Model
• Content: Helping a Child Learn from a Textbook
• Content: Using Online Math Resources
• Content: Helping a Student Learn to use a Calculator
• Links for More Information
• Content: Better Questions
• Content: Practice Asking Good Questions
• Content: Applying Poly’s Method to a Life Decision
• Content: Learning Progression Activities
• Content: Connecting Concepts and Procedures
• Content: Resources
• Activity: The Old Guy’s No-Math Test
• Take Notes and Post-Test
• Open All · Close All

Contact: [email protected] 

The Ohio Partnership for Excellence in Paraprofessional Preparation is primarily supported through a grant with the Ohio Department of Education and Workforce, Office for Exceptional Children. Opinions expressed herein do not necessarily reflect those of the Ohio Department of Education or Offices within it, and you should not assume endorsement by the Ohio Department of Education and Workforce.

Powerful online learning at your pace

What IS Problem-Solving?

Ask teachers about problem-solving strategies, and you’re opening a can of worms! Opinions about the “best” way to teach problem-solving are all over the board. And teachers will usually argue for their process quite passionately.

When I first started teaching math over 25 years ago, it was very common to teach “keywords” to help students determine the operation to use when solving a word problem. For example, if you see the word “total” in the problem, you always add. Rather than help students become better problem solvers, the use of keywords actually resulted in students who don’t even feel the need to read and understand the problem–just look for the keywords, pick out the numbers, and do the operation indicated by the keyword.

This post contains affiliate links, which simply means that when you use my link and purchase a product, I receive a small commission. There is no additional cost to you, and I only link to books and products that I personally use and recommend.

Another common strategy for teaching problem-solving is the use of acrostics that students can easily remember to perform the “steps” in problem-solving. CUBES is an example. Just as with keywords, however, students often follow the steps with little understanding. As an example, a common step is to underline or highlight the question. But if you ask students why they are underlining or highlighting the question, they often can’t tell you. The question is , in fact, super important, but they’ve not been told why. They’ve been told to underline the question, so they do.

The problem with both keywords and the rote-step strategies is that both methods try to turn something that is inherently messy into an algorithm! It’s way past time that we leave both methods behind.

First, we need to broaden the definition of problem-solving. Somewhere along the line, problem-solving became synonymous with “word problems.” In reality, it’s so much more. Every one of us solves dozens or hundreds of problems every single day, and most of us haven’t solved a word problem in years. Problem-solving is often described as  figuring out what to do when you don’t  know what to do.  My power went out unexpectedly this morning, and I have work to do. That’s a problem that I had to solve. I had to think about what the problem was, what my options were, and formulate a plan to solve the problem. No keywords. No acrostics. I’m using my phone as a hotspot and hoping my laptop battery doesn’t run out. Problem solved. For now.

If you want to get back to what problem-solving really is, you should consult the work of George Polya. His book, How to Solve It , which was first published in 1945, outlined four principles for problem-solving. The four principles are: understand the problem, devise a plan, carry out the plan, and look back. This document from UC Berkeley’s Mathematics department is a great 4-page overview of Polya’s process. You can probably see that the keyword and rote-steps strategies were likely based on Polya’s method, but it really got out of hand. We need to help students think , not just follow steps.

I created both primary and intermediate posters based on Polya’s principles. Grab your copies for free here !

I would LOVE to hear your comments about problem-solving!

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Do you tutor teachers?

I do professional development for district and schools, and I have online courses.

You make a great point when you mentioned that teaching students to look for “keywords” is not teaching students to become better problem solvers. I was once guilty of using the CUBES strategy, but have since learned to provide students with opportunity to grapple with solving a problem and not providing them with specified steps to follow.

I think we’ve ALL been there! We learn and we do better. 🙂

Love this article and believe that we can do so much better as math teachers than just teaching key words! Do you have an editable version of this document? We are wanting to use something similar for our school, but would like to tweak it just a bit. Thank you!

I’m sorry, but because of the clip art and fonts I use, I am not able to provide an editable version.

Hi Donna! I am working on my dissertation that focuses on problem-solving. May I use your intermediate poster as a figure, giving credit to you in my citation with your permission, for my section on Polya’s Traditional Problem-Solving Steps? You laid out the process so succinctly with examples that my research could greatly benefit from this image. Thank you in advance!

Absolutely! Good luck with your dissertation!

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Easy Problem Solving Using the 4-step Method

June 7, 2017  by  Jennifer Haury Category:  Guest Author ,  Management

At a recent hospital town forum, hospital leaders are outlining the changes coming when a lone, brave nurse raises her hand and says, “We just can’t take any more changes. They are layered on top of each other and each one is rolled out in a different way. We are exhausted and it’s overloading us all.”  

