example of polya's problem solving techniques

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Polya’s Problem-Solving Process

Emma Moore, Teaching Excellence Program Master Teacher 

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

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

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

Understanding Polya's Problem-Solving Process

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

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

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

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

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

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

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

Step 1: Understanding the Problem

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

Figure 4: Example prompt for Step 1.

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

Student: I just don’t get it.

Teacher: What part don’t you get?

Student: All of it!

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

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

Step 2: Devising a Plan

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

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

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

Figure 5: Example prompt for Step 2.

Step 3: Try

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

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

Figure 6: Example prompt for Step 3.

Step 4. Re-visiting the solution

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

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

Figure 7: Class display showing our questions.

  Figure 8: Student samples from the task.

Impact and Benefits:

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

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

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

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

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

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

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

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

References:

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

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

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

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

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

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

Intermediate Algebra Tutorial 8

• Use Polya's four step process to solve word problems involving numbers, percents, rectangles, supplementary angles, complementary angles, consecutive integers, and breaking even. 

Whether you like it or not, whether you are going to be a mother, father, teacher, computer programmer, scientist, researcher, business owner, coach, mathematician, manager, doctor, lawyer, banker (the list can go on and on),  problem solving is everywhere.  Some people think that you either can do it or you can't.  Contrary to that belief, it can be a learned trade.  Even the best athletes and musicians had some coaching along the way and lots of practice.  That's what it also takes to be good at problem solving.

George Polya , known as the father of modern problem solving, did extensive studies and wrote numerous mathematical papers and three books about problem solving.  I'm going to show you his method of problem solving to help step you through these problems.

If you follow these steps, it will help you become more successful in the world of problem solving.

Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:

Step 1: Understand the problem.  

Step 2:   Devise a plan (translate).  

Step 3:   Carry out the plan (solve).  

Step 4:   Look back (check and interpret).  

Just read and translate it left to right to set up your equation

Since we are looking for a number, we will let 

x = a number

*Get all the x terms on one side

*Inv. of sub. 2 is add 2  

FINAL ANSWER:  The number is 6.

We are looking for two numbers, and since we can write the one number in terms of another number, we will let

x = another number 

ne number is 3 less than another number:

x - 3 = one number

*Inv. of sub 3 is add 3

*Inv. of mult. 2 is div. 2  

FINAL ANSWER:  One number is 90. Another number is 87.

When you are wanting to find the percentage of some number, remember that ‘of ’ represents multiplication - so you would multiply the percent (in decimal form) times the number you are taking the percent of.

We are looking for a number that is 45% of 125,  we will let

x = the value we are looking for

FINAL ANSWER:  The number is 56.25.

We are looking for how many students passed the last math test,  we will let

x = number of students 

FINAL ANSWER: 21 students passed the last math test.

We are looking for the price of the tv before they added the tax,  we will let

x = price of the tv before tax was added. 

*Inv of mult. 1.0825 is div. by 1.0825

FINAL ANSWER: The original price is $500.

Perimeter of a Rectangle = 2(length) + 2(width)

We are looking for the length and width of the rectangle.  Since length can be written in terms of width, we will let

length is 1 inch more than 3 times the width:

1 + 3 w = length

*Inv. of add. 2 is sub. 2

*Inv. of mult. by 8 is div. by 8  

FINAL ANSWER: Width is 3 inches. Length is 10 inches.

Complimentary angles sum up to be 90 degrees.

We are already given in the figure that

x = one angle

5 x = other angle

*Inv. of mult. by 6 is div. by 6

FINAL ANSWER: The two angles are 30 degrees and 150 degrees.

If we let x represent the first integer, how would we represent the second consecutive integer in terms of x ?  Well if we look at 5, 6, and 7 - note that 6 is one more than 5, the first integer. 

In general, we could represent the second consecutive integer by x + 1 .  And what about the third consecutive integer. 

Well, note how 7 is 2 more than 5.  In general, we could represent the third consecutive integer as x + 2.

