5 step problem solving process math

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New Designs for School 5 Steps to Teaching Students a Problem-Solving Routine

Jeff Heyck-Williams (He, His, Him) Director of the Two Rivers Learning Institute in Washington, DC

We’ve all had the experience of truly purposeful, authentic learning and know how valuable it is. Educators are taking the best of what we know about learning, student support, effective instruction, and interpersonal skill-building to completely reimagine schools so that students experience that kind of purposeful learning all day, every day.

Students can use the 5 steps in this simple routine to solve problems across the curriculum and throughout their lives.

When I visited a fifth-grade class recently, the students were tackling the following problem:

If there are nine people in a room and every person shakes hands exactly once with each of the other people, how many handshakes will there be? How can you prove your answer is correct using a model or numerical explanation?

There were students on the rug modeling people with Unifix cubes. There were kids at one table vigorously shaking each other’s hand. There were kids at another table writing out a diagram with numbers. At yet another table, students were working on creating a numeric expression. What was common across this class was that all of the students were productively grappling around the problem.

On a different day, I was out at recess with a group of kindergarteners who got into an argument over a vigorous game of tag. Several kids were arguing about who should be “it.” Many of them insisted that they hadn’t been tagged. They all agreed that they had a problem. With the assistance of the teacher they walked through a process of identifying what they knew about the problem and how best to solve it. They grappled with this very real problem to come to a solution that all could agree upon.

Then just last week, I had the pleasure of watching a culminating showcase of learning for our 8th graders. They presented to their families about their project exploring the role that genetics plays in our society. Tackling the problem of how we should or should not regulate gene research and editing in the human population, students explored both the history and scientific concerns about genetics and the ethics of gene editing. Each student developed arguments about how we as a country should proceed in the burgeoning field of human genetics which they took to Capitol Hill to share with legislators. Through the process students read complex text to build their knowledge, identified the underlying issues and questions, and developed unique solutions to this very real problem.

Problem-solving is at the heart of each of these scenarios, and an essential set of skills our students need to develop. They need the abilities to think critically and solve challenging problems without a roadmap to solutions. At Two Rivers Public Charter School in Washington, D.C., we have found that one of the most powerful ways to build these skills in students is through the use of a common set of steps for problem-solving. These steps, when used regularly, become a flexible cognitive routine for students to apply to problems across the curriculum and their lives.

The Problem-Solving Routine

At Two Rivers, we use a fairly simple routine for problem solving that has five basic steps. The power of this structure is that it becomes a routine that students are able to use regularly across multiple contexts. The first three steps are implemented before problem-solving. Students use one step during problem-solving. Finally, they finish with a reflective step after problem-solving.

Problem Solving from Two Rivers Public Charter School

Before Problem-Solving: The KWI

The three steps before problem solving: we call them the K-W-I.

The “K” stands for “know” and requires students to identify what they already know about a problem. The goal in this step of the routine is two-fold. First, the student needs to analyze the problem and identify what is happening within the context of the problem. For example, in the math problem above students identify that they know there are nine people and each person must shake hands with each other person. Second, the student needs to activate their background knowledge about that context or other similar problems. In the case of the handshake problem, students may recognize that this seems like a situation in which they will need to add or multiply.

The “W” stands for “what” a student needs to find out to solve the problem. At this point in the routine the student always must identify the core question that is being asked in a problem or task. However, it may also include other questions that help a student access and understand a problem more deeply. For example, in addition to identifying that they need to determine how many handshakes in the math problem, students may also identify that they need to determine how many handshakes each individual person has or how to organize their work to make sure that they count the handshakes correctly.

The “I” stands for “ideas” and refers to ideas that a student brings to the table to solve a problem effectively. In this portion of the routine, students list the strategies that they will use to solve a problem. In the example from the math class, this step involved all of the different ways that students tackled the problem from Unifix cubes to creating mathematical expressions.

This KWI routine before problem solving sets students up to actively engage in solving problems by ensuring they understand the problem and have some ideas about where to start in solving the problem. Two remaining steps are equally important during and after problem solving.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them.

During Problem-Solving: The Metacognitive Moment

The step that occurs during problem solving is a metacognitive moment. We ask students to deliberately pause in their problem-solving and answer the following questions: “Is the path I’m on to solve the problem working?” and “What might I do to either stay on a productive path or readjust my approach to get on a productive path?” At this point in the process, students may hear from other students that have had a breakthrough or they may go back to their KWI to determine if they need to reconsider what they know about the problem. By naming explicitly to students that part of problem-solving is monitoring our thinking and process, we help them become more thoughtful problem solvers.

After Problem-Solving: Evaluating Solutions

As a final step, after students solve the problem, they evaluate both their solutions and the process that they used to arrive at those solutions. They look back to determine if their solution accurately solved the problem, and when time permits they also consider if their path to a solution was efficient and how it compares to other students’ solutions.

The power of teaching students to use this routine is that they develop a habit of mind to analyze and tackle problems wherever they find them. This empowers students to be the problem solvers that we know they can become.

Jeff Heyck-Williams (He, His, Him)

Director of the two rivers learning institute.

Jeff Heyck-Williams is the director of the Two Rivers Learning Institute and a founder of Two Rivers Public Charter School. He has led work around creating school-wide cultures of mathematics, developing assessments of critical thinking and problem-solving, and supporting project-based learning.

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5 Easy Steps to Solve Any Word Problem in Math

• February 27, 2021

Picture this my teacher besties.  You are solving word problems in your math class and every student, yes every student knows how to solve word problems without immediately entering a state of confusion!  They know how to attack the problem head-on and have a method to solve every single problem that is presented to them.  

How Do You Solve Word Problems in Math?

Ask yourself this, what do you think is the #1 phrase a student says as soon as they see a word problem? 

You guessed it, my teacher friend,  I don’t know how to do this!  I think the most common question I get when I’m teaching my math classes, is how do I solve this?  

Students see word problems and immediately enter freak-out mode!  Let’s take solving word problems in the classroom and make it easier for students to SOLVE the problem!

How to Solve Word Problems Step by Step 

There are so many methods   that students can choose from when learning how to solve word problems.  The 4 step method is the foundation for all of the methods that you will see, but what about a variation of the 4 step method that every student can do just because they get it. 

Students are most likely confused about how to solve word problems because they have never used a consistent method over the years.   I’m all about consistency in my classroom.  Fortunately, in my school district, I get to teach most of the students year after year because of how small our class sizes are.   So I’m going to give you a method based on the 4 step method, that allows all students to be successful at solving word problems.  

Even the most unmotivated math student will learn how to solve word problems and not skip them!

Tips, Tricks, and  Teaching Strategies to Solving Word Problems in Math

Going back to the 4 step method just in case you need a refresher.  If you know me at all a little reminder of “oh yeah I remember that now” always helps me!  

