Challenging teacher perceptions of student capabilities (post 3 of 4)

Professor Roberta Hunter, Dr Jodie Hunter, and Professor Glenda Anthony, Massey University

This is post 3 in a four-part series based on a symposium presented by the authors at the American Educational Research Association’s 2018 conference in New York. This symposium was supported by NZARE.

The other posts in this series are:

  • Post 1 – Joining the pieces of the tivaevae to enact strength-based mathematics learning for Pāsifika students in Aotearoa New Zealand
  • Post 2 – Teachers and teacher educators working together in professional learning
  • Post 4 – Student voice: Being Pāsifika in New Zealand mathematics classrooms

The previous post in this series explored the rich, high-challenge/high-support professional development approach used in the Developing Mathematical Inquiry Communities (DMIC) project in Aotearoa New Zealand, highlighting the model’s alignment with Pāsifika values reflected in Maua-Hodges’s (2000) tivaevae model. This post looks more closely at the impact that this professional learning process had on teachers’ views of their students’ capabilities.

In New Zealand, deficit-orientated views of Māori and Pāsifika students, their families, and the communities in which they live, along with the widespread practice of ability grouping, can constrain students’ opportunities to learn and participate within mathematics classrooms. Teachers’ (often unconscious) perceptions of students play out in a range of ways including in expectations for student achievement; students’ assignment to ‘ability’ groups; the feedback provided on student learning; and differential opportunities for students to engage with challenging tasks, to participate in mathematical discourse, and to develop positive mathematical identities.

Tracking changes in teacher perceptions

A major aim of the DMIC project is to transform teachers’ deficit views of Māori and Pāsifika students. One way we measure progress in this area is by analysing teachers’ problem framing – what teachers see as the reasons for student underachievement (diagnostic problem framing) and the solutions or intervention strategies they propose (prognostic problem framing). As part of our research, we asked teachers questions like “Who are the strugglers in your class and why do you think they struggle?” and “How do you support students who experience difficulty in maths?” We then categorised the teachers’ responses as productive, unproductive, or mixed depending on how they explained student performance and whether the teacher viewed particular students as being mathematically capable.

Diagnostic framings

Diagnostic framings are concerned with what the teacher sees as being to blame for student underachievement. These can be productive, unproductive, or mixed.

  • Productive framing: Student performance is described as a relationship between the student and their instruction or opportunity to learn

“Anybody could do maths … I have got children with very little English and children from pretty traumatic backgrounds, and they come in and they believe they can solve the problem as well as anybody else and they give it a go”

  • Unproductive framing: Student performance is attributed to an inherent property of the student or their home or community

“It’s just home life. Pure and simple. It’s those first five years. And the moment we meet the families, we can tell why the child is like they are.”

  • Mixed framing: Some but not all of student performance is framed productively or unproductively, or performance is seen as a combination of factors

“Generally, those children are low in all areas. They have difficult homes that they have come from. Maybe they haven’t had breakfast. Maybe they’ve been up late, they’re tired, they don’t like maths. Their experience[s] of maths aren’t positive. Maths is boring. Maths is repetitive. Maths is pointless.”

Prognostic framings

Teachers’ prognostic framings (how they try to address underachievement) give us insight into how well their current teaching approaches reflect best practice in ‘ambitious mathematics teaching’. These approaches can also be productive, unproductive or mixed.

  • Productive framing: Instructional support for underachieving students is aimed at rigorous learning goals

“I look at three different ways – some kids struggle to explain things – through words or pictures or materials. I don’t care how they explain it as long as it’s in some form. I know a lot of this is based around verbalising and talking.”

  • Unproductive framing: Instructional support for underachieving students is aimed at lessening the cognitive demands of a task

“I’ve usually been a teacher that’s explained a lot and set it up for them just so they can figure it out a lot easier.”

  • Mixed framing: Instructional support is aimed at supporting rigorous mathematical activity, but some teacher actions lesson the cognitive demands

“The constraint around it is that a lot of those kids that are less capable sometimes sit back a lot more and take a bit more. And often they don’t like maths because they’re not good at it, and because they don’t like maths, they then don’t participate in the way that we would like them to – but then you just ask the right question.”

One school, one year

The diagrams below show the shifts we saw in teachers’ problem framings at one school during its first year involved with the DMIC project. Across the school year, all 17 teachers made positive shifts in their prognostic framings of student achievement, increasingly recognising the pedagogical strategies that were most likely to raise student outcomes in mathematics. Most teachers (15/17) also made positive shifts in their diagnostic framings, indicating that they were focusing increasingly on students’ educational experiences and opportunities to learn as explaining their achievement rather than using deficit characterisations.

