Motivating talented students in mastering mathematically more demanding learning material

Paper

Through my years of teaching, I have realized, how important student motivation is. During the daily commute to work, I always think about, how to best conduct that day's lessons and at the same time motivate the students well. In the third year of secondary school, the teaching material of the exponential function appears.

This learning material has always been difficult for students to understand, abstract... What is this anyway? How is a graph drawn? What does this curve mean? What does it represent? So one day in the car, I was thinking about, how to relate the exponential function to the things the students were doing. This thing must be well known to them, maybe some kind of board game?

I remembered my childhood and the games we used to play as a children. A man does not get angry, black Peter cards, sinking ships, between two fires, ... It must be related to mathematics, more precisely to the exponential function. I really didn't want to explain it to them in the usual way, with bacteria multiplying or cell division, like in the textbook. Suddenlly, I got an idea. A game that has a lot to do with logic, mathematics and we all love to play it. Of course it's a game of Chess. No matter how many times my grandfather and I played it, he always beat me. I remembered the story he told me, about how chess was created. Maybe it's even real, who knows. I immediately associated it with mathematics, specifically the exponential function.

So I came to class, where there are mostly talented students, with a chess board and a handful of cereal grains. I immediately started telling the story about the origin of chess....

Along with the story, I also drew the subject and wrote it on the board. I showed the grains on the chessboard, tabulated everything nicely, drew a graph, and at the end, together with the students, we derived the formula for the exponential function. First for our story, and then in general.

So, the students realized that, for each subsequent field, the number of grains increases two times in realtion with the previous one. The base number is two. With the squares on the chessboard, the number of grains increases by leaps and bounds, I explained that exponentially. So for grains the function is f(x) = 2x….