Re-learning math from the basics. Should I go through grades or go through topics?

[Zephyr1779]

Hi, everyone!

I'm planning on restudying math from the beginning (K-12), via KhanAcademy, MathIsFun, and plenty of other resources.

Now, what I'd like to ask is, as the title says, should I study material grade by grade or topic by topic?

Additionally, is there a way to test myself to know from which grade/topic I should start, like doing some sort of "evaluation test" or something similar whether on KhanAcademy or some other website?

I'm asking this primarily because I know that early math will be a breeze to go through, so instead of wasting time on that, I would like to know if there is a way to start from somewhere where I'm weak and have holes to fill in?

Or should I ignore that and immediately start from the 1st grade and reconsolidate my foundations?

Any advice?

[joigus]

If you want to go from A to B, it's only natural that the answer will depend on where's A, and where's B.

Are you already fluent in algebra, geometry, and analysis? (where's A?)

Do you intend to tackle very sophisticated and recent mathematics, like ,eg, Grothendieck's Motives? (where's B?)

If you already have a reasonable A, are not too ambitious about B, and also perhaps are relatively young, I see no reason why you wouldn't get there with the sources you propose by following your nose, and intuitively finding where the boundary between what you ignore and you already know actually is.

I hope that was helpful.

[mathematic]

If you know elementary arithmetic, start with elementary algebra.

[MigL]

As a Physicist, I consider Math a set of tools that I can use to build models, that explain and make predictions about the workings of the universe.

Learning the use of these tools by going 'up through the grades', would be equivalent to learning how to use your hammer and saw to initially make a bookshelf. Then framing a shed or garage, until you are finally proficient enough to frame a house.

Going 'through topics' would be equivalent to taking a tool type, such as a table saw to cut lumber, a band saw to cut wood shapes, a chainsaw to cut trees, etc., and becoming proficient in all saw types before switching to another tool type.

What do you want to do with your tools ?

[Ken Fabian]

If you are confident you know what it is you don't know then skip to the parts you feel you need, but if you aren't sure, go through them all in order and see. It shouldn't take long to find out whether each element is understood, then jump ahead, without doing all the exercises. Or not.

My own experience is that missing something along the way can make what you are trying to learn a lot more difficult - the curriculam tends to designed to provide foundations that can be built on.

I tried something similar, more to see if I could recover what I'd learned and lost than learn from zero - I can't say it went well and I suspect some of the parts I struggled with went all the way back to missed lessons at school, far too long ago. In my late 60's I don't take it in as readily as back then. Or retain it so easily... better than average recall got me through school, but now I struggle to remember where my glasses are... when they are hanging on a cord around my neck.

[Zephyr1779]

On 10/13/2022 at 5:04 PM, joigus said:

If you want to go from A to B, it's only natural that the answer will depend on where's A, and where's B.

Are you already fluent in algebra, geometry, and analysis? (where's A?)

Do you intend to tackle very sophisticated and recent mathematics, like ,eg, Grothendieck's Motives? (where's B?)

If you already have a reasonable A, are not too ambitious about B, and also perhaps are relatively young, I see no reason why you wouldn't get there with the sources you propose by following your nose, and intuitively finding where the boundary between what you ignore and you already know actually is.

I hope that was helpful.

 

18 hours ago, mathematic said:

If you know elementary arithmetic, start with elementary algebra.

 

16 hours ago, MigL said:

As a Physicist, I consider Math a set of tools that I can use to build models, that explain and make predictions about the workings of the universe.

Learning the use of these tools by going 'up through the grades', would be equivalent to learning how to use your hammer and saw to initially make a bookshelf. Then framing a shed or garage, until you are finally proficient enough to frame a house.

Going 'through topics' would be equivalent to taking a tool type, such as a table saw to cut lumber, a band saw to cut wood shapes, a chainsaw to cut trees, etc., and becoming proficient in all saw types before switching to another tool type.

What do you want to do with your tools ?

 

16 hours ago, Ken Fabian said:

If you are confident you know what it is you don't know then skip to the parts you feel you need, but if you aren't sure, go through them all in order and see. It shouldn't take long to find out whether each element is understood, then jump ahead, without doing all the exercises. Or not.

My own experience is that missing something along the way can make what you are trying to learn a lot more difficult - the curriculam tends to designed to provide foundations that can be built on.

I tried something similar, more to see if I could recover what I'd learned and lost than learn from zero - I can't say it went well and I suspect some of the parts I struggled with went all the way back to missed lessons at school, far too long ago. In my late 60's I don't take it in as readily as back then. Or retain it so easily... better than average recall got me through school, but now I struggle to remember where my glasses are... when they are hanging on a cord around my neck.

Thank you all very much for your suggestions and opinions, I really appreciate it.

What I forgot to mention in the OP about my knowledge was that the last time I did math was in high school which was about 6-7 years ago. Each time I did math tests I managed to get a C and B (sometimes A's, but those were rare).

The problem with the method of studying back then that I was using was rote learning. I crammed everything the night before tests, so everything that I learned all those days at school, I basically forgot now. Which is the reason why I'm planning on restudying everything from the point where I'm weakest all the way up to the pre-college material.

