Sandra Herbert

This paper reports on a phenomenographic investigation for which both participant utterances and their gestures were analysed in order for researchers to gain insight into their understanding of the concept of rate. Video-recordings were made of twenty interviews with Year 10 students. Detailed analysis, of both the sound and images, illuminated th...

Despite considerable research with students of calculus, rate and hence derivative, remain difficult concepts to teach and learn. The demonstrated lack of conceptual understanding of introductory calculus limits its usefulness in related areas. Since rate is such a troublesome concept this study piloted reversing the usual presentation of introduct...

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students’ conceptions of rate, focussing on the influence of...

Rate (of change) is an important but complicated mathematical concept describing a ratio comparing two different numeric, measurable quantities. Research referring to students’ difficulties with this concept spans more than 20 years. It suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incor...

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 teachi...

Mathematical reasoning is crucial for a deep understanding of mathematics, yet many primary teachers have a limited conception of reasoning. A deeper knowledge of reasoning is required to notice, teach, and assess it effectively. Sixteen pairs of teachers from four primary schools in Victoria, Australia, engaged in a professional learning program i...

Abstract: 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 facilitat...

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 secon...

Many elementary teachers find the complexity of understanding and teaching mathematical reasoning challenging. Teachers can benefit from professional learning programs designed to develop strategies to identify reasoning and implement it in mathematics lessons. This paper reports on a professional learning program designed to support a Peer Learnin...

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 v...

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 lesso...

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...

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 justifyi...

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...

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...

The mathematical concept of function is an essential underpinning for advanced study in mathematics, such as calculus, and influences success in higher mathematics. Teaching about functions is challenging as many students find it difficult to understand. Effective teaching strategies are reliant on a teacher’s knowledge of the current understanding...

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.

The purpose of this chapter is to consider the threats and challenges which impact on the sustainability of a partnership. By identifying elements that contribute to success and underpin the future sustainability of the relationships, an understanding of how the theoretical framing (Interpretive Framework) for university–school partnerships draws t...

This chapter describes the background and context surrounding the STEPS project and articulates both the process and goals established at the outset of the research endeavour. The STEPS research responded to a continuing concern regarding primary teachers’ acquisition of scientific understanding, confidence to teach science and persistent questions...

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....

Despite mathematical reasoning being a proficiency included in mathematics curricula around the world, research has found that primary teachers struggle to understand, teach, and assess mathematical reasoning. A detailed rubric involving the three reasoning actions of analysing, generalising and justifying at five proficiency levels was refined acc...

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 o...

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...

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...

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 t...

Abstract: 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...

Keeping classroom animals is a common practice in many classrooms. Their value for learning is often seen narrowly as the potential to involve children in learning biological science. They also provide opportunities for increased empathy, as well as socio-emotional development. Realization of their potential for enhancing primary children’s learnin...

Excellent mathematics teachers make a major difference to the learning outcomes of the students they teach. What are the professional skills and knowledge that really matter?..Teaching Secondary School Mathematics is a research based introduction to the professional knowledge, attributes and practices needed to teach mathematics well at secondary l...

Reasoning underpins students’ mathematical understanding and promotes creative thinking. It is regarded as a key mathematical proficiency. In this article Vale, Bragg, Widjaja, Herbert and Loong discuss the range of reasoning actions that primary children employed and teachers noticed for ‘What else belongs?” a task focused on forming and testing c...

This paper presents an Interpretive Framework stemming from a longitudinal and iterative multiple case study of five Australian universities examining the cogent and unique practices underpinning their established and successful school-based science teacher education programs. Results from interviews with teacher educators, school staff and pre-ser...

Mathematical reasoning is now featured in the mathematics curriculum documents of many nations, but this necessitates changes to teaching practice and hence a need for professional learning. The development of children’s mathematical reasoning requires appropriate encouragement and feedback from their teacher who can only do this if they recognise...

PhD thesis: This study identified four educationally critical aspects of ‘rate’ through analysis of phenomenographic, video-recorded interviews with Year 10 students. Further analysis indicated understandings in one representation or context were not necessarily transferable.

Professional learning is crucial for the ongoing development of teachers and the improvement of student outcomes. Professional learning in mathematics and science education has the potential to address concerns about shortages in these areas and their impact on economic growth. However, attendance at face-to-face professional learning is problemati...

Explaining appears to dominate primary teachers’ understanding of mathematical reasoning when it is not confused with problem solving. Drawing on previous literature of mathematical reasoning, we generate a view of the critical aspects of reasoning that may assist primary teachers when designing and enacting tasks to elicit and develop mathematical...

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...

A description of how phenomenography was employed as a research methodology for several onf my projects. Click on the DOI link to access the presentation

Encouraging students to develop effective use of Computer Algebra Systems (CAS) is not trivial. This paper reports on a group of undergraduate students who, despite carefully planned lectures and CAS availability for all learning and assessment tasks, failed to capitalize on its affordances. If students are to work within the technical constraints,...

The introduction of linear functions is the turning point where many students decide if mathematics is useful or not. This means the role of parameters and variables in linear functions could be considered to be ‘threshold concepts’. There is recognition that linear functions can be taught in context through the exploration of linear modelling exam...

School-wide curriculum initiatives are complex fields of activity, held together by a cast of heterogeneous actors who put diverse discourses to work in their everyday efforts to shape their work. This paper draws upon qualitative data collected across an 18-month period in a regional Australian primary school that, since the beginning of 2012, has...