 “Flavor of the Month” Fatigue

Change fatigue. You hear about it in every industry, from government sectors to software design to manufacturing to healthcare and more. When policy and leadership changes and process improvement overlap it’s no surprise when people complain about “flavor of the month,” and resist it just so they can keep some routine to their days.

In a time where change is required just to keep up with the shifting environment, one way to ease fatigue is to standardize HOW we change. If we use a best practice for solving problems, we can ensure that the right people are involved and problems are solved permanently, not temporarily. Better yet, HOW we change can become the habit and routine we long for.

The 4-step Problem Solving Method

The model we’ve used with clients is based on the A3 problem-solving methodology used by many “lean” production-based companies. In addition to being simpler, our 4-step method is visual, which helps remind the user what goes into each box.

The steps are as follows

• Develop a Problem Statement
• Determine Root Causes
• Rank Root Causes in Order of Importance
• Create an Action Plan

Step 1: Develop a Problem Statement

Developing a good problem statement always seems a lot easier than it generally turns out to be.  For example, this statement: “We don’t have enough staff,” frequently shows up as a problem statement. However, it suggests the solution—“GET MORE STAFF” — and fails to address the real problem that more staff might solve, such as answering phones in a timely manner.

The trick is to develop a problem statement that does not suggest a solution.  Avoiding the following words/phrases: “lack of,” “no,” “not enough,” or “too much” is key. When I start to fall into the trap of suggesting a solution, I ask: “So what problem does that cause?” This usually helps to get to a more effective problem statement.

Once you’ve developed a problem statement, you’ll need to define your target goal, measure your actual condition, then determine the gap. If we ran a restaurant and our problem was: “Customers complaining about burnt toast during morning shift,” the target goal might be: “Toast golden brown 100% of morning shift.”

Focus on a tangible, achievable target goal then measure how often that target is occurring. If our actual condition is: “Toast golden brown 50% of the time,” then our gap is: “Burnt toast 50% of the time.” That gap is now a refined problem to take to Step 2.

Step 2:  Determine Root Causes

In Step 2, we want to understand the root causes. For example, if the gap is burnt toast 50% of the time, what are all the possible reasons why?

This is when you brainstorm. It could be an inattentive cook or a broken pop-up mechanism. Cooks could be using different methods to time the toasting process or some breads toast more quickly.  During brainstorming, you’ll want to include everyone in the process since observing these interactions might also shed light on why the problem is occurring.

Once we have an idea of why, we then use the 5-why process to arrive at a root cause.  Ask “Why?” five times or until it no longer makes sense to ask. Root causes can be tricky.  For example, if the pop up mechanism is broken you could just buy a new toaster, right? But if you asked WHY it broke, you may learn cooks are pressing down too hard on the pop up mechanism, causing it to break. In this case, the problem would just reoccur if you bought a new toaster.

When you find you are fixing reoccurring problems that indicates you haven’t solved for the root cause. Through the 5-why process, you can get to the root cause and fix the problem permanently.

Step 3: Rank Root Causes

Once you know what’s causing the problem (and there may be multiple root causes), it’s time to move to Step 3 to understand which causes, if solved for, would close your gap. Here you rank the root causes in order of importance by looking at which causes would have the greatest impact in closing the gap.

There may be times when you don’t want to go after your largest root cause (perhaps because it requires others to change what they are doing, will take longer, or is dependent on other things getting fixed, etc). Sometimes you’ll find it’s better to start with a solution that has a smaller impact but can be done quickly.

Step 4: Create an Action Plan

In Step 4 you create your action plan — who is going to do what and by when. Documenting all of this and making it visible helps to communicate the plan to others and helps hold them accountable during implementation.

This is where your countermeasures or experiments to fix the problem are detailed. Will we train our chefs on how to use a new “pop-up mechanism” free toaster? Will we dedicate one toaster for white bread and one for wheat?  

Make sure to measure your results after you’ve implemented your plan to see if your target is met. If not, that’s okay; just go through the steps again until the problem is resolved.

Final Thoughts

Using the 4-step method has been an easy way for teams to change how they solve problems. One team I was working with started challenging their “solution jumps” and found this method was a better way to avoid assumptions which led to never really solving their problems.  It was easy to use in a conference room and helped them make their thinking visual so everyone could be involved and engaged in solving the problems their team faced. 

Do you have a problem-solving method that you use at your worksite?  Let us know in the comments below. 

MRSC is a private nonprofit organization serving local governments in Washington State. Eligible government agencies in Washington State may use our free, one-on-one Ask MRSC service to get answers to legal, policy, or financial questions.

About Jennifer Haury

Jennifer Haury is the CEO of All Angles Consulting, LLC and guest authored this post for MRSC.

Jennifer has over 28 years learning in the healthcare industry (17 in leadership positions or consulting in performance improvement and organizational anthropology) and is a Lean Six Sigma Black Belt.

