The Value of Manipulatives

The week’s math class, which focused primarily on fractions, demonstrated the value of manipulatives in learning. Manipulatives allow students to think and reason in more meaningful ways as students view and physically interact with physical objects that represent abstract mathematical ideas. Chapter 1 of Making Math Meaningful to Canadian Students, K-8 (Third Edition) discusses how research since the mid-1960s has shown that “the use of manipulative materials – concrete representations of mathematical ideas – is powerful in developing mathematical understanding” (pg. 4). In this blog post, I would like to focus on three reasons why manipulatives are powerful learning tools.

Manipulatives Make Abstract Concepts Concrete

Manipulatives allow students to interact with physical objects that illustrate abstract mathematical concepts. By viewing and manipulating physical objects, students are able to connect abstract mathematical ideas to the real world. Manipulatives help students to understand how math relates to their personal lives. For example, in class we read The Hershey’s Milk Chocolate Bar Fractions Book by Jerry Polatta which helps students to discover and understand equivalent fractions.  As the teacher reads the book, students use their own chocolate bars  as a manipulative by breaking  the chocolate bar into pieces and organizing those pieces into various groups to create different fractions. Thus, students are able to visually see and physically create a fraction such as one-quarter or ten-twelfths in order to understand what these fractions really mean. Chocolate bars are also a fun (and delicious!) manipulative as they help students to see how fractions are found in their daily life when they divide and share food.

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Olij, B. ©2016

Manipulatives Allow Students to Actively Explore

It is important to recognize that children are active learners. Manipulatives allow students to explore math concepts by actively engaging with concrete objects. Manipulatives encourage students to take risks, ask questions, test their ideas, and discover new knowledge about math processes and procedures as they experiment with physical objects. From my own personal experience, I have noticed that I am much more willing to take risks and experiment with different ideas when I am working with manipulatives. In elementary school, I loved to work with manipulatives such as Cuisenaire rods, tangrams, and fraction circles as it was easy to move them around and try different things. I found this easier and far less intimidating than trying to test something on paper.

Manipulatives Encourage Math Talk

Manipulatives are also valuable as they encourage collaboration and discussion. During my experiences as a volunteer in a Grade 3 classroom, I noticed that many student struggled  to discuss the more abstract ideas of math as they felt pressured to use the precise terminology. They were, however, able to verbalize their thinking and discuss mathematical procedures and processes when they described what they did with their manipulatives. Similarly, the teacher was able to promote math talk when she asked students to prove a math idea by using their manipulatives. Given the fact that each student might experiment with different manipulatives, there can be valuable discussions as students share their ideas and findings. For example, one student might use the manipulative of paper clocks to add fractions while another student might use fraction strips. These students could compare and discuss their strategies and results.

This week, therefore, I was reminded of the importance of manipulatives. Before this course, I had the misconception that manipulatives were only helpful for students who struggled with math. I now see that manipulatives are a fantastic resource for all students in the classroom as they encourage students to connect math to their daily life, explore new ideas, and verbalize their thinking.