The transition to equitable grouping practices in junior secondary mathematics classrooms

Most New Zealand secondary mathematics classes are organised in ways that group students with relatively similar achievement. However, contrary to beliefs that these grouping practices improve achievement, ‘ability grouping’ exacerbates existing achievement differences. Māori, Pāsifika, and low-SES students are over-represented in ‘bottom’ classes which frequently experience a limited and limiting curriculum. Despite strong evidence for the benefits of mixed ability grouping, few secondary schools have shifted their achievement grouping practices. This qualitative study involves three mathematics departments which took the unusual step of independently self-initiating reduced use of ‘ability grouping’. Utilizing co-generative dialogues, the teachers share and critically reflect on the rationale, expectations, and ongoing adaptations of classroom routines, pedagogies, and student learning outcomes associated with the transition process.   

Research Team: Professor Glenda Anthony and Dr David Pomeroy (University of Canterbury)

Funding: Woolf Fisher Trust and Massey University (CeRME) and University of Canterbury

 

Developing Mathematical Inquiry Communities

This project explores how culturally responsive pedagogy influences the mathematical disposition and achievement outcomes of diverse learners (Māori and Pāsifika nations students) in high poverty areas in urban Auckland. We investigate how attending to culture, language, and identity affects the construction of mathematical dispositions and how the elements of ambitious or inquiry teaching support students developing rich mathematical understandings. Using classroom data we examine the role of mentors working with teachers to co-construct mathematical inquiry communities and explore how this is achieved in culturally responsive ways.

Research team: Associate Professor Roberta Hunter, Dr Jodie Hunter, Trevor Bills, Generosa Leach, Professor Glenda Anthony

Video resource outputs: see the NZ Maths website.

A series of 14 videos featuring the Developing Mathematical Inquiry Communities - Hangaia te Urupounamu Pāngarau Mō Tātou is available on the Education Counts website.

Funding: New Zealand Ministry of Education

Teacher knowledge in early algebra

This project involves an international comparative study of UK and NZ primary teachers' mathematical and pedagogical content knowledge of the equal sign. This includes an investigation of (i) teachers’ conceptions of equality and use of relational thinking, (ii) awareness of students’ potential responses to equality tasks, and (iii) awareness of students’ developmental understanding of the equal sign and associated teaching strategies. Questionnaires are used with both teachers and students to investigate their understanding in this area.

Principal investigator: Dr Jodie Hunter

Collaborator: Dr Ian Jones, Loughborough University

Funding: Massey University International Visitor Research Fund

 

 

Mathematics Anxiety

Our work on mathematics anxiety builds from the research finding that, for twenty percent of the population, mathematics triggers fear, frustration and panic. In classrooms these emotions lead to students’ avoidance of mathematics classes and initiate negative conceptions of mathematical abilities and identities. Our work is investigating the link between negative emotions and students’ mathematical learning. Using classroom data, we have been developing a theoretical explanation for why mathematics anxiety develops.

Principal investigator: Professor Margaret Walshaw

Collaborators: Wolff-Michael Roth, Lansdowne Professor, Applied Cognitive Science, University of Victoria, Victoria, Canada; Shane Harvey, Psychology Clinic Director, Massey University, New Zealand

Co-teaching to support pedagogical shifts to raise achievement in mathematics

This 18-month project aims to investigate how teachers might collaborate in ways that can support them to promote the mathematics learning of students who are at risk of underachievement. It involves implementing and further developing a model of collaborative inquiry for teachers which involves the co-teaching of mathematics lessons as a core component. Key outcomes of the project are expected to include design principles and associated tools for an adaptive model of collaborative teacher inquiry aimed at strengthening teachers’ knowledge for mathematics teaching as a lever for improving the impact of teaching/learning practice on student learning.

