Sharyn Livy
Monash University, Faculty of Education, Faculty Member
- Dr Sharyn Livy is a Senior Lecturer of mathematics education in the School of Curriculum, Teaching and Inclusive Educ... moreDr Sharyn Livy is a Senior Lecturer of mathematics education in the School of Curriculum, Teaching and Inclusive Education, Faculty of Education, Monash University. Her research and teaching are driven by the desire to understand how teachers can be supported to extend their knowledge and pedagogical approaches for teaching mathematics.edit
Research Interests: Psychology and Practicum
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... more
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 educators and pre-service teachers, and to reveal tensions that exist between these spaces. Our analysis of the research highlighted the multiple roles of teacher educators—as researchers, teachers, collaborators and curriculum designers—as they mediate the tensions that occur between the spaces.
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Different styles of argumentation require different methods of writing and proving claims. Academic argumentation requires the author to provide strong evidence to support their claim on any subject. In doing so the author has to find,... more
Different styles of argumentation require different methods of writing and proving claims. Academic argumentation requires the author to provide strong evidence to support their claim on any subject. In doing so the author has to find, understand and decide which evidence to use. Other forms of argumentation are toulmin, debate, Rogerian, satire and persuasive. In debate form of argumentation the author must take a stand if they are for and against the claim. They must also prepare strong arguments for counterclaims and need to finish the debate with a strong and impactful conclusion. In Toulmin argumentative essay the author needs to provide evidence to state their claim with the help of data and numerical statistics. In Rogerian argumentative essay, the author needs to find the strengths and weakness for the claim, for this argumentation the conclusion asks for a change or action. In persuasive essay, the author needs to persuade the readers for a change or new idea. In order to do so the author needs to present strong arguments and make impactful conclusion. In satire argumentative essay, the author takes up a claim and tries to make argument with the help of satire. For this reason the essay has an ironical tone underlying its arguments. One of the biggest issues that have been identified over time is the acceptance of humanities as a concept. Even though it is common knowledge that humanities forms the basis of most cultures. Humanities have however become one of the underrated issues in the new era or generation, where money, status and wealth is given more importance. Even though there are talks about how culturally aware the new generation is, it does not surpass the importance of making money. Nowadays it seems that education, art, religion and culture as well have taken a second seat when it comes to money. This has not only led to conflicts and debates but has also created disinterest and unrest among people.
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Engaging children in mathematics through the use of children's literature has become increasingly popular in primary classrooms (Muir, Livy, Bragg, Clark, Wells, & Attard, 2017). Through considered selection of appropriate... more
Engaging children in mathematics through the use of children's literature has become increasingly popular in primary classrooms (Muir, Livy, Bragg, Clark, Wells, & Attard, 2017). Through considered selection of appropriate children's literature, teachers can utilise stories to help children learn mathematical concepts and skills within a context that is meaningful to them. Children's literature offers opportunities for rich mathematical discussions, problem solving, reasoning, and assists with improving children's attitudes towards mathematics (Schiro, 1997). Picture books in particular can provide a non-threatening environment through which a knowledgeable teacher can capitalise on the mathematics inherent within the text and illustrations, and facilitate learning. Anecdotal evidence and observations, however, indicate that while teachers may use children's literature to engage and stimulate students in mathematical experiences, much of the potential for capitalising on important mathematical concepts is not realised. Furthermore, not all children's literature is appropriate for enhancing a mathematics lesson or providing a stimulus for mathematical discourse (Muir, et al., 2017). To address these concerns, the authors of this paper conceptualised a teaching resource book to assist teachers to engage children with mathematics through rich mathematical and literacy experiences. Chapters in the book followed a similar structure, with features including identification of key mathematical 'big ideas', anticipation of misconceptions and difficulties, and planning frameworks showing how lessons could be enacted and extended. When selecting children's literature for inclusion in the book, we were guided by Marston's (2010) framework which was developed for comparing the efficacy of different types of 'mathematical' picture books, which included books where the mathematics was unintentional, explicit or embedded (Marston, 2010). To evaluate the appropriateness of the books for use in early childhood and primary classrooms, the authors trialled the lessons with participating classes. This paper reports on the results of two lessons trialed with early childhood classes, to answer the research question: How does the use of children's literature as a stimulus engage young children in the learning of mathematics?
