About This Chapter
Mathematical Process & Perspectives - Chapter Summary
Check out this collection of simple math lessons to study concepts related to mathematical processes and perspectives. As you work through the chapter, you'll explore the types of reasoning that are typically used in math, as well as several mathematical proofs and models. You'll also see how mathematical models are used in the real world. When you're finished with the chapter, you should be able to:
- Recognize examples of mathematical proofs
- Differentiate between connective, inductive, deductive, formal and informal reasoning in math
- Explain several mathematical problem solving principles
- Evaluate a mathematical model's fit into a real-world situation
- Assess multiple representations of a math concept
- Understand the use of mathematical models in art, science, business and social science
- Use a variety of representations to communicate mathematical ideas
Each lesson comes with a short quiz to help you solidify your comprehension of these math concepts. If you have any questions about the chapter concepts, feel free to reach out to our instructors at any time. To make your studying experience flexible and convenient, we've made the chapter accessible on any device that has an Internet connection.
1. Mathematical Proof: Definition & Examples
Have you ever made a statement that someone challenged you to prove to be true? You have to explain things in a logical and indisputable way in order to do that. In this lesson, you'll learn different ways that statements can be proven in mathematics.
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. 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.
4. 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.
5. Using Multiple Representations of a Mathematical Concept
Many mathematical concepts can be represented in multiple ways. Concepts include a point and its coordinates, area of a circle as a quadratic function of the radius, probability as the ratio of two areas and area of a plane as a definite integral.
6. How Mathematical Models are Used in Art
In this lesson, you'll learn how math helps artists create realistic work that looks three-dimensional. You'll also learn how math is involved in photography.
7. How Mathematical Models are Used in Science
Do you ever wonder how scientists make predictions? Instead of a crystal ball, they actually use mathematical models! In this lesson, learn about how these models are used in science.
8. How Mathematical Models are Used in Social Science
In this lesson, you will learn about mathematical models and how they are used in social sciences. It explores their use in economics, sociology, political science, and history.
9. How Mathematical Models are Used in Business
This lesson will help you understand mathematical models and how they are used in the context of business. You will learn various use-cases of these models in business with the help of relevant examples.
10. Communicating Mathematical Ideas Using a Variety of Representations
Many mathematical ideas can be communicated or illustrated using a variety of representations. In this lesson, we'll explore ways you can communicate ideas to your students using written, verbal and symbolic forms as well as visual aids and technology.
Earning College Credit
Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the TExES Mathematics 7-12 (235): Practice & Study Guide course
- About the TExES Math 7-12 Exam
- Real Numbers
- Mathematical Models
- Complex Numbers & the Complex Plane
- Number Theory
- Number Patterns
- Functions and Graphs
- Linear Functions
- Quadratic Functions & Polynomials
- Evaluating Piecewise & Composite Functions
- Rational and Radical Functions
- Inequalities and Absolute Values
- Exponentials & Logs
- The Unit Circle
- Trigonometric Functions
- Using a Scientific Calculator for Calculus
- Understanding Limits in Math
- Understanding Rate of Change
- Calculating Derivatives of Functions
- Derivatives and Graphs
- Optimization in Calculus
- Definite Integrals and Sums
- Integration Applications in Calculus
- Working with Measurement
- Finding Volume, Area & Perimeter
- Introduction to Proofs and Constructions
- Congruence and Similarity
- Real World Shapes
- Coordinate Geometry
- Understanding Transformations in Math
- Conic Sections
- Understanding Vectors
- Measuring & Displaying Data
- Data Distribution Overview
- Sampling in Statistics
- Distribution & Inference in Statistics
- Inference About a Mean
- Regression and Correlation
- Finding Probability
- Probability Distributions and Statistical Inference
- Experiments and Surveys
- Teaching Strategies & Activities for the Math Classroom
- Differentiated Instructional Strategies for the Math Classroom
- Using Student Assessments in the Math Classroom
- TExES Mathematics 7-12 Flashcards