37 Chapters
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Introduction

Nolan, Edward C.; Dixon, Juli K.; Safi, Farshid; Haciomeroglu, Erhan Selcuk Solution Tree Press ePub

Introduction

The only way to learn mathematics is to do mathematics.

—Paul Halmos

When teaching, much of the day is spent supporting students to engage in learning new content. In mathematics, that often means planning for instruction, delivering the planned lessons, and engaging in the formative assessment process. There are opportunities to attend conferences and other professional development events, but those are typically focused on teaching strategies or on administrative tasks like learning the new gradebook program. Opportunities to take on the role of learner of the subject you teach are often neglected. As you read Making Sense of Mathematics for Teaching High School, you will have the chance to become the learner once again. You will learn about the mathematics you teach by doing the mathematics you teach.

There is a strong call to build teachers’ content knowledge for teaching mathematics. A lack of a “deep understanding of the content that [teachers] are expected to teach may inhibit their ability to teach meaningful, effective, and connected lesson sequences, regardless of the materials that they have available” (National Council of Teachers of Mathematics [NCTM], 2014, p. 71). This lack of deep understanding may have more to do with lack of exposure than anything else.

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Medium 9781942496397

Appendix B: Completed Diagram for Classifying Quadrilaterals

Juli K. Dixon Solution Tree Press ePub
Medium 9781942496489

Chapter 2: Structure of Equations

Nolan, Edward C.; Dixon, Juli K.; Safi, Farshid; Haciomeroglu, Erhan Selcuk Solution Tree Press ePub

CHAPTER 2

Structure of Equations

The initial focus of this chapter is solving systems of two linear equations. The discussion will then focus on exploring different forms of linear and quadratic functions and linking expressions and equations to their visual representations. This exploration sets the stage for later work with other types of functions.

The Challenge

The initial task in this chapter provides an application of linear functions (see figure 2.1). This application is an extension from the context presented in chapter 1 (see figure 1.1, page 16).

Figure 2.1: A race between a father and son.

In this task, the two linear graphs representing distance over time intersect at a single point, indicating that the system of equations has a unique solution. In high school, there has traditionally been an emphasis on two methods for finding the solution of a system of linear equations—substitution and elimination. These methods don’t always address the meaning of the solution to a system of equations. What does the solution mean within a given context? This chapter explores various methods to make sense of solving systems of equations to illustrate the mathematical reasoning behind why different methods work and how they are interconnected graphically and algebraically. What does the solution mean graphically? What does a solution to a system of equations mean algebraically? You may wish to consider these questions before reading the discussion on graphical and algebraic solutions of the initial task in the following paragraphs.

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Chapter 5: Modeling With Functions

Nolan, Edward C.; Dixon, Juli K.; Safi, Farshid; Haciomeroglu, Erhan Selcuk Solution Tree Press ePub

CHAPTER 5

Modeling With Functions

How does the understanding of various function types enable you to make sense of and mathematize the world around you? This chapter explores ways to integrate the understanding of functions and algebraic concepts to make sense of the world around you. Real-world situations provide the setting to investigate functions and to purposefully use mathematics to explain, interpret, and make predictions through the use of modeling with functions.

The Challenge

A critical part of learning mathematics involves connecting mathematical content to relevant contexts in order to explore and analyze situations. Mathematical Practice 4, “Model with mathematics,” focuses on this aspect of mathematizing the world by using mathematics to examine, predict, and gain greater insight into everyday phenomena. What are some different ways that you can make sense of data using the mathematics studied in high school? Consider the task in figure 5.1.

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Medium 9781942496427

Appendix B: Completed Diagram for Classifying Quadrilaterals

Juli K. Dixon Solution Tree Press ePub

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