Why do I forget math concepts so easily?

[Fanger]

I'm kind of a late boomer when it comes to math, or maybe liking math...

Anyways in junior high(I live in Canada), I found math easy and boring and I ace the class without ever listening in class or doing any homework and I continued that habit in my first year of high school which ended really badly for me. Well, maybe not THAT bad. For grade 10 I ended up learning the entire semesters material in a few hours before the final exam and my final mark was 79. In grade 11 I started homeschooling for some reason and I learned the math curriculum that year in 2 months(would have been faster if there weren't so many stupid lengthy projects) and also aced it. In grade 12 I returned to study at a school and I returned to study math with the approach that I had in junior high(but maybe a little more work, instead of not working on it at all I use the class time to work at my own pace) and I kinda nailed it?

I don't know how to classify myself in terms of my aptitude in math because while there are certainly people who seem much slower than I am when it comes to math, I have a hard time keeping up with the teachers. Sometimes either they are teaching too slow or too fast and I just have to do everything on my own. Also while I seem to be really good at cramming everything in before an exam I couldn't seem to remember much that I have learned from the previous math classes other than PEDMAS(more like an instinct). I'm also not the fastest problem solver because my brain seems to hate just simply memorizing things it has to think consciously through every step every time(Idk but I've heard from people that this is a sign that you need to practice more).

I suspect that the reason why I don't remember the math that I learned is that: 1. lack of real-life application 2. lack of interest at the time of learning 3. lack of practice
Now that I start to see the beauty and usefulness of math I really regret not putting more effort into it. I want to change that but my foundation is so weak I don't even know where or how to start. I'm also really nervous because I'm thinking of studying maths at university. Can anyone give some tips on how to strengthen your foundation in math when you don't even know where to start? Or if anyone has similar experiences feel free to comment. Thank you for reading!

 

[Mark44]

The thread title you chose is "Why do I forget math concepts so easily?
Here are a couple reasons for this:

For grade 10 I ended up learning the entire semesters material in a few hours before the final exam and my final mark was 79. In grade 11 I started homeschooling for some reason and I learned the math curriculum that year in 2 months(would have been faster if there weren't so many stupid lengthy projects) and also aced it.

Also while I seem to be really good at cramming everything in before an exam I couldn't seem to remember much that I have learned from the previous math classes other than PEDMAS(more like an instinct).

These may have been good tactics for getting through a test, but they are terrible strategies if you want to really learn something.

Can anyone give some tips on how to strengthen your foundation in math when you don't even know where to start?

Start with the topics you're weak in. If that includes algebra, get an algebra book and work through the homework problems. If you're getting a large percentage of them right, move on to topics that you have a harder time with. Do the same with precalculus and trigonometry, and once you're competent with these subfields, move on to calculus.

 

[jedishrfu]

Related to what @Mark44 is saying:

1) Work through Khan Academy math courses: Algebra, Geometry, Advanced Algebra, Precalculus, Calculus 1,2,3 Differential Eqns, Linear Algebra, Statistics (calculus-based)

2) Alternatively, work through MathIsPower4U.com math videos for these same subjects.

3) There are some good math books on openstax.org if you prefer reading

Doing problems is the only way to solidify your math concepts. Of course, there are some key formulas to remember like the quadratic formula, pythagorean theorem, trig formulas and series, sequence and counting formulas.

You could create a crib sheet with them on it or learn to derive them in case you don't trust your memory. Or get some study sheets from quickstudy.com

Learning math and taking tests requires different skills.

I would sometime panic when taking HS math tests especially in trig and I remember writing mnemonic math expressions at the top of my page to refer to in case my memory failed due to the panic.

An example: s2a = 2saca for:

$sin(2*\theta) = 2*sin(\theta)*cos(\theta)$

I also drew stick figures to represent certain triangle ratio concepts.

To really like math you need to develop a curious mind and explore beyond what you're being taught while keeping in mind what you need to know for an upcoming test or quiz. One gotcha here is that you might learn so cool new way to solve a problem but you can't use it on the test because the teacher may take off points for it.

