Search

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 implemented a student-centred pedagogical approach when teaching with challenging tasks. While they had some initial success implementing the pedagogical approach and a three-phase lesson structure, they struggled to do so online during the lockdown. It is the experiences of these teachers, in particular their experience of confusion relating to aspects of the pedagogical approach, and how this confusion was overcome, that is reported in this paper. Central to our findings is the importance of teachers reflecting on their own experiences of struggle and the impact this had on their professional learning, as well as the notion that adversity can be a catalyst for change.

This article is based upon Peter Sullivan's (2021) structured inquiry approach to teaching mathematics, in which the authors take a deep dive into the technique of "Spotlighting" in the "Explore" phase of this model to assist in optimal learning experiences for students. Working from the premise that students are best placed to connect with instruction after a powerful and sometimes confusing learning experience, Sullivan et al.'s (2021) model provides three distinct phases to structure a mathematics lesson. They are: (1) The Launch phase--poses the task to students without any further instruction about the strategies required to solve the task; (2) The Explore phase--where collaboration and peer learning is encouraged as a support for students to consider multiple solutions and solution pathways; and (3) The Summarise/Review phase--provides an opportunity for the teacher to orchestrate class discussions by presenting various student solutions that reflect the mathematical focus of the lesson. The authors conclude they have been pleasantly surprised at how particular student explanations, derived from real time spotlight moments, were critical in shaping successful learning opportunities for the rest of the class.

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 from interviews with G.R.I.N. tutors and classroom teachers are presented. Findings suggest that participating in G.R.I.N. enhanced student engagement in mathematics and helped foster a growth mindset. Analysis of interviews also revealed some of the challenges associated with the initiative, in particular, issues relating to communication and coordination, such as: understanding the purpose of G.R.I.N., timetabling, planning and having sufficient students in the target group. In addition, in some instances, tensions between the professional and pedagogical expertise of the G.R.I.N. tutor and classroom teacher required navigation. Recommendations for mitigating these challenges and tensions are put forward, all of which are reliant on strong leadership and support for the program at the school level.

Peter Sullivan and colleagues present a report on an initiative at a Victorian primary school which embraced opportunities offered by purposeful collaborative professional learning communities. They utilised a form of Japanese Lesson Study as part of their approach. There are three parts to the story of this initiative: (1) a description of the approach to professional learning; (2) an explanation of the model of instruction being explored; and (3) a summary of the 'polished' lesson on middle primary mathematics (fractions).

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.

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 during the implementation of a set of challenging tasks related to geometric reasoning. The teachers launched the suggested tasks, ensuring that the challenge was maintained. The students explored these tasks with minimal input from the teacher, and learning was summarised and extended. The teachers were positive about the intervention. The challenging task approach enabled students' thinking became visible and, at times, the teachers' prior perceptions of their students' ability were challenged. A highly significant difference between the students' pre- and post-assessment scores was found. The students were supported to have autonomy in their learning and make mathematical connections themselves. The students became less reliant on their teachers' help and were positive about their involvement in the project.

The fear of making mistakes and avoidance of risks can create disabling anxiety and limit learning opportunities. However, it is possible to teach mathematics in ways that not only reduce student agency but also have the effect of excluding some students. This article proposes approaches that are intended to both foster student decision making and a sense of inclusion in classroom learning. It describes some characteristics of classrooms that may go some way to minimising student anxiety without reducing the opportunities for cognitive activation. There are three parts that are discussed: features of tasks posed, pedagogical approaches, and classroom culture.

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.

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

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 mathematical literacy assessment framework (OECD, 2013) provided theoretical framing for the study, which examined the use of a "financial dilemma" titled "Shopping for shoes" in a Year 5/6 composite class in a suburban Australian primary school. The social and mathematical dimensions of the task, together with a particular lesson structure, successfully engaged 10 to 12-year-old students in exploring mathematics through a financial problem-solving experience. The findings reveal that students' notions of friendship and fairness guided the way they "formulated" the problem and "employed" mathematics. Strategies intended to encourage students to "interpret" the alignment and reasonableness of their social and mathematical thinking against the problem context were critical to the lesson.

As part of a research and professional development project that focused on the opportunities and constraints provided by different kinds of mathematical tasks, a group of 67 primary and 40 secondary practising teachers of mathematics were asked to complete a survey focusing on their use of tasks. In this article, we discuss responses to one particular item which sought teachers' ideas on taking a fraction comparison task (which is larger: 2/3 or 201/301?) and converting it into a mathematics lesson in the middle years of schooling. Drawing upon a number of components of "mathematical knowledge for teaching" as a framework, we attempt to examine those aspects of mathematical knowledge which are involved in making such a conversion. Our recommendation following this analysis is that greater emphasis is necessary in professional development settings on taking a potentially useful task and converting it into a worthwhile mathematics learning experience for students. Knowing the relevant mathematics also seems necessary even if not sufficient to make this conversion. (Contains 4 tables and 1 note.)