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Online learning has made higher education accessible for more students, yet there are ongoing concerns about low student engagement, retention and progression rates in this sector. Online students often experience a sense of isolation and... more
Online learning has made higher education accessible for more students, yet there are ongoing concerns about low student engagement, retention and progression rates in this sector. Online students often experience a sense of isolation and disconnection with their studies and institution, with instructor presence identified as an influential factor in terms of student motivation to engage. This presentation will share the results of a study that investigated the factors which impacted upon students’ engagement with a fully online course. Findings indicated that the presence of the instructor was particularly influential in motivating students to engage with the course.
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This paper reports on a mathematics leader who participated as a co-teacher alongside a teacher educator in a university classroom. The collaboration was designed to bring the profession into the university. Case study research design and... more
This paper reports on a mathematics leader who participated as a co-teacher alongside a teacher educator in a university classroom. The collaboration was designed to bring the profession into the university. Case study research design and qualitative methods were used to analyse written self-reflections, transcripts of interviews and the co-teachers’ post-lesson discussion notes. Along with identifying the benefits of the co-teaching for pre-service teachers, it became evident that the mathematics leader also benefitted from this experience. The findings suggest that such collaborative co-teaching experiences may be a legitimate professional learning experience for school mathematics leaders.
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Teacher educators can use students’ work samples to introduce pre-service teachers to the selection and appropriate sequencing of tasks in a classroom. This not only allows PSTs to engage in an authentic act of teaching, but also reveals... more
Teacher educators can use students’ work samples to introduce pre-service teachers to the selection and appropriate sequencing of tasks in a classroom. This not only allows PSTs to engage in an authentic act of teaching, but also reveals insights into their mathematical content knowledge.
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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... more
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 collected from 104 early years primary school teachers. Findings suggest that two-thirds of these generalist teachers expressed an interest in specialising in either English, mathematics, and to a far lesser extent, science, such that they would be responsible for exclusively teaching this subject. Preferences for specialisation were based on teachers’ self-perceived content and pedagogical expertise and/ or their enjoyment of teaching in this content area. By contrast, the one-third of teachers who would choose to remain generalists referred to the value in a variety of teaching experiences, teaching from a whole child perspective and co...
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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... more
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 ofpre-service teachers’ learning experiences
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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... more
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.
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Research Interests: Dice and Prime Number
In recent years there has been growing concern as to how to bridge the gap between the theory pre-service teachers engage with as part of their learning in their tertiary classrooms and the profession. To enable pre-service teachers to... more
In recent years there has been growing concern as to how to bridge the gap between the theory pre-service teachers engage with as part of their learning in their tertiary classrooms and the profession. To enable pre-service teachers to make stronger connections with the profession, a mathematics teacher educator worked collaboratively with a practicing teacher by co-teaching two cohorts of pre-service teachers studying primary mathematics education. As well as providing benefits to the pre-service teachers, the project allowed the mathematics teacher educator to reflect upon her own practice and the impact of the co-teaching experiences and learning. In this paper we present two snapshots of this experience and a framework that was used to identify how the co-teachers helped the pre-service teachers to make connections between theory and practice, when engaged in mathematical discourse.
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Using the notion of relentless consistency, we are exploring an approach for providing advice to teachers on characteristics and structure of tasks and lessons, the creation of sequences of learning experiences and the classroom culture... more
Using the notion of relentless consistency, we are exploring an approach for providing advice to teachers on characteristics and structure of tasks and lessons, the creation of sequences of learning experiences and the classroom culture that supports this approach. An extract from an illustrative sequence is presented to exemplify the associated classroom practice. Some implications for initial and continuing teacher professional learning are suggested.
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Research Interests: Mathematics and Splash
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BoxCars cover skills and concepts taught from K–12 and allows students to learn in a relaxed, motivating way—REPETITION WITHOUT BOREDOM. Using games as a teaching strategy has been documented as beneficial in breaking down learning... more
BoxCars cover skills and concepts taught from K–12 and allows students to learn in a relaxed, motivating way—REPETITION WITHOUT BOREDOM. Using games as a teaching strategy has been documented as beneficial in breaking down learning barriers and ...
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Survey data from a sample of 102 teachers and teacher-leaders (Foundation to Year 2) from a professional learning day in Melbourne, Australia. Amongst other things, the data set captures teacher attitudes towards student struggle, teacher... more
Survey data from a sample of 102 teachers and teacher-leaders (Foundation to Year 2) from a professional learning day in Melbourne, Australia. Amongst other things, the data set captures teacher attitudes towards student struggle, teacher enjoyment of teaching mathematics and instructional time.