4 steps in solving word problems in math:

• Understand the Problem
• Plan the solution
• Solve the Problem 
• Check the solution

This 4 step method is the basis of the method I’m going to tell you all about.  The problem isn’t with the method itself, it is the fact that most students see word problems and just start panicking!

Why can they do an entire assignment and then see a word problem and then suddenly stop?  Is there a reason why books are designed with word problems at the end? 

These are questions that I constantly have asked myself over the last several years.  I finally got to the point where my students needed a consistent approach to solving word problems that worked every single time.  

The first thing I knew I needed to start doing was introducing students to word problems at the beginning of each lesson.

Once students first see the word problems at the beginning of the lesson, they are less likely to be scared of them when it comes time to do it by themselves! 

This also will increase their confidence in the classroom.  In case you missed it, I shared all about how I increase my students’ confidence in the classroom.  

Wonder how increasing their confidence will help keep them motivated in the classroom?

So confident motivated students will see word problems that could be on their homework, any standardized test, and say I GOT THIS! 

Steps to Solving Word Problems in Mathematics

We are ready to SOLVE any word problem our students are going to encounter in math class.  

Here are my 5 easy steps to SOLVE any word problem in math:

• S – State the objective
• O – Outline your plan
• L – Look for Key Details – Information 
• V –  Verify and Solve
• E – Explain and check your solution

Do you want to learn how to implement this 5 steps problem-solving strategy into your classroom?  I’m hosting a FREE workshop all about how to implement this strategy in your classroom!  

I am so excited to be offering a workshop to increase students’ confidence in solving word problems.  The workshop is held in my Facebook Group The Round Robin Math Community. It also will be sent straight to your inbox and you can watch it right now!

If you’re interested, join today and all the details will be sent to you ASAP!

I will see you there!

PS.  Need the SOLVE method for your bulletin board for your students’ math journals/notebooks?  Check out this bulletin board resource here:

Love, Robin

• Latest Posts

Robin Cornecki

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• Here’s a Quick Way to Convert Percents to Fractions and Decimals. - July 21, 2022
• How to use the Four-Function Calculator for the Praxis Core Math Test.  - April 23, 2022

Hi, I'm Robin!

 I am a secondary math teacher with over 19 years of experience! If you’re a teacher looking for help with all the tips, tricks, and strategies for passing the praxis math core test, you’re in the right place!

I also create engaging secondary math resources for grades 7-12! 

Learn more about me and how I can help you here .

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5 Steps to Word Problem Solving

How to Factorise a Quadratic Expression

Word problems often confuse students simply because the question does not present itself in a ready-to-solve mathematical equation. You can answer even the most complex word problems, provided you understand the mathematical concepts addressed. While the degree of difficulty may change, the way to solve word problems involves a planned approach that requires identifying the problem, gathering the relevant information, creating the equation, solving and checking your work.

Identify the Problem

Begin by determining the scenario the problem wants you to solve. This might come as a question or a statement. Either way, the word problem provides you with all the information you need to solve it. Once you identify the problem, you can determine the unit of measurement for the final answer. In the following example, the question asks you to determine the total number of socks between the two sisters. The unit of measurement for this problem is pairs of socks.

"Suzy has eight pairs of red socks and six pairs of blue socks. Suzy's brother Mark owns eight socks. If her little sister owns nine pairs of purple socks and loses two of Suzy's pairs, how many pairs of socks do the sisters have left?"

Gather Information

Create a table, list, graph or chart that outlines the information you know, and leave blanks for any information you don't yet know. Each word problem may require a different format, but a visual representation of the necessary information makes it easier to work with.

In the example, the question asks how many socks the sisters own together, so you can disregard the information about Mark. Also, the color of the socks doesn't matter. This eliminates much of the information and leaves you with only the total number of socks that the sisters started with and how many the little sister lost.

Create an Equation

Translate any of the math terms into math symbols. For example, the words and phrases "sum," "more than," "increased" and "in addition to" all mean to add, so write in the "+" symbol over these words. Use a letter for the unknown variable, and create an algebraic equation that represents the problem.

In the example, take the total number of pairs of socks Suzy owns -- eight plus six. Take the total number of pairs that her sister owns -- nine. The total pairs of socks owned by both sisters is 8 + 6 + 9. Subtract the two missing pairs for a final equation of (8 + 6 + 9) - 2 = n, where n is the number of pairs of socks the sisters have left.

Solve the Problem

Using the equation, solve the problem by plugging in the values and solving for the unknown variable. Double-check your calculations along the way to prevent any mistakes. Multiply, divide and subtract in the correct order using the order of operations. Exponents and roots come first, then multiplication and division, and finally addition and subtraction.

In the example, after adding the numbers together and subtracting, you get an answer of n = 21 pairs of socks.

Verify the Answer

Check if your answer makes sense with what you know. Using common sense, estimate an answer and see if you come close to what you expected. If the answer seems absurdly large or too small, search through the problem to find where you went wrong.

In the example, you know by adding up all the numbers for the sisters that you have a maximum of 23 socks. Since the problem mentions that the little sister lost two pairs, the final answer must be less than 23. If you get a higher number, you did something wrong. Apply this logic to any word problem, regardless of the difficulty.

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• Mt. San Antonio College: Five-Step Strategy to Solving Word Problems

About the Author

Avery Martin holds a Bachelor of Music in opera performance and a Bachelor of Arts in East Asian studies. As a professional writer, she has written for Education.com, Samsung and IBM. Martin contributed English translations for a collection of Japanese poems by Misuzu Kaneko. She has worked as an educator in Japan, and she runs a private voice studio out of her home. She writes about education, music and travel.

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Overview of the Problem-Solving Mental Process

Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Rachel Goldman, PhD FTOS, is a licensed psychologist, clinical assistant professor, speaker, wellness expert specializing in eating behaviors, stress management, and health behavior change.

• Identify the Problem
• Define the Problem
• Form a Strategy
• Organize Information
• Allocate Resources
• Monitor Progress
• Evaluate the Results

Frequently Asked Questions

Problem-solving is a mental process that involves discovering, analyzing, and solving problems. The ultimate goal of problem-solving is to overcome obstacles and find a solution that best resolves the issue.

The best strategy for solving a problem depends largely on the unique situation. In some cases, people are better off learning everything they can about the issue and then using factual knowledge to come up with a solution. In other instances, creativity and insight are the best options.

It is not necessary to follow problem-solving steps sequentially, It is common to skip steps or even go back through steps multiple times until the desired solution is reached.

In order to correctly solve a problem, it is often important to follow a series of steps. Researchers sometimes refer to this as the problem-solving cycle. While this cycle is portrayed sequentially, people rarely follow a rigid series of steps to find a solution.

The following steps include developing strategies and organizing knowledge.

1. Identifying the Problem

While it may seem like an obvious step, identifying the problem is not always as simple as it sounds. In some cases, people might mistakenly identify the wrong source of a problem, which will make attempts to solve it inefficient or even useless.

