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In fluvial dynamics studies, there are instances where it becomes necessary to estimate the daily discharge of a river in locations where only one instantaneous level record is available per day. In such cases, there may be no rating curve, or one that is unreliable, making it difficult to make accurate discharge estimates. A daily rating curve would be an estimate of the daily discharge of a river, from a single instantaneous stage level. This work proposes to estimate synthetic (non-gauged) daily rating curves from nearby gauged locations using a rainfall-runoff model. A rainfall-runoff model (GR4J) is coupled with an instantaneous/stage–daily/discharge relationship based on third order Chebyshev polynomials. The parameters in the joint daily rating curve and rainfall-runoff model are optimized and uncertainty is quantified with Bayesian inference and the Delayed Rejection Adaptive Metropolis algorithm assuming model residuals to be normally distributed N(0,σ). A case study with four gauging sites in New South Wales, Australia, and periods with no changes in the stage-discharge relationship were selected. The method is implemented four times across the gauging sites, where three sites are assumed gauged and one site is assumed to have only instantaneous water level records. The results of this methodology can help provide a more comprehensive understanding of the hydrological functioning of systems, where only one instantaneous stage level per day is available. This is particularly useful in situations where historical observations or satellite altimetry data in rivers is used to estimate daily flows. [ABSTRACT FROM AUTHOR]

From the standpoint of a MOOC practitioner (i.e., a MOOC provider) instead of a rigorous comparative law researcher, this article attempts to analyze the potential legal issues and risks underlying instruction via MOOCs and compare these legal issues and risks between the small jurisdiction Macao and such major jurisdictions as the United States, the United Kingdom, Australia, and the European Union. These legal issues and risks so identified concern the three perspectives intellectual property, privacy, and accessibility. Supported by academic literature, statutes, acts, and court cases, this article elaborates on these three perspectives with respect to MOOC providers, quotes the key legal statutes and acts in these three perspectives in the context of MOOC providers, elucidates the statutes' and acts' emphases and the related remedies and penalties for breaches, and probably other details, and compares them across the aforesaid jurisdictions. Some prominent findings are that Macao, the United Kingdom, Australia, and the European Union appear to practice clearly defined and compendious laws to protect privacy whereas the United States' counterparts seem to be circumscribed by, for example, the ages of the individuals to protect. As such, for MOOC providers, the former four jurisdictions sound to be more critical than the latter jurisdiction in the perspective of privacy. As for accessibility, Macao's, the United States', the United Kingdom's, and Australia's laws focus on educational institutions. Nonetheless, whether the majority of MOOC providers can be regarded as such "education institutions" under such laws may likely be disputable. In contrast, the European Union more generically enacts a law on accessibility of digital products and services. Even so, to what extent and how MOOCs are supposed to conform to such a law may arguably still be contingent upon each particular scenario. [For the full proceedings, see ED636095.]

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.

This paper reports on 73 Grades 3 to 6 students' written responses to equal groups, arrays, multiplicative comparison and Cartesian product word problems. It is part of a larger study relating to students' development of multiplicative thinking (MT). The potential of using multiplicative word problems as a diagnostic assessment to reveal students' transition barriers from additive thinking to MT was explored. The development of the assessment and some of the research findings are described here. Findings show that students experience different types of barriers during their transition from additive to MT. Some recommendations are given on how these barriers might be overcome during primary school years.

Calls for high levels of participation and success in Science, Technology, Engineering and Mathematics (STEM) by all Australians exacerbates the need for research into improving participation in mathematics by students from disadvantaged backgrounds. Rogoff's three planes of analysis is used to foreground the institutional plane in a low socioeconomic status school with sustained increased enrolments in Mathematics B (now replaced by Mathematics Methods). Processes in this plane are examined by drawing on semi-structured interviews with a Deputy Principal and Head of Mathematics. Contributing factors appear to be the way that the Mathematics Program and Pastoral Care Program are delivered at the school.

