velvetpage | Hands-on math: Manipulatives in Brief (Reply)

Hands-on Learning with Manipulatives: An Overview for Parents and
Administrators

1) What are manipulatives?

Manipulatives are concrete objects that are used in the teaching and
learning of mathematics. Some of them are very simple - small plastic
shapes for counting and sorting, coloured squares of plastic (tiles) and
interlocking blocks are all useful as manipulatives. Some of them, like
tangram sets or geometric solids, are more complex. All of them are
designed to help students develop their mathematical understanding.

2) Why should teachers use manipulatives to teach mathematics?

Manipulatives help access all of the learning styles that come into our
classroom. For a kinesthetic learner (someone who learns through
movement) the act of moving the materials around can help them see
patterns and develop concepts in a way that pencil-and-paper activities
simply don't. For a visual learner, the opportunity to manipulate
visual patterns and features without having to conceptualize and draw
each one individually is a huge boost to understanding. For an oral
learner, having a concrete object whose properties and movements can be
described is a good way to support the development of mathematical
language. No matter which learning style your child prefers,
manipulatives help support all of them, leading to a deeper conceptual
understanding of mathematics.

All students move through several steps in learning mathematical
concepts, beginning with a concrete step (dealing with objects they can
touch and manipulate) through a representational step (where they can
draw or otherwise describe something that is concrete) and eventually to
symbolic and abstract understanding (representing with symbols and
manipulating concepts in their heads.) Manipulatives help them with the
transitions through these steps, especially the concrete and
representational steps. Since teachers' goal is to get students
thinking about mathematical concepts using symbols and abstract
thinking, it is logical that they would seek tools to move students
through these stages.

3) How should manipulatives be used to get the most out of math lessons?

First, manipulatives need to be available when students conceive of a
need for them - even if teachers haven't planned for their use that day.
That means there need to be organized, available supplies of materials
in every classroom or group of classrooms. Second, students need the
opportunity to mess around with manipulatives, exploring their
properties through play, before being asked to do purposeful activities
with them; in addition to solidifying the basic properties of the
materials in their minds, this will serve to limit off-task behaviour
when there is a purpose for using that material later. Third, students
need the opportunity, not just to use manipulatives in proscribed ways,
but also to use them as a problem-solving tool, allowing them to engage
their hands and minds in activities that will stretch their
understanding of mathematical concepts.

4) What can parents do to support the use of manipulatives at school?

Let your children explore numbers through objects at home. Support them
doing Cheerio Math. Provide them with tape measures and rulers (in
metric units!) and let them measure objects around the house, and the
house itself! Expect that math homework will involve touching and
manipulating objects to discover their properties and to turn those
properties into mathematical understanding. Give your children
opportunities to talk about how they used manipulatives at school, and
what they learned from them. Then watch and enjoy your children's
exploration of their world through mathematics.