Some strategies that you might use to figure out the source of a problem include :

• Asking questions about the problem
• Breaking the problem down into smaller pieces
• Looking at the problem from different perspectives
• Conducting research to figure out what relationships exist between different variables

2. Defining the Problem

After the problem has been identified, it is important to fully define the problem so that it can be solved. You can define a problem by operationally defining each aspect of the problem and setting goals for what aspects of the problem you will address

At this point, you should focus on figuring out which aspects of the problems are facts and which are opinions. State the problem clearly and identify the scope of the solution.

3. Forming a Strategy

After the problem has been identified, it is time to start brainstorming potential solutions. This step usually involves generating as many ideas as possible without judging their quality. Once several possibilities have been generated, they can be evaluated and narrowed down.

The next step is to develop a strategy to solve the problem. The approach used will vary depending upon the situation and the individual's unique preferences. Common problem-solving strategies include heuristics and algorithms.

• Heuristics are mental shortcuts that are often based on solutions that have worked in the past. They can work well if the problem is similar to something you have encountered before and are often the best choice if you need a fast solution.
• Algorithms are step-by-step strategies that are guaranteed to produce a correct result. While this approach is great for accuracy, it can also consume time and resources.

Heuristics are often best used when time is of the essence, while algorithms are a better choice when a decision needs to be as accurate as possible.

4. Organizing Information

Before coming up with a solution, you need to first organize the available information. What do you know about the problem? What do you not know? The more information that is available the better prepared you will be to come up with an accurate solution.

When approaching a problem, it is important to make sure that you have all the data you need. Making a decision without adequate information can lead to biased or inaccurate results.

5. Allocating Resources

Of course, we don't always have unlimited money, time, and other resources to solve a problem. Before you begin to solve a problem, you need to determine how high priority it is.

If it is an important problem, it is probably worth allocating more resources to solving it. If, however, it is a fairly unimportant problem, then you do not want to spend too much of your available resources on coming up with a solution.

At this stage, it is important to consider all of the factors that might affect the problem at hand. This includes looking at the available resources, deadlines that need to be met, and any possible risks involved in each solution. After careful evaluation, a decision can be made about which solution to pursue.

6. Monitoring Progress

After selecting a problem-solving strategy, it is time to put the plan into action and see if it works. This step might involve trying out different solutions to see which one is the most effective.

It is also important to monitor the situation after implementing a solution to ensure that the problem has been solved and that no new problems have arisen as a result of the proposed solution.

Effective problem-solvers tend to monitor their progress as they work towards a solution. If they are not making good progress toward reaching their goal, they will reevaluate their approach or look for new strategies .

7. Evaluating the Results

After a solution has been reached, it is important to evaluate the results to determine if it is the best possible solution to the problem. This evaluation might be immediate, such as checking the results of a math problem to ensure the answer is correct, or it can be delayed, such as evaluating the success of a therapy program after several months of treatment.

Once a problem has been solved, it is important to take some time to reflect on the process that was used and evaluate the results. This will help you to improve your problem-solving skills and become more efficient at solving future problems.

A Word From Verywell​

It is important to remember that there are many different problem-solving processes with different steps, and this is just one example. Problem-solving in real-world situations requires a great deal of resourcefulness, flexibility, resilience, and continuous interaction with the environment.

Get Advice From The Verywell Mind Podcast

Hosted by therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares how you can stop dwelling in a negative mindset.

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You can become a better problem solving by:

• Practicing brainstorming and coming up with multiple potential solutions to problems
• Being open-minded and considering all possible options before making a decision
• Breaking down problems into smaller, more manageable pieces
• Asking for help when needed
• Researching different problem-solving techniques and trying out new ones
• Learning from mistakes and using them as opportunities to grow

It's important to communicate openly and honestly with your partner about what's going on. Try to see things from their perspective as well as your own. Work together to find a resolution that works for both of you. Be willing to compromise and accept that there may not be a perfect solution.

Take breaks if things are getting too heated, and come back to the problem when you feel calm and collected. Don't try to fix every problem on your own—consider asking a therapist or counselor for help and insight.

If you've tried everything and there doesn't seem to be a way to fix the problem, you may have to learn to accept it. This can be difficult, but try to focus on the positive aspects of your life and remember that every situation is temporary. Don't dwell on what's going wrong—instead, think about what's going right. Find support by talking to friends or family. Seek professional help if you're having trouble coping.

Davidson JE, Sternberg RJ, editors.  The Psychology of Problem Solving .  Cambridge University Press; 2003. doi:10.1017/CBO9780511615771

Sarathy V. Real world problem-solving .  Front Hum Neurosci . 2018;12:261. Published 2018 Jun 26. doi:10.3389/fnhum.2018.00261

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

Problem Analysis in Math: Using the 5-Step Problem-Solving Approach

This blog will explore the ways in which problem analysis of student mathematics difficulties can be applied within a problem-solving approach. We will review the core principles of a multi-tier system of support (MTSS) framework, identify the steps within a problem-solving approach, and explore the ways in which problem analysis helps to inform intervention development within the context of mathematics instruction.

Core Principles of an MTSS Framework

A variety of definitions of an MTSS framework exist within the field of education; however, several common principles are apparent and have helped to shape much of the work within this area. The National Association of State Directors of Special Education (Batsche et al., 2006) define eight core principles that capture some of the most important aspects and core beliefs of an MTSS framework:

• We can effectively teach all children.
• Intervene early.
• Use a multi-tier model of service delivery.
• Use a problem-solving model to make decisions within a multi-tier model.
• Use scientific, research-based validated intervention and instruction to the extent available.
• Monitor student progress to inform instruction.
• Use data to make decisions.
• Use assessment for screening, diagnostics, and progress monitoring.

The fourth core principle refers to utilizing a problem-solving model to make decisions. More specifically, educators and administrators should use a clearly defined problem-solving process that guides their team in identifying the problem, analyzing the size and effect of the problem, developing a plan for intervention to address the problem, implementing the plan, and examining the effectiveness of the intervention plan.

5-Step Problem-Solving Approach

The problem-solving approach utilized by the FastBridge Learning ® system includes the following five steps:

Problem identification

• Problem analysis
• Plan development
• Plan implementation
• Plan evaluation

Following this 5-step problem-solving approach helps to guide school teams of educators and administrators in engaging in data-based decision making: a core principle of the MTSS framework.

The first step in this problem-solving approach is problem identification. Christ and Arañas (2014) define a problem as a discrepancy between observed and expected performance. Regularly scheduled universal screening plays an important role in problem identification. The FastBridge Learning ® system offers a variety of screening measures for mathematics, which are summarized in the table below. While the results of regularly scheduled universal screening help to inform whether or not a discrepancy between observed and expected performance exists, problem analysis aims to identify the size and effects of the problem.

