Ch 17: Illinois TAP Math: Reasoning Skills

About This Chapter

Let us show you how to develop and utilize mathematical reasoning skills to draw conclusions and recognize errors. The video lessons and self-assessment quizzes show you several techniques that will aid you with these types of questions on the TAP Math exam.

Illinois TAP Math: Reasoning Skills - Chapter Summary

This chapter's lessons will help you prepare for the Illinois TAP - Test of Academic Proficiency by learning to apply math reasoning skills to solve problems and detect patterns. You'll explore inductive and deductive reasoning techniques and learn to pick out errors in mathematical explanations. The topics covered in these lessons include:

  • Drawing conclusions using inductive and deductive reasoning
  • Identifying errors in mathematical explanations
  • Logical math connectors: conjunctions and disjunctions
  • Conditional statements
  • Logical equivalence: converse, inverse, contrapositive and counterexample
  • Logical fallacies: hasty generalization, circular reasoning, false cause and limited choice
  • Logical fallacies: appeals to ignorance, emotion or popularity

An expert instructor will explain each topic, guiding you through the videos in preparation for the TAP exam. With the knowledge of mathematical logic and reasoning gained in these fun lessons, you'll be ready for the TAP's questions.

Objectives of the Illinois TAP Math: Reasoning Skills Course

Passing the TAP exam is required in order to be licensed as a teacher in Illinois. The TAP is divided into three portions with a total of 170 multiple-choice questions as well as a writing section. The topics in the Reasoning Skills chapter are covered in the TAP's mathematics section, which has 50 questions. You'll be able to test your mastery of the subject through the self-assessment tests found at the end of each lesson.

6 Lessons in Chapter 17: Illinois TAP Math: Reasoning Skills
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.

Logical Math Connectors: Conjunctions and Disjunctions

2. 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.

Conditional Statements in Math

3. 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

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

5. 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

6. 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.

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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