It is generally understood that both clear teacher instruction and orderly classroom climates support student achievement in mathematics. However, to what extent does instructional clarity "compensate" for classroom disorder? In this exploratory study, we analyse data from 8,864 Year 8 students sampled by TIMSS 2019 to investigate the relationship between instructional clarity, classroom disorder, and mathematics achievement. The findings demonstrate the deleterious effects of classroom disorder for mathematics achievement, even in the presence of high instructional clarity. The findings contribute to an emerging international body of work and reinforce the importance of teachers having an optimal combination of classroom skills to support student learning.

This paper explores use of a set of diagrammatic tools for representation and analysis of the moves a teacher makes implementing a mathematical modelling task. The focus here is on identifying what the teacher did so we can subsequently interrogate this, as to the why. Data include pre and post lesson teacher interviews and transcripts of a video and audio-recorded task implementation. The analytical tools developed, with one teacher and one task early in a three-year project were particularly useful in ascertaining what the teacher moves were as we subsequently sought to determine reasons for these.

The current study explored the reasons for students' preferences for the teach-first and task-first lesson structures, and whether students' preferences were influenced by their perceptions of the teacher's preference. Students (n=18) from two composite Year 3 and 4 classes (aged 8-10 years) completed a post-lesson drawing task and participated in a semi-structured interview following a series of lessons. Findings indicated students had a variety of reasons for their preference of lesson structure. Most focus students reported noticing aspects of the teacher's enjoyment during instruction. The results have implications for the way teachers inadvertently influence their students' own enjoyment of and preferences for instructional approaches.

This paper reports on students' experiences of describing and representing variation in hypothetical data. Fifty-six students (8-9 years-old) experienced collecting and working with quantitative data for two years as part of a STEM education project. The task described here was an end-of-year survey question, with three parts about a hypothetical context for surveying students in two different Australian cities: recording the data, describing the potential variation in the data, and creating a representation of what the data might look like when only a descriptive account of the context and variables were provided. The data analysis framework utilised provides a means of determining students' readiness for further development of statistical ideas.

Typically, more primary students qualify for mathematics intervention support than schools have the capacity to assist. This highlights the importance of every primary mathematics teacher having the expertise to design inclusive and responsive curricula and instruction for students who may experience difficulty. Our study addresses this issue through exploring how specialist intervention teachers can support the mathematics professional learning of teachers using co-teaching cycles. The findings provide insight about the challenges experienced by classroom teachers when teaching students who experience difficulty with mathematics, and the actions of the specialist intervention teachers that assisted the teachers' professional growth.

Informed by teaching statistics across curriculum areas strategies, this study investigated the skills of 36 pre-service teachers (PSTs) who designed numeracy activities that focused on the statistics strand of the Australian curriculum. The data were analysed using descriptive statistics. The results showed that the PSTs designed numeracy activities focused on the science curriculum area. The results further showed that PSTs emphasised a few year levels and focused on collecting and recording data. The first stage of teaching statistics (designing effective questions) is often ignored in their activities. The approach adopted in this study can be used to identify PSTs' knowledge gaps and their professional learning requirements.

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.

This qualitative study investigates remote Australian primary school parents' attitudes towards their children's learning of mathematics and the role of technology. Using semi-structured interviews and thematic analysis, results revealed that parents aimed to provide the best mathematics learning opportunities for their children, yet they felt obsolete and isolated from their children's learning. Additionally, they valued the role of technology, but did not think school was providing adequate digital literacy skills. Discussion about what changes to the educational community are suggested to support parents in their children's learning.

This study examined the types of mathematical connections established by four secondary school students while constructing concept maps on transformations of the parabola. The use of concepts maps revealed students' understandings--including some misconceptions--of transformations of the parabola and confirmed the usefulness of a model for categorising types of connections.

