Multi-Sensory Manipulatives in Mathematics: Linking the Abstract to the Concrete
Judith L. Bellonio
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Levels of Mastery
Sharma feels there are six levels of mastery of mathematical concepts: intuitive, concrete, representation (pictorial), abstract, applications and communication. According to Sharma, ideally, each mathematics concept should be introduced beginning at the communication level. However, almost all mathematics-teaching activities take place at the abstract level. It is believed that students have a tendency to forget when taught only at the abstract stage. Students therefore become frustrated because mastery was never fully attained. Students will then have difficulty in learning mathematics.
