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Math Manipulatives in the Upper Grades
Manipulatives are a popular and effective learning tool in elementary level math classes.
Manipulatives are a popular and effective learning tool in elementary level math classes. However, by the middle and high school grades, students rarely get the chance to have hands-on learning experiences in math class. The effectiveness of hands-on learning does not end in 5th grade however.
Research indicates that students of all ages can benefit by first being introduced to mathematical concepts through physical exploration. By planning lessons that proceed from concrete to pictorial to abstract representations of concepts, you can make content mastery more accessible to students of all ages.
Long-Lasting Understandings
With concrete exploration (through touching, seeing, and doing), students can gain deeper and longer-lasting understandings of math concepts.
Many middle and high school math concepts can be taught using manipulatives. For example, students can explore the concept of least common multiple with integer bars. They can place the integer bars side by side, experiment, and discover how to create a combination of bars that are the same length.
Once students have a concrete understanding of the concept of greatest common factor (GCF) as matching lengths, they will find it easier to use a number line or make lists to identify the GCF. Similarly, if students use grid paper, pencils, and scissors to discover the formulas for computing the areas of parallelograms, triangles, or trapezoids, the formulas will make sense to them and they will be more likely to remember the formulas.
Managing Manipulatives
Using manipulatives can present classroom management challenges. Teachers find that manipulatives can get lost or broken. Students sometimes use manipulatives for other than the intended purpose. Distributing the manipulatives takes away from valuable class time. Yet many teachers use manipulatives in a highly effective manner by following a few basic guidelines.
· Set Up Simple Storage SystemsSet up a simple system to store the manipulatives. Some teachers arrange shelves or cupboards with plastic boxes or snap-and-seal bags. Others place their materials in the center of tables or desks. Clearly label your storage containers. Make sure students understand the system and have easy access to it. Give students jobs that help manage the system. For example, assign one student in a group or pair to retrieve the manipulatives and another to make sure they are returned.
· Establish Clear Rules Prior to your first use of manipulatives in a grading period, discuss a clear set of rules for using the manipulatives with your students. You may want to explain what manipulatives will be used for and include the following information:
- appropriate uses for learning
- handling
- storage
- distribution and return
- student roles and responsibilities
You may want to create a poster or chart to help remind the students of these rules.
Structured Learning Experiences
The key to successful hands-on activities is to provide a structured learning experience in which students learn how to use manipulatives. To maximize learning, teachers should provide three levels of practice.
1. Modeled tasks
Before distributing materials, provide clear instructions and model the tasks the students will carry out. If it is appropriate, you can invite students to help you model. For example, if the students are going to use spinners to perform probability experiments, you might invite two students to demonstrate, one to spin while the other records the results on a projector.
2. Guided Practice
Give students opportunities to practice prior to working individually or in small groups. If this is the first time the student is handling the manipulative, consider allowing extra time for exploration. You might ask the students to construct the largest possible right angle on a geoboard and give them time to figure out how to work with the pegs and rubber bands. Monitor students practice during this phase to give them the support they need to be successful when they work independently.
3. Independent Work
Once students know how to use manipulatives, they can complete problems on their own or in small groups with less support. This is an excellent time to informally assess learning and provide intervention where needed.
By following these guidelines and with time and practice, you will be able to introduce concepts through hands-on activities as easily you can lead pencil-and-paper activities.
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