The Importance of Problem Solving Strategies

Return to: Kimberly Brooks's Homepage, Problem Solving Strategies in a Math Classroom

Overview

During this unit we will be covering the importance of teaching problem solving skills in the math classroom. We will also be discovering the benefits that students receive that will not only effect their success in the classroom but outside of the classroom solving non-mathematical problems. Finally, we will discuss where students will be using problem solving skills outside of the classroom environment. You will be asked to create a concept map in addition to being asked to read an article and to participate in a short discussion.

Warm-up

For this exercise first read the article | The Role of Problem Solving in High School Mathematics. When you have finished reading the article in the discussion tab of this page please write a response to the question "How do you think you could alter your instruction in order to better incorporate the teaching of problem solving skills in your classroom?" and respond to at least one other post.

Mini-Lecture

Importance of Problem Solving Skills

In math class with almost every problem that is presented there is some sort of method that is followed that places the student at the solution, however, there is not always one single method that leads to the answer. There can be many different solution paths that allow someone to reach the answer to a problem but every person looks at a problem in a different way, which is why some people may choose one method over another. By teaching students this discipline of solving problems the students will be better equipped to reach their goals in the future because they will learn that there are different ways to approach a problem and if the "problem solver" gets stuck they can try to look at the problem from a different angle and attempt a different method to reach a solution.

Another idea that is too often overlooked is that being a problem solver is not an ability it is a a character trait and a mind-set because it takes a person who is motivated intrinsically to go out and solve a problem. However, math teachers have the ability to shape the minds of their students to become problem-

solving minds. Problem solvers often take control of their own learning and persevere when faced with adversity. Everyday a student asks why they are learning something in math class and want to know when they will ever use it again. While there are many concepts that can be applied to math, every concept requires some sort of problem solving which allows the students to learn to think like a problem solver, which is something that can be applied to any aspect of life.

Members of society that lack problem solving skills are not as driven, if they run into an obstacle during the course of obtaining a goal he or she may simply give up rather than try to look at a problem from a different angle or they may not even realize that there could be another way to achieve the goal they believe they have failed to reach. Since people that have a problem solving mindset are conditioned to not give up on a problem they have a better sense of confidence and self-esteem when faced with adversity. This is because they know that there has to be a solution but they simply are not sure what approach will lead them to said solution and they do not become defeated when they cannot find the solution.

Benefits of Learning Problem Solving Skills

The first proven benefit of teaching students problem solving skills is that their achievement, confidence, and skills in mathematics and other curriculums increases. The main reason for this is that problem solving provides students with with ability to look at a situation from different points of view using critical and analytical thinking. By being a more critical thinker students can better foresee outcomes of a situation which allows them to decide what pathway to the desired solution would be most efficient. Another characteristic that is effected by the instruction of problem solving skills is a person's metacognitive skills. Metacognition is most often described as thinking about thinking and because problem solving is a decision making process metacognition plays a large role in the process. Metacognition is so important in the decision making and problem solving process because it allows the "problem solver" to be able to think about a plan of action and then determine if it will be effective or not by analyzing the outcome that will follow, or if the path taken does not lead to the desired solution the "problem solver" can reflect on their decision making process to find where he or she went wrong. Another benefit that students gain from learning problem-solving skills is that they learn how to collaborate and work cooperatively with their peers which will benefit them not only during school but also in sports that they may play, at home, and at current and future jobs. The ability to effectively work in a group or on a team is often a quality that employers look for because a team that works well together will produce better results than a team that does not work well together.

Activity

Please create a concept map showing the relationships between problem solving skills and the important reasons it is to learn them, the benefits students gain from learning them, and where these skills can be applied. This will act as a summary activity and allow participants to analyze the relationships amongst the topics discussed in Unit 2. Follow the concept map style shown below and please submit your concept maps Here.

Sample Map

Your map should follow the general format that is shown before there is no branch minimum please extend each second level branch to at least three third level branches.

References

Charles, R. (2009). The Role of Problem solving in High school Mathematics. Retrieved May 10, 2015, from http://assets.pearsonschool.com/asset_mgr/current/201033/ProblemSolvingResearch.pdf
Frederick, Michelle. "With A Little Help From My Friends: Scaffolding Techniques in Problem Solving." Investigations in Mathematics Learning 7.4 (2014): 21-32. Print.
Talpin, Margaret. "Teaching Values Through A Problem Solving Approach to Mathematics." Math Goodies. Math Goodies. Web. 9 May 2015. .
"Problem Solving Information." NZ Math. New Zealand Ministry of Education. Web. 14 May 2015.
Gok, Tolga. "Students' Achevement, Skill and Confidence in Using Stepwise Problem-Solving Strategies." EURASIA Journal of Mathematics, Science & Technology Education 10.6: 617-24. Print.

Go to: Unit 3