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Despite mathematical reasoning being necessary for in-depth understanding of mathematical concepts, many teacher experience difficulty in assessing it. Data were collected from 34 primary teachers at 4 Victorian government schools at two post-lesson reflective sessions following lessons with a focus on reasoning. These sessions facilitated teachers' collaborative efforts to assess their students' reasoning from students' work samples. The data included transcripts of all the reflective sessions; written work samples; and associated completed rubrics. Analysis of these data enabled identification of seven challenges teachers experienced in assessing reasoning: Limited guidance provided by curriculum documents; Teachers' knowledge of reasoning; Teacher noticing and interpretation of student reasoning; Students' difficulties in articulating their reasoning; Assessing progress in reasoning; Inadequacy of work samples; and Challenges in tracking and reporting student progress in reasoning. The discussion presents strategies to overcome these challenges.

Australian students' attitudes to mathematics are in decline relative to other countries. Their participation in senior secondary mathematics that provide pathways to further study is also falling. Pedagogical approaches that improve students' attitudes to mathematics and knowledge of mathematics are required. This paper reports on preservice secondary mathematics teachers' objectives for their students' learning and their anticipated teaching and learning activities. The study was conducted over one year using quantitative analysis of paired responses to items in pre and post questionnaires. At the end of the year, the preservice teachers emphasised objectives for understanding and positive disposition but anticipated using fluency activities almost daily. Investigations involving problem solving and reasoning were anticipated to occur at least weekly. However, a significant decline in their anticipated use of activities that link mathematics to other disciplines or applying mathematics to real world problems occurred. Other data suggest a lowering of emphasis on developing students' disposition and interest in mathematics. The findings suggest that more attention needs to be given to raising preservice teachers' awareness of the importance of students' disposition. Further research on the impact of teaching experience and opportunities to develop all proficiencies and to link mathematics to other disciplines and real-world problems during preservice teacher education is recommended.

Mathematical reasoning, which plays a critical role in students' capacity to make sense of mathematics, is now emphasised more strongly in various curricula internationally. However, reasoning is sometimes difficult for teachers to recognise, let alone teach. This case study considers video of one teacher's implementation of a problem-solving lesson in a year 1 primary school class in Australia. It examines the opportunities this teacher provided to leverage reasoning and contributes to the body of knowledge on ways reasoning may be elicited during problem solving. The new Eliciting Mathematical Reasoning Framework arising from the analysis of the data in this study builds on and extends previous research. It provides a tool to support researchers, teacher educators, professional learning providers, and teachers in recognising and eliciting reasoning.

Within vocational education and training (VET), mathematics learning is often complicated by students' problematic prior mathematics education experiences and associated low confidence and limited prerequisite knowledge. Teachers have insights into students' mathematics learning needs and appropriate curriculum and assessment responses, but their views are often neglected within VET policy contexts. To better understand the challenges of mathematics education within VET programmes in Australia, we focused on three vocational qualifications within a rural VET institution in Victoria, chosen to vary the visibility of mathematics content, learning environment, and curriculum philosophy. Despite this diversity, teachers from each qualification made similar criticisms of the ways their institution implements mathematics curricula. They described how a behaviourist approach to competency-based education (CBE) constrains their capacity to respond to students' needs, with adverse effects on students' mathematics learning. We argue that the assessment and reporting regimes that currently govern education within Australian VET institutions contribute to negative experiences for already disadvantaged mathematics learners. We suggest that the disconnect that teachers described between students' needs and the approach to curriculum and assessment speaks to a larger inconsistency between the social inclusion aims of Australian VET and the way that CBE is implemented.

In primary science education, we face an ongoing concern of helping classroom teachers overcome negative associations with science content, teaching and learning. These associations can often impact how they view the value of science in their classroom teaching and impede the development of innovative teaching practice. This research effort investigated in-service teachers' perceptions, reflections and considerations that resulted from their direct involvement within a science-focused school university partnership. Utilizing a multiple case study design, this research effort analyzed partnership efforts across five established science-focused partnership programs in the Australian states of Victoria and Tasmania. Analysis of interview data with 80 in-service teachers from across partner sites indicated an increased valuing of science, where teachers viewed working with pre-service teachers as a professional development opportunity, resulting in additional time spent on developing and teaching through inquiry-based science practices.

