Because of the abstract nature of mathematical concepts, instruction in mathematics at every level benefits from the use of multiple teaching strategies which include a variety of hands-on tools that augment verbal instructions. This is known as the dual-code theory. Creative teachers can use a variety of common items to assist in math concepts from bottle caps, straws, dice, and dominos to playing cards. However, there are tried and true manipulatives that are widely used and easily accessible o most schools.
• A good manipulative will have the ability too function in multiple ways: addition, subtraction, grouping, division, patterning and more.
• Can be used at multiple levels so remains appropriate as the student progresses through concepts
• Is fun and enjoyable, encouraging imaginative play.
• Can be used individually or in pairs and groups. (I,e,blocks)
• Is safe and durable.
Pattern Blocks and geometric blocks:
For young students, these colorful blocks come in a variety of shapes and colors and can be used for adding, subtracting, fractions, building and for learning geometric concepts. They encourage play and group participation and can be applied to many problem-solving skills and can be used throughout many levels by increasing the challenge of the exercises.
Base Ten Blocks:
Base 10 blocks include small cubes which represent one (one cube = one unit) as well as “rods” (ten cubes connected) and a 100 –flat. The youngest to the oldest of elementary students can benefit from the hands-on nature and multiple concepts explored with base-ten blocks. At the earliest level, these blocks introduce students to the concepts of one, ten and one hundred and begin to recognize the patterns. They learn important language concepts (one cube is a unit) and through the levels eventually use the blocks to learn multiplication, division and even decimals, fractions and place-value. Once a teacher explores the possibilities of the base-ten blocks, they can be used all through the elementary levels of math.
As the name implies, geoboards are considered tools for exploring geometric shapes and concepts; however, they can be used for much more. A geo-board is a flat tray measuring 11 x 11 with tiny “pegs” protruding around which one can wrap elastics to make various designs and shapes. With them, students can explore spatial relationships, area and perimeter as well as concepts such as symmetry.
While these are the top three choices, if I were restricted to three, I would also recommend tangrams, dice and even dominos. And of ocurse, thee are many online sources of manipulatives, as well.
Increasing in use and popularity or virtual manipulatives which not only address math standards for [problem solving and reasoning but also address the growing focus on technology in education. Virtual manipulates are two-dimensional representations of such tools as tangrams, geoboards, and base-ten blocks. A good source of online math manipulates can be found at the National Library of Virtual Manipulatives.