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Ch 16: MTTC Elementary Education: Mathematical Reasoning & Development

About This Chapter

Learn about development and reasoning in mathematics using this chapter of the MTTC Elementary Education exam study guide. Video lessons and self-assessment quizzes teach you all you need to know about elementary education in preparation for the MTTC exam.

MTTC Elementary Education: Mathematical Reasoning and Development - Chapter Summary

The lessons in this Mathematical Reasoning and Development chapter of the MTTC study guide explore the basics of mathematics, including ancient number systems, historical development of mathematics, and critical thinking. Axiomatic geometry, mathematical models, and Polya's four-step problem-solving process are all covered in this chapter. Additionally, by the end of this chapter, you should be familiar with:

  • Mathematical principles for problem solving
  • Solving word problems by restating them
  • How to use math manipulates to solve word problems
  • Applications of math in everyday life
  • Math technology in the classroom

Mathematical reasoning is thoroughly explained through the video lessons in this chapter. Any questions you have can be answered by the knowledgeable instructors, and each video lesson is accompanied by a transcript to help you study. Take the accompanying self-assessment quizzes to test your understanding of the material.

8 Lessons in Chapter 16: MTTC Elementary Education: Mathematical Reasoning & Development
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.

Critical Thinking and Logic in Mathematics

2. 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.

The Axiomatic System: Definition & Properties

3. 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

4. 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.

Using Mathematical Models to Solve Problems

5. 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.

Mathematical Principles for Problem Solving

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.

How to Use Math Manipulatives to Answer Word Problems

7. How to Use Math Manipulatives to Answer Word Problems

After watching this video lesson, you will see what a math manipulative is, how you can use almost anything as a math manipulative, and how you can use these manipulatives to help you solve word problems.

Using Math in Everyday Life

8. Using Math in Everyday Life

While not everyone loves math, it is extremely useful. Learn about just a few of the dozens of ways that math can be used in everyday life: for money matters, to improve decision-making, and in many other little ways.

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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