# Ch 1: Mathematical Reasoning & Problem-Solving: Help and Review

### About This Chapter

## Who's It For?

Anyone who needs help learning or mastering reasoning and problem-solving math material will benefit from the lessons in this chapter. There is no faster or easier way to learn reasoning and problem-solving in math. Among those who would benefit are:

- Students who have fallen behind in understanding mathematical reasoning and problem solving
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about reasoning and problem-solving in math
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How It Works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Mathematical Reasoning and Problem-Solving chapter exam.

## Why It Works:

**Study Efficiently:**Skip what you know, review what you don't.**Retain What You Learn:**Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day:**Use the mathematical reasoning and problem-solving chapter exam to be prepared.**Get Extra Support:**Ask our subject-matter experts any math question. They're here to help!**Study With Flexibility:**Watch videos on any web-ready device.

## Students Will Review:

This chapter helps students review the concepts in a reasoning and problem-solving unit of a standard contemporary math course. Topics covered include:

- Critical thinking
- Logical fallacies, such as false cause, hasty generalization, limited choice and circular reasoning
- Appeals to popularity, ignorance and emotion
- Proposition, truth value, negation and truth tables in math problems
- Conditional statements in problem solving
- Inductive, deductive and connective reasoning and how those can be applied in math reasoning and problem solving
- Polya's problem-solving method
- The Three-Way principle and estimation to solve math problems
- Mathematical models

### 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 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.

### 3. 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.

### 4. 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.

### 5. 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.

### 6. 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.

### 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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.

### 15. Abductive Reasoning: Definition & Examples

In this lesson, you will learn the definition of abductive reasoning as opposed to deductive and inductive reasoning, and will be given examples to further your understanding of this concept. Following the lesson, there will be a brief quiz.

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### Other Chapters

Other chapters within the Contemporary Math: Help and Review course

- How to Solve Word Problems: Help and Review
- Statistics Overview: Help and Review
- Probability Overview: Help and Review
- Understanding Discrete Probability Distributions: Help and Review
- The Normal Curve & Continuous Probability Distributions: Help and Review
- The Mathematics of Voting: Help and Review
- The Mathematics of Apportionment: Help and Review
- Graph Theory: Help and Review
- Operations with Basic Algebraic Expressions
- Conics in Algebra
- Algebraic Concepts of Groups & Sets
- Notation, Sequences & Series
- Matrices and Determinants in Algebra
- Combinatorics
- Fractions, Decimals & Mixed Numbers
- Approaches to Math Word Problems
- Performing Basic Arithmetic
- Operations with Monomials and Polynomials
- Number Line & the Coordinate Graph