# Ch 1: ILTS Mathematics: Concepts & Skills

### About This Chapter

## ILTS Mathematics: Concepts & Skills - Chapter Summary

As part of a study guide course for the Illinois Licensure Testing System (ILTS) Mathematics exam, this chapter will help you improve your understanding of the processes of learning, mathematical principles and basic mathematical problem solving skills. In these mobile device-compatible lessons, our expert instructors will discuss:

- The definition of learning and the different types of learning
- Uses of cooperative and collaborative learning in the classroom
- How language art skills, such as reading, are used in mathematics
- Principles of understanding math problems verbally, graphically and by example
- Other principles used to solve mathematical problems
- How to use estimation to discover the solution to a math problem
- Polya's Four-Step Problem-Solving process
- The use of models to solve math problems

Following the lesson videos, read the lesson transcripts to fortify your retention of the information and study the key terms and figures of the chapter. You can take the lesson quizzes to discover topics you don't understand and use the tags in the video lessons to return to and study the parts of the lessons that explain them. At the end of the chapter, take the practice chapter exam to test your overall understanding of the material. If you have any questions, you may send them to our instructors via the lessons' 'teacher' tabs.

### 1. What is Learning? - Understanding Effective Classroom Strategies

We all learn new things every day, but how is 'learning' defined in educational psychology? This lesson covers the definition of learning, different types of learning, and discusses learning styles.

### 2. Cooperative and Collaborative Learning in the Classroom

It's extremely common for teachers to require students to work in groups. However, certain types of groups and activities are preferred over others. In this lesson, we define cooperative learning and discuss its advantages in the classroom. We also define collaborative learning and explain how it is different than cooperative learning.

### 3. How Language Skills Apply to Mathematics

Just because you are learning math does not mean that you can totally skimp on your language skills. In this lesson, you'll learn that improving in your language skills can actually help improve your math skills as well.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. How to Use Models to Solve Math Problems

In this lesson, we will discuss using models to solve math problems. We will look at two examples together, modeling and measuring the area of a quadrilateral and the volume of a cube.

### 9. Special Strategies for Solving Math Problems

Special strategies for solving more complex math problems can be carried out with the use of a scientific calculator. Many exams, whether in schools or on standardized tests, allow for the use of a scientific calculator. We are going to go over a couple of concepts or strategies -implementing the Texas Instruments TI-84.

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### Other Chapters

Other chapters within the ILTS Mathematics (208): Test Practice and Study Guide course

- ILTS Mathematics: Logic & Reasoning
- ILTS Mathematics: Using Technology for Math
- ILTS Mathematics: Number Theory
- ILTS Mathematics: Solving Number Problems
- ILTS Mathematics: Real & Complex Numbers
- ILTS Mathematics: Measurement
- ILTS Mathematics: Multidimensional Objects
- ILTS Mathematics: Variables & Patterns
- ILTS Mathematics: Linear Relations & Functions
- ILTS Mathematics: Quadratic Relations & Functions
- ILTS Mathematics: Absolute Value
- ILTS Mathematics: Polynomials
- ILTS Mathematics: Radical Functions
- ILTS Mathematics: Rational Functions
- ILTS Mathematics: Exponential Functions
- ILTS Mathematics: Logarithmic Functions
- ILTS Mathematics: Trigonometric Functions
- ILTS Mathematics: Calculus
- ILTS Mathematics: Points, Lines, Planes & Space
- ILTS Mathematics: 2D & 3D Shapes
- ILTS Mathematics: Spatial Visualization
- ILTS Mathematics: Congruence, Similarity & Symmetry
- ILTS Mathematics: Probability Theory & Techniques
- ILTS Mathematics: Collecting & Representing Data
- ILTS Mathematics: Using Data to Make Predictions
- ILTS Mathematics Flashcards