Ch 1: MTTC Math (Secondary): Reasoning & Problem Solving

About This Chapter

As you prepare for the MTTC Mathematics (Secondary) exam complete the activities of this chapter to increase your understanding of Euclid's axiomatic geometry, mathematical reasoning, mathematical logic and principles of problem solving.

MTTC Math (Secondary): Reasoning & Problem Solving - Chapter Summary

Watch the lesson videos in this chapter to improve your understanding of the use of logic and critical thinking in mathematics when solving problems. These lessons are taught by expert instructors who are available to clarify any confusion you may have about any of the topics of these lessons so that you will be prepared for questions on the MTTC Mathematics (Secondary) test about:

  • Inductive and deductive reasoning
  • Geometric postulates and algebraic laws
  • The significance of undefined terms of geometry
  • Conjunctions, disjunctions and mathematical conditional statements
  • Kinds of problem solving strategies
  • Polya's four-step problem-solving process
  • Using estimation to solve mathematical problems
  • Solving math problems with technological and manipulative tools

Following these lessons be sure to complete the lesson assessments to confirm your understanding of the material and find any topics of the chapter that you could improve upon. You can use the video tags to locate any segments you want to reexamine after the quizzes. Alternatively, you could read over the lesson transcripts that present a written outline of the material.

14 Lessons in Chapter 1: MTTC Math (Secondary): Reasoning & Problem Solving
Test your knowledge with a 30-question chapter practice test
The Axiomatic System: Definition & Properties

1. The Axiomatic System: Definition & Properties

Learn what kinds of things are included in an axiomatic system in this video lesson. Also learn why consistency, independence, and completeness are important in axiomatic systems.

Euclid's Axiomatic Geometry: Developments & Postulates

2. Euclid's Axiomatic Geometry: Developments & Postulates

Learn how the way we do proofs in geometry had its start with Euclid in this video lesson. Learn about his contributions to the geometry we know today. Also learn about the five basic truths that he used as a basis for all other teachings.

Reasoning in Mathematics: Inductive and Deductive Reasoning

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.

Critical Thinking and Logic in Mathematics

4. 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.

Conjecture in Math: Definition & Example

5. Conjecture in Math: Definition & Example

This lesson will define the term conjecture, provide examples, and discuss conditions for writing them. We'll also highlight the use of conjectures by professionals and other people in their daily routines.

Counterexample in Math: Definition & Examples

6. Counterexample in Math: Definition & Examples

Counterexamples are a useful tool in mathematics. Learn what a counterexample is and how it can be used to prove the boundaries of theorems. You will also look at some examples across different branches of mathematics.

Direct & Indirect Proof: Differences & Examples

7. Direct & Indirect Proof: Differences & Examples

This lesson defines both direct and indirect proofs and, in turn, points out the differences between them. We'll also look at some examples of both types of proofs in both abstract and real-world contexts.

Algebra Vocabulary Terms

8. Algebra Vocabulary Terms

Watch this video lesson to learn about some basic vocabulary words that you will come across again and again in the course of your studies in algebra. After you finish this video, you should know and be able to identify each term.

Translating Words to Algebraic Expressions

9. Translating Words to Algebraic Expressions

When it comes to word problems, the easiest way to solve them is to look for keywords and change them into math symbols. Watch this video lesson to find out what keywords you should look for and what math symbols they represent.

Communicating Mathematical Ideas Using a Variety of Representations

10. 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.

Types of Problems & Problem Solving Strategies

11. Types of Problems & Problem Solving Strategies

We solve hundreds of small problems everyday. This lesson covers different types of problems, such as routine vs. non-routine, and many of the different problem-solving strategies we use, including algorithms, heuristics, graphic representations and the IDEAL Strategy.

Mathematical Principles for Problem Solving

12. 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.

Polya's Four-Step Problem-Solving Process

13. 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.

Solving Mathematical Problems Using Estimation

14. 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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

Other chapters within the MTTC Mathematics (Secondary) (022): Practice & Study Guide course

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