Peter Sullivan

• PhD
• Professor Emeritus at Monash University (Australia)

The different contributions offered in this paper are intended to prompt discussion in schools about ways of communicating with students about learning processes and some ways in which their learning will be assessed.

Traditionally Australian primary school teachers have been viewed as generalists responsible for instruction across all content areas. Adopting self-determination theory as a lens, the aim of the study was to explore the extent to which generalist primary school teachers are interested in becoming subject matter specialists. Questionnaire data were...

The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their participation in a professional learning project. Findings suggest that teachers’: view prompts as important whe...

Just as students experience productive struggle or spend time in the ‘zone of confusion’ when engaging with challenging tasks, teachers also experience similar difficulties and periods of confusion when engaging with new pedagogical approaches. Prior to a 19-week lockdown due to Coronavirus (COVID-19) during 2020, two Foundation teachers implemente...

In this article, educational and psychological perspectives are used to examine how anxiety and uncertainty in the mathematics classroom can be reframed to benefit mathematical teaching and learning. Links between anxiety and uncertainty are discussed and from this discussion, two methods are proposed for reducing the negative impact of mathematics...

Insights into aspects of teachers’ planning reported here were gathered as part of a broader project examining aspects of the implementation of the Australian curriculum in mathematics. In particular, responses of teachers to a survey of various aspects of decisions that inform their planning are discussed. While there is diversity in processes tea...

All students should have access to learning experiences that help them make sense of important mathematical concepts. This study highlights teacher actions for consolidating student learning during teacher-lead discussion in the early years. We report on a case study of a Year 1 teacher involving a lesson observation. Highlights of the lesson inclu...

In this article, three of David Clarke’s long time collaborators offer perspectives on how David shaped and continued to influence projects in which they were involved, over a 30 year period. The three sections of the article focus on David’s contributions to original research on high stakes assessment, research on the development and use of assess...

In this article, the authors from Monash University and the University of Sydney have collaborated to present a research-informed model to support the planning and teaching of mathematics, using a student centred structured inquiry approach.

The purpose of this article is to consider the connections between teaching with challenging tasks and the 10 High Impact Teaching Strategies (H.I.T.S.) identified by the Victorian Department of Education and Training. We are often asked the question by Victorian teachers when providing professional learning around teaching with challenging tasks,...

Despite the construct of challenge being recognized as an essential element of mathematics instruction, concerns have been raised about whether such approaches benefit students with diverse academic needs. In this article, we focus on the beliefs and instructional practices of teachers teaching students in the first three years of school (5 to 8 ye...

Despite teacher enjoyment of teaching being associated with a range of benefits for teachers and their students, little research exploring the characteristics of teachers who enjoy teaching mathematics exists. Semi-structured interviews were conducted with ten teachers who scored in the top third in terms of their enjoyment of teaching mathematics...

Given what is known about the importance of productive struggle for supporting student learning of mathematics at all levels, the current study sought to examine teacher attitudes towards student struggle when students learn mathematics in remote learning settings compared with classroom settings. Eighty-two Australian early years primary teachers...

Teacher reluctance to teach mathematics through challenging tasks is frequently linked to beliefs that such approaches are not appropriate for students perceived as less mathematically capable. One potential means of shifting such beliefs is inviting teachers to reflect on students that surprise them when working on such tasks. Early years' primary...

The fear of making mistakes and avoidance of risks can create disabling anxiety and limit learning opportunities. The team from Monash University and the University of Sydney describe the features of learning environments which increase enjoyment and engagement of students who experience anxiety.

Australian schools, like schools elsewhere, have been through a period of closure. The closure creates both threats and opportunities for teachers and students. In the context of a project exploring approaches to teaching in early years, we outline some considerations and offer advice to teachers and educators on strategies for welcoming students b...

Teaching assistants are not always utilised effectively in mathematics classrooms. Moreover, there is limited research examining instructional models that might more meaningfully incorporate teaching assistants into the teaching and learning of mathematics. To address this gap in the literature, the current study explored three distinct teacher-tut...

