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Manipulatives in Mathematics Classrooms
by Sean Monaghan and Wanda Kowalski
At one time we used a pencil, paper and our minds; that was math and every other subject area. In math, we depended on our abstract thinking to pull most of the weight. Manipulatives did not even exist – they were considered toys not tools. We really did not consider that there might just be an easier way to teach these abstract concepts using these “toys”.
Many people, theorists and teachers, realized that using toys to connect with kindergarten students was so beneficial. In the later 1800’s in Germany, the first kindergarten was established that focused on the use of toys as a means to “teach” kids. They used concrete and manipulative objects to construct meaning for kids. When children went to grade one, these “toys” were left behind. Kids somehow jumped the abstract barrier that was not present in kindergarten and could now learn the “real” way.
In the early 1900’s we focused on the pen and paper routine demanding that our children learn with their minds. Later that century, when the constructivists theorized that people need a connection to their real lives to learn abstract concepts and manipulatives that the idea of using “toys” changed to something of a consideration. Toys and games were deemed worthy and proven useful in the classroom as learning tools for math.
Today, the curriculum requires that students learn concepts concretely, visually and abstractly in that, or some permutation of that order, beginning with the concrete. We currently use manipulatives, such as base-ten blocks, bingo chips, and everything else in the classroom, to help division one students grasp the elemental concepts of math. They learn how to add, subtract, group, categorize, chart, shape using all kids of materials. In division two, manipulatives disappear.
This is where the journey for manipulatives has ended. We are currently situated in the transition between abstract and concrete teaching.
Many argue that the use of manipulatives is a crutch toward student learning. Others suggest manipulatives are a tool to solidifying abstract concepts. The trend now seems to follow the “pro-manipulatives” movement. Many teachers recognize the need for adapting concepts and lessons for all learning styles. Not everyone is the same.
Topic: Manipulatives versus
visualization
Sean Monahan & Wanda
Kowalski
February 13, 2001
Page Two
To find this article go to www.ascd.org and search for Karen Tankersley.
ARTICLE SUMMARY:
Karen Tankersley, the principal at Cardova School in Phoenix Arizona, reports on the general results of creating and using a manipulatives lab for students in grades four and above.
After a year-long investigation, teachers at Cardova became convinced of the need to recapture the concrete experience that small children bring to learning math. They organized a lab on site, where children could learn new concepts at concrete levels. The lab, infused with solid and colorful commercial objects, added interest and made learning math more fun for students.
After the lab was set up, the teachers attended “a week-long workshop at which committee members offered training to using the new materials and techniques.” During the school year, students were offered a variety of creative drill-and-practice activities on computers and higher-level thinking skills exercises, depending upon their assessed needs.
As a result, students are more excited about math, their test scores have increased and the parents are enthusiastic as well. They report that the “program has instilled an enjoyment of math in their students and has helped them understand the hows and whys of math operations in concrete ways.”
DISCUSSION QUESTIONS:
OPEN DISCUSSION WITH THESE QUESTIONS:
Topic: Manipulatives versus
visualization
Sean Monahan & Wanda
Kowalski
February 13, 2001
Page Three
FINAL REFLECTION QUESTIONS:
* WHAT DID YOU LEARN ABOUT THE USE OF MANIPULATIVES
IN CLASS?
* WHAT DID YOU LEARN ABOUT YOURSELF AS A LEARNER?
