All I say in this forum is always: “just my opinion, sometimes is a mixture of experience and experiments which is almost the same.”
There’s a thing about the modern teaching of math. At one hand, teachers seem to want the student to figure out the origin of formulas and concepts by themselves, instead of simply expressing the meaning of the formulas and how to visualize what they mean.
Don't limit your imagination; all images can be memorized, but always as memorable. Always build the associations.
In the other hand, there’s the problem of the algorithms to solve problems in math. Some math problems only exist within math and function to advance math, without any application in reality although sometimes the relationship between variables are imaginable within the cartesian plane or 3D plane or even with any other metaphoric representation, as not even the plane is what the variables are. The equations are always concepts: numbers are representations. Even the symbols we use are arbitrary but all is set from logical axioms defined and from those generalizations are made, it is interesting that math appears in reality, however there’s an infinite amount of math that simply isn’t part of reality and it’s by definition impossible to imagine. But… every representation, every step to solve the problems, the problem themselves are all “mnemonicizable”.
What to memorize and what to visualize:
- Understand, visualize in non intuitive ways a means to bring out understanding. Ask suggestions to your teachers, peers or the Internet. Understanding is key to the use of the math in real life, otherwise is just a course.
- Memorize the formulas if you’re not allowed to read the study material. (I wouldn’t make pegs, rather see patterns in the formulas and make smart images)
- Memorize the algorithms to solve problems, make sure every step is understood for you. Sometimes you just don’t remember the factorization strategies.
- Memorize strategies even more than algorithms to solutions. Ex. Factorization techniques are just strategies to simplify expressions, these you will need forever in most math and even when not need you just could figure out a simplification and solve the problem faster.
- Despite what people say: memorize and memorize, but do smart memorization.
On making images for the representation of symbols and algorithms involving symbols:
What if, instead of trying to memorize the long set of x,y, and z and 1, and -1, you do transform the entire formula into a textual version of itself. Also, isn’t this really memorizing your understanding, as you have to transcribe?
Take this expression, although this can be represented as squares (remember the squares are in themselves a visualization and not an actual definition of what these symbolic representation means, as these could be variables of real life entities…):
You could read over and over, you could see the patterns or… you could simply transcribe the expression from a bunch of letters and hanging digits to an idea:
You memorize this >
“The square of sum of four variables is equal to the sum of the square of each of the four variables plus the double of the sum of the product of each variable by each other”
and you would memorize this >
At least for me the easiest thing to memorize with images is texts. If it is the case for you, you’re welcome. It may look that the text is longer but in actuality the text is what the expression means and it’s more accurate as the variables in the expression are named, don’t waste time using alphabet pegs (I ill advised that in the past). Another thing, as you transform the text into images you’re no longer concern in the mathematical format of writing equations, the format is inherent to the expression itself. I think that, when teachers write the text of the formulas they intended us to learn because of that, however maybe none of them ever taught you how to memorize text. Use the method of loci in any form for all this memories (if you have peg list memorized, you can use the images as loci…).
I still remember how to deal with inequations thanks to the loci method, never actually felt confident about them (confidence is key).
Make them at the same time: as descriptive as possible and as simplified as possible. Nothing more to add.
Gather as much from the study material, some teachers are either: evil, forgetful, biased (it’s too easy, they should know). So, don’t expect they will tell you what comes for the exams, or that they will teach you all the important strategies. Be resourceful.
Memorize, review and test your recall with the problems, try new problems and seemingly more difficult problems.
Don’t procrastinate, just because you know you can memorize, just because you know you can nailed it. Memorize with time. Do your homework exercises (best moment to test your recall…). When you arrive at the exam, you should just get out of there with an expectation of an A, nothing else. You can do it, you should be able to do it, you want to do it, then do it. It’s worth the effort.
This advice is more a self reflection, like the Meditations of Aurelius, after the experience came “wisdom”. Geesh, have I thought of this before… t1: But I’m alive another day… dance!