Problem Analysis

After a problem has been identified, the problem must be defined through the method of problem analysis. Only after a problem has been sufficiently analyzed and defined, can the significance of a problem be understood (Brown-Chidsey & Bickford, 2016). Problem analysis can occur at both the individual level and the group level.

Problem Analysis at the Individual Leve l

At the individual level, a discrepancy between observed and expected performance may appear within an individual’s universal screening results. FastBridge Learning ® Individual Skills Reports can provide detailed information to support problem analysis. The Individual Skills Report provides a snapshot of a given student’s risk, relative to benchmark goals, and also provides detailed results on an item-by-item basis. This item-by-item analysis provides insight into the skills the student demonstrates and which skills may require additional instructional support.

If the student’s performance is relatively close to the benchmark goal, the problem is likely to be understood as a minor problem. Item-by-item analysis can help a teacher determine if targeted reteaching of specific content may help the student to reach the goal, or if more intensive intervention may be necessary. An example of a FastBridge Learning ® Individual Skills Report for the earlyMath subtest Numeral Identification (Kindergarten) may be seen below.

The above report suggests that the sample student is at “some risk” for difficulty with numeral identification. It also reveals that the student was able to identify the given numerals with 91% accuracy. Additionally, the item-by-item analysis indicates that the student struggled to identify the following numerals: 12, 14, and 19. In this case, problem analysis may suggest that this is a minor problem, which may be remedied through targeted reteaching of the numerals 12, 14, and 19. In contrast, if during problem analysis, an Individual Skills Report for Numeral Identification indicated very low accuracy and a substantial number of misidentified numerals, the results would suggest a more significant problem. Significant problems warrant planning for more intensive intervention.

Problem analysis at the group level

At the group level, problem analysis seeks to determine the size and effects of a problem at the class, grade, or school-wide level. FastBridge Learning ® Group Screening Reports and Group Skills Reports help to provide insight about groups of students at risk for learning difficulties. An example of a Group Screening Report for earlyMath may be seen below.

The Group Screening Report pictured above indicates that approximately 77% of Ms. Horst’s kindergarten class scored at or above the benchmark goal on the earlyMath Composite during the fall benchmark period, while 6% and 18% were identified as being at “some risk” and “high risk” respectively.

All students should demonstrate growth in math achievement throughout the school year. If there are students who met the fall benchmark for mathematics, but not the winter and/or spring benchmarks, problem analysis must occur. In Ms. Horst’s class, we can see by the spring benchmark period, only 12% of her kindergarten class scored at or above the benchmark goal on the earlyMath composite, while 18% and 71% were identified as being at “some risk” and “high risk” respectively.

Problem analysis at the group level may aim to answer questions such as the following:

• What type of mathematics instruction was provided for these students?
• Did other kindergarten classrooms within the school experience a similar pattern of mathematics difficulty?
• With which specific mathematics skills (e.g., decomposing, number sequencing, numeral identification) did the group demonstrate success and difficulty?
• How close to the end-of-year mathematics goals are the students now?

In order to complete a thorough problem analysis, supplemental data about student performance and instructional practices may need to be collected.

For instance, classroom observations and/or a teacher interview would provide insight into the first question. Group Screening Reports for the other kindergarten classrooms in the school could help identify if this is a schoolwide pattern of difficulty or a classroom-specific pattern of difficulty. An analysis of the Group Skills Report for Ms. Horst’s class would provide insight into students’ strengths and weaknesses across the earlyMath Composite’s subtests. Additional, targeted, follow-up assessment using selected FastBridge Learning ® earlyMath subtests could help to gather information about the final question.

The goal of problem analysis is to determine the significance of a problem and to develop a hypothesis about why a problem has occurred. The information gathered during the problem analysis stage is then used to inform the third step of the 5-step problem-solving approach: plan development.

Batsche, G., Elliott, J., Graden, J. L., Grimes, J., Kovaleski, J. F., Prasse, D., Schrag, J., & Tilly, W.D. (2006). Response to intervention: Policy considerations and implementation. Alexandria, VA: National Association of State Directors of Special Education, Inc.

Brown-Chidsey, R. and Bickford, R. (2016). Practical handbook of multi-tiered systems of support: Building academic and behavioral success in schools. New York, NY: The Guilford Press.

Christ, T.J., & Arañas, Y.A. (2014). Best practices in problem analysis. In A. Thomas & J. Grimes (Eds.), Best Practices in School Psychology VI . Bethesda, MD: National Association of School Psychologists.

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The 5 steps of the solving problem process

August 17, 2023 by MindManager Blog

Whether you run a business, manage a team, or work in an industry where change is the norm, it may feel like something is always going wrong. Thankfully, becoming proficient in the problem solving process can alleviate a great deal of the stress that business issues can create.

Understanding the right way to solve problems not only takes the guesswork out of how to deal with difficult, unexpected, or complex situations, it can lead to more effective long-term solutions.

In this article, we’ll walk you through the 5 steps of problem solving, and help you explore a few examples of problem solving scenarios where you can see the problem solving process in action before putting it to work.

Understanding the problem solving process

When something isn’t working, it’s important to understand what’s at the root of the problem so you can fix it and prevent it from happening again. That’s why resolving difficult or complex issues works best when you apply proven business problem solving tools and techniques – from soft skills, to software.

The problem solving process typically includes:

• Pinpointing what’s broken by gathering data and consulting with team members.
• Figuring out why it’s not working by mapping out and troubleshooting the problem.
• Deciding on the most effective way to fix it by brainstorming and then implementing a solution.

While skills like active listening, collaboration, and leadership play an important role in problem solving, tools like visual mapping software make it easier to define and share problem solving objectives, play out various solutions, and even put the best fit to work.

Before you can take your first step toward solving a problem, you need to have a clear idea of what the issue is and the outcome you want to achieve by resolving it.

For example, if your company currently manufactures 50 widgets a day, but you’ve started processing orders for 75 widgets a day, you could simply say you have a production deficit.

However, the problem solving process will prove far more valuable if you define the start and end point by clarifying that production is running short by 25 widgets a day, and you need to increase daily production by 50%.

Once you know where you’re at and where you need to end up, these five steps will take you from Point A to Point B:

• Figure out what’s causing the problem . You may need to gather knowledge and evaluate input from different documents, departments, and personnel to isolate the factors that are contributing to your problem. Knowledge visualization software like MindManager can help.
• Come up with a few viable solutions . Since hitting on exactly the right solution – right away – can be tough, brainstorming with your team and mapping out various scenarios is the best way to move forward. If your first strategy doesn’t pan out, you’ll have others on tap you can turn to.
• Choose the best option . Decision-making skills, and software that lets you lay out process relationships, priorities, and criteria, are invaluable for selecting the most promising solution. Whether it’s you or someone higher up making that choice, it should include weighing costs, time commitments, and any implementation hurdles.
• Put your chosen solution to work . Before implementing your fix of choice, you should make key personnel aware of changes that might affect their daily workflow, and set up benchmarks that will make it easy to see if your solution is working.
• Evaluate your outcome . Now comes the moment of truth: did the solution you implemented solve your problem? Do your benchmarks show you achieved the outcome you wanted? If so, congratulations! If not, you’ll need to tweak your solution to meet your problem solving goal.