 

Principal investigator: Raewyn Eden

Collaborators: Nicki Read and Sally Hunter (Newtown School), Jeannette Gubb (Berhampore School), Hannah Steele (Brooklyn School), Gillian Kissling (Cognition Education Ltd), Associate Professor Joanna Higgins (Victoria University of Wellington)

Funding: Ministry of Education – Teacher-led Innovation Fund

 

 

Outputs:

 

Doctoral Studies

Mary Rahiti

Optimal practices for effective school leadership in implementing evidence based mathematics professional learning and development: New Zealand education has many evidence based projects designed to meet needs across the school curriculum. These PLD projects are available to schools to select from as determined by the needs of their learners. At the forefront of the selection and implementation process are school leadership. This project will focus on the optimal practices for effective school leadership in implementing evidence based projcts. The key focus will be on the factors that influence the success of one such PLD projects: Developing Mathematical Inquiry Communities.

 

Melinda Dixon

Community building of culturally contextualised tasks: Designing mathematical tasks that are situated within real-life contexts has been shown to support students in understanding and engaging with mathematical content. This can be challenging for teachers when they are unfamiliar with the cultures and world views of their students. This study uses participant action research and qualitative methods to deliver professional learning to teachers on designing culturally contextualised tasks and evaluate subsequent changes in students' mathematical identities and dispositions.

 

Generosa Leach

Positioning and status within a community of learners: This study aims to investigate the ways in which students are positioned for agentic participation in mathematics problem solving. Positioning theory offers a lens through which to examine how students’ participation may be developed in ways that make possible meaningful contribution to group activity. Based on the hypothesis that if students are participating they are learning, and when status is equal, everyone learns; individual case studies will be used to investigate the following questions: How does student positioning or status change over time? What do teachers do to (re)position students? How does repositioning change students’ outcomes in participation and achievement?
 

Julie Whyte

Mathematics Anxiety: Reducing the Fear Factor: This research investigates the mathematical experiences of primary teachers through a large-scale survey. It then seeks to deepen understanding of those experiences through interviews with teachers who have had negative mathematics experiences. The study has its genesis in the researcher’s own observations and knowledge of primary teachers’ conceptions of and experiences with mathematics.

Masters Studies

Trevor Bills (2019 - 2020)

Critical pedagogy, a pedagogy of discomfort: Challenges and tensions for teachers: This case study will explore the internal tensions and external challenges that teachers face when introducing a critical pedagogical approach to the teaching of mathematics and examine what support teachers need to be able to achieve this. Teacher interviews and diaries along with in classroom observations will be used to investigate what teacher actions support student learning through critical mathematics as well as any dissonance this may create when trying to balance curriculum requirements.

 

Bronwyn Gibbs (2019 - 2020)

Developing functional thinking through culturally located tasks: This design research study aims to explore how mathematical tasks embedded in children's cultural lives support Maori and Pasifika learners to develop their conceptual understanding of functional relationships. The research looks at the representations students use when engaging with conceptual functional tasks, and how Maori and Pasifika students generalise culturally located tasks involving functions.

 

Andrew Johnson (2019 - 2020)

Factors affecting students' mindsets towards mathematics and their ability to learn from mistakes: This case study examines factors such as classroom culture, task, whanau beliefs, and teacher interactions to see what influence these have on student mindsets towards mathematics and their ability to learn from mistakes. A series of open-ended mathematical tasks are to be recorded and student responses to mistakes analysed. Student interviews are also used to inform the study and evaluate the factors that lend themselves to positive or negative mindsets towards mathematics.

 

Megan Kanz (2019)

Teacher judgement of students' conceptual understanding in mathematics: This design research study looks at how teachers can be supported to make judgements on students developing conceptual understandings in mathematics. The project involves iterations of collaborative planning to build collective understanding, teaching/learning, and assessment using open tasks in two areas of mathematics. Teacher interviews are used to inform the study and evaluate the factors that support or hinder teachers as they make judgements.  

