Final Thoughts

Hi all
I was supposed to try and clue up on Friday evening but I am glad the course is still open.
I had a busy weekend between kids and hockey practise and promising my wife we could clean the house and begin to decorate for Christmas.
Just wanted to say that the course has been interesting and I have enjoyed sharing and reading you stories as well in this format. I will keep my blog going if possible and hope to link it to my website I am building for mathematics support on our school's website, I got the idea a couple of years ago to develop a webpage to help parents ans students alike if they were experiencing difficulties with homework or math in general. I am linking the websites to the page we use in class as well other sites such as Pearson Math, where the videos and texts are available for use as an instructional aid.
If you want to see what it will look  like I hope to have it up and running before we break for the Holidays.
Have a safe and relaxing holiday

Chapter 11: Looking at the future

This was a surprising read indeed to some extent. The pressure to conform and perform must have certainly changed the climate at Phoenix Park school indeed. I feel this is a bit of a sad reflection upon what governments see as the priority in education today. Student achievement is indeed one of the  main priorities of any educational institution, however how we measure this achievement, I feel, is fundamentally flawed.

Success to me lies is developing well rounded solid thinkers, not only in mathematics, but in all areas in general. We are not measuring and developing this in our current system in my opinion and need to readdress this situation. From some research I reviewed it seems as though we are not alone in this dilemma, it seems to be a universal situation. As educators we are the front line soilders who need to take up this cause for the sake of all learners.
  

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.

The Text So Far

This has been a very interesting read to date. I am still not sure if either approach was any more successful than the other when it came to standardized assessment results. However it seems clear to me that the advantages of the open ended approach at Phoenix Park has produced students that are more mathematically competent and able to recall and use their mathematical skills for a longer period of time in a wider range of situations. I guess the approach we tend to take toward our mathematics teaching is a product of the pressures and freedoms we face as educators. There is no doubt that we need to have our students perform at a certain level on our standardized assessments or we our under the microscope. The one drawback to such assessments I truly feel is that these pressure and scrutiny has taken away from us a certain degree of creativity and diversity in our teaching and this is very unfortunate. After all do we want good test takers or good mathematical thinkers  and problem solvers? I feel that the latter would be a far more well rounded student.

Schoenfeld Article

This article strikes a chord with me and my experiences in teaching mathematics at the intermediate level especially over the past ten years or so. It is not that the students and teachers did not necessarily cover the material in their curriculum per say, but rather the way in which some of the concepts were constructed in the mathematical repertoire. The vast amount of misconceptions I find myself unravelling on a daily basis is often times astonishing. I have been trying to make the case for years that the availability of specialist teachers for each subject area is one of the keys for student success in any discipline. This is not to say that I have not experienced a similar experience in my teaching experience myself, however having some expert knowledge and specialized training in the field of mathematics education, I am able to pick up on these misconceptions and set things straight for my pupils.
When I spent a year with the district office as an itinerant for math teacher support in our small schools I was immediately placed in a classroom with teachers who had little or no training in teaching mathematics, and to make things worse, they were expected to multi-grade or multi-course at the same time. I realise that this ism an extreme situation, however it is a more common occurrence that we would care to think.
I have to agree completely with the authors assessment of the situation here, fundamentals and basics need to be taught properly in order for pupils of mathematics to build their foundations for future success in the field.