Posted on by Aaron

Restarting Math

I’ve been working on getting back up to speed on math for the last few months.  Okay, in truth, I started this more like a few years ago, but if we’re talking serious concentration, it wasn’t until the last few weeks.  You know what?  None of that matters.  What matters is that I’ve been giving it another honest go, and this time things have been working.  Though not perfectly.

Wanting to get a college-level understanding of a few subjects has lead me to believe I need to do the same with some math. This is definitely true if I decide to go for that paper, but it would be pretty useful even if not. I’ve been staring down the barrel of a Stats class I’ve been meaning to master for a while, and that would absolutely be helpful in any direction I take my career. But in looking at that class and thinking about taking others, I have been feeling pretty behind. So I tried some problems that I found online to figure out where I am.  Sort of like giving myself a “placement test”, I suppose. It seemed reasonable to start pretty low, so I did, going through a bunch of simple arithmetic stuff.  That stuff was, thankfully, pretty easy, and I was honestly worried it wouldn’t be. I kept working up the scale of difficulty and continuing to be surprised by my success in each level. It was starting to make me cocky, frankly. I got particularly cocky when I found I could still do quite well in Algebra.  I managed most of the problems pretty well with little to no refreshers on the subject. But as I continued through the work, it started to highlight some holes in my knowledge.  Those holes grow as I continued and it reminded me that there are some lower level things I’ve never really been good at.  I thought about stepping it back again to refocus on those lower level topics, but decided to keep on moving forward. This has, so far, turned out to be the right choice. it turned out that the Algebra classes and practice problems already included a mix of those arithmetic problems I needed to work on. Better yet, the more abstract ways that Algebra presents problems work better for my way of understanding things.  

Fractions are a good example.  I’ve never been great at them, which is tough because they are absolutely foundational. You can do higher math without them.  I remember doing OK with fractions in grade school, but when we moved past them and they showed back up a just part of bigger problems, I struggled. Something about how those classes on fractions were taught and tested didn’t really get me up to speed and basically allowed me to bullshit through the answers. I would later find that other classmates experienced something similar, though for different reasons. They had all memorized things, important and useful things. But I’m not a memorizer.  This is a big drawback for early math learning, and many of my classmates sailed through early math because they could memorize to the point they sounded like old pros. But memorization has never been my strong suite. I do better when I understand something on a more fundamental level, really getting all up in its conceptual guts. What I now know better as “intuition” – a term it seems I’ve long misunderstood. Anyway, I really started to lag when I not only didn’t have the memorization skills to just fudge my way through nor to build intuition off of. It’s really hard to build your math skills when you lack the memorized foundation of basics like times tables, formulas, and identity rules.

I’ve been working on writing this post for weeks and keep getting lost in it.  A big part of that was trying to list out my various Math pitfalls.  I have many, and the more I think about it, the more I think I should take each of those on in their own posts.  I think maybe the next time I talk about Math, I’ll talk more about my problems with fractions.  Today is more of a statement of where I’m at.

I am in Trig, I think.  Let’s back up.

So when I settled in on Algebra, I picked a couple of online learning platforms to try and catch up.  The main ones are saylor.org and mondernstates.com.  I had looked at the lectures and coursework from big colleges, much of which is free (like MIT’s Open Coursework [https://ocw.mit.edu] – Algebra I [https://ocw.mit.edu/courses/18-701-algebra-i-fall-2010/]), but I was looking for something a little more interactive and structured.  Given that, the logical next step would be to go to a learning system like Brilliant.org.  I’ve used Brilliant before and liked it, so that seems fair.  A few years ago, I got a deep discount from my job for an annual subscription, but I was busy with work and didn’t have much time for it.  Then it lapsed and they didn’t offer the discount the next year.  The little I did do I liked, but it was never an immediate “click” for me. Still, I could see myself going back in the future if I have another pitfall. But what I’m using now is really working for me, so we’ll continue with that until further notice.

