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Opportunities for self-determined online professional development (OPD) are emerging, but their potential for increasing adult learners' agency is not yet fully realised. Faced with the problem of successfully designing a self-determined comprehensive evidence-based online numeracy resource for educators who are often time poor and do not engage with online learning unless they are intrinsically motivated, we engaged in design research to conceptualise the "Birth to Level 10 Numeracy Guide" for educators and families. The "Birth to Level 10 Numeracy Guide" fosters educators' and adult learners' numeracy capability across numeracy focus areas from birth to level 10 (16-year-olds). This extensive OPD resource incorporates consistent design elements, double-looped learning, nonlinear learning, self-reflection, and metacognition activities to foster educators' pedagogical content knowledge (PCK) through experiential learning. With a section dedicated to families, the resource provides suggestions and advice to parents and carers on everyday, authentic activities to develop children and young people's numeracy understandings at home and in the local community. As education systems continue to grapple with the disruption brought about by the COVID-19 pandemic, the "Birth to Level 10 Numeracy Guide" is a timely, freely accessed, viable, and scalable option for providing low-cost OPD.

Mathematics curricula have traditionally focused on content knowledge, often in the form of a scope and sequence of increasingly difficult mathematics. The importance of using and applying mathematics is recognised in the current Australian Curriculum Mathematics (AC: M) as 'proficiencies' that are intended to be integrated with the content. There is little support for teachers to develop these proficiencies -- reasoning, understanding, problem solving and fluency. Learning progressions are sequences of learning that focus on cognitive processes, and thus provide a useful basis for curriculum development. Using an empirical Statistical Reasoning Learning Progression as an exemplar, a new approach to curriculum development is suggested that links content knowledge with the proficiencies. The outcome is a zone-based, rather than year level based, curriculum that allows teachers to target their teaching, so that students develop increasingly sophisticated understanding of statistics and probability.

The COVID-19 pandemic has significantly impacted on schools globally with closures and the implementation of online learning (UNESCO, 2020). This rapid shift has resulted in a significant change to traditional modes of delivery, including classroom teaching and professional learning opportunities for teachers, as well as thinking differently about how families can support learning at home. COVID-19 restrictions meant that teachers were suddenly tasked with online modes of delivery, necessitating the uptake and use of digital technologies and resources. Parents have found themselves taking on the role of home educators, rather than assisting with homework tasks, which may have formed the basis of previous 'home learning'. Understandably, teachers, families, and students turned to digital resources to supplement this rapid shift to online learning. In this article, the authors discuss the Victorian Government's Birth to Level 10 Numeracy Guide, an online self-determined professional learning resource for educators and families, which aims to foster dynamic approaches to developing student numeracy in schools and at home.

Research in science, technology, engineering, mathematics (STEM) education suggests development of STEM competency requires effective learning environments, including the use of varied representations (e.g., visual, symbolic) and opportunities for students to make connections among them. Although such practices have been advocated in the teaching of mathematics and science for some time, there has been a renewed focus on representations in the teaching and learning of STEM (e.g., Australian Curriculum, Assessment and Reporting Authority [ACARA], 2018a; Glancy & Moore, 2013). Working with representations plays a critical role in helping students develop flexible thinking and problem solving, and provides multiple entry points and access to individual STEM subjects such as mathematics (Huinker, 2015). This article describes the experiences of a peer learning circle as they developed their understanding of representational fluency in mathematics. The outcomes of this learning circle suggest useful approaches for pre-service teacher education, and development of teacher knowledge and expertise in the use of varied representations.

Explaining the complexity of mathematics teaching to others can be challenging. The Knowledge Quartet, a pedagogical content knowledge (PCK) framework from the UK, provides a fresh lens to reflect on mathematics classroom practice. Developed from videotaped mathematics lessons taught by final year pre-service teachers, the Knowledge Quartet describes four dimensions of teachers' knowledge for teaching mathematics: Foundation, Transformation, Connection, and Contingency. Each of these categories has several indicators that may be observed in the overall process of teaching, including during planning and preparation, classroom instruction, and reflection and evaluation phases.

