Rant coming up...
I see a lot of posts and videos about kids learning "new math". Parents are complaining about it. Many times, they show their kids doing the "new math", and it doesn't make sense to them because their child is doing it wrong. The other times, the parents who are saying it's so confusing are the same ones who say they're bad at math, and math is hard.
The "new math" is really teaching the same concepts, while making sure the students aren't just able to follow steps to solve the problem, but instead are developing a conceptual understanding of what's happening. We're teaching them how numbers work.
Example: 30 + 35 = ____
The old way: 5 + 0 = 5, 3 + 3 = 6, so 30 + 35 = 65. The problem with that is that it doesn't teach students that you're not really adding 3 + 3. Those threes are worth 30 because they are in the tens place and represent three 10s.
The "new" way: Understanding that 35 is really 30 + 5 (that's called decomposing numbers, which causes people to struggle with math if they don't fully understand it). Therefore we are adding our tens together first, so 30 + 30 = 60. Then we have 5 ones, so 60 + 5 = 65.
The new way provides a much deeper understanding of how numbers work. The old way is a process to get the correct answer, without having a deep understanding of how numbers work.
The goal is not just to produce the correct answer. The goal is to develop a deep understanding of algebra and numbers & operations. Having the deep understanding leads to higher level thinking, which in turn helps students when they enter the workforce.
Just because the parent doesn't understand it, doesn't make it wrong. We aren't trying to make it so the "parents can't teach their kids math" (literally a comment I saw accusing teachers). We're trying to make it so we don't have generations of people who think math is hard and can't do mental math... which is where we are at right now. I know I would be so much better at math had I been taught the ways I'm currently teaching. I was never good at math, because I didn't understand what was happening. I was just taught how to put numbers into an equation or process to produce a correct answer.