About This Chapter
Problem Solving & Mathematical Reasoning - Chapter Summary
You can discover new strategies or review ones you already know about how to solve mathematical problems by taking a look at the lessons in this chapter. When you are done, you will be more familiar with the following topics:
- Using the language of logic
- Analyzing truth tables
- How statements and math differ from the real world
- Difference between converse, inverse, contrapositive and counterexamples
- Deductive reasoning vs. inductive reasoning
- Five major logic connectives
- Method for solving problems
- Examples of how to use principles for problem solving
- How to use verbal, graphical and example methods to understand math problems
- How to use estimation techniques
- Using formulas for math problems
You have the convenience and flexibility to study how you want. All of the resources in this chapter, such as the video lessons, timeline feature, lesson quizzes and chapter test, are mobile-friendly. Whether you like studying on your home computer or on-the-go on your tablet or phone, you have choices.
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. Propositions, Truth Values and Truth Tables
Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.
3. 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.
4. Logic Laws: Converse, Inverse, Contrapositive & Counterexample
Logical statements can be useful, but only if we are able to determine their validity. In this lesson, we'll look at the various forms of a logical statement and see how they relate to each other.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. Using Mathematical Models to Solve Problems
Mathematical modelling 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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