There has been some talk here recently about the fact that most mathematics textbooks are trying to serve as both reference texts and instructional materials and that, inevitably, being the first almost guarantees that nothing of quality can happen in the second. In other words, if you are telling a student what/how to think (by offering a reference to someone else's mathematics) you can never have quality instruction (which, to me, would mean having students create their own mathematics). 

I would argue pretty intensely for taking any reference material out of students' hands (I mean, did you you miss the fact that the site was titled DOING mathematics?!?). I wonder, however, if there is space for helping teachers learn to use textbooks that already exist as a launching point for creating their own quality instructional materials? This, I hope, is the beginning of a post "series" about infusing "doing" into existing curriculum.

"Ok class, turn to page 900 (because there are way too many pages of reference and practice problems) and find the section on "Exponential Growth:"

This is the classic example of textbook as reference. It does everything short of telling you what a, b, y, and x represent (which came on the very next page). There is no opportunity for students to engage in creating mathematics here. But what if we change things just a bit. Have students watch this (live) and ask them this (or a variety of other questions...or have them ask one themselves):

I like this population clock because it doesn't give them any other information (births, deaths, etc) which allows us to generate that on our own. I also think there are more intriguing questions but I like this one because it allows them to make an initial estimate/calculation and then, ultimately, test the accuracy of THEIR model at the end of the unit/investigation (as opposed to asking "when will it hit 8 billion," which we won't see in our school year).

The point here is that NONE of the reference material is present...at all! Students don't need a definition for exponential growth until they want one to verbalize what they are noticing about how population grows. They don't need variables and models until they introduce/create them themselves to describe the patters they see in that growth. They need to create this for themselves, not learn how someone else does it. The beauty here is that students will create their own models and we can discuss the benefits and pitfalls of each.

This simple redesign, or infusion, is a simple recreation of what already existed in a reference text. We can teach/trust teachers to create this experience for their classes without putting the reference text in the hands of every student (or trying to create a curriculum that is widely distributable). Of course, even with the "infusion" a lot of harm can still be done in how we help guide students in creating their own model...but that is a topic for a later post.