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 self-reports. Over 3500 Australian middle school students responded to a free-format prompt and reported diverse but overwhelmingly positive aspirations related to intrinsic motivational features inherent in their disposition and to extrinsic factors in their environment, such as the learning context and activities provided. Evidence of all four goal orientations was found in the students' responses but most noticeably for the productive mastery-approach orientation. When these students described what they wish for in their mathematics classrooms, they mentioned challenging work, interesting work, and opportunities to collaborate.

Productive struggle leads to productive classrooms where students work on complex problems, are encouraged to take risks, can struggle and fail yet still feel good about working on hard problems (Boaler, 2016). Teachers can foster a classroom culture that values and promotes productive struggle by providing students with challenging tasks. These tasks are designed in such a way that they are accessible to all students and the expectation is that everyone will persist when solving challenging mathematical tasks. This article looks at examples of challenging mathematical tasks designed to enable students of all abilities to experience productive struggle, and examines the lesson structure and teacher's role when implementing a challenging task, along with students' responses to being challenged through the tasks. It adds to existing research on challenging tasks, including in previous editions of "Australian Primary Mathematics Classroom" (APMC) (e.g., Cheeseman, Clarke, Roche, & Walker, 2016; Roche & Clarke, 2014; Russo, 2016) through challenging tasks being used to evoke productive struggle, and illustrative examples of what productive struggle 'looks like.'

Schematic models have been used extensively in educational research to represent relationships between variables diagrammatically, including the interrelationships between factors associated with teachers' beliefs and practices. A review of such models informed the development of a new model that was used to plan an investigation into primary school teachers' problem-solving beliefs and practices. On the basis of the findings from the research, the model was revised to include the important variable of prior mathematics learning, as well as a repositioning of the influence of teaching experiences in classrooms. (Contains 9 figures and 5 tables.)

This article from Carly Sawatzki and Peter Sullivan encourages schools and teachers to consider ways to embed financial literacy tasks in mathematics lessons more often, and includes an authentic task to try with your students.

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 responded to survey items in both Likert and free format style after teaching the ten lessons. The responses of the teacher participants indicate that the lesson structure we proposed was helpful, and the elements of the lessons suggested to teachers were both necessary and sufficient for supporting students in engaging with the challenging tasks. Implications for teacher educators and curriculum developers are offered.

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 possible elements of written unit plans for primary mathematics, and the relative importance which teachers attributed to these elements. We then discuss 48 written unit plans which were provided to us by primary schools from which the 357 teachers were drawn. There was considerable variation in the length, intended teaching time, and level of specification of key ideas in these plans. We discuss this variation, and some discrepancies between the ratings of teachers of the importance of certain elements and their presence in the plans we examined. We also suggest potentially productive areas of future enquiry.

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 intended mathematics and they reacted positively to the challenges. The teachers identified both opportunities and constraints in such teaching, especially those related to changes to their pedagogies and assessment of student work.

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 documents and assessment processes to plan their teaching are discussed. Teachers appear to have a clear idea of the overall topic as the focus of their planning, but they are less clear when asked to articulate the important ideas in that topic. While there is considerable diversity in the processes that teachers use for planning and in the ways that assessment information informs that planning, a consistent theme was that teachers make active decisions at all stages in the planning process. Teachers use a variety of assessment data in various ways, but these are not typically data extracted from external assessments. This research has important implications for those responsible for supporting teachers in the transition to the "Australian Curriculum: Mathematics."

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 approach had been successful in a diverse setting in California, the project team sought to implement and evaluate the possibilities of such reform in a context in which the need for a culturally responsive pedagogy was critical. Elements of complex instruction offered considerable possibilities in aligning with the cultures of the remote communities, but with recognition of the possibility that some elements may not be workable in these contexts. Complex instruction also valued deep knowledge of mathematics rather than a tokenistic, impoverished mathematics. The strategies within complex instruction allowed for mathematical and cultural scaffolding to promote deep learning in mathematics. Such an approach was in line with current reforms in Indigenous education in Australia where there are high expectations of learners in order to break away from the deficit thinking that has permeated much education in remote Australia. The overall intent is to demonstrate what pedagogies are possible within the constraints of the remote context.

This article promotes the use of mathematically appropriate, engaging and challenging tasks to support learning that is worthwhile. The authors share insights from a three-lesson design experiment and the three tasks along with the results from their implementation are explored.

The Australian Curriculum: Mathematics encourages teachers to consider seriously the four proficiencies: Understanding, Fluency, Problem Solving and Reasoning. In responding to the reasoning proficiency, many teachers may find that the language of the classroom may well change. In this article, we discuss the meaning given to the term reasoning within the AC:M and elsewhere, share an example of a classroom task with the potential to develop mathematical reasoning, consider the language involved in describing reasoning, and present some survey responses on teachers' current understanding and use of the relevant terms. (Contains 3 tables, 2 figures and 1 footnote.)

