About This Chapter
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.
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.
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.
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.
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.
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.
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.
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.
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Other chapters within the College Preparatory Mathematics: Help and Review course
- Math Foundations: Help and Review
- Percents in Math Basics
- Decimals & Fractions Overview
- Understanding Fractions & Mixed Numbers
- Linear Equations: Help and Review
- Solving and Graphing Inequalities: Help and Review
- Graphing and Factoring Quadratic Equations: Help and Review
- Complex and Imaginary Numbers: Help and Review
- Properties of Exponents: Help and Review
- Praxis I Math: Square Roots
- Properties of Polynomial Functions: Help and Review
- Simplifying and Solving Rational Expressions: Help and Review
- Praxis I Math: Algebraic Expressions
- Properties of Functions: Help and Review
- Logarithms and Exponential Equations: Help and Review
- Data & Estimation
- Logic in Math: Help and Review
- Sets: Help and Review
- Basic Probability and Statistics: Help and Review
- Praxis I Math: Basic Statistics and Probability
- Geometric Laws & Proofs
- Grade Level Math Vocabulary: Help and Review
- MTEL Middle School Math/Science: History of Geometry
- MTEL Middle School Math/Science: Geometric Properties & Theorems
- MTEL Middle School Math/Science: Principles of Geometry
- MTEL Middle School Math/Science: Algebraic Applications in Geometry
- MTEL Middle School Math/Science: Using Trigonometric Functions
- MTEL Middle School Math/Science: Trigonometric Identities
- MTEL Middle School Math/Science: Trigonometric Applications
- Praxis I Math: Ratio and Proportions
- Praxis I Math: Congruence and Similarity
- Praxis I Math: Geometric Measurement and Dimension