How out-of-field mathematics teachers can be more ‘flamboyant’

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Flamboyance: Teaching maths out of the box

“[They] were not qualified to teach it, did not have stories to tell students and did not personally identify with the subject and so lacked confidence and ‘flamboyance’ in their teaching,” says Dr Linda Hobbs.

Almost four out of 10 educators teaching high-school mathematics (years 7 to 10 inclusive) in Australia aren’t qualified to do so, according to the Australian Council of Educational Research.

It’s often cited as a reason for Australian students’ mostly declining maths scores in the Program for International Student Assessments (PISA) ranking. And, with fewer senior high school students tackling harder maths subjects, concern is growing about fewer of them going onto university maths. It might follow then, there’ll be fewer maths graduates. So, how will this bode for Australia’s productivity if we fall short of the science, technology, engineering and maths (STEM) graduates we need to turbo-boost future innovation?

Sounds like I’m blaming out-of-field maths teachers for not doing a good job and therefore short-circuiting Australia’s future economy.

But, that whole line of thought above isn’t quite evidence-backed. There’s no clear link between student achievement and teacher qualifications, says Dr Linda Hobbs, an associate professor at Deakin University in Geelong, Victoria, Australia. A key research interest for her is out-of-field teaching, particularly in STEM subjects.

“Years teaching can actually be a more important predictor of the quality of learning outcomes in maths,” says Hobbs.

So, let’s flip the idea that out-of-field teaching is the root of all evil.

Rather than talk about those teachers’ supposed deficits in maths training and perspectives they’re lugging into their classrooms, let’s focus on what they do bring to their learners.

They’re still qualified teachers, after all.

What all good teachers bring to the table

Hobbs shared with me her comprehensive list of the skills and dispositions teachers bring to their profession, no matter what subject they’re tasked with teaching and their qualifications. Here it is with a couple of extras I’ve humbly added:

  • Adaptability
  • Thinking skills
  • Can learn content
  • Flexibility with knowledge — they can make connections as well as between general education units and curriculum units. They can also find links between what’s known (background) and the teaching-out-of-field subject (common areas)
  • Can reflect, learn and be innovative
  • Open-mindedness, initiative, innovative
  • They learn on the job and use what they know then start building upon it
  • Problem-solving ability — they know not to bring just a problem to their manager, but a bank of solutions to kick-start a discussion about options, too
  • Reflection on their practice, interrogate/audit it to identify news skills they need to develop
  • Know how to find resources
  • Negotiation skills
  • Risk-taking (in a good way!)
  • Teamwork mentality
  • Can develop relationships and understand their success as a teacher hinges upon strong professional working relationships with their peers, senior leaders, and of course, their students
  • Strong general teaching skills
  • Communication skills — verbal, written, listening, writing, etc
  • A great observer of children and able to check in constantly about their learning
  • Student behaviour management strategies, tactics and skills, which they’re constantly testing and finessing
  • Multitasking — able to juggle different tasks such as instruction, managing students’ behaviours, thinking on their feet simultaneously. Teachers actually make about 1,500 decisions a day, according to Edutopia
  • Have practical skills grounded in theory — evidence-based and evidence-informed, and
  • As minimum, real-life numeracy skills.

At the crux: Subject expertise and how to teach it

There’s plenty in that list, but here are two more huge ones:

  • Subject content knowledge, and
  • Pedagogical content knowledge.

In short, out-of-field teachers know the subjects they’re trained to teach and the teaching practices that emerge from those disciplines to make that learning — and knowledge — stick.

They’re bringing a hell of a lot to the table. So, is it fair just to focus on them not necessarily knowing mathematics or how to teach it when they’re assigned maths classes?

Focus on discipline approaches

Global Teacher finalist Yasodai Selvakumaran agrees sometimes teaching out-of-field is treated as a deficit. She talks about each subject having specific teaching methods and its own key concepts.

“That should be used as a strength,” she told me, for a story I wrote for the LeadershipED magazine.

