# A Mathematical Exploration for Practicing Special Education and Classroom Teachers: Additive Reasoning, Multiplicative Reasoning, Proportional Reasoning and Rational Numbers

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### Course Description

This course is designed for the practicing educator (referred to as participant) to develop a stronger understanding of the mathematics and research about how students learn mathematics in the areas of: additive reasoning, multiplicative reasoning, proportional reasoning, and rational numbers. We will begin with a review of the National Math Panel Report and the NCTM Focal Points to focus on the “non-negotiable” content within the school math curriculum. Each math topic will be addressed within the context of understanding student work and the strategies that will assist professionals to work with students who struggle in these areas of mathematics. Participants taking this course will need to have access to three to five students who have a variety of mathematical abilities.

### Learning Objectives:

- Participants will become familiar with the body of mathematical research about how students learn and understand mathematics.

- Participants will be able to identify a student’s developing understandings in the areas of additive, multiplicative, proportional reasoning and rational numbers.

- Participants will increase their understanding of mathematics, specifically additive reasoning, multiplicative reasoning, proportional reasoning and rational numbers.

- Participants will be able to construct and conduct clinical interviews that will answer the question, “How does Student X understand the mathematical topic being studied?”

- Participants will be able to construct instructional plans based on the mathematical understanding of their students.

**Required Text and resources:**

Van de Walle, John A. (2007). *Elementary and Middle School Mathematics: Teaching Developmentally*.* *Boston: Allyn and Bacon. (Seventh Edition )

Petit, M., Laird, R., Marsden, E. (2010). *A Focus on Fractions: Bringing Research to the Classroom.* Chapters 1-5

NCTM Focal Points –found at http://www.nctm.org/standards/focalpoints.aspx?id=282

Vermont Standards and Grade Level Expectations – found at http://education.vermont.gov/new/html/pubs/framework.html

National Math Panel Report – found at http://www.ed.gov/about/bdscomm/list/mathpanel/index.html

Adding it Up, Chapter 4

*Hong, B. & Ehrensberger, W. (2007). Assessing the Mathematical Skills of Students with Disabilities.

*National Research Council (2009). *How Students Learn: Mathematics in the Classroom. *Chapter 5 pages 267-279. ISBN 0-309-089492

*Provided for you in digital form through the wiki