 

Jenna Hatch (2019-2020)

Catering for diverse learning needs in Intermediate level maths: Exploratory case studies of three Intermediate schools will explore the variety of ways schools and teachers provide differentiated opportunities for students to lean mathematics. Bounded cases will include schools that use in-class 'ability' grouping, mixed attainment grouping, and/or teach within ILE.  

 

Maree Logan (2018)

Learning mathematics in an Innovative Learning Environment: This exploratory case study examines the opportunities afforded to Year 7 and 8 students to learn mathematics in a newly-formed Innovative Learning Environment (ILE). Teacher interviews, classroom observations and student focus group discussions will explore classroom organisational structures and students' perceptions of their opportunities for learning mathematics.
 

Fiona Rice (2018-19)

Learning to learn in a mathematical community of inquiry: This research asks, "What can co-generative dialogues reveal about students' experiences within mathematical communities of inquiry?" The research is particularly interested in the identification of benefits or barriers to learning mathematics and the development of student agency as the learning environment shifts towards a more collaborative approach.
 

 

Professional Inquiry

2019

Giichi Oyanagi: Interviews with a group of primary and group of secondary teachers to explore there perceptions around the role of basic facts in learning mathematics 

Jane McLeod: Teachers' perspectives on using materials to build mathematical understanding in a Montessori setting

Amy Thomas: Considerations that teachers make when assessing students in mathematics

Eva Cornforth: Engagement of priority learners in STEM

Suzanne Taylor: Dynamic mentoring as a professiona practice across schools, mentoring for mathematical inquiry

 

 

Learning the work of ambitious mathematics teaching

This project explores how practice-based pedagogies within initial teacher education can support prospective teachers to learn the work of ambitious mathematics teaching. Underpinned by the belief that all students can develop positive mathematical identities and become powerful mathematical learners, ambitious mathematics teaching involves skilled ways of eliciting and responding to students so that they learn worthwhile mathematics and come to view themselves as competent mathematicians. Coaching of instructional activities within a rehearsal format, both in the university and school setting, alongside the development of peer communities of inquiry are central to the design.

Download the final summary report

Research team: Professor Glenda Anthony, A/Professor R Hunter, Dr J Hunter, Dr P Rawlins

Collaborators: Dr Robin Averill, Dr Michael Drake, Dr D Anderson (Victoria University)

International advisor: Professor Elham Kazemi, Washington State University, USA

Funding: NZCER Teaching and Learning Research Initiative

 

Publications:

Final TLRI report

Anthony, G., & Hunter, R. (2012). (Re)thinking and (re)forming initial mathematics teacher education New Zealand Journal of Educational Studies, 47(1), 145-151.

Anthony, G., Hunter, J., & Hunter, R. (2015). Learning to professionally notice students' mathematical thinking through rehearsal activities. Mathematics Teacher Education & Development, 17(2), 7-24.

Anthony, G., Hunter, J., & Hunter, R. (2015). Prospective teachers development of adaptive expertise. Teaching and Teacher Education, 49, 108-117.

Anthony, G., Hunter, R., Hunter, J., & Duncan, S. (2015). How ambitious is "ambitious mathematics teaching"? Set: Research Information for Teachers, 2, 45-52.

Averill, R., Anderson, D., & Drake, M. (2015). Developing culturally responsive teaching through professional noticing within teacher educator modelling. Mathematics Teacher Education and Development, 17(2), 64-83.

Averill, R., Drake, M., Anderson, D., & Anthony, G. (2016). The use of questions within in-the-moment coaching in initial mathematics teacher education: enhancing participation, reflection, and co-construction in rehearsals of practice. Asia-Pacific Journal of Teacher Education, 1-18. doi:10.1080/1359866X.2016.1169503

Drake, M. (2016). Learning to coach in practice-based teacher education: A self-study Studying Teacher Education.

Hunter, J., Anthony, G., & Hunter, R. (2015). Exploring and critiquing practice-based approaches in teacher education Mathematics Teacher Education & Development, 17(2), 1-6.