It is possible that learning from home during the COVID-19 lock down can be productive especially if teachers developed mathematical learning experiences that challenge student thinking. But it is also possible that time away from school might have exacerbated differences in learning opportunities. This article explores ways to reengage students wh...

Reform-oriented approaches to mathematics instruction view struggle as critical to learning; however, research suggests many teachers resist providing opportunities for students to struggle. Ninety-three early-years Australian elementary teachers completed a questionnaire about their understanding of the role of struggle in the mathematics classroo...

This chapter uses the notion of relentless consistency, elaborated by Laurinda Brown, to describe an approach to teaching mathematics we are researching. A fundamental assumption is that students learn better and engage actively when tasks on which they are working on are more rather than less challenging. The article describes how challenge is con...

In this study we explored the relationship between teacher enjoyment of teaching mathematics, their attitudes towards student struggle, and the amount of time teachers spent teaching mathematics. Ninety-eight primary educators were surveyed regarding their attitudes and behaviors towards mathematics instruction. Hierarchical regression analyses rev...

The authors describe a mathematics lesson designed to allow students to use their own thinking to solve elapsed time problems. Their approach emphasises student-centred structured inquiry, and follows a ‘Launch, Explore and Summarise’ format.

This paper outlines a tutoring initiative intended to re-engage students who have become alienated from mathematics class at school. The initiative is focused on priming students for their subsequent mathematics lessons, and is referred to as “Getting Ready in Numeracy” (G.R.I.N.). Following a discussion outlining the principles of G.R.I.N., data f...

In this paper we report on changes to teachers’ practices as a result of their participation in a research-based program of professional learning focused on challenging tasks. Seventy early years teachers responded to a survey at the end of a year-long program asking them to nominate and describe the teaching practices that changed most as a result...

This paper reports on a New Zealand iteration of the Encouraging Persistence, Maintaining Challenge (EPMC) project, which proposes that students learn mathematics best when they build connections between mathematical ideas for themselves. This iteration explores the actions, perceptions and learning of 12 primary teachers and their 281 students dur...

In this article, the authors emphasise the importance of purposeful mathematical discussion and using sequences of connected, cumulative, and challenging tasks in advancing students' spatial reasoning in the early years of schooling.

This article reports on a project which involved introducing challenging tasks in the early years’ classrooms of twenty Victorian primary schools. The obstacles teachers encountered and how they overcame those obstacles are discussed.

Using open tasks effectively can lead to powerful learning. Teachers often ask me: How can I create my open tasks? Here I share four strategies I have found effective over the years for developing open-middled, or open-ended tasks.

In this article we focus on ways that the documented curriculum can inform the construction and implementation of planned sequences of experiences to support mathematics learning. We report on the early stages of a research project which is examining ways that thoughtfully created, cumulative, challenging and connected experiences can both initiate...

Middle school students have been pervasively described in the research literature as exhibiting disaffection, disengagement, and a lack of interest in mathematics classrooms. This study investigated this notion empirically using students’ own voice on their wishes for mathematics learning to see if they characterise themselves in this way in their...

Challenging mathematical tasks can be designed to allow students of all abilities to experience productive struggle. It is important for teachers to communicate with students that productive struggle is important and it is what mathematicians do

This final chapter provides a synthesis of the research and scholarship presented by the 26 contributing authors about the nature and focus of actions that early years educators and professionals can take as part of their work to engage families in supporting the mathematics learning of their very young children. Each chapter contributed to one of...

This chapter introduces the premises of this book including the theoretical basis of early learning of mathematics. The chapter describes how research and policies recognise early learning as important and how families (and educators) are considered to be an integral part of the learning process in early childhood experiences. This chapter also out...

This chapter is written to inform the subsequent design of intentional experiences for young children, especially in family settings. There is clearly a world of mathematical possibilities for young children but it will assist in ensuring that children have experiences that can assist them in interpreting the world mathematically and in adapting to...

