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This paper reports on the development of complex unfamiliar mathematics questions using conventional mathematics questions. The autoethnographic research data included retrospective reflections of two educators and review of literature. Data analysis resulted in a three-phase development process: identifying conventional questions and subject matter to be modified to enhance levels of understandings and skills, modifying conventional questions and subject matter to complex unfamiliar questions, and identifying enhanced understandings and skills in modified questions. The paper then discusses the educators' insights developing complex unfamiliar mathematics questions for the practice of teaching and learning.

This paper reports on part of a longitudinal project investigating the formation of preservice secondary mathematics teachers' identities at one Australian university. Given that school-based placement experiences impact teacher identity development, the Flourishing Mathematics Teacher (FMT) project focuses on this experience and aims to identify features of placement experiences that enable beginning secondary mathematics teachers to flourish, and remain, in their teaching careers. In this paper, we report on preliminary data exploring changes to 23 preservice secondary mathematics teachers anticipated job enjoyment after their first teaching placement.

This paper explores the complex problem of project sustainability, focusing on the leadership of three primary school mathematics leaders. Using cultural-historical activity theory (CHAT), the leaders' efforts are reported, highlighting their contribution to project sustainability. The CHAT-informed research design supported the generation of findings, revealing how the mathematics leaders enacted a form of resourceful practice. This paper contributes new knowledge about mathematics leaders, characterising how they acted as agents of project sustainability. Implications for mathematics education project design are also offered.

This paper explores factors that contribute to increased self-efficacy in preservice teachers as they practise teaching mathematics in a primary classroom. Thirteen preservice teachers completing a Master of Primary Teaching contributed to the research, four of whom became the focus of intense examination during two professional practices conducted over a 12-month period. Findings revealed six factors. When conceptualised into a framework the factors contributed to a better understanding of ways to support preservice teachers' self-efficacy for teaching mathematics.

This paper presents an analysis of how resources were designed to support implementation of the new Queensland senior secondary mathematics syllabuses. The analysis draws on the concept of educative curriculum materials that build teachers' subject matter knowledge and pedagogical content knowledge. Such resources are intended to help teachers "learn how to learn" to teach mathematical content that is new or unfamiliar to them.

Concern regarding the prevalence of out-of-field teaching continues to grow, as does the body of literature calling for a better understanding of the nuanced complexities associated with out-of-field teaching. In this paper, we extend our previous analysis of data from a survey of the profession teaching Years 7-10 mathematics in South Australia. Analysing the data through an identity lens indicates that out-of-field teachers who self-identify as mathematics teachers and express a preference for teaching mathematics are more likely to exhibit levels of interest, enjoyment, confidence, and commitment that align with those of in-field teachers.

Differentiated Instruction (DI) is a philosophical and pedagogical approach supporting diverse student engagement in learning, but limited research exists in DI in senior-secondary mathematics. Using semi-structured interviews, the perceived use of DI of two senior secondary mathematics teachers was investigated. One of three themes is discussed in this paper; using strategies to enable student choice and voice. Results indicated teachers used various DI strategies to support students to understand their current levels of need, allowing student choice in their tasks, and supporting student reflective practice. DI in senior-secondary mathematics is complex, but achievable.

The study reported in this paper is on the professional development (PD) of primary school mathematics teachers. Teachers from two primary schools participated in the PD for two years. High-stakes mathematics examination tasks were used to kick start awareness and thinking about teaching for big ideas. Teachers did the tasks and discussed their solutions focusing on how their instruction could facilitate the acquisition of mathematical ideas as a body of connected knowledge. Data presented in this paper show that the tasks teachers worked with at the start of the PD did impact their understanding and instructional practice specific to big ideas in mathematics. Some challenges the teachers faced during the PD are also noted.

In this paper we report on an aspect of the findings of a larger three-phase study exploring the factors that influence teachers implementing pedagogies that cultivate students' STEM capabilities and 21st century skills. Data were collected through an online questionnaire, semi-structured interviews, focus groups and case studies. This paper will focus on the findings from the first phase of this study and initial analysis of focus groups and semi-structured interviews data. Preliminary findings show that participants hold mixed beliefs concerning student proficiency in mathematics and there are common factors that influence decisions concerning the use of pedagogical practices that support students' mathematical proficiency and the development of students' 21st century skills. These factors include teachers' personal beliefs and attitudes, perceived time and curriculum constraints, student behaviour and students' academic ability.

