How to Get Better Conceptual Understanding in Subjects (1 Viewer)

[Dominator.]

Hello, I'm a Year 9 Student and am doing well in all my subjects (the ones that count in my GPA that is). Recently, I've been learning how to study effectively and feel like I've been learning the wrong way my whole life (although it is limited to only 14yrs). I believe that I need to understand the fundamentals of my concepts very thoroughly and find out why they are the way that they are. For example, for something as basic as y = mx + b, I tried to think of why the equation was presented in this particular way and in all honesty it just made me realise that a lot of my concepts have been memorised rather than properly learnt (partially at fault for my maths teacher who literally doesn't teach us).

As for the future, I've become aware that it is gonna be imperative that I learn in a way that will allow me to get a very thorough understanding on the concepts and fundamentals so that I can apply them by linking them together.

This leads me to my question: How do I do this?

I know it may sound dumb, but I'm genuinely stuck on how I should relearn all the fundamentals and genuinely understand them. Although, for maths I'm still learning at a very elementary level I feel like I need to drill in the conceptual understanding of certain topics to ensure that I do much better in the future.

This then leads me to my second question: Are there any particular resources that could assist me (at a year 9/10 level), for example, youtube channels that would help me to understand my subjects (not just limited to maths but also sciences) and find out why certain things are the way in which they are OR textbooks which provide a very comprehensive understanding on the fundamentals.

I've noticed something in common with the highest ranking students in Yr12, and that is they have a very strong conceptual/foundational understanding of their respective subjects, and I genuinely want to become like that so that in the future I can do INCREDIBLY well in my HSC.

I know that I may have rambled on about this, but I'm kinda happy that I realised this only in Yr9, and want to improve so I can do better in the future and tackle even harder problems (due to a strong conceptual foundation). Some of my questions may sound blurred, but I feel like I've given quite a lot of context so even alternative answers (extending beyond my weirdly worded questions) would be very helpful!

ALTHOUGH I'VE MAINLY TALKED ABOUT MATHS DURING THIS QUESTION, IM ALSO IN THE SAME PREDICAMENT FOR SCIENCE, AND HENCE WOULD APPRECIATE ANY RESOURCES FOR BOTH SUBJECTS IN RELATION TO MY QUESTION!!!

 

[cossine]

Hello, I'm a Year 9 Student and am doing well in all my subjects (the ones that count in my GPA that is). Recently, I've been learning how to study effectively and feel like I've been learning the wrong way my whole life (although it is limited to only 14yrs). I believe that I need to understand the fundamentals of my concepts very thoroughly and find out why they are the way that they are. For example, for something as basic as y = mx + b, I tried to think of why the equation was presented in this particular way and in all honesty it just made me realise that a lot of my concepts have been memorised rather than properly learnt (partially at fault for my maths teacher who literally doesn't teach us).

As for the future, I've become aware that it is gonna be imperative that I learn in a way that will allow me to get a very thorough understanding on the concepts and fundamentals so that I can apply them by linking them together.

This leads me to my question: How do I do this?

I know it may sound dumb, but I'm genuinely stuck on how I should relearn all the fundamentals and genuinely understand them. Although, for maths I'm still learning at a very elementary level I feel like I need to drill in the conceptual understanding of certain topics to ensure that I do much better in the future.

This then leads me to my second question: Are there any particular resources that could assist me (at a year 9/10 level), for example, youtube channels that would help me to understand my subjects (not just limited to maths but also sciences) and find out why certain things are the way in which they are OR textbooks which provide a very comprehensive understanding on the fundamentals.

I've noticed something in common with the highest ranking students in Yr12, and that is they have a very strong conceptual/foundational understanding of their respective subjects, and I genuinely want to become like that so that in the future I can do INCREDIBLY well in my HSC.

I know that I may have rambled on about this, but I'm kinda happy that I realised this only in Yr9, and want to improve so I can do better in the future and tackle on even harder problems (due to a strong conceptual foundation). Some of my questions may sound blurred, but I feel like I've given quite a lot of context so even alternative answers (extending beyond my weirdly worded questions) would be very helpful!

There are many theorem and axioms. Unfortunately, some of content can be quite advance so you may need accept a theorem at face value but understand what it means. Similarly you could get stuck on various low level details like how do you prove a/b * c/d = ac/bd. What you want to instead do is strike balance between understanding and not understanding.

I think it might be worthwhile to refer textbook on openstack particularly algebra 1, algebra 2. The benefit of this approach would be textbooks are completely free. The 2nd benefit is all solutions are available online on quizlet.com.

For study resources in general regarding extracirricular-mathematics you might want to look into programming(languages such as Python, C, C++), operation research, discrete maths (This will help in understanding the fundamentals that you have mentioned in your post).

 

[Dominator.]

