Ch 2: CEOE Middle Level/Intermediate Math: Reasoning & Logic

About This Chapter

Use this chapter on reasoning and logic as preparation for your upcoming Certification Examinations for Oklahoma Educators (CEOE) Middle Level/Intermediate Math test. These engaging lessons and quizzes were assembled by a panel of experts.

CEOE Middle Level/Intermediate Math: Reasoning & Logic - Chapter Summary

These lessons on the math principles of reasoning and logic are intended as a refresher for you before taking the CEOE test on math. They will improve your knowledge of the subject matter and aid you with test questions on such things as:

  • Using critical thinking and logic in mathematics
  • Inductive and deductive reasoning in math
  • Applying connective reasoning in mathematics
  • Familiarizing yourself with conditional statements in math
  • Differentiating between converse, inverse, contrapositive and counterexample logical equivalencies
  • Working with the logical math connectors of conjunctions and disjunctions
  • Proving by contradiction
  • Problem solving by using Polya's four-step process
  • Understanding the three-way principle of math
  • Applying direct proofs
  • Defining logical mathematical intelligence

The Study.com team of experts uses 5-10 minute videos and text lessons that focus on one aspect of reason and logic in math per lesson. A quiz at the end of each tests your comprehension. If you need to go back over some part of the lesson, you can either refer to the text or take advantage of the timeline tool that uses key words to take you straight to the point in the video that addresses the material you need. There is also a feature for asking a question of a Study.com expert.

11 Lessons in Chapter 2: CEOE Middle Level/Intermediate Math: Reasoning & Logic
Test your knowledge with a 30-question chapter practice test
Critical Thinking and Logic in Mathematics

1. 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.

Reasoning in Mathematics: Inductive and Deductive Reasoning

2. 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

3. 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.

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.

Logical Math Connectors: Conjunctions and Disjunctions

6. 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.

Proof by Contradiction: Definition & Examples

7. Proof by Contradiction: Definition & Examples

One of several different ways to prove a statement in mathematics is proof by contradiction. Learn the definition of this method and observe how it is applied to proving a statement's truth value through examples and exploration.

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.

The Three-Way Principle of Mathematics

9. 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.

Direct Proofs: Definition and Applications

10. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

Logical Mathematical Intelligence: Definition & Examples

11. Logical Mathematical Intelligence: Definition & Examples

What do Albert Einstein, Sherlock Holmes, and Mark Zuckerberg all have in common? They all have logical/mathematical intelligence. Learn more about logical/mathematical intelligence from examples and test your knowledge with a quiz.

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

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Other Chapters

Other chapters within the OSAT Middle Level/Intermediate Mathematics (CEOE) (125): Practice & Study Guide course

Support