She’s relieved as a headteacher (teaching and learning) at Rooty Hill High School in Western Sydney, Australia, Selvakumaran has also been a Teacher Ambassador for the NSW Department of Education. After a decade in the classroom, she’s taking a sabbatical, currently based in Canada.

She talks about the need to ensure discipline approaches are kept true.

“Without that, we’re not getting to what Professor Lee Schulman talks about in his signature pedagogies’ approach … the deep knowledge ways of doing, knowing and being in subjects. If we don’t allow that, then our students aren’t going to get access to the highest quality education they can have.”

Let’s take a moment to ponder this. So, it sounds like non-maths-qualified teachers have quite a gap in ‘doing, knowing and being’ to bridge. Gulp.

So, is Selvakumaran at the helm of a maths faculty or does she teach maths out-of-field?

Actually, no, but by inhabiting a different faculty — humanities — she’s able to shine a light from that particular perspective. For example, the subject of history has a strong theme of contestability. You’ll see that where there can be different interpretations about a historical person, concept or event.

At her own school, Selvakumaran and her team have been keen to ensure out-of-field humanities’ teachers became competent in the ‘signature pedagogies’ within those subjects. But, that word ‘signature’ rankled with them.

Once they started talking about ‘subject-based teaching and learning practice’, it had more meaning and gained traction. The out-of-field teachers were on track to develop their subject expertise and build an appreciation for the subject culture. Her school actually encouraged these teachers to use their professional judgement to “adapt, own and develop their subject culture in their own classroom”.

So, once teachers do this intellectual work, they have a mental framework that could technically allow them to teach subjects beyond their qualification areas. The process also gives them further insights into the subject-based teaching and learning practices of the areas in which they’re trained. When I spoke to Selvakumaran in late 2019, the process had been going on for more than a year and wasn’t quite finished yet. It definitely takes time.

It sounds to me like out-of-field teachers at Rooty Hill are welcomed with open arms into the faculties in which they teach. It’s not one-off professional development, but a sense they’re being continually nurtured.

Collaboration as a hinge for greater things

Consider if teachers could pace themselves through this process solo?

Possibly, but perhaps it would be more powerful if they do it through collaborative professionalism. That’s what Andy Hargreaves talks about in the book he co-authored with Michael T O’Connor, Collaborative Professionalism: When Teaching Together Means Learning For All. Here’s a 24-page summary they wrote about it for a seminar, by the way.

They didn’t coin the term, but unpack how it differs from professional collaboration.

“Professional collaboration is a descriptive term referring to how teachers collaborate together, in one way or another, here or there, [but] collaborative professionalism is prescriptive. It is about how to collaborate more deeply, in ways that achieve a greater impact.”

I’d posit that Selvakumaran and her colleagues at Rooty Hill High took a collaborative professionalism approach. The impacts their collaboration across the school delivers are more effective teachers who pivot off their qualifications. They do this by connecting their understanding of subject content knowledge and pedagogical content knowledge from their qualification areas to new disciplines. In so doing, they develop more competence as out-of-field teachers.

Sadly, what they’re doing isn’t the norm in schools across Australia. And that’s been my experience as an out-of-field but enthusiastic casual maths teacher. In fact, usually, when I asked to join a professional development session at a school where I’ve worked, I was strongly discouraged from attending. That’s even when I said I’d be happy to do so in my own time, so they’d be no charge to the school.

Often out-of-field teachers are left to fend for themselves on many fronts, particularly if they’re in casual, relief and temporary roles. They can lack a supportive environment to start building and finessing that bridge from their subject specialities to those in which they’re expected to teach.

Selvakumarian’s mentor in her school’s excellent work in supporting all of its teachers is Deakin University’s Associate Professor Hobbs. And there’s a lot more to this research area.

Confidence to teach a subject out-of-field

Hobbs wrote in a peer-reviewed journal article highlighting teachers who didn’t have a background in the subject they were teaching.

“[They] were not qualified to teach it, did not have stories to tell students and did not personally identify with the subject and so lacked confidence and ‘flamboyance’ in their teaching,” she says.

