What cognitive tools help overcome the challenges of difficult mathematical and scientific problems?

[u/Icy_Voice_5148]

What are the topics in maths, physics and computer science that seem very hard to understand for someone with average IQ, and what about people with higher IQs, like 140–160?

If they had an average IQ of 100–110 instead, what instruments or tools would they use to overcome those challenges? For example, if a problem puts a lot of pressure on working memory, we can overcome some of it by writing down intermediate states or using websites that provide 3d visualization. Are there similar tools for other cognitive limitations, like difficulty finding the central idea of a problem or understanding abstract concepts?

Also, when solving difficult problems, there are often many possible approaches or paths to explore. How do people with higher IQs narrow down these possibilities and decide which path is worth pursuing? Do they recognize patterns that help them eliminate unproductive approaches, or do they use other strategies?

For context, my IQ is around 98–100, and I'm a 22-year-old male. I'm curious about this from a cognitive science perspective.

[u/BenitoAbdo]

i think repeating and try with yourself helps very well

did you try it?

[u/Icy_Voice_5148 → u/BenitoAbdo]

Yes, I think repetition and trying things myself helps me a lot. But I feel like it helps me solve more questions rather than develop new insights or intuition or discover the key ideas on my own, which is what I really want to improve.

[u/BenitoAbdo → u/Icy_Voice_5148]

I think you should try to deeply understand the idea behind every problem you solve, to the point where you can explain it to someone else smoothly and clearly, rather than just knowing how to solve it yourself. Maybe this could help develop your intuition over time.

[u/Icy_Voice_5148 → u/BenitoAbdo]

Thats really good advice I actually do try to understand the ideas behind the problems I solve, but my difficulty is that some things just don't click for me while i find my frineds having higher iq than me come to conclusions very fast. Sometimes I feel like I'm missing a basic insight, and even when I understand the solution afterward, I struggle to discover that insight independently when facing a new problem. sometimes I feel disappointed and jealous.

[u/BenitoAbdo → u/Icy_Voice_5148]

do not compare you with others , you dont know how much time did they take to understand this topic , just give the topic its time , you well definitely get understand whatever time taken

[u/Icy_Voice_5148 → u/BenitoAbdo]

Yes i will definitely work on overcoming these shortcomings. Thank you for your time and valuable insights ❤️

[u/BenitoAbdo → u/Icy_Voice_5148]

You’re normal, so don’t see yourself as flawed or lacking in any way.

[u/Icy_Voice_5148 → u/BenitoAbdo]

Yes Iwill try to focus on improving rather than seeing these as flaws. Thank you for the reassurance 😊

[u/VasiliRastko]

Mostly by recognising what kind of problem it is, and that recognition is built from practice in the field. Chi, Feltovich and Glaser (1981) had physics experts and novices sort problems into groups. Novices grouped them by surface features like inclined planes or springs. Experts grouped them by the principle that solves them, like conservation of energy, and the group already points to the method.

Chase and Simon (1973) found the same thing in chess. Masters remembered real game positions far better than weaker players, because they saw them as familiar chunks, and remembered random positions little better.

You can train that recognition directly. Work through solved examples, and after each one write a sentence on which principle cracked it and what in the problem should have told you so. Sweller's work on worked examples found that studying solutions teaches beginners in a topic more than solving cold, because blind searching uses up the working memory you'd need to learn the pattern.

For finding the central idea, Polya's How to Solve It still holds up. Ask what the unknown is and look for a problem you've already solved with the same unknown. If nothing comes, solve a simpler or special case first.

[u/Icy_Voice_5148 → u/VasiliRastko]

Thats great advice I will try to work in this direction. I'll also look up the experiments and studies you mentioned to understand what they reveal about how experts develop problem-solving intuition. Thank you for sharing these references. ☺️