I've seen a lot of complaining on the internet by parents about the new way addition and multiplication is taught in American schools. I looked at it, and have to admit, at first, I thought it was insanely overcomplicated and worse than the way I was taught where you did one digit at a time and worked right to left. Then I started to realize that the way they were doing it was actually what I do in my head all day every day and I think anyone in a mathematical job would agree. If you haven't heard of it yet, addition is done like this: 37542 + 34726 used to be done by adding the 6 and the 2, then moving to the left and repeating with the carry if there is one. In algorithm terms: recursion. The new way is to do it via recursion too, but starting on the other side and using rounded values instead. 37K + 34K, then 500+700, then 42+26. (In school they'd actually teach 30K+30K then 7K + 4K, but we're not children so we can handle two digits at once.) The obvious advantage is that you have a reasonably precise estimate after only the first step. Multiplication looks really weird. 432 * 286. They're taught to built a table with the modulus' of the placeholder's position in the table across one axis, then the same across the other. Code (Text): ____|_400_|_30_|_2_ 200_|_____|____|___ _80_|_____|____|___ __6_|_____|____|___ Then they fill in all of the boxes and add them up. I have to admit, it looked really weird to me, but then I just decided to do the big calculation in my head and see how I got there. I realized that I do the same splitting up into boxes in my head, but I do it to scale, where I envision my 400 much larger than the 30. So I quickly understood that this is using geometry to solve the equation by breaking the multiplication of arbitrary numbers into adding areas of nice round numbers. Do you think there is a specific advantage to teaching children to think this way? I developed my way of doing arithmetic this way over years of working with hexidecimal numbers. Do you think this will be a passing fad or a paradigm shift for how children are taught math.