## Article, Book Resources

By Marilyn Burns
• Grades: PreK–K, 1–2, 3–5, 6–8

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Q.

Manipulatives help my slower learners, but do my better math studentsneed them?

A.

Absolutely. The challenge of teaching any subject is to find activities that are accessible to all learners and have the richness to challenge more interested or capable students. Manipulatives are a wonderful resource for this. For example, I introduced fourth graders to Build the Yellow Hexagon. All students found different ways to build the hexagon and recorded their constructions with correct fractional notation. I asked the students who finished quickly: "How much larger is the red trapezoid than the blue parallelogram?" This challenged them to figure out how much more 1/2 is than 1/3.

Q.

How often should I use manipulatives in my teaching?

A.

Ideally, the materials are available for students to use atany time to help them think, reason, and solve problems. When a manipulativematerial is key to a lesson, I initiate its use.

Q.

What about students who work well with manipulatives but have troublewith textbooks?

A.

Showing the bridge from concrete experiences to symbolism isessential. While it may be obvious to adults, it can be a stretch for students tosee how a 3-by-4 rectangle built with tiles relates to the textbook explanationthat 3 x 4 means three groups of four. I help children make connections bydemonstrating how a rectangle can be separated into three rows with four tiles.
If your textbook doesn't reference manipulatives, talk about what students mightuse to help solve a problem. Often, students don't realize that what they use inone setting can be helpful in another.

Q.

How many kinds of manipulatives do I need?

A.

It makes sense to introduce one material and provide time forin-depth exploration. But one advantage of using a variety is that children canthink about ideas in different ways. For example, we wouldn't want children tothink of fractions as related only to round pies.

Q.

Can't I make cheaper manipulatives?

A.

For years I've had children cut paper cookies to explorefractions, fold shapes for geometry, and use strips for measurement. Studentsalso cut paper squares into the seven tangram puzzle pieces to see that thepieces make a square. However, to create other shapes, compare areasandperimeters, or make observations over time, paper pieces aren't durable orexact. Manipulatives stand the test of time and are precise. They also allowstudents to discover the mathematical relationships inherent in them.

Q.

Where do I fit manipulatives in when there's so much to do?

A.

I use manipulatives as a support for teaching the math topicsthat are in the curriculum. I don't reserve materials for special days orassignments, but make them a regular and integral part of my general teaching.

Q.

I worry that children will see the same materials year after year andlose interest. Do they?

A.

Schoolwide planning to discuss which manipulatives you'll useand how to use them can be valuable. However, be careful not to designatecertain materials or activities for only one grade. Most are appropriate fordifferent levels, and repeat experiences help students stretch their thinking.For example, asking primary children to find different ways to make trains of sixinterlocking cubes using just two colors helps them explore different addends of6. Older students can be challenged to figure out how many arrangements thereare, not only for trains of 6, but also for trains of other lengths.

Q.

I don't have enough of any one kind of manipulative to use with mywhole class. What can I do?

A.

Some teachers I know organize learning centers and have smallgroups work at them. Others introduce a few activities to be done over severaldays, and students make choices based on which materials are available. Stillothers pool materials for a week with other teachers to create class sets. In allcases, having students work cooperatively not only cuts down on the amount ofmaterial you need, but also encourages communication--which in turn promoteslearning.

Q.

How do I know when it's time for students to put away the materials?

A.

I let students be my guide. Observing them gives me valuable information. Sometimes I've assigned students the problem of finding all of therectangular arrays using 6, 12, and 24 tiles. While some need to build all of therectangles with tiles and then record them, other students stop using the tilesand are comfortable drawing the rectangles.

Q.

I worry older students will complain that manipulatives are babyish.Any advice?

A.

I rarely get this reaction. Most are delighted to get theirhands on concrete materials. If you anticipate naysayers, talk about how, forexample, architects often build models of buildings and engineers constructprototypes. Tell students that they'll use materials to model a problem orsituation. Then be sure they first experience something that offers a challengeand that you provide free exploration time.

• Part of Collection:
• Subjects:
Manipulatives, Learning and Cognitive Development, Teacher Tips and Strategies

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