When given a question to answer, many students think only for a few seconds to figure whether they can see a method to answer the question, and give up otherwise. They are habituated to being given “exercises”, questions that test whether you can apply a known method for calculating the answer. But what is one to do when it’s not at all clear what method to use? A “problem” is a question that one does not know (at the outset) how to solve, and which hence appears to be difficult. In contrast to exercises, solving problems requires a very different mindset. You need to take time to patiently explore an unknown terrain, get your hands dirty, investigate what happens if you turn left or turn right, come up with strategies to get to the desired ‘destination’ (the solution), and see where they lead you. You have to learn to cope with failure, to encounter dead ends, to get lost, and keep exploring. All this makes solving problems more difficult than solving exercises, but also more fun. Isn’t hiking in an unknown terrain more fun than doing repetitive exercises in a gym? You can expect surprises, thrilling moments of discovery along with frustrating moments of feeling lost and confused.
In this course aimed at middle school students, we will learn the art of solving problems in mathematics. It will not only prepare you for contests like the Math Olympiad and deepen your understanding of the school curriculum, but also provide you plenty of moments of thrill and discovery where you will learn to use effective strategies to find your own creative solutions to problems. The problems will be drawn from the history of mathematics, from games and puzzles, from math contests and from real world situations. Continue reading