About This Chapter
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.
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.
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.
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.
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.
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.
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.
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Other chapters within the ILTS TAP - Test of Academic Proficiency (400): Practice & Study Guide course
- About the Illinois TAP Test
- Illinois TAP Reading Comprehension: Vocabulary & Language
- Illinois TAP Reading Comprehension: Find the Main Idea & Supporting Details
- Illinois TAP Reading Comprehension: Inference & Interpretation
- Illinois TAP Reading Comprehension: Critical Reasoning
- Illinois TAP Reading: Summarizing & Interpreting Information
- Illinois TAP Language Arts: Grammar
- Illinois TAP Language Arts: Writing Mechanics
- Illinois TAP Writing: Understanding Audience
- Illinois TAP Writing: Development & Organization
- Illinois TAP Writing: Editing & Revision
- Illinois TAP Writing: Clarity
- Illinois TAP Writing: Practice
- Illinois TAP Math: Integers
- Illinois TAP Math: Fractions, Decimals & Percents
- Illinois TAP Math: Estimation & Measurement
- Illinois TAP Math: Algebra
- Illinois TAP Math: Geometry
- Illinois TAP Math: Data & Statistics
- ILTS TAP - Test of Academic Proficiency Flashcards