Ch 2: Problem Solving & Reasoning Skills

About This Chapter

This chapter helps you go over the problem solving and reasoning skills you'll need to be familiar with for the FTCE Middle Grades Math exam. Our lessons help you review how different math problems can be solved.

FTCE Middle Grades Math: Problem Solving & Reasoning Skills - Chapter Summary

Make sure you're ready for the FTCE Middle Grades Math exam by going over the problem solving and reasoning skills content you'll find on the test. This chapter includes lessons that help you study:

  • Different principles for solving math problems
  • Various problem-solving strategies
  • Connective reasoning
  • Logical equivalence
  • Conditional statements in mathematics
  • Propositions and truth values

The quizzes at the end of the chapter will give you the chance to check your understanding of what you've reviewed. You can look over the lessons again if there are certain topics you'd like to review further.

7 Lessons in Chapter 2: Problem Solving & Reasoning Skills
Test your knowledge with a 30-question chapter practice test
Reasoning in Mathematics: Inductive and Deductive Reasoning

1. Reasoning in Mathematics: Inductive and Deductive Reasoning

Inductive and deductive reasoning are two methods of reasoning used in mathematics. Explore the definitions of inductive and deductive reasoning, review examples of each in action, and learn when and how to use them.

Mathematical Principles for Problem Solving

2. Mathematical Principles for Problem Solving

Solving problems, both in math and in life, involves five mathematical principles: always, counterexample, order, splitting hairs, and analogies. Delve into the definition of each principle and learn when and how to use them.

The Three-Way Principle of Mathematics

3. The Three-Way Principle of Mathematics

The three-way principle of mathematics states that there are three ways to solve a math problem: verbally, graphically, or by example. Learn how to use these methods and explore the strengths and limitations of each.

Polya's Four-Step Problem-Solving Process

4. Polya's Four-Step Problem-Solving Process

Mathematician George Polya constructed a specific system used to approach problem-solving, known as the Polya 4-Step Problem-Solving Process. Learn to understand the problem, devise a plan, carry out the plan, and 'look back' on your work through a provided example.

Solving Mathematical Problems Using Estimation

5. Solving Mathematical Problems Using Estimation

When you are busy it is easy to accidentally get behind and end up late for appointments and using estimating in things like time can help make sure this doesn't happen. Learn more about solving mathematical problems using estimation.

Types of Problems & Problem Solving Strategies

6. Types of Problems & Problem Solving Strategies

Prior to implementing your problem-solving strategies, you should know what types of problems are you facing. Learn about the different types of problems according to educational psychology and review some of the different problem-solving strategies we use, including algorithms, heuristics, graphic representations and the IDEAL strategy.

How to Solve Visualizing Geometry Problems

7. How to Solve Visualizing Geometry Problems

Visualizing geometry problems involves knowing the expected results, and identifying the important pieces of information to make sure all the mathematical details match the word problem. See several examples of how to solve these problems correctly.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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More Exams
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Other Chapters

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