This chapter mostly centers around the idea of equity - that is that every student should receive an education that makes accommodations to promote access and attainment. Some of the arguments in the chapter seem a bit specious - with an assumption that if we just teach everyone in a way that is tailored just to them (or their gender, ethnicity, whatever), then all disparities in performance between groups would disappear. But then, I am getting on my soapbox.
The first subsection is about students with special needs. The main idea of this section is that special needs kids do especially well with physical models. I would agree that physical models are a great way to introduce a topic. Where it becomes a bit of a time drag is when you are trying to review material they should have learned last year. This section also talks a little bit about the IDEA act (Individuals with Disabilities Education Act).
The next section talks about gender equity. The main argument seems to be "sexism is bad." Gee, I didn't know that. Also, girls work well in groups. Well, some do - some not so much. It also says that girls tend to blame "luck" for their good performances - or at least they will tend to say that they were lucky if they do well. Apparently, we must squash this behavior, because math was created by highly competitive nerdy men and therefore modesty about doing well on a math test IS BAD!
The next session talks about ethnic and cultural issues. For some reason, the author seems to think that Native Americans would really love math problems dealing with weaving rugs and this would really make a math teacher hip with the locals - and it wouldn't make them seem condescending at all!
The chapter ends with some reasonable recommendations:
One thing to keep in mind when dealing with a gifted student is that no one wants to do extra work just to get the same grade they could have gotten with a lot less work. In that respect, kids are not that different from most teaching credential students! So, if you are going to make extra challenging work available to your gifted students, you should make it available in exchange for avoiding easier, more tedious assignments that would take about the same amount of time. Either that, or you should come up with some sort of way to see the extra work rewarded in their transcript (like getting credit for honors class or something). Just like adults, most kids are working in exchange for getting paid (in grades).
I think another possibility is to sometimes allow students to decide for themselves whether they want to do their homework in class during lecture. I know a lot of teachers think this is a terrible thing to do - like the brighter students are going to miss the wisdom of the ancients just because they can figure out how to do things on their own - but really, isn't this simply being fair? Why should someone waste their time listening to a lecture if they don't really need to listen in order to master the material for the class? How is this really in their best interests?
Yes, everyone is capable of learning mathematics - although everyone learns at different speeds and at different depths of understanding. However, I don't believe everyone really needs higher mathematics, and I reject the notion that we must cram it down a student's throat whether he or she is interested in the subject or not. What makes mathematicians think our subject is so much more important than art, English, shop, or whatever it is that a particular students is actually interested in? Plenty of people make good money without ever doing math more complicated than fractions.
I think all students should be introduced to some of the basic ideas of algebra, geometry, etc., just so they all get some kind of idea what it is about. However, I think we need to get over this idea that every student needs to get past a set of standards labeled "algebra I" or whatever. It's a waste of an enormous amount of time and resources.