We had our first free math contest prepration session which was overbooked just like all our other programs. We focused on teaching repeatable process of problem solving to the kids. We call this process a technique of connecting dots. Many kids who could not attend also requested us to record the session. Here is the summary of the process which you can review in detail in the video along with a number of complex math problems.
There are four main steps in successful problem solving — not just in math or even computer science, but also in everyday life (even figuring out how to beat your rival in a video game).
- Identify dots to understand the Problem: The very first step in problem solving is to identify the problem. Problem solving is harder if one doesn’t know what “problem” to solve! This is often seen in engineering and math by reading the problem statement. Think of various elements of a problem as dots and make a note of these dots.
- Develop a strategy to understand connection between the dots: The next step is to have a plan on what to do. In other words, just rushing in won’t usually go through. Know what skills, properties, and information would be useful in aiding your decisions. With everything you know, try to make connections between dots identified in the first step.
- Connect the dots to solve a problem: Sometimes, you just have to do something. A problem can’t be solved by just staring at it, hence, start exploring dots you know even if you have just identified one tiny dot. This tiny dot may magically spill some beans and give you more dots to connect.
- Reflect on actions to understand better connection between the dots: Skilled problem solvers look back at their work. In math, it usually means figuring out if an answer is reasonable. In engineering (and other areas), problem solvers can look back and see what went right and what went wrong, so they can tackle a similar problem better next time.