Cophnia61's Math Log

Before I start with high-school algebra, I want to refresh my arithmetic knowledge in order to fill potential gaps.

Do you think “Pre-Algebra For Dummies” will do the job?

I’ve never seen that one, personally.

I got a lot of use out of Khan Academy when I was going through all of that when I started college. The lessons can be a bit slow paced, but they provide good ways to think about a problem. I didn’t dig their practice problems, though.
If I remember the other site that helped me a lot with math, I’ll post it.

I’d say the prereq’s for algebra are the following:

  • Arithmetic (addition, subtraction, multiplication, division)
  • Exponents and roots
  • The difference between a relation and a function
  • Order of operations (PEMDAS, or however they say it where you’re from)
  • Fractions
  • The different number sets (i.e. natural, integer, real); just getting a feel.
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Ok, I’ve got that book (Math and pre-algebra for dummies) and it explain those topics. The best part is that fortunately I remember almost everything, in the end I just needed a review just to be sure.

I was thinking about using Anki for review but I’m unsure of how to use it. Any suggestion with examples? What to put on front of the card?

I don’t know much about math myself but my father is a mathematician. However I think that maybe it could be useful to try to find a book series that aimed to teach the mathematics that we learn throughout school(including high school) at a more fundamental level. In my country we have a series of books that do just that, they’re still technically at pre-college level(as far as I’m aware), but they go very deep with all elements of pre-college math, much deeper than the textbooks that are used in school and high school. If one finishes those book series one is supposed to get a much deeper understanding of basic math, however take what I say with a grain of salt, as I’ve never finished such a series myself.

Maybe there is something like that available in English(I’m sure there is), my two cents are if I were to start a college course based on math, that I would like to study by such kind of books, just take caution that it isn’t too much for a first refresher, maybe it would be better to finish a more compact and straight-to-the-point course, in order to regain an “overall knowledge” of things, and then after that proceed to learn things more deeply.

By the way I think the idea of studying mathematics to be pretty interesting, maybe I will do something like that after I’m done with Japanese…

Tbh I just wanted to find something to learn beside Japanese those times of the day when I’m tired of Japanese.
For example if I watch 1 hour of youtube in Japanese, I’ll be tired of it for a while but still in the mood for learning other things, just not in Japanese xD
So, instead of doing nothing or watching memes, I’m studying math.
I always liked math and switching through two different topics towards the day helps me to not get bored of Japanese.
When I end math and start again Japanese, I’m more relaxed and enthusiastic about it.
Also, as lately I watch and read a lot of scientific stuff in Japanese, it increased my desire to understand more about the topic.
Thank you for the suggestion, I’ll try to find some textbooks aimed at teachers.

Can you guys tell me what’s the difference between high school and college in the USA?

What is the difference between an high school algebra textbook and a college algebra textbook?
It seems that the topics match.

Same topic, probably just how the explanations are done.

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I went to public school where I took pre-algebra in 8th or 9th grade and then later retook it in college because I tested so low on my math scores (lol). I’d agree that both high school and college pre-algebra present the same content, but the teaching methods differed. I don’t recall much difference between the textbooks either, if any.

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I’m still struggling with this. I mean, I don’t know how to formulate math knowledge in a way that would fit in an Anki note.

For example a way to sum fractions with different denominators is to find the LCM of denominators, then multiply each fraction for a number which will give you that LCM for the denominator.

I’m unsure of how should I put this info in Anki (or even in my notebook) in a way that is fast to review and effective.

I’ve always taken notes as questions + answers (Q: what is a protein? A: a protein is…) and I would read the question and test myself for the answer.
If the question is too complex I split it in more questions.

I wonder if for such a practical topic as math isn’t better to put directly an example on the question side, and then ask for the answer.

Example: 2/3 + 5/9

instead of: "how do you sum two fractions with different denominators?

What do you guys think?

I feel like if you just put a specific example and ask for the answer, you’re going to end up remembering that 2/3 + 5/9 is 11/9, rather than anything about the method.

(For that specific method, I would expect it to fairly quickly become second nature anyway in the course of doing problems, because it comes up so often.)

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I don’t think Anki is well suited to learning math as it’s more of a memorization tool than an understanding tool. It’s great for helping you remember facts (A is B), but not very good at helping you understand concepts.
I can’t really recommend any books for studying math, but “The Man Who Loved Only Numbers” is a great book about a mathematician named Paul Erdos, that includes some of his proofs that are simple enough to be understood by laymen (it’s aimed at a general audience), and is otherwise just a very interesting book.
You may also want to check out the youtubers vihart and 3blue1brown. The former is more recreational, the later more educational, but both very interesting.

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So, in other words I should focus more on understanding and do a lot of exercises?

