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
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)
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)
Manipulatives show positive impacts when combined with:
- virtual manipulative software
- reflective practices
- cooperative learning
- activities that are exploratory and deductive in their approach
Types and Uses
Unifix Cubes (colored linking cubes)
- learn measurement using nonstandard units
- visualize concept of area and geometric shapes
- percent, probability and fractions
- 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)
Research has shown that long-term use of manipulatives is more effective than short-term use (Hartshorn, 1990).
“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).
Using manipulatives in math help students to understand and analyze concepts with a concrete purpose.
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.
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
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.