Hunter, R., Hunter, J., & Anthony, G. (2013). Using instructional activities to learn the work of ambitious mathematics in pre-service teacher educator settings. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia) (pp. 703-706). Melbourne, VIC: MERGA.

 

The effects of structural changes on teacher educators

Our project explores how structural and policy changes influence teacher education practices ‘on the ground’ at two distinct sites: Massey University and Manchester Metropolitan University, UK. The project investigates teachers’ differential responses to structural and policy change. It represents theoretical development, providing an explanation for the implementation of new policy. The project is also a political contribution, allowing an understanding of change processes around teacher education and through the findings from the two sites, providing suggestions for change.

Principal investigator: Professor Margaret Walshaw

Collaborator: Professor Tony Brown, Manchester Metropolitan University, United Kingdom<

Funding: Massey University International Visitor Research Fund

Theory meets method in mathematics education research

This project is about ideas and different ways of theorizing and analyzing mathematics education. It explores the fundamental philosophical tenets underpinning key theoretical frameworks and investigates how these tenets map onto particular kinds of research practice in mathematics education research. Our focus is on six key philosophical sources, namely Vygotsky, Foucault, Lacan, Deleuze, Latour, and Braidotti. Insights from these theorists provide the means for reflecting on classroom data gathered from two year 9 mathematics classrooms—one in New Zealand and the other in United States.

Principal investigator: Professor Margaret Walshaw

Collaborator: Professor Elizabeth de Freitas, Department of Curriculum and Instruction, Adelphi University, New York

Funding: Massey University International Visitor Research Fund

Recently Completed Postgraduate Projects

Professional Inquiries (2016)

Frances Gasson

"In my hands I can tell my words properly": This inquiry investigates the use of sign language to facilitate mathematical talk and reveal mathematical thinking within communities of mathematical inquiry.

Mary-Anne Judd

A whānau perspective: This inquiry uses a Kaupapa Maori research approach to investigate how whanau and teachers can engage productively together to support mathematical learning for under-achieving learners.

Jo Knox

Am I "good" at maths? This study examines what factors serve to shape students’ perceptions of what being “good” at mathematics means and how these factors may contribute towards students’ self-efficacies and mindsets in mathematics.

Professional Inquiries (2017)

Leo Frank

Leadership approaches that support primary teachers to use a problem solving approach for mathematics.

Lisa Heap

Professional learning post-formal professional development.

Jessica MacCarthy

Primary school students' experiences of mathematics.

Professional Inquiries (2018)

Melissa Absolum

Teacher actions that position students to successfully participate in mathematical inquiry communities

Melissa Coton 

Factors that struggling students identify as supporting them to re-engage (or 'positively engage') with mathematics learning

Louise Fitzgerald

Changes in teachers’ beliefs about grouping practices through involvement in professional learning related to developing mathematical inquiry communities

Helen Maxey

Integration of financial literacy in primary school curricula

Raeleen Simpson

Strategies that teachers use to provide opportunities for diverse students (Pāsifika and Māori students) to participate equitably in mathematics

Masters Thesis (2016)

Kat Freeman

Enacting Challenging Tasks: Maximising Opportunities for Students’ Mathematical Learning: This study worked with three year 7 and 8 teachers to explore pedagogical approaches that would maximise opportunities for students to engage with and learn from challenging mathematics tasks. The learning opportunities afforded by the task enactment and the role of teacher planning, and the extent to which the mathematical ideas inherent in tasks were explicitly addressed. Through case studies across three tasks, the study highlighted the importance of teacher planning, noticing and monitoring of mathematical activity, and sequencing of student presentation in ways that supported the development of a generalised solution.

Masters Thesis (2017)

Rosemary Curwen

How does cultural identity shape how Pāsifika students view themselves as mathematicians?  There is an urgent need to address the continual underachievement and disengagement of Pāsifika students. Current educational practices are not effectively addresing the different cultural needs of Pāsifika learners. By interviewing high-achieving Year 8 Pāsifika students and their teachers, this research aimed to explored the affordances for students to develop strong cultural identities and mathematical dispositions.

