Overview

This course will help middle school teachers learn approaches to teaching functions using visual models. Participants in this workshop will become familiar with strategies to help students develop a strong conceptual understand of functions and with tasks that allow students to explore situations of both linear and non-linear functions. Participants will also engage in creating classroom tasks to help students make connections between multiple representations of functions. Participants will evaluate a variety of applets throughout this course, and they will conduct an interview with a small group of students about their experiences using an applet. In the final project for this course, participants will design a lesson plan using an applet to explore the concept of function.

Goals and Products

This course will enable participants to:

• Learn approaches to teaching functions using visual models
• Become familiar with strategies to help students develop a strong conceptual understanding of function
• Become familiar with tasks that allow middle school students to explore situations of both linear and non-linear functions
• Create classroom tasks that allow students to make connections between multiple representations of functions (patterns, tables, graphs and equations)
• Develop strategies for generalizing a pattern or situation
• Explore the use of technology in supporting student learning about functions

Format and Requirements

This course is divided into six one-week sessions which each include readings, an activity and an online discussion among course participants. The time for completing each session is estimated to be two to four hours.

The outline for the course is as follows:

Prerequisites

This is an introductory course for teachers, technology specialists, curriculum specialists, professional development specialists, or other school personnel. Participants are expected to have regular access to computers and proficiency with e-mail and current web browsers.

Content and Technology Standards

The standards addressed in this course are:

Algebra Strand:

Understand patterns, relations and functions

- Represent, analyze and generalize a variety of patterns with tables, graphs, words and, when possible, symbolic rules

- Relate and compare different forms of representation for a relationship

- Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations

Use mathematical models to represent and understand quantitative relationships

- Model and solve contextualized problems using various representations, such as graphs, tables and equations

Analyze change in various context

- Use graphs to analyze the nature of changes in quantities in linear relationships

Problem-Solving Standard

- Solve problems that arise in mathematics and other contexts

- Apply and adapt a variety of appropriate strategies to solve problems

Connections Standard

- Recognize and use connections among mathematical ideas

Representation Standard

- Select, apply and translate among mathematical representations to solve problems

Technology Principle

- Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances student’s learning