Thinking time vs. Writing Time

In summary, the conversation discusses the trade-off between the time spent writing out a full solution to a problem versus solving it in one's mind. The speaker raises the question of what ratio of writing time to thinking time is acceptable, considering the benefits and drawbacks of each approach. They also mention the potential for mistakes when only sketching out a solution.

What is the maximum ratio for you?

  • 1-2

    Votes: 0 0.0%
  • 3-4

    Votes: 1 50.0%
  • 5-6

    Votes: 0 0.0%
  • 7-8

    Votes: 0 0.0%
  • 9-10

    Votes: 0 0.0%
  • 11-15

    Votes: 1 50.0%
  • 16-20

    Votes: 0 0.0%
  • It doesn't matter. I must write it out.

    Votes: 0 0.0%

  • Total voters
    2
  • #1
andytoh
359
3
This may seem a very strange poll but I honestly want to know what others think. I just spent 1 hour writing out a full, rigourous solution to a problem. I formulated the main idea in about 5 minutes and I knew that my proof (once written out) would be correct. After spending about 12 times longer to write it out than "proving it in my mind" I wonder whether it was worth it (the question is not part of an assignment).

On the one hand, I picked up details that was not in my mind at first, and my fully written solution is forever saved and I can look it up if I ever want to try the problem again. I also exercised my mathematical rigour and proof-writing in general. Besides, by writing it out I could have realized that the solution in my mind was wrong. On the other hand, I spent 12 times longer than solving it in my mind and I could have done many other questions in that time.

So my poll question is: What is the greatest writing-time-to-thinking-time ratio that you would accept to write out the full solution to a problem? When I say thinking time, I mean solving the question in your mind (or scribbling the key ideas) to the point where you know you are correct (up to minor details that you know can be filled if you choose to write out the full solution). For example, if your ratio is 1:6, it means that if you can solve a problem in your mind in, say, 5 minutes, but it will take you 30 minutes to write it out fully (and the question is not an assignment question), you would just forego writing out the solution (or just scribble out the key ideas) and move on. Sorry I could not phrase the question more informally.
 
Last edited:
Mathematics news on Phys.org
  • #2
Or perhaps if your question is not an assigment question, just jot down the key steps and then move on to your next question? This sure saves a lot of time and thus allows you to do more questions, but some of your "sketched solutions" may actually turn out to be wrong (and you will erroneously continue to believe that your sketched solution is correct).
 
  • #3



This is a very interesting question and one that I'm sure many people struggle with when it comes to problem-solving. Personally, I believe that the writing-time-to-thinking-time ratio varies depending on the individual and the specific problem at hand. For some people, writing out the full solution may help solidify their understanding and reinforce their thought process. For others, they may be able to accurately solve a problem in their mind without needing to write it out. As for myself, I tend to fall somewhere in the middle - I often find that writing out the solution helps me identify any errors or gaps in my thinking, but I also don't want to spend an excessive amount of time on it if it's not necessary.

In terms of setting a specific ratio, I don't think there can be a one-size-fits-all answer. It ultimately depends on the individual's learning style and the complexity of the problem. I think it's important to prioritize understanding and accuracy over speed when it comes to problem-solving. So if it takes longer to write out the solution but it ensures a correct and thorough understanding, then it is worth the extra time.

Additionally, as you mentioned, writing out the solution can also serve as a reference for future problems. This can save time in the long run as it eliminates the need to re-solve the same problem or figure out where the original solution went wrong. So in that sense, the time spent writing out the solution can also be seen as an investment in future problem-solving.

Overall, I don't think there is a right or wrong answer to this question. It ultimately comes down to personal preference and finding a balance between thinking and writing time that works for each individual and each problem.
 

1. What is the difference between thinking time and writing time?

The main difference between thinking time and writing time is the mental process involved. Thinking time refers to the time spent processing and organizing ideas in one's mind, while writing time is the physical act of putting those ideas into written form.

2. Which is more important, thinking time or writing time?

Both thinking time and writing time are equally important in the writing process. Thinking time allows for critical analysis and organization of ideas, while writing time brings those ideas to life and allows for refinement and revision.

3. How much time should be spent on thinking vs. writing?

The amount of time spent on thinking vs. writing can vary depending on the individual and the project. However, it is generally recommended to spend a significant amount of time on thinking and planning before dedicating a substantial amount of time to writing.

4. How can I improve my thinking time and writing time?

To improve thinking time, it is helpful to practice techniques such as brainstorming, mind mapping, and outlining to generate and organize ideas. To improve writing time, it is beneficial to practice regularly, seek feedback and constructive criticism, and continuously revise and edit your work.

5. Can thinking time and writing time overlap?

Yes, thinking time and writing time can overlap. Sometimes, while writing, new ideas may come to mind that require additional thinking and planning. Similarly, during thinking time, one may start writing down their thoughts to better organize and develop them.

Similar threads

  • General Math
Replies
1
Views
856
Replies
14
Views
1K
  • General Math
Replies
13
Views
1K
  • STEM Career Guidance
Replies
3
Views
1K
  • General Math
Replies
1
Views
1K
Replies
9
Views
2K
  • General Math
2
Replies
66
Views
4K
  • General Math
Replies
3
Views
961
  • Precalculus Mathematics Homework Help
Replies
6
Views
801
Replies
4
Views
911
Back
Top