# Ch 1: CEOE Advanced Math: Mathematical Reasoning & Ideas

### About This Chapter

## CEOE Advanced Math: Mathematical Reasoning & Ideas - Chapter Summary

This chapter can simplify the process of preparing for the CEOE assessment by giving you access to key mathematical reasoning and ideas concepts you'll see on the exam. By watching the video lessons, you'll be able to:

- Discuss inductive and deductive reasoning in mathematics
- Describe critical thinking and logic in math, as well as properties and postulates of geometric figures
- Explain algebraic figures and geometric postulates, as well as logical math connectors
- Provide details about the undefined terms of geometry, along with conditional statements in math
- Solve visualizing geometry problems, and identify types of problems and problem-solving strategies
- Examine mathematic principles for problem solving, and examine Polya's four-step problem-solving process
- Use manipulative and technological tools to solve math problems, and translate words into math symbols

When studying for a certification test, you typically have to worry about identifying and compiling the appropriate materials to review. This chapter does the hard work for you, allowing you to relax and watch engaging lessons presented by quality instructors.

### CEOE Advanced Math: Mathematical Reasoning & Ideas Chapter Objectives

A primary objective of this chapter is to prepare you to answer mathematical reasoning and ideas questions on the CEOE Advanced Math assessment. In addition to reviewing the lessons in their video and transcript formats, you can ask questions about lesson topics to our experts. Self-assessment quizzes are also available with the lessons to gauge your comprehension of the materials.

Educators are required to take the assessment to secure the certification they need to teach advanced math in Oklahoma classrooms. The computer-based test is divided into five subareas and consists of 80 selected-response questions and 1 constructed-response assignment. Topics covered in this chapter are found in the mathematical processes and number sense subarea, which constitutes about 18% of the total test. Success in this subarea improves your chances of passing the entire test with a minimum score of 240.

### 1. 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.

### 2. 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.

### 3. Properties and Postulates of Geometric Figures

In geometry, there are some basic postulates that are relied upon as the basis for other theorems. Watch this video to learn about the postulates that deal with points, lines, and planes.

### 4. Algebraic Laws and Geometric Postulates

Watch this video to learn about the basic algebraic laws that are also part of the basic geometric postulates that form the basis for the geometry that we know and study today.

### 5. Undefined Terms of Geometry: Concepts & Significance

What do points, lines, planes, and sets have in common? Watch this video lesson to find out what they are, what they look like, and why they are called undefined terms.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. Types of Problems & Problem Solving Strategies

We solve hundreds of small problems everyday. This lesson covers different types of problems, such as routine vs. non-routine, and many of the different problem-solving strategies we use, including algorithms, heuristics, graphic representations and the IDEAL Strategy.

### 10. 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.

### 11. 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.

### 12. Translating Words Into Math Symbols

Math is its own language, which can make solving problems difficult. This lesson will help you translate words into math symbols, so you can easily solve word problems.

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### Other Chapters

Other chapters within the OSAT Advanced Mathematics (CEOE) (111): Practice & Study Guide course

- CEOE Advanced Math: Origins of Math
- CEOE Advanced Math: Absolute Value
- CEOE Advanced Math: Inequalities
- CEOE Advanced Math: Integers
- CEOE Advanced Math: Operations with Fractions
- CEOE Advanced Math: Operations with Decimals
- CEOE Advanced Math: Percents
- CEOE Advanced Math: Rational & Irrational Numbers
- CEOE Advanced Math: Complex Numbers
- CEOE Advanced Math: Properties of Numbers
- CEOE Advanced Math: Exponents & Exponential Expressions
- CEOE Advanced Math: Roots & Radical Expressions
- CEOE Advanced Math: Number Theory
- CEOE Advanced Math: Vectors, Matrices & Determinants
- CEOE Advanced Math: Properties of Functions
- CEOE Advanced Math: Graphing Functions
- CEOE Advanced Math: The Coordinate Graph & Graph Symmetry
- CEOE Advanced Math: Linear Equations
- CEOE Advanced Math: Systems of Linear Equations
- CEOE Advanced Math: Quadratic Functions
- CEOE Advanced Math: Polynomial Functions Basics
- CEOE Advanced Math: Higher-Degree Polynomial Functions
- CEOE Advanced Math: Piecewise, Absolute Value & Step Functions
- CEOE Advanced Math: Rational Expressions & Function Graphs
- CEOE Advanced Math: Exponential & Logarithmic Functions
- CEOE Advanced Math: Measurement
- CEOE Advanced Math: Perimeter & Area
- CEOE Advanced Math: Symmetry, Similarity & Congruence
- CEOE Advanced Math: Properties of Lines
- CEOE Advanced Math: Angles
- CEOE Advanced Math: Triangles
- CEOE Advanced Math: Triangle Theorems & Proofs
- CEOE Advanced Math: Similar Polygons
- CEOE Advanced Math: The Pythagorean Theorem
- CEOE Advanced Math: Circles
- CEOE Advanced Math: Circular Arcs & Measurement
- CEOE Advanced Math: Transformations
- CEOE Advanced Math: Analytic Geometry & Conic Sections
- CEOE Advanced Math: Trigonometric Functions
- CEOE Advanced Math: Trigonometric Graphs
- CEOE Advanced Math: Trigonometric Applications
- CEOE Advanced Math: Limits
- CEOE Advanced Math: Continuity
- CEOE Advanced Math: Rate of Change
- CEOE Advanced Math: Derivative Calculations & Rules
- CEOE Advanced Math: Graphing & Applying Derivatives
- CEOE Advanced Math: Area Under the Curve & Integrals
- CEOE Advanced Math: Integration Techniques
- CEOE Advanced Math: Differential Equations
- CEOE Advanced Math: Data & Graphs
- CEOE Advanced Math: Samples & Populations
- CEOE Advanced Math: Probability
- CEOE Advanced Math: Sets
- CEOE Advanced Math: Statistics
- CEOE Advanced Math: Number Patterns & Sequences
- CEOE Advanced Math: Number Patterns & Series
- CEOE Advanced Math: Discrete Math
- OSAT Advanced Mathematics (CEOE) (111) Flashcards