Teacher education programs are pivotal in the professional preparation and formation of pre-service secondary mathematics teachers (PSMTs), but there appears to be a lack of understanding of how best to prepare PSMTs for the profession. The purpose of this study was to examine and monitor changes over time in PSMTs' views about approaches to teaching mathematics in secondary schools, before and after undertaking mathematics teaching methods courses (including practicum teaching). These views included their perceived readiness to teach secondary mathematics, as well as an indication of their likelihood to use particular teaching approaches for mathematics. PSMTs at two Australian universities were surveyed before and after they undertook their respective teaching methods courses, and interviewed upon course completion. Overall, survey data did not indicate a significant change in PSMTs' views of readiness to teach mathematics from either university (N = 61 pre-survey, N = 34 post-survey). An analysis of interview data revealed that PSMTs were not ready to teach secondary mathematics, with their emphasis focused on their mathematical content knowledge and mathematical pedagogical knowledge as areas of requiring improvement. Nearly half of the interviewees reported feeling confident to teach mathematics to lower secondary classes (Years 7-10). Despite these concessions, all interviewed PSMTs outlined at least one area where they had experienced professional growth since commencing a teacher education degree.

This research effort investigates principal perceptions regarding the impact of science-focused school university partnership programs in primary school contexts. Utilizing a multiple case study design, this research effort analyzed the nature and structure of the partnership efforts across five established science-focused partnership programs in the Australian states of Victoria and Tasmania. Analysis of interview data from principals across twelve separate school partner sites indicated that principals depicted that partnership arrangements increased their staffs valuing of science and was a mechanism for teachers to reflect on their practices. Consequently, principals often viewed partnerships as an additional level of professional development. Most importantly, principals articulated that the partnership programs were an important aspect of the school-based culture and they harbored strong desires to continue the partnerships well into the future. Implications for partnership development and key elements of trust, mutuality and reciprocity are discussed.

Improved pedagogical practice does not happen in a silo; it requires impetus. External influences and pressures and internal motivations are drivers for pedagogical change. Professional learning (PL) programs, in their multitude of forms, are key tools for affecting teacher change. In response to an increased focus on fostering students' reasoning in curriculum documents, our team developed the Mathematical Reasoning Professional Learning Research Program (MRPLRP) to support teacher change. This two-phased project aimed to build teachers' knowledge of the critical aspects of reasoning pedagogical approaches that foster students' development of reasoning. Phase One involved researchers' planning and demonstrating a lesson with a focus on reasoning. In Phase Two, a peer learning team (PLT) is formed to plan a lesson to elicit reasoning and to observe each other teach the lesson. This article reports on Phases One and Two of the MRPLRP from the perspective of one teacher who participated in both phases. The findings provide insights into the aspects of PL that were critical in shifting this teacher's understanding of reasoning and approaches to teaching reasoning. Whilst the results of a single case cannot be extrapolated to a larger population, we present and discuss the factors of this PL program in raising the awareness of critical aspects of reasoning, and thus this paper has the potential to impact future PL design.

Science education starts at primary school. Yet, recent research shows primary school teachers lack confidence and competence in teaching science (Prinsley & Johnston, 2015). A Victorian state government science specialist initiative responded to this concern by providing professional learning programs to schools across Victoria. Drawing on cultural historical activity theory (CHAT), this paper reports the analysis of transcripts of interviews with 17 science specialists from eleven schools. It presents the various perceived and enacted science specialist roles, and how they changed over time. The CHAT analysis of the transcripts revealed seven different stages describing trajectories of the science specialism. The variation in the trajectories indicate the importance of the influence of the community in the enactment of the science specialism. Affordances, constraints and challenges of implementing the science specialist role are discussed.

This paper reports on the impact of a professional learning programme on participating teachers' perceptions of mathematical reasoning. A total of 26 teachers participated in this study from four schools in Victoria, Australia and one school in British Columbia, Canada. The participants observed two demonstration lessons prepared and taught by the research team, attended pre- and post-demonstration lesson group discussions and taught each lesson in their classroom. Interviews with participating teachers before beginning the program, after trialling the first demonstration lesson, and after trialling the second lesson provided data for analysis. The Primary Teachers' Perceptions of Mathematical Reasoning Framework previously established by the research team was used to track the shifts in teachers' perceptions and understanding of mathematical reasoning across the program. We theorise that intentional foci on salient aspects of reasoning demonstration lessons, highly collaborative reflections, and teacher enactment of the demonstrated lessons have the potential to develop teachers' perceptions and understanding of reasoning.

