The Importance of Math Manipulatives


Manipulatives are essential in the early stages of mathematics. I often see children who struggle with math after 4th grade. What I find is that they have not had a lot of experience with the manipulatives or developed a conceptual understanding of mathematics. Conceptual understanding, where children can grasp ideas in a transferable way, can help students take what they learn in class and apply it across domains. Not having these early experiences causes children to struggle to perform even the most basic operations, even after repeated instruction. If children do not develop a conceptual understanding, they tend to struggle even more as they get older. I am here to say that worksheets are okay, but you have to have manipulative to use with them. There is a sequence to learning and a lot of times teachers skip the concrete method and go straight to representational methods (see below for details). If students can see math, move it, they will develop a concrete understanding of math. Give your students/child the gift of conceptual understanding. Visit my website and I will show you the importance of manipulatives and how to use them with your students or child. You can also check out Math Mantic website for more details on how to use manipulatives. Please subscribe to my Blog for updates. As I will be added more resources.

Here are the top three reasons why I use math manipulatives:

  1. Manipulatives can provide a bridge between the concrete and abstract levels of many mathematical topics. There is a sequence to teaching mathematics: concrete-to-representational-to-abstract. This sequence of instruction ensures students develop a tangible understanding of the math concepts/skills they learn. If one of these steps is skipped or not developed fully, you most likely will find holes in mathematical understanding. 

    1. Concrete-You first begins with concrete instruction using manipulatives such as chips, unifix cubes, base ten blocks, beans and bean sticks, pattern blocks, fraction circles. A teacher must provide many opportunities to develop a concrete understanding.

    2. Representational- involves drawing pictures that represent the concrete objects previously used (e.g. tallies, dots, circles, stamps that imprint images for counting). They are now one step closer to abstraction.

    3. Abstraction-Students have developed conceptual understanding because they used concrete and representational skills. Now it is time to show what they learned in an abstract model, using only numbers and mathematical symbols. 

  2. Manipulatives can serve as visual models that support the student as the problem solve. Manipulatives help them think about, remember about, and communicate about the concept being learned. If students make a mistake, they will see the error. Manipulatives can be used as a control or an answer sheet. The ability to problem-solve and make educated decisions is essential, like skill. Problem-solving and modeling in mathematics can and will cross over to problem-solving in other areas of life.  

  3. Manipulatives support student engagement and differentiation. I teach with the hands-on, mind-on philosophy. If students are doing, they are engaged. Manipulatives naturally help teachers and parents see where the student needs more or less support

If students struggle (even older students) with abstract concepts, please reintroduce the lesson with visual models. It's better to rewind, develop visual representation, and then move forwards again. 

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