Last week I attended the 42nd annual MERGA (Mathematics Education Research Group of Australasia) conference in Perth, Western Australia. What a privilege it was to listen to so many knowledgeable and engaging presentations of current research into mathematics education. The theme for this year’s conference was Mathematics Education Research: Impacting practice, and it was clear the impact on both teachers’ classroom practice and student outcomes that a wide range of the reported studies were having here in Australia and elsewhere across Australasia.
This blog is just a snapshot of some of the paper presentations and keynotes I attended (the conference was over 4 days!). I may write another reflections blog to expand on some of the other sessions I attended, particularly the keynotes by Di Siemon and Paul Cobb. There were a few overarching themes woven through the presentations that frame the current climate of mathematics education research. This is not an exhaustive list, but simply the themes I took away:
Learning trajectories
In the opening keynote, Doug Clements and Julie Sarama shared their seminal research and ongoing development of student learning trajectories in mathematics. Their focus is on creating trajectories from children’s thinking through discovering the meaning students bring to the task. Their curriculum research framework explores the effects and conditions necessary for policy and theory to impact practice. The trajectories provide a developmental path of learning leading to an instructional path of teaching.
Trajectories were also discussed by Jere Confrey (day one’s keynote). Confrey proposed using learning trajectories to personalise and improve maths instruction at scale. A key take away message was in relation to how we view student movement and progression through trajectories. We need to see their journey as more of rock climbing wall than a ladder, where students may move across and back and forth, not just up. This reminded me of Pirie and Kieren’s (1994) model of the growth of mathematical understanding where student development is not linear, but a dynamic, recursive process of “folding back”.
Learning trajectories have an impact on classroom practice when they are explored, as Confrey worded, in a ‘trading zone’, where researchers work with schools to improve and change and adapt the research within learning communities.
What is the right metaphor for learning trajectories? Jere Confrey argues for climbing walls over ladders. #merga42 @tobyrusso @MAWAinc @NumeracyNow @MERGA_maths @attard_c @mav_info @aamtinc @kath_cartwright pic.twitter.com/9ndhaSwpmK
— James Russo (@surfmaths) July 1, 2019
Teacher noticing
Teacher noticing of both teachers’ practice and students’ mathematical thinking was a reoccurring theme across the conference. This type of research involving working with teachers relates to my own research study and this probably indicates why I see it as a theme. Aside from my own personal interest though, it was clear that teacher noticing is becoming more prevalent as a way to conduct research and analyse data. Along with a number of paper presentations, there was also a symposium on teacher noticing over the course of the conference.
Thanks @DJazby for sharing your ideas and research on teacher noticing of mathematical reasoning. How can we redesign tasks to make reasoning cues less subtle. #MERGA42 pic.twitter.com/yhnsypbphM
— katherin cartwright (@kath_cartwright) July 1, 2019
Dan Jazby’s session was of particular interest as he utilises multiple videos and microphones within a specialised classroom at RMIT university. From Jazby’ perspective, it’s about purposefully creating moments to highlight student cues to make the action of teacher noticing proactive more so than a passive process. He explored how to increase teacher noticing of ‘noteworthy’ events to assist in “purposeful deployment of attention” so teachers can position themselves in the right place at the right time to notice.
Teaching noticing and teacher learning “to what things do they attach significance?” David Clarke. Sharing teacher learning mechanisms, what was consolidation and what was new realizations? #MERGA42 pic.twitter.com/kY8SS4qjr9
— katherin cartwright (@kath_cartwright) July 1, 2019
Other sessions also mentioned teacher noticing as part of an approach to reflecting on teacher practice and/or as part of professional learning within the research study. The symposium on teacher noticing was also a great opportunity to share definitions and interpretations of the process. Some questions discussed include: How are we applying the steps of noticing, interpreting and deciding? Where does reflecting fit in? How do the create conditions so that the noticing is active? What role does anticipating play? How can you notice what you don’t know?
Student representations (drawings)
Young children’s representations was the focus of Jennifer Way’s paper presentation and also of the symposium Research methods involving children’s drawings in mathematical contexts. Within Way’s session, she focused on the phases children go through of drawing and representing their ideas and thinking. Way mentioned that drawings are often a personal expression, an extension of self, as a way to represent external objects or as a way express themselves artistically. It is only us, as adults and teachers, who interrupt this process by placing ‘other’ values on these drawings, shifting our expectations to a more mathematical context.
