My motivation for the study came from my experiences as a mathematics teacher. In January 2008, an event caused me to rethink the traditional approach to teaching mathematics I was implementing. In particular, to question my assumptions regarding the role of the learner. It started with a student who took her GCSE mathematics examination twenty months early, at the start of Year 10.
Getting it wrong
Kaome (real name withheld) was one of the students in what was then my Year 10 mathematics class, whom the faculty considered to have difficulty learning mathematics, but who, with academic support, could achieve a passing grade of C in the GCSE examination at the end of their secondary education (June 2009 for Kaome).
In January 2008, Kaome achieved a grade B in GCSE Mathematics. Her parents had sent her to a Saturday school in preparation for the November 2007 GCSE examinations.
Changing perceptions
After achieving a B grade, Kaome moved to the higher-ability mathematics class. The faculty now considered that she was capable of reckoning with more advanced material. The move changed her self-perception, and she behaved like a competent mathematics student. Subsequently she achieved an A grade in both GCSE Mathematics and GCSE Statistics.
As a mathematics teacher, I had judged Kaome wrongly. I had relied on statistical information, preconceptions, to limit my expectations of my students, including Kaome and I justified the restriction of the mathematics learning I made accessible to them. Based on my experience with Kaome, I decided to change this approach.
Students Taking Responsibility for their Mathematics Knowledge
As the Head of Faculty, I gave all students in Year 11 the opportunity to enter their GCSE examinations early.
In 2009, I allowed students in any secondary-level year group to sit GCSE Mathematics at a time of their choosing. Expectations for achievement became the responsibility of the individual students themselves. Expectations became an index of students’ beliefs about themselves and their agency. What students could achieve were no longer limited by teachers or past examination performance.
What became immediately noticeable was the change in students’ participation in their learning once they had decided to sit their GCSE examinations. They took responsibility for what they did not know and sought to know. They became more tenacious and creative in their desire for knowledge and supported each other’s learning. In September 2013, however, the government began to penalise schools for early entry examinations, and our faculty stopped offering this opportunity to students.
Questioning the Taken-for-Granted
Having observed how early entry for the GCSE examination challenged the taken-for-granted relationships between assessment procedures and student performance, I challenged myself to look beyond my current thinking. Subsequent independent research confirmed what I had realised. My perception of my students influenced my behaviour towards them and their experiences in my classroom. I decided to attempt to bring my actions in line with my expectations of the students.
The aims of the study
This research study was undertaken to discover the most effective means for improving my students’ engagement with mathematics.
Thus, this study aims to empower students to actively participate in all aspects of their mathematics learning to improve their relationship with the subject and their grasp of it. Most concretely, I am concerned about discovering more effective forms of pedagogy that encourage students to apply their knowledge rationally to solve problems in the secondary school mathematics classroom.
The central concept of this study
To this end, I explore how a kind of student agency called “shared epistemic agency” is developed and sustained in mathematics classrooms. Shared epistemic agency, discussed in further chapters, is the central concept I have developed and used to describe and analyse students’ participation to create knowledge. I propose that students with this type of agency actively engage in their learning. They take responsibility for what they know and do not know and act to further theirs and their peers’ knowledge.