My kids are now college age, but when they were in K-12, I looked up common core, since the standards are published in several states. Honestly it looked quite a lot like the math that I learned in school, give or take. I took exactly the same school math subjects.
The one noticeable difference was that my kids did virtually no proofs. When I was in school, my district used a "new math" curriculum that introduced sets in first grade, and included derivations and proofs. (I'd call a derivation a lightweight proof). High school geometry was almost 100% proofs, and it was a class that a lot of students remembered as their favorite.
My kids: No proofs. They solved lots of problems where they were expected to inspect a problem, choose an algorithm, then crunch through it to an answer.
Proofs were what made math come alive for me. I could crunch numbers in science class, or on a computer, as I learned programming in 11th grade. I ended up majoring in math, and then added a physics major as well.
Math is an extremely confusing and fraught topic for parents, because we all viscerally know it's important for some reason, but nobody can really put their finger on why. Some parents treat it as a form of obedience training, or expect that it will magically confer special thinking skills. We know math is a sorting hat for getting into vaunted STEM programs in college.
Very few people use their school math after they finish school. In school, it's treated as a tournament, to reach "levels" and get good "scores." Many of the brightest kids are repelled by this. I would have been.
The college math topics are the same as they've been for 50 years. A number of years ago, in between jobs, I taught an introductory math course at a Big Ten university, and the students didn't touch a computer for the entire course. My office didn't have a network connection.
If it were up to me, I'd add a lot more computation and data work to K-12 math. And I'd bring back proofs. I envision a balance of four quadrants, not in any particular sequence, but perhaps in a cycle:
1. Arithmetic, which is symbol manipulation up through calculus
2. Computation, which is using computers to solve problems
3. Working with data
4. "Theory" which I associate with proofs and abstract topics
My advice as a parent is, first, be prepared for them to follow their own interests. This might include not being interested in math. Be prepared to help them deal with the competition, and to not let it cause them to lose interest. Next, treat it as something interesting and fun at home, separate from grinding through problems.
I’d just add to this excellent comment that, when I was in school a few decades ago, we also did essentially no proofs. Geometry was presented as rote memorization (as was pre-calc). I was utterly unprepared for college physics and differential equations (the mathy freshman CS courses) as a result - I struggled to figure out how to build on equations to find new solutions, and struggled with understanding the logical rules of things like Scheme.
I wish we had had a more proof-based math education in high school. But I’m also unconvinced that the quality of math teachers in this country is up to that task (though maybe I just had a string of really mediocre ones, punctuated with a couple exceptions).
The one noticeable difference was that my kids did virtually no proofs. When I was in school, my district used a "new math" curriculum that introduced sets in first grade, and included derivations and proofs. (I'd call a derivation a lightweight proof). High school geometry was almost 100% proofs, and it was a class that a lot of students remembered as their favorite.
My kids: No proofs. They solved lots of problems where they were expected to inspect a problem, choose an algorithm, then crunch through it to an answer.
Proofs were what made math come alive for me. I could crunch numbers in science class, or on a computer, as I learned programming in 11th grade. I ended up majoring in math, and then added a physics major as well.
Math is an extremely confusing and fraught topic for parents, because we all viscerally know it's important for some reason, but nobody can really put their finger on why. Some parents treat it as a form of obedience training, or expect that it will magically confer special thinking skills. We know math is a sorting hat for getting into vaunted STEM programs in college.
Very few people use their school math after they finish school. In school, it's treated as a tournament, to reach "levels" and get good "scores." Many of the brightest kids are repelled by this. I would have been.
The college math topics are the same as they've been for 50 years. A number of years ago, in between jobs, I taught an introductory math course at a Big Ten university, and the students didn't touch a computer for the entire course. My office didn't have a network connection.
If it were up to me, I'd add a lot more computation and data work to K-12 math. And I'd bring back proofs. I envision a balance of four quadrants, not in any particular sequence, but perhaps in a cycle:
1. Arithmetic, which is symbol manipulation up through calculus
2. Computation, which is using computers to solve problems
3. Working with data
4. "Theory" which I associate with proofs and abstract topics
My advice as a parent is, first, be prepared for them to follow their own interests. This might include not being interested in math. Be prepared to help them deal with the competition, and to not let it cause them to lose interest. Next, treat it as something interesting and fun at home, separate from grinding through problems.