Probability requires teaching approaches that allow children to predict, observe and experiment with concreate materials, games and simulations. In this study, we explored one teacher's beliefs and practices of teaching probability using game-based approaches. We employed a design-based research approach to explore how our case study teacher engaged with an hour-long professional learning on using a game-based probability teaching sequence. We found that our case study teacher's espoused beliefs and self-reported practices aligned with knowledge of teaching probability demonstrated during the professional learning activity.

Creativity is a task-specific construct that exhibits diverse characteristics depending on the context it operates in. Currently, there is little consensus on how creativity can be defined and taught within STEM education. In this study, mathematics teachers' beliefs about STEM creativity and their pedagogical approaches to teaching creativity within a novel STEM creativity framework have been explored. Results show that mathematics teachers have a variety of beliefs and practices about creativity that can be grouped into four pedagogical themes: exposure, exploration, experimentation, and execution.

Teaching resources and professional development based on mathematics education research have the potential to support teachers to develop and sustain improved pedagogies. The Queensland Department of Education provided online professional learning modules for teachers of Prep (Foundation) to Year 10 mathematics. To support implementation of the Australian Curriculum: Mathematics this evidence-based resource would assist teachers in understanding the curriculum and providing support for quality teaching and learning. This resource exemplifies the partnerships between the department, researchers and teachers in building capability in mathematics teaching.

The exploratory study combined an online survey and interviews with Australian primary and secondary mathematics teachers to examine their views on "Active, Bodily experience Mathematics learning activities." The research sought to identify teachers' expectations, challenges, and limitation for their implementation. Initial results indicate teachers recognise the value of such activities in deepening students' understanding and increasing engagement but encounter obstacles such as time constraints, insufficient resources, and difficulties in managing the classroom, underscoring the need for further investigation into effectively incorporating these activities into teaching practices.

Semi-structured interviews are used to gain insights into participants' lived experiences and perspectives on issues, but they are open to subjectivity. To address this issue our study explored the combination of timeline graphic elicitation tools with semistructured interviews as an approach to gain insights into teachers' experiences of mathematics teaching and professional learning. A qualitative study was conducted with ten participants from two schools who took part in professional learning activities for mathematics teaching. Findings indicated that combining these instruments can support researchers in gathering deeper insights into teachers' lived experiences.

For students to engage in mathematical thinking, a greater emphasis is needed on the expectations of students, by themselves and others, as active listeners and explainers. As student responsibility for mathematical thinking and participation increases, the roles of the teacher and learner change. A qualitative study of changing classroom expectations in a Grade 2 class was conducted. The teacher saw her role shifting to that of facilitator and the students' expectations were as active listeners and explainers. The type of questions asked by the teacher was instrumental in whether justification and mathematical reasoning was elicited from all learners.

Whilst educational goals in recent years for mathematics education are foregrounded the development of mathematical competencies, little is known about mathematics teachers' competencies. In this study, a group of practising teachers were asked to solve an algebra problem, and their solutions were analysed to determine the competencies apparent (or, equally importantly, absent) in these solutions. The most demonstrated competencies were "devising strategies" and "mathematising," whilst "communication" and "reasoning" were mostly missed. The research provides a detailed methodology on how mathematical competencies can be assessed in the context of problem solving.

We report on findings from a study involving 15 secondary mathematics teachers from Fiji. The aim of the study is to describe teachers' current approaches to teaching probability and statistics; and to share their views on using game-based teaching approaches. We report briefly on the first stage of follow-up on one teacher who agreed to develop and implement a lesson. The findings suggest teachers use of concrete materials is limited to conducting simple demonstrations. In statistics, teachers reported using data derived from real life scenarios. Teachers also registered strong support for using game-based teaching. Lack of time was listed as the major inhibiting factor.

Leading primary school mathematics involves stimulating teacher learning for the purpose of improving students' mathematical outcomes. Currently there are staff shortages and school mathematics leadership may have changed. The results of a semi-structured interview with an experienced School Mathematics Leader who reflected on her work are reported here. She was asked about her "classroom work" and to describe her goals for mathematics learning. Fullan's (2001) "Framework for Leadership" was used to shape conclusions to the study around: moral purpose, knowledge building and sharing, coherence making, understanding change and relationship building.