Engaging students in comparing and contrasting, forming conjectures, generalising and justifying is critical to develop their mathematical reasoning, but there are untapped opportunities for primary school students to improve these reasoning processes in mathematics lessons. Through a case study of one task, this paper reports on levels of justifying and the connections to other reasoning processes of comparing and contrasting, forming conjectures and generalising observed among Year 3-4 Australian and Canadian students (9-10-year olds) using the mathematical reasoning actions and levels (MRAL) framework (Authors 2017). The findings revealed that examining commonalities and differences was critical to allow Year 3-4 students to form conjectures and generalise for themselves. Justifying by examples and seeking counterexamples to evaluate the conjecture were prevalent with some students attempting to develop logical argument. The findings have implications for frameworks that assess students' levels of justifying and for teacher actions that encourage students to communicate their reasoning through oral and non-verbal as well as written communications.

Many elementary teachers find the complexity of understanding and teaching mathematical reasoning challenging. Teachers can benefit from professional learning (PL) programs designed to develop strategies to identify reasoning and implement it in mathematics lessons. This paper reports on a PL program designed to support a Peer Learning Team (PLT) of elementary teachers in Canada who were assisted by a researcher to peer-plan, peer-observe, and reflect on lessons fostering reasoning. Recorded data from PLT meetings were analysed against a planning framework to study the teachers' growth in understanding reasoning. The findings revealed teachers engaged in a PLT which plans together to embed reasoning in a lesson, followed by peer-observation and reflection is a powerful and effective model of PL for understanding mathematical reasoning and pedagogical approaches that foster students' reasoning.

While it is recognised that a teachers' mathematical content knowledge (MCK) is crucial for teaching, less is known about when different categories of MCK develop during teacher education. This paper reports on two primary pre-service teachers, whose MCK was investigated during their practicum experiences in first, second and fourth years of a four-year Bachelor of Education program. The results identify when and under what conditions pre-service teachers' developed different categories of their MCK during practicum. Factors that assisted pre-service teachers to develop their MCK included program structure providing breadth and depth of experiences; sustained engagement for learning MCK; and quality of pre-service teachers' learning experiences.

According to international studies of achievement in mathematics amongst Australian secondary school students, results have declined over time when compared with other countries. The National Assessment Program -- Literacy and Numeracy (NAPLAN) is an Australian government initiative to measure whether students have the knowledge, understanding, skills and values required for a productive and rewarding life. This paper presents a case study of a school with improved NAPLAN numeracy results to provide insights into factors that influenced student performance. The findings are structured according to themes evident in the data. The discussion explores these themes in relation to Hattie's areas of influence on success in students' learning: the school, the student, the home, the curriculum, the teacher, and the approaches to teaching. Through the analysis of data collected from a variety of stakeholders in the school, this case study highlights the importance of school-wide policies towards learning mathematics and adopting effective approaches to teaching it. These insights have implications for teachers, school leaders and systems who are working towards improving numeracy results.

Families lay the foundation for their children's future educational success. Engaging families in mathematics education has positive benefits for their child's attitude, motivation to learn, and academic achievement. Fostering school-home partnerships are essential to ensure that mathematics learnt in the classroom have wider applicability to home and community and assist with classroom learning of mathematics. Collaboration and communication between school and home offers families an understanding of the language of education and how mathematics teaching occurs today, while offering schools a rich source of personalised expertise about their students, along with greater support from home. In this paper the authors present a synthesis of contemporary research evidence relevant to the issue of schools working collaboratively with families to enhance the mathematical learning of primary students. Essential factors in establishing working relationships with families are: a range of communication; respect between all parties in the relationship; positive attitudes to mathematics; and, building an understanding of mathematics and current approaches to teaching mathematics.

This article explores the approaches used to plan mathematical reasoning tasks by two peer learning teams, one based in regional Victoria and the other in Vancouver, Canada. The results revealed that planning and peer observation support teachers' knowledge of mathematical reasoning and the pedagogy required to promote it.

In this article, the authors discuss two ways of improving the rigour and integrity of mathematics in STEM programs drawing on examples from their research. The authors examine how mathematics can be made a stronger part of a STEM unit using examples from two pairs of teachers engaged in a STEM teacher professional development program, conducted across two years in thirty schools with sixty teachers. The article discusses how teachers can start with the mathematics and build a STEM unit using an example from the reSolve: Mathematics by Inquiry project. In each example the authors provide links to the Mathematics Curriculum, but one of the joys of teaching mathematics within a STEM unit is that it addresses the curriculum in multiple and rich ways.

