I'm sorry, but the fellow businessmen I know - employers all - echo my gripe....the new, "improved" standards are producing kids/entry-level employees less capable of basic math than those taught 20 years ago the old, "inferior" way. When addition/subtraction were first mastered, then multiplication/division, kids understood the relationships between the two. Now, kids don't master anything. I can't afford to hire people who can't multiply and divide - and I am not talking in the Biblical sense. I don't want idiots working for me...but that's all the schools are putting out.
They feel good about themselves, though.
If you think about it, under the traditional math, all the student would be mastering is elementary geometry because the time involved to teach math by going from addition, then subtraction, then multiplication, then division, then algebra then geometry, then calculus and trig would take more than 15-16 years to do. Furthermore, the relationships of addition to multiplication is not as evident if we completely separate them.
We now teach multiplication along with addition and here, we directly teach how multiplication is like addition, but a lot quicker to add a set of numbers together rather than stringing a bunch of facts together. Same with subtraction and division.
The traditional method assumes the teacher is teaching math by rote memory, by requiring students to memorize a bunch of facts and figures, not teaching that math is an abstract concept
where particular problems don't always coincide what people do in real life. Here is the key component. Traditional math requires rote memorization, where the newer math is an abstract reasoning of math, where the focus is not how the problem is solved, but the whys of how math is computed.
With the problem of 26+17=43, traditional math teaches the concrete answer of 43 and stops right there. The newer math teaches the process of how 43 is the answer by making it understood that 26 and 17, reorganized is made into a base 10 formula, and calculating it so the 26 becomes 30, and the 17 becomes 13, then adding 30 to 13, making 43. Here we teach kids multiplication process at the same time we are examining addition but doing it in an abstract form.
We use base 10 in how place value is determined and how most items are sold in multiples of 10, 12 and so forth. This streamlines a whole bunch of numbers that can easily be calculated without much trouble.
Years ago, math was first taught in first grade, but now Kindegarteners are learning what first and second graders learned years ago.
I have been doing this for the last 28 years, and I have seen traditional math to the new math and see the way it is taught. It takes practice getting out of rote memory, but I see the new math teaching kids math in ways that would have taken a lot longer to compute years ago, but now takes less than a minute to do.