We report on three approaches taken to incorporate collaborative activities into undergraduate mathematics classes. There is strong evidence from research in K-12 classrooms that these, and similar, approaches support a range of positive learning outcomes for students. Despite the potential benefits the cited studies have shown, research into the use of such methods at the tertiary level is limited. We describe the ways in which we have implemented research projects, collaborative tutorials, and team-based learning in a range of undergraduate mathematics classes in two countries. We present quantitative and qualitative evidence from these teaching experiences to support our claim that there is a definite mandate for significant opportunities within our courses for students to work cooperatively, talk together, and argue about mathematics.

In a 2-year project, we developed and trialled a mode of lecturing professional development amongst staff in our department of mathematics. Theoretically grounded in Schoenfeld's resources, orientations, and goals (ROG) model of teacher action, a group met regularly to discuss both the video excerpts of themselves lecturing along with written pre- and post-lecture statements of their "ROGs". We found evidence of improved teaching performance but more interestingly, identified key aspects of our practice and of undergraduate mathematics that received repeated attention and developed further theoretical insight into lecturer behaviour in mathematics. The trial has been successful enough to be expanded into further groups that now constitute a professional development culture within our department.

An introduction is presented in which the editor discusses various reports presented at the Fourteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics, held in Cape Town, South Africa in November 2023.

With the proliferation of new affordable recording technologies, many universities have begun offering students recordings of live lectures as a part of the course resources. We conducted a survey to investigate why some students choose to attend lectures in person rather than simply watching the recordings online, and how students view the two types of lectures. Students attending live lectures in five large undergraduate mathematics lecture streams were invited to respond to the survey. A significant number of respondents viewed recorded lecture as superfluous to their needs which were met upon attending live lecture. Surprisingly, however, an equally large number of students described compelling reasons for watching both live and recorded lectures. A number of factors were identified as determining students' perceptions of live and recorded lectures as competing or complementary: personal learning styles, study habits, esteem for the lecturer, and the possibility of interaction in the lecture.

The effective integration of technology into the teaching and learning of mathematics remains one of the critical challenges facing contemporary tertiary mathematics. This article reports on some significant findings of a wider study investigating the use of technology in undergraduate mathematics. It first discusses a taxonomy developed to describe and compare technology use within individual courses and departments that identifies a complex range of factors, summarized under six defining characteristics of an "integrated technology mathematics curriculum" (ITMC). An instrument for a simple comparison of technology use employing the elements of this taxonomy is provided. It then presents evidence gathered from an observational study of technology implementation at The University of Auckland, and examines this evidence against the taxonomy. The findings suggest that while the underlying complexity of the taxonomy limits a categorical definition of integrated technology, it does provide an effective means for examining the issues confronting those wishing to implement and sustain integrated technology in undergraduate mathematics. An integrated, holistic approach, which aims for curricular consistency across all the characteristics described in the taxonomy, provides the basis for a more effective and sustainable ITMC. Key findings, some of which will be considered in more detail in this discussion, include: the importance of mandating technology use in official departmental policy; paying attention to consistency and fairness in assessment; re-evaluating the value of topics in the curriculum; re-establishing the goals of undergraduate courses; and developing the pedagogical technical knowledge of teaching staff. (Contains 4 tables and 2 figures.)

Papers presented at earlier Delta conferences reported on the use of collaborative tutorials and peer-tutors in undergraduate mathematics courses at The University of Auckland. This paper reports on significant developments within the Department's programmes, including the extension of the collaborative small-class tutorials to cover all first-year undergraduate courses in the department. It provides evidence of the effectiveness of the tutorial programme, as gauged from a survey of students' perceptions. Many of the students enrolled in the "Tutoring in Mathematics" course that initially trains and provides the peer-group tutors continue on as tutors in other mathematics courses within the Department. Some subsequently enroll in the University's Graduate Diploma in Teaching (Secondary). The effects of the tutoring course on tutors continuing to tutor at higher levels, and their performances as novice teachers in the Diploma course are examined. (Contains 3 tables and 1 figure.)

An editorial is presented on Delta conference held in charming Fremantle, Australia, in November 2019. Topics include contributing the research for dissemination in special issue having the certainty of participation without the need for travelling; and focusing on active learning, student engagement, social interaction and student support considering critical issues associated with online assessment.