@Way8Jennifer sharing the importance of children’s own drawings and representations of mathematical ideas #MERGA42 pic.twitter.com/hCjIAhwBNH
— katherin cartwright (@kath_cartwright) July 2, 2019
The take away message was that students need help to make connections between their internal and external world as they sharing their thinking through drawings. We need to support and encourage students’ own representations. Validating them as an important phase of development, allowing students to linger longer on their own representations instead of immediately imposing our own models and abstract representations when they begin school.
During the symposium a number of researchers shared their studies that utilised student drawings as evidence of conceptual learning. Amy McDonald highlighted the importance of needing both the visual and oral description of the drawing. We need to stop and listen to capture the student voice, we can only infer from drawing a certain amount, it’s your inference, you need the voice to be sure of what the child is meaning. Jennifer Way mentioned Jennifer Thom’s work and the need for student justification more so than just an explanation of what was drawn. The recording process is really important, it is not just about the product at the end, it is important to record through observation or the use of a digital tool to capture what the student is thinking and doing mathematically. Joanne Mulligan also pointed out the importance of the process of drawing to develop thinking and reasoning.
Reasoning
“We should be supporting and valuing students to write reasoning arguments” Dianne Siemon
So excited to be listening to Rebecca Seah discuss her research on reasoning about symmetry #merga42 @CatholicEdParra @NumeracyNow @MERGA_maths pic.twitter.com/MXazSUZPfE
— Kathryn Salkeld (@SalkeldKathryn) July 1, 2019
Mathematics learning is fundamentally spatial in nature. Number emerges from spatial interaction with the real world. Jo Mulligan #MERGA42
— Bruce Ferrington (@BruceFerrington) July 2, 2019
Evidence for strategy difference on some maths tasks based on spatial ability level - @AForndran_at_UC #MERGA42 pic.twitter.com/w9Lbg24wm6
— SERC at UC (@UC_SERC) July 3, 2019
Reasoning across various aspects of the curriculum were presented, studies involving spatial reasoning in particular were shared by Joanne Mulligan, Rebecca Seah, and also from members of the research team from the university of Canberra (Danielle Harris, Tracy Logan, Tom Lowrie and Alex Forndran). The session I attend was presented by Alex Forndran, their study reported on the links between spatial reasoning and mathematics achievement. Their research raised questions regarding the increasing demand for students to have high spatial reasoning skills as the use of graphical and digital assessments also increase. From their findings, students with high level spatial reasoning skills had more ways to access visual/ spatial tasks and were “better equipped” to engage with novel and graphically rich tasks.
Supporting out-of-field teachers
I did not attend the forum discussing out-of-field teachers but it is a current issue that many educators have opinions about and suggestions for ways forward. To showcase some of these ideas I have included a number of tweets from the symposium that highlight aspects of the discussion.
Our #MERGA42 forum on the issue of out-of-field teaching is underway. pic.twitter.com/9gs50trlF4
— MERGA (@MERGA_maths) July 2, 2019
Our findings from a dozen High Schools show that a lot of out of field teachers are open to content relevant professional learning. An issue we found was limited district capacity to satisfy their specific needs.@MERGA_maths @aamtinc #MERGA42 https://t.co/nDMullTUcK
— Rob Proffitt-White (@robproff1) July 2, 2019
Colleen Vale suggests some potential solutions to the out-of-field maths teacher issue #MERGA42 pic.twitter.com/hWpZVS6Rwk
— AMSI Schools (@AMSIschools) July 2, 2019
In addition to these specific themes there were also excellent presentations about research into: STEM, teacher identity, challenging tasks, pedagogical reasoning, teacher subject matter knowledge, classroom interventions, ambitious instruction, cultural contexts, lesson study, learning communities and co-teaching, just to name a few! If you believe, as I do, that there is a special and important relationship between research and our classroom practice, then I highly recommend attending MERGA (or other international conferences) to learn more about the connection between teachers and researchers. There continues to be more and more research emerging where the teachers are the researchers or are part of a learning community alongside the researchers. Overall it was apparent that we all are aiming towards a common goal – improving the depth and breadth of students’ mathematical thinking.
“It was critical that districts were aiming for students to learn mathematics that was actually worth knowing” Paul Cobb
For further reflections on the conference, search for #MERGA42 on Twitter. To access previous MERGA conference proceedings visit the MERGA website. Becoming a member will also allow you to access other publications.
References
Pirie, S. E., & Kieren, T. E. (1994). Beyond metaphor: Formalising in mathematical understanding within constructivist environments. For the learning of Mathematics, 14(1), 39-43.