At some stage in the planning process, teachers develop or select tasks which prompt the type of activity that can offer students experiences that can help them learn the intended content. This article presents results from an item on a survey that invited teachers to match particular content descriptions with selected tasks. While many teachers matched the tasks with the content descriptions that we anticipated they would, there were also many teachers who chose descriptions that we consider do not match the tasks. It is suggested that teachers should discuss within their planning teams the purpose and potential of particular tasks, and that such discussions also form part of teacher professional learning. It is recommended that the notion of matching tasks to the curriculum is incorporated into teacher learning sessions. (Contains 1 table.)

In recent years, there has been greater attention in research and professional development work to discussion of the kinds of knowledge teachers need to teach effectively in the mathematics classroom. It seems reasonable that in planning at the school level, teaching team level and then specifically for a given lesson, teachers might have a sense of the most important mathematical ideas on which they wish to focus. In this article, we discuss written statements by teachers in surveys regarding the most important ideas on which they intended to focus in their next teaching topic. There was considerable variation in teachers' capacity to articulate these important ideas. We discuss the implications of this for teacher professional learning and planning. (Contains 1 footnote.)

The Australian Curriculum: Mathematics (AC:M) prompts consideration of planning processes teachers typically use (as a whole school, in grade levels, and at the classroom level). In order to gain insights into the nature of the planning decisions teachers make, Australian teachers drawn from every state and territory were invited to respond to a survey on planning processes, during professional learning programs or voluntarily online through the Australian Association of Mathematics Teachers' website. In this article, we provide background to the overall project in which this survey was situated, and describe the process through which the survey was developed. Subsequent articles in this journal detail some important findings from the survey data. (Contains 1 table and 1 footnote.)

Essential to teachers' planning are decisions regarding what should be taught. Curriculum documents are the most obvious authority. But what is a "curriculum document" for a mathematics teacher in Australia? Are there other credible sources of information that Australian teachers draw on when deciding what to teach? This article examines the responses of a national sample of Australian teachers to a survey examining their planning practices. (Contains 2 figures.)

The Task Types and Mathematics Learning project is investigating the opportunities and constraints that teachers experience when using particular types of mathematics tasks. Some assumptions underlying this aspect of the project are: (1) that teachers seeking a balanced curriculum choose to use a mix of types of tasks; (2) open-ended questions offer students and teachers opportunities for both creativity and different ways of thinking about mathematics; and (3) trialling exemplars of particular types of tasks, reflecting on the experience by writing a report, and reporting back to colleagues involves substantial teacher learning, and can form the basis of sustainable professional development. This article explains what is meant by content specific open-ended tasks, illustrates the ways that teachers wrote up trials of such tasks in their classrooms, and uses excerpts from teachers' reporting on their trials at meetings of project teachers from a cluster of nearby schools, to illustrate the type of teacher learning that resulted from this process. (Contains 1 figure.)

This article illustrates a teaching exploration at an Indigenous Community School in the Kimberley region of Western Australia that sought to use a specific way of thinking about particular content domain, subtraction, to develop focused, mathematically-rich learning experiences. First, the authors explain the importance of having clear mathematical goals (knowing where you are going), and then they describe some illustrative activities (how to get there) that were used over the four 90-minute lessons. They also present data that indicate that there was positive student achievement as a result of the experience. (Contains 2 figures.)

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11-12) class.

Many students are unsuccessful in the study of school mathematics, not because of some innate ability, but because of pedagogical practices. Bernstein (1996) has argued that pedagogy serves as a mechanism for cultural reproduction, so that for those students whose cultures are different from that represented in and through pedagogy, the task of constructing school mathematics is made more difficult. The paper explores the ways in which a teacher changes the pedagogic relay in order to be more inclusive of her students. Her practice is informed by understanding the ways in which pedagogy is a subtle tool for marginalization in mathematics.

Reviews studies featured in this issue of "Journal of Mathematics Teacher Education" and examines the way that the study of practice can contribute to mathematics teacher education. Studying teaching in simulated or real situations offers considerable potential for both stimulating thinking about the application of theory to practice and creating personal theories for the study of practice. (KHR)

Discusses the advantages of teaching with open-ended tasks and compares students' responses to open-ended, closed-area, and perimeter tasks. (ASK)

Reports results from one component of a larger project that explored the classroom potential of content-specific, open-ended tasks. Examines responses from 1200 students to comparable closed and open-ended tasks and explores the effect of using specific contexts for such tasks. Concludes that both open-ended and closed tasks can contribute to effective classroom programs. (Contains 14 references.) (Author/ASK)

A survey of 125 teacher educators' and experienced teachers' views of quality mathematics teaching identified 6 major components: communicating, problem solving, building understanding, engaging, nurturing, and organizing for learning. Presents a model that suggests a way to link the categories. (24 references) (Author/MKR)