Associate Professor Fiona Ell, University of Auckland
Research in education is sometimes seen as dull, boring, removed from real life, obscure and irrelevant. What is interesting to researchers seems unimportant to educators, while researchers bemoan their perception that teachers don’t pay attention to their findings. This is particularly true in mathematics education internationally, where there is general confusion about what direction to take and what information to attend to. With a curriculum comprising broad two-year goals and no set texts or defined approaches, mathematics teachers in Aotearoa have a lot of scope to find their own way – and the potential to get lost.
Can mathematics education research prove its relevance and provide a map to help?
Mathematics Education as a map
The terrain in the map below is a tongue-in-cheek summary of some of the features of the mathematics education landscape in Aotearoa at the moment.
The cities represent destinations for our ākonga / learners:
- innovation and creativity,
- growth mindset and positive attitudes,
- collaborative skills, and
- a sound grasp of ‘the basics’.
The other geographical features represent some of the key things that teachers and researchers in mathematics education need to ‘visit’ and think about:
- culturally sustaining pedagogy,
- computational thinking,
- digital technologies,
- procedural fluency,
- ability grouping, and
- community perceptions.
Some of these features come from social and policy influences (for example: digital technologies, computational thinking), and some from research findings (for example: ability grouping, procedural fluency).
This is not an exhaustive list, but rather an attempt to exemplify how complex the context is. Teachers are making choices and designing learning experiences in a landscape that is hard to navigate. To stretch the metaphor further, the landscape is dynamic. It changes. Teachers need guidance that is principled and able to be applied in a range of contexts.
What does this have to do with teachers?
Teachers will be very familiar with the terrain of the map above – it’s where they and their learners are exploring. It’s not an easy terrain to navigate, however, and wandering without signage could be hazardous!
Research can help teachers by providing some signposts and then trusting teachers’ ability to find their way. In my experience, teachers are deeply interested in research and what it says about practice. All practice is guided by reasons, or principles, of some sort or other (why we choose to do things the way we do – our ‘theories-in-action’). In mathematics education, teachers want to know what the reasons or principles are that they should follow. They know mathematics is an important learning area for students and they want to do the best they can for their classes.
Texts, professional learning opportunities, colleagues, blogs and curriculum support materials are all sources of principles for mathematics teaching. Research lies behind all of these things. It is unreasonable to expect all individual teachers to engage with research literature on all areas of their practice. Teachers deserve sound messages from research delivered to them in ways that they can use – signposts for navigating, not step-by-step instructions.
I have suggested some ‘signposts’ from research on the map above. These signposts support teachers’ decision making as they find the path to the ‘peak’ of conceptual understanding of mathematics and equitable participation for all. The four clear signposts I see emerging from mathematics education research are:
Others might label these signposts differently, but the key idea is that research can provide signposts that give principled direction to educators’ choices.
What is the role of research and researchers?
So what is our role as mathematics education researchers in helping Aotearoa’s learners become confident and competent users of mathematics, and Aotearoa’s teachers become confident and competent navigators of the changing mathematics learning terrain? We have two responsibilities: one is to provide a ‘treasure chest’ of powerful research findings to inform and guide practice, and the other is to recognise the responsibilities of our role as pathfinders and treasure hunters. Each of these is discussed below.
Filling the treasure chest
The collage below comprises some of the treasures that Aotearoa’s mathematics education researchers have sought and found in recent times. We are privileged to have the Best Evidence Synthesis on effective pedagogy in mathematics / pāngarau and its associated exemplars and materials, the nzmaths website which provides research summaries, and Aotearoa-authored compendiums of research written for teachers. Our researchers are well-known internationally, and projects such as Developing Mathematical Inquiry Communities exemplify how research can positively impact practice and learners’ experiences of mathematics.
Having a sound compass
As researchers, it is easy to forget that we exercise power when we choose what to research. In the same way that teachers’ selection of what to teach frames learners’ experiences of mathematics, what researchers choose to research frames teachers’ (and others’) ideas about what is valuable and how things can or should be done. If we focus on problem solving, or collaboration, or equity, we send important messages to practitioners and policy makers about what they should pay attention to – and we can only supply guidance through the mathematics education landscape for the things that we have researched.
To extend the map metaphor, we can use a compass to give us direction. I suggest that there are six elements to this compass – elements that I see emerging from the treasure chest of work mathematics education researchers are doing in Aotearoa.
- Mathematics education research in Aotearoa should speak to our challenges and aspirations and explore international findings in our particular context, so that we can choose wisely rather than borrowing overseas approaches wholesale without considering the significance of our setting.
- We need to be signpost-creators, helping practice communities navigate the mathematics education landscape by being clear about key principles for practice that arise from research.
- Taking opportunities to communicate and participate in public debate using our knowledge will help us be clear and be heard.
- Research choices in education are imbued with power and surrounded by politics – recognising that our work is not neutral is a first step to attending to these dimensions in the ways that we work with people, share our findings and adapt our practice.
- Findings from our local context can have global impact – it is important to recognise how our research can help mathematics education around the world.
- Finally, being clear about our theoretical frameworks and how these shape our questions and our methods is important for responsible treasure hunting. The questions we find interesting and the ways we seek answers shape what is found and what is discussed, so we need to be transparent about our frameworks and their implications.
Research has more impact than we realise. Educators seek research evidence to help them make and sustain changes in practice. Seeking mathematics education treasure and sharing it with research and practice communities is a valuable contribution to improving mathematics learning and teaching in Aotearoa.
This post is based on Dr Ell’s keynote address at the first meeting of NZARE’s new Mathematics and Statistics / Pāngarau Education special interest group in February 2019.
The graphics in this blog were drawn and compiled by Megan Clune and are reproduced by permission. Thank you, Megan!
Dr Fiona Ell is the Associate Dean of Initial Teacher Education at the Faculty of Education and Social Work, University of Auckland. Her research work focuses on how people learn to teach and school improvement, both with an emphasis on improving outcomes for marginalised learners.