How do I use manipulatives to enhance learning in my classroom?
Anita L. Gordon, Former ACSI Math Services Consultant, Math Instructor—University of Colorado, Colorado Springs
Color tiles, base ten blocks, tangrams, algebra tiles, and other manipulatives are essential for introducing new mathematical concepts to students. In the Purposeful Design Mathematics series, manipulatives are used extensively throughout all grade levels.We have included them in the list of materials for each lesson for which they are appropriate, and the teacher edition lesson gives detailed directions for their use in the corresponding student lesson.
Are you as a teacher using manipulatives to their full potential? Their use can better equip students to communicate their mathematical reasoning and to solve problems. They also provide an opportunity for informal assessment of a student’s understanding. As you observe students in your classroom using base ten blocks to add two numbers when regrouping is necessary, you will be able to tell at a glance whether the students are grasping the concept of trading one ten for ten ones. This hands-on practice is essential for tactile and visual learners.
Distributing, using, and collecting manipulatives can proceed quite smoothly without disrupting your classroom. In fact, enlisting the aid of students in this task can actually help them develop organizational skills. Consider the following ideas:
- Have the manipulatives packaged in individual student- or group-size containers before class.
- Ensure that the storage of manipulatives in your classroom provides easy access.You will be much more inclined to use them. Clear plastic tubs and zippered plastic bags work well.
- Have a routine for distributing and collecting manipulatives. This practice will decrease having to repeat instructions.
- Establish a noise level that you are comfortable with but that allows students to communicate with one another when working in groups. Maintaining order is essential, but student discussion that indicates engagement with math is profitable for learning.
- Have a math manipulative envelope for each student. It could be an inexpensive clear plastic envelope. It is especially useful for mats, game boards, paper manipulatives, and grids that are used over and over.You can assign each student a number that also serves as a label for every piece in the kit.When you find a game board labeled with a number, you will know to whom it belongs. Students should be held responsible for any missing items.
- Prolong the usefulness of game cards, flash cards, and paper manipulatives by laminating them.
- Use placemats to define a workspace for an individual student and possibly to keep things quieter.
- Use objects other than the ones in the kit for manipulatives. Have students bring in tiny plastic animals, beads, shells, and craft sticks. Making their own manipulatives may encourage them to use them and care for them. Be creative. Edible manipulatives, such as small fish crackers, have a special appeal!
- Have classroom centers where students can explore with manipulatives. For example, building with base ten blocks will familiarize students with the relative value of each piece. They will learn by experience that ten longs (rods) take up the same space as one flat.
- Have a variety of manipulatives available for students to use for problem solving. Examples include constructing models with connecting cubes to determine volume, using base ten blocks to represent sets of items, and building a graph with color tiles.
As a supplement to the activities specified in the teacher editions of the Purposeful Design Mathematics series,we recommend the Super Source series, published by ETA/Cuisenaire. Each book in the series is a collection of valuable lessons using a specific manipulative to teach a wide variety of mathematical concepts for a specific grade range. We have included representative activities in this issue of Math by Design. Permission has been granted for limited reproduction of these pages for use in your classroom. We encourage you to try one or more of these activities. If an activity corresponds with a lesson you will be teaching in the near future, you may want to copy it now and integrate it at the appropriate time. Visit the ETA/Cuisenaire website to learn more about this excellent resource, including the K–8 Super Source Reference Library on CD.
*Examples and practice sheets are available in the attached PDF.
Math by Design volume 1 number 3