Overview

In this course, participants will learn about different components and levels of proportional reasoning. They will complete classroom tasks that illustrate ways to develop stronger conceptual understanding and target different components of proportional reasoning. They will use video and written examples of student work. They will also conduct a student interview in order to reflect on students’ approaches to proportions problems and to identify evidence of proportional reasoning at various levels. For the final project, participants will create a lesson that targets a component of proportional reasoning and that incorporates questioning techniques learned in the course. They will provide a rationale for the lesson that relates to the material learned in the course and reflect on their own learning.

Goals and Products

This course will enable participants to:

• Understand and identify different components and levels of proportional reasoning
• Broaden their repertoire of classroom tasks to use to develop students' conceptual understanding of proportionality
• Develop skills and tools for analyzing students' thinking about proportionality
• Apply those skills and tools to a lesson on proportional reasoning that is appropriate for middle school students

As a final product, participants will create a lesson plan related to proportional reasoning promoting both conceptual and procedural understanding that can be used in the classroom. The Final Project Description outlines the specific elements that should be included in the lesson. It provides a table that summarizes the components of the final project and benchmark dates to help you in planning your project. The lesson plan should be designed around particular learning goal(s) connected to an area of proportional reasoning. There are two key companion elements to the Lesson Design: The Student Interview and The Personal Reflection. The Student Interview is described in Session 4 and is to be conducted in Session 5. The Personal Reflection consists of a series of questions that you will answer throughout the course and complete during Session 6.

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:

The first session introduces the concepts that will be used throughout the course. Session 2 focuses on determining when a situation is proportional. Sessions 3 and 4 investigate three additional components of proportional reasoning: understanding the invariance of ratio, seeing ratios as composite units or “units of units,” and using proportional reasoning to focus on the relationships rather than specific values. Session 5 connects math with pedagogy by exploring student questioning techniques. The final session guides participants to reflect on their learning in the course and complete their final projects.

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

This course will help teachers to enable their students to meet the following Content Standards as identified by National Council for Teachers of Mathematics (NCTM) (http://standards.nctm.org/document/chapter6/index.htm) .

Number Strand: Understand numbers, ways of representing numbers, relationships among numbers, and number systems
- Understand and use ratios and proportions to represent quantitative relationships

Number Strand: Compute fluently and make reasonable estimates
- Develop, analyze and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Algebra Strand: Analyze change in various contexts
- 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
- Understand how mathematical ideas interconnect and build on one another to produce a coherent whole

This course will also help participants meet the ISTE Educational Technology Standards and Performance Indicators for All Teachers.