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Students in secondary school often find mathematics abstract and irrelevant, frequently questioning its usefulness and purpose. The discourse around STEM education has encouraged secondary teachers to attempt connecting mathematics with other STEM disciplines, most commonly with science. By making connections between content and skills through applications, it is anticipated that secondary school students will engage more in class that may result in improved mathematics achievement. This paper explores the rationale for making connections with science, examines the impact on student achievement in mathematics from previous research and discusses challenges for schools and teachers.

This paper reports on a study of choices about the use of a computer algebra system (CAS) or pen-and-paper (p&p) by a class of seven Year 11 Mathematical Methods (CAS) students as they completed a calculus worksheet. Factors that influenced students' choices are highlighted by comparing and contrasting the use of CAS and p&p between students. Teacher expectation of students' use of CAS and p&p reveals that, even in a small class, the students' use of CAS and p&p sometimes differed from what was expected. The analysis here indicates that there are a variety of factors that influence students' decisions, including speed of calculation and accuracy of p&p work.

From 2011-2013 the VCAA conducted a trial aligning the use of computers in curriculum, pedagogy and assessment culminating in a group of 62 volunteer students sitting their end of Year 12 technology-active Mathematical Methods (CAS) Examination 2 as a computer-based examination. This paper reports on statistical modelling undertaken to compare the distribution of results for this group with the standard cohort, and any differences in student response between the two groups at the item level.

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.

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.

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.

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.

This paper examines the types of teacher questions that assist young students to interpret and explain their critical mathematical thinking (CMT). Focusing on students who enter their first year of formal schooling (aged 5-6 years), this paper draws on data from a one-on-one task based clinical interview conducted with 16 students. Teacher questioning data were analysed for question type (probing, factual, guiding) and further analysed against the conceptualized critical mathematical thinking framework for young students. Findings indicated that when teachers used clarifying, noting relationships, and offering opinions style probing questions, young students were supported to interpret and explain their critical mathematical thinking.

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.

Engagement in mathematics education is an important factor in a successful student experience. This paper reports findings from a study of Year 5 student perceptions of engagement during a two-week, inquiry-based learning (IBL), problem-posing investigation. The study triangulated data from semistructured interviews, video observations and student work samples to understand the student's perspectives of IBL; however, this paper reports the interview data. The findings indicate that most of the students were behaviourally, emotionally, and cognitively engaged during the IBL investigation, and that the investigation provided an opportunity for students to experience levels of competence, relatedness, and autonomy need satisfaction.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

In 2011, the "Let's Count" professional learning program was developed into an elective distance education subject offered at Charles Sturt University. The resulting subject, EMC101: Let's Count, has been offered every year since 2012, and has to date been completed by 796 students. This paper details the subject design and provides enrolment and evaluation data that attest to the success of the subject. [This paper is the second in a symposium of three papers. For the first paper, "'Let's Count' in an Online Learning Environment", see ED616193. For the third paper, "'Let's Count' and Community Professionals", see ED616191.]

"Let's Count Online" is a new e-learning approach to delivering "Let's Count" professional learning. It was evaluated in 2018. The findings suggest that the e-learning platform was successful, and that the outcomes for educators were similar to those achieved by participants using the face-to-face workshop professional learning model. Several key differences in outcomes were noted, and these inform recommendations for refining "Let's Count Online." [This paper is the first in a symposium of three papers. For the second paper, "'Let's Count' in Early Childhood Teacher Education," see ED616194. For the third paper, "'Let's Count' and Community Professionals," see ED616191.]

The "Let's Count" Community Professional Pilot 2019 took place in six sites across three states (New South Wales, Queensland and South Australia). The aim of the pilot program was to implement the "Let's Count" face-to-face program for the first time with a group of people who work with young children and their families but who are not trained early years educators working within early childhood education and care centres. This paper reports on the evaluation of the pilot program with specific emphasis on expanding the reach of "Let's Count" whilst maintaining its integrity and outcomes. [This paper is the third in a symposium of three papers. For the first paper, "'Let's Count' in an Online Learning Environment," see ED616193. For the second paper, "'Let's Count' in Early Childhood Teacher Education," see ED616194.]

This paper contributes to the Research Symposium, "Strengths approaches in early childhood mathematics education" by providing an illustration of how an early childhood centre adopts a strengths approach to mathematics education for birth to three-year-old children. A case illustration is drawn from a current Australian Research Council-funded study focusing on mathematics education for children under three years of age. The case is analysed and described using a five-step strengths-based framework. [This paper is the second in a symposium of three papers. For the first paper, "An Introduction to the Strengths Approach," see ED616177. For the third paper, "Leadership of Strengths-Based Approaches for Early Years Mathematics Education: Using CHAT as a Framework for Educational Leaders' Professional Learning Leadership," see ED616189.]