This chapter illustrates the perceptions of a small community of parents from a disadvantaged area in Victoria, Australia, on what they think about their family access to resources (in the form of capitals) and the importance of early learning in preparation for formal schooling especially in relation to mathematical learning. A total of 23 parents...

This article outlines teaching ideas appropriate for primary mathematics. It is mainly aimed at primary school teachers and teacher-researchers. We present the principle of Dynamic Counting, and a set of activities related to this principle, as a teaching tool that might be useful for encouraging students to 'trust the count' and develop fluency wi...

This article reports the findings of classroom research exploring the potential of posing challenging mathematical problems situated in real-world financial contexts to activate mathematical knowledge, skills and reasoning. The Organisation for Economic Cooperation and Development (OECD) Programme for International Student Assessment (PISA) 2012 ma...

While the general planning advice offered to mathematics teachers seems to be to start with simple examples and build complexity progressively, the research reported in this article is a contribution to the body of literature that argues the reverse. That is, posing of appropriately complex tasks may actually prompt the use of more sophisticated st...

Consumer, economic and financial literacy education at school is central to active and informed citizenship. Over the past decade, the Australian Securities and Investments Commission has led various policy initiatives and influenced curriculum and resource development in this area. However, there remains a paucity of research exploring how Austral...

This book explores how professionals can engage and inspire parents to support their young children’s mathematics learning. Bringing together international experts, researchers and scholars, it proposes a framework for engaging with and supporting parents, including those who are less aware of the crucial development of children’s mathematical skil...

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks...

The explication by Steve Lerman of a social perspective on teaching and learning informed a classroom based research program including five funded projects. This chapter elaborates Lerman's perspective, illustrates how it informed each of the projects, and presents a specific lesson to exemplify the key elements of this social perspective. The chap...

Ongoing improvement in teaching and learning in ways that maximise opportunities for success for all students is dependent on a range of factors: a well-structured, relevant and balanced curriculum; school-based decisions on ways of addressing diversity; sustainable approaches to teaching improvement; access to high-quality resources that facilitat...

The argument in this chapter, and indeed this book, is that researchers can inform systems, schools, and teachers about factors that contribute to inequitable education outcomes. Further, it is argued that researchers can go beyond this to indicate ways that such factors can be addressed by practitioners. In particular, there are advantages if rese...

This chapter describes the interplay between task design and student learning that informs teachers’ decisions about goals and pedagogies. Based on their mathematical goals for students, teachers face many choices: choosing or designing tasks and sequences of tasks; selecting media for presenting tasks to students and for students to communicate re...

The tradition of the MERGA four-year review provides evidence of sustained and evolving research within the Australasian mathematics education community. As part of the editing team for the previous review (Forgasz et al., 2008) we appreciate the opportunity to reflect on that review and to provide some personal insights into recent developments.

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks...

The content and purpose of written unit plans in mathematics is an under-researched area. In this article, we provide a brief overview of research on teachers’ planning processes and the place of mental and written plans. We report on data from a questionnaire completed by 357 teachers from Victorian Catholic primary schools, where we focused on po...

Challenges for researchers wishing to gain insights into student beliefs about mathematics and learning include the identification of prompts to which young children can respond easily and which have the potential to provide meaningful insights into their beliefs. This article reports on a selection of such prompts used within an exploratory study...

The following is a report of an exploration of what mathematical reasoning might look like in classrooms. Focusing on just one lesson in one classroom, data are presented that indicate that upper primary students are willing and able to reason for themselves, especially in classrooms in which the culture for such reasoning has been established. It...

The following is a report on an investigation into ways of supporting teachers in converting challenging mathematics tasks into classroom lessons and supporting students in engaging with those tasks. Groups of primary and secondary teachers, respectively, were provided with documentation of ten lessons built around challenging tasks. Teachers respo...

