I work with a lot of people starting out in IT, and I notice many struggle with problem solving approaches when they hit difficult homework. They know the concepts but can't apply them to new problems. What homework problem solving tips have helped you the most when you're stuck on a problem that doesn't seem to have an obvious solution? I'm looking for practical approaches to developing problem solving skills rather than just getting answers.
When I'm stuck on a problem, I ask myself what do I know for sure?" and write that down. Then "what am I trying to find?" Then "what's the gap between these?" This systematic approach often reveals the next step. Also, I try to solve a simpler version of the problem first. If I can't solve the simple version, I definitely can't solve the complex one.
In design and development, we use a lot of debugging techniques that apply to homework problems. One is rubber duck debugging" where you explain the problem to an inanimate object. The act of explaining often reveals the solution. Another is changing one variable at a time to see what effect it has, which works for math and science problems too.
I'm still learning this myself but what's helped is looking for patterns in solved problems. Like in programming, if I see how similar problems were solved, I can often adapt that approach. Also, breaking the problem into inputs, processes, and outputs helps me understand what's being asked.
For programming problems, I use a technique called divide and conquer." Break the problem into subproblems that are easier to solve. Solve each subproblem, then combine the solutions. This works for math problems too. Also, I always check my work with sample inputs or known cases to make sure I'm on the right track.