In her article, Hobbs cites research that shows out-of-field teaching can “compromise ‘teaching competence’ and can disrupt a teacher’s identity, self-efficacy and wellbeing”. It’s a research area that needs more attention to understand teaching out-of-field’s impact on educators’ efficacy and identity.

“When teachers step outside their comfort zone, they risk disruption to how they see themselves as teachers — such is the case for many out-of-field teachers.”

She draws on Beauchamp & Thomas (2009) to delve into what underpins a teacher’s identity:

  • The link between identity and self
  • Emotion’s role in shaping identity
  • The power of stories and discourse to understand identity
  • How reflection shapes identity
  • Identity’s link with agency
  • Geographical context — such as urban or rural/remote/regional — and how it helps or hinders building an identity, as well as
  • The role of initial teacher education programs in creating opportunities to explore new and developing teaching identities.

Constantly morphing teacher identities

Teachers’ self identifies are multi-faceted, kaleidoscopic, and importantly, not fixed.

Take, for example, a specialist primary-school music teacher with 15 years’ experience. Her principal then asked her to move to a Year 6 class to teach maths and science.

“She ended up asking questions about her teaching career. She felt burnt out, not supported and her confidence dropped from being very organised to not knowing what to do in her next class,” says Dr Anna Du Plessis. She’s a senior lecturer in the School of Education and Professional Studies at Griffith University and has completed not one but two PhDs in out-of-field teaching.

Du Plessis shares another anecdote about a successful second-year teacher who was moved from a Year 6 class onto a pre-primary one. That class was experiencing trauma after their previous teacher left the school.

“This highly successful teacher suddenly struggled, had problems with parent relationships and student behavioural issues in an already traumatised kindy classroom,” she says.

In that case, the principal acknowledged the dilemma. The whole leadership team jumped in to support this teacher to recover and experience success again.

These anecdotes about polarising experiences point to an aspect of impermanence and vulnerability of teachers’ professional identities.

Buffering the winds of change

There’s a sense that permanent as well as out-of-field teachers need more of a buffer for their identity to withstand the winds of change in their school. After all, generally in Australia, teachers are hired as ‘teachers’, not necessarily a teacher of a particular subject. If their principal moves them to an out-of-field teaching area, they do it or hunt for another job. It’s a rare teacher who refuses an internal transfer.

So, they can end up teaching out of field even if they’re permanent. Supportive peers and leadership are definitely necessary to help build a robust sense of identity as a teacher, but what can educators themselves do?

Let’s start with the individual teacher. Du Plessis urges out-of-field teachers to find their sense of agency.

“Teachers’ responsibility to manage the situation also should be respected. Teachers need to VOICE their lived experiences and challenges — claim the out-of-field space — and tap into internal expertise, ask for mentors make sure leaders at different levels of leadership know you are teaching outside your qualifications and expertise — ask for the support you need, stay positive for the students in your classroom.

“You became a teacher because you wanted to make a difference — make the difference. We need your VOICE to impact policy development.”

But, for some out-of-field teachers, this move to be an active agent of their circumstances may be too much of a leap. On this, Hobbs offers an adaptability scale for teaching out-of-field — some consider themselves as ‘just filling in’, others are ‘making the most of it’, while the more active ones are ‘pursuing an interest’.

She says teachers in the latter category have:

  • A personal interest
  • High level of self-efficacy
  • Have had positive historical interactions with the subject, and therefore
  • Have expanded their identity to become a teacher of that subject.

It’s not clear if they then call themselves a ‘maths teacher’ because that’s what they teach competently, although they lack qualifications in that area. Perhaps it’s more about uttering, ‘I teach maths’, rather than ‘I’m a maths teacher’. Leave it to the listener to work out the distinction.

Over time, do you become what you teach? What about those who are qualified in a particular area and never teach it? For example, a septuagenarian friend of mine who qualified as a biology and science teacher, but became a social worker for the next 50 years instead. She never describes herself as a biology and science teacher, not even a former one. She has the qualification to ‘acquire’ an identity as a biology and science teacher, but chooses not to use it.

The notion of what constitutes creating a professional teacher identity is intriguing.

Professional teacher identity: becoming what you teach?

