The Student as a Learner, a Knower, and a Facilitator

As previously explained, my study aims to empower students to actively participate in all aspects of their mathematics learning. This is to improve their relationship with the subject and their grasp of it. From my experiences as a teacher I realised the need to change my conventional pedagogy. I also needed to change my perceptions of the students role, if I was to achieve these aims

Searching for the kind of agency that empowers students

I started my search of the existing literature with three conceptualisations of agency.

• The first perspective, of Bandura’s (2001) views learning as a reciprocal triad of personal factors, environmental variables, and behaviour. What is in students’ minds and the teacher’s expectations influence students’ actions and the outcome of these actions.
• The second perspective of Dewey (1900) and Mead (1932) represents knowing as based on one’s experiences in one’s environment. It informs the viewpoint of Emirbayer & Mische (1998). This view recognises that each student experiences the world uniquely and can react to this experience idiosyncratically.
• The third perspective of Bereiter (2002) and Scardamalia (2002) argues in favour of students taking responsibility for what they know and do not know. In this way, they create knowledge from this process.

These three perspectives show that students can change and adapt to innovative pedagogy. They can create knowledge as they take responsibility for their learning in a secondary school mathematics classroom.    I then continued searching for a pedagogy that would aid in developing this kind of agency.

Searching for the classroom culture that empowers students.

I now desired a classroom environment that can sustain the collective contributions of students who take responsibility for their learning. This kind of agency, leads to the creation of knowledge new to the students. One goal of this study is the designing of a pedagogy that supports students in the development of such agency

I examined the pedagogy critiqued by Paulo Freire (1970) and Jacques Rancière (2010 ). It holds similarities to the conventional pedagogy experienced by students in many present-day classrooms in England. In contrast, the proposed innovative pedagogy will seek to facilitate co-participation and interdependence between students and teachers (Benne, 1970).  In sharing authority, they will learn from each other. They will negotiate how best to use their different skills and experiences in mathematics learning.

The knowledge-creation metaphor (Paavola & Hakkarainen, 2011), which represents learning as an individual and collective endeavour, will underpin the pedagogy. This metaphor for learning prepares the way for the possibility of a dynamic pedagogy. Learning will occur as students interact, rather than where knowledge is merely transmitted into their passive minds by a teacher.  The individuals’ initiative feeds the communal effort to innovate, while the social environment feeds the individual’s initiative and cognitive development.

As such, the classroom relationships will not depend on how they benefit each other, or individual achievement. It will be about reciprocal caring for how each other feel in the classroom as they learn together as equals.  I propose a democratic community. Where the relations of equality and freedom, include participation with a democratic stance (Vinterek, 2010). That is, a classroom where the students trust and respect each other. Where they have the freedom to take control of how they learn and what they learn. They exhibit a  “willingness to listen to others, to speak up and a willingness to give voice to their own thoughts” (p. 373). 

Searching for theoretical constructs that empower students – Knowledge Building

I found the concept of knowledge building (Scardamalia & Bereiter, 2010) helpful for my study. It encourages students to intentionally execute higher level cognitive processes on their own. In a classroom community that provides opportunities for student-to-student feedback.  The pedagogy is based on twelve principles (Lai & Campbell, 2018; Scardamalia, 2002). Six of these principles align with the aims of my study and the innovative pedagogy I propose.  The other are less relevant to secondary school mathematics pedagogy that follows the GCSE curriculum.    The relevant principles are:

• Community knowledge, collective responsibility. This encapsulate the aim of knowledge-building pedagogy to produce knowledge that is useful to and usable by the participants of a classroom community
• Epistemic agency which is essential for supporting the collective efforts of knowledge advancement beyond the individual performance of tasks. 
• The collective improvement of ideas. There are no final truths; learners view every idea as having the potential to be improved.  There is the “continual application of a ‘make it better’ heuristic” (Scardamalia & Bereiter, 2014, p. 400). 
• Knowledge-building discourses for the improvement of ideas . Bereiter (2002) argues that classroom discourse should mimic professional science discourse.  It should, i be cooperative and more concerned with creatively advancing the collective knowledge beyond what is currently known. 
• The democratising of knowledge that is a result of such discourses. In a classroom based on the knowledge-building paradigm, all participants are deemed legitimate contributors to collective knowledge.   
• The use of authoritative information, such as multimedia resources, in these classrooms.  This could involve the careful use of textbooks, and online media to construct coherent knowledge from diverse representations.

In classrooms organised around knowledge-building pedagogy, individual students are recognised for their contributions to collective knowledge advancement rather than for what is “in their minds”.  In these classrooms, students find respect and acceptance as contributors in knowledge creation (Scardamalia & Bereiter, 2006). 

Searching for theoretical constructs that empower students – Shared Epistemic Agency

Damşa et al.(2010) construct of shared epistemic agency, lies within the knowledge-creation perspective of learning. It depicts a specific form of epistemic agency that emerges during collaboration to create shared knowledge objects. 

It can be understood as the “capacity that enables individuals, groups, or collectives to make appropriate judgments, to make plans, and to pursue these through purposeful action, in order to achieve the construction of knowledge” (Damşa, 2014, p. 446). In addition to sharedness, this definition emphasises epistemic productivity and negotiation within the community.  The emergent nature of the agency suggests a kind of practice that is reflexive and iterative. Past practices and experiences are considered metacognitively to solve present problems and create plans that lead to future desired outcomes. 

Shared epistemic agency for a mathematics secondary school classroom community

Damşa et al.’s shared epistemic agency cannot be applied without modification to a secondary mathematics classroom.   Thus, I proceed with my study by apprehending and developing the notion of shared epistemic agency in this new context. I determine that the shared epistemic agency that I want to emerge is a quality of students. It is an index of active participation in all aspects of their mathematics learning. An index of improved relationship with mathematics, which leads to enhanced mathematics learning.  Good GCSE grades will evidence this improved learning in the students’ terminal secondary school examinations

The characteristics of my shared epistemic agency are:

1. Intention. The proactive commitment to resolve an unknowing (cf. Bandura, 2001; Damşa et al., 2010; Scardamalia & Bereiter, 2014). 
2. Extension. Students deliberately seek to extend their existing knowledge(cf. Bereiter & Scardamalia, 2011).
3. Explication. Students purposefully engage in dialogue to make knowledge explicit to others (cf. Nonaka, 1991).
4. Expertise. Students as expert learners in control of the learning culture of the classroom (cf. Damşa & Andriessen,2012). 
5. Mutual Relations. Students develop relations that enable knowledge advancement (cf. Macmurray 1950; Wenger, 1998).
6. New Knowledge – The resolution of the unknowing (cf. Bereiter, 2002; Bereiter & Scardamalia, 2011)

The Five Pedagogic Principles that underpin my innovative pedagogy

I clarify the principles of the innovative pedagogy I propose as stipulating that students are responsible for:

1- Building objects of mathematical knowledge

2- The process that makes this knowledge explicit so that it can be shared, internalised, and used by all the classroom participants

3 – The discursive process that communicates this knowledge to the classroom community

4 – Maintaining the social relations and communicative processes that are conducive to the advancement of mathematical knowledge

5 – Reflecting on practice and making plans for the improvement of ideas and activities 

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