Jenna Crowley

Impact of teacher collaborative planning in mathematics: This case study research investigated teachers' experiences of collaborative planning for mathematics problem-solving lessons, using planning practices based on the work of Smith, Hughes, Engle, and Stein (2009). The research interest was in the experiences and perceived outcomes of teachers as they planned collaboratively.

Julia Hill

What do culturally diverse middle school students value for their mathematics learning?  Achievement goals are an integral component of our learning experience; they guide our behaviour to achieve desired outcomes and avoid undesired outcomes. This research aimed to better understand the mathematical goals, aspirations and motivatinos of a group of culturally diverse learners in middle school. The results o this study may assist middle school teachers to positively influence student motivation and mathematics achievement. Click here to read a summary of the findings of this research.

Lee Mann

Math is a four-letter word: Unpacking anxiety in mathematics classrooms. For some students, mathematics generates intense fear, frustration and feelings of anxiety. These effects emerge as early as the first year of schooling and often retain their group throughout the year levels. This study used questionnaires and interviews to explore the prevalence of mathematics anxiety (including mathematics learning anxiety and mathematics test anxiety) in year 9 secondary school students in one geographic region of New Zealand. Click here to read a summary of the findings of this research.

Masters Thesis (2018)

Libby Cunningham

Culturally responsive tasks and Pasifika students' engagement in mathematics: This case study involves developing mathematics learning tasks that build on Pāsifika students' and families' cultural funds of knowledge. Tasks are designed around this cultural knowledge and photographs that students have shared to document their out-of-school mathematical experiences. Student interviews and observations are used to investigate students' engagement when working on these culturally responsive tasks in their mathematics classroom.

Doctoral Thesis (2016)

Margaret Crawford

Acceleration and Gifted Girls: The research investigates acceleration as an intervention in secondary education within girls’ schools in New Zealand. It explains the extent that mathematics is used as an accelerated subject and for whom it is used. A national survey of girls’ schools which offer secondary education provided information on schools’ provisions for gifted girls, and case studies of three schools which offer acceleration as an intervention were designed to reveal the perceptions and experiences of teachers, students, and parents/caregivers.

Doctoral Thesis (2018)

Zaenal Abidin

Online community of Practice: Leveraging information and communication technology for reflective practice in promoting mathematical practices: Set in the context of Indonesia, this study explores the use of an online community of practice built to foster the process of collaborative teacher learning. The study aims to investigate the use of this on-line community as a way to support teachers in promoting mathematical practices. It uses an action research approach to explore the ways teachers use the on-line communities of practice, and ways that this community can support the integration of technology into the mathematics curriculum in Indonesia.
 

Fatimah Alsaleh

Prospective mathematics teachers’ perceptions of preparedness: Being well prepared and experiencing a sense of preparedness for teaching is a key learning outcome of any teacher education program, with research documenting a positive connection between teachers’ subject matter preparation and teaching quality and student achievement in the classroom. This study explores the perceptions of preservice teachers in their final year of teacher education within a range of Saudi Arabia universities using a mixed-methods methodology.

How should we group students in primary maths classrooms?

Author: 
Professor Glenda Anthony, Professor Roberta Hunter, and Dr Jodie Hunter

Grouping students in maths classrooms based on their ability or prior attainment is a notion that is increasingly being challenged by research. When we have engaged in so-called ‘ability grouping’ practices for so long, why should we think about changing? And what would the change involve?

What do culturally diverse students value for their mathematics learning?

Author: 
Julia Hill (Master of Educational Psychology, 2017)

It is now recognised that mathematics education is value-laden - so it is important for teachers to understand the values that their students hold. This blog post summarises a Master of Education study exploring the values that Māori, Pāsifika, European and Asian students in New Zealand middle schools held in relation to their mathematics learning.