The atmosphere in the room was heavy. On the whiteboard was a classic, dry calculus problem: “Take a 20cm x 20cm sheet of cardboard, cut squares of side length x from the corners, and fold it into a box. Find the maximum volume.”

Instead of giving the students the formula, they were given 20cm x 20cm sheet of cardstock and a scissors. The students were split into three factions; each convinced they had the winning strategy for the “cut-out” square of side x. The room was a map of different ideas:

The “Deep Box” Group: They believed height was key. They cut large x squares, resulting in a tall, narrow box that looked like a chimney. The “Wide Base” Group: They thought a massive floor was the secret. They cut tiny 1cm squares, creating a box that was wide but almost as flat as a pancake. The “Middle Ground”Group: They tried to guess the balance, cutting x at about 5cm.

As the students finished taping their boxes, the teacher pulled up GeoGebra on the main screen. A digital version of their cardboard sheet appeared, with a slider for x. As the slider move , a live graph began to trace the volume. The students watched their own boxes appear on the screen. The “Wide Base” group saw their point on the far left of the graph—their volume was low because the walls were too short. The “Deep Box” group saw their point on the far right – their volume was low because the base had vanished. The “Middle Ground” group saw they were higher up, but they hadn’t quite hit the “peak”.

Where is the absolute highest point this graph can go?

One student pointed to the very top of the curve. “Right there, where the graph stops climbing and starts falling. Then started the actual calculus by taking volume function, finding the derivative, and setting it to zero, they calculated the “Magic Number” 3.33 cm. The groups looked at their boxes. The “Deep Box” group (who cut 7cm and the “Wide Base” group (who cut 1cm realized their volumes were nearly identical, despite looking so different. They were both far below the peak. To prove it, the teacher brought out a group of students who had used the 3.33cm measurement. They filled the “Calculus Box” with beads and then tried to pour those same beads into the “Deep” and “Wide” boxes. The beads overflowed every time. The classroom shifted from doubt to total conviction. They didn’t just see the answer on a screen; they saw their own physical models fail against the precision of the derivative. The “Magic Number” wasn’t just a number anymore – it was the physical limit of the material they held in their hands. Using the beads to show that the 3.33cm box could hold more than both the tall and the wide boxes provided the “proof” their brains needed to trust the math.

When we bridge the gap between Dynamic Technology and Physical Experimentation, we remove the “fear of the formula.” We replace it with a sense of discovery that motivates students to tackle even the most complex senior-level topics with confidence.

-ASHA REGHUNANDAN – HOD MATHEMATICS