This paper reports on early years teachers and how often they should devote planning time to anticipating student responses in advance of the lesson. Sixty-five Foundation to Year 2 teachers (students 5-8 years of age) completed questionnaires at the beginning and end of a year-long research-based professional development program. Participants were learning to teach with sequences of challenging tasks. Post-program data showed a shift in the frequency of time participants believed teachers should devote to anticipating student responses prior to teaching. Supporting teachers' mathematical knowledge for teaching with an emphasis on how they plan and anticipate student responses has implications for improving practice and student outcomes.

Providing opportunities for students to demonstrate their mathematical thinking can be challenging. This paper reports on a case study conducted with a teacher and her class of Grade 3/4 students which investigated this phenomenon. Following collection of baseline data that showed her students were not demonstrating evidence of mathematical thinking, the teacher implemented teaching approaches designed to address this. The findings indicated the teaching approaches were effective and led to changes in the teacher's practice and professional growth. The study has implications for teachers who are looking to make changes to their practice based on evidence-informed teaching approaches.

Two case studies of Australian primary school students tracked changes in their data interpretation and representation over three years. Students were engaged in predictive reasoning tasks based on their interpretation of a data table showing temperature change over time. Students' explanations and graphical representations were collected at the beginning of Years 3 and 4 and the end of Years 4 and 5. The first case study was a student mathematically weaker than her peers while case study two was within the average range for her year. Despite differences in starting points, both case studies followed a similar developmental sequence of predicting, interpreting and representing, with the first case generally lagging one stage behind the second case. Similarities and contrasts between the two students are discussed.

Place value is one of the 'big ideas' in number and plays a critical role in helping students develop their number sense, problem solving and computation skills. Yet, the elegant simplicity of our place value system belies the abstract nature of the construct. This paper presents data from 606 Year 3-6 students (ages 8-12) from two metropolitan Melbourne primary schools who completed the Place Value Assessment Tool (PVAT). Each student's place value knowledge was categorised according to the Place Value Developmental Progression (PVDP). The results highlight the wide range of understanding in each year level and challenge the efficacy of a number magnitude-based progression in place value.

Teachers often perceive barriers to integrating technology with Mathematics. In the study, teachers participated in professional development about considerations for and examples of integrating Digital Technologies into Mathematics learning in primary schools meeting the "Australian Curriculum: Mathematics and Digital Technologies" requirements. This exploratory multiple case study included preand post-surveys, mentoring conversations and interviews to explore their beliefs and perceived barriers to integrating mathematics and digital technologies. This paper provides insights into their perceived barriers to integrating digital technologies.

Despite curriculum expectations, many students, including a disproportionate number of girls, do not 'just know' (retrieve) single-digit addition facts by Year 3. The current study employed structured interviews to explore which strategies Year 3/4 students (n = 166) used when solving more difficult addition combinations. Results revealed that students preference the near-doubles strategy when the difference between the addends was one, the bridging-through-10 strategy when one of the addends was a nine, and the count-on-from-larger strategy when a derived strategy was more effortful. Moreover, whereas boys were more inclined to use derived strategies, girls were almost three times more likely to use the count-on-from-larger strategy.

We explore how relational trust was evidenced within the leadership activity of one mathematics leader using cultural-historical activity theory as a theoretical perspective. We use data from interview and observation sources to suggest that relational trust was a motive object of that mathematics leader's activity. Findings contribute knowledge about how relational trust dimensions, originally situated within middle leadership theory, were evidenced within that mathematics leader's activity whilst leading a professional learning experience in their school.

South Australia's PISA performance has been in constant decline since 2003 with the proportion of PISA participants meeting the Australian national proficient standard dropping from 73% (in 2003) to 50% (in 2018). In contrast, Singapore is a consistently strong performer. To better understand student readiness in answering PISA questions, this paper reports a curriculum comparison between Australia and Singapore for Years 9 and 10 in Measurement and Geometry. The findings highlight the similarities and differences in the topics covered in both countries' curricula and raise questions about potential implications for student outcomes in PISA.

