Chapter 10 : Ability Grouping

I am still on the fence with this one. There are clearly pros and cons with the methods one uses to select and assign students to a given ability group. At Amber Hill it appears far to much emphasis was placed on factors which are far less relevant to creating a group which will function properly and at Pheonix Park I feel that the pedagogy was the main factor in the results and not a lot had to do with groupng per say.
As I mentioned in my posting to the discussion forum I only have classes of about 25 in intermediate math so my grouping opportunities are limited to once or twice per week. However having a limited number of pupils does give me an advantage in that I do know them a lot better as individuals since we all live in the same communities and have opportunities to meet in social settings as well as in the classroom.
Depending upon the topics being studied I can choose my groups carefully, not necessarily always based solely upon abilities, but rather on real life experiences which I know they can bring to the group. More of a social experiences grouping strategy as it were. It does seem to work well for the most part. This is not to say that I do not consider ability, it just plays less of a role in my grouping strategy.

Gender Issues

After reading chapter 9 of the Boaler text and the class postings I was taken back to my high school experiences in mathematics and science classes. During the mid 80's I recall our school board putting a push on trying to have more females enrolled in advanced/academic math and science courses. My classes, along with a lot of schools in our district, had a large ratio of boys to girls and the board was looking to equalize this ratio. The term used at the time was that girls were experiencing a fear of failure and were avoiding these courses at all costs. I guess there was some truth to this, however, most of these courses were a very traditional sit and get nature. From this perspective and the current knowledge of learning styles there may have been more to this phenomena than was understood at the time.
If girls are truly better at learning math and science in an exploratory type of learning environment it is not surprising that they avoided these courses. I noticed a change in this ratio in my two courses in high school physics when we had a new teacher fresh out of university for science and his approach was far from this traditional one we were used to. It wasn't long before his reputation as an interesting and dynamic teacher was recognized and there were nearly as many females in physics and chemistry as males. Our classes were grounded in exploring, labs, and field trips and obviously must have appealed to a lot more of the female learners in our high school.
I recall being at our science teacher's wedding a few years after graduating as he married a girl from our home town, and we had a conversation about what I was studying at MUN. He was somewhat surprised when I told him that I was also studying physics as he was the person responsible for developing My interest in the field. At this time I was not sure if I would pursue a career in science or some other area. A year or so later, I realized after demonstrating labs for the physics department and doing some tutoring for extra cash, that I both enjoyed teaching and was quite good at it.
From my past 18 years or so I still see a few more males than females in these courses, however it is not far from equal.

The Authors Referenced in Chapter 8

Anyone looking for an interesting should check out the work by Brown, Collins and Duguid, 1989, referred to on page 123 of the text. Their analogies and common sense comparisons really bring the light the notion of having our students use their mathematical tools in a hands on manner. It would be very unlikely that an instructor of carpentry for example would spen their time showing their students tools such as a hammer or a square and never letting them use these tools for themselves in a variety of situations before expecting them to preform with their tools in a testing situation.
We need to take the same approach with our students and their mathematical tools we are teaching them to use. The authors have a section of their work called cognitive apprenticeship that is really worth reading. It definitely shows the need to approach teaching and learning of mathematics in a different way. In particular they discuss Schoenfield's work on problem solving.  By having the students wrok with him on problems he had given them he was able to let the students see how these situations are viewed and solved through the eyes of a mathematician. The refer to this as bringing the students into the culture of mathematics.
There is also discussion of how Lampert uses coins to teach multiplication to fourth graders, the idea here is of course how in their real lives the coins and money are something these students are both familiar and comfortable with.
All very interesting and very real mathematics that may be missing from our classrooms from time to time.