Who decides when someone crosses the line from a teacher of mathematics to become a fully-fledged mathematics teacher? Is it the teacher themselves, ie. self-identification, or do they gain that ‘hallow’ from someone else such as a head maths teacher, principal, or years notched as a member of a maths teaching association? Or does a group or community bestow the mantle of a teacher of mathematics to another? I suspect the maths faculty at a high school wouldn't be impressed at those who self-anoint as a maths teacher, particularly without a maths qualification. After all, those years of hard slog studying maths at university should sort count for something.

Teacher identity is a vexed issue. It lacks a definition and a common language. Actually, it’s nebulous and subjective.

That’s according to Lisa Darragh, a lecturer in the Faculty of Education at New Zealand’s University of Auckland. She’s delved into two-decades’ worth of academic literature on teacher identity within mathematics education. In short, theories about identity clashed within the 188 articles she pored over, but she can see a way through. Or two distinct paradigms, as she puts it.

“Identity may be seen as an action and [therefore] fit within a sociological frame or it may be seen as an acquisition, fitting within a psychological framing,” writes Darragh in her 2016 paper.

In other words, you gain an identity through action — doing or performing something, she argues. But performative is really only one way of defining identity, and Darragh lists the domains of:

  • Participative (taking part and engaging in a social group, such as a community of practice)
  • Narrative (some describe this as taking part in master narratives … think ‘being Black’ or more recent movements such as ‘Black Lives Matter’. It’s about the stories people tell about themselves as shaping their identity.)
  • Discursive (this might take a gendered perspective, for example, some academics use Foucauldian analysis to bolster their view maths is constructed as masculine), or
  • Psychoanalytic (this can be a way of deepening or critiquing other more superficial perspectives of identity).

So, above are five different ways of achieving a professional identity, according to Darragh.

And there’s a bonus one — micro-identity, enacted in a moment of time. That was me as a casual out-of-field maths teacher at a high school. When a student asked me if I was a ‘real’ maths teacher, I replied, ‘yes, I teach maths’.

“But is this what you’re supposed to teach? Do you normally teach maths,” she asked, brows furrowing as she seemed to struggle to work out the distinction between her ‘real’ and my implied ‘real’. She lacked the language to ask if I’d studied maths at university (yes I had, briefly, but I’d pulled out of that subject after a few weeks) or if was qualified as a maths teacher (to that, I wasn’t going to lie. I’m not maths qualified).

“Yes, I’m doing a lot of maths shifts at this school,” was my response.

Unsatisfied, she probed for more clarification.

But, I left it there and got on with teaching the class.

When I managed student behaviour well, my classes ran smoothly. I was privy to many mathematical ‘penny dropping’ moments of learning. Once, after taking up my encouragement to wield coloured textas to work out and discuss their maths via the whiteboard, a small group of students returned to their seats glossy-eyed and genuinely quipped, “Miss, I love doing maths like this. I hated it before. You’re a good maths teacher”.

A nice chink in my professional teacher identity, but momentary nonetheless. I’m not a maths teacher. Wanna-be maths teacher is a more apt description.

And that places me in the ‘psychological’ theoretical camp when it comes to defining oneself as a maths teacher, ie not really valid, according to Darragh. So, technically I’m not a ‘real’ maths teacher — just a maths teacher in my head, sometimes, and perhaps, at some indeterminate time in the future, I’ll morph into a ‘real’ one.

‘Real’ maths teachers according to Darragh, are formed through the socio-cultural lens — they do it, they perform it, they are ‘it’ in a context and social grouping.

Darragh writes: “This view of identity keeps in mind the audience at all times as the ultimate identifier and enables us to consider the ways in which power is exerted in this recognition.”

Her work builds on that of Dr Rochelle Gutiérrez, a professor of education at the University of Illinois at Urbana-Champaign. She looks at how identity and power affect maths teaching and learning among different racial, class and language groups.

So, circling back to those, like me, who teach or have taught maths out of field as well as those qualified to do so, there’s something emerging on the horizon. It’s a new framework specifically created for those in regional, rural and remote Australian teaching contexts (aka schools) as a starting point.