This paper reports on the STEPS project which addressed international concerns about primary teachers' lack of confidence to teach science, and on-going questions about the effectiveness of teacher education. The five universities involved had each independently established a science education program incorporating school-based partnerships between the university and local schools to enable primary pre-service teachers (PSTs) to teach science. The diversity of the programs enabled an examination of the relevant literature underpinning the approaches and comparison of data from participants to identify key features and success factors for establishing and maintaining working relationships with schools. This preliminary analysis of learning from STEPS uses case studies and feedback from PSTs who participated. These findings indicate that authentic teaching experiences build the confidence of PSTs to teach science. Ultimately, the project will develop an Interpretive Framework which will articulate the characteristics of partnerships to be validated through feedback from other science educators from Australia and overseas.

There is a consensus that we need to improve the quality of pre-service teacher education, and teachers' mathematical content knowledge is critical for teaching. Identifying opportunities and influences that assist pre-service teachers to extend their mathematical content knowledge throughout their teacher education programme is important. This paper reports on qualitative data, collected over 4 years from two typical pre-service teachers whose developing mathematical content knowledge was investigated during their primary and secondary programme. These data were analysed and reported using the four dimensions of the Knowledge Quartet: foundation knowledge, transformation, connection and contingency. The results highlight the consequences of programme structure in order to help pre-service teachers to establish and sustain a positive mathematics learner identity, build teacher identity and develop mathematical content knowledge.

Attention to mathematical reasoning in curriculum standards is part of an international trend, but identifying and understanding reasoning continues to challenge teachers. We report on one component of an Australia-wide initiative supporting teachers to implement innovative pedagogies. This paper contains insights from design research that focused on trialling classroom materials to support elementary teachers in their planning and assessment of mathematical reasoning. Findings confirmed planning is a critical step to developing learning experiences that elicit student reasoning, including consideration to task modifications and teacher questioning. Teachers' capacity to assess their students' reasoning was explored using the purposefully designed Assessing Mathematical Reasoning Rubric. The results reveal the complexity involved in constructing accurate judgements of students' reasoning capabilities, particularly appreciating the non-linear nature of mathematical reasoning and the need to draw on multiple sources of evidence. Implications for supporting teachers in their planning for, and assessing of, mathematical reasoning are raised.

A recent international study of pre-service teachers identified that proportional reasoning was problematic for pre-service teachers. Proportional reasoning is an important topic in the middle years of schooling and therefore it is critical that teachers understand this topic and can rely on their Mathematical Content Knowledge (MCK) when teaching. The focus of this paper is second-year Australian primary pre-service teachers' MCK of real number items related to ratio, rate, proportion and proportional reasoning. This paper reports on strengths and weakness of pre-service teachers' MCK when responding to test items; including a method suitable for analysing responses to five items and ranked by three levels of difficulty. The results revealed insights into their correct methods of solutions and common incorrect responses, identifying difficulty, where multiplication and division were required. The method of coding test items by difficulty ranking may assist with developing an appropriate learning trajectory, which will assist pre-service teachers develop their MCK of this and other difficult topics. (Contains 7 tables and 4 figures.)

This paper seeks to theorise primary teachers' degree of integration of digital technology in the mathematics classroom. In an age where digital technology use is ubiquitous, the issues surrounding teachers' choice, and ultimately their uptake of digital technologies in the classroom, is an area that need to be further unpacked. Cross-case analysis of the two teachers' uptake of digital technologies in their classroom, their pedagogical approaches and the reason for their choices provide insight into teachers' technological, pedagogical and content knowledge (TPACK). Differences in the way the teachers use digital technology in their classroom seem to be connected to their TPACK developmental stage.

Primary pre-service teachers (PSTs) in Australia often have low confidence and negative experiences in relation to science and teaching science. This paper reports on pre-post survey data produced by four institutions involved in a multi-institutional project exploring the use of university-school partnerships for primary science teacher education. The findings show that the experience of engagement in school-based science teaching contributed to the development PST classroom readiness particularly with respect to statistically significant increases in confidence. We argue that moving tutorials from university into schools supports PSTs' engagement with the teaching profession and teaching science.

Since 2008, all Australian students in Years 3, 5, 7 and 9 have been assessed in literacy and numeracy through an annual National Assessment Program--Literacy and Numeracy (NAPLAN) test. In 2015, a team of mathematics education researchers across Australia conducted a nationwide research project to identify school practices and policies that were consistent between schools that showed growth and/or improvement in their NAPLAN numeracy results. This paper reports findings from three case study schools, using a school improvement framework to interpret evidence gathered from the schools' principals and school leaders. The study has particular implications for policy makers and school leaders who may be seeking ways to improve mathematical practices in their own jurisdictions and schools.

This article provides a classroom resource for identifying, assessing and promoting one aspect of reasoning--analysing--through the Assessing Mathematical Reasoning Rubric. Practical examples of student work and rubric levels are offered.