In practice, you might not hit a home-run with every solution you execute. But the beauty of a repeatable process like problem solving is that you can carry out steps 4 and 5 again by drawing from the brainstorm options you documented during step 2.

Examples of problem solving scenarios

The best way to get a sense of how the problem solving process works before you try it for yourself is to work through some simple scenarios.

Here are three examples of how you can apply business problem solving techniques to common workplace challenges.

Scenario #1: Manufacturing

Building on our original manufacturing example, you determine that your company is consistently short producing 25 widgets a day and needs to increase daily production by 50%.

Since you’d like to gather data and input from both your manufacturing and sales order departments, you schedule a brainstorming session to discover the root cause of the shortage.

After examining four key production areas – machines, materials, methods, and management – you determine the cause of the problem: the material used to manufacture your widgets can only be fed into your equipment once the machinery warms up to a specific temperature for the day.

Your team comes up with three possible solutions.

• Leave your machinery running 24 hours so it’s always at temperature.
• Invest in equipment that heats up faster.
• Find an alternate material for your widgets.

After weighing the expense of the first two solutions, and conducting some online research, you decide that switching to a comparable but less expensive material that can be worked at a lower temperature is your best option.

You implement your plan, monitor your widget quality and output over the following week, and declare your solution a success when daily production increases by 100%.

Scenario #2: Service Delivery

Business training is booming and you’ve had to onboard new staff over the past month. Now you learn that several clients have expressed concern about the quality of your recent training sessions.

After speaking with both clients and staff, you discover there are actually two distinct factors contributing to your quality problem:

• The additional conference room you’ve leased to accommodate your expanding training sessions has terrible acoustics
• The AV equipment you’ve purchased to accommodate your expanding workforce is on back-order – and your new hires have been making do without

You could look for a new conference room or re-schedule upcoming training sessions until after your new equipment arrives. But your team collaboratively determines that the best way to mitigate both issues at once is by temporarily renting the high-quality sound and visual system they need.

Using benchmarks that include several weeks of feedback from session attendees, and random session spot-checks you conduct personally, you conclude the solution has worked.

Scenario #3: Marketing

You’ve invested heavily in product marketing, but still can’t meet your sales goals. Specifically, you missed your revenue target by 30% last year and would like to meet that same target this year.

After collecting and examining reams of information from your sales and accounting departments, you sit down with your marketing team to figure out what’s hindering your success in the marketplace.

Determining that your product isn’t competitively priced, you map out two viable solutions.

• Hire a third-party specialist to conduct a detailed market analysis.
• Drop the price of your product to undercut competitors.

Since you’re in a hurry for results, you decide to immediately reduce the price of your product and market it accordingly.

When revenue figures for the following quarter show sales have declined even further – and marketing surveys show potential customers are doubting the quality of your product – you revert back to your original pricing, revisit your problem solving process, and implement the market analysis solution instead.

With the valuable information you gain, you finally arrive at just the right product price for your target market and sales begin to pick up. Although you miss your revenue target again this year, you meet it by the second quarter of the following year.

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The Problem-Solving Process

Looking at the basic problem-solving process to help keep you on the right track.

By the Mind Tools Content Team

Problem-solving is an important part of planning and decision-making. The process has much in common with the decision-making process, and in the case of complex decisions, can form part of the process itself.

We face and solve problems every day, in a variety of guises and of differing complexity. Some, such as the resolution of a serious complaint, require a significant amount of time, thought and investigation. Others, such as a printer running out of paper, are so quickly resolved they barely register as a problem at all.

Despite the everyday occurrence of problems, many people lack confidence when it comes to solving them, and as a result may chose to stay with the status quo rather than tackle the issue. Broken down into steps, however, the problem-solving process is very simple. While there are many tools and techniques available to help us solve problems, the outline process remains the same.

The main stages of problem-solving are outlined below, though not all are required for every problem that needs to be solved.

1. Define the Problem

Clarify the problem before trying to solve it. A common mistake with problem-solving is to react to what the problem appears to be, rather than what it actually is. Write down a simple statement of the problem, and then underline the key words. Be certain there are no hidden assumptions in the key words you have underlined. One way of doing this is to use a synonym to replace the key words. For example, ‘We need to encourage higher productivity ’ might become ‘We need to promote superior output ’ which has a different meaning.

2. Analyze the Problem

Ask yourself, and others, the following questions.

• Where is the problem occurring?
• When is it occurring?
• Why is it happening?

Be careful not to jump to ‘who is causing the problem?’. When stressed and faced with a problem it is all too easy to assign blame. This, however, can cause negative feeling and does not help to solve the problem. As an example, if an employee is underperforming, the root of the problem might lie in a number of areas, such as lack of training, workplace bullying or management style. To assign immediate blame to the employee would not therefore resolve the underlying issue.

Once the answers to the where, when and why have been determined, the following questions should also be asked:

• Where can further information be found?
• Is this information correct, up-to-date and unbiased?
• What does this information mean in terms of the available options?

3. Generate Potential Solutions

When generating potential solutions it can be a good idea to have a mixture of ‘right brain’ and ‘left brain’ thinkers. In other words, some people who think laterally and some who think logically. This provides a balance in terms of generating the widest possible variety of solutions while also being realistic about what can be achieved. There are many tools and techniques which can help produce solutions, including thinking about the problem from a number of different perspectives, and brainstorming, where a team or individual write as many possibilities as they can think of to encourage lateral thinking and generate a broad range of potential solutions.

4. Select Best Solution

When selecting the best solution, consider:

• Is this a long-term solution, or a ‘quick fix’?
• Is the solution achievable in terms of available resources and time?
• Are there any risks associated with the chosen solution?
• Could the solution, in itself, lead to other problems?

This stage in particular demonstrates why problem-solving and decision-making are so closely related.

5. Take Action

In order to implement the chosen solution effectively, consider the following:

• What will the situation look like when the problem is resolved?
• What needs to be done to implement the solution? Are there systems or processes that need to be adjusted?
• What will be the success indicators?
• What are the timescales for the implementation? Does the scale of the problem/implementation require a project plan?
• Who is responsible?

Once the answers to all the above questions are written down, they can form the basis of an action plan.

6. Monitor and Review

One of the most important factors in successful problem-solving is continual observation and feedback. Use the success indicators in the action plan to monitor progress on a regular basis. Is everything as expected? Is everything on schedule? Keep an eye on priorities and timelines to prevent them from slipping.

If the indicators are not being met, or if timescales are slipping, consider what can be done. Was the plan realistic? If so, are sufficient resources being made available? Are these resources targeting the correct part of the plan? Or does the plan need to be amended? Regular review and discussion of the action plan is important so small adjustments can be made on a regular basis to help keep everything on track.

