Hi, thanks for commenting.

Mental math definitely has its place. So does algebra. I’ve always bought the argument that full understanding of algebraic procedures comes later because that’s exactly what happened with me in my own classes. I’m one that made it through though, and I don’t think it’s great policy to assume that what worked for me will work for everyone. Moving from abstract to concrete is the more traditional route – teach a concept, practice, and then apply it in a word problem. I think we need to be thinking in the other direction and NOT insist on an algebraic approach as the only ‘real’ way to explore a subject.

The graphing calculator is fascinating. Wireless technology was not built in to them from the beginning, so getting them to network (for good use) in the classroom has always required an external device to handle that communication. With tons of wireless devices now available and capable of so much more than a bulky plastic box with monochrome LCD screen, graphing calculators just look like dinosaurs.