http://www.youtube.com/watch?v=a81YvrV7Vv8 and another version of the same song:
I studied the New Math. It meant I did Boolean algebra in 4th grade (age 8 and 9). I loved it. It also helped me a great deal when I did my doctorate and when I used engineering skills at work. I get tired of hearing people bad-mouthing New Math because I believe it helped give me a basis for understanding all sorts of computerized lab equipment and also wave and tide recorders used in the field to predict tsunamis.
We did not memorize the (base ten) times tables, however we could multiply and divide in bases 2, 8, 10, and, 16. We could readily set up and solve problems. And, we could do all these things without a calculator and even without a slide rule. I do feel memorizing the times tables for base ten would have been useful and therefore, taught them to myself so I could do freshman chemistry problems quickly. That helped with rapid responses in physics, too. But, engineering courses and logic were much easier having had the bases and the Boolean algebra background in grade school.
So, based on my own experience, I suggest adding times tables and also radians to the, "New Math," but, I would not trade my, "New Math," experience. I loved it and found it very helpful toward my science career and to every day life in a computerized world. I understand the 1's and 0's so prevalent today.
I have come across a way of teaching math that I like that uses languages. More on that another day.
(c) 2008 J S Shipman