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.