Sharyn Livy

Monash University (Australia) · Faculty of Education

Prior research has revealed a variety of factors associated with teacher views around when to incorporate challenging mathematical tasks into instruction, such as teachers' pedagogi-cal content knowledge and their prior assumptions about student ability. There has been less focus on how motivational beliefs (teacher anxiety, enjoyment, confidence)...

Leading school mathematics is a complex task and the responsibilities and activities involved are not always clearly defined. School mathematics leaders (SML) in Australian schools are often expected to lead improvement in mathematics teaching and learning. Previous research typically focuses on the qualities of effective leaders rather than the pr...

Traditionally Australian primary school teachers have been viewed as generalists responsible for instruction across all content areas. Adopting self-determination theory as a lens, the aim of the study was to explore the extent to which generalist primary school teachers are interested in becoming subject matter specialists. Questionnaire data were...

The current study explores how teachers report using enabling and extending prompts when teaching with sequences of challenging mathematical tasks. Twenty-nine early years primary school teachers completed a questionnaire following their participation in a professional learning project. Findings suggest that teachers’: view prompts as important whe...

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...

Just as students experience productive struggle or spend time in the ‘zone of confusion’ when engaging with challenging tasks, teachers also experience similar difficulties and periods of confusion when engaging with new pedagogical approaches. Prior to a 19-week lockdown due to Coronavirus (COVID-19) during 2020, two Foundation teachers implemente...

In March 2020, COVID-19 restrictions required our university courses to be offered in online mode only. This quick transition meant that lecturers were suddenly tasked with adapting their classroom-based teaching approaches and materials to the online space. For mathematics teacher educators (MTEs), whose on-campus classes were characterized by par...

Whilst spatial reasoning skills have been found to predict mathematical achievement, little is known about how primary (elementary) students’ conceptual understanding of three-dimensional objects develops. In this article, we report a qualitative study and the impact of rich learning experiences on 48 Years 3–6 students’ geometric reasoning relatin...

This qualitative survey study set out to investigate in-service and pre-service primary school teachers’ perceived barriers to and enablers for the integration of children’s literature in mathematics teaching and learning in an Australian educational context. While research over the past three decades have documented pedagogical benefits of teachin...

Effective middle leading of mathematics is a complex task as it requires a focus on improving learning outcomes for students. This study gathered information about the activities of middle leaders of mathematics using a survey of primary and secondary mathematics leaders. Both primary and secondary mathematics leaders more often focussed on interac...

All students should have access to learning experiences that help them make sense of important mathematical concepts. This study highlights teacher actions for consolidating student learning during teacher-lead discussion in the early years. We report on a case study of a Year 1 teacher involving a lesson observation. Highlights of the lesson inclu...

In this article, the authors from Monash University and the University of Sydney have collaborated to present a research-informed model to support the planning and teaching of mathematics, using a student centred structured inquiry approach.

As mathematics teacher educators (MTEs), our teaching and research is informed by frameworks and explanations of terms to guide our thinking about the knowledge an effective mathematics teacher might use. This chapter investigates whether or not the Knowledge Quartet (KQ) framework can be applied to the work of MTEs. Using the context of a co-teach...

Despite the construct of challenge being recognized as an essential element of mathematics instruction, concerns have been raised about whether such approaches benefit students with diverse academic needs. In this article, we focus on the beliefs and instructional practices of teachers teaching students in the first three years of school (5 to 8 ye...

Despite teacher enjoyment of teaching being associated with a range of benefits for teachers and their students, little research exploring the characteristics of teachers who enjoy teaching mathematics exists. Semi-structured interviews were conducted with ten teachers who scored in the top third in terms of their enjoyment of teaching mathematics...

Given what is known about the importance of productive struggle for supporting student learning of mathematics at all levels, the current study sought to examine teacher attitudes towards student struggle when students learn mathematics in remote learning settings compared with classroom settings. Eighty-two Australian early years primary teachers...

Teacher reluctance to teach mathematics through challenging tasks is frequently linked to beliefs that such approaches are not appropriate for students perceived as less mathematically capable. One potential means of shifting such beliefs is inviting teachers to reflect on students that surprise them when working on such tasks. Early years' primary...

The fear of making mistakes and avoidance of risks can create disabling anxiety and limit learning opportunities. The team from Monash University and the University of Sydney describe the features of learning environments which increase enjoyment and engagement of students who experience anxiety.

