I don’t know what relates to philosophy and what doesn’t. I’ll just list what areas of math related to arithmetic and algebra I don’t have much experience with/I know I mess up a lot with.
I just kinda of looked at various sources to break down these subjects.
Arithmetic:
- From your philosophy outline from May 2022.
In the sub-tree numbers, I don’t have much experience working with number lines. In LMD’s tutoring category, he used a definition of addition based on number lines and successors and stuff. First time hearing of that. LMD Async Tutoring - #75 by LMD
I also remember having a pretty high error rate for percents and ratios for the problems in the textbook I was using(Art of Problem Solving - Pre-Algebra). Some of it could be attributed to how hard the problems are but I remember having some conceptual difficulties.
- From the Pre-Algebra textbook
I remember really sucking at word problems.
“Whenever a quantity changes by a certain amount in a fixed unit of time, we have a rate.” - ch 7.6
Rate problems I was pretty bad at. I think i struggled on all the basic problems and skipped the challenge problems for this section.
Huh, there’s a chapter on counting.
I never got to it because the basic geometry before it made me drop the textbook for a while. I also saw counting was a node on the arithmetic tree. I don’t know much on counting problems I guess.
Algebra;
In general i’d say I’m rusty at doing algebra.
In Cycle Between Learning Critical Fallibilism and Its Prerequisites you say
(Note: Algebra classes commonly teach quadratics, but that’s not a core part of algebra and shouldn’t be taught to most high school kids at all. Quadratics aren’t relevant for CF. More core parts of algebra, that are more relevant to CF, include understanding variables, equations, substitution, grouping and functions.)
So I’m just ignoring quadratics. I think I was pretty mediocre at them. Mostly just memorized stuff.
- From the philosophy outline
The whole functions sub-tree is stuff I’m vaguely aware of and pretty unfamiliar with. Graphing and coordinate plane are probably fine, but sequences and mapping I got no clue on. Sequences I remember vaguely and I did them in a memorized manner. Same with mapping.
- From AOPS Intro to Algebra textbook
I have not used this textbook. I’m just glancing over the table of contents as reference for stuff in algebra.
I’m unfamiliar with this proportion stuff:
I suck at optimization problems.
My understanding of complex numbers is pretty non-existent. My math knowledge of them is purely on the memorization level and even then not that much.
Hmm, looking at the functions chapter and the problems. I think I can do the problems pretty ok. Could I explain to you functions? Nope.
My knowledge of logarithms is all memorized moving stuff around.