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... more
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 from a sample of 118 generalist, early-year primary school teachers. Thematic analysis of interview data revealed that negative-to-positive turning point experiences were commonplace amongst high-enjoyment primary teachers, but so too were reports of consistently positive feelings towards mathematics throughout their entire lives. While most articulated a passion for teaching mathematics, all teachers considered instances when students experienced ‘light bulb’ moments in their mathematical understanding that made a mathematics lesson enjoyable to teach. An important implication of our research is that one need not be a ‘maths person’ to co...
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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’... more
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.
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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... more
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. Narratives from the co-teachers and two colleagues who observed lessons and interviewed the pre-service teachers tell the story of a co-teaching experience which developed relationships, a sense of community, and diverse skills and expertise of the co-teachers, along with the impact that the experience had on the participants.
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The fear of making mistakes and the avoidance of risk can create disabling anxiety and limit learning opportunities. The team from Monash University and University of Sydney describe the features of learning environments which increase... more
The fear of making mistakes and the avoidance of risk can create disabling anxiety and limit learning opportunities. The team from Monash University and University of Sydney describe the features of learning environments which increase enjoyment and engagement of students who experience anxiety.
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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... more
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 teaching mathematics using children’s literature, research into teachers’ perceptions regarding the use of such resources is virtually non-existent. The study thus filled this research gap by drawing responses from open-ended survey questions of 94 in-service and 82 pre-service teachers in Australia. A thematic analysis revealed 13 perceived barriers classified under five themes with Lack of Pedagogical Knowledge and Confidence, and Time Constraint, representing 75% of all perceived barriers. Moreover, 14 perceived enablers were identified and classified under five themes with Pedagogical Benefits and Love of Stories representing around 70% of al...
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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... more
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 years of age). These teachers participated in professional learning focused on challenging mathematical tasks differentiated through their open-ended design and the use of enabling and extending prompts. The instructional practices are explained using the Theory of Didactical Situations. Questionnaire data from pre-intervention (n = 148) and post-intervention (n = 100) groups of teachers indicated that teachers in the post-intervention group held more negative beliefs than those in the pre-intervention group about the capability of instructional approaches involving a priori grouping of students by performance levels. Interviews with ten tea...
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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... more
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 teachers (n = 160) participated in a professional learning initiative that supported them to implement up to ten sequences of challenging tasks in their classrooms across the school year. When asked to describe a student who surprised them when working on the sequences, approximately half (47%) of teachers described students previously assumed to be less mathematically capable being successful in their mathematical learning. Most remaining teachers (36%) commented on the depth of student mathematical thinking and positive learning dispositions demonstrated, without making any explicit reference to preconceptions of student capability. By ...
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Abstract 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... more
Abstract 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 classroom. Thematic analysis of data revealed that most teachers (75 %) held positive beliefs about struggle, with four overlapping themes emerging: building resilience, central to learning mathematics, developing problem solving skills and facilitating peer-to-peer learning. Many of the remaining teachers (16 %) held what constituted conditionally positive beliefs about struggle, emphasising that the level of challenge provided needed to be suitable for a given student and adequately scaffolded. The overwhelmingly positive characterisation of student struggle was surprising given prior research but consistent with our contention that an emphasis on growth mindsets in educational contexts over the last decade has seen a shift in teachers’ willingness to embrace struggle.
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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... more
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 involved in a professional learning initiative focused on teaching mathematics through sequences of challenging tasks completed a questionnaire inviting them to compare the two settings. Drawing on a mixed-methods approach, we found that teachers were more positive about the value of student struggle in classroom-based settings compared with remote learning settings. Qualitative analysis of open-ended responses revealed four themes capturing why teachers viewed efforts to support productive struggle in a remote learning setting as potentially problematic: absence of a teacher-facilitated, synchronous, learning environment; parents’ negativ...
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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... more
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 implemented a student-centred pedagogical approach when teaching with challenging tasks. While they had some initial success implementing the pedagogical approach and a three-phase lesson structure, they struggled to do so online during the lockdown. It is the experiences of these teachers, in particular their experience of confusion relating to aspects of the pedagogical approach, and how this confusion was overcome, that is reported in this paper. Central to our findings is the importance of teachers reflecting on their own experiences of struggle and the impact this had on their professional learning, as well as the notion that adversity can be a catalyst for change.
