Take a Sherlock Holmes approach to math
Math problems are first and foremost puzzles. We look at a math problem as a “crime scene”. The greatest detective – Sherlock Holmes – was exceptional because he was observant, knowledgeable, and used the science of deduction. To solve math problems you must do the same.
First, in every problem there are clues to be found. Some are obvious and others are hidden and require great skill to be discovered. There is lots of external knowledge of possibly relevant facts that can be applicable. A mathematician draws on experience and understanding of the relationships between mathematical objects. Finally, the clues rarely directly point to the answer. To find out “who did it” one must combine the clues in many ways, and use deduction step-by-step to learn more, eliminate what is not possible, and then conclude what the answer is.
So, a young mathematician must learn to be a Sherlock Holmes of math – to observe, analyze and explore. He or she must try different strategies until the solution is at hand. Doing math is not a simple matter of following prescribed rules – it is a path through unknown in search of clues and new discoveries.
Discover it yourself
It is a known fact that most people, kids and adults alike, learn better when they discover things themselves, rather than when they are taught how to do it. Going through the process of discovery helps make sense of the final result, understand why and how it was arrived at. A child who discover a pattern in numbers, or proves a theorem in geometry, by themselves will more likely remember it forever, or will be able to re-discover it again if they forget it. Further, the process of discovery is more enjoyable and brings greater confidence in one’s abilities.
In light of this, many lessons in our program are organized so that students work in small groups to discover math for themselves. The kids get to be Euclid, Pythagoras, Descartes, and other greats. We help them and guide them. We give them a series of problems solving which leads them to a broader understanding. But we try our best to let the students find the answers on their own!
Yes, you need to do things many times to excel at them. But that is only true for a technique. Thinking is a whole different matter. Once we repeat something enough times, we stop thinking. Endless repetition is the death for the brain! The fundamental problem with study through repetition is that while a student might excel in a particular technique, he or she does not learn to think and will be stumped when faced with a different kind of a problem.
In our program, we teach many different topics and we only go far enough with practice to when students understand how to solve the problem of each type. Once they understand and do it a few times, we move on. Granted, we certainly do not object if the students do more repetition in extra time (during practice sessions and through a lot of Extra Credit homework), but the focus of the program is to cover a lot of ground and force kids to think – to “stretch their brains”. Ultimately, when they learn to think they will be able to fight and solve any kind of a problem.