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What would be the best order to learn math for someone who's completely new to it (esp. a young child)?
I dream to maybe become a college professor in math one day. Whether or not I do become one, though, I would be interested in what would be the best way to teach a child who is just starting from the ground up. I feel like our current way of being taught maths (as well as the order) is flawed here in the USA. Here is what I think. Let me know if you disagree or what you would change:
1.
Reading, writing
Numbers
2.
Logic and reasoning
Mainly sets, truth values, and arguments
3.
Addition, subtraction
Multiplication, division, fractions
Powers, roots
Factorials
Logarithms
4.
Plotting points on graph paper (2D) and a computer (3D)
5.
Basic algebra (just PEMDAS)
Word problems
6.
Geometry
Trigonometry
7.
Graphing different kinds of graph for discrete data
Graphing continuous functions (polynomials, then other ones)
8.
Probability
Statistics
9.
Precalculus
10.
Calculus I (differentiation and integration in 1 var)
11.
Linear algebra
Programming
12.
Calculus II (differentiation and integration in 2 vars, series, sequences, errors, etc.)
Calculus III (Same as the above, but in vector functions)
13. Differential equations
From here on, one could expand to whatever. Don't get me wrong. I want my children to have a childhood. If I realized I'm hurting them, then I'd probably stop. But I think it'd be fine as long as I allow them to have a social life. Moreover, I'm more interested in the idea of there possibly being a tree (or trees) of knowledge, starting from a very binary and Boolean set of rules to higher maths.
The numbers are, roughly, the "bundles" in which I'd teach. You're right. Perhaps algorithms would be at the end of algebra. What I mean by "graphing", I mean plotting coordinate points on a graph. I did that before algebra. Yes, precalc would include advanced algebra, since they're similar.
They're not idiots, in fact, because they know that if they scream, then they'll get what they want (an example of an if-then syllogism - valid logic, nonetheless). Now, if they scream and they get what they want, then it's because the parents let them because either they're the stupid ones, or they're too lazy.
I'm not so much concerned about the times or time intervals, but rather the chronological order. That's something I'd have to investigate further, as it'd require me to learn some psychology, as well as a recapitulation on how much material gets covered for each of those "bundles."
As for the linear algebra, perh
1 Answer
- 8 years agoFavorite Answer
I'm not sure what the numbers are supposed to indicate aside from order, but it seems like logarithms is too early, graphing is too far apart from algebra, you don't seem to have any algebra between basic and linear (but I'm assuming precalc is advanced algebra?), logic and reasoning is too early (kids are idiots, you need to keep that in mind - their logic is scream loud enough and you get what you want), and you haven't actually introduced any times at which these would be taught. And I wouldn't put linear algebra ahead of anything. I watch countless college students curse their very life because of linear algebra.