Consecutive EVEN integers are even integers that follow one another in order.     

If we let x represent the first EVEN integer, how would we represent the second consecutive even integer in terms of x ?   Note that 6 is two more than 4, the first even integer. 

In general, we could represent the second consecutive EVEN integer by x + 2 . 

And what about the third consecutive even integer?  Well, note how 8 is 4 more than 4.  In general, we could represent the third consecutive EVEN integer as x + 4.

Consecutive ODD integers are odd integers that follow one another in order.     

If we let x represent the first ODD integer, how would we represent the second consecutive odd integer in terms of x ?   Note that 7 is two more than 5, the first odd integer. 

In general, we could represent the second consecutive ODD integer by x + 2.

And what about the third consecutive odd integer?  Well, note how 9 is 4 more than 5.  In general, we could represent the third consecutive ODD integer as x + 4.  

Note that a common misconception is that because we want an odd number that we should not be adding a 2 which is an even number.  Keep in mind that x is representing an ODD number and that the next odd number is 2 away, just like 7 is 2 away form 5, so we need to add 2 to the first odd number to get to the second consecutive odd number.

We are looking for 3 consecutive integers, we will let

x = 1st consecutive integer

x + 1 = 2nd consecutive integer

x + 2  = 3rd consecutive integer

*Inv. of mult. by 3 is div. by 3  

FINAL ANSWER: The three consecutive integers are 85, 86, and 87.

We are looking for 3 EVEN consecutive integers, we will let

x = 1st consecutive even integer

x + 2 = 2nd consecutive even integer

x + 4  = 3rd  consecutive even integer

*Inv. of add. 10 is sub. 10  

FINAL ANSWER: The ages of the three sisters are 4, 6, and 8.

In the revenue equation, R is the amount of money the manufacturer makes on a product.

If a manufacturer wants to know how many items must be sold to break even, that can be found by setting the cost equal to the revenue.

We are looking for the number of cd’s needed to be sold to break even, we will let

*Inv. of mult. by 10 is div. by 10

FINAL ANSWER: 5 cd’s.

To get the most out of these, you should work the problem out on your own and then check your answer by clicking on the link for the answer/discussion for that  problem .  At the link you will find the answer as well as any steps that went into finding that answer.

  Practice Problems 1a - 1g: Solve the word problem.

(answer/discussion to 1e)

http://www.purplemath.com/modules/translat.htm This webpage gives you the basics of problem solving and helps you with translating English into math.

http://www.purplemath.com/modules/numbprob.htm This webpage helps you with numeric and consecutive integer problems.

http://www.purplemath.com/modules/percntof.htm This webpage helps you with percent problems.

http://www.math.com/school/subject2/lessons/S2U1L3DP.html This website helps you with the basics of writing equations.

http://www.purplemath.com/modules/ageprobs.htm This webpage goes through examples of age problems,  which are like the  numeric problems found on this page.

Go to Get Help Outside the Classroom found in Tutorial 1: How to Succeed in a Math Class for some more suggestions.

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Polya’s problem-solving process: finding unknowns elementary & middle school, by: jeff todd.

In this article, we'll explore how a focus on finding “unknowns” in math will lead to active problem-solving strategies for Kindergarten to Grade 8 classrooms. Through the lens of George Polya and his four-step problem-solving heuristic, I will discuss how you can apply the concept of finding unknowns to your classroom. Plus, download my Finding Unknowns in Elementary and Middle School Math Classes Tip Sheet .

It is unfortunate that in the United States mathematics has a reputation for being dry and uninteresting. I hear this more from adults than I do from children—in fact, I find that children are naturally curious about how math works and how it relates to the world around them. It is from adults that they get the idea that math is dry, boring, and unrelated to their lives. Despite what children may or may not hear about math, I focus on making instruction exciting and showing my students that math applicable to their lives.

Problem solving is a fundamental means of developing students' mathematical knowledge and it also shows them that math concepts apply to real-world concepts.

