Math Manipulatives Help All Students

14 Mar

Pure mathematics is, in its way, the poetry of logical ideas.  ~Albert Einstein

I never did very well in math – I could never seem to persuade the teacher that I hadn’t meant my answers literally.  ~Calvin Trillin

Introduction

Manipulatives are proving to be effective tools for teaching certain math concepts to all students (Berkas, 2007).  Students learn best through active experiences rather than lectures or passive listening.  Visual images stick with people longer and better than abstract or language based concepts. (Stover, ret. 2011)  Manipulatives are objects that can be touched and moved by students to introduce or reinforce a math concept.  Since 1940 to the present day, the National Council of Teachers of Mathematics (NCTM) has encouraged all grade levels to use manipulatives in daily math instruction.  Many concepts in math are abstract.  Manipulatives are useful in helping students move from the concrete to abstract level. (Hartshorn, 1990)  Students are being encouraged to use manipulatives to demonstrate understanding in representational and abstract stages (Berkas, 2007).  They are beneficial for students who have been diagnosed with a learning disability.  Manipulatives provide additional reinforcement of basic math skills and enables them to complete math problems independently. (Schreiner, 2010)

Manipulative Toolbox

Once a child is familiar with a manipulative it should be made available to use at any time to help them think, reason and solve problems.  After a while, they begin to develop a great toolbox of ideas for solving problems. (Rudnicki, 2010)

Positive Impacts

Manipulatives show positive impacts when combined with:

1. virtual manipulative software
2. reflective practices
3. cooperative learning
4. activities that are exploratory and deductive in their approach

(Berkas, 2007)

Types and Uses

• learn measurement using nonstandard units
• visualize concept of area and geometric shapes
• percent, probability and fractions

Two-Color counters

• teach equivalence
• number concepts/ strategies for addition and subtraction
• create visuals showing ratio, proportion, fractions
• understand odd/even numbers
• create patterns

Playing cards, dominoes and number cubes

• illustrate decimals or whole numbers
• mental math games (addition, subtraction and/or multiplication war)
• understand probability and logical reasoning

Pattern blocks and tangrams

• understanding of spatial sense and geometry
• create shapes with certain number of sides, angles, complex patterns
• solving word problems

Measuring cups, volume containers, rulers, scales, and clocks

• concept of measurement

(Stover, ret. 2011)

Critique

Research has shown that long-term use of manipulatives is more effective than short-term use (Hartshorn, 1990).

Interesting Facts

“Some state and local systems have mandated the implementation of manipulatives through policy, law, or curriculum documents.  Some have also provided funding.” (Hartshorn, 1990)

Manipulatives help hold the attention of the inattentive learner (Stover, ret. 2011).

Multiple Intelligences

Logical Mathematical

Using manipulatives in math help students to understand and analyze concepts with a concrete purpose.

Bodily Kinesthetic

In terms of mental and physical activities, manipulatives allow students to use their mind and parts of their body to solve problems.  To show students how much a gallon is, start with cups of water, then pour those cups to make pints, then quarts to the eventual gallon.  This is both a physical and mental process that show students the meaning of a gallon.

Interpersonal

Often times in the fields of math and science we work with a group of people to solve a problem. Using manipulatives in groups allow students to work together and to listen to the ideas of their peers to come to a conclusion.

Universal Design for Learning

I. Provide Multiple Means of Representation

1. Provide options for perception

• Options that customize the display of information
• Options that provide alternatives for visual information

2. Provide options for language and symbols

• Options that illustrate key concepts non-linguistically

II. Provide Multiple Means of Action and Expression

5. Provide options for expressive skills and fluency

• Options in the tools for composition and problem solving

III. Provide Multiple Means of Engagement

7. Provide options for recruiting interest

• Options that enhance relevance, value and authenticity

8. Provide options for sustaining effort and persistence

• Options that foster collaboration and communication

“7 Musts for Using Manipulatives”

Resources

Berkas, N. & Pattison, C. (2007). “Manipulatives: more than a special education intervention.” National  Council of Teacher of Mathematics.

Hartshorn, R. & Boren, S. (1990). “Experiential learning of mathematics: using manipulatives. ERIC Digest

Rudnicki, A. (2010). “Why use manipulatives to teach math.”       http://www.ehow.com/print/about_664188_use-manipulatives-teach-math_.html.

Schreiner, E. (2010). “How to use manipulatives to teach math to ld students.”                http://www.ehow.com/print/how_5991197_use-teach-math-ld-student.html.

Stover, E. (ret. 2011). “About the use of manipulatives in math.”               http://www.ehow.com/print/about_5048097_use-manipulatives-math.html.

Stover, E. (ret. 2011). “How to use math manipulatives in the classroom.”                http://www.ehow.com/print/how_5031920_use-math-manipulatives-classroom.html.

Posted by on March 14, 2011 in Uncategorized

2 responses to “Math Manipulatives Help All Students”

1. March 20, 2011 at 11:06 pm

Hello Michael!