Ch 39: MTEL Middle School Math/Science: Basics of Logic

About This Chapter

The video lessons in this chapter will allow you to review the fundamentals of logic and reasoning. The skills you broaden through this chapter will help you feel prepared when taking the MTEL Middle School Mathematics/Science exam.

MTEL Middle School Math/Science: Basics of Logic - Chapter Summary

Review methods for thinking logically and learn about inconsistencies in the way we interpret information and create solutions for problems. Use the critical thinking processes highlighted in these lessons to help you better solve mathematical problems before you take the exam. By the end of this chapter, you will have worked through:

  • Fallacies in logical thinking
  • Inductive and deductive reasoning
  • The different types of logical equivalence
  • Conditional statements regarding math
  • The three-way, four-step and other principles for problem solving
  • Using estimation in math
  • Critical thinking
  • Connective reasoning
  • Truth values and tables

The instructors of this chapter will walk you through the various factors involved in logical thinking and go over with you efficient strategies for solving mathematical problems. Use the timeline underneath each video to replay a particular portion of the video lesson.

MTEL Middle School Math/Science: Basics of Logic Objectives

The MTEL Middle School Mathematics/Science exam is a required test for all teachers aspiring to teach these subjects in the state of Massachusetts, and a passing grade will result in professional certification. The skills reviewed in this chapter will help you successfully complete the mathematical portion of the exam, which accounts for 50% of the 10 subareas on the test.

The MTEL Middle School Mathematics/Science exam is computer-based and consists of 100 multiple-choice questions (accounting for 80% of the final score) and 2 open-response questions (accounting for 20% of the score). A score of 240 is needed to pass the exam and qualify for professional certification.

13 Lessons in Chapter 39: MTEL Middle School Math/Science: Basics of Logic
Test your knowledge with a 30-question chapter practice test
Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

1. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

Watch this video lesson to see how you can identify cases where logic is not sound. Learn the characteristic traits of hasty generalization, circular reasoning, false cause, and limited choice.

Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

2. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

Watch this video lesson to see examples of the logical fallacies of appeals to ignorance, emotion, and popularity. You will also see how to identify them.

Propositions, Truth Values and Truth Tables

3. 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.

Conditional Statements in Math

4. 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

5. 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.

Reasoning in Mathematics: Inductive and Deductive Reasoning

6. 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

7. 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.

Polya's Four-Step Problem-Solving Process

8. 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.

Mathematical Principles for Problem Solving

9. 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.

The Three-Way Principle of Mathematics

10. The Three-Way Principle of Mathematics

What methods are there to solve and understand mathematical problems? This lesson will review three methods to understand mathematical problems (verbal, graphical, and by example). Each will be illustrated with examples.

Solving Mathematical Problems Using Estimation

11. 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.

Using Mathematical Models to Solve Problems

12. 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.

Critical Thinking and Logic in Mathematics

13. 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.

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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Other Chapters

Other chapters within the MTEL Mathematics/Science (Middle School)(51): Practice & Study Guide course

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