There has been a lot of media attention about 'out-of-field' teaching, but much of it does not capture the complexities of the term or account for the range of knowledge, experience, and attitudes relevant for teaching mathematics in the middle years. In this paper we report on a survey conducted to better understand the diversity of the profession teaching middle school mathematics (Years 7-10) in South Australia. A preliminary analysis indicates that self-identification as a teacher of mathematics is a key contributing factor to confidence in teaching mathematics. We suggest that looking through an identity lens will better inform planning and support for out-of-field teaching in mathematics.

The phenomenon of teachers designing their own instructional materials is gaining more attention in research. Different aspects of this enterprise have been examined--its potential to reveal the complexity of teachers' instructional planning considerations, the design principles employed by teachers to realise instructional goals, among others. In the study reported in this paper, the focus was on its utility as a form of teacher professional development. In particular, evidence was sought for this claim: not only is teacher-designed instructional materials a useful tool for professional development, it can capture usable knowledge teachers appropriate from professional development.

Teaching towards big ideas provide opportunities for teachers to think deeply about content and pedagogy in order to support their students to see connections in mathematics. However, teachers may not always activate or mobilise their knowledge in classroom situations. This paper looks into how a teacher, Peter, think about the tasks in his instructional materials he crafted to uncover what he may notice about the affordances of the tasks for teaching proportionality.

It is well accepted and understood amongst the mathematics education community that numeracy is the responsibility of all teachers, across all levels of schooling. However, the way numeracy is understood and actioned across the Early Childhood, Primary and Secondary contexts is different. This paper reports on a case study of secondary school teachers seeking to be more intentional in embedding numeracy across the curriculum. The findings indicate that dialogue and support to see, and make, numeracy connections result in greater cohesion in terms of understanding numeracy and making numeracy more visible for students.

Climate change is a complex issue that requires collective actions from various disciplines, including educating future generations about sustainability. Some countries such as Indonesia and Australia have included sustainability into their school curricula, which require teachers to design and implement tasks related to a sustainability issue. However, teachers may not have the capability and understanding to do so. The challenges are difficult for mathematics teachers because designing a mathematics task pertaining to sustainability is rarely explored. Therefore, this paper draws from mathematics education literature to provide and discuss a new framework for designing sustainability-related, mathematics tasks (green mathematic tasks).

This paper reports on one aspect of a bigger project: teachers' design of instructional materials. We found a number of design moves used by the teachers in our study. In this paper, we report three of them: Making things explicit, making connections, and resequencing practice examples. [This paper is the fourth in a symposium of four papers. For the first paper "Models of Mathematics Teaching Practice in Singapore Secondary Schools," see ED616186. For the second paper "An Experienced and Competent Teacher's Instructional Practice for Normal Technical Students: A Case Study," see ED616178. For the third paper "Imbuement of Desired Attitudes by Experienced and Competent Singapore Secondary Mathematics Teachers," see ED616187.]

This paper reports how 30 experienced and competent Singapore secondary mathematics teachers attempted to imbue desired attitudes in their students and some possible factors that might have influenced the teachers' choice of instructional approaches. It was found from the analysis of lesson observations of these teachers that most of those teaching lower-ability students tended to build their students' confidence and perseverance, while those teaching higher-ability students were more inclined to help their students appreciate the relevance of mathematics. Only a minority of the teachers tried to make lessons fun by using mathematics-related resources or telling non-mathematics-related jokes. It was also discovered from the teacher interviews that two factors appeared to influence the teachers' choice of the types of positive attitudes to develop in their students: the abilities of their students and the beliefs of the teachers on what mathematics is. [This paper is the third in a symposium of four papers. For the first paper "Models of Mathematics Teaching Practice in Singapore Secondary Schools," see ED616186. For the second paper "An Experienced and Competent Teacher's Instructional Practice for Normal Technical Students: A Case Study," see ED616178. For the fourth paper "Singapore Mathematics Teachers' Design of Instructional Materials," see ED616188.]