We explored primary pre-service teachers' beliefs about challenging mathematical tasks and the role they perceived their initial teacher education played in influencing those aspects. Fifty-seven pre-service teachers completed an online questionnaire, and four participants were individually interviewed. Results showed that most participants recognised the importance of teaching with challenging mathematical tasks even prior to exposure to such content in their teacher education program. The teacher education program was perceived to have positively impacted final year pre-service teachers' perspectives about challenging tasks. Implications for teacher education regarding challenging tasks are discussed.

Place value is a foundational competency for primary school mathematics and for this reason we have sought to investigate what the recent and current academic conversations are around this important concept. In this paper we present a survey of literature presented in the Australasian, European and Southern African contexts through a review of purposively selected conference proceedings and journals to establish what the conversations have been about the teaching and learning of place value in these research communities from 2013 to 2022.

There is an educational expectation that children's natural drawing will develop into proficient mathematical representations and formal diagrams, yet there is little research available to guide the assessment and development of children's mathematical drawing skills. The aim of this paper is to explore how Year 2 children (approx. 7 years) chose to represent their interpretations of a simple story that is suggestive of the take-away subtraction process, and what changes occurred when the drawing task was repeated 6 months later. Analysis of 13 pairs of drawings revealed changes in what the children drew (categories of number representations) and how they drew it (style). The findings suggest that substantial change in children's representational ability can occur in within 6 months.

In this paper we compare the early years mathematics curricula of Germany, South Africa, and Australia in relation to the place value concept. Place value is an important topic as it underpins much of the number work completed by learners in the early years of schooling. We found that there were differences between the three curricula that could be summarised using five themes: namely, number range, place value structure, role of the zero, influence of language, and use of materials. We argue that how the different curricula deal with these five themes influences the quality of learning provided and we highlight key areas of concern. In concluding we identify three important implications for our future research project.

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.

For learners to be individuals equipped with the 21st-century skills when they start business life after graduation, they must be able to gain these skills during their education. However, due to their nature, it's not possible for students to acquire these skills under a specific course. For these skills to be achieved, they must be integrated across all curricula. In this study, an evaluation was conducted to see whether various countries incorporate the 21st-century skills in their curricula, how these skills are applied, and how these skills should be handled in their curricula. Within the scope of this research, the curricula applied in Australia, New Zealand, Canada, England, Ireland, and Turkey were examined. When the 12 skills defined by the P21 platform are considered, it can be seen that all skills are interconnected and that one cannot fully exist without the other. It can be said that starting to gain these skills, which are required by the 21st-century professions and which employers expect from graduates, from an early age it is important for individuals to be properly and fully prepared for the future. In accordance with the 21st-century expectations, evaluations, educational materials, teaching methods, professional growth opportunities, and learning environments should all be synchronized to create a supportive framework that generates the 21st-century results for contemporary students. [This paper was published in: "EJER Congress 2023 International Eurasian Educational Research Congress Conference Proceedings," Ani Publishing, 2023, pp. 97-126.]

Augmented reality (AR), a cutting-edge technology, has the potential to change the way students learn by superimposing virtual items and information onto the real environment. Through more immersive and interesting interactions with digital content, AR might help students better understand difficult concepts and boost their drive to learn. As a result of its contribution to student learning, AR has become increasingly appealing to educational researchers. This study aimed to descriptively explore the characteristics of AR studies in education and to qualitatively analyze the most influential ones indexed in the Web of Science (WoS) between 2000 and 2022. A scoping review was conducted to determine the sample of the AR studies in education based on the inclusion criteria. Accordingly, descriptive analyses were conducted to identify the characteristics of the AR studies in education between 2000 and 2022 in terms of publication year, country, affiliations, journals, funding agencies, and citation trends. Then, the research methodologies and implications were found among the most influential AR studies in education between 2000 and 2022 by synthesizing qualitatively. The overall results indicated that AR studies in education have been conducted since 2008, with an increasing number of studies over time. Based on the implications of the most influential studies identified in terms of citation numbers, it was detected that AR has the potential to enhance education and training by providing interactive and engaging environments, linking real-world contexts with digital resources, and promoting efficiency and effectiveness in learning. [This paper was published in: "EJER Congress 2023 International Eurasian Educational Research Congress Conference Proceedings," Ani Publishing, 2023, pp. 273-291.]

