About This Chapter
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.
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. 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.
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.
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.
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.
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.
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.
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.
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Other chapters within the MTTC Elementary Education (103): Practice & Study Guide course
- MTTC Elementary Education: Language Acquisition & Literacy
- MTTC Elementary Education: Foundations of Literacy
- MTTC Elementary Education: Phonics & Fluency
- MTTC Elementary Education: Vocabulary & Reading Comprehension
- MTTC Elementary Education: Narrative & Expository Texts
- MTTC Elementary Education: The Writing Process
- MTTC Elementary Education: Types of Communication
- MTTC Elementary Education: Michigan History
- MTTC Elementary Education: Geography
- MTTC Elementary Education: Civics & Government
- MTTC Elementary Education: Economics
- MTTC Elementary Education: Social Studies
- MTTC Elementary Education: Visual Arts
- MTTC Elementary Education: Performing Arts
- MTTC Elementary Education: Art & Culture
- MTTC Elementary Education: Number Systems
- MTTC Elementary Education: Whole Number Operations
- MTTC Elementary Education: Ratios, Percents & Proportions
- MTTC Elementary Education: Units of Measurement
- MTTC Elementary Education: Geometry Concepts
- MTTC Elementary Education: Algebra Concepts
- MTTC Elementary Education: Data Analysis & Probability
- MTTC Elementary Education: Scientific Knowledge
- MTTC Elementary Education: Life Sciences
- MTTC Elementary Education: Earth & Space Science
- MTTC Elementary Education: Physical Science
- MTTC Elementary Education: Health Education
- MTTC Elementary Education: Physical Education
- MTTC Elementary Education Flashcards