I made it through all of the Modern States – College Algebra course and most of the Saylor stuff.  I also picked up some books on the subject:

They are all helpful, though the first two have mostly been as additional practice problems.  Anyone who has gone through a few books of the “for Dummies” variety will likely agree they are pretty hit or miss.  This edition is from 2005 and some of the phrasing really shows it, but I’ve found it helpful.  As it is, it’s a great backup to reference in case the structure and wording from my other sources just aren’t doing it.  

That last one, though, is an actual textbook, and it is fantastic.  I know this is something teachers and dedicated academics already know, but textbooks are sort of amazing when it comes to documenting and transferring knowledge.  There was a subject near the end of the Modern States course that I was just confounded by.  I can’t remember what it was exactly, something in the logarithms and factorials zone. I just couldn’t get there, and I was starting to think that this whole experiment was coming to an end. Just too stupid to move forward.  I watched the Modern States lecture, read some of the materials from there and Saylor, and even watched some of my favorite youtube teachers.  I just wasn’t getting it.  But I wasn’t about to give up just yet and figured it was time to fall back onto what has worked best for me thus far – trying and failing.

So I cracked open that textbook and flipped to the section that went over the offending subject.  I decided to go for a practice problem right away.  I tried two.  I bombed both.  That feeling of failure was creeping back in, but I was still determined.  I went to the front of the chapter and read through it.  I still didn’t get it.  But I came across a couple of problems with the work shown and explanations of the work with it.  That completely cracked it for me. Bam! Just like Emril and a fistful of cayenne, it suddenly made sense.

I had a few more stumbling blocks, but between all of those materials and some youtube teachers, I got through the rest of the course.  There is just the final exam, which I haven’t taken yet. I think I’ve still got a little polishing left on a few subjects, and I also found that I better understand each level work if I can start putting it together with the next level up.  For that, I figured it was time to make the jump to Calculus.  I decided to go with the course from Modern States again, which started out pretty well.  And then I failed the shit out of the first two tests.  Between the two, there were something like 8-10 questions.  I got one right.  Yikes.

But this isn’t a give up point either.  Instead, I recognized that many of the questions included information that I am just not familiar enough with.  Stuff I vaguely remember from years ago, but not enough to actually use. Reflecting on my past, I can’t exactly remember what classes I took in high school. I remember doing calculus and doing pretty poorly in it.  What I don’t have any memory of is a full pre-calc or trigonometry class.  In fact, I’m now pretty sure that I skipped those, which if true is fucking batshit. That leap to Calculus is massive, and it is crazy that some people can just make that leap. Absolutely nannercakes.

The thought brings me back around to that missing set, the memorization and intuition that I had to rebuild for Algebra. What this informs me now is just how dependent each new piece of math is dependent on the previous sets.  What I do remember of Calculus, it seems like everything up to this point is basically just learning the language and syntax, and it isn’t until Calc that you really apply it. And I’m definitely missing something between the end of Algebra I and Calc I.

So I decided to fall back again, but this time on a different familiar platform – Udemy.  I have, in truth, some mixed feelings about this platform.  I’m not going to get into them now, but maybe we add that topic to the ever growing list “for another day”.  What I will say is that they regularly have sales and discounts (which sure seem shady) that bring expensive courses down to reasonable prices.  Most of these courses are basically overblown youtube playlists, but some of the presenters really go above and beyond.  A great example of that kind of presenter is Krista King [https://www.udemy.com/course/calculus-2/?couponCode=ST21MT30625G1#instructor-1].  I really like the way she presents things.  Her courses are set up to follow the standard academic categories, which is pretty common.  What’s different is her style, which I’m afraid I don’t have a good description for. It’s like a teacher that doesn’t feel condescending.

Within the courses, she breaks topics down with a video, some reading, and a quiz.  She also provides a great handout with some of the stuff you should get familiar with.  The combination really helps to build up both confidence and intuition, so I’m pretty into that.

Okay, this post is going longer than I’d meant it to and I’ve got some CS50 coursework I need to finish.  But before I go, here are a few of the free youtube teachers that I’ve also really liked:

These are each great. Their styles are all a little different from each other, but they all share a sort of “here’s the thing, just give it a go and you’ll get it”, which is an attitude I can really appreciate.

Alright, Imma fuck off for today. Peace.