This study aimed to reveal general landscape of research on teacher resilience, employing descriptive and bibliometric analyses. Descriptive analyses were performed utilizing Web of Science's internal system, while bibliometric analyses were executed through the VOSviewer program. Web of Science Core Collection was used as a data source. Citation analyses of publications, authors, and journals, as well as co-authorship, co-citation, and common word analyses were conducted. The research reveals a timeline of publications, indicating a notable surge in 2006, and a substantial increase in 2021. The countries with the highest number of publications on teacher resilience, in descending order, are the United States of America (USA), Australia, the United Kingdom (UK), and the People's Republic of China (PRC), according to the research findings. Authors such as Gu, C. Day, S. Beltman, C. Mansfield, and A. Price emerged from the citation analysis. Based on the results from the co-citation analysis, C. Day and Q. Gu were identified as the most frequently co-cited authors. The co-occurrence analysis of keywords highlighted key terms like resilience, teacher education, early career teachers, teacher candidates, professional learning, school leadership, and COVID-19. The findings were contextualized within the existing literature, leading to recommendations for future research. [This paper was published in: "EJER Congress 2023 International Eurasian Educational Research Congress Conference Proceedings," Ani Publishing, 2023, pp. 591-611.]

The purpose of this paper is to present an empirical investigation of the critical determinants for the adoption of learning analytics in higher education. A conceptual model was proposed to understand better the adoption of learning analytics in higher education by teaching staff. Structural equation modelling is used for testing and validating the proposed conceptual model based on the survey data collected from Australia, South Africa, and Zimbabwe. Five study hypotheses were statistically significant, while two were statically insignificant. A positive relationship was revealed between user preparedness, technology preparedness, perceived usefulness, and social influence with behavioural intentions to adopt learning analytics in higher education. Hypotheses between user preparedness and perceived usefulness as well as user preparedness and learning analytics adoption were rejected. This study contributes to the learning analytics adoption research by proposing and validating a research model for the adoption of learning analytics in higher education. [For the full proceedings, see ED639633.]

Learning objectives, especially those well defined by applying Bloom's taxonomy for Cognitive Objectives, have been widely recognized as important in various teaching and learning practices. However, many educators have difficulties developing learning objectives appropriate to the levels in Bloom's taxonomy, as they need to consider the progression of learners' skills with learning content as well as dependencies between different learning objectives. To remedy this challenge, we aimed to apply state-of-the-art computational techniques to automate the classification of learning objectives based on Bloom's taxonomy. Specifically, we collected 21,380 learning objectives from 5,558 different courses at an Australian university and manually labeled them according to the six cognitive levels of Bloom's taxonomy. Based on the labeled dataset, we applied five conventional machine learning approaches (i.e., naive Bayes, logistic regression, support vector machine, random forest, and XGBoost) and one deep learning approach based on pre-trained language model BERT to construct classifiers to automatically determine a learning objective's cognitive levels. In particular, we adopted and compared two methods in constructing the classifiers, i.e., constructing multiple binary classifiers (one for each cognitive level in Bloom's taxonomy) and constructing only one multi-class multi-label classifier to simultaneously identify all the corresponding cognitive levels. Through extensive evaluations, we demonstrated that: (i) BERT-based classifiers outperformed the others in all cognitive levels (Cohen's K up to 0.93 and F1 score up to 0.95); (ii) three machine learning models -- support vector machine, random forest, and XGBoost -- delivered performance comparable to the BERT-based classifiers; and (iii) most of the binary BERT-based classifiers (5 out of 6) slightly outperformed the multi-class multi-label BERT-based classifier, suggesting that separating the characterization of different cognitive levels seemed to be a better choice than building only one model to identify all cognitive levels at one time. [For the full proceedings, see ED623995.]

