About text books: we should get rid of them.

I’ve got plans on creating a website that will have lots and lots of problems. My hope is that over a couple years I’ll have a large resource that I can just give away. Of all the things schools spend money on, cheesy word problems and ridiculously irrevelant color images is not one of them.

Besides, as you say, we only use them as problem banks. Very heavy problem banks.

Actually I don’t even use them for that. I just use the supplements and photocopy a worksheet for homework and then create problems for in class work.

(1) Skills and Drills. You want to make sure certain skills, procedural stuff, is covered and mastered. Ideally this should be done on a computer with software that automatically differentiates and provides instant feedback. ALEKS is a good example of this, though it would be nice if it were free and designed to run on clunkier machines.

(2) A warehouse of topics and ideas. Not necessarily lesson plans, but ideas, problems, examples and techniques. I’ll give you an example: ever taught linear programming? Its cute in the usual way its offered. Two dimensions which tie in the solving systems of equalities and inequalites. However, its still very limited. I’ve recently learnt that Excel has a tool called Solver that will allow you to do much more realistic linear programming problems. Who knew?

There’s also a part 3. I think the problem of part 2 is bound up in the fact that we teach mathematics in isolation. I have an extremely broad knowledge of mathematics. I have taught everything from prealgebra to calc 2 and have taken such courses as Measure Theory and Homological Algebra. However, its ridiculous for us to expect math teachers to also have a broad knowledge all of science, economics, construction etc.

Instead we need to integrate math and science together. Science is just overflowing with useful mathematics. Such an integration (not two classes in one, but two classes coordinate) would allow a double helping of math and science and then you’ve got the modeling aspect and the critical reasoning skills that come from discussing data, errors, modeling, etc.

I’ve been frustrated by the fact that half of my students might have taken physics, or maybe most are in biology but some aren’t, etc.

I think its a good idea and practical. I don’t think it takes any money, just time. Done over four years (freshmen, then sophomores, etc) you could create a curriculum map and then execute it jointly. Teachers could take turns developing the content (worksheets etc).

my two cents.

We’ll have to have a voice chat if we can pull this within a couple zip codes. One step in that direction: would well designed S5 presentations with embedded video potentially be a sufficient wrapper for these resources?

Then I realised the maths teacher inside me had made a fundamental mistake. I hadn’t taken a picture of the 3 cubic metres of top soil after it was dumped by the truck!

We only *think* we have to teach curiosity because student brains have been so dulled by procedures that they merely memorize without stimulating existing neural pathways.

Touché.