In 2010, the Australian government established the Higher Education Participation and Partnerships Programme – a funding agenda to promote programmes that respond to the under-representation in higher education of people from low socioeconomic status (SES) backgrounds. Many government-funded programmes and projects have since emerged that respond t...

THIS STUDY INVESTIGATED THE teaching and learning approaches of three Victorian early childhood kindergarten teachers to science education, and how they used the Victorian Early Years Learning and Development Framework (VEYLDF) to support them in the development of science in their curriculum. A qualitative, collective case study was designed to in...

Reasoning in mathematics plays a critical role in developing mathematical understandings. In this article, Bragg, Loong, Widjaja, Vale & Herbert explore an adaptation of the Magic V Task and how it was used in several classrooms to promote and develop reasoning skills

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...

Exploring and developing primary teachers’ understanding of mathematical reasoning was the focus of the Mathematical Reasoning Professional Learning Research Program. Twenty-four primary teachers were interviewed after engagement in the first stage of the program incorporating demonstration lessons focused on reasoning conducted in their schools. P...

The quality of science education has been the focus of a number of research projects nationally and internationally, including concerns about primary teachers’ lack of science knowledge and confidence to teach science. In addition, the effectiveness of traditional approaches to teacher education have been questioned. The Science Teacher Partnership...

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...

Reasoning is essential for developing mathematical proficiency and flexibility. However, often teachers feel unsure how to support reasoning within their classroom activities. The Mathematics Reasoning Research Group (MaRRG) at Deakin University has been exploring ways to promote and assist teachers' and students' awareness of reasoning through tas...

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....

This paper presents the results of a survey conducted with students (N = 97) whose teachers have used the Web in their mathematics classes. Their responses to the use of the Internet for learning mathematics are reported here Factor analyses were used to determine the constructs that underlie the survey. These constructs were found to be ‘Valuation...

This paper reports on the different gesture types employed by twenty-three Year 10 students as they endeavoured to explain their understanding of rate of change associated with the functions resulting from two different computer simulations. These gestures also have application to revealing students’ understanding of functions. However, interpretat...

The mobile phones that we carry with us all the time have started becoming increasingly sophisticated and consequently are referred to as “Smartphones”. Smartphones today are extremely powerful and, in addition to making phone calls, are capable of performing a variety of other functions. One very important function is the ability to access the Int...

Despite considerable research with students of calculus, rate and hence derivative, remain troublesome concepts to teach and learn. The demonstrated lack of conceptual understanding of introductory calculus limits its usefulness in related areas. Since rate is such a troublesome concept this study trialled reversing the usual presentation of introd...

Rate is an important, but difficult mathematical concept. More than twenty years of research, especially with calculus students, report difficulties with this concept. This paper reports on an alternative analysis, from the perspective of multiple representations and context, of interviews probing twenty Victorian Year 10 students' conceptions of r...

Rate is an important, but difficult mathematical concept. More than twenty years of research, especially with calculus students, report difficulties with this concept. This paper reports on an alternative analysis, from the perspective of multiple representations and context, of interviews probing twenty Victorian Year 10 students’ conceptions of r...

Rate of change is an important mathematical concept often found to be difficult by calculus students. Research referring to the troublesome nature of rate of change for calculus students spans more than twenty years. It may be that the problems experienced by some calculus students are a result of pre-existing conceptions of rate of change. This pa...

Rate of change is an important mathematical concept. Research referring to students’ difficulties with this concept spans more than twenty years. Research suggests that problems experienced by some calculus students are likely a result of pre-existing limited or incorrect conceptions of rate of change. This study investigated 23 Victorian Year 10 s...

Does speed provide a ‘model for’ rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the ‘model for’ rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14–15year old students at a...

A well-developed understanding of rate is foundational to conceptual under-standing of introductory calculus. Many students achieve proceduralcompetence with the application of rules for differentiation without develop-ing an awareness of the connection between derivative and rate. In addition,rate-related reasoning is needed to make informed decis...

This paper reports on insights into students' understanding of the concept of rate of change, provided by examining the gestures made, by 25 Year 10 students, in video- recorded interviews. Detailed analysis, of both the sound and images, illuminates the meaning of rate-related gestures. Findings indicate that students often use the symbols and met...

This paper reports on insights into students’ understanding of the concept of rate of change, provided by examining the gestures made, by 25 Year 10 students, in videorecorded interviews. Detailed analysis, of both the sound and images, illuminates the meaning of rate-related gestures. Findings indicate that students often use the symbols and metap...

Students’ concept image of rate of change may be incomplete or erroneous This paper reports a pilot study, with secondary school students, which explores the potential of technology (JavaMathWorlds), depicting a familiar context of motion, to develop students’ existing schema of informal understandings of rate of change to more formal mathematical...

Strategy games can provide an opportunity to develop higher order thinking skills in students gifted in mathematics. Extending and engaging gifted students is a demanding task. This paper reports on a twelve-week project undertaken with a group of nine gifted lower secondary school students. These students played and analysed five traditional strat...

The term affordances is rising in prominence in scholarly literature in mathematics education generally and in technology in mathematics education in particular. A proliferation of different uses and meanings is evident. The roots and use of the term and some of its applications are explored in order to clarify its many meanings. Its potential usef...

Encouraging students to develop effective use of Computer Algebra Systems (CAS) is not trivial. This paper reports on a group of undergraduate students who, despite carefully planned lectures and CAS availability for all learning and assessment tasks, failed to capitalize on its affordances. If students are to work within the technical constraints,...

This paper reports on "Introduction to Computer" classes conducted in Ballarat, Victoria as part of Adult Learners' Week, 2002. It outlines the background to the classