In conclusion, I review the central arguments of my study. This highlights students’ competence and their potential for transforming mathematics education.
A contribution to the field of mathematics education
I present an alternative perspective of the Participant and Educator. These conceptualisations of student and teacher roles challenge current educational policy and practice. I also show my innovative pedagogy that is purposeful for the emergence of the Participant in the Learning Community.
A contribution – The Participant and the Educator
This study started with my desire to improve students’ participation in their learning. Breaking down the crystallised power-relations within the classroom that frame and limit students’ participation in the secondary school classroom. I hoped to empower students towards active participation in their learning process.
My study demonstrates that students can transcend the confines of the conventional teacher-student roles and take charge of their learning. In doing so, they exhibit the power to change the existing notions of “student”, “teacher”, and “mathematics classroom”. Emerging from this study is a transformative conceptualisation of the student as a Participant, and the teacher as an Educator. I identify the essential feature of the Participant in the Learning Community as their competence. This Participant can be a learner, knower, or facilitator at any given moment in the learning community. As a learner, knower, or facilitator, during interactions, the Participants can advance their knowledge and that of other Participants.
The Educator
In addition to my re-conceptualisation of the Participant, I contribute the possibility of conceiving the teacher as an Educator. The Educator’s role is to draw out the Participants’ latent potential. The Educator recognises that Participants behave in unpredictable ways. This means that the rules and regulations that underpin conventional educational policy and practice are ultimately provisional. These rules are unable to account for differences in individuals and environments. The Educator does not rely on such conventions but instead possesses situational understanding. They consistently make contextual judgments to empower Participants to take responsibility for their advancement. I discovered that the participant’s development is conditional on the presence of the Educator, who constantly verifies their capabilities.
A challenge to educational policy
I have characterised the Participant as competent and an authority as a learner, knower, and facilitator in the Learning Community. The dominant discourse of the learner, used to describe the subjects of education, is construed in terms of a deficit. Educational policy contributes to this notion of the student as being equated with “stultification”. It presents the pupil as of lesser intelligence and as incapable of taking responsibility for directing their learning.
In addition, policy undermines the importance of the role of the Educator as vital for the empowerment of the Participants. Rather, it is explicit in its demands for instituting the supreme authority of the teacher.
Thus, my contribution to policy is the recommendation and imploration that it presupposes the subject of education as competent. This presupposition could change the dominant discourse of the learner, pupil, student towards one that recognises their empowerment and agency. I have shown that this empowered learner can emerge and that this emergence does improve mathematics learning.
A challenge to educational practice
In presenting this Participant as competent, I cast into question practices by which teachers take responsibility for the learning process. Practices include exposition of subject knowledge, classroom differentiation, and determining the role of questioning in the classroom.
The conception of the student as incapable has infiltrated the education discourse and impacted recommended strategies. These strategies seem to improve the education of “incapable” students. However, as in the case of questioning, they can arrest children’s natural propensity to learn. The Mathematics Program of Study (Department for Education, 2014) aims to have pupils reason mathematically and apply their mathematics knowledge. It needs students who are aware of their unknowing and seek to know. Students who are creative in extending their knowledge in adaptable ways and interact with others to create knowledge. I contend that this student is in every classroom, in front of every teacher, ready to be empowered.
A contribution – The innovative pedagogy
I designed the pedagogy to advocate for the participation and empowerment of my students. So that they can achieve the grades that would avail them of better opportunities in life.
My pedagogy is unique. It focuses on changing its perception of the subject of the pedagogy to achieve the desired outcome. This is rather than changing the concepts of study, the curriculum, or the classroom environment. The subject of the pedagogy is the student. The pedagogy described this student within the existing structures of the school. Saying the pedagogy described the student, I mean that I designed the pedagogy to be enacted by students who already owned the qualities the pedagogy aimed to produce. This is rather than designing a pedagogy that would produce the desired qualities in students.
