What are your preferred methods of learning?

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The discussion centers on effective methods for learning new concepts, particularly in problem-solving contexts. One participant shares their experience with two study approaches: one involving extensive worked examples and solutions, which proved effective, and another focusing solely on textbook examples without additional practice, which was less beneficial for problem-solving skills. The importance of practice is emphasized, likening it to learning to ride a bike—understanding theory is not enough without hands-on experience. The conversation references resources like Schaum's outlines and Quizlet for quality examples, highlighting that daily study and practice are crucial for mastering concepts. The need for learners to engage with various situations to apply principles effectively is also noted, underscoring that real-world applications often disguise fundamental concepts. Overall, the consensus is that a combination of theory, worked examples, and consistent practice leads to deeper understanding and proficiency.
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TL;DR Summary: What has helped you the most learning new concepts

I recently came across this article

https://openlearning.mit.edu/mit-faculty/research-based-learning-findings/worked-and-faded-examples

I have studied 2 ways, one was using similar to the method above, theory followed but loads of worked examples and solutions, until I felt comfortable solving most problems about that topic.

The other method, which I have been using recently, is to read and study the material only solving the examples given in the text and not do any of the problems or study the solutions. (In the hope that this would be quicker meaning i can read more books about the same topic)

I’ll be honest the latter doesn’t seem to be serving me much when it comes to solving the problems, I reckon that article is absolutely bang on and to say MIT uses the same way to teach says a lot.

What are your experiences?

With books such as Schaums outlines and websites such as clegg and quizlet there is no shortage of quality worked out examples.
 
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You can know everything about classical mechanics and how a bike works but without actually practicing you can’t just pick up a bike and make it work. Sure, you may be able to understand what happened when you failed and correct it more easily than if you did not have the theory background, but to ride a bike you must practice riding a bike.
 
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bigmike94,
Your way of understanding is the better way. Also one should not ignore DAILY study and practice.
 
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To paraphrase Feynman: "You can't solve the problems? You don't know nothing!"
 
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It's one of many strategies. The important part of them all is that they encourage learners to think about the processes they are going through to solve problems. It forces learners to make a map of their mental processes.
 
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Physical principles are very often presented in their most obvious forms and laid bare for you to more easily understand them without any distractions. The real world rarely ever presents itself to you in this obvious form. In the real world, these principles are dressed in various disguises and so one must be able to see the principles through these disguises.

The lever is a simple machine easily understood but can you identify all the levers in a car?

The only way to become proficient is to practice on a variety of situations that use these principles.
 
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Hey, I am Andreas from Germany. I am currently 35 years old and I want to relearn math and physics. This is not one of these regular questions when it comes to this matter. So... I am very realistic about it. I know that there are severe contraints when it comes to selfstudy compared to a regular school and/or university (structure, peers, teachers, learning groups, tests, access to papers and so on) . I will never get a job in this field and I will never be taken serious by "real"...
Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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