MANIPULATIVES IN MATHEMATICS I
Ma 515
Course Description
This course explores the use of
manipulatives such as geoboards, Cuisenaire rods, number lines, software and CD
ROM materials in the teaching of
mathematics in the elementary and middle schools. Both commercial and teacher-made
manipulatives will be utilized.
Goals of the Course
1.
To enable students to attain a level of comfort and excellence in
creating and conducting activities in mathematics using manipulatives.
2.
To provoke thinking about mathematics and thinking about mathematics
education.
3.
To emphasize the importance of exploration and the actual doing
of mathematics in the classroom.
4.
To instill the importance of problem solving, communication, and
reasoning in the mathematics curriculum.
5.
To emphasize the importance of estimation, number sense, spatial sense,
patterns and relationships, making sense of data, and making mathematical
connections in the mathematics curriculum.
6.
To model the use of experimentation, games, cooperative learning, and
the use of technology in the classroom.
7.
To provide insight into assessment procedures.
Instructional Procedures
The course is designed to enable students
to attain a familiarity and proficiency in using manipulatives to teach K-8
mathematics. The course is
conducted in such a way that it provides a model for the teaching process and
thus includes hands-on use of manipulatives that engages students to reflect on
mathematical ideas. The course should include discussion on how we know what
children are learning, how they communicate this, and what we do with this
knowledge. The course emphasizes
cooperative learning, writing, and assessment procedures.
Course Content
1.
Introduction to a variety of mathematical concepts.
2. Introduction to the wide variety of
commercial manipulatives that are available such as Cuisenaire rods, geoboards,
origami (paper folding), base ten blocks, and pattern blocks.
3.
Introduction to commercial software, LOGO, and CD ROM’s that are
available for the teaching of mathematics at the K-8 level.
4.
The teaching of K-8 mathematics through the use of manipulatives that
can be made or obtained inexpensively.
5.
The use of manipulatives in learning through games, exploration,
experimentation, and group work.
6.
The use of manipulatives in teaching mathematical concepts such as
estimation and measurement, base ten arithmetic, pattern recognition,
probability and statistics, and problem solving.
Evaluation Measures
1.
Class participation in activities.
2.
Reaction papers on films or lessons and activities.
3.
Projects (e.g., invent a game or activity which implements the
"doing" of math)
4.
Formal write-up for the thought process involved in the solution to a
math problem.
Bibliography
A.
Required Text
Elementary School Mathematics: Teaching Developmentally, 2d ed., by John A. Van de Walle,
Longman Publishing Group,
About Teaching Mathematics: A K-8 Resource by Marilyn Burns, Cuisenaire Company of
B.
Additional Required
Addenda Series: Grades K-6, National Council of Teachers of
Mathematics,
Subject-Matter Books: Grades K-6, National Council of Teachers of
Mathematics,
Geometry and Spatial Sense
Making Sense of Data
Number Sense and Operations
Patterns
Addenda Series: Grades 5-8, National Council of Teachers of
Mathematics,
Dealing with Data and Chance
Developing Number Sense in the Middle
Grades,
Geometry in the Middle Grades,
Measurement in the Middle Grades
Patterns and Functions
Understanding Rational Numbers and
Proportions
C.
Supporting Bibliography
Instructor's Manual to accompany Elementary School
Mathematics: Teaching
Developmentally, 2d ed., by John A. Van de Walle.
Standards for Curriculum and Evaluation, National Council of Teachers of
Mathematics, Reston, VA, 1989.
D.
Relevant Periodical Sources
Teaching Children Mathematics (formerly Arithmetic Teacher),
National Council of Teachers of Mathematics.
Elementary Mathematician, Consortium of Mathematics and Its
Application (COMAP).
Mathematics Teaching in
the Middle School,
National Council of Teachers of Mathematics.
E.
Other Resources
Videos
Mathematics: What are you teaching my child?
featuring Marilyn Burns, Scholastic, Inc.*
Mathematics with Manipulatives Series:*
Pattern Blocks
Cuisenaire Rods
Base Ten Blocks
Geoboards
Color Tiles
Six Models
Mathematics: Teaching for understanding.
Cuisenaire Company of America.*
Manipulatives
Geoboards*
Mira Math*
Algeblocks*
Instructor's Cuisenaire Manipulatives Set
and resource book*