Problem solving is one way I show my students that math relates to their lives! Problem solving is a fundamental means of developing students' mathematical knowledge and it also shows them that math concepts apply to real-world concepts.

Who Is George Polya?

George Polya was a European-born scholar and mathematician who moved to the U.S in 1940, to work at Stanford University. When considering the his classroom experience of teaching mathematics, he noticed that students were not presented with a view of mathematics that excited and energized them. I know that I have felt this way many times in my teaching career and have often asked: How can I make this more engaging and yet still maintain rigor?

Polya suggested that math should be presented in the light of being able to solve problems. His 1944 book,  How to Solve It  contains his famous four-step problem solving heuristic. Polya suggests that by presenting mathematical thinking as a way to find “unknowns,” it becomes more engaging for students.

He even goes as far as to say that his general four-step problem-solving heuristic can be applied to any field of human endeavor—to any opportunity where a problem exists.

Polya suggested that math should be presented in the light of being able to solve problems...that by presenting mathematical thinking as a way to find “unknowns,” it becomes more engaging for students.

Polya specifically wrote about problem-solving at the high school mathematics level. For those of us teaching students in the elementary and middle school levels, finding ways to apply Polya’s problem-solving process as he intended forces us to rethink the way we teach.

Particularly in the lower grade levels, finding “unknowns” can be relegated to prealgebra and algebra courses in the later grades. Nonetheless, today’s standards call for algebra and algebraic thinking at early grade levels. The  download  for today’s post presents one way you can find unknowns at each grade level.

Presenting Mathematics  As A Way To Find "Unknowns" In Real-Life Situations

I would like to share a conversation I had recently with my friend Stu. I have been spending my summers volunteering for a charitable organization in Central America that provides medical services for the poor, runs ESL classes, and operates a Pre-K to Grade 6 school. We were talking about the kind of professional development that I might provide the teachers, and he was intrigued by the thought that we could connect mathematical topics to real life. We specifically talked about the fact that he remembers little or nothing about how to find the area of a figure and never learned in school why it might be important to know about area. Math was presented to him as a set of rules and procedures rather than as a way to find unknowns in real-life situations.

That’s what I am talking about here, and it’s what I believe Polya was talking about. How can we create classrooms where students are able to use their mathematical knowledge to solve problems, whether real-life or purely mathematical?

As Polya noted, there are two ways that mathematics can be presented, either as deductive system of rules and procedures or as an inductive method of making mathematics. Both ways of thinking about mathematics have endured through the centuries, but at least in American education, there has been an emphasis on a procedural approach to math. Polya noticed this in the 1940s, and I think that although we have made progress, there is still an over-emphasis on skill and procedure at the expense of problem-solving and application.

I recently reread Polya’s book. I can’t say that it is an “easy” read, but I would say that it was valuable for me to revisit his own words in order to be sure I understood what he was advocating. As a result, I made the following outline of his problem-solving process and the questions he suggests we use with students.

Polya's Problem-Solving Process

1. understand the problem, and desiring the solution .

• Restate the problem
• Identify the principal parts of the problem
• Essential questions
• What is unknown?
• What data are available?
• What is the condition?

2. Devising a Problem-Solving Plan 

• Look at the unknown and try to think of a familiar problem having the same or similar unknown
• Here is a problem related to yours and solved before. Can you use it?
• Can you restate the problem?
• Did you use all the data?
• Did you use the whole condition?

3. Carrying Out the Problem-Solving Plan 

• Can you see that each step is correct?
• Can you prove that each step is correct?

4. Looking Back

• Can you check the result?
• Can you check the argument?
• Can you derive the result differently?
• Can you see the result in a glance?
• Can you use the result, or the method, for some other problem?

Polya's Suggestions For Helping Students Solve Problems

I also found four suggestions from Polya about what teachers can do to help students solve problems:

Suggestion One In order for students to understand the problem, the teacher must focus on fostering in students the desire to find a solution. Absent this motivation, it will always be a fight to get students to solve problems when they are not sure what to do.