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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... more
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 and consolidate mathematics learning. It is intended that through an iterative cycle of design-test-redesign-retest we will ultimately transform the documented curriculum into a set of refined and empirically developed sequences of learning experiences that are accessible by a diverse range of students.
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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... more
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 nature of common incorrect responses for one whole-whole ratio question. Results suggested pre-service teachers had difficulty interpreting a worded multi-step, ratio (scale) question, with errors relating to ratio and/or conversion of measurement knowledge. These difficulties reveal underdevel-oped knowledge of mathematical structure and mathematical connections as well as an inability to deconstruct key components of a mathematical problem. Most pre-service teachers also lacked knowledge of standard procedures and methods of solutions.
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The concept of functional thinking as a foundational idea associated with algebraic thinking is explored by Tracey Muir, Leicha Bragg and Sharyn Livy. They provide ideas for using children's literature as a context to promote... more
The concept of functional thinking as a foundational idea associated with algebraic thinking is explored by Tracey Muir, Leicha Bragg and Sharyn Livy. They provide ideas for using children's literature as a context to promote functional thinking
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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... more
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.
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... more
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 teaching. Data were collected from field notes, audio recording of part of a lesson, and an interview with the pre-service teacher after the lesson. Discussion focuses on the four characteristics of the ‘knowledge quartet’: foundation, connection, transformation and contingency. Conclusions suggested that pre-service teachers need to continue developing their mathematical content knowledge to assist with future planning and teaching of primary mathematics lessons.
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The following describes the rationale and processes of a professional learning initiative that offered specific suggestions for the teaching of geometric reasoning (mainly angles) and to foster discussion around the experience. The... more
The following describes the rationale and processes of a professional learning initiative that offered specific suggestions for the teaching of geometric reasoning (mainly angles) and to foster discussion around the experience. The intention was that the suggestions require students to persist with tasks for some time so that they have opportunity to engage with the specific content for themselves prior to instruction from the teacher. The initiative built on previous similar interventions the results of which were explained to participating teachers. For example, Sullivan, Clarke, Cheeseman, Mornane, Roche, Sawatzki, and Walker (2014) argued that not only do students not fear challenges in mathematics, many welcome them (see also Dweck, 2000). Further, rather than preferring teachers to instruct them on solution methods, students prefer to work out solutions and representations for themselves. The earlier result that students learn substantive mathematics content from working on ch...
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Since 2008, Australian students in Years 3, 5, 7 and 9 have been assessed through the National Assessment Program – Literacy and Numeracy (NAPLAN). In 2015, the Office of the Chief Scientist commissioned a study into the processes used by... more
Since 2008, Australian students in Years 3, 5, 7 and 9 have been assessed through the National Assessment Program – Literacy and Numeracy (NAPLAN). In 2015, the Office of the Chief Scientist commissioned a study into the processes used by schools that demonstrated successful outcomes in NAPLAN numeracy. A team of researchers across Australia conducted a total of 55 case studies in order to identify practices and policies that were consistent between successful schools. Data were gathered through surveys, classroom observations and interviews conducted with school leaders, teachers, students, and parents. Overall findings indicated there were a number of characteristics that were common to schools who achieved sustained growth in NAPLAN results. These characteristics included the development and implementation of policies that specifically supported numeracy learning and teaching, use of a variety of data sources to develop and refine mathematics teaching programs, team planning, str...
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The theoretical understanding that underpins a teacher’s foundation knowledge draws on their common content knowledge (CCK) and influences their mathematics’ teaching (Rowland, Turner, Thwaites, & Huckstep, 2009). Teachers who have... more
The theoretical understanding that underpins a teacher’s foundation knowledge draws on their common content knowledge (CCK) and influences their mathematics’ teaching (Rowland, Turner, Thwaites, & Huckstep, 2009). Teachers who have specialised content knowledge (SCK) demonstrate a unique kind of content knowledge which is more than knowing the content (Ball, Thames, & Phelps, 2008). This study reports on a comparison of two second-year pre-service teachers who had varied mathematical content knowledge (MCK) at the beginning of their Bachelor of Education course. It investigated whether knowing more advanced mathematics or foundation knowledge (Rowland et al., 2009) facilitates working towards demonstrating SCK. The results draw on a qualitative analysis, categorising lesson observation and interview responses using foundation knowledge and connections constructs of the ‘Knowledge Quartet’ framework (Rowland et al., 2009). Both pre-service teachers experienced course opportunities th...