Math assessment: Teaching the language

Teaching Pre K-8, Jan 1995 by Moore, Carolyn

No longer is mathematics instruction limited to assigning page after page of computations. The standards developed by the National Council of Teachers of Mathematics (NCTM) have brought to light strands that had long been missing from the everyday classroom routine.

Assessment is a prime example. Performance tasks and other forms of alternative assessment call for the communication of math knowledge. Not only do our students have to be able to solve the problem, they must be able to explain how they arrived at the answer and why the answer is correct.

In response to the NCTM standards, many teachers have begun to change math instruction to include oral and written communication. They help students become more comfortable with "math language" through a variety of strategies. Math and literature, manipulatives, games, writing math stories, oral explanations and math journals are some of the ways students practice math language.

Cooperative learning. My years of teaching experience have led me to believe that children learn best from other children. Since children share information and strategies with each other in non-threatening situations, cooperative learning strategies are essential if we wish to encourage students to use math language. But it's not just a case of forming learning groups and letting the kids take it from there. These groups require open communication.

Recently, I watched some tapes of a well-known math specialist discussing assessment. I thought, "She has time for individual interviews. She doesn't have a class to teach." I didn't think I could take that amount of time away from my class.

One day, however, I began to ask students how they arrived at answers and I discovered that I had to conduct individual interviews to know who really understood the concept. I quickly saw the value in what I had done.

That afternoon, my partner and I had a lengthy conversation about whether or not individual assessments were worth the time and effort they took. We knew that some children had the basic idea, but could not elaborate on it or explain their thinking.

In order to find out where the children's thought processes were breaking down, it was (and is) necessary to individualize assessments. Once we know what the problem is, we can reteach the concept.

My teammate and I agreed that it was definitely valid to devote a full class period to assess understanding. We also agreed to provide children with opportunities to explain their problem-solving strategies.

Children aren't the only ones to benefit from open communication. Parents benefit, too. While we're teaching problem-solving in the classroom, some parents--perhaps remembering their own school days--are wondering, "Where are the worksheets?" Obviously, we must keep parents informed.

All about pumpkins. Writing stories that feature math is one way for students to demonstrate their reasoning. We've found that "math writing" is fun and easy to do. Not long ago, we did a pumpkin unit. Our math activities included weighing, measuring, estimating, graphing, counting, comparing, sorting and, of course, writing.

One of the activities we did included most of the above skills. The children had 15 pumpkins to work with. Each child measured the pumpkin stems; estimated whether they were long, short, medium or no stems at all; sorted them into the four categories; and counted them. The final step for each child was to make a simple graph of the findings and write about them. Both graph and writing went into the child's math journal.

We continued the unit by reading Mousekin's Golden House by Edna Miller (Prentice Hall, 1971). The children then created interior designs for their pumpkins. They chose a tiny inhabitant and drew its home. Each drawing included shape, size and necessary rooms.

After completing the drawings, the students wrote about their own "golden house." Since it was a creative math writing activity, the students included as many math-related words as they could. Many of the students chose this sample to put in their portfolio.

Day by day. In our daily calendar activities, we emphasize place value, which has long been a difficult concept for children to master. Giving children meaningful practice will develop their understanding of place value.

Using the date on the calendar is a good starting point for tens and ones. We use tally marks with circles around the tens; then write the number. Children can explain their knowledge of place value by demonstrating with manipulatives and/or orally stating their reasoning.

Other calendar activities are based on the day, date, month and year. The children color code even and odd numbers on the calendar. They're often asked, "How do you know if it's even or odd?" Some answers: "by the color," "can (or can't) count by twos," and "yesterday's was even, so today's must be odd" (a sure-fire tip-off that the children have noticed a pattern).

Dollars and cents. Our calendar activities are student-led and include a weather graph, a tally of the number of days that have passed in the month, a lost tooth chart and a monetary value as it relates to the date--for example, April 4 = $4.04. We then convert the money: five pennies for one nickel, ten nickels for two quarters and so on. This helps children master counting money and the value of coins.