Thanks for the response. I'll look at the textbooks you referred!

 

[mmmmmmmmaaaaaaa]

Recently, I've been learning how to study effectively

curious what you been doin to do this

 

[wizzkids]

I will attempt to give you a new direction in your learning. You have written a very clear explanation of your dilemma, and this deserves a clear answer.
It is never too late to try a different way of learning.
Both Mathematics and Science are highly structured in their theory of knowledge (their way of comprehending the world).
There is another theory of knowledge which is faith-based (accepting wisdom from an authority, for example Koran or the Bible) and this is quite acceptable for people who can accept that there are mysteries that will never be adequately explained.
Science and Mathematics start with simple concepts, reliable statements that have never been contradicted, or which have passed every test we could throw at them. Then we build these up to become a huge edifice of knowledge, but really at the bottom it is all based on simple axioms (in Mathematics) or we call them Laws (in Science). For example, the axiom that for every counting number "n" there is another number "n+1" so we know that there must be an infinite number of counting numbers, so infinity must exist. An example from Science would be the law of thermodynamics, "That heat only flows from a hot body to a cold body, and never the other way". From this we know there must be a temperature scale.
Whenever you encounter a complicated problem, keep asking the question "Why do we know that is true?". What assumed knowledge does this statement depend on? It will lead you on a long journey of deductions that take you right back to the axioms or Laws of knowledge.
At some point, you might reach a dead-end where you can't go any further due to your own lack of knowledge, but at least you have clarified the question and what it depends on.
At that point you are "in the zone of proximal development". You might need a teacher to help you at this point, or you might need to turn to the Internet or a good textbook to find the missing piece of the puzzle.
Now I know that for most people that is too much trouble, and they would rather just take statements as true at their face value, and then use these identities or equations to get the answer that they want as quickly as possible. That's what we do in exams, we just want the correct answer, without wasting any time explaining why it has to be like that.
Now if that is the only method you use, then you are always going to be weak on conceptual understanding and problem solving.
When you encounter a strange problem out of the normal context, you are going to have a panic attack because it is not something you have seen before. But if you have the time, and you are not under exam pressure, take the time to keep asking the "Why?" question, and this will train your mind to understand things conceptually. Then you won't panic when you encounter something that is completely new.
I hope this helps!

 

[Dominator.]

curious what you been doin to do this

Recently, I've been watching lots of videos from this YouTuber called 'Justin Sung,' he's very educated on how to study effectively and what techniques are used to do so. I've been implementing a lot of the techniques he used (at a basic level, but am trying to refine them as I go on). For example, before classes now I try to do what he calls 'prestudy' and briefly go through the content of the day and find relations in what I already know about this topic based on my prior learning (as this is a way of higher order learning).

Other than this, I also try to learn based on my own curiosity, 'inquiry-based learning,' that way I ensure that I keep asking questions such as 'why,' and 'how,' to get a comprehensive understanding of the topics at hand, and also make my learning more relevant so that I encode it better and am able to retain the information for longer periods of time.

After I believe that I have a genuine understanding of the topics, I begin to make mindmaps (for subjects that are heavily based on concepts) and often add to them as I continue learning. This way, I can find relationships between what I am learning and how it fits into the broader context. I try to minimise the amounts of words in these mindmaps and make them concise but also understandable (for me).

I've probably missed quite a few steps, but this is at a basic level, the techniques I'm trying to use to study more effectively. I'm only just starting to implement these techniques within my routine, as I've only recently learned of them.

 

[mmmmmmmmaaaaaaa]

Recently, I've been watching lots of videos from this YouTuber called 'Justin Sung,' he's very educated on how to study effectively and what techniques are used to do so. I've been implementing a lot of the techniques he used (at a basic level, but am trying to refine them as I go on). For example, before classes now I try to do what he calls 'prestudy' and briefly go through the content of the day and find relations in what I already know about this topic based on my prior learning (as this is a way of higher order learning).

Other than this, I also try to learn based on my own curiosity, 'inquiry-based learning,' that way I ensure that I keep asking questions such as 'why,' and 'how,' to get a comprehensive understanding of the topics at hand, and also make my learning more relevant so that I encode it better and am able to retain the information for longer periods of time.

After I believe that I have a genuine understanding of the topics, I begin to make mindmaps (for subjects that are heavily based on concepts) and often add to them as I continue learning. This way, I can find relationships between what I am learning and how it fits into the broader context. I try to minimise the amounts of words in these mindmaps and make them concise but also understandable (for me).

I've probably missed quite a few steps, but this is at a basic level, the techniques I'm trying to use to study more effectively. I'm only just starting to implement these techniques within my routine, as I've only recently learned of them.

ah yes Justing Sung

the 'pre-study' thing you're referring to is actually called priming