# Ch 1: Overview of Mathematical Reasoning

### About This Chapter

## Overview of Mathematical Reasoning - Chapter Summary

The study materials in this chapter were designed to help you study the historical development of mathematics and the basic topics that make up mathematical practice and theory. For example, you can review how communicating mathematical ideas is done using a variety of representations and see how to draw connections between mathematical concepts and procedures. Additional lessons look at various kinds of reasoning in math, as well as the role of both critical thinking and logic. By the end of this chapter, you could be able to:

- Explain inductive, deductive, and connective reasoning
- Define propositions, truth values, and truth tables
- Understand logical math connectors, such as conjunctions and disjunctions
- Explain conditional statements in math
- Discuss logic laws, including converse, inverse, contrapositive, and counterexample

Each lesson is presented with your success in mind. You can go through them at your own pace, using the aspects of the lesson that are most in line with your learning nature. Be sure to test your knowledge using the self-check quizzes that were designed to help you prepare to be successful on your exam.

### 1. Historical Development of Mathematics

This lesson gives a brief overview of the historical development of mathematics from pre-historic times to today. Math is a truly international creation with significant contributions from Africa, Asia, and Europe.

### 2. Communicating Mathematical Ideas Using a Variety of Representations

Many mathematical ideas can be communicated or illustrated using a variety of representations. In this lesson, we'll explore ways you can communicate ideas to your students using written, verbal and symbolic forms as well as visual aids and technology.

### 3. Connecting Mathematical Concepts & Procedures

Mathematical concepts can be linked to mathematical procedures. Many real-world problems can be solved by first applying a mathematical concept to said problem and then carrying out a corresponding procedure (or mathematical operation) to derive an actual solution . There is a plethora of examples to illustrate the importance of connecting mathematical concepts to mathematical procedures.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. Logical Math Connectors: Conjunctions and Disjunctions

Watch this video lesson to learn how to identify conjunctions and disjunctions. Also learn the connectors that are used with each. Learn how you can use them to make statements.

### 9. 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.

### 10. 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.

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### Other Chapters

Other chapters within the NES Mathematics Middle Grades & Early Secondary (105): Practice & Study Guide course

- Introduction to Mathematical Problem Solving
- NES Math: Properties of Real Numbers
- Understanding Relations & Functions
- Overview of Linear Functions & Equations
- Quadratic Equations, Functions & Inequalities
- Overview of Polynomial Equations, Functions & Inequalities
- Working with Absolute Values
- Overview of Rational & Radical Functions
- NES Math: Piecewise Functions
- NES Math: Exponential & Logarithmic Functions
- Scientific Measurement Principles & Calculations
- NES Math: Foundations of Geometry
- NES Math: Geometric Figures
- Triangle Properties & Proofs
- NES Math: Parallel Lines & Polygons
- NES Math: Circles & Arc of a Circle
- NES Math: Conic Sections
- NES Math: Geometric Solids
- NES Math: Analytical Geometry
- Statistics: Principles & Techniques
- Probability: Principles & Techniques
- Overview of Discrete Mathematics
- Performing Operations on Matrices & Vectors
- Solving Problems with Sequences & Series
- NES Mathematics Middle Grades & Early Secondary Flashcards