About This Chapter
Algebraic Thinking in the Classroom - Chapter Summary
This helpful chapter outlines ways for using patterns, logic and algebraic thinking to solve problems. In these lessons, you'll review solving and recognizing mathematical patterns as well as see ideas for activities that help students understand relationships and studying patterns. Each lesson is followed by a short, multiple-choice quiz that can help identify any areas that need further study as you work through the chapter. If you like to work offline while you're learning, our printable lesson transcripts make handy study guides. After completing this chapter, you should be ready to:
- Recognize effective methods to teach reasoning in math
- Teach students to use sense-making when solving math problems
- Understand how to estimate in math
- Utilize mental math games
- Detail Polya's four-step problem-solving process
- Give an example of a critical thinking math problem
1. 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.
2. Recognizing and Solving Mathematical Patterns
Patterns show up in the world around us on a daily basis. In this lesson, we will define mathematical patterns and look at recognizing and solving these patterns. We will examine examples to solidify our understanding of this process.
3. Activities for Studying Patterns & Relationships in Math
Did you know that math patterns and relationships can be taught in the classroom using simple things such as beads? Learn how in this lesson, along with how little items such as paperclips can be used to teach relationships.
4. Teaching Reasoning in Math: Types & Methods
This lesson will introduce several types of reasoning, including: connective, inductive, deductive, abstract, quantitative, and adaptive. Further, we will discuss methods for teaching students to use connective reasoning to solve mathematical problems.
5. Teaching Students Sense-Making in Math Problems
Teaching math strategies is one of the more challenging subjects teachers face. We will identify how and why to teach students to use logical reasoning in solving math problems and identify useful tools for doing so.
6. Mental Math Games
Mental math can be a difficult concept for some students to learn. Regular practice with games is a great way to teach students how to learn mental math which they will often use as adults. Read on to learn about different types of games you can use in your classroom.
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. Critical Thinking Math Problems: Examples and Activities
Critical thinking can be as much a part of a math class as learning concepts, computations, formulas, and theorems. Activities that stimulate critical thinking will also encourage students to think and speak in mathematical terms.
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Other chapters within the Education 211: Teaching Elementary Math course
- Understanding Math Standards
- Developing Math Curriculum
- Planning Math Instruction
- Instructional Strategies for Math Teachers
- Creating Math Learning Environments
- Assessments for Teaching Math
- Educational Resources for Teaching Math
- Counting & Cardinality in the Classroom
- Teaching Mathematical Operations
- Teaching Base 10 & Fractions
- Teaching Standard & Metric Measurements
- Teaching Time & Money
- Teaching Geometry Basics
- Geometric Measurements in the Classroom
- Teaching the Coordinate Plane
- Teaching Graphical Data Identification