Another great reference is Schaum's Math Tables and Formulas book which should have everything you need.

 

[PeroK]

I'm kind of a late boomer when it comes to math, or maybe liking math...

From what you've said, you seem to be good at storing a lot of short-term information but not so good at storing things in long-term memory. Everyone's brain does what it wants to do and we don't have direct control over what it decides to do with information. In general, most people need to go over things several times before the brain decides to store it somewhere more permanent.

You need to find what works for you.

It's also very difficult to give advice when we can't see what you can do and how you do it. For example, we see a lot of the "plug and chug" approach here. That approach seems to me to give little prospect of permanent understanding of the material.

Maybe if you posted some problems that you are stuck with in the homework section?

Alternatively, there are monthly maths challlenges on here with some "High School" level problems. You could take a crack at some of those (they are not easy, though!). You'll find them in the general math forum.

 

[DEvens]

Like many aspects of humans, the way to get the maximum improvement is to challenge yourself.

To get your muscles to become stronger you must lift weights that you are just able to lift without harming yourself. To increase your endurance you must raise your heart rate above normal, by some such exercise as jogging or swimming or something, so that you increase your heart and lung capability.

And a single challenge is not going to make much difference. Helping your buddy move that couch up three flights of stairs won't do much for your overall strength. Especially if you spend the next three months sitting on that couch and snacking.

Your brain is, in some sense, very like that. You must challenge it. You must find problems that you are only just able to solve. Especially, you must use concepts that you are just able to begin to grasp. And you must practice.

There are lots of places to find such problems at various levels. One of the places that helped me in high school was prize exams. You mention Canada. I studied like mad for the Canadian Association of Physicists prize exam. And the University of Waterloo physics department has a prize exam called the Sir Isaac Newton exam. If you cruise to their website you should be able to find some back exams.

https://www.cap.ca/programs/medals-...-prize-exam/cap-high-school-cegep-prize-exam/

https://uwaterloo.ca/sir-isaac-Newton-exam/

If you Google around you may be able to find other such.

So you find you can't do a particular problem. That shows you a place you could develop more mental strength. Or academic flexibility, depending on how you want to push the metaphor. You can't do a problem involving ballistic projectile motion, then you open the text to that part and read. And do the homework from that text on that subject. Then come back. Now you can do it? Great! Do it, and go on to the next one. No? Then read more in the text, or get a new text.

 

[Stephen Tashi]

Now that I start to see the beauty and usefulness of math I really regret not putting more effort into it. I want to change that but my foundation is so weak I don't even know where or how to start.

First make sure you are really interested in math as it is practiced. There are plenty of popularizations of math and compelling biographies of mathematicians. However, they fail to convey the essential feature of formal mathematics - it is legalistic!

A person who is skilled in pattern recognition can often look at a few examples and quickly pick up how to do certain types of mathematical problems. That's a different skill than remembering what paragraph 23 of your home insurance policy said, if you ever bothered to read it in the first place.

Fortunately, legalism in math isn't as bad as legalism practiced by non-lawyers. After you study a subject for awhile, you develop an intuition for how things go. For example, you probably have an intuition for how the real numbers behave, even if you don't remember all the axioms that define their properties. However, when facing a new mathematical structure for the first time, legalism is important. Mathematical definitions mean what they say - not what we think they ought to say. Common language is not reliable guide to mathematical terminology. And it need not be immediately obvious why mathematical definitions and assumptions say what they say.

I think most people can remember legalistic material if they recognize it is crucial to them. If you lived in an area where some type of disaster was frequent, you'd probably pay attention to whether your home insurance policy covered it. The failure of people to remember mathematical material is often due to their attitude toward it. If they have a good intuitive grasp of certain things, they think the associated legalism is unnecessary.

You've been given good advice about what to do if you are seriously contemplating a career related study of mathematics. If you are doing this as hobby or pastime, I suggest you begin by studying a short book on formal logic (propositions, negations, the quantifiers "for each" and "there exists"). That's the fundamental legalistic language of modern mathematics.