The chapter starts with a discussion of NCTM curriculum standards, and how math is important in todays world. Then it goes on to talk about how the NCTM standards may (or may not) serve as a model for state standards depending on the decisions made by the state. Oddly, there was no mention of No Child Left Behind, which has had a pretty profound influence on standards in the last few years.
Then the book discusses the idea of "core curriculum" which is the idea that every student, regardless of ability, should be exposed to key topics like applied math, algebra, geometry, statistics, and discrete math. It talked about serving all students with this core via curriculum alternatives like "crossover model", "enrichment model", and "differentiated model".
The last part of the chapter was devoted to a discussion of traditional curriculum versus integrated sequences. The authors contention was that integrated math leads to better connections between concepts and encourages more students to advance higher in math, although there is little, if any, increase in things like SAT scores. At the end the chapter discusses why schools may be reluctant to use integrated approaches, although I think he failed to discuss the biggest reason, which is maintaining compatibility between schools.
Next week in my pre-algebra class I'm going to be teaching a chapter on geometry and measurement, including three dimensional figures. We have some manipulatives to let the students use with cones, pyramids, and other solids, and the students will be able to use these directly. I plan a demonstration to show how a cone has one third of the volume of a cylinder of the same height.
Also, I have to assume there are websites (technology) which can be used to illustrate areas and volumes of figures. Interestingly, when I went searching some of the websites the book mentions in appendix A, I found out that the Eisenhower National Clearinghouse website is no longer being funded by the federal government and has gone subscription only. This is a rather scary trend. Anyway, I found a nice lesson plan for building a box using nets at http://illuminations.nctm.org/LessonDetail.aspx?id=L570 - but this is more of a manipulative than a technology. I found a nice site at http://www.geom.uiuc.edu/ that had some interesting links, but I didn't have time to hunt down more specific information. Also, the site is now unsupported. It seems like it is hard to find the perfect site that has all the material I want and is still alive.
As far as applied problems are concerned, for nets I could talk about how much cardboard is needed to make a box, or how much sheet metal would be needed to make different kinds of tanks.
Right now the big educational trend seems to be standards testing. Because this is the big thing right now and because school funding is tied to test results, all the current math education is aimed at raising test scores. This means little (if any) time is left over to do the kinds of activities that actually get students interested in math as opposed to getting them ready for the next big test.
I think this is a mistake which will ultimately be reflected in the number of students who graduate with any real mathematical problem solving ability or interest in math, and in a few years their will be fewer people going into math oriented areas than ever, because they will all think that math is the most boring subject on earth. No doubt this will result in an outcry about the state of math education, and the pendulum will swing the other way again.