Australian schools, like schools elsewhere, have been through a period of closure. The closure creates both threats and opportunities for teachers and students. In the context of a project exploring approaches to teaching in early years, we outline some considerations and offer advice to teachers and educators on strategies for welcoming students b...

It is possible that learning from home during the COVID-19 lock down can be productive especially if teachers developed mathematical learning experiences that challenge student thinking. But it is also possible that time away from school might have exacerbated differences in learning opportunities. This article explores ways to reengage students wh...

The purpose of this chapter is to explore the influences on, and tensions within, initial teacher education in mathematics, and to identify the research outcomes that might advance our understanding of learning and practices in this context. We have used a socio-spatial approach to organise our review into the three ‘spaces’ of policy, teacher educ...

Reform-oriented approaches to mathematics instruction view struggle as critical to learning; however, research suggests many teachers resist providing opportunities for students to struggle. Ninety-three early-years Australian elementary teachers completed a questionnaire about their understanding of the role of struggle in the mathematics classroo...

This chapter uses the notion of relentless consistency, elaborated by Laurinda Brown, to describe an approach to teaching mathematics we are researching. A fundamental assumption is that students learn better and engage actively when tasks on which they are working on are more rather than less challenging. The article describes how challenge is con...

In this study we explored the relationship between teacher enjoyment of teaching mathematics, their attitudes towards student struggle, and the amount of time teachers spent teaching mathematics. Ninety-eight primary educators were surveyed regarding their attitudes and behaviors towards mathematics instruction. Hierarchical regression analyses rev...

The authors describe a mathematics lesson designed to allow students to use their own thinking to solve elapsed time problems. Their approach emphasises student-centred structured inquiry, and follows a ‘Launch, Explore and Summarise’ format.

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, skil...

In this paper we report on changes to teachers’ practices as a result of their participation in a research-based program of professional learning focused on challenging tasks. Seventy early years teachers responded to a survey at the end of a year-long program asking them to nominate and describe the teaching practices that changed most as a result...

This paper reports on a New Zealand iteration of the Encouraging Persistence, Maintaining Challenge (EPMC) project, which proposes that students learn mathematics best when they build connections between mathematical ideas for themselves. This iteration explores the actions, perceptions and learning of 12 primary teachers and their 281 students dur...

In this article, the authors emphasise the importance of purposeful mathematical discussion and using sequences of connected, cumulative, and challenging tasks in advancing students' spatial reasoning in the early years of schooling.

This article reports on a project which involved introducing challenging tasks in the early years’ classrooms of twenty Victorian primary schools. The obstacles teachers encountered and how they overcame those obstacles are discussed.

In this article we focus on ways that the documented curriculum can inform the construction and implementation of planned sequences of experiences to support mathematics learning. We report on the early stages of a research project which is examining ways that thoughtfully created, cumulative, challenging and connected experiences can both initiate...

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 pap...

While some teacher educators work alongside teachers with their pre-service teachers in school settings, it is less common for teachers to work alongside teacher educators in university settings. The following chapter provides insights on how a mathematics lecturer and a Year 1 teacher taught primary pre-service teachers in a university classroom....

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 co...

Exploring how students learn mathematics and what types of tasks promote mathematical reasoning may assist pre-service teachers to develop their pedagogical content knowledge (PCK) for teaching. This study reports on an experience of a cohort of Australian primary (elementary) pre-service teachers, destined to become specialist mathematics teachers...

Challenging mathematical tasks can be designed to allow students of all abilities to experience productive struggle. It is important for teachers to communicate with students that productive struggle is important and it is what mathematicians do

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...

Understanding the development of pre-service teachers’ mathematical content knowledge (MCK) is important for improving primary mathematics’ teacher education. This paper reports on a case study, Rose and her opportunities to develop MCK during the four years of her program. Program opportunities to promote MCK when planning and practicing primary t...

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....

Use this new framework to select and analyze picture books for their mathematical content, such as the accuracy of the number of cans that stack in a shopping cart.

In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range and...

This paper draws on observation of a primary mathematics lesson prepared and taught by a second-year pre-service teacher who lacked mathematical content knowledge. A 'knowledge quartet' (Rowland, Turner, Thwaites, & Huckstep, 2009) was used to investigate when and how a pre-service teacher drew on their knowledge of mathematics during primary teach...

Improving numeracy performance of all students across Victoria is a government priority. A key element of this initiative lies with tertiary institutions that are responsible for adequately preparing pre-service teachers for teaching primary mathematics. This paper examines data from a larger, longitudinal study of primary pre-service teachers' mat...