Teaching Mathematics with Manipulatives, Grades 7-12

A. Course Number and Title: EDSE 660: Teaching Mathematics with Manipulatives, Grades 7-12

B. Catalog Description: Methods and materials for using manipulative devices to teach middle and high school level mathematics.

C. Credit: 3 hours (undergraduate or graduate)

D. Prerequisite: none

E. Intended Audience: middle and high school teachers of mathematics

F. Instructor: Dr. Ed Dickey

1. an understanding of how hands-on manipulative devices support teaching and learning within the five content area of the South Carolina Mathematics Academic Standards.

2. an appreciation of how manipulative devices can address the learning needs of a diverse population of mathematics learners.

3. skills needed to use manipulative devices in the teaching of mathematics.

4. skills to assess if manipulative devices foster understanding of mathematics.

** B. Objectives: The Collaborative Educational Leader in
mathematics will: **

1. develop skills needed to select and use manipulative devices for teaching about numbers and numeration systems.

2. develop skills needed to select and use manipulative devices for teaching about probability and statistics.

3. develop skills needed to select and use manipulative devices for teaching about patterns, relationships, and functions.

4. develop skills needed to select and use manipulative devices for teaching about algebra concepts and operations.

5. develop skills needed to select and use manipulative devices for teaching about geometry and spatial sense.

6. develop skills needed to select and use manipulative devices for teaching about measurement.

7. develop the ability to construct alternative assessment techniques involving the use of manipulative devises in the teaching of mathematics.

8. identify strategies for using manipulatives in the teaching of mathematics cooperatively.

9. identify strategies for using manipulatives in the teaching of mathematics within realistic contexts.

· Dickey, E. M. Course Materials for Teaching Middle and High School Mathematics with Manipulatives. University of South Carolina: 1999.

· Middle and High School Mathematics Manipulatives Kit including overhead set of Algebra Lab Gear, overhead geoboard, Mira, and other devices.

1. Viewing all videotapes or DVDs.

2. Completion of all homework assignments.

3. Submission of four Lab Assignments.

4. Submission of Assessment Project (graduate students only).

5. Final examination.

1. All students must have access to items in the supplied manipulative kit.

2. Submission of Lab Assignments on or before due dates (to be specified).

3. Submission of Assessment Project as described below on or before due date.

4. Submission of a Final Examination on or before due date.

Grading will be on a traditional A-F scale. The Lab Assignments will account for 20% of the final grade, the Project will account for 45%, and the Final Examination will account for 35%. For undergraduate students, the Lab Assignments will account for 40% of the final grade and the Final Examination will account for 60% of the grade.

93-100=**A** 86-92=**B+** 80-85=**B** 76-79=**C+**
70-75=**C** 60-69=**D** 0-59=**F**

1. Manipulatives: What and Why?

2. Integers and Integer Arithmetic

3. Rational Numbers

4. Data Analysis

5. Probability and Statistics

6. Patterns

7. Algebra: Multiplication and Factoring

8. Algebra: Polynomial Arithmetic

9. Algebra: Equations

10. Geometry: Triangles and Polygons

11. Geometry: Transformations

12. Geometry: Solids

13. Measurement: Length, Angles and Weight

14. Measurement: Volume and Surface Area

Fourteen video lessons containing approximately 90 minutes of direct instruction and one hour of self-check activities will be provided to each student. The Course Materials book contains the Lab Assignments and supplemental readings. The course is offered during the Fall and Summer terms. During summer sessions, lessons may be completed during the first summer session (June), during the second summer session (July), or over a combination of both summer sessions (June to early August). There will be one 3-hour class meeting in Columbia to be scheduled early each semester.

___________________________________________

**Assessment
Project for EDSE J660**

Throughout this course, we have highlighted how different assessment strategies might be used to gain information about student learning in mathematics. In this project, you will develop an assessment strategy and rubric to be used with a mathematics lesson involving manipulatives. Your project will consist of four sections: 1. The Lesson, 2.The Assessment Strategy, 3. Student Work, and 4. The Scoring Rubric.

1. The Lesson. Select one of the strands from the South Carolina Mathematics Academic Standards. Describe a lesson within that strand involving one or more manipulatives for students in any grade between 7 and 12. The lesson may be something you have taught before or something you have read about in a journal such as the Mathematics Teacher or a book such as one of the Addenda Series books. The lesson may NOT be something that is covered in the videotapes or Study Guide for this course. This section need not be very detailed but should include enough information so that the reader can have a clear idea of what has happened in the classroom. Be sure to include the instructional objective(s) for this lesson, that is, state clearly what you expect students to learn and be able to do as a result of completing the lesson.

2. **The Assessment Strategy. **
Describe an assessment strategy for the lesson you have selected. The
assessment strategy you select must be one of the five we have highlighted in
this course: writing, performance tasks, observations, portfolios, and extended
investigations. This section should include a detailed description of what the
students will do in the assessment activity. For example, if the assessment
strategy is a writing task, describe what they will do prior to writing, provide
any writing prompts you think they might need, and produce the instruction sheet
they will receive. Be sure to list the manipulative(s) used and clearly
describe their role in the assessment. The assessment strategy should relate to
at least one of the objectives of the lesson, that is, through this assessment
strategy you will gain information about how well students have learned what
they were supposed to learn or how well they can do what it was they were
supposed to be able to do as a result of completing the lesson.

3. **Student Work. **Produce at
least one example of student work based on the assessment strategy you described
in #2. If you have access to students, the easiest way to do this is have them
use the assessment strategy and submit a copy of their work. If you have no
access to students or teen-agers who can act like students, you will need to
make up a response on your own.

4. **Scoring Rubric. **Develop a
scoring rubric to assess student work using your assessment strategy. The
rubric must have at least four levels (assuming one level is no response).
Score the sample student work from #3 using your rubric including an explanation
of how the score was derived.

**Scoring Rubric for this Assessment Project**

Each of the sections above will be assessed 0, 1, 2, or 3 points:

**
0**
points -- section not addressed

**
1**
point -- significant information is missing or not described clearly; another
teacher would not understand how to implement what is being described

**
2**
points -- only minor items are not addressed; a few parts are not clear; most
teachers would understand how to implement what is being described

**
3**
points -- all items are fully addressed; all descriptions are clear; teachers
would find this easy to implement