Classroom Scenarios

The stories below describe two mathematics classroom environments. One is a
familiar scene of the presentation of abstract concepts; the other reflects
the learning environment this grant proposes to create: a vision of concrete
and meaningful mathematics.

Scenario 1 - A Typical Snapshot of Today's Algebra Classroom

On a Tuesday morning in September, Sylvia enters her typical Algebra I classroom, sets her books down, and prepares for her daily dose of confusion and despair. The teacher begins by writing the "equation of the day" on the chalk board: S = D / T . The daily routine continues: a review of skills. Students are asked to plug numbers into this equation and to solve for one of three variables. They review the cross multiplication skill that enables them to rearrange the equation so they can solve for the missing variable. They plug and they plod. Sylvia struggles to maintain focus and begins to strategize how to best avoid being called upon.

Scenario 2 - The Vision for Tomorrow's Algebra Classroom

On a Tuesday morning in September, Sylvia enters an Algebra I classroom that looks more like a news briefing room. Looping animations of current satellite views of a hurricane captured from the Internet appear on several computer screens. News footage of the devastation caused by the storm also appears on the classroom television. When the news broadcast is over, the teacher begins to pose some problems. How does the severe weather tracking service predict where this hurricane will make landfall? How does this affect early warning strategies? How does the weatherman know the storm is moving at a speed of 35 miles per hour? How is algebra used to make predictions about positions of storms at certain times of the day?

To answer these and other questions, students divide into groups. Sylvia's group explores time-lapse Internet satellite images using NIH (National Institute of Health) image software to track the motion of a hurricane. The distance equation helps them predict the position and time of the landfall of the hurricane. In a follow-up activity, students learn about the meaning of slope in a distance vs. time graph using a computer-interfaced motion sensor that tracks the motion of objects in real time. Walking toward and away from the sensor, students get a feel for how it responds to motion. They attempt to match a set of data on a graph of distance vs. time and learn what kind of motion causes the slope to be steep and straight or shallow and straight; they also explore negative and changing slope.

Finally, they pose various what-if questions and label graphs to explain what happened. These students actually try things out to answer questions posed within the activity. Then they are invited to assign a numerical value to the slope and to associate this numerical value with the direction and speed at which they are walking in various experiments. As in the hurricane activity, students use a formula to calculate speed, but this time they use their own collected data. The gap between abstract and concrete algebra is bridged and the teacher can literally "see the lights come on" in Sylvia's mind.