# Ch 42: TExES Physics/Math 7-12: Mathematical Reasoning

### About This Chapter

## TExES Physics/Math 7-12: Mathematical Reasoning - Chapter Summary

Understanding the logical reasoning behind mathematical functions is key when preparing for any math-based exam, including the TExES Physics/Mathematics 7-12 test. This series of lesson videos will help you review the logical fallacies to avoid, propositions, inductive reasoning, deductive reasoning, problem solving and uses of estimation. After this series of lesson videos you should have a firm understanding of:

- Logical fallacies
- Propositions
- Conjunctions and disjunctions
- Conditional statements
- Logical equivalence
- Inductive and deductive reasoning
- Connective reasoning
- Processes and principles of problem solving

Every lesson video is taught by expert instructors who are available to answer any questions you may develop during the course of the chapter. Reinforce your knowledge of the material by completing the lesson worksheets and discover areas you have not mastered with lesson quizzes. Returning to the lesson videos may help you fortify these areas of weakness.

### 1. 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.

### 2. Logical Fallacies: Hasty Generalization, Circular Reasoning, False Cause & Limited Choice

Watch this video lesson to see how you can identify cases where logic is not sound. Learn the characteristic traits of hasty generalization, circular reasoning, false cause, and limited choice.

### 3. Logical Fallacies: Appeals to Ignorance, Emotion or Popularity

Watch this video lesson to see examples of the logical fallacies of appeals to ignorance, emotion, and popularity. You will also see how to identify them.

### 4. Propositions, Truth Values and Truth Tables

Watch this video lesson and learn what truth values are and what a truth table looks like. Learn how to go from a proposition to its negation and how that affects the truth values and the truth tables.

### 5. 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.

### 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. 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.

### 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. 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.

### 10. 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.

### 11. 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.

### 12. The Three-Way Principle of Mathematics

What methods are there to solve and understand mathematical problems? This lesson will review three methods to understand mathematical problems (verbal, graphical, and by example). Each will be illustrated with examples.

### 13. 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.

### 14. 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.

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### Other Chapters

Other chapters within the TExES Physics/Mathematics 7-12 (243): Practice & Study Guide course

- TExES Physics/Math 7-12: Teaching Math & Science
- TExES Physics/Math 7-12: Basic Arithmetic
- TExES Physics/Math 7-12: Real Numbers
- TExES Physics/Math 7-12: Decimals & Fractions
- TExES Physics/Math 7-12: Ratios, Percent & Proportions
- TExES Physics/Math 7-12: Exponents & Exponential Expressions
- TExES Physics/Math 7-12: Algebraic Expressions & Equations
- TExES Physics/Math 7-12: Rational Expressions
- TExES Physics/Math 7-12: Radical Expressions
- TExES Physics/Math 7-12: Complex & Imaginary Numbers
- TExES Physics/Math 7-12: Number Theory
- TExES Physics/Math 7-12: Vector Operations
- TExES Physics/Math 7-12: Sequences & Series
- TExES Physics/Math 7-12: Functions
- TExES Physics/Math 7-12: Graphing & Functions
- TExES Physics/Math 7-12: Linear Equations
- TExES Physics/Math 7-12: Quadratic Equations
- TExES Physics/Math 7-12: Graphing & Factoring Quadratic Equations
- TExES Physics/Math 7-12: Matrices & Determinants
- TExES Physics/Math 7-12: Polynomials
- TExES Physics/Math 7-12: Exponential & Logarithmic Functions
- TExES Physics/Math 7-12: Trigonometry
- TExES Physics/Math 7-12: Continuity in Calculus
- TExES Physics/Math 7-12: Limits in Calculus
- TExES Physics/Math 7-12: Derivatives & Differentiation in Calculus
- TExES Physics/Math 7-12: Foundations of Geometry
- TExES Physics/Math 7-12: Geometry and Measurement
- TExES Physics/Math 7-12: Geometric Figures
- TExES Physics/Math 7-12: Parallel Lines & Polygons
- TExES Physics/Math 7-12: Properties of Triangles
- TExES Physics/Math 7-12: Geometric Solids
- TExES Physics/Math 7-12: Analytical Geometry
- TExES Physics/Math 7-12: Similar Polygons
- TExES Physics/Math 7-12: Conic Sections
- TExES Physics/Math 7-12: Circular Arcs & Circles
- TExES Physics/Math 7-12: Triangle Theorems & Proofs
- TExES Physics/Math 7-12: Statistics
- TExES Physics/Math 7-12: Probability
- TExES Physics/Math 7-12: Discrete Probability Distributions
- TExES Physics/Math 7-12: Continuous Probability Distributions
- TExES Physics/Math 7-12: Statistical Inference
- TExES Physics/Math 7-12: Applied Math
- TExES Physics/Math 7-12: Scientific Inquiry & Process
- TExES Physics/Math 7-12: Vectors & Scalars
- TExES Physics/Math 7-12: Kinematics
- TExES Physics/Math 7-12: Motion
- TExES Physics/Math 7-12: Fluid Mechanics
- TExES Physics/Math 7-12: Linear Momentum
- TExES Physics/Math 7-12: Work, Energy & Power
- TExES Physics/Math 7-12: Laws of Gravitation
- TExES Physics/Math 7-12: Oscillations
- TExES Physics/Math 7-12: Rotational Motion & Conservation of Energy
- TExES Physics/Math 7-12: Heat & Energy
- TExES Physics/Math 7-12: Thermodynamics
- TExES Physics/Math 7-12: Electrical Forces & Fields
- TExES Physics/Math 7-12: Potential & Capacitance
- TExES Physics/Math 7-12: Current Circuits
- TExES Physics/Math 7-12: Magnetism
- TExES Physics/Math 7-12: Waves, Sound & Light
- TExES Physics/Math 7-12: Quantum Physics
- TExES Physics/Mathematics 7-12 Flashcards