Once all the indicators have been met and the problem has been resolved, consider what steps can now be taken to prevent this type of problem recurring? It may be that the chosen solution already prevents a recurrence, however if an interim or partial solution has been chosen it is important not to lose momentum.

Problems, by their very nature, will not always fit neatly into a structured problem-solving process. This process, therefore, is designed as a framework which can be adapted to individual needs and nature.

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4. Estimate and compare.

5. Solve and check back.

Common Problem-Solving Strategies

1. Act it out.

2. Use a model.

3. Draw a picture.

4. Simplify

5. Make a table. Find a pattern.

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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.)

The 5 Steps of Problem Solving

Problem solving is a critical skill for success in business – in fact it’s often what you are hired and paid to do. This article explains the five problem solving steps and provides strategies on how to execute each one.

Defining Problem Solving

Before we talk about the stages of problem solving, it’s important to have a definition of what it is. Let’s look at the two roots of problem solving — problems and solutions.

Problem – a state of desire for reaching a definite goal from a present condition [1] Solution – the management of a problem in a way that successfully meets the goals set for treating it

[1] Problem solving on Wikipedia

One important call-out is the importance of having a goal. As defined above, the solution may not completely solve problem, but it does meet the goals you establish for treating it–you may not be able to completely resolve the problem (end world hunger), but you can have a goal to help it (reduce the number of starving children by 10%).

The Five Steps of Problem Solving

With that understanding of problem solving, let’s talk about the steps that can get you there. The five problem solving steps are shown in the chart below:

However this chart as is a little misleading. Not all problems follow these steps linearly, especially for very challenging problems. Instead, you’ll likely move back and forth between the steps as you continue to work on the problem, as shown below:

Let’s explore of these steps in more detail, understanding what it is and the inputs and outputs of each phase.

1. Define the Problem

aka What are you trying to solve? In addition to getting clear on what the problem is, defining the problem also establishes a goal for what you want to achieve.

Input:  something is wrong or something could be improved. Output: a clear definition of the opportunity and a goal for fixing it.

2. Brainstorm Ideas

aka What are some ways to solve the problem? The goal is to create a list of possible solutions to choose from. The harder the problem, the more solutions you may need.

Input: a goal; research of the problem and possible solutions; imagination. Output: pick-list of possible solutions that would achieve the stated goal.

3. Decide on a Solution

aka What are you going to do? The ideal solution is effective (it will meet the goal), efficient (is affordable), and has the fewest side effects (limited consequences from implementation).

Input:  pick-list of possible solutions; decision-making criteria. Output: decision of what solution you will implement.

4. Implement the Solution

aka What are you doing? The implementation of a solution requires planning and execution. It’s often iterative, where the focus should be on short implementation cycles with testing and feedback, not trying to get it “perfect” the first time.

Input:  decision; planning; hard work. Output:  resolution to the problem.

5. Review the Results

aka What did you do? To know you successfully solved the problem, it’s important to review what worked, what didn’t and what impact the solution had. It also helps you improve long-term problem solving skills and keeps you from re-inventing the wheel.

Input:  resolutions; results of the implementation. Output: insights; case-studies; bullets on your resume.

Improving Problem Solving Skills

Once you understand the five steps of problem solving, you can build your skill level in each one. Often we’re naturally good at a couple of the phases and not as naturally good at others. Some people are great at generating ideas but struggle implementing them. Other people have great execution skills but can’t make decisions on which solutions to use. Knowing the different problem solving steps allows you to work on your weak areas, or team-up with someone who’s strengths complement yours.

Want to improve your problem solving skills? Want to perfect the art of problem solving?  Check out our training programs or try these 20 problem solving activities to improve creativity .

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22 thoughts on “The 5 Steps of Problem Solving”

very helpful and informative training

Thank you for the information

YOU ARE AFOOL

I’m writing my 7th edition of Effective Security Management. I would like to use your circular graphic illustration in a new chapter on problem solving. You’re welcome to phone me at — with attribution.

Sure thing, shoot us an email at [email protected] .

i love your presentation. It’s very clear. I think I would use it in teaching my class problem solving procedures. Thank you

It is well defined steps, thank you.

these step can you email them to me so I can print them out these steps are very helpful

I like the content of this article, it is really helpful. I would like to know much on how PAID process (i.e. Problem statement, Analyze the problem, Identify likely causes, and Define the actual causes) works in Problem Solving.

very useful information on problem solving process.Thank you for the update.

Pingback: Let’s Look at Work Is Working with the Environment | #EnviroSociety

It makes sense that a business would want to have an effective problem solving strategy. Things could get bad if they can’t find solutions! I think one of the most important things about problem solving is communication.

Well in our school teacher teach us –

1) problem ldentification 2) structuring the problem 3) looking for possible solutions 4) lmplementation 5) monitoring or seeking feedback 6) decision making

Pleace write about it …

I teach Professional communication (Speech) and I find the 5 steps to problem solving as described here the best method. Your teacher actually uses 4 steps. The Feedback and decision making are follow up to the actual implementation and solving of the problem.

i know the steps of doing some guideline for problem solving

steps are very useful to solve my problem

The steps given are very effective. Thank you for the wonderful presentation of the cycle/steps/procedure and their connections.

I like the steps for problem solving

It is very useful for solving difficult problem i would reccomend it to a friend

this is very interesting because once u have learned you will always differentiate the right from the wrong.

I like the contents of the problem solving steps. informative.

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The Five-Step Problem-Solving Process

Sometimes when you’re faced with a complex problem, it’s best to pause and take a step back. A break from…

Sometimes when you’re faced with a complex problem, it’s best to pause and take a step back. A break from routine will help you think creatively and objectively. Doing too much at the same time increases the chances of burnout.

Solving problems is easier when you align your thoughts with your actions. If you’re in multiple places at once mentally, you’re more likely to get overwhelmed under pressure. So, a problem-solving process follows specific steps to make it approachable and straightforward. This includes breaking down complex problems, understanding what you want to achieve, and allocating responsibilities to different people to ease some of the pressure.

The problem-solving process will help you measure your progress against factors like budget, timelines and deliverables. The point is to get the key stakeholders on the same page about the ‘what’, ‘why’ and ‘how’ of the process. ( Xanax ) Let’s discuss the five-step problem-solving process that you can adopt.

Problems at a workplace need not necessarily be situations that have a negative impact, such as a product failure or a change in government policy. Making a decision to alter the way your team works may also be a problem. Launching new products, technological upgrades, customer feedback collection exercises—all of these are also “problems” that need to be “solved”.

Here are the steps of a problem-solving process:

1. Defining the Problem

The first step in the process is often overlooked. To define the problem is to understand what it is that you’re solving for. This is also where you outline and write down your purpose—what you want to achieve and why. Making sure you know what the problem is can make it easier to follow up with the remaining steps. This will also help you identify which part of the problem needs more attention than others.

