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Group 4a - Modelling in mathematics teaching

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Group 4a - Modelling in mathematics teaching

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1) Mathematics teacher education is not the same as mathematics teaching so the idea of "look at me as I teach you to become a teacher (or to work on your practice) needs to be interrogated
2) Some related/overlapping questions:
a) WHAT are we modelling - mathematics/teaching/both?
b) WHERE are the models - in our heads, images of others and to what extent are we explicitly aware of the models?
c) WHO are the models - ourselves, our own teacher educators, images of experienced teachers in classrooms
3) What can be learned from modelling practice in MTE? To what extent should the elements be made explicit/left implicit? If left implicit, then how do we know that are being seen to be learned?
4) Lesson study may provide a rich opportunity for modelling many different practices - for MTEs, for teachers

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Methodological approach: Starting by studying ourselves as MTEs, reflective discussion sharing ideas and asking reasons for our own answers

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Methodological approach: Starting by studying ourselves as MTEs, reflective discussion sharing ideas and asking reasons for our own answers

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RQs: How do we transfer PhD candidates to become MTEs (helping them in thinking about teaching more than about teachers)? How can we describe MTEs expertise and knowledge? 

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RQs: How do we transfer PhD candidates to become MTEs (helping them in thinking about teaching more than about teachers)? How can we describe MTEs expertise and knowledge? 

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1) Conduct a review of how to become TE in different countries. What is the status quo?

2) What should the requirements be regarding theoretical knowledge and personal practical experience of teaching in order to become a TE?

3) Should there (does there) exist a formal means of induction in order to become a TE?

4) How to create bridges/connections between TE lecturers of mathematics and TE lecturers of pedagogy in order to create a mutually enhanced system?

5) How do existing TEs enhance their practice?

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How do we evaluate any of the issues we are discussing?
e.g., how would we ever know it was a story that has been significant?
Learning to teach is so complex how do we research it in a way that respects that complexity?

Perhaps interviews over time? eg we might be able to observe views moving away from a static position

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The MTE role as widening your awareness of possibilities

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Should TEs be prescriptive in what is  'better practice' or rather allow pre-service teachers to develop their own teaching identity?

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Should TEs be prescriptive in what is  'better practice' or rather allow pre-service teachers to develop their own teaching identity?

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Where does the balance between the two come in?

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Collecting stories from PSTs at certain times - inviting stories about a significant piece of learning they have done - and how does this relate to the way the MTE has been working with them?
What would PSTs' stories be about their MTEs?

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How many/how deeply should a TE  know about different pedagogical strategies (especially beyond their own preferences)?

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How many/how deeply should a TE  know about different pedagogical strategies (especially beyond their own preferences)?

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Research problems:
How do the MTEs support teachers in reflecting on teaching models?
How can we conceptualize the roles of MTEs as a model for the teachers? What kind of differences are there when the MTE acts as a model in pre-service teacher education or in-service teacher education?
How can the MTEs manage the interplay between the level of mathematics teaching and the level of theoretical reflections on mathematics teaching?
How can the MTEs notice and challenge the teachers' beliefs about teaching?

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Difficulties of being a MTE in an online context when you cannot see expressions on faces, or "feel" the engagement of the room, or know if they are distracted.

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Sharing stories as MTEs as a form of PD for MTEs

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How does/should TE requirements change depending on which level of preservice teachers one is teaching (e.g. foundation phase / primary school / high school)?

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How does/should TE requirements change depending on which level of preservice teachers one is teaching (e.g. foundation phase / primary school / high school)?

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- Do our positions as mathematics education researchers necessarily make us mathematics teacher educators?
- How are we perceived by teachers if we are working with them for the purpose of research? What are the expectations they have of us?

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What level of university qualification should be required in order to be a TE?

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What level of university qualification should be required in order to be a TE?

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How does one balance theoretical pedagogical knowledge with practical classroom experience in TEs? 

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How does one balance theoretical pedagogical knowledge with practical classroom experience in TEs? 

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Is either option more important?
Is either option more valued (by pre-service teachers/university leadership etc)?
Which develops better teachers?
Which leads to positive change in classroom practice?

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How do we find out what our PSTs know? And how can our finding out what they know support PSTs to find out what their students know?

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Teaching PSTs to use Excel - all the PSTs saying it is going fine. One PST in the 3rd class wanted to speak privately, to say "I don't understand how to input formulas". MTE move was to abandon the spreadsheet and offer the tasks differently.

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To describe the expertise of MTEs we need to agree about what is becoming a mathematics teacher

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To describe the expertise of MTEs we need to agree about what is becoming a mathematics teacher

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How can theories help in describing the phenomenon of “being a MTE”? And what a about how to become a MTE?

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How can theories help in describing the phenomenon of “being a MTE”? And what a about how to become a MTE?

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Trying to describe MTEs' expertise needs to previously agree about what is a MTE. There are many different figures of MTEs, and different ways to become one.  

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Trying to describe MTEs' expertise needs to previously agree about what is a MTE. There are many different figures of MTEs, and different ways to become one.  

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- How do we support teachers if we may not have enough knowledge to offer in terms of the diversity of educational landscapes/ communities/ contexts / languages?

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Offering teaching strategies in teacher education that are not used in the classroom by PSTs - how could this situation be different?

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What form of induction exists to become a TE?

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What form of induction exists to become a TE?

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What pathways exist to become TE?

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What is the gap between experienced learning/lectures at university (as pre-service teachers) and expected classroom practice as an in-service teacher?

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What is the gap between experienced learning/lectures at university (as pre-service teachers) and expected classroom practice as an in-service teacher?

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How does sharing stories about common approaches to teaching teachers to teach using manipulative help improve our own practice as MTEs?

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Should one have personal school teaching experience in order to become a TE?

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Should one have personal school teaching experience in order to become a TE?

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PSTs coming back in a few years "I want to do the things you showed me, but the school doesn't allow me"

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What is the difference between being a teacher and being a teacher educator?

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What is the difference between being a teacher and being a teacher educator?

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MTE explicit about trying to convey love of mathematics eg using geoboards - at end of course, explicit about hope course has provoked PSTs to think in a different way, response from PSTs often: "Why didn't they teach me like this?"

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A story of stories ... My development as a MTE is a story-telling issue - link my own development to stories. Asking PTEs: "What is your relationship to mathematics?", one year a PST said "I hate it" at start - last day of class, same student: "I still hate mathematics but I think I can try to make it fun for my students". As a MTE need to pay attention to PSTs emotions.

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PSTs' personal experiences - leading to raising of general issues which go across teaching

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Teaching problem solving in school and at university on the same day - sharing story from school with the PSTs - in both cases students being stuck!

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- Drawing on personal experiences to PSTs / in service teachers by sharing stories/vignettes
- Do we have to be teachers ourselves (MTEs) to be able to tell stories to our students (teachers)?
- Where can we find the sources for stories? What if we are teaching in a different context? Are some stories "better" or "more applicable" than others?

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Teaching PSTs Pythagoras Theorem using squares, or showing the trigonometry circle image - PST response "Why wasn't I taught like this" - predictable arising of emotion.

MTE working at the meta-level - raising meta-issues having done some "teaching"

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Where is the mathematics in these stories?

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Where is the mathematics in these stories?

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- things that MTEs do may not be necessarily related to mathematics content e.g. pedagogy/motivation
- can we always bring in the mathematics to these stories?

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tracy.helliwell@bristol.ac.uk
sean_chorney@sfu.ca