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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 collected from 104 early years primary school teachers. Findings suggest that two-thirds of these generalist teachers expressed an interest in specialising in either English, mathematics, and to a far lesser extent, science, such that they would be responsible for exclusively teaching this subject. Preferences for specialisation were based on teachers' self-perceived content and pedagogical expertise and/ or their enjoyment of teaching in this content area. By contrast, the one-third of teachers who would choose to remain generalists referred to the value in a variety of teaching experiences, teaching from a whole child perspective and content integration. Implications for educational policy are discussed.

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.

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 from a sample of 118 generalist, early-year primary school teachers. Thematic analysis of interview data revealed that negative-to-positive turning point experiences were commonplace amongst high-enjoyment primary teachers, but so too were reports of consistently positive feelings towards mathematics throughout their entire lives. While most articulated a passion for teaching mathematics, all teachers considered instances when students experienced 'light bulb' moments in their mathematical understanding that made a mathematics lesson enjoyable to teach. An important implication of our research is that one need not be a 'maths person' to come to love teaching mathematics. Rather, positive experiences in one's pre-service teacher education, or in-service teacher professional learning, have the potential to transform one's attitude towards 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 involved in a professional learning initiative focused on teaching mathematics through sequences of challenging tasks completed a questionnaire inviting them to compare the two settings. Drawing on a mixed-methods approach, we found that teachers were more positive about the value of student struggle in classroom-based settings compared with remote learning settings. Qualitative analysis of open-ended responses revealed four themes capturing why teachers viewed efforts to support productive struggle in a remote learning setting as potentially problematic: absence of a teacher-facilitated, synchronous, learning environment; parents' negative attitudes towards struggle when learning mathematics; lack of social connection and peer-to-peer collaboration; and difficulties accessing learning materials. Suggestions for mitigating some of these challenges in the future are put forward.

Learning mathematical concepts and procedures typically requires extended cognitive effort, presenting a challenge for many children. People can make tracing actions with the index finger, as well as mimic another's movements, with little or no conscious effort. From the perspective of cognitive load theory, such biologically primary actions may facilitate learning biologically secondary concepts and skills requiring extensive cognitive effort, such as mathematics. The present study investigated effects on learning processes and outcomes of students mimicking a teacher's tracing actions from the perspective of an evolutionarily informed cognitive load theory. One hundred and thirteen Grade Two children learned about number lines, either observing a teacher tracing out elements of worked examples with her index finger, or mimicking the teacher's tracing actions with their own index finger. In accord with hypotheses, results indicated enhanced performance due to mimicking on cognitive load, motivation, and post-test performance. Directions for future research are discussed.

Student engagement in mathematics in the early secondary years can be fragile. Engagement in learning fluctuates in response to students' mathematics experiences and is underpinned by numerous adaptive and maladaptive factors. Thirty-seven 11-12 year old students (grades 6-7) responded twice to a questionnaire to measure shifts in their engagement and motivation over a 1-year period as they transitioned from primary to secondary school. When plotted on spider graphs, the results of specific adaptive and maladaptive factors visually demonstrate "in and out" movements as students' engagement levels shifted from time 1 to time 2. Subsequent semistructured interviews complemented questionnaire data by eliciting student beliefs about their achievement, feelings and behaviours towards mathematics. Interview data shed light on the reasons for individual student shifts in motivation and engagement during the transition. Together, data reveal four unique engagement/achievement characteristics. Significantly, students who were more alike in terms of their engagement reported similar factor patterns regardless of their achievement level. Findings draw attention to the importance of addressing mathematics engagement for students of all achievement levels.

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.

Mathematics teachers' identities profoundly influence how they interact with and position their students to learn mathematics. In this paper, we examine how a year-long teacher learning intervention supportive of student engagement in mathematics helped shift teachers' mathematics-related identities. We use an implied identity perspective as a theoretical lens to explore changes in what teachers perceive as legitimate ways of being as a result of their participation in the intervention. Data from pre- and post-intervention concept maps and focus groups with 15 grade 5-7 teachers of mathematics were integrated for this purpose. Teachers reported shifts in their identities, describing themselves as "facilitators," "learners" and "co-creators" of knowledge. We argue that such shifts in the mathematics-related identities of teachers can have practical consequences in terms of improving students' engagement, and in particular, their autonomy for learning mathematics.

According to the self-determination theory, autonomy-supportive teaching is considered an effective approach to motivate students to learn. The present study investigates the effect of students' perceived autonomy support on math achievement over time, i.e. from grades 4 to 6, using a longitudinal survey administered in Chinese elementary schools. A total of 1624 participants were assessed over four waves. Autonomy need satisfaction and classroom engagement were included as predictors of achievement growth. Latent growth curve modelling (LGCM) indicated that perceived autonomy support accounted for more variance in mathematics achievement among 4th- and 5th-grade students than it did for 6th-grade students. Furthermore, student autonomy need satisfaction positively predicted the growth rate of their achievement, while behavioural engagement significantly and positively predicted both the growth rate and the average initial level of mathematics achievement.

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 back to school.

Increasing student exposure to autonomy-supportive teaching approaches has been linked to enhanced student intrinsic motivation to learn. However, such approaches are rare in mainland Chinese science classrooms. An intervention-based study with quasi-experimental design and mixed methods was conducted to explore the impact of a 9-month-long autonomy-supportive teaching intervention on a physics teacher and 147 grade 8 students attending a middle school in China. Data collected through questionnaires, interviews, and observations were analyzed to elicit and track shifts in teacher practices and students' perceptions of learning physics at pre-, post-, and follow-up intervention phases. General linear modeling confirmed significant changes in students' perceptions of their learning environment over time in terms autonomy, satisfaction of autonomy needs, and agentic engagement. Interview and observational data analyses confirmed increased use of autonomy-supportive teaching behaviors and provided further insights into teacher and students' perceptions of the impact on student learning.

