Building Math Concepts with Manipulatives

January 5, 2018 – AWE Learning Staff

Manipulatives, often associated with learning mathematical concepts, are physical objects that are used as teaching tools to engage students in hands-on learning. These objects can be integrated into lessons to introduce, practice, or remediate a concept.

Learning occurs in three stages: Concrete Stage, Representational or Pictoral Stage, and Abstract Stage. Manipulatives play an integral part in the Concrete Stage. This is where a concept is introduced and early learners explore the concept using the manipulatives in a meaningful way. In the Representational Stage, the manipulatives used in the Concrete Stage are now represented as pictures, rather than concrete objects. Finally, in the Abstract Stage, mathematical signs (i.e. numerals, addition or subtraction signs, etc.) are used to express the concept in symbolic language. A student progresses through the stages of learning; learners must master the concrete and representational stages, prior to understanding concepts abstractly.

Through these three stages of learning, learners are able to transform thinking from simply using a manipulative, to using mathematical language and symbols. Manipulatives are a building block in teaching these mathematical concepts. Using manipulatives is a constructivist approach to education because it gives students the opportunity to be actively engaged in their learning. Teachers, librarians, and parents or guardians, play an essential role in helping early learners to use manipulatives successfully to build their mathematical knowledge.  The students explore the manipulatives and are encouraged to ask questions before and during the lesson.

According to the National Council of Teachers of Mathematics (NCTM), manipulatives should be used in teaching a wide variety of topics. These topics include, but are not limited to, sorting, ordering, distinguishing patterns, making measurements, exploring and describing spatial relationships, and engaging in problem solution. Furthermore, the use of manipulatives encourages the evaluation of items being used. Early learners will explore the characteristics of and distinguish between weight, height, length, shape, and size of the object.

Manipulatives are a great way for early learners to begin building their mathematical knowledge, especially when starting to learn the beginning concepts of sorting, or math operations of addition and subtraction. For visual and tactile learners, this helps them to ‘see’ the concept and make sense of it. Furthermore, using objects helps to keep early learners engaged, and opens the chance to ask questions, furthering their learning. The use of manipulatives has proven to have many benefits for early learners. In fact, since the early 1900s, manipulatives have been considered essential in teaching mathematics at the elementary school level. To this day, they are still highly encouraged and used in all grade level classrooms, including elementary school.

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