Knowledge, Beliefs & Mathematical Identities

The information presented in this chapter was, to some degree, not surprising. It was evident from preceding chapters that the experiences and development of mathematical knowledge at Amber Hill was very different from those experiences of Phoenix Park students. From preceding chapters it was apparent where the real learning took place- Phoenix Park. This occurred despite the efforts put forth by the teachers at Amber Hill- methodologies which they perceived would ensure student success, particularly on GCSE’s.

Amber Hill’s traditional methods and Phoenix Park’s open-ended approaches were not on “separate ends of the spectrum,” rather they fostered a different development of mathematical knowledge. The two schools differed in many aspects:
· Amber Hill students lacked confidence in their mathematical abilities and relied heavily on teacher support and cueing. In comparison, students at Phoenix Park were considerably more confident in their mathematical abilities.
· Amber Hill students made no connection of maths taught in the classroom to “real world” situations. Students at Phoenix Park were continually applying the math they learned in school to out-of-school situations.
· The students at Amber Hill were perceived as what Belencky, Clinchy, Goldberger and Tarule refer to as received knowers- expecting to accept knowledge from authoritative sources without contributing to knowledge or making connections across areas. In comparison, students at Phoenix Park were very mathematically empowered- they possessed the power to develop and use mathematical knowledge in the school setting.
· Unlike their Phoenix Park counterparts, the teachers at Amber Hill were continually motivating students and enforcing the importance of the upcoming GCSE’s. The students at Phoenix Park were largely self motivated, and the importance of the GCSE’s was rarely discussed (with exception to the couple of weeks leading up to the GCSE’s).
· Students at Amber Hill viewed mathematics as isolated and fragmented concepts. Their lack of success on applied assessment can be attributed to this notion that mathematical concepts are isolated.

It is evident that both sets of teachers believed they were using methodologies that worked best for the students. However, there was no mention of teachers taking the time to reflect and determine student areas of both strength and weakness. I, as do many teachers, often get wrapped up in the notion that “I know what work’s best” for my students. However, as is apparent in Boaler’s study, this is not always true. It is important to reflect, determine what “works” for students and what approaches to teaching are not as successful as others. That being said, it is very important to remember that what students find helpful one year may not be applicable the next. Although I have always considered myself to be aware of what methodologies are successful for students, I am continually exploring approaches that may work better. I am both anxious and excited to make use of Phoenix Park teaching strategies when I return to teaching in the upcoming year.