In Australia, all teachers are expected to explicitly attend to numeracy in the subjects they teach. Pre-service teachers, therefore, need to begin to develop effective numeracy teaching strategies but there is a limited research base to inform the design of courses that address this need. This paper reports on findings from a study investigating the impact of one such course. The paper draws on data from two pre-service teachers: two course tasks completed at the beginning of the course and interviews conducted at the end of the course. Data were analysed using the 21st Century Numeracy Model. Findings suggest there were changes to the pre-service teachers' understanding of numeracy and their capacity to embed numeracy in the subjects they will teach.

The senior secondary Mathematical Methods subject was introduced in Queensland in 2019 and parents were concerned with the low grades attained. Students in the subject need to develop extensive procedural knowledge and fluency to participate and engage successfully. This mixed methods study informed by constructivism investigated teachers' perceptions on how procedural flowcharts can enhance procedural fluency in the subject. Data were collected through a survey and semi structured interviews with the subject teachers. The study found that procedural flowcharts can foster a classroom environment that stimulates procedural fluency and student-centred teaching and learning of mathematics. The study suggests the potential for using procedural flowcharts in other mathematics subjects at different levels of study.

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.

This study reports on an early career Year 2 teacher's reflections of enacting specifically structured resource materials and her practice change when participating in a mathematics professional learning project. A qualitative case study was designed to examine the reflections of a teacher's pre-service and in-service teaching experiences. Data collection instruments included a timeline graphing tool and a semi-structured interview to capture and communicate her reflections. Findings reveal that providing structured resource materials within a professional learning project supported changes in pedagogical practice.

In the context of a professional learning research project we investigated the nature of support offered to classroom teachers and school mathematics leaders to facilitate teachers' implementation of sequences of challenging tasks. End of year questionnaire data were collected from 70 Foundation to Year 2 teachers and ten numeracy leaders who participated in the project. Thematic analysis was used to analyse the open response questionnaire items. Findings reveal that two forms of support were helpful: in-class support, such as co-teaching, observation, followed by co-debriefing; and facilitated planning prior to instruction.

School Mathematics Leaders seek to improve the mathematical learning outcomes of the students in their schools. Recognising that improved learning is dependent on high quality teaching, leaders are often keen to support teachers' knowledge of mathematics content and pedagogy. This paper reports ways in which School Mathematics Leaders support and lead the professional development of teachers in team meetings. Results from survey data and case study research are reported in this paper to describe and highlight the supportive actions undertaken by School Mathematics Leaders as they provide professional learning opportunities for teachers.

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.

The intangible concept of data, as part of statistical literacy, can be complex for young children to grasp. Inquiry as a pedagogy has potential for supporting student development of statistical literacy as the investigation process is driven by the inquiry question. The aim of this paper is to gain insight into how a teacher's communication processes with her students supported their emerging understandings about the abstract concept of data. In this exploratory case study, we present data from a Year 4 classroom (age 9) in a guided mathematical inquiry within the STEM context of agricultural science. The inquiry question the students addressed was, "How big is a leaf?" The inquiry focused on linking data to the real-life context the data represented.

Professional learning for school mathematics leaders is a key aspect of the Victorian Government's strategy for improving mathematics for Victorian students. This is because middle leaders in schools play a vital role in designing and leading school improvement. As part of the Numeracy Suite, four online courses were designed in 2020 to support the professional learning of mathematics leaders. The courses were implemented and evaluated across 2020-2021. The evaluation showed that each online course was effective in meeting the professional learning needs of primary and secondary mathematics leaders.

This case study aims to describe the learning characteristics of a child and evaluate his preferences for using physical manipulatives (PM) and virtual manipulatives (VM) to solve fraction problems. The participant in this study was a fourth-grade child. The child was given similar problems to solve using PM and VM. Data sources were observations and interviews conducted with the child during and after the tasks were completed. The results showed that the child engaged and preferred solving fraction problems using PM more than VM. The child stated that PM helped him quickly understand the relationship between various representations of fractions and model them using manipulatives. He reported the VM did not help him solve the problems.

This study reports part of a larger study that explores three technologies--Padlet, video-embedded quizzes and Google docs and their effectiveness for enhancing pre-service teachers' (PSTs) learning engagement in online mathematics education. The data reported in this study are a survey, learning analytics and observation data. We found that Padlet heightened PSTs' social and collaborative engagement, and these dimensions were further enhanced in Google Docs activities. PST's cognitive engagement was enhanced through adding quizzes based on lecture videos. This study contributes to selecting relevant technologies to enhance PSTs' engagement in online learning in general and in mathematics education more specifically.

How a sample of university educators described STEM, expected outcomes of STEM, expertise of STEM educators, and STEM learning environments were investigated through drawing- and text- based responses. Data were examined by applying the "Legitimation Code Theory (LCT) Specialisation" plane (Maton, 2014). Participants generally held "knowledge-code" (epistemic relations are foregrounded) or "mixed-code" (sometimes epistemic and sometimes social relations are foregrounded) perceptions. Further analysis showed that participants value both disciplinary knowledge and discipline-related practices such as analysing data and providing evidence-based discussions. The LCT approach has been found powerful in its ability to represent the kind of knowledge that might be valued, and the kind of knowers that might be desired by educators of STEM or individual STEM disciplines including mathematics.

Mathematics self-efficacy is considered an important variable in mathematics education because of its links to mathematics achievement. This paper reports on the development of the "Self-efficacy-effort in Mathematics Scale" (SEEMS), an instrument that has strong theoretical and psychometric properties. Based on a sample of n = 224 Australian primary students and n =133 secondary students, the instrument demonstrated positive correlations with related measures of mathematics achievement and mathematics self-concept. Girls had higher mathematics achievement within the primary and secondary school data. There were no significant gender difference in mathematic self-concept scores for the primary and the secondary school students. For mathematics self-efficacy, a gender difference was only identified in the high school data. The implications of this research to mathematics education practices are reviewed in the paper.

In this paper we report on an aspect of a larger study and explore whether a framework for teacher STEM Capability Sets (SCS) enhanced teacher planning and the implementation of mathematics active STEM tasks. A case study approach was employed to understand how a classroom teacher used the digital resource, Gapminder, to teach a Year 5/6 cohort of students to interpret data as the basis for a STEM assessment. The research found that using the SCS as a guide, and emphasising mathematics in STEM learning and assessment, allowed the teacher to: reflect on existing STEM capabilities; observe the enhancement of other capabilities; and identify areas for future development.

Making accurate judgements and interpretations about student growth and progress in mathematics can be problematic when using open-ended assessments. This study reports on the development of a class-based assessment instrument and marking key designed to assess Year 2 students' mathematics competence to reflect their learning of mathematics through a challenging tasks approach. A qualitative coding process was undertaken to analyse the written responses of 59 Year 2 students resulting in the development of a 7-point marking key to identify levels of progress. The marking key proved effective in supporting the interpretation of the written responses and identifying future learning pathways.

In this paper we reflect on our combined work in some of the most marginalised educational contexts in the Southern Hemisphere. We draw on the work of Bourdieu to frame the paper. We propose the working in marginalised education settings requires a particular habitus or way of being to be able to play the research game. Underpinning our approach is the South African construct of Ubuntu, which is very much about collaboration--I am because we are--so that there is a move away from doing research "on" participants and contexts to one which is very much about doing research "with" participants and contexts. We find Bourdieu's notion of game as a powerful construct to theorise ways of thinking about the field of educational research.

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.