About This Chapter
Numerical Reasoning - Chapter Summary
Using this chapter's lessons will help you hone your mathematical reasoning skills. These videos explore areas including critical thinking, generalizations and math connectives, teaching you to analyze problems in order to reach logical conclusions. The video lessons will aid you in answering exam questions dealing with these topics:
- Logical math connectors: disjunctions and conjunctions
- Conditional statements
- Logical fallacies: hasty generalizations, false cause, limited choice and circular reasoning
- Logical fallacies: appeals to emotion, popularity or ignorance
- Logic and critical thinking in mathematics
- Propositions, truth tables and truth values
- Logical equivalence: converse, inverse, counterexample and contrapositive
- Argument validity
- Generalizations: appropriate, inappropriate and hidden assumptions
Instructors will lead you through each lesson, explaining the topics and showing you how to use your knowledge to prepare for your test. You'll learn different ways of thinking about these topics through the engaging video lessons. You can gauge your knowledge through the self-assessment exams that accompany each lesson.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
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Other chapters within the Math Review for Teachers: Study Guide & Help course
- Fundamental Number Concepts
- Operation Properties & Computation
- Ratios, Proportions and Percents
- Equations and Inequalities
- Geometric Properties of Shapes
- Coordinate Geometry Concepts & Practice Problems
- Systems of Measurement
- Measurement & Scaling for Simple & Complex Figures
- Data Analysis & Visualization
- Probability Concepts & Calculations