I never really understood the whole freak out about common core. I have a kid in 8th and a kid in 3rd, and for the most part I’ve found the methodology much easier to grasp than the rote memorization I grew up with. As a not-naturally-mathematically-inclined person, I found understanding the concepts that address *why* equations work the way they do to be very helpful. I don’t do abstract very well when it comes to math.
I'm glad that some students and parents have good experiences with the Common Core approach. I wish I could say the same. I have four kids who survived the transition and all of them now hate math.
My youngest is near the top of his class in precalc, and wants to skip AP calculus and take AP statistics instead. His reasoning is simply that precalc is constantly frustrating. I observe his frustration is mostly coming from automated computer-based exercises that are required but not adequately scaffolded by the teacher.
I understand that Common Core was "well thought out" in terms of math concepts and progression into deeper areas of math. The implementation was and continues to be awful, and it is turning kids away from math. Statistics and computer science are picking up kids wherever they can count as math alternatives.
I took HS calculus my junior year, then 3rd semester calculus at the local community college the fall of my senior year. To keep doing math, I took statistics at the CC in the spring. Which is the last time I formally studied statistics. And then in several physics classes, one lab section would have a little bit on error propagation and the like. But what I didn't realize until much later is that statistics is great for dealing with statistical error, but quite often in a physics lab, statistical error isn't really the main source of uncertainty. Are you really better off measuring a voltage several times to get a standard deviation to use as an error bar? (And in a modern digital voltmeter, there's probably statistical averaging built in.) Or should you think about calibration, voltage drop across the leads, and other systematic errors?
Where I do wish I knew more statistics would be to be able to read papers written by economists. Although we joke (https://xkcd.com/793/) about physicists trying to model everything, it seems that economists have a outsized influence on influence on any sort of policy, and although the math and statistics they use isn't somehow too hard for a physicist to follow, it's also a way of working with data I'm not really fluent in.
I actually wrote an article that explains your confusion. You, being a bright guy, liked the focus on abstraction in Common Core. That's because they shoved the abstraction of algebra down five or six years, their (poor) logic being that the reason elementary school kids did great in naep math but high school ones did poorly is that elementary math was too algorithmic. The kids couldn't absorb the shift that quickly. So they pushed the abstraction earlier. (they also did a lot of other stupid stuff, and your colleague got paid a lot of money to copy someone else's ideas and do a lot of damage, but whatever).
You, being a smart guy good at math, liked the focus on abstraction. So do other bright kids. The NAEP results show the top kids doing better. But everyone else did worse. Quite possible that focusing on abstraction instead of algorithms meant that the weaker kids didn't learn either.
You are correct, by the way, that focusing on stats would require rejiggering math but they won't do that. They aren't looking to improve math instruction at this point. Just get more transcripts that are facially acceptable for college.
I think that rote memorisation and blind algorithmic calculations are underrated. There's no way to do multiplication without memorizing the times tables. And for higher math I find it's better to learn the algorithm first and worry about why later. When you calc the derivative of bx^a are you thinking a*bx^(a-1) or lim(h->0){ b(x+h)^a}? I damn near failed linear algebra because I tried and failed to wrap my head around just what a determinant IS instead of simply learning how to calculate it and moving on with my life.
Also math teachers could save their colleagues a lot of grief if when they taught subtraction they said what is x in 2 + x = 4 instead of what is ?? in 2+??=4.
Speaking of equity, my wife teaches at an "underprivileged" elementary school. There is a widespread lack of basic math skills like adding one digit numbers without counting, even stuff like recognizing a number rolled from the pips on a die without counting. This is a much bigger issue than what they will (maybe) take in 12th grade.
I never really understood the whole freak out about common core. I have a kid in 8th and a kid in 3rd, and for the most part I’ve found the methodology much easier to grasp than the rote memorization I grew up with. As a not-naturally-mathematically-inclined person, I found understanding the concepts that address *why* equations work the way they do to be very helpful. I don’t do abstract very well when it comes to math.
I'm glad that some students and parents have good experiences with the Common Core approach. I wish I could say the same. I have four kids who survived the transition and all of them now hate math.
My youngest is near the top of his class in precalc, and wants to skip AP calculus and take AP statistics instead. His reasoning is simply that precalc is constantly frustrating. I observe his frustration is mostly coming from automated computer-based exercises that are required but not adequately scaffolded by the teacher.
I understand that Common Core was "well thought out" in terms of math concepts and progression into deeper areas of math. The implementation was and continues to be awful, and it is turning kids away from math. Statistics and computer science are picking up kids wherever they can count as math alternatives.
I took HS calculus my junior year, then 3rd semester calculus at the local community college the fall of my senior year. To keep doing math, I took statistics at the CC in the spring. Which is the last time I formally studied statistics. And then in several physics classes, one lab section would have a little bit on error propagation and the like. But what I didn't realize until much later is that statistics is great for dealing with statistical error, but quite often in a physics lab, statistical error isn't really the main source of uncertainty. Are you really better off measuring a voltage several times to get a standard deviation to use as an error bar? (And in a modern digital voltmeter, there's probably statistical averaging built in.) Or should you think about calibration, voltage drop across the leads, and other systematic errors?
Where I do wish I knew more statistics would be to be able to read papers written by economists. Although we joke (https://xkcd.com/793/) about physicists trying to model everything, it seems that economists have a outsized influence on influence on any sort of policy, and although the math and statistics they use isn't somehow too hard for a physicist to follow, it's also a way of working with data I'm not really fluent in.
I actually wrote an article that explains your confusion. You, being a bright guy, liked the focus on abstraction in Common Core. That's because they shoved the abstraction of algebra down five or six years, their (poor) logic being that the reason elementary school kids did great in naep math but high school ones did poorly is that elementary math was too algorithmic. The kids couldn't absorb the shift that quickly. So they pushed the abstraction earlier. (they also did a lot of other stupid stuff, and your colleague got paid a lot of money to copy someone else's ideas and do a lot of damage, but whatever).
You, being a smart guy good at math, liked the focus on abstraction. So do other bright kids. The NAEP results show the top kids doing better. But everyone else did worse. Quite possible that focusing on abstraction instead of algorithms meant that the weaker kids didn't learn either.
https://educationrealist.wordpress.com/2020/10/05/bush-obama-ed-reform-core-damage/
You are correct, by the way, that focusing on stats would require rejiggering math but they won't do that. They aren't looking to improve math instruction at this point. Just get more transcripts that are facially acceptable for college.
I think that rote memorisation and blind algorithmic calculations are underrated. There's no way to do multiplication without memorizing the times tables. And for higher math I find it's better to learn the algorithm first and worry about why later. When you calc the derivative of bx^a are you thinking a*bx^(a-1) or lim(h->0){ b(x+h)^a}? I damn near failed linear algebra because I tried and failed to wrap my head around just what a determinant IS instead of simply learning how to calculate it and moving on with my life.
Also math teachers could save their colleagues a lot of grief if when they taught subtraction they said what is x in 2 + x = 4 instead of what is ?? in 2+??=4.
Not sure why it needs to be either/or.
Speaking of equity, my wife teaches at an "underprivileged" elementary school. There is a widespread lack of basic math skills like adding one digit numbers without counting, even stuff like recognizing a number rolled from the pips on a die without counting. This is a much bigger issue than what they will (maybe) take in 12th grade.