A model of instruction is a set of strategies that guide teachers in their instructional practice. The purpose of this paper is to dispel the myth that mathematics teaching in Singapore schools is all about drill and practice, as perceived of many Asian systems. This paper draws on data of a large project that examined the enactment of school mathematics curriculum in Singapore secondary schools. Based on the teaching practices of 30 experienced and competent teachers, a survey was constructed and administered to 677 teachers. The data from the survey showed that teachers go well beyond traditional forms of instruction in their teaching practices in Singapore secondary schools. [This paper is the first in a symposium of four papers. For the second paper, "An Experienced and Competent Teacher's Instructional Practice for Normal Technical Students: A Case Study," see ED616178. For the third paper, "Imbuement of Desired Attitudes by Experienced and Competent Singapore Secondary Mathematics Teachers," see ED616187. For the fourth paper, "Singapore Mathematics Teachers' Design of Instructional Materials," see ED616188.]

This paper presents a case study of an experienced and competent mathematics teacher's classroom instructional practice in a Normal Technical Mathematics course. The topic that was observed was Volume and Surface Area of a Pyramid, a subtopic within the mensuration topic in Secondary Two syllabus. The teacher used a video clip on the Egyptian Pyramids to integrate students' prior knowledge on pyramids, which raised their attention on the topic. This was followed by engaging the students in hands-on activity to understand the formulae. [This paper is the second in a symposium of four papers. For the first paper, "Models of Mathematics Teaching Practice in Singapore Secondary Schools," see ED616186. For the third paper, "Imbuement of Desired Attitudes by Experienced and Competent Singapore Secondary Mathematics Teachers," see ED616187. For the fourth paper, "Singapore Mathematics Teachers' Design of Instructional Materials," see ED616188.]

Action research is a means for teachers and researchers to develop evidence-based practices. This paper reports the process and outcomes of "teaching sprints," an approach to action research, conducted by secondary school mathematics leaders as part of a professional learning program. Mathematics leaders consistently reported the value of developing collaborative practices throughout the planning, enacting and reflection of the teaching sprint.

As teachers begin to construct an understanding of 'inquiry', and incorporate IBL into their classroom practice, they are challenged to be sensitive to the 'constructivist' nature of the CLD. This paper presents a reflection model structured to trigger thinking about beliefs in teaching and learning in order for teachers to re-examine their practice and adopt new pedagogies. The reflections by two secondary school mathematics teachers are presented as they experiment with inquiry-based learning in the CLD. The teachers showed awareness, monitoring and regulation of their teaching practices including new and existing beliefs.

The description "primary mathematics specialist" has become more frequently used in Australia in the past 10 years, suggesting sustained interest in deepening teacher expertise. Despite this, there is limited contextual research about how to prepare in-service teachers for such roles, and the organising structures needed to facilitate their progress. This paper describes background and emerging insights from a project offering sustained and supported learning experiences for in-service teachers to become primary mathematics specialist teachers in and across their school. Curriculum and contextual experiences designed around a theoretical framework of leadership development implemented over 2 years are described. Early insights include the "priming" influence of an extended focus on mathematical content and pedagogical knowledge on participants' confidence to lead others, and the benefits of being explicit about enabling structures that promote sustainable growth and change.

Primary mathematics leadership has become a focus for improving the teaching of mathematics within Australian primary schools. Much of the training and support for those in the role have concentrated on content knowledge, rather than leadership training. There are currently no guidelines or standards in place to support the complex and multi-faceted roles and responsibilities of primary mathematics leaders. This paper reports on the initial stage of a research project examining how primary mathematics leadership is conceptualised and experienced. It reports on survey findings regarding teachers and leaders' understanding of primary mathematics leadership.

Listening is involved in daily school activities, but its importance is often overlooked and underestimated. Good teaching practices evolve from telling to listening in order to understand the needs of the student. In this paper, lesson study, a form of teacher professional development, is used as a contextual platform for developing the practice of listening pedagogy. The findings suggest that lesson study provided a conducive and favourable context for the learning of listening pedagogy. At the same time, it also allowed for rich teacher learning to take place which had an impact on teacher beliefs that contributed to the thinking of listening pedagogy.

All teachers of mathematics aim to provide productive learning experiences that cater for students in their care. The planning of effective and engaging mathematics lessons is complex and requires expertise. In a larger study survey data, observations and interviews were used to investigate the ways in which School Mathematics Leaders supported teachers to learn. This paper reports results from case study research and focuses on the actions of one School Mathematics Leader during planning meetings. Findings highlight a range of supportive actions, which included developing constructive working relationships with teachers, fostering knowledge of mathematical content and curriculum and facilitating collaborative team planning.

