# Human Intelligence: Theories and Developmental Origins

## CONTENTS OF CURRICULUM UNIT 01.06.12

- Narrative
- Math Anxiety
- Types of Learners
- The Kinesthetic Learner
- Levels of Mastery
- Types of Manipulatives
- Incorporating the Computer
- Why don't all Teachers use Manipulatives?
- Lesson 2 - Fractions with Tangrams
- Lesson 3 - Fractions with Cuisenaire Strips (or rods)
- Manipulatives that can Enhance Math Skills - Ideal for Kinesthetic Learners
- Games That can Enhance Math Skills - ideal for Intrapersonal, Verbal, Visual and Kinesthetic Learners
- Internet Sites That Can Enhance Math Skills
- Internet Sites to Integrate Mathematics into the Curriculum
- Commercial Software Programs That Can Enhance Math Skills
- Parent Resources
- Teacher Resources

### Unit Guide

## Multi-Sensory Manipulatives in Mathematics: Linking the Abstract to the Concrete

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## Why don't all Teachers use Manipulatives?

- 1) Lack of training, many teachers feel that they do not know how to teach using manipulative and, therefore, are not comfortable using manipulatives and hesitate to use them in the classroom. New Haven teachers are fortunate to have access to numerous classes and workshops to learn how to teach using manipulatives. In addition, the companies that distribute the manipulatives provide books; pamphlets and videos on ways the materials can best be used. There are also countless articles on using manipulatives in mathematics teaching journals such as the NCTM's Arithmetic Teacher magazine.
- 2) Availability of manipulatives, although New Haven teachers are very fortunate to have an ample and varied supply of manipulatives at their disposal. Even without resources any teacher can easily come up with a can of buttons or straws.
- 3) Lessons using manipulatives may perhaps be noisier and not as neat. Using manipulatives works nicely in a cooperative learning setting. It is a good idea to use plastic cups or zip-lock sandwich bags as a way to keep manipulatives organized.
- 4) A fear of the breakdown in classroom management. Manipulatives require a great deal of prior planning and organization.

I enjoy mathematics and I believe that the learning process should be enjoyable for all types of learners. I believe that the use of manipulatives is beneficial in all areas of mathematics. The focus of this unit is the use of multi-sensory manipulatives in the teaching/learning of mathematics. The unit is intended for 5th and 6th grade students. The area of mathematics that is being covered is fractions. I have chosen fractions because it appears to me that that is the area in which the majority of my students have not mastered through conventional (worksheets, etc.) means. When learning fractions there are so many rules to know, there are rules for adding and subtracting fractions, different rules for multiplying fractions, and then dividing fractions is another story altogether. Students have to learn about denominators, numerators, proper and improper, mixed numbers. The students probably start learning about fractions informally at a young age when simply sharing a snack with a sibling. Formal education of fractions probably begins in the 4th grade. Students then learn about fractions each year from then on, yet very few 8th graders have a good handle on fractions. There is no ownership. The concepts of fractions are very abstract. I feel that through the use of multi-sensory manipulatives I might afford my students the opportunity to buy into fractions.

This unit includes lessons that extensively use pattern blocks, tangrams, and Cuisenaire strips. Pre-lesson activities include the making of tangram sets and Cuisenaire strips. In addition, the lessons include interactive Internet activities that coincide with each manipulative type. The unit will culminate with a Family Math Night at which time the students, along with their families, will partake in mathematics activities to include pattern blocks, tangrams, various computer software programs and several Internet activities. I have also compiled a Mathematics Guide to Parents, 'Everything You Ever Wanted to Know About Math But Were Afraid to Ask' which will be made available to each family.

The problem that I see is that the students in New Haven (and Betsy Ross Arts Magnet School in particular) are substantially behind the rest of the State in Mathematics Mastery. I believe that the use of multi-sensory manipulatives will help but I can only reach the 90 or so students that I teach. I feel that in order for this unit to be fully effective it will be necessary for me to reach out to my fellow Mathematics teachers at Betsy Ross.

I am excited and motivated to use multi-sensory manipulatives in teaching mathematics. As a new teacher I have been exposed to (through recent training) and have researched various manipulatives and techniques for their using. I have also observed that many of the veteran mathematics teachers are not using manipulatives (this is not due to lack of supplies because the New Haven district Mathematics Department is very generous). Due to the extensive research that I have done using the Internet I was chosen to present a teacher workshop on 'Using the Internet to Integrate Mathematics into the Curriculum' at a recent in-service training session (see attached listing of internet sites). The workshop was well received, gaining me the respect of my fellow teachers. Since then several teachers have come to me for direction. Now that I have the support and confidence of our staff it is my hope to present future workshops. It is my intention to make this unit available to all mathematics teachers at Betsy Ross Arts Magnet School by way of a Multi-Sensory Manipulatives Mathematics Teachers' Workshop.

Lesson 1: Fraction Puzzles with Pattern Blocks

Purpose: Develop an understanding of fraction using pattern blocks as well as to reinforce geometric shapes.

Materials: Overhead projector

Overhead pattern block pieces

Pattern Block pieces - each student needs 3 red trapezoids, 3 blue rhombuses and 12 green triangles

This is a teacher-directed activity. Students will, in the following sequence:

*(figures available in print form)*

Pre-Lesson Activity: Have students stand around a table that has an ample supply of pattern blocks placed in the center of the table. The teacher, using a timer, will allow the students to create a design, when the timer sounds (says 1 minute) the students will move to their right and build upon (not destroying or taking away from) their neighbor's creation. Activity ends when students arrive back at their original location.

- 1) build a triangle that is 1/1 green
- 2) build a triangle that is 4/4 green
- 3) build a triangle that is 2/4 (1/2) blue and 2/4 (1/2) green
- 4) build a triangle that is 4/4 green (helpful to repeat this step before doing #5)
- 5) build a triangle that is ¾ red and ¼ green
- 6) build a triangle that is 9/9 green
- 7) build a triangle that is 1/9 green, 2/9 blue, 6/9 (2/3) red
- 8) build a parallelogram (each pair of sides is parallel) that is 8/8 green
- 9) build a parallelogram that is 6/8 (3/4) blue and 2/8 (1/4) green
- 10) build a parallelogram that is 6/6 green
- 11) build a parallelogram that is 4/6 (2/3) blue and 2/6 (1/3) green
- 12) build a trapezoid (only one pair of sides is parallel) that is 12/12 green
- 13) build a trapezoid that is 6/12 (1/2) green and 6/12 (1/2) blue

Pre-lesson Game: Teacher creates a design out of connected hexagons. Two students play the game by taking turns placing either a green, blue or red pattern block pieces on the design. A player losses if they place the last pattern block piece on the design.

Internet Activity: http://math.rice.edu/~lanius/Lessons. Click on pattern blocks (yellow hexagon)