About This Chapter
Logical Problem Solving in Mathematics - Chapter Summary
If you are in need of a resource that can help you better understand logical problem solving in mathematics, you've reached the right place. Our lessons provide in-depth analyses of this subject by closely examining connective reasoning, the three-way principle, conditional statements and more. By the end of this chapter, you will be able to do the following:
- Describe logic and critical thinking in mathematics
- Discuss conditional statements in math
- Differentiate between inductive, deductive and connective reasoning
- Explain Polya's Four-Step Problem-Solving Process
- List and describe the mathematical principles for problem solving
- Define the three-way principle of mathematics
- Use estimation to solve math problems
- Solve problems using mathematical models
The lessons in this chapter are available as short videos that average about 8 minutes and feature clickable timelines you can use to skip to key topics. They are also accessible as full transcripts you can read online or print to review offline. With each lesson is a short quiz designed to check your knowledge of its contents. To get a comprehensive review of this chapter, be sure to take our practice exam.
1. Critical Thinking and Logic in Mathematics
Logic has its own unique language and way of defining what is true and false. Watch this video lesson to learn how you can critically think in the language of logic while working with math.
2. Conditional Statements in Math
Sometimes, what is true in the mathematical world of logic is false in the real world. Check out this lesson to learn how to identify conditional statements and how you can differentiate between what is logically true and what is true in reality.
3. Reasoning in Mathematics: Inductive and Deductive Reasoning
Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.
4. Reasoning in Mathematics: Connective Reasoning
Connective reasoning is reasoning that has an operation, or a way to connect two phrases. The five main logic connectives will be reviewed in this lesson.
5. Polya's Four-Step Problem-Solving Process
Problem solving can be a problem. Any problem is solved easier with an action plan. Polya's 4-Step Problem-Solving Process is discussed in this lesson to help students develop an action plan for addressing problems.
6. Mathematical Principles for Problem Solving
Solving problems is not just a simple, straightforward process. There are a few principles that can help you as you approach any problem solving scenarios. This lesson covers those principles with examples.
7. The Three-Way Principle of Mathematics
What methods are there to solve and understand mathematical problems? This lesson will review three methods to understand mathematical problems (verbal, graphical, and by example). Each will be illustrated with examples.
8. Solving Mathematical Problems Using Estimation
Estimating is a method of calculating a result that is close to, but not exactly, the correct answer to a math problem. Why would you ever need to do this? This lesson reviews estimating and answers the question as to why you would do it.
9. Using Mathematical Models to Solve Problems
Mathematical modeling simply refers to the creation of mathematical formulas to represent a real world problem in mathematical terms. This lesson reviews the creation and pitfalls of mathematical models.
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