For many adults, the mere mention of math is met with downcast eyes. Fear of math is learned somewhere around the 4th grade. What causes such a drastic shift in attitude and self-concept? In the early years, children learn mathematical concepts first by association with concrete objects and later by symbolic representation. They have no fear or lowered sense of self-esteem associated with “doing math.” Then, around 4th grade, teachers leave the world of the concrete, opting for the abstract.
At Cordova, an urban school in Phoenix, Arizona, serving 1,125 children in grades K–8, teachers wanted to develop a math program that was not only effective, but that also generated student interest and positive self-esteem. During a yearlong investigation, they read the latest research, attended workshops, visited schools in the area, and listened to guest speakers. They became convinced of the need to recapture the concrete experience that small children bring to learning math.
Despite limited space on campus, Cordova set aside a classroom and a large enclosed porch area to house a math manipulative lab, where children could learn new concepts at the concrete level. To provide instructional consistency, our math committee looked for a schoolwide textbook series that emphasized hands-on teaching, used spiral curriculum reinforcement, and included current topics such as calculators and problem-solving exercises. After examining many textbooks, the committee, with input from parents, selected a series. To help teachers spend more time on instructional activities and less time grading papers and processing paperwork, the school purchased a computer management system.
Understanding that teaching with objects can be as simple as using beans or cups, committee members recommended the purchase of commercial items. They felt that commercial objects, which were solid and colorful, would add interest to the program and make learning math more fun for students. Further, valuable preparation and instruction time would be saved, since teachers would not have to create or locate materials.
Volunteers spent much of the summer installing shelves, unpacking and categorizing resource books and materials, installing computer units, and making an attractive, fun place for children. In late August, all but 2 teachers out of 50 attended a week-long workshop at which committee members offered training in using the new materials and techniques. Enthusiasm was very high!
Making Math Lab Fun
Cordova students attend the math lab at least once a week for about 45 minutes. Each classroom teacher coordinates lab time with the concepts being taught in class. By using student and class profile reports to shape instruction, teachers decide who proceeds to the computer area of the lab for enrichment work and who goes to the hands-on instructional area to work with Cuisenaire rods, counting cubes, or base 10 blocks. Some times teachers might choose to keep the more advanced students in the instructional center for work on higher-level thinking skills or problem-solving exercises, while students who need more practice use the computers for creative drill-and-practice in areas needing work. With a full-time classroom assistant assigned to the math lab, students receive more individualized assistance and expertise.
Parents smile knowingly when we talk about the math lab, one of the most popular stops during monthly parent tours. Visitors cannot miss the excitement on the children's faces while they are busy at work using math manipulatives. We invite parents to sit down with the students and learn math for a few minutes. To show parents how to help their children at home, and to help them feel less threatened by our new teaching methods, we also hold Family Math one evening per month. Taught by two classroom teachers and a parent volunteer, the program lets students and parents share in completing hands-on math activities. Many parents have told us that for the first time in their lives, they have a different view of math. This positive attitude carries forward to their children.
Outstanding Results
Cordova students are excited about math, and their test scores reflect it. Over the last four years, our students have made substantial gains on state achievement tests. The subtest that reflects student understanding of math concepts showed an average increase of between two and eight months of additional student growth over previous years. In the National Mathematics League Competition, some of our 6th graders are placing in the top 1 percent of the nation. Our junior high students have also received several ribbons in Arizona Math Challenge competitions. Teachers say they can see a real difference between new students and continuing students who have been taught with a hands-on approach.
Over the last four years, our hands-on math concept has been presented with a prestigious Golden Bell Award by the Arizona School Board Association for program excellence. Arizona ASCD named our math lab program as one of seven outstanding programs in the state in 1991. That same year we also received an Educational Showcase award from Phi Delta Kappa. We have since served as a model for many other schools in the state.
The program has instilled an enjoyment of math in our students and has helped them understand the hows and whys of math operations in concrete ways. Not only can they add 245 + 365 symbolically, but they can also demonstrate their understanding of the process of addition by representing the ones, tens, and hundreds using base 10 blocks. With hands-on teaching at all grade levels, our students are developing exciting, new understandings about the world of mathematics.
