Manipulatives: How They Make Better Math Students ...
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One of the easiest ways to motivate math learners of all ages is to allow them to explore mathematical concepts
using manipulatives.
Manipulatives are concrete tools or models that assist students in thinking about and testing their mathematical
ideas. Researchers in math education, such as John A. Van De Walle, have shown that children learn mathematics when
they are allowed to participate actively in the process of constructing mathematics.
Gone are the days of “just tell me the answer”. Parents can help their children, elementary through highschool
age, by asking how they did their problem solving and by allowing them to demonstrate using manipulatives.
Parents can purchase manipulatives such as fraction circles, algebra scales, or base10 blocks. However, children
can be encouraged to take ownership of their learning by making their own tools and models.
Math learners are never too old to use manipulatives. High school students struggling with concepts in algebra,
trigonometry, and geometry also benefit because these tools make the abstract more concrete.
Here are several ways to use manipulatives to motivate the mathematics learner:
Numbers. Buttons or blocks can be used initially for counting, comparing quantities, and making patterns.
Math Operations. Young children enjoy hopping down giant, homemade number lines to do addition and subtraction. The
cubes, rods, and squares of base10 blocks are used to represent place value. Older children become developmentally
ready to accept the same blocks as representative of decimal place value.
Time and Money. Students enjoy solving money matters using coins and bills. Simple analog clocks can be constructed
from paper plates. For simplicity, time is told initially using only the hour hand; the minute hand can be added
later.
Measurement. Children benefit from using rulers, meter sticks, yard sticks, and measuring cups found around the
house.
Fractions. Even high schoolers have difficulty explaining fractions and equivalency. A set of fraction circles and
a set of fraction bars are a good investment.
Geometry. The world is full of geometrical patterns, symmetry, angles, plane figures, and polyhedra. A 2007 study
(Martin, Lukong, & Reaves) concludes that concrete, virtual, and software manipulatives all contribute to
children’s understanding of geometry.
A set of geometry sticks is a useful tool for older students to investigate angles, perimeter, bisection,
parallelism, and perpendicularity. Cubes can be used to determine area or volume and later generalized into
algebraic concepts.
Algebra and Functions. Algebra tiles or balance scales are used to express equations. Students can measure change
in everyday events and determine functions using manipulatives. High schoolers will naturally end up discussing
derivatives.
Manipulatives are an enjoyable way to bring math learning into the home. Parents should consult the Help Me With Math website for more resources and
tips.
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