Phoenix Park

Standard 1 of NCTM's 'Professional Standards',(1991)is entitled "Worthwhile Mathematics Tasks"
The teacher of mathematics should pose tasks that are based on-sound and significant mathematics:
-knowledge of students' understandings, interests, and experiences;
-knowledge of the range of ways that diverse students learn mathematics
and that:
-engage students' intellect;
-develop students' mathematical understandings and skills;
-stimulate students to make connections and develop a coherent framework for
mathematical ideas;
-call for problem formulation, problem solving, and mathematical reasoning;
- promote communication about mathematics;
- represent mathematics as an ongoing human activity;
-display sensitivity to, and draw on, students' diverse background experiences
and dispositions;
and
-promote the development of all students' dispositions to do mathematics.

Phoenix Park's mathematics program certainly met this standard. The curriculum at Phoenix Park was teacher designed, it required the teachers to "know a lot about the students - what they knew what would be most helpful for them to work on" in this they meet the descriptors from the NCTM standards. In fact the mathematics tasks that the students of Phoenix Park were given to work on allowed for openness and creativity. The teachers supported this creativity by making "deliberate efforts not to structure the work for students", they did not give closed answers to student questions instead they would reform the question in a way that invited the students to explain what they knew and to identify what they needed to find out, something I am currently working on in my own instructional style. The students were guided to make connections and to reason and communicate their thinking and in doing so developed a mathematics disposition that was based on the belief that it was more important to think in mathematics than to remember rules. I was very impressed with the learning opportunities for students at Phoenix Park.
It was very surprising to me that time on task for both Amber Hill and Phoenix Park was about equal. I would say that I had a very strong reaction to the descriptions of students being permitted to wander at will and to be noticeably off task for long periods. There was no attempt by the teacher to refocus or encourage them to return to the work at hand and I found this disturbing. I couldn't help but think that a little structure in this area would have benefited the students. I can only suppose that the teachers felt it more important to create an atmosphere in the classroom where students were unafraid of being wrong and willing to explore mathematics concepts then it was to impose any useful level of discipline. I'm not 100% sure that they aren't right in this but I'm a long way from this in my teaching.