Suggestion Two A second key feature of this first phase of problem-solving is giving students strategies forgetting acquainted with problems.

Suggestion Three Another suggestion is that teachers should help students learn strategies to be able to work toward a better understanding of any problem through experimentation.

Suggestion Four Finally, when students are not sure how to solve a problem, they need strategies to “hunt for the helpful idea.”

Whether you are thinking of problem-solving in a traditional sense (solving computational problems and geometric proofs, as illustrated in Polya’s book) or you are thinking of the kind of problem-solving students can do through STEAM activities, I can’t help but hear echoes of Polya in Standard for Math Practice 1: Make sense of problems and persevere in solving them.

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

In Conclusion

We all know we should be fostering students’ problem-solving ability in our math classes. Polya’s focus on “finding unknowns” in math has wide applicability to problems whether they are purely mathematical or more general.

Grab my  download  and start  applying Polya’s Four-Step Problem-Solving Process in the lower grades!

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Polya theory to improve problem-solving skills

K R Daulay 1 and I Ruhaimah 2

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1188 , The Sixth Seminar Nasional Pendidikan Matematika Universitas Ahmad Dahlan 2018 3 November 2018, Yogyakarta, Indonesia Citation K R Daulay and I Ruhaimah 2019 J. Phys.: Conf. Ser. 1188 012070 DOI 10.1088/1742-6596/1188/1/012070

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1 Universitas Negeri Medan, Jalan Willem Iskandar Pasar V, Medan Estate, Sumatera Utara, Indonesia

2 SMP Muhammadiyah 8 Medan, Jl. Utama No.170 Kota Matsum II, Medan Area, Kota Medan, Sumatera Utara 20215 Indonesia

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This research is to improve problem-solving skills in SMP Muhammadiyah 8 Medan students through Polya learning theory in the material of linear equation systems in two-variable. This research method is Classroom Action Research. The research subjects were class VIII SMP Muhammadiyah 8 Medan totalling 29 students. The object of research is the ability to solve mathematical problems — data from research results obtained from observation and test results. The results showed that the use of Polya learning theory could improve students' mathematical problem-solving abilities. In the pre-cycle, there was 10.34% (3 students) of the 29 students who achieved the passing grade. The test results in cycle 1 showed there was 51.72% (15 students) of the number of students who reached passing grade, whereas in cycle 2 there was 75.86% (22 students) of the number of students who reached passing grade. The average value before the cycle is 54.50, while at the end of cycle 1 the average value of the test is 64.60, and at the end of the second cycle is 85.72. Then it can be concluded that the objectives of the research carried out have experienced success. In other words, the application of Polya learning theory can improve students' mathematical problem-solving abilities.

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2.1: George Polya's Four Step Problem Solving Process

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Step 1: Understand the Problem

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

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

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What is Problem Solving? Process, Techniques, Examples

Home Blog others What is Problem Solving? Process, Techniques, Examples

Whether tackling a technical issue at work or finding our way around a roadblock unnoticed by Google Maps, problem-solving is a daily occurrence for most people. But how prepared are you to overcome life's challenges? Do you rely on a structured process to ensure successful outcomes, or do you navigate through problems impulsively? 

Here's the crux: the strength of your problem-solving skills significantly impacts the ease and success of your life, both professionally and personally. Practical problem-solving is a valuable career and life skill. You're in the right place if you're eager to enhance your problem-solving abilities efficiently. 

In this blog post, I will delve into what is problem solving the steps, techniques, and exercises of the problem-solving process. Whether seeking to troubleshoot technical issues or navigate life's complexities, mastering organized problem-solving can elevate your capabilities and lead to more favorable outcomes. 

What is Problem Solving? And Its Importance

First, let me help you understand what is problem solving. Problem-solving is a comprehensive process involving identifying issues, prioritizing based on urgency and severity, analyzing root causes, gathering pertinent Information, devising and assessing solutions, making informed decisions, and planning and executing implementation strategies. 

