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Lesson 1: Thinking About Mathematical Thinking

Introduction

Keywords: Common Core State Standards, Standards for Mathematical Practice, mathematical proficiency, conceptual understanding, procedural understanding or procedural fluency, instrumental understanding, relational understanding, strategic understanding, adaptive reasoning, productive disposition

In this lesson, we will consider what is unique and valuable about mathematical thinking:

  • What does it mean for you, as a teacher, to be thinking mathematically?
  • How about your students?
  • How do you know your students are thinking "mathematically" as opposed to some other way of thinking and reasoning?

The goal in this lesson is for us to develop some shared language and for each of us to develop a personal, working definition of what it means to think mathematically. But we're not just going to be working on instinct! Many experts have discussed what makes thinking mathematical, so we're going to familiarize ourselves with several ways of thinking about this issue.

Stop and Think!

What does it mean to think mathematically? Brainstorm five verbs and five adjectives that come to mind as you think about doing mathematics or about thinking mathematically. It might help if you especially think about how mathematics is different or distinct from other subjects. We will use the class list to create a course word cloud.

Remember that the purpose of Thought Questions is not to evaluate your understanding of course content but rather to provide you the space and time to reflect on your initial ideas about a topic. Your answers to Thought Questions are seen primarily by your instructor; however, your instructor may use some of your responses for discussion or demonstration purposes. The quality of your answers to Thought Questions is used to evaluate your participation in the course.

Objectives

At the end of this lesson, you should be able to

  • compare recent and influential documents that describe mathematical thinking and
  • synthesize a variety of perspectives on mathematical thinking into a personal, working understanding.

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