Thus, the latent potential already inhering in the student had to emerge to meet the expectations of the pedagogy. For this reason, I refer to my pedagogy as a “pedagogy of trust”. I trusted the subject of the pedagogy to embody its purpose. I trusted in the student’s ability to enact the pedagogy. As a result, I achieved a new arrangement which transformed the student into a Participant. The teacher was transformed into an Educator, and the classroom into a Learning Community
A contribution to theory
The construct shared epistemic agency originated from a study undertaken in the context of undergraduate collaboration (Damşa et al., 2010). In light of my wider reading, I synthesised six characteristics of shared epistemic agency that shaped my analytic framework. Through my empirical actions, I have refined, operationalised, and made the construct relevant to a secondary school classroom. I offer these as contributions to theory.
This contribution extends the original construct of shared epistemic agency. The extension includes the continuous and spontaneous interactions that take place in a secondary school classroom. A classroom enacting a knowledge creation pedagogy.
I put forward terms that indicate this distinction between the two constructs of shared epistemic agency: collaboration and interaction. I propose that Damşa’s construct be referred to as epistemic agency through collaboration. On the other hand, this research has identified a different kind of shared epistemic agency. I propose that the construct identified by this research should be referred to as “shared epistemic agency through interaction”.
A contribution as a teacher-researcher
I advocate action research as suitable for teachers to transform their classroom practice and the education profession at large. A culture of action research could enable teachers to turn their personal knowledge into knowledge they can be share.
Researchers such as, Schon, 2008; Stenhouse, 1981 have canonically called upon teachers to conduct research to improve and change their practices. This is even more crucial if students are expected to be fluent in the fundamentals of mathematics. That is, reason mathematically by following a line of inquiry, develop an argument, justification, or proof, and solve problems. To promote the emergence and sustenance of problem-solving and agency in the mathematics classroom, mathematics teachers need to adopt an alternative to the conventional pedagogy that is typical across England. It would be difficult to bring about this change if teachers themselves are not engaged in research that effects change. Change to classroom practices comes from a teacher’s belief that such change is needed, and their ownership in implementing this change.
Extending the argument, students as subjects of the change also need to be involved. They should even direct the change, as it is ultimately, them who will benefit.
Conclusion
This study is a counterexample of what is possible in a secondary school mathematics classroom where authority circulates amongst participants. The student emerges as a competent individual who forms a community with other students who. Through their agency, they advance their collective mathematics knowledge. It presents the mathematics classroom as a democratic community. A community in which the teacher and the students can learn, know, and facilitate each other’s education. Each bringing their unique skills and experiences in a blending of authority.
This has implications for how the students in the study viewed the field of mathematics education and education in general. The conventional view of the teacher as a necessary authority is fundamental to the discourse of schooling. It reflects the beliefs that most potently informs government policy, professional development, and teacher training. Against this, the views of the student and their competence advanced in this study relate a call for reforming of the pedagogy and the institutional ways in which teachers interact with students in classrooms and schools.
Concluding Statement.
This study raises the question of what further potential may be possessed by our students, waiting to be drawn out. To answer this question requires other teacher-researchers to carry out similar research in their classrooms. I have shown that it is possible to transform the pedagogy within the structures of the mathematics curriculum. The uniqueness and narrow focus of this study may lead to its non-replicability. However, I believe that within the body of evidence that I present in the full thesis, sympathetic teachers and researchers can decipher the principles of my pedagogy. They can adapt these principles to their contexts bringing about a comparable pedagogy of trust. A pedagogy designed to be enacted by students who already own the qualities it aims to produce. A pedagogy that, in an appropriately egalitarian manner, believes in the competence of students, and allows this competence to emerge in its own way.
Thus, I call on teachers to become researchers. I believe that the process of applying the principles of this study to further research areas will provide yet more evidence of the immeasurable competence of the young people we teach. My hope is that “not only scholars of teaching but also those whose learning experiences they intend to support, would seek to renew our common world” (Kreber, 2011, p. 866). To this end I hope that this study contributes a kind of answer to the question that educators persistently ask of themselves: “What works, what is and what is possible?” (Hutchings, 2000)