AERA blog - shifts in one year

Five key levers for change

What prompted these changes in teacher beliefs and understandings? The teacher interview data highlighted five key features of the DMIC professional learning approach.

1.  Making sense of the reasons behind students’ differing achievement
The new teaching practices required within DMIC challenged and stretched teachers’ perceptions of what students could do. Teachers reported that, given different learning opportunities within the new teaching approach, their students were more confident and open-minded, more independent of the teacher, and more purposeful in their mathematics learning.

“I am really surprised when I hear some of the kids I thought were lowies asking good questions or sharing their thinking, really good thinking … I really thought they knew nothing and so I just used to tell them what to do.”

2.  Supporting students in ways that maintained cognitive challenge
The ‘unproductive’ prognostic (intervention strategy) framings involved keeping work simple and removing challenge for struggling students. In contrast, the tasks and pedagogies involved in DMIC were challenging for all students, and, as one teacher noted,

“the mixed ability groups promote the risk taking, questioning and changes in the classroom culture.”

3.  Monitoring ongoing instructional improvement
Teachers were encouraged to shift out of being the ‘explainer’ within the classroom and instead listen more to students’ thinking. Teachers reported surprise at what their students could achieve with the support of others in their group, the stimulus of greater challenge and the permission to take risks. This discovery reinforced the importance of teachers maintaining an ongoing disposition of inquiry:

“I’m listening more. I hope I was listening to them before, but it’s definitely a lot more balanced out [now] with them telling me, teaching me what they know. I’m learning more about their different thought processes and the reasoning behind the maths.”

4.  Developing expertise around cultural responsive pedagogy
Teachers were encouraged to consider how their own and others’ values (e.g., Pāsifika values of family, respect, reciprocity, inclusion, love, leadership, belonging, spirituality, and service) were enacted within their classroom communities. Designing culturally appropriate tasks also required some “hard thinking” and learning on the part of teachers:

“It’s easy to assume we know about culture, and this year I’ve learnt to let the experts—the students in my class—share about their culture, and making it very comfortable for them, and celebrating that they have that knowledge … It’s been a big learning curve; you have to change your mind-set.”

5.  Working as a community of learners
We noticed patterns in the shifts in problem framing for the teachers in each syndicate within the school. This finding could be related to the extensive teacher collaboration involved in DMIC including through shared planning, shared teaching, whole-school professional development, and in-class mentoring, all of which provided valuable opportunities for teachers to be part of a community of learners.


One important indicator of successful reform and improvement in ambitious mathematics teaching is seeing teachers using more productive framings of the ‘problem’ of underachieving students. The findings reported above indicate that the cluster of simultaneous interactions within DMIC (the combination of pedagogical practices, core messages and professional learning opportunities – depicted in the bubbles in the diagram below) supported positive shifts over the school year in teachers’ diagnostic and prognostic framings of student achievement and capability.

AERA cluster of interventions.png

The final post in this series explores what these shifts looked and felt like for the students in these teachers’ classrooms.

Other posts in this 4-part series:

  • Post 1 – Joining the pieces of the tivaevae to enact strength-based mathematics learning for Pāsifika students in Aotearoa New Zealand
  • Post 2 – Teachers and teacher educators working together in professional learning
  • Post 4 – Student voice: Being Pāsifika in New Zealand mathematics classrooms

BobbieRoberta Hunter is a Professor in the Institute of Education at Massey University. She developed her love of maths through watching her Cook Islands mother measuring and making geometric patterns for intricate tivaevae (fabric art) patterns. She originally developed the pedagogical approaches used in the Developing Mathematics Inquiry Communities (DMIC) project for her PhD and since then has overseen implementation of DMIC in low-decile schools across NZ. 

JodieJodie Hunter is a senior lecturer in the Institute of Education at Massey University and teaches papers in the area of Mathematics Education and Pāsifika education. She has previously worked in the area of mathematics education at Plymouth University, UK, and worked in the US as a Fulbright New Zealand Scholar. Jodie’s current research interests include effective mathematics teaching and culturally responsive teaching for Pasifika learners, including within the DMIC project.

Glenda picture 2Glenda Anthony is the co-director of the Massey University Centre for Research in Mathematics Education. Her research interests include effective mathematics teaching and professional learning. Glenda’s current focus on equity of access and participation for students involves research in the Developing Mathematics Inquiry Communities project led by Roberta and Jodie Hunter.



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