# Experiencing Mathematics Differently

The most important benefit of authentic learning is that it prepares students for the real world more effectively than traditional classroom-based learning. Mathematical demonstrations tend not to be common in higher classes, but at MIS, we try to use every opportunity to display and demonstrate this understanding of an abstract concept visually. Once the students learn this technique of visualization, they start to make better connections and eventually develop higher-order thinking skills.

DP-2 students recently had the opportunity to explore how to calculate an area under an irregular curve using calculus, specifically integration. Definite integrals and areas found under the curve are essential in physics, statistics, engineering, and other applied fields. Seeing the concept unfolding on a floor was a unique thrilling experience and made students appreciate what they have learnt. This hands-on learning helped them achieve accuracy through the method of integration. Some reflections from students speak the difference felt:

Sharwari – Math Analysis and Approaches SL student:

Last week in Math class, we conducted an activity to understand the applications of integration—calculating the area under a curve on a graph. Using a marker and the two square feet tile on the floor, we first drew any non-linear curve of our choice. To calculate the area of this manually, we divided the curve into rectangles and found the areas both under and over the curve. We then calculated the exact area by finding several coordinates, deriving a function from them, and then integrating it using a graphing calculator. I learned that this value fell somewhere in between the areas over and under the curve that we calculated manually. Using integration gave us a more accurate value as it considers all the minute changes in the curve. This was a fun activity; it really helped expand my understanding of integrals and turn it from an abstract concept into one I can visualize and use easily.

Dheer – Math Analysis and Approaches HL student:

During math class, we worked on an activity that would help us understand the concept of integration in a more practical way, specifically the area under a curve and the definite integral. My peers and I were supposed to draw any non-linear function and try to find out the area under the curve, without using a graphing calculator. This is done through a simple process where the function is split into five or more equal rectangular sections (more is better) which are both above and below the curve. It took us to the era where people managed all their calculations without calculators and a realization into how mathematical concepts have evolved in these years. This experience will go a long way for me as it will help me visualize graphs in any critical scenario and lower the probability of misinterpreting.

Applying knowledge and skills in real life situations definitely goes a long way, doesn’t it?

Anjali Singh