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Making the Most of Manipulatives
Shifting from concrete to abstract
As students work to develop their thinking skills and their understanding of math concepts, manipulatives can assist a student by providing a concrete model of an abstract idea or method. Visual and especially kinesthetic learners benefit from seeing a word problem illustrated or by being shown how to solve an equation using manipulatives. However, these tools are not necessary for all learners. If a student can complete a problem easily without using the manipulatives or is confused by using them, let it go. Not all pedagogy is equally good for all students. Differentiating instruction is key to helping all students learn the content and skills they need to be successful in math.
If a manipulative is used in instruction, I allow students to use the same items on the formative assessment tools, at least for starters. All I need to do is provide the materials during the assessment. When a student is ready to do the math without the manipulative, they will. I can also gauge where students are in their understanding of the math being assessed by permitting them to use the manipulatives on certain assessment items and then asking them to not use them on others. Analyzing the data to see whether they are able to complete the problems without the hands-on materials informs my planning and instruction.
Modeling their use
When teaching students how to use manipulatives, strategically show them how to do so and let them practice. Several methods are successful: small groups, magnets, overhead projectors or document cameras. The best method to me is the one that fits the materials I have that year. If I do not have the technology to show the entire class how to use the manipulatives, I do so in small groups. Attaching small magnets to a teacher set of the hands-on materials, I can model how to use them and have students do the same, providing there is a magnetized wall surface (not all boards work for this). Overhead projectors work best when working with transparent manipulatives. Fortunate teachers possess a document camera and a projector with which they can easily model the use of any type of material with their students. (The prices of document cameras have come down dramatically in the past few years, allowing the purchase of this tool for more and more classrooms.) Whatever method this year’s classroom set-up affords, I am quick to shift the action from me to my students, having them model how to use the materials for each other. Students work in pairs to practice, collaborate and teach each other.
Managing the materials
To begin with, students see manipulatives as toys. Let them play with them for a few minutes to explore. Then teach them how to use them as a tool and expect that they do so. But what if they don’t?
When a student is using hands-on materials inappropriately I move them to a seating position I call the “observation chair.” All this means is that the student must move back so that they are more than an arms length away from the table. They are still responsible for the assignment at hand, but they are not allowed to touch the materials. After five minutes of good behavior, the student is allowed to scoot back up to the table and resume using the materials. If for some reason this does not work, a second offense (of a behavior such as building unnecessary skyscrapers or launching projectiles) is met with a ten minute period of observation. Rarely is this necessary, as the student typically wants to be involved and is not entertained by only being able to observe. When I do a good job of showing them how to use the materials and presenting them with challenging and interesting work, there are few (if any) off task moments.
Baggies are your friend
Store hands-on materials in plastic baggies, which come in a variety of sizes. I have a bag for each pair of students. If it is possible to color code them, I do so. For example, when making my own manipulatives from regular paper, I draw a colored line across the back of the paper before laminating. This takes very little time and each set has its own color so it can be returned to the appropriate baggie if it gets left on the floor by accident. Storing the little baggies in larger baggies also helps to keep the storage area organized, as the different materials will not migrate into foreign territory. Number each of the smaller baggies and then label the big baggie with the total number of sets and the name for easy use next time.
Planning, clear directions and expectations, and a few baggies make manipulatives a meaningful and easy tool to assist students in making sense of the abstract.