My hope is it’s the context for anyone who teaches maths in high schools to be nourished to do so with what Hobbs calls ‘flamboyance’. Both ‘brands’ of teachers may be able to ‘drink’ from the same pool, and be comforted as if basking in warm mineralised waters.

Why the strange water analogies?

The framework is being piloted in the northern NSW town of Moree, under which sits the Great Artesian Basin. Holding an estimated 64,900 cubic kilometres of groundwater, it’s the world’s largest and deepest. So, let’s dive into this promising framework.

Teacher of Mathematics Identity (ToMI) Framework

Researchers at TeachLab at Southern Cross University have developed the Teacher of Mathematics Identity (ToMI) Framework and published a paper about it in a peer-reviewed journal in late 2020.

The ToMI framework places the teacher of mathematics at its core. Because the paper talks about out-of-field teaching of maths as a “common” challenge that lacks a sustainable solution, that convinces me it brings into the fold qualified and unqualified teachers of maths.

This is how the framework looks on the ground.

Teachers of maths’ interaction with leadership, other staff and students would happen within a ‘community of practice’. And that community sits in a local rural/regional/remote school context that the professional organisation supports. Teacher identity is built through a set of capabilities, developed attitudes and perceptions, specialist knowledge and skills, and participation within a professional community.

The researchers spell out factors that nurture that identity including:

  • The negotiated experience of self
  • A learning journey … or trajectory
  • Various forms of membership within a single identity
  • Member of a community, and
  • (Assumed) participation in local and global contexts.

It’s a dynamic way of looking at identity formation and maintenance taking in internalised and externalised processes. A continuum. I like the notion of linking locally and possibly globally through one’s (outwardly) affirmed identity.

They describe ToMI as a framework to identify systemic challenges and offer adaptive solutions. It’s not one-size-fits-all, but nuanced to the local/regional context. It derives power from these dimensions:

  • Addresses the localised challenges that teachers in rural, remote and regional communities face
  • (In the future) creates interconnected collaborative networks for teachers of mathematics to help them foster their professional network
  • Offers professional learning opportunities
  • Gives systematic feedback
  • Creates support regimes, and
  • Mentoring.

In short, a professional affiliate organisation will support these teachers of mathematics’ community of practice. The researchers talk about important elements also include leadership and the local (educational) system context.

But, what does leadership mean here? The researchers talk about three dimensions:

  • Senior leaders within a school including head maths teachers and principals
  • Educational district heads
  • Educational policymakers.

It’s so new, they’ve only just started a longitudinal study to set it up. The research team has the backing of a professional organisation — the Mathematical Association of NSW (MANSW). Over time, that association will morph from an ‘outside-system’ element to one that is embedded at all levels of interaction. It will work the same way as medical training colleges prepare and support their student fraternity to enter medical practice.

Let’s sidestep here into the world of medical doctors. Knowledge doubles every 73 days just during their training. That’s why they’ve come up with a better system than just pacing people through medical degrees in isolation, then unleashing them into the field. Would-be doctors need to cross-fertilise, so to speak, with industry as well as medical settings and build their networks to keep abreast of that new knowledge while they’re in training.

But, what about maths? Despite many mathematical theorems nudging hundreds if not thousands of years old, the half-life of mathematical knowledge is 9.17 years. That’s the time it takes before half the knowledge or facts become obsolete. Balance that with what pre-service teachers hear from their professors at university — don’t use an academic reference that’s more than five years old. Certainly, research into pedagogical theories tends to take a faster knowledge trajectory than the discipline of mathematics.

Throw into the mix that teachers of mathematics are transient, particularly in rural, regional and remote Australia. And those researchers nudging the ToMI framework along in its pilot Moree site, have acknowledged they’ll need to keep “re-configuring and retheorising” it.

Adaptive is its middle name — that’s the only way they can ensure their agile framework creates a legacy.

And, not just for mathematics. The Southern Cross University researchers see the potential for their framework to be applied to STEM and other teaching disciplines. Flamboyance in action, fingers’ crossed.

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Education writer MTeach|GradDip Comm Mgmt |BA Journalism

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