Some of the manipulatives that are commonly used in teaching mathematics are blocks, bear counters of different colours and sizes, base ten, patterning tasks and many more. These manipulatives are very helpful for children to used for classification, addition and substraction, patterning and even fraction.
How effective are these manipulatives to children in learning the concept of Math?
Research in England, Japan, China, and the United States supports the idea that mathematics instruction and student mathematics understanding will be more effective if manipulative materials are used (Improving Mathematics Teaching by Using Manipulatives; James W.Heddens, Kent State Unversity)
Take the fraction circles, it is a terrific ways for teaching students about fractions and their relationships.
Fraction circles are a set of nine circles of various colours. Each circle is broken into equal fractional parts and uses the same-sized whole. The circles included are one whole as well as circles divided into halves, thirds, quarters, fifths, sixths, eighths, tenths, and twelfths.
Depending on the manufacturer, fraction circles can be transparent for use on an overhead projector for whole class activities or opaque for use at students’ desks or with a document camera. Fraction rings are clear plastic rings that are open in the middle and can hold the fraction circles in the center. (http://www.edugains.ca/resources)
Example how you can use manipulative (concrete materials) to teach Maths.
Jerome Bruner 3 stages of learning theoryJerome Bruner develops 3 stages of learning theory such as :
1) direct manipulation of objects (concrete),
2) representation of external objects visually as images (pictorial),
3) symbolic representation (abstract)
Jerome Bruner believes that when we teach, we should first present a concept that involve concrete objects. Using of concrete materials to count will make them understand clearly the concept of counting. Children love to play and they learn better through play.