This skill set also encompasses critical thinking, effective communication, active listening, creativity, research, data analysis, risk assessment, continuous learning, and decision-making abilities. Effective problem-solving strategies mitigate potential losses or damages and enhance self-confidence and reputation. Problem-solving is essential in personal and professional contexts as it allows individuals and teams to navigate obstacles, make informed decisions, and drive progress. 

Importance: 

• Enhances Decision-Making: Effective problem solving leads to better decision-making by evaluating various options and selecting the most suitable solution. 
• Promotes Innovation: Problem solving encourages innovation and creativity as individuals seek new approaches to tackle challenges. 
• Improves Efficiency: By resolving issues efficiently, problem solving helps streamline processes and optimize resource allocation. 
• Builds Resilience: Successfully overcoming obstacles builds confidence and resilience, enabling  
• individuals and teams to tackle future challenges with greater confidence.  

Problem-solving Process 

Now that we have a clear understanding of the problem solving definition as to what is problem solving let us now navigate the problem solving process. Effective problem-solving is a valuable skill sought after by employers in various fields. Here's a breakdown of a common problem-solving process, presented in a pointwise manner: 

1. Identifying the Problem 

The first step in the problem-solving process is clearly defining the issue. This involves gathering relevant Information, observing patterns or trends, and understanding the impact of the problem on stakeholders. 

2. Analyzing the Situation 

Once the problem is identified, it's essential to analyze its root causes and contributing factors. This may involve conducting research, gathering data, and exploring different perspectives to comprehensively understand the situation. 

3. Generating Solutions 

With a clear understanding of the problem solving methods, brainstorming potential solutions is the next step. Encouraging creativity and considering various alternatives can lead to innovative ideas. Evaluating each solution based on feasibility, effectiveness, and alignment with goals and values is crucial. 

4. Evaluating Options 

After generating a list of potential solutions, it's essential to carefully evaluate each option. This involves weighing the pros and cons, considering potential risks and benefits, and assessing the likelihood of success. Consulting with relevant stakeholders or experts can provide valuable insights during this stage. 

5. Selecting the Best Solution 

Based on the evaluation, one or more solutions are the most viable options. It's essential to prioritize solutions that address the root cause of the problem and have the most significant potential for long-term success. Communicating the chosen solution effectively to stakeholders is crucial for garnering support and buy-in. 

6. Implementing the Solution 

Once a solution is selected, it's time to put it into action. This involves developing a detailed action plan, allocating resources, and assigning responsibilities. Effective communication, coordination, and monitoring are essential during the implementation phase to ensure smooth execution and timely resolution of the problem. 

7. Monitoring and Reviewing 

After implementing the solution, it's essential to monitor its progress and evaluate its effectiveness over time. This may involve collecting feedback, analyzing performance metrics, and making adjustments as needed. Continuous monitoring and review allow for ongoing improvement and refinement of the problem-solving process.  

How to Solve Problems in 5 Simple Steps? 

Here's a breakdown of the 5 problem-solving steps for your understanding: 

1. Define the Problem (Understand & Gather Information)  

• Identify the Issue: Clearly understand what the problem is. What isn't working, or what needs improvement? 
• Gather Information: Talk to people involved, collect data, and research relevant details to get a well-rounded picture of the situation. 
• Ask Why? Don't just focus on symptoms. Ask "why" several times to identify the root cause of the problem. 

Example: Let's say customer complaints about slow website loading times have increased. 

2. Brainstorm Solutions (Think Creatively & Be Open-Minded)  

• Think Outside the Box: Don't settle for the first solution that comes to mind. Brainstorm a variety of options, even seemingly unconventional ones. 
• Consider All Angles: Evaluate the problem from different perspectives. What are potential solutions from a technical standpoint? From a user experience point of view? 
• Build on Ideas: Don't shut down ideas prematurely. Encourage others to build upon and refine suggestions collaboratively. 

Example: Potential solutions for slow website loading times could include optimizing images, upgrading server capacity, or implementing a content delivery network (CDN). 

