# Ch 45: FTCE Math: Mathematical Reasoning

### About This Chapter

## FTCE Math: Mathematical Reasoning - Chapter Summary

As you prepare for the Florida Teacher Certification Examination (FTCE) Mathematics exam, be sure to include this chapter in your studies to improve your mathematical reasoning, logic, critical thinking and problem solving skills. In these short engaging lessons, you will be able to follow along with our professional instructors as they explain:

- How to convert complex problems into visual representations
- Uses of connective reasoning in mathematics
- Polya's four-step problem-solving process
- Critical thinking skills and logic in mathematics
- Converse, inverse, contrapositive and counterexamples of logical equivalence
- Conditional statements and logical math connectors
- Inductive and deductive reasoning in mathematics
- Applications of direct and indirect proofs

Read the lesson transcripts for written overviews that will reinforce your retention of the information presented and help you study the key vocabulary of the chapter. To test your understanding of the material and discover topics you don't understand, complete the lesson quizzes. After each quiz, review your results and use the video tags to return to and study the parts of the lessons that explain the topics you missed.

### 1. How to Solve Visualizing Geometry Problems

A picture is worth a thousand words, but sometimes drawing that picture can be like doing origami with your eyes closed. Practice translating complex problems into simple, meaningful images in this lesson.

### 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. 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.

### 4. 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.

### 5. 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.

### 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. 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.

### 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. 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.

### 10. Direct Proofs: Definition and Applications

In math, we can't explain that something is true just because. That's not enough. In this lesson, we'll learn to prove things using one of our most straightforward tools, the direct proof.

### 11. Indirect Proof in Geometry: Definition & Examples

There are many different methods that can be used to prove a given theory. One of those methods is indirect proof. In this lesson, we will explore indirect proof and learn the steps taken to use this method to prove a given theory.

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### Other Chapters

Other chapters within the FTCE Mathematics 6-12 (026): Practice & Study Guide course

- About the FTCE Math Test
- FTCE Math: Properties of Real Numbers
- FTCE Math: Linear Equations
- FTCE Math: Linear Inequalities
- FTCE Math: Absolute Value Expressions & Equations
- FTCE Math: Systems of Linear Equations
- FTCE Math: Ratios & Proportions
- FTCE Math: Rational Expressions & Equations
- FTCE Math: Radical Expressions & Equations
- FTCE Math: Complex Numbers
- FTCE Math: Quadratics
- FTCE Math: Polynomials
- FTCE Math: Exponential & Logarithmic Equations
- FTCE Math: Vector Operations
- FTCE Math: Sequences & Series
- FTCE Math: Matrix Operations & Determinants
- FTCE Math: Functions
- FTCE Math: Piecewise Functions
- FTCE Math: Area & Perimeter
- FTCE Math: Surface Area & Volume
- FTCE Math: Foundations of Geometry
- FTCE Math: Lines & Angles
- FTCE Math: Geometric Construction
- FTCE Math: Properties of Triangles
- FTCE Math: Similar & Congruent Triangle Proofs
- FTCE Math: Right Triangle Proofs
- FTCE Math: Quadrilaterals & Polygons
- FTCE Math: Circles & Arcs
- FTCE Math: Conic Sections
- FTCE Math: Coordinate Geometry
- FTCE Math: Transformations in Geometry
- FTCE Math: Trigonometry
- FTCE Math: Overview of Statistics
- FTCE Math: Data Analysis & Statistics
- FTCE Math: Regression & Correlation
- FTCE Math: Graphic Representations of Data
- FTCE Math: Sampling in Statistics
- FTCE Math: Probability
- FTCE Math: Limits
- FTCE Math: Rate of Change
- FTCE Math: Calculating Derivatives & Derivative Rules
- FTCE Math: Graphing Derivatives
- FTCE Math: Integration & Integration Techniques
- FTCE Math: Integration Applications
- FTCE Math: Teaching Strategies & Methods
- FTCE Math: Assessing Student Learning
- FTCE Math: Manipulatives & Models in the Classroom
- FTCE Math: Problem-Solving Strategies
- FTCE Mathematics 6-12 Flashcards