What about taking notes? Once I understand a concept, I want to write it down for future review. What’s the best way to take such kind of notes?

What I did for notes back when I was doing A-Level maths was that during classes as we worked through the textbooks I would just take whatever notes seemed useful for my understanding, and work through the exercises and problems, and keep all those notes. Then a year later when exam time was approaching I went back through everything and wrote out much more condensed notes, containing only the key points and things that didn’t seem obvious. Those I then used for review and revision for the exams.

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When I was in school, each math lesson introduced new material with examples and commentary, followed by exercises. The exercises started with a warm-up section, which included questions from topics covered earlier course. Our textbooks were by Paul Foerster, but they all work like that, ね?

Math courses are cumulative, so you’ll end up reviewing previously-learned techniques, even if you skip the “review” questions. The same principle applies for learning foreign languages, although the “intake” process is a bit different. I think it’s easy to overuse SRS and thereby lower per-hour learning productivity for both subjects, to the extent that we should drastically lower the frequency and number of reviews, or eliminate it entirely. SRS makes a lot more sense for courses like history, where you may need to produce facts (like names and dates) that are harder to absorb then the larger historical themes and trends for a given time period.

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Oh, sorry about that, for some reason I thought that you were doing prep work for a college course that required knowledge of math.
I understand what you mean, I also get the feeling that languages aren’t quite like other subjects where you can study for a great many hours straight without breaks, as in that languages “wear out” your brain after a while, and require a break, at least that is what I also think. Your idea of learning math in the break time is quite interesting, and, as I said, is something that I might possibly do in the far future when I’m done with Japanese.

I’m not sure if the resources I mentioned earlier are meant for teachers really, more like to expand upon the knowledge of the fundamentals of high school math(not just algebra), or something among those lines, without going into Calculus and college stuff.

I went ahead and looked for the first volume of the series, this one teaches “sets” and “functions”(each book of the series is about one or a few topics, so the coverage is extensive).

Just as a reference for possibly finding an alternative in English or another language that you know(assuming that you don’t know Portuguese).

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I haven’t read all of the comments but I agree with this, I think math is more like to spend the time it needs to understand the concepts and then applying it by doing exercises, easiest to hardest-which means doing the old fashioned way.

If more training is needed, then just do more exercises, or exercises that are “challenges” etc.

EDIT: It would be helpful I think if the forum had the same feature that the koohii forums had, where your posts would “merge”(with a somewhat thick black line dividing them) if you posted more than one post within a set time interval.

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Thank you for the answers!

I understand what you guys mean, but my fear is that I forget things if I don’t review the core concepts.

Some times ago I reviewed all high school math but because I didn’t review now I’ve forgotten everything.

What kept me from reviewing was that I didn’t have notes so I needed to review directly from the textbook and it required too much time.

I just want to have something more “condensed” to go through from time to time. Even exercises are ok, as long as there is no redundancy or noise (unnecessary explanations).

But I’m not sure what to put in my notes (or anki, tbh I just wanted to use it as a note taking app because I’m so used to it, it’s free, there is synchronization, app for Android etc…)

EDIT:

luri, can I ask you where are you from? I’m from Italy and Italian is similar to Portuguese, and here in Italy I used to have a lot of friends who where L1 in Portuguese

I’m from Brazil, born and raised. :slightly_smiling_face:

I don’t know Italian, but I think it’s an interesting language, I like especially the fact that it is the only romance language(that I know of) that kept the Latin infinitive verb ending, also the phonetics is pleasing, probably the closest to how Latin might have sounded from my limited knowledge on the subject.

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Re: math in Anki.
I found it useful for trig and calculus (remembering indefinite integrals and derivatives). Didn’t use it for algebra.

If I had, I’d make cards for PEMDAS, what the root symbol is, and other definition-type info. Actual application requires practice problems, IMO. As others have said, though, math builds on itself. You won’t do any higher math without using algebra or arithmetic (or trig, or calculus, if you go further than that).

And yes, a lot of it requires understanding to really get it. The first time I thought about polar coordinates (and doing calculus with them) by thinking of a hdd, it all suddenly made sense to me.

I second the recommendation for 2blue1brown.
I also recommend Mathologer. He goes more into abstract mathematics vs keeping it more grounded like 2blue1brown, but his presentation is fun and he generally scripts the videos so that you only have to go as deep as you want. Recently did a video on lasering turtles to find the roots of a polynomial (and divide it by a root). I’m on a phone, but check YouTube for it.

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Are you aware of any math resources similar to those mentioned in this thread, but in Japanese? Blogs, YouTube channels etc…

NHK’d high school education lecture series (https://www.nhk.or.jp/kokokoza/) includes some maths programmes.

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