He intimidado a alguien de las siguientes maneras:

I do not expect my students to understand what signifies classrooms built on the

connectionist orientation, unless they can understand features of classrooms that do not. Most report a dominant transmission orientation in their own secondary school experience, which is reproduced during many of their early PGCE observations in schools. For some, learning to teach mathematics becomes an exercise in reproducing the practices observed in school, with the outcome that early habits become instinctive practice. Time, difficulty and ‘being watched’ are cited as constraints on their practice, leading to the “awful but easier” transmission teacher orientation if their learning is situated within this constrained school culture. My teaching at the university is removed from this culture, separated by location as much as it is by pedagogy. In order to give my students a site for reflexivity in their practice I need to open up the possibility that they can critically reflect on their

teaching and teach simultaneously. I need to give my students a site for reflection that leads to action, using Freire’s notion of praxis; "reflection and action upon the world in order to transform it” (1970, p. 36). In this case, the part of the world that is transformed is my students’ mathematics classroom. Freire’s notion of praxis arose from his pedagogical developments in situations of Poverty in South America, leading to potentially emancipatory education and a more democratic model of learning than the one that existed in the 1960s. Freire’s aim was to literally transform the world for South Americans of the lowest social and economic status, which does not necessarily translate to transforming the world of secondary school teacher education (Adams, Cochrane & Dunne, 2012). An absence of praxis for beginning teachers does not have the same consequences as for the subjects in Freire’s work, but the principles of emancipation and agency still apply; in the absence of

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reflection and action in mathematics classroom the probability of transformative teacher education is limited.

Adam’s “bridge between the two worlds” analogy suggests that it is possible for the worlds of school and university to connect. The day that allowed Peter to “stop and think and re- evaluate” was characterised by complementing pedagogical messages because the divorcing parents shared a belief and understanding about the effectiveness of certain aspects of pedagogy. There is, as Adam said, room for more days like that. But immersion days in schools should not form the exclusive model of my teacher education. My students do need to step away from the school environment in order to reflect on their teaching and to learn about research informed practice away from the school culture. Unless they step away from the situated culture, the only stimuli for understanding practice are the traits that characterise that culture. My student teachers cannot take action in their teaching, action that they govern while they are being watched by teachers who tell them, explicitly or implicitly how to teach. The main issue that separates my teaching from their school practice is their inability to respond reflexively to what they are learning because of the culture and activity that surrounds their situated learning in school.

The second issue relating to situated cognition, which poses a threat to my students’ reflexivity, is that part of university-based teacher education that is perceived as wholly separate from what they do in school. When I ask my students to talk to me about their university teacher education, they directly reflect on aspects that are separate from their

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mathematics education sessions. The application of what they learn with me is immediately apparent, whereas aspects of whole school professional learning and research informed seminars relating to assignments are not immediately perceived as useful in what they are learning to do. They do not instinctively identify their mathematics education sessions as university teacher education until I direct them to. This was apparent in my interviews with all of the participants in the study as much as it is in end of course evaluation meetings with students. Their criticisms of these sessions suggest that an experience based model is absent. Paradoxically, some have commented that they are taught that transmission classroom orientations are less effective in lectures that are characterised by transmission. My teaching is located alongside the more separated world of general teacher education even though the pedagogy that I adopt is not situated within the culture of learning that they criticise. For some students, like Adam, Sam and Ben, my teaching has immediate authenticity. Yet for others, like Luke, Rachel and Anna, there is scepticism and doubt about how the mathematics pedagogy that they are taught can be enacted in school. It is possible that some of the authenticity, perceived as missing in general teacher education lectures, reduces the plausibility of what I am teaching them. For the sceptics, my teaching is situated in a culture that is removed from practice.

The bridge between the two worlds offers a route for channelling teacher education into school. It also offers an opportunity to step out of school, to stand and watch the school for a while, so that when student teachers return to school they might be able to act or think differently about teaching and learning than if they were exclusively immersed in the world of school.

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