In my learning career math was easiest my weakest-weak point. I found it the least interesting, most difficult and tedious of the subjects to study. This is also backed up by my standardized test scores always being lowest in the math sections. Not being a particular genius anywhere that doesn’t mean much but still.
One issue for me, in math, was that I am more visual in learning and equations simply do not really make visual sense or use to me: f(x) = x + 1 just really doesn’t hold my attention. Meanwhile:
Something like this graph is quite interesting, at least to look at.
That is besides this point though. Another issue was the ever-present question of, when is this ever going to be useful? Sure some cool graphs, solving some problems that could be fulfilling but just repeating an algorithm to solve for x when x is utterly meaningless to me was hard to get motivated for outside of the external motivation of passing.
Now, being older and pretending to be wiser, I think I have stumbled across a way to make at least algebra more engaging for someone and teach them another set of useful skills. Teach solving equations through bookkeeping problems.
We will circle back to starting accounting/bookkeeping. Everything I have come across seems to start at discussing double-entry bookkeeping and the “Accounting Equation”: Assets = Liabilities + Equity. There are variations but essentially that. Which, then somehow someone who has not been in a math class for a while is supposed to just put together and see how this equation leads to double-entry accounting and just sort of ‘get it.’
In my attempting to teach adults some basic bookkeeping for their jobs, they do not just ‘get it’ surprisingly enough. I always have to preface this piece of teaching with reminding the students that they are normal human beings and accountants are actually beings from some other universe which is why the section of our book is so poorly written, makes no sense and they assume that the above equation is just known intuitively.
I have learned to actually enjoy solving bookkeeping/accounting problems and am currently doing it as a side-gig hoping to convert it to my full time work. So, perhaps I am evolving.
In my evolution, I was just contemplating the accounting equation as an idea and mathematics in general. I realized that the accounting equation is actually the exact same as an algebraic equation convert the words in the accounting equation to letters: A = L + E and well, you get a nice beverage but also, these letters can be switched out for any other ones: x = y + z. Which, in itself shows how much of a genius I am, that it took several years to figure that out.
This idea though, I found interesting because now, I can plug in partial numbers, as we usually have in algebra and bookkeeping and suddenly the reasoning for double-entry accounting makes sense and does work. How is it that if I put in money, something else has to change? It does not make intuitive sense, if I get money in my bank account, it is not as if something else in my life increases as well in any real sense. But, in this equation, as in algebra, if something happens on one side of the equal sign the same thing has to happen on the other side. One can also take a dig at taxes in this way in that taxes end up simply taking money out of this equation without necessarily increasing anything on either side.
Anyway, back to algebra. When it is taught in the first place, I was just told that it will be useful to know, to be able to solve the equations and that what you do to one side you must do to the other. In general it seemed to be pointless though. Had my math teachers brought up how this is the same reasoning used for bookkeeping and tracking money, perhaps it would have interested me more and been more immediately understandable as to the why I should be learning these algorithms, having an actual utility to it may have ended up helping more more than solve the equations in questions 1-37 each having a-f equations within the questions.
Fleeting Thoughts of a Bad Student 