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.

WHY?

How many times have I gotten this question Why? As in why learn this math? Why do I need to know this math? etc. I am sure most of us can relate. The reading addressing this question was quite enlightening for me. Trying to answer these questions on a daily basis, both for my student's need and for my own personal peace of mind is an issue I have been struggling with for years.
I began my teaching career as a science teacher which I feel has helped me on most occasions as I can relate the mathematics in science fields such as physics, chemistry and geology to the real world as it were. Being able to give students something tangible to connect the mathematics to is paramount in dealing with such issues in the mathematics classroom.

Sir Ken Robinson

While no doubt entertaining there was a very serious and clear issue for teachers of mathematics conveyed in this video. I have always held the belief that students do have creative avenues natural to them and it is a simple fact that the wrote mathematics algorithms or formulae may not be their strong suit. When it comes to student evaluation for example I always encourage students to show me in an means feasible to them how they would solve a given problem. I always model the traditional algorithm with the use of manipulatives and diagrams where possible and relating the situation to their everyday life experiences.
I have seen several cases of students over the years whom have been labelled with LDs or other disorders and have often wondered if there was really another issue at work here. Since it is often times out of our control as classroom teachers we do not usually get the opportunity to test our hypothesis. I think this may be an area worth looking into. After all if a kid can tap dance they can, in all likelihood follow a pattern.

Romance in Mathematics

I hold a deeply profound notion that the ability of mathematics to explain and model so much that is in our universe as we know it,  mathematics must indeed be of a truly devine nature. Is this romantic? Maybe from the point of view that  true romance is somewhat mystical yet completely visible at the same time.
My passion for the art of mathematics comes out in my teaching on a regular basis. I am far too often disappointed by the lack of enthuiasim I recieve from students and colleagues alike when it comes to marveling at how mathematics can model and predict events in the world on a regular basis at such a far reaching extreme.
I marvel at both the inherent simplicity in mathematical functions as well as their extreme complexity at the same time.
Call me a fool but I truly feel mathematics does indeed comprise a romantic relationship with the  world and it is both mystical and predictable.

Describing my Teaching

This is an interesting one for me. Some would describe it as eccentric or even unusual. I am teaching mathematics from grades 8 -12  and, especially at the intermediate level, I strive to make the mathematics learning as relevant as possible to the daily lives of my learners. I use materials such as wal mart receipts, they or me supply, sears catalogs, when I can get them away from my wife, recipe books, food, road trips to stores , ramps, hockey rinks and even 2 and 4 stroke engines on occasion. The students need to see mathematics functioning and explaining daily events and occurrences in their lives in order to make that deep connection to the concepts being taught.
We play all sorts of games from cards to jeopardy to bingo in class. This makes the learning experience fun as well as meaningful. I regularly encourage their participation in school run or nationally run mathematics competitions and showoff their results at the end. I hold an annual pi day in March where all 7 - 12 students participate as teams in a mathematics scavenger hunt. Everyone gets a mathematically inspired prize at the end with the winners getting a little extra of course. My 3103 classes run the show, from budget, shopping, cooking ( pies and pizzas of course), to creating and hiding both the questions and solutions to the mathematical scavenger hunt questions.
Active engagement, enjoyment and ownership are at the hearty of my mathematics teaching philosophy.

My Mathematics Experiences at University

When I entered MUN at 17 years of age I really did not know what i was going to study. I nearly flunked first year math, completely unpreparewd for the transition, and nearly gave up on University. In second year I decided to do a science degree , majoring in Physics. Naturally several math courses were required for this degree and I went on to even do a few electives in linear algebra and statistics as well simply out of interest.
I  currently teach math from grade 8 - 12 , and have been for the past 6 years. It has been out of this experience and PD etc that I have developed my love for mathematics and it's ability to explain nearly every facet of the universe. I continuosly strive for examples and stories of how math influences and escribes everyday life.

My Early Mathematics Education

Since about grade 2 when me and a fellow student were put ahead to do grade 2 and 3 mathematics I felt that I had a special ability to underrstand the mathematical relationships we were studying. However soon after this we seemed to get lost in the crowd as it  were and we were doing the same material aseveryone else for the next 8 years. A number of my teachers used me as an inclass tutor but there was never any real challenge anymore. Most of my high school mathematics was of the traditional set and get nature and again was no real fun or challenge. The real problem for me was to realize that I was actually teaching in the same manner for the few years of my teaching career and soon realized that this was very ineffective with the learners I was involved with.