2. Analyzing the Problem

Analyze why the problem occurred and go deeper to understand the existing situation.  If it’s a product that has malfunctioned, assess factors like raw material, assembly line, and people involved to identify the problem areas. This will help you figure out if the problem will persist or recur. You can measure the solution against existing factors to assess its future viability.

3. Weighing the Options

Once you’ve figured out what the problem is and why it occurred, you can move on to generating multiple options as solutions. You can combine your existing knowledge with research and data to come up with viable and effective solutions. Thinking objectively and getting inputs from those involved in the process will broaden your perspective of the problem. You’ll be able to come up with better options if you’re open to ideas other than your own.

4. Implementing The Best Solution

Implementation will depend on the type of data at hand and other variables. Consider the big picture when you’re selecting the best option. Look at factors like how the solution will impact your budget, how soon you can implement it, and whether it can withstand setbacks or failures. If you need to make any tweaks or upgrades, make them happen in this stage.

5. Monitoring Progress

The problem-solving process doesn’t end at implementation. It requires constant monitoring to watch out for recurrences and relapses. It’s possible that something doesn’t work out as expected on implementation. To ensure the process functions smoothly, you can make changes as soon as you catch a miscalculation. Always stay on top of things by monitoring how far you’ve come and how much farther you have to go.

You can learn to solve any problem—big or small—with experience and patience. Adopt an impartial and analytical approach that has room for multiple perspectives. In the workplace, you’re often faced with situations like an unexpected system failure or a key employee quitting in the middle of a crucial project.

Problem-solving skills will help you face these situations head-on. Harappa Education’s Structuring Problems course will show you how to classify and categorize problems to discover effective solutions. Equipping yourself with the right knowledge will help you navigate work-related problems in a calm and competent manner.

Explore topics such as  Problem Solving , the  PICK Chart ,  How to Solve Problems  & the  Barriers to Problem Solving  from our Harappa Diaries blog section and develop your skills.

Math Interventions

• Introduction
• Subitizing Interventions
• Counting Interventions: Whole Numbers Less Than 30
• Counting Interventions: Whole Numbers Greater Than 30 (Place Value)
• Counting Interventions: Fractions
• Counting Interventions: Decimals
• Composing and Decomposing Numbers Interventions
• Rounding Interventions
• Number Sense Lesson Plans
• Addition and Subtraction Facts
• Multiplication and Division Facts
• Computational Fluency Lesson Plans
• Understanding the Problem Interventions
• Planning and Executing a Solution Interventions
• Monitoring Progress & Reflecting on a Solution Interventions
• Problem-Solving Process Interventions

Problem-Solving Process

Response to error: using the problem-solving process, feedback during the lesson, strategies to try after the lesson.

• Problem-Solving Lesson Plans
• Identifying Essential Variables Interventions
• Direct Models Interventions
• Counting On/Back Interventions
• Deriving Interventions
• Interpreting the Results Interventions
• Mathematical Modeling Lesson Plans
• Math Rules and Concepts Interventions
• Math Rules and Concepts Lesson Plans

A student who has difficulty understanding the problem, planning and executing a solution , self-monitoring progress toward a goal, and evaluating a solution will benefit from intervention around the problem-solving process. The following interventions  support  students  in internalizing this process from start to finish. This page includes intervention strategies that you can use to support your students in this area. Remember, if you're teaching a full process from start to finish, you probably want to use the Self-Regulated Strategy Development approach, which spreads explicit instruction of a full process across a series of intervention lessons.  As you read, consider which of these interventions best aligns with your student's strengths and needs in the whole-learner domains.

Self-Regulated Strategy Development 

Self-Regulated Strategy Development (or SRSD) is one way to teach the problem-solving process. The SRSD model "requires teachers to explicitly teach students the use of the strategy, to model the strategy, to cue students to use the strategy, and to scaffold instruction to gradually allow the student to become an independent strategy user." (Reid, Leinemann, & Hagaman, 2013). The steps of teaching SRSD are slightly different from the steps of explicit instruction because, in SRSD, each step must be mastered before the next one is started. For example, you might spend an entire lesson on Developing Background Knowledge before moving on to Discuss It (see below). The longterm goal of SRSD is for students to be able carry out the strategy independently, and so time is dedicated to teaching each step of the strategy in such a manner as enables students to internalize the material. 

Teaching SRSD model requires six steps:

• Develop Background Knowledge. Define the key ideas that students need to know in order to apply the strategy.
• Discuss It. Tell the student what the strategy is called, and describe each step.
• Model It. Use a think-aloud to demonstrate the strategy.
• Memorize It . Internalize strategy.
• Support It. Gradually release responsibility to students.
• Independent performance. Give students opportunities to practice strategy without support.

SRSD Explicit Instruction Six-Step Model: 

To support your students' ability to apply SRSD, you should start by explicitly teaching the six-step model. Keep in mind that this type of explicit instruction may take place over a number of days. 

Step 1: Set the Context for Student Learning and Develop Background Knowledge.  

• Introduce Word Problem Mnemonics, and discuss the use of the mnemonic: "Today you will be learning a new trick to help you solve problems. This strategy is called CUBES." (Teacher gets out chart paper and markers and writes down C, U , B, E, and S vertically.) "CUBES is a self-regulated strategy, which means that you will learn to memorize the strategy and use it without my support. Let's go through each step of CUBES and see how it will help you go through the problem-solving process. First, C-Circle the Numbers" (Teacher write this next to C.) "U - Underline important words." (Teacher writes next to U.)  B- Box the question " (Teache r writes next to B). E- Eliminate unnecessary information. S - Solve and Check. (Teacher writes these terms next to E and S). "Now, what do we need to know when we are doing CUBES?  We need to know which words are important. We also need to eliminate unnecessary information" (Teacher goes on to define these terms.)

Step 2: Discuss It. 

• Discuss the significance and benefits of using CUBES. Discuss and determine goals for using the strategy. At this point, students can examine their past work to set an individual goal: "So, how is a self-regulated strategy going to help us? Well, it gives us an easy way to remember the five steps to solving the problem. How else does it help us?" (Teacher elicits student responses.) "When we are using a SRSD, we ask ourselves questions to make sure we are following the steps. We call these self-statements.  My self-statements are 'What's my first step?' and 'What am I supposed to do now?' I ask myself self-statements so I can make sure that I am using each step of the strategy, and that I don't miss any steps." (Teacher and students discuss benefits of self-statements.)  "Now let's take some time to set goals for using this strategy...." (Teacher and students set goals, such as "students will each have two self-statements they use when employing the CUBE strategy.")

Step 3: Model It.