3. Evaluate & Choose a Solution (Consider Feasibility & Impact)  

• Weigh the Pros & Cons: Analyze the feasibility, resource requirements, and potential risks and benefits of each solution. 
• Align with Goals: Ensure the chosen solution directly addresses the root cause of the problem and aligns with your overall objectives. 
• Prioritize Impact: Choose the solution with the most significant potential to achieve a positive outcome and lasting improvement. 

Example: Upgrading server capacity might be a very effective solution, but it could be expensive. Optimizing images is a more feasible solution that could yield significant improvement. 

4. Implement the Solution (Take Action & Communicate Clearly)  

• Develop a Plan: Create a clear action plan outlining the steps involved in implementing the chosen solution. Assign tasks and set deadlines. 
• Communication is Key: Clearly communicate the plan to everyone involved, including stakeholders and team members. 
• Monitor Progress: Track the implementation process and make adjustments as needed based on the results. 

Example: The website optimization plan might involve tasks like image resizing, code minification, and implementing caching mechanisms. 

5. Evaluate the Outcome (Learn & Adapt)  

• Measure Success: Assess whether the implemented solution effectively resolved the problem. Did it meet your goals? 
• Lessons Learned: Reflect on what worked well and what could be improved during the problem-solving process. 
• Continuous Improvement: Use this experience to refine your problem-solving approach and enhance your skills for future challenges. Enroll in free online certification courses for professional development and skill enhancement. 

Example: After website optimization, monitor website loading times and customer feedback to see if the issue has been resolved. If not, repeat the process, considering new solutions based on the learnings from this attempt. 

Remember, problem-solving is an iterative process. Be prepared to adapt your approach as you gather more Information and evaluate the effectiveness of your solutions.  

Essential Things to Consider in Each of the Problem-solving Steps

Creative problem solving requires careful consideration at each stage. Here are vital things to focus on: 

1. Identifying & Defining the Problem 

• Gather Information: Consult stakeholders, review data, and gain insights from various perspectives. 
• Identify Root Cause: Address the underlying reason, not just symptoms. 
• Define Scope: Clearly outline the problem's boundaries to maintain focus. 

2. Analyzing the Problem 

• Consider Multiple Perspectives: Explore diverse angles to uncover potential factors. 
• Brainstorm Freely: Foster creativity without judgment to generate innovative ideas. 
• Analyze Impact: Evaluate the severity and consequences of the problem if left unresolved. 
• Think Creatively: Explore unconventional solutions beyond initial ideas. 
• Consider Feasibility: Assess the practicality and resource requirements of each option. 
• Identify Potential Risks & Benefits: Weigh the pros and cons to select the most balanced approach. 

4. Evaluating and Selecting a Solution 

• Align with Goals: Ensure the chosen solution addresses the core issue and aligns with objectives. 
• Consider Long-Term Impact: Choose solutions with lasting benefits beyond immediate results. 
• Team Input: Involve team members to gain diverse perspectives during evaluation. 

5. Implementing the Solution  

• Develop a Clear Plan: Outline implementation steps with clear timelines and responsibilities. 
• Communication is Key: Ensure all stakeholders understand the plan to facilitate smooth execution. 
• Monitor Progress: Track implementation and adjust as needed based on results. 

6. Evaluating the Outcome  

• Measure Effectiveness: Assess if the solution effectively resolves the problem or needs refinement. 
• Lessons Learned: Identify successes and areas for improvement to enhance future problem-solving efforts. 

Problem Solving Examples

Let us look at problem solving example scenarios in a typical workplace: , example 1: project deadline challenge .

• Situation: You're a project manager leading a team that is developing a new marketing campaign website. The launch date is approaching, but a critical developer is unexpectedly out sick for a week. 
• Action: You immediately assess the workload and delegate tasks among the remaining team members. You identify an opportunity to streamline a design element, reducing development time. You also reach out to a freelancer with a proven track record to fill in for the missing developer on specific tasks. 
• Result: The team successfully launches the website on time and within budget. The streamlined design element is praised by stakeholders for its user-friendliness. 
• Highlight: This example showcases your problem-solving skills, leadership, adaptability, and ability to manage resources effectively under pressure. 