This paper focuses on the time teachers take to adapt to a student-centred inquiry approach to teaching mathematics, the nature of those changes and the reasons for variations in both these aspects among teachers within and across schools. Five numeracy experts, who worked with 200 Foundation to Year 2 teachers to facilitate the implementation of the approach, were individually interviewed at the end of the year to obtain their perspectives on teachers' adaptation. Thematic analysis of the data revealed two overarching themes--context and teacher agency. The findings reinforce recommendations that professional learning providers acknowledge and take account of individual teacher learning trajectories to maximise potential change in practices.

Prospective secondary mathematics teachers in Australia are typically taught by mathematics educators and mathematicians who work in different faculties and seldom collaborate--a situation that can lead to conflicting views about how to teach mathematics. This paper reports on findings from semi-structured interviews with three mathematics teacher educators in a hybrid mathematics/mathematics education department. Valsiner's zone theory is used to analyse how their beliefs, institutional context and professional learning opportunities shape their identities as MTEs. Findings reveal that the MTEs had developed similar beliefs within supportive institutional context but drew on different sources of professional learning.

Current trends in mathematics education emphasise student-centred learning; and internet-based pedagogies, such as online mathematics instructional platforms, go even further in reducing the role of the classroom teacher. In this paper I consider how teachers may exercise agency and professionalism in the context of online mathematics instruction. Whilst there is some evidence for the reduction of the teacher role, there is also considerable space for teachers to enact professional identities as teachers of mathematics. However, I suggest that care needs to be taken to ensure that there is a balance to the overall mathematics programme, including opportunity for teachers to make their own decisions and assessments regarding students' learning.

The professional lexicons of middle school mathematics teachers in communities around the world were documented as part of The International Classroom Lexicon Project. This vocabulary captured teachers' naming of classroom pedagogical practice. Reported in this paper are attributes of the lexicons of teachers from Australia and Chile. A comparison of the lexical items revealed commonalities and differences in the named phenomena and in the schema employed for their organisational structure. The analysis revealed differences attributable to cultural and contextual factors. A categorisation system was developed to classify the complexity of similarity of lexical items of one lexicon with another.

In this paper, we report on the pedagogical actions of one teacher in eliciting and developing students' mathematical reasoning during one mathematics lesson. The findings illustrate that through the careful design and planning of a contextually relevant task (the construction of a manu tukutuku), and the implementation of specific teacher actions, a group of marginalised students were provided access to exploring the concept of equivalence.

In this paper, we present a case study of a secondary mathematics teacher, Isaac (pseudonym), and his considerations for teaching with multiple methods for solving missing-value problems. While his students preferred methods that drew more closely on their intuitive understanding of proportionality, Isaac emphasised the algorithmic cross-multiplication method. Analysis of Isaac's introduction and use of the cross-multiplication method suggest his key considerations were linked demonstrating the efficiency of the cross-multiplication method, while also helping students to make making meaning from the cross-multiplication method.

Pedagogical Content Knowledge (PCK) is a powerful construct for examining the complexity of teacher knowledge. Together with teachers' moment-by-moment choices of action, it provides insight into teachers' knowledge and its influence on student learning. This paper investigates the PCK experienced by a senior secondary mathematics class during a lesson on probability. Data were gathered through observation, and student and teacher interviews. Multiple aspects of PCK were evident and were used in complex and dynamic ways.

To foster effective teaching and quality education, professional development (PD) is imperative. This paper explores the perspectives of junior secondary mathematics teachers in two Queensland schools as part of a broader case study that investigated the perspectives of junior secondary mathematics teachers on the transition of Year 7 to secondary schooling in Queensland. The study explored existing PD practices and sought to identify perspectives of how PD can be better utilised to improve teacher quality. The theoretical lens of teacher identity was adopted, and the key findings indicated a lack of existing PD practices; the need for further PD; and a process for implementing mathematically focused PD in the future.

