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Ch 1: Overview of Mathematical Reasoning

About This Chapter

10 Lessons in Chapter 1: Overview of Mathematical Reasoning
Test your knowledge with a 30-question chapter practice test
Historical Development of Mathematics

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.

Communicating Mathematical Ideas Using a Variety of Representations

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.

Connecting Mathematical Concepts & Procedures

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.

Reasoning in Mathematics: Inductive and Deductive Reasoning

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.

Reasoning in Mathematics: Connective 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.

Critical Thinking and Logic in Mathematics

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.

Propositions, Truth Values and Truth Tables

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.

Logical Math Connectors: Conjunctions and Disjunctions

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.

Conditional Statements in Math

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.

Logic Laws: Converse, Inverse, Contrapositive & Counterexample

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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