Example 2: Client Communication Breakdown 

• Situation: You're a Customer Service Representative for an e-commerce company. A regular customer expresses extreme dissatisfaction with a recent purchase due to a malfunctioning product and a negative experience with a previous representative. 
• Action: You actively listen to the customer's concerns, apologizing for the inconvenience. You then troubleshoot the product issue and offer a solution (replacement or refund). Additionally, you acknowledge the previous negative experience and offer to ensure better communication going forward. 
• Result: The customer is satisfied with the resolution and expresses appreciation for your attentiveness and problem-solving approach. They remain a loyal customer of the company. 
• Highlight: This example demonstrates your active listening skills, empathy, ability to de-escalate situations, and commitment to customer satisfaction. 

By following these examples of problem-solving skills, you can effectively tackle challenges and achieve successful outcomes. Also, explore KnowledgeHut’ s best online courses for further skill enhancement. 

Problem Solving Techniques

Effective problem-solving techniques are essential for tackling challenges and achieving desired outcomes. Here are some problem solving tools and techniques commonly used in problem-solving: 

• Brainstorming : Encourages the generation of a wide range of ideas and solutions in a non-judgmental environment. This technique promotes creativity and can uncover innovative approaches to problems. 
• Root Cause Analysis : Focuses on identifying the underlying causes of a problem rather than just addressing its symptoms. By pinpointing root causes, solutions can be targeted more effectively to prevent recurrence. 
• Fishbone Diagram (Ishikawa Diagram): Provides a visual representation of the various factors contributing to a problem, categorized into branches such as people, process, equipment, environment, and management. This technique helps analyze complex issues and identify potential causes. 
• SWOT Analysis : Evaluates the strengths, weaknesses, opportunities, and threats associated with a problem or situation. This technique helps assess the internal and external factors influencing the problem and guides decision-making. 
• Pareto Analysis: Focuses on identifying and prioritizing the most significant causes contributing to a problem. By allocating resources to address the vital few rather than the trivial many, this technique maximizes impact and efficiency. 
• 5 Whys : Involves asking "why" repeatedly to trace the root cause of a problem. This iterative questioning technique helps uncover more profound layers of causation beyond surface-level symptoms. 
• Decision Matrix Analysis: Helps evaluate multiple options by systematically comparing their pros and cons against predetermined criteria. This technique facilitates objective decision-making by considering various factors and their relative importance. 

By incorporating these problem-solving techniques in the workplace, you can approach problems systematically, generate creative solutions, and develop a well-rounded plan for achieving success.  

Conquering challenges is a key to professional success, and practical problem-solving equips you to do just that. By following a structured approach, you can transform from a bystander to a solution-oriented individual. This involves gathering Information to clearly define the problem and identify its root cause. Analyzing the situation from various angles and brainstorming freely unlock creative solutions. Evaluating potential solutions ensures you choose the one that aligns with your goals and is feasible to implement. Clear communication and a well-defined plan are crucial for successful execution. Finally, reflecting on the outcome allows you to learn and continuously improve your problem-solving skills, making you an invaluable asset in any environment. 

Frequently Asked Questions (FAQs)

The best method involves identifying the problem, brainstorming solutions, evaluating options, implementing the chosen solution, and assessing outcomes for improvement.

The principles include defining the problem, generating alternatives, evaluating options, implementing solutions, and reviewing outcomes for continuous improvement.

Different types include analytical problem-solving, creative problem-solving, critical thinking, decision-making, and systematic problem-solving.

The significant elements include understanding the problem, devising a plan, executing the plan, and evaluating the results.

The skills encompass critical thinking, decision-making, and analytical reasoning. These abilities aid in identifying, analyzing, and resolving problems effectively. 

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