• The teacher models the strategy using think alouds and self-statements: "Watch as I show you what CUBES looks like when I use it. See if you can notice my self-statements. What am I supposed to do? I'm supposed to to follow the five steps to solve a problem. What is my first step? C. That's right, C. I need to circle the numbers. I'll do that now, and then check that off my CUBE S  list. (Teacher circles numbers). Okay, I'm going to check my CUBES list again. I've already completed C. Now, on to U. I have to Underline important words. (Teacher continues to model the entire CUBES process with 1- 3 problems. The session ends. Teacher starts Model It with new problems on Day 2.)

Step 4: Memorize It . 

• Students memorize the mnemonic and each of the steps of CUBES. The idea is that the students will not be able to implement the strategy if they cannot recall the steps. "Next, we are are going to take some time to memorize each step. What is C?" "Circle the numbers!"What is U?" (Teacher completes this process for all the letters. At this time, students also write the mnemonic down so they can use it as a reference. If they need to, they can come up with a beat or a chant to remember the mnemonic.)

Step 5: Support It.

• In step 5, the teacher gradually releases responsibility to the students. This is the most important stage, especially for struggling readers. In order for students to be able to implement this strategy on their own, they must be supported as needed. Graham, Harris, Mason, and Friedlander (2008), SRSD experts and authors, often tell their teachers, "Please Don't P.E.E. in the Classroom - P ost, E xplain, E xpect. Success with SRSD depends on using all the stages for students who have difficulty with [reading]." SRSD instruction and implementation are only successful when students are given multiple opportunities to practice using their strategy with teacher support before trying it on their own.  "Let's read the next problem and do CUBES together this time..." Teacher follows the steps of gradual release to transfer responsibility to students. The teacher first engages students with guided support. She might read the problem and allow students to complete different parts of the strategy. Then, students might do CUBES in groups. This part of the strategy might take multiple days, until students are effectively completing the strategy by using self-statements. 

Step 6: Independent Practice

• In the final step, students practice using the strategy independently. "Now, you are ready to use CUBES on your own! Remember to use your self-statements, like What do I do next? and What am I supposed to do now? and I'll look at my CUBES sheet to see what I do next. as you employ this strategy!" Teacher circulates and provides support for students who are not yet ready to work independently.  

Activity A: Word Problem Mnemonics

One way to support your student's problem-solving ability is to teach her a mnemonic for a series of steps to take whenever she encounters a story problem. The following brief, developed by the Evidence Based Intervention Network at the University of Missouri, describes this strategy. As you read, consider how each mnemonic breaks down the problem-solving process.

Click here  to read the brief. 

Word Problem Mnemonics in Action

In the video below, Emily Art explicitly models how to use the word mnemonic, CUBES, to teach the problem solving process.

As you watch, consider: How do mnemonics support a student's ability to independently carry out the problem solving process?

Another strategy to use to teach your student the problem-solving process is called Self-Organizing Questions. Gifford (2005) advocates for teaching students a series of questions to ask themselves that will guide them through the problem-solving process. Read through each prompt below and consider its purpose. 

• Getting to Grips:  What are we trying to do?
• Connecting to Prior Knowledge:  Have we done anything like this before?
• Planning:  What do we need?
• Considering Alternative Methods:  Is there another way?
• Monitoring Progress:  How does it look so far?
• Evaluating Solutions:  Does it work?   How can we check? Can we make it better?

  Self-Organizing Questions in Action 

Give the student a problem. Then, go through the six self-organizing questions to guide the student through the problem-solving process. This example refers to the problem below. 

Lamont had 14 pumpkin seeds. He also had 32 apple seeds. He planted 41 of the seeds. How many seeds did Lamont have left?

Teacher: We are going to use the self-organizing questions to solve this problem. Frank, what are we trying to do?

Frank: We are trying to figure out how many seeds Lamont has left, after he plants the pumpkin and apple seeds.

Teacher: Let's think about similar problems we've had in the past. Have we done anything like this before?

Frank: Yes, yesterday, we solved a problem about how many baseball and soccer balls Jamie had. 

Teacher: So, what do we need to do to plan to solve this problem?

Frank: We need to add up the total number of seeds, and then subtract how many he planted.

Teacher: Is there another way to solve this problem?

Frank: We could probably draw it, or use manipulatives to help us. 

Teacher: Okay, go ahead and execute it! How does it look so far?

Frank: It's working for me. I added the types of seeds together, which gave me 46. Then, I subtracted the 41 seeds he planted. That gave me 5 seeds leftover, which seems about right. 

Teacher: How can we check our answer?

Frank: I'll see if I can add it back up. My solution was 5, so I'll add that to 41, which gives me 46. Then, I'll add the number of seeds he had total, which gives me 46! So, it matches!

Activity C: Solve It

If your student has particular struggles with understanding the problem, use Solve It, which is an explicit approach to teaching the problem-solving process, with an emphasis on understanding what the problem is about. The following brief, developed by the Evidence Based Intervention Network at the University of Missouri, describes this strategy. As you read, consider how this approach supports student understanding of problems.

Click  here  to read the brief. 

Solve It in Action Read the sample lesson plan (Montague, 2006) below to see what Solve It looks like in action. For your reference, click here to access a  self-regulation script  for students.

SolveItLesson.pdf

Gifford, S. (2005). Teaching mathematics 3-5: Developing learning in the foundation stage. Berkshire:  McGraw-Hill Education. Graham, S., & Harris, K.R. (2005).  Writing better: Effective strategies for teaching students with learning difficulties.  Baltimore, Maryland: Paul H. Brookes Publishing Co. Hughes, E.M. (2011). Intervention Name: Solve It! Columbia, Mo: The Evidence Based Intervention Network, The University of Missouri. Retrieved from https://education.missouri.edu/ebi/math-acquisition/ Hughes, E.M. & Powell, S. (2011). Intervention Name: Word-Problem Mnemonics. Columbia, Mo: The Evidence Based Intervention Network, The University of Missouri. Retrieved from https://education.missouri.edu/ebi/math-acquisition/ Montague, Marjorie. (2006). Self-regulation strategies for better math performance in middle school. In M. Montague and A. Jistendra (Eds.), Teaching mathematics to middle school students with learning disabilities. New York: The Guilford Press.   Reid, R., Lienemann, T. O., & Hagaman, J. L. (2013). Strategy instruction for students with learning disabilities. New York: The Guilford Press.

Think about the following scenario, which takes place after a teacher has explicitly taught a student to use the problem-solving process. The following example refers to the problem below. 

Lamont had 14 pumpkin seeds. He also had 32 apple seeds. He planted 41 of the seeds. How many seeds did Lamont have left?      Teacher: "Now that you understand the problem, what are you doing to do next?"      Student: "Solve it! 41-32 = 9. He had nine seeds left." 

In such a case, what might you do? 

When you are planning your lessons, you should anticipate that your student will make errors throughout. Here are a series of prompts that you can use to respond to errors. Keep in mind that all students are different, and that students might respond better to some types of feedback than to others.

If your student struggles to meet your objective, there are various techniques that you might try in order to adjust the activity so as best to meet your student's needs. 

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