Three Musts for Manipulatives in Math Class

It's Friday. You're having guests over later and want to serve a delicious meal. You decide on homemade pizza and a salad. The only problem is you’ve never actually made pizza, so now you have to learn how to create a dish that will delight your guests and leave them thinking you’re a culinary genius. Which option would you choose?

1: Read a recipe in a cookbook.
2: Watch a video online.
3: Have a personal chef accompany you in the kitchen as you create your masterpiece.

Chances are option three is most appealing (assuming that personal chef was free). Why? This scenario combines two powerful learning opportunities: a concrete, hands-on experience and on-the-spot feedback when you need it.

Hands-On Learning Builds Conceptual Understanding

As a math coach and teacher for 31 years, I often approached math instruction the same way a master chef would guide culinary students. I would provide math manipulatives whenever possible to help develop the conceptual understanding necessary to build procedural knowledge.

This is known as the Concrete Representational Abstract (CRA) approach. This strategy uses physical and visual materials to develop students’ understanding of abstract topics. Think of CRA as the stages of learning mathematics. Concrete is the “doing” stage. Representational is the “seeing” stage. Abstract is the “symbolic” stage.

As adults, we might look at eight plus five and automatically think 13. We don't realize how abstract this idea is to most students in Grades 1 and 2. Using visual models like double 10-frames and manipulatives like counters helps students experience the relationship between physical and symbolic ideas. When students literally build a quantity of eight on one frame and five on the other, they can move two counters to fill a 10-frame. Eight plus five becomes 10 + three. Why is this powerful? At this stage, students have already been exposed to complements of 10. They can transfer learning and apply this strategy to other addition facts. We’re not asking a student to memorize that eight plus five equals 13; we’re helping them develop a strategy that can be used for other facts as well.

Misconceptions of Manipulatives

Why is it important to use manipulatives in math class? Why aren’t math manipulatives used as often as they should be? Let’s look at three reasons why teachers avoid using them during instruction.

“Manipulatives take too much time to manage.”

Many educators are often allotted 40–60 minutes for math instruction. Distributing and collecting materials can consume three to 10 minutes of valuable instruction time. Over the course of a school year, that adds up to days of lessons lost from just having to manage these resources.

Solution: Provide individual toolkits for each student.
Toolkits can be filled with the items most commonly used throughout the school year. For example, Grade 1 toolkits could include counters, dice, connecting cubes, and base-10 blocks. Pencil cases or even quart-size sandwich bags can easily store these materials. The secret is to have the materials at their fingertips at the start of the lesson. The time you spend organizing these individual toolkits in August will be rewarded with more time for learning throughout the school year.
“Students are distracted and end up playing with manipulatives.”

Some educators see the materials as more of a distraction than a desirable learning tool for students. Manipulatives may become toys rather than tools during instruction. Teachers assume it’s easier to get through the lesson without having to stop and redirect students.

Solution: Build in time for exploration, and establish class expectations.
Self-discovery is a powerful force when developing conceptual knowledge. Always give students a few minutes to explore new materials. Allow them to construct towers, build piles, and extend patterns.

Class expectations are also important. Once instruction begins, prompt students with the “ready position.” For example, if they are using 10-frames and counters, you might say, “Our ready position will be 10-frames and counters on your desk with hands on heads.”

TIP: Project a picture of the items and a classroom timer to hold students accountable and increase self-regulation.
“I’m not sure which manipulatives to use during instruction and how to use them.”

Educators may not understand which manipulatives should be used and how they can model mathematical concepts in a variety of ways. Teachers may jump to traditional algorithms, bypassing building critical conceptual understanding.

Solution: Read the teacher’s manual.
This may sound obvious, but it’s easy to forget to refer to this resource. You may glance at the lesson objective and “wing it” instead of preparing and planning for upcoming instruction. Manuals often provide guidance on how, when, and why manipulatives should be used during a lesson. Be sure to read through the resources available and anticipate how the manipulatives can be used.