# Introduction to Problem Solving Skills

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## Overview

In this unit we will begin covering the importance of incorporating problem solving strategies into a math classroom. There will be a brief review of the components of a problem solving strategy as well as the importance of these skills and how they benefit students. At the beginning of the unit there will be a brainstorming activity to attempt to activate your prior knowledge from your own brainstorming as well as the responses that the other participants post. At the end of the unit there will be a discussion to summarize your learning and lead into our next unit.

### Brainstorm

The link above will bring you to a page where you can post your prior experiences with problem solving in a Math Classroom, ways that you think you can improve your prior practices, and everyday activities that require problem solving skills.

## Mini-Lecture

### What is a Problem?

A problem is defined by the Oxford-English Dictionary as "A matter or situation regarded as unwelcome or harmful and needing to be dealt with and overcome". and a solution is defined as a means of solving a problem or dealing with a difficult situation. Therefore, problem solving strategies are used to achieve the solution to a given problem.

### What is Problem Solving?

Problem solving is a methodic way of discovering a solution to a given problem. We must remember that there is not always only one method or path to the solution from the problem that is at hand. Problem solving is considered to be one of the most complex intellectual processes and one that children today struggle with. The reason for this struggle has a lot to do with the technological age that we live in; children can have almost any problem solved within seconds by simply "Googleing it" therefore, they see no reason to know how to methodically learn to solve problems.

### Method to Solve a Problem

When solving any problem there are always four steps that are followed. The first step to solving the problem is to to identify and understand the problem, this is typically done by gathering information about the problem. In a math classroom students should be reading the problem, pulling out the important information from a problem, creating a visual model, or determine what information is missing and must be found. The second step is create a plan to solve the problem. In a math classroom students should be working independently or with other students to make estimates and discuss possible strategies and why they may or may not work. The third step is to put the plan created in step two to the test. In a math class this means testing different solution plans, showing all

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work that is done when testing solutions, comparing the problem to similar problems, and checking the solution. The fourth and final step is to reflect on the process that was taken to get from the problem to the solution. In a math class this means to check the work that was done, to justify the solution that was reached, and determine if the steps that were taken were the most efficient. These steps have been tailored to a math classroom however, the generic steps can be used to solve any problem that someone may face, the processes under each step may vary depending on what setting the problem that needs to be solved occurs.

### Problem Solving Strategies

There are a few problem solving strategies that will be discussed in Unit 3. This is just a preview of the strategies that will be discussed:

• SQR
• Frayer Vocabulary Model
• Mnemonics
• Graphic Organizers
• Paraphrasing
• Visualization
• Cooperative Learning

It is important to understand that there is not always one correct way to solve a problem.

### Importance of Teaching Problem Solving Skills

Many times in a mathematics classroom you hear that the most important topics are algebraic concepts, geometry topics, and trigonometry topics, however, the most important concept that encompasses all the previous topics is often overlooked: problem solving. Without knowing how to problem solve being successful in a mathematics classroom would be extremely difficult. Problem solving can be considered applying skills to known concepts in order to reach a solution. Additionally, many types of skills that are used to solve a mathematical problem can be applied to any problem inside and outside of the classroom. This concept will be further discussed in Unit 2.

## Activity

Below is a link to an article titled "The Do's and Dont's of Teaching Problem Solving in Math " that you will be expected to read. Then when you are finished reading the article click the discussion tab at the top of this page. Here we will conduct a discussion covering topics that were discussed in this unit. Some topics to keep in mind are the importance of problem solving skills, any of the problem solving strategies listed above and your experience with them, additional steps taken to solve a problem, etc.. You may also begin to brainstorm other reasons problem solving strategies are important to learn and the positive effects students will see from learning these skills. Please remember to use proper online etiquette and be respectful and formal in your postings and responses to your peers posts. The language used in these posts should be language that would be used in a discussion being conducted in a face-to-face environment.

Go to: Unit 2