Math Manipulatives, K-9

Math Manipulatives, K-9
  • Publisher: ETA/Cuisenaire

Models help children think and reflect on new ideas. To that end, they should always be accessible for students to select and use freely.
- John A. Van de Walle, Elementary and Middle School Mathematics: Teaching Developmentally

Manipulatives are brightly coloured, mathematically provocative, and have an allure that even the most reluctant cannot overcome. And, with “hands-on-learning” becoming almost synonymous with good teaching, manipulatives have garnered a heightened interest all across the country.

There is good reason for the enthusiasm. Manipulatives enhance student understanding, enable students and teachers to have a conversation that is grounded in a common model, and help students recognize and correct their own errors in thinking.

Tips to using manipulatives successfully:

  • The concept must first be understood by the student and the manipulative must be appropriate.

    Manipulatives do not by themselves develop a concept. For example, unless a student understands the relationship between 1’s, 10’s and 100’s, place value blocks will be nothing more than rectangular prisms that are fun to stack! However, once students understand that relationship, and they see a “flat” can represent 100, and a “stick” can represent 10, they can use the manipulative effectively as a “thinker toy” (Seymour Papert) to investigate, hypothesize, explore, and extend the concept.
  • Students need adequate time if they are to use a mathematical model effectively.

    Students need to explore the attributes of the manipulative and to see its mathematical relevance. In fact, initially the physical characteristics of the manipulative often prove distracting for students; so teachers need to help students make the connection between the concept and the relevant attribute. For this reason, research suggests that fewer manipulatives used over sustained periods of time are more effective than a variety of models used with limited experience. (Adding It Up, 2001, p. 198)
  • Classroom routines need to be established to maximize learning.

    By thinking about organizational issues in advance, teacher stress can be reduced and on-task time can be increased. Buckets, bins and baggies make for easy storage, but the storage decisions should reflect the grouping arrangement of the classroom. If there are six groups, there need to be six containers; sixteen pairs means sixteen baggies. Distribution, usage and clean-up routines are needed: Who gets the materials? Who returns them? How is congestion reduced? Where can they be used? Where are they returned? How will students avoid losing items?