This thread reminded me of a theory I have about people who excel at high school math, versus those who do not. In my experience, many of those who do well at algebra do not do well at geometry, and many of those who do well at geometry do not do well at algebra.
I am curious if this observtion holds up in a larger sample, and if it correlates with other talents. Please post your experience with algebra and geometry, and include your ultimate career discpline, such as technical/engineering, creative/artistic, busiiness/finance, healthcare, law/politics, service, construction/manufacturing, etc.
I don’t think your theory will bear out here. The problems which beset effective instruction in one area of the field will beset the other, assuming one stays in the same school/school system.
Also, you need to distinguish between “hating” math and “being good at” math. Math was my best subject (both geometry and algebra equally), but it wasn’t that interesting to me. I ended up in language education.
I found geometry to be incredibly easy and actually kind of enjoyed it. It was the only math class I ever aced.
OTOH I found algebra to be tedious and boring so I didn’t try very hard and got only average grades, but the math itself wasn’t that much more difficult than geometry. I could have gotten an A if I cared about it at all.
I didn’t have much of a problem with either one despite never cracking a book in high school. The last semester of math was called ‘Analysis’ (or something like that) and I passed it by the skin on my teeth. College calculus was quite difficult for me since I had not really learned to study but I managed to get by. I are now a computer scientist.
Algebra I sort of enjoyed. Geometry, I found difficult. We had integrated math so all three years were a mix of algebra, geometry and trigonometry.
Calculus, which I took in High school, was taught with more algebraic focus and I enjoyed it too. I also took Calculus in college, and it was taught with a geometric focus and if I hadn’t already done 70% of the work in high school, I would have failed. (not the teacher’s fault. he was fine and there were only 20 people in my class).
Left school after 8th grade, and we never really got to “geometry” (which seems to be a couple different types of classes judging by the experiences of folks I’ve spoken with; one a proof-heavy/Euclid-heavy thing, the other a typical “memorize these formulae for length, area, volume” for polygons and solids, maybe with some trig and analytic geometry). I did okay, but started to not care about school as algebra was in full swing, and I started to do poorly there. I do recall having difficulty learning my multiplication tables as an elementary school student, FWIW.
…now, looking for a grad school math program after getting a university degree (and top senior honors) in pure mathematics. Funny how a bit of aging and access to good teachers can change your relationship with math.
I do think it’s funny that I have most of the hallmarks listed in that thread of “dyscalculia.” Supposedly, I should be poor in my chosen field.
Mediocre algebra skills and horrible at geometry in high school - wasn’t motivated to put to work in and had a self-perception that I wasn’t very good at it.
Fast-forward to today, wherein I’m majoring in physics, have gotten A’s in almost every math course I’ve taken*, love mathematics, and have successfully tutored the stuff I used to hate.
The key, for me, was becoming motivated enough to put the work in. A large part of that motivation was realizing how darned interesting and important math is, how it underpins the entire universe, and how the whole of mathematics fits together into an elegant language of the cosmos. Said realization did not happen until I started taking Calculus, which is why I think that kids should be exposed to high-level math a lot earlier then they are.
*Full disclosure: the first Calculus class I ever took I flunked, hard, but that’s a whole 'nother can 'o worms
It took me a short time to really understand algebra and then it was easy. I understood geometry immediately. It was so obvious that I understood all of it (at least what was going to be covered in the class) that the teacher allowed me to treat the class as a study hall. I didn’t have to complete the homework or participate in class; I just took the tests and got all A’s. Trigonometry was similarly easy. Calculus was the first time I was challenged.
I was not good at basic math, failed Algebra completely and never took geometry so I chose the last option.
I had no problem with other subjects but something about numbers always throws me off. My oldest was formally diagnosed with dyscalculia and I have a strong suspicion I have it too.
Good at both. I even came third in the school math contest one year.
Analytical geometry was fun, like figuring out things with Legos. Geometry was pictures, and, hence, often plain to see. I’ve never had this division between “art” and “math”, between “creative” and “technical”; to me they’ve always been part of the same thing.
My father was a high school math teacher when I was growing up (although he changed careers before I was in high school). So I think what came natural for me was partly learned through osmosis of hearing my dad and brothers talk constantly about it at the dinner table.
Oh yea, I was also one of those sick kids who loved word problems.
However, I dropped out of Calculus my senior year because I didn’t need it for my major (English) and wanted to have a free period after gym so I could go back to my dorm room to shower.
Why are you stopping at geometry? I went all the way through calculus in high school.
Anyway, I was good at both, if by algebra you mean Algebra II. I was so-so in Algebra I, but something in my head clicked when I started geometry, and I got straight As in that, Algebra II, trig, and elementary functions, and a succession of Bs in calculus.
I hated high school and barely applied myself. It wasn’t till college that I began to study math seriously, after a lot of remedial work. If I’d applied myself in HS I probably would have been good at both.