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.

People can make pointing gestures and tracing actions with the index finger with little or no conscious effort. From the perspective of cognitive load theory, such "biologically primary" gestures and actions might help people learn "biologically secondary" concepts and skills requiring extended cognitive effort, such as reading, science, or mathematics. Studies on tracing or tracing and pointing have yielded mixed findings regarding hypothesized effects on intrinsic and extraneous cognitive load. The present study investigated whether computer-based instructions to trace elements of worked examples on angle relationships would affect school students' (N = 106) self-reports of intrinsic and extraneous cognitive load, as well as problem-solving transfer test performance. The tracing effect on transfer posttests seen in prior studies was replicated, but cognitive load hypotheses were not supported. Implications for educational practice and future research are discussed.

Concerns about the negative mathematical beliefs of prospective primary teachers have arisen from evidence that such beliefs detrimentally impact future teaching practices. The aim of this study was to explore factors contributing to the effectiveness of a mathematics content-focused intervention designed to nurture positive mathematical beliefs. Utilising interviews, concept mapping, workshop observations and document analysis, shifts in the mathematical beliefs of prospective primary teachers were revealed. The role of the mathematics education tutors was critical in contributing to the development of positive beliefs. In particular, their abilities to develop a positive rapport with prospective teachers and to create learning environments conducive to increased understanding of mathematics concepts were most influential. Implications for primary mathematics teacher education courses are addressed.

Cognitive load theory seeks to generate novel instructional designs through a focus on human cognitive architecture including a limited working memory; however, the potential for enhancing learning through non-visual or non-auditory working memory channels is yet to be evaluated. This exploratory experiment tested whether explicit instructions to trace out elements of geometry worked examples with the index finger would enhance learning, as measured by error rates and problems solved. Compared to a non-tracing condition, students in the tracing condition correctly solved more practice problems, and made fewer errors on a subsequent test. Recommendations for subsequent more sensitive experiments are made.

Using growth modeling, this study examined trajectories of 'switching on' (aspirations) and 'switching off' (disengagement) in mathematics across middle school and high school. In addition, guided by principles under expectancy-value theory, the study sought to determine the extent to which patterns of growth differed by motivation (self-efficacy and valuing) and socio-educational attributes (gender, language background, and achievement). The sample comprised 194 students from four schools who participated in three rounds of data collection across five academic years of their schooling, spanning middle school and high school. In the main, mathematics aspirations declined over time while mathematics disengagement increased. However, initial levels of aspirations and disengagement and their rates of change over time were impacted by motivational and socio-educational factors. Salient findings and their implications for educational assessment and practice are discussed.

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.

With deliberate system-level reform now being acted upon around the world, both successful and unsuccessful cases provide a rich source of knowledge from which we can learn to improve large-scale reform. Research surrounding the effectiveness of a theory-based system-wide numeracy reform operating in primary schools across Australia is examined to extract the elements most influential for the sustainability and scaling-up of this reform. The evidence suggests that key mechanisms or tools such as a framework in number and diagnostic interview, alongside a focus on deep understanding in teachers of children's mathematical thinking strategies and the strategic placement of support structures at various levels of program implementation are important elements for the sustainability and scale-up of this program. This article introduces the professional development program in question, presents an overview of three research studies, and then links their findings to Coburn's (2003) multi-dimensional conceptualisation of scale. (Contains 2 figures.)

Recognition of the importance of the early childhood years in the development of numeracy is a significant characteristic of the New Zealand Numeracy Development Project, the Victorian Early Numeracy Research Project and the Count Me In Too program in New South Wales, Australia. This article outlines the background, key components and major impacts of these three innovative and successful professional development and research initiatives. Juxtaposing the three projects highlights important commonalities--research-based frameworks, diagnostic interviews, and whole-school approaches to professional development. Each program has been significant in rethinking what mathematics and how mathematics is taught to young children. (Contains 2 tables and 4 figures.)

Teaching mathematics through themes has been praised for relating mathematics to real-life situations. However, research shows that the implementation of teaching mathematics thematically has not been widely adopted. In the present study, instructional, curricula and organisational factors that teachers perceive as obstacles to the implementation of a thematic approach to teaching mathematics were explored. Findings from interviews with 10 secondary mathematics teachers who were implementing a curriculum requiring a thematic instructional approach are reported. The findings of the study extend the literature concerning teachers' beliefs and practices in the teaching of mathematics, and broaden understandings of the issues surrounding the implementation of a thematically taught mathematics curriculum. Sample Items of the Questionaire and Sample Questions from the Interview are Appended.

We started with a classic research question ("How do teachers motivate and engage middle year students in mathematics?") that is solidly underpinned and guided by an integration of two theoretical and multidimensional models. In particular, the current study illustrates how theory is important for guiding qualitative analytical approaches to motivation and engagement in mathematics. With little research on how teachers of mathematics are able to maintain high levels of student motivation and engagement, we focused on developing a qualitative framework that highlights the influence of teacher-student interactions. Participants were six teachers (upper primary and secondary) that taught students with higher-than-average levels of motivation and engagement in mathematics. Data sources included one video-recorded lesson and associated transcripts from pre- and post-lesson interviews with each teacher. Overall, effective classroom organisation stood out as a priority when promoting motivation and engagement in mathematics. Results on classroom organisation revealed four key indicators within teacher-student interactions deemed important for motivation and engagement in mathematics--confidence, climate, contact, and connection. Since much of the effect of teachers on student learning relies on interactions, and given the universal trend of declining mathematical performance during the middle years of schooling, future research and intervention studies might be assisted by our qualitative framework.