She is a trusted, experienced leader with a keen interest in performance improvement and organizational anthropology. Jennifer is particularly concerned with the sustainability of continuous improvement programs and the cultural values and beliefs that translate into behaviors that either get in our own way or help us succeed in transforming our work.

The views expressed in guest columns represent the opinions of the author and do not necessarily reflect those of MRSC.

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Four-Step Math Problem Solving Strategies & Techniques

• Harlan Bengtson
• Categories : Help with math homework
• Tags : Homework help & study guides

Four Steps to Success

There are many possible strategies and techniques you can use to solve math problems. A useful starting point is a four step approach to math problem solving. These four steps can be summarized as follows:

• Carefully read the problem. In this careful reading, you should especially seek to clearly identify the question that is to be answered. Also, a good, general understanding of what the problem means should be sought.
• Choose a strategy to solve the problem. Some of the possible strategies will be discussed in the rest of this article.
• Carry out the problem solving strategy. If the first problem solving technique you try doesn’t work, try another.
• Check the solution. This check should make sure that you have indeed answered the question that was posed and that the answer makes sense.

Step One - Understanding the Problem

As you carefully read the problem, trying to clearly understand the meaning of the problem and the question that you must answer, here are some techniques to help.

Identify given information - Highlighting or underlining facts that are given helps to visualize what is known or given.

Identify information asked for - Highlighting the unknowns in a different color helps to keep the known information visually separate from the unknowns to be determined. Ideally this will lead to a clear identification of the question to be answered.

Look for keywords or clue words - One example of clue words is those that indicate what type of mathematical operation is needed, as follows:

Clue words indicating addition: sum, total, in all, perimeter.

Clue words indicating subtraction: difference, how much more, exceed.

Clue words for multiplication: product, total, area, times.

Clue words for division: share, distribute, quotient, average.

Draw a picture - This might also be considered part of solving the problem, but a good sketch showing given information and unknowns can be very helpful in understanding the problem.

Step Two - Choose the Right Strategy

It step one has been done well, it should ease the job of choosing among the strategies presented here for approaching the problem solving step. Here are some of the many possible math problem solving strategies.

• Look for a pattern - This might be part of understanding the problem or it might be the first part of solving the problem.
• Make an organized list - This is another means of organizing the information as part of understanding it or beginning the solution.
• Make a table - In some cases the problem information may be more suitable for putting in a table rather than in a list.
• Try to remember if you’ve done a similar problem before - If you have done a similar problem before, try to use the same approach that worked in the past for the solution.
• Guess the answer - This may seem like a haphazard approach, but if you then check whether your guess was correct, and repeat as many times as necessary until you find the right answer, it works very well. Often information from checking on whether the answer was correct helps lead you to a good next guess.
• Work backwards - Sometimes making the calculations in the reverse order works better.

Steps Three and Four - Solving the Problem and Checking the Solution

If the first two steps have been done well, then the last two steps should be easy. If the selected problem solving strategy doesn’t seem to work when you actually try it, go back to the list and try something else. Your check on the solution should show that you have actually answered the question that was asked in the problem, and to the extent possible, you should check on whether the answer makes common sense.

4-step problem solving model

Description

Questions & answers, mandy's math world.

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QazUNTv2: Dataset of high school math problems on english and russian languages

Description.

This dataset is intended for the subsequent verification of the correctness of LLM (GPT-3.5 Turbo) generated responses to mathematics problems similar to those found in exams for graduate schools. The dataset includes problems and their types in both Russian and English, along with five options, manually solved answers, and detailed solutions in both languages. The primary goal is to analyze and compare LLM (GPT-3.5 Turbo)-generated answers with provided correct solutions. The data has been collected and structured across the following sections of mathematics: Algebra, Probability and Logic. We ensured a comprehensive evaluation of GPT's capabilities in understanding and solving these problems. The dataset is divided into the following sections with the corresponding number of problems: 1. Algebra: 436 problems; 2. Logic: 312 problems; 3. Probability: 163 problems. This dataset will facilitate a detailed assessment of GPT's performance in mathematical problem-solving across various domains. For the future analysis, we also calculated quantity of tokens that may help to generate responses from ChatGPT-3.5 Turbo: The English math problems comprise 37563 tokens. The Russian math problems comprise 66406 tokens. The average number of tokens per English task is approximately 39.96 and for the problems in Russian this number is approximately 70.64.

Steps to reproduce

1-step: Parsing pdf to text, filtering only text-based math problems; 2-step: Manual categorization of problems by following math areas: Algebra, Logic and Probability; 3-step: Data cleaning: filtering out bad parsed problems and adding new problems to balance the dataset; 4-step: Creating new columns of problem description and options in English language by using Google Translator; 5-step: Manually solving problems in Russian and English languages and adding a category column; 6-step: Statistical analyzing with Pandas and Tiktoken libraries of Python for the understanding the scale of the dataset.

Institutions

The Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan

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