# Ch 21: PECT PAPA: Problem Solving & Reasoning in Math

### About This Chapter

## PECT PAPA: Problem Solving & Reasoning in Math - Chapter Summary

Use this chapter to get the detailed overview of problem solving and reasoning in math you need to answer related questions on the PECT PAPA exam. Upon completion of this chapter, you will be able to answer test questions that ask you to:

- Identify mathematical principles for problem solving
- Explain the five main logic connectives in mathematical reasoning
- Describe inductive and deductive reasoning
- Define counterexample in math and solve math problems using estimation
- Share the meaning of function notation and set notation
- Describe the order of operations in math
- Discuss the interrelationships between STEM and society

Subject-matter experts present the lessons in an easy-to-follow manner with plenty of definitions and examples to ensure you understand problem solving and reasoning in math. You can watch the videos in any order and as often as needed to make studying effective.

### PECT PAPA: Problem Solving & Reasoning in Math Chapter Objectives

The topics covered in this PECT PAPA: Problem Solving & Reasoning in Math chapter are found in the mathematics module of the exam, which consists of 36 selected-response questions and is 75 minutes in length. You can use the lessons in this chapter to increase your chances of getting the passing score you need to gain initial educator certification as an undergraduate candidate in the state of Pennsylvania.

A self-assessment quiz is available with each lesson that allows you to test your understanding of the materials, while giving you practice with questions formatted similarly to those you'll see on the exam. If you want a more comprehensive assessment of your readiness for the exam, take advantage of the chapter exam.

### 1. 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.

### 2. 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.

### 3. 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.

### 4. Counterexample in Math: Definition & Examples

Counterexamples are a useful tool in mathematics. Learn what a counterexample is and how it can be used to prove the boundaries of theorems. You will also look at some examples across different branches of mathematics.

### 5. 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.

### 6. What is Function Notation: Definition & Examples

After completing this lesson, you will be able to recognize function notation. You will also be able to evaluate functions correctly using function notation.

### 7. Set Notation: Definition & Examples

After completing this lesson, you will know how to write a set using words and using mathematical symbols. You will also know how to define sets and how to interpret sets that are displayed in set notation.

### 8. What Is The Order of Operations in Math? - Definition & Examples

The order of operations is the steps used to simplify any mathematical expression. In this video, learn how to solve problems using these steps and easy tricks to remember them.

### 9. The Interrelationships Between STEM & Society

As time goes on, science, technology, engineering, and math become more and more tangled in current society. This lesson will give an overview of various ways in which STEM and society have become intertwined.

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### Other Chapters

Other chapters within the PECT PAPA: Practice & Study Guide course

- PECT PAPA: Meaning of Words & Phrases in Text
- PECT PAPA: Purpose, Main Idea & Organization of Texts
- PECT PAPA: Analyzing & Interpreting Texts
- PECT PAPA: Drawing Inferences from Texts
- PECT PAPA: Numbers & the Number System
- PECT PAPA: Whole Numbers
- PECT PAPA: Positive & Negative Numbers
- PECT PAPA: Integers
- PECT PAPA: Rational & Irrational Numbers
- PECT PAPA: Decimals
- PECT PAPA: Percents
- PECT PAPA: Fractions
- PECT PAPA: Exponents
- PECT PAPA: Linear & Nonlinear Functions
- PECT PAPA: Inequalities
- PECT PAPA: Basic Measurement
- PECT PAPA: Geometric Concepts
- PECT PAPA: Measuring Geometric Figures
- PECT PAPA: Data & Statistics
- PECT PAPA: Probability
- PECT PAPA: Writing Structure
- PECT PAPA: Syntax, Grammar & Sentence Structure
- PECT PAPA: Spelling, Capitalization & Punctuation
- PECT PAPA: Writing Strategy
- PECT PAPA: Revising Your Writing
- PECT PAPA Flashcards