Problem Solving vs. New Material

In summary, the conversation is about a student who is starting their freshman year in college and has been spending their summer working on math. They are currently studying from a book called "Baby Rudin" and are wondering if it's important to focus on problem solving rather than learning new material. They also mention owning copies of "Spivak's Calculus on Manifolds" and "Engel's problem solving strategies" and are trying to decide what to study next. The other person in the conversation suggests spending more time on learning than practicing, but also acknowledges that practicing can be helpful. They have only done a few problems from Engel's book so far and have found it enjoyable and beneficial.
  • #1
musicheck
29
0
I'm going to be starting my freshman year in college this september, and I've been spending my summer working on math. So far I've been working on baby Rudin (on chapter 5, plan to stop after chapter 7). I'm wonder whether people (*cough* mathwonk *cough* :-) ) thinks that it is important to spend time focusing on problem solving rather than learning new material. I currently own copies of Spivak's Calculus on Manifolds and Engel's problem solving strategies, and I'm trying to pick what to study next.
 
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  • #2
I think it's better to spend more time on learning than practising those topics you've learned because chances are, you are going to have lots of time consolidating your knowledge in university and so why not spend time exploring? at least you have an idea of what's ahead. Of course, that's just what works for me. If you think you wouldn't really understand what you've learned without some thorough practising, I would practise if I were you. But, well, it's always more fun learning than practising.
 
  • #3
I've done only a small handful of problems from Engel so far. It's fun and definitely worth spending a bit of time with.
 

Related to Problem Solving vs. New Material

1. What is the difference between problem solving and learning new material?

Problem solving involves using critical thinking skills to find solutions to specific challenges or issues. Learning new material, on the other hand, involves acquiring new knowledge or information through studying, reading, or instruction.

2. Which is more important, problem solving or learning new material?

Both problem solving and learning new material are important in their own ways. Problem solving allows us to apply the knowledge we have acquired to real-life situations, while learning new material expands our understanding and allows us to approach problems from different perspectives.

3. Can problem solving skills be taught?

Yes, problem solving skills can be taught and developed through practice and guidance. This includes learning techniques such as brainstorming, critical thinking, and decision making, as well as developing a growth mindset and being open to new ideas.

4. How can problem solving help in the learning process?

Problem solving can enhance the learning process by allowing individuals to actively engage with new material and apply it to real-life situations. It also promotes critical thinking and problem solving skills, which are essential for understanding and retaining new information.

5. Is it better to focus on problem solving or learning new material?

It is important to balance both problem solving and learning new material. While problem solving allows us to apply our knowledge in practical ways, learning new material expands our understanding and provides a foundation for problem solving. Both are necessary for success in any field.

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