This is the report of an investigation in partnership with a team of junior secondary classroom teachers of the potential of posing more challenging tasks to their students. A range of data sources are used to represent the experience of teachers and students in a unit of work that incorporated a range of challenging tasks. Students learned the int...

One of the key strategies when teaching mathematics to Indigenous students is to connect the mathematics they are intended to learn to their experience. To illustrate one approach to connecting learning to students’ experience, this chapter uses two lesson sequences focusing on geometry that were developed collaboratively by the authors. The lesson...

This book describes research undertaken by leading Australian researcher in Indigenous communities. While the chapters are Australian in their focus, the issues that are discussed are similar to those in other countries where there are indigenous people. In most cases, in Australia and internationally, Indigenous learners are not succeeding in scho...

The focus in this chapter is on ways that students respond to the tasks as set up by the teacher, which in turn are related to the students’ learning. In our project we sought insights into students’ reactions to different types of tasks. This chapter gives a rationale for seeking students’ opinions and describes data collection on their confidence...

In the Task Types in Mathematics Learning Project and in this book, we sought to describe how different kinds of tasks contribute respectively to mathematics learning: The features of successful exemplars of different types of tasks Constraints teachers might experience when using tasks Associated teacher actions that can best support students’ lea...

Under the auspices of its ‘Education Revolution’, the Federal Labor Government is currently implementing a national curriculum for schools. Representing an important intervention into educational practice and governance, the Australian Curriculum offers a unique research opportunity, providing substantial scope for the examination of the changing s...

This article draws on the outcomes of a 4-year project where complex instruction was used as the basis for a reform in mathematics teaching in remote Aboriginal communities in Australia. The article describes the overall project in terms of the goals and aspirations for learning mathematics among remote Indigenous Australians. Knowing that the appr...

It is widely accepted that mathematical learning builds upon students’ prior knowledge and understandings, and their identities. In this study, this phenomenon is explored with indigenous students in remote community schools in outback Australia. Through one-on-one task-based interviews, it was found that these students had some clear understanding...

1. Researching Tasks in Mathematics Classrooms.- 2. Perspectives on Mathematics, Learning and Teaching.- 3. Tasks and Mathematics Learning. 4. Using Purposeful Presentational Tasks.- 5. Using Mathematical Tasks Arising from Contexts.- 6. Using Content-Specific Open-Ended Tasks.- 7. Moving from the Task to the Lesson: Pedagogical Practices and other...

This chapter explains the ways that open-ended tasks might contribute to learning, it gives the details of a specific open-ended task and how it might be used in a “lesson”, it indicates the challenges that teachers may experience when using such tasks, it presents a range of examples of this type of task to illustrate the scope and nature of the t...

This book is intended to provide some insights into the types of tasks that can assist students in learning mathematics. The insights though need to be interpreted in the context of our perspectives on some key issues. This chapter discusses what we see as the goals of teaching mathematics, it describes our perspectives on what it means to do mathe...

We alluded in earlier chapters to the many challenges and considerations faced by teachers as they seek to take a task and build a coherent lesson around it. We talked about research on task choice, the role of teachers’ content and pedagogical content knowledge, the need to consider extending and enabling prompts to use alongside the task, and the...

This chapter summarises some research results and scholarly commentary that emphasise the importance of mathematical tasks, and the ways they contribute to learning, the role of teacher knowledge in the effective use of tasks, the ways that teacher beliefs and attitudes influence the use of tasks, the nature of the constraints that teachers can ant...

This book is about the selection and use of tasks that can facilitate the learning of mathematics. It focuses on the choices of tasks that teachers make and the actions they take in using tasks. It describes tasks that can be used to facilitate the learning of mathematics, and can make the experience of learning mathematics engaging and rewarding a...

In addition to seeking students’ opinions about the types of tasks they like and can learn from, we also sought their opinions on the types of mathematics lessons they prefer. It was hoped to gain insights into the ways students described their desired characteristics of lessons, rather than through their ratings of lesson characteristics prepared...