When mathematics teachers plan lessons, they interact with curriculum materials in various ways. In this paper, we draw on Brown's (2009) "Design Capacity for Enactment" framework to explore the practice of "adapting" curriculum materials in the case of a Singapore secondary mathematics teacher. Problems from the textbook used and the worksheets she crafted were compared to determine how she adapted the content. Video-recordings of the lessons and post-lesson interviews were used to clarify how her personal "teacher resources" contributed to her design decisions. The findings suggest that her seemingly casual use of problems from the textbook are in fact unique variations of adapting curriculum materials.

Despite recent calls to adopt practice-embedded approaches to teacher professional learning, how teachers learn from their practice is not clear. What really matters is not the type of professional learning activities, but how teachers engage with them. In this paper, we position learning from teaching as a dialogic process involving teachers' pedagogical reasoning and actions. In particular, we present a case of an experienced teacher, Mr. Robert, who was part of a primary school's mathematics professional learning team (PLT) to describe how he learned to teach differently, and how he taught differently to learn for a series of lessons on division. The findings reiterate the complexity of teacher learning and suggest possible implications for mathematics teacher professional development.

This paper provides an overview of a programmatic research project, the Enactment Project, at the National Institute of Education in Singapore. The project studies the enactment of school mathematics by competent experienced teachers in secondary schools and also how widespread practices of these competent experienced teachers are in the classrooms of mathematics teachers in general. It elaborates the two studies and two phases of the project. [This paper is the first in a symposium of four papers. For the second paper "Instructional Strategies Adopted by Experienced Secondary Teachers When Enacting the Singapore School Mathematics Curriculum," see ED604247. For the third paper "Chronologically-Grounded Survey," see ED604248. For the fourth paper "Singapore Secondary Mathematics Pedagogy: The DSR DNA," see ED604249.]

"The Enactment Project" seeks to find out in more detail what is happening in Singapore mathematics classrooms. In particular, the video data of 30 teachers suggests that there is a distinctive Singapore secondary mathematics pedagogy, almost like its DNA, which is characterized by cycles of Development, Seatwork and Review (DSR). This paper reports findings from the statistical analysis of a survey on a further 689 teachers regarding aspects of the DSR. [This paper is the fourth in a symposium of four papers. For the first paper "A Study of School Mathematics Curriculum Enacted by Teachers in Singapore Secondary Schools," see ED604245. For the second paper "Instructional Strategies Adopted by Experienced Secondary Teachers When Enacting the Singapore School Mathematics Curriculum," see ED604247. For the third paper "Chronologically-Grounded Survey," see ED604248.]

Classroom instructional quality is seen as crucial to student learning. Of particular interest is the interpretation and enactment of the intended mathematics curriculum in Singapore schools by experienced mathematics teachers towards quality learning outcomes. This paper discusses the findings from the study which investigate the instructional strategies that are adopted by experienced mathematics teachers based on the intended Singapore school mathematics curriculum. Findings from the study provide important implications for educational policy makers and practitioners on improving teaching and learning. [This paper is the second in a symposium of four papers. For the first paper "A Study of School Mathematics Curriculum Enacted by Teachers in Singapore Secondary Schools," see ED604245. For the third paper "Chronologically-Grounded Survey," see ED604248. For the fourth paper "Singapore Secondary Mathematics Pedagogy: The DSR DNA," see ED604249.]

This is a common experience among education researchers: we notice a surprising instructional move enacted by a teacher. After deeper reflection, we ask, "How many other teachers in Singapore do this?" In this paper, we describe an instrument we designed that is part of the resource needed to answer such questions. [This paper is the third in a symposium of four papers. For the first paper "A Study of School Mathematics Curriculum Enacted by Teachers in Singapore Secondary Schools," see ED604245. For the second paper "Instructional Strategies Adopted by Experienced Secondary Teachers When Enacting the Singapore School Mathematics Curriculum," see ED604247. For the fourth paper "Singapore Secondary Mathematics Pedagogy: The DSR DNA," see ED604249.]

This study examines mathematics teachers' assessment practices for senior high school students in Ghana. Formative assessment has been identified in the literature as having a significant impact on students' learning. However, less attention has been given to students' perceptions of teachers' assessment practices in Ghana. Data involved questionnaires for 420 senior high school students and 308 senior high school teachers in the Ashanti Region of Ghana. The results showed that students and teachers hold different perceptions of assessment practices, and suggest teachers should pay more attention to questions, homework, student observation, student demonstration and group work to support students' progress and better examination attainment.