This is the reason why I'm looking for some sort of "evaluation" or "diagnostic" test to see where I should start.

For example, I know how to do arithmetic operations (ASMD) with whole numbers, fractions, decimals, etc. I know percentages, exponentiation, rooting, ratios, proportions, and elementary algebra. But that's about all I can remember right now, so I don't know where to start right now.

Thanks again for the replies guys, it really means it

[studiot]

On 10/13/2022 at 3:52 PM, Zephyr1779 said:

Hi, everyone!

I'm planning on restudying math from the beginning (K-12), via KhanAcademy, MathIsFun, and plenty of other resources.

Now, what I'd like to ask is, as the title says, should I study material grade by grade or topic by topic?

Additionally, is there a way to test myself to know from which grade/topic I should start, like doing some sort of "evaluation test" or something similar whether on KhanAcademy or some other website?

I'm asking this primarily because I know that early math will be a breeze to go through, so instead of wasting time on that, I would like to know if there is a way to start from somewhere where I'm weak and have holes to fill in?

Or should I ignore that and immediately start from the 1st grade and reconsolidate my foundations?

Any advice?

I hate to tell you this but it is just about impossible to learn any technical subject topic by topic.
This is particularly true for Mathematics.

The reason for this is that all the topics are inter-related.
You need to know a little bit of arithmetics to study algebra and a little bit of algebra to study geometry, but also a little bit of geometry at the beginning of algebra and so on.

That is why the the same topics are revisited at every grade, but at a higher level.

[Zephyr1779]

On 10/15/2022 at 12:52 AM, studiot said:

I hate to tell you this but it is just about impossible to learn any technical subject topic by topic.
This is particularly true for Mathematics.

The reason for this is that all the topics are inter-related.
You need to know a little bit of arithmetics to study algebra and a little bit of algebra to study geometry, but also a little bit of geometry at the beginning of algebra and so on.

That is why the the same topics are revisited at every grade, but at a higher level.

Hi, studiot!

Thank you for the reply.

If what you say is true, then how would you suggest I take on this restudying plan?

What would be in your opinion most efficient way to plan on re-studying math? Go grade-by-grade or some other method?

Additionally, I replied before with what topics I'm comfortable right now in this post, so I'm not sure from where exactly to start my re-learning process.

On 10/14/2022 at 8:19 PM, Zephyr1779 said:

What I forgot to mention in the OP about my knowledge was that the last time I did math was in high school which was about 6-7 years ago. Each time I did math tests I managed to get a C and B (sometimes A's, but those were rare).

The problem with the method of studying back then that I was using was rote learning. I crammed everything the night before tests, so everything that I learned all those days at school, I basically forgot now. Which is the reason why I'm planning on restudying everything from the point where I'm weakest all the way up to the pre-college material.

This is the reason why I'm looking for some sort of "evaluation" or "diagnostic" test to see where I should start.

For example, I know how to do arithmetic operations (ASMD) with whole numbers, fractions, decimals, etc. I know percentages, exponentiation, rooting, ratios, proportions, and elementary algebra. But that's about all I can remember right now, so I don't know where to start right now.

[studiot]

4 hours ago, Zephyr1779 said:

Hi, studiot!

Thank you for the reply.

If what you say is true, then how would you suggest I take on this restudying plan?

What would be in your opinion most efficient way to plan on re-studying math? Go grade-by-grade or some other method?

Additionally, I replied before with what topics I'm comfortable right now in this post, so I'm not sure from where exactly to start my re-learning process.

I suggest the following strategy.

1.   Start at the beginning and attempt maths questions from that year's material, from any source that you can get hold of so long as the answers are also provided.
   You don't need to achieve grades or marks, just to find out what you know and what you don't know.
    
2.   Hopefully, as you say, it will come easy at this stage and you will fly through the material.
   Quickly review wrong answers and check the teaching material for that topic if you get several wrong on a particular thing.
    
3.   Eventually you will find questions you can't answer.
   This is where you stop, go back and study the teaching material for that year, going forward at your own pace.
   Make sure you try the questions again and even if you don't get them all right, make sure you understand how to do them.
    
4.   Finally you will decide that you are no longer just filling in gaps but need to take your studies forward from where you left off a few years ago.

Edited October 16, 2022 by studiot

[Zephyr1779]

On 10/16/2022 at 9:49 PM, studiot said:

I suggest the following strategy.

1.   Start at the beginning and attempt maths questions from that year's material, from any source that you can get hold of so long as the answers are also provided.
   You don't need to achieve grades or marks, just to find out what you know and what you don't know.
    
2.   Hopefully, as you say, it will come easy at this stage and you will fly through the material.
   Quickly review wrong answers and check the teaching material for that topic if you get several wrong on a particular thing.
    
3.   Eventually you will find questions you can't answer.
   This is where you stop, go back and study the teaching material for that year, going forward at your own pace.
   Make sure you try the questions again and even if you don't get them all right, make sure you understand how to do them.
    
4.   Finally you will decide that you are no longer just filling in gaps but need to take your studies forward from where you left off a few years ago.

That looks like good plan! Thanks studiot! I'll try it out this way, and hopefully will be able to manage to pass through much without too many problems.

 

Cheers!