In considering the range of tasks that can be effectively used to support student mathematics learning, tasks that make use of materials and visual support need to be considered. In this chapter we discuss tasks that use models, tools, and representations, present some examples, and discuss the challenges for teachers in their use. Data are present...

This chapter describes the second of the types of tasks that we focused on in our project. We argue consistently throughout this book that a teacher’s choice and use of tasks is a major determinant of the nature and quality of student learning in the mathematics classroom. In this chapter, we present data from teachers indicating that the use of ta...

The Task Types and Mathematics Learning (TTML) research project investigated how three types of mathematics tasks contribute to mathematics learning in the middle years of schooling. As part of the data collection, teachers were provided with three tasks of different types (open-ended, contextual, representational) that focused on the relationship...

In earlier chapters, we reported a range of experiences from the use of tasks in the Task Types and Mathematics Learning Project. In this chapter, we present descriptions of 15 tasks. The structure of these tasks is not intended as a recipe for their use by teachers and teacher educators, but is a collection of insights from their use, highlighting...

While tasks are the basic building block, teachers need to create lessons to ensure that the potential of tasks are realised, and also need to plan sequences of such lessons to build coherent learning experiences for students. The following presents some details of the development process and tasks used in one of the sequences created by project te...

Insights into teachers’ planning of mathematics reported here were gathered as part of a broader project examining aspects of the implementation of the Australian curriculum in mathematics (and English). In particular, the responses of primary and secondary teachers to a survey of various aspects of decisions that inform their use of curriculum doc...

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We are researching actions that teachers can take to improve mathematics learning for all students, with particular attention to specific groups of students who might experience difficulty. After identifying possible barriers to learning, we offered teachers mathematics lessons structured in a particular way. Teachers' use of the model outlined in...

One of the goals of teaching mathematics is to commu- nicate the purpose and nature of mathematical proof. Jahnke (2008) pointed out that, in everyday thinking, the domain of objects to which a general statement refers is not completely and definitely determined. Thus the very notion of a “universally valid statement” is not as obvi- ous as it...

This book is about tasks that teacher educators might use with prospective or practicing secondary mathematics teachers. There is a substantial literature that has established the critical role that tasks play in the teaching and learning process for school mathematics classes. Kilpatrick et al. (2001), for example, claim that the quality of teachi...

Much research on early measurement learning is small-scale and dependent on the items used. While such research is helpful for indicating the key aspects of learning length, it does not give teachers a clear indication of the expectations for student learning of them. This paper presents substantial data from a large project that used individual in...

This chapter describes a task for prospective teachers in which they use a particular planning and teaching model as a way of coming to understand the challenges and opportunities in non-routine tasks, and in particular considering the steps that are necessary in converting the tasks into learning opportunities. A particular focus of the planning a...

In this study, 42 Australian Indigenous children were posed a series of related questions on addition and subtraction. The questions were posed both in the context of money and without any context. The data revealed an alignment between the students' capacity to work with money and to work with numbers. The money context did not increase the cognit...

The performance of Australian Indigenous1 learners is a national concern. The federal government has recognised that health and education are keys to closing the gap between the achievement of Indigenous and non‑Indigenous people and has made health and education a national priority. Through its 'Closing the Gap' initiative, the Rudd government is...

We are examining actions that teachers take to convert tasks into learning opportunities. In this paper, we contrast ways that three teachers convert the same task into lessons, and the way that their lessons reflect their intent. We found that the teachers did what they intended to do, that this was connected to their appreciation of the mathemati...

The poor mathematical achievement of remote Indigenous students continues to be a significant educational issue. The Maths in the Kimberley project seeks to implement an innovative pedagogical reform in six remote Indigenous schools to explore reforms that may lead to improved outcomes for Indigenous students in mathematics. This paper reports on t...

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It is widely accepted that teaching should build on what students already know and understand. In this study, 42 Aboriginal children in Grades 3 to 6 were posed a series of related questions on addition and subtraction. The question items were posed in a one-on-one interview situation both in the context of money and with just numbers. The data rev...