Mathematical self-concept refers to the perceived ability that one has in being able to do mathematics. While it has been shown to be a significant predictor for how students learn and apply mathematics, little research has been conducted into the relationship between the mathematical self-concept of teachers and their pedagogical practices in the mathematics classroom. This paper reports on a section of the findings from a small mixed methods study that sought to ascertain the nature of primary teachers' mathematical self-concept and how it is related to their teaching practices. Findings suggest that a teachers' mathematical self-concept does not necessarily reflect the mathematics practices evident in their classroom.

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.

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 outlines the rationale for, and some elements of, a particular approach to teaching and learning mathematics in the early years. The researchers worked with two school systems to offer both centrally delivered and school-based teacher professional learning, which included the application of illustrative teaching resources. The project gathered a range of data from teachers and leaders on their dispositions and knowledge, as well as the opportunities and constraints they experienced, and the influence these variables had on planning, teaching and student learning outcomes.

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.

While interdisciplinary approaches in the STEM subjects are widely advocated there are concerns that disciplinary learning can be compromised, especially in mathematics. The Interdisciplinary Mathematics and Science (IMS) project is a three-year longitudinal study in four Victorian primary schools that has developed a pedagogical approach to mathematics and science learning where data modelling and representation are common to each. Investigations include astronomy, ecology, chemistry, fast plant growth, force and motion, water use, heat and temperature, body height, light and microorganisms. The paper describes the role of mathematics in the IMS pedagogical model and design of learning sequences.

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.

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.

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.

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of information and demonstrate cognitive flexibility in their use of visualisation, diagrams, language, and symbols.

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.

The transition between arithmetic and algebraic thinking is challenging for students. One notable difficulty for students is understanding algebraic symbols--pronumerals. Researchers are exploring pedagogical approaches in seeking to address this issue. The current paper is contributing to this body of literature by illustrating how an online card matching game-based learning activity supports students' understanding of pronumerals.

The Early Learning STEM Australia (ELSA) pilot was a year-long investigation involving 300 educators and 4 500 four-year old children in one hundred learning centres across Australia. This paper reports on a pedagogical and design framework that was constructed to promote children's STEM engagement across digital and non-digital learning environments. This paper describes this process in terms of a heuristic; since the educators in the study became part of the design team as they modified and adapted the activities developed by our team. The heuristic helped the educators modify and adapt the learning experiences to accommodate the diverse cultural and social needs of the students. [This paper is the second in a symposium of three papers. For the first paper, "The Role and Nature of Digital Technology Use in Preschool STEM," see ED604741. For the third paper, "The ERA Heuristic in Action: Observations from the ELSA Pilot," see ED604739.]

This paper contributes to the Symposium: "Research methods involving children's drawings in mathematical contexts" by providing insight into young children's attitudes towards mathematics through the use of drawings. Children in Years 2 and 3 (n=25) participated in this study which aimed to identify a range of attitudes towards mathematics using the Three-dimensional Model of Attitude (Zan & Di Martino, 2007). The analyses illustrate drawings in conjunction with written responses, interviews and classroom observations offers authentic evidence of young children's attitudes towards mathematics. Further, findings indicate that children's Vision of Mathematics contributes significantly to their overall attitude. [This paper is the third in a symposium of four papers. For the first paper, "Using the Drawing-Telling Approach to Reveal Young Children's Mathematical Knowledge," see ED604537. For the second paper, "Capturing the Mathematical Drawing Process Using a Digital Pen," see ED604538. For the fourth paper, "Coding Young Learners' Pictorial Responses to an Open-Ended Assessment Task," see ED604540.]

This paper contributes to the Symposium: "Research Methods Involving Children's Drawings in Mathematical Contexts" by exploring the use of digital pens as a data gathering tool. The availability of digital recording devices has been a boon to researchers wanting to capture the real-time dynamics of a research situation. When capturing a child's drawing process, an alternative to cumbersome video-recording equipment is a digital pen that records both the creation of the drawing and any nearby utterances. To highlight the affordances and limitations of the digital pen as a data collection tool for children's drawing we utilise examples from two different research projects, one with Australian children and the other with Canadian children. [This paper is the second in a symposium of four papers. For the first paper, "Using the Drawing-Telling Approach to Reveal Young Children's Mathematical Knowledge," see ED604537. For the third paper, "The Nature of Young Children's Attitudes towards Mathematics," see ED604539. For the fourth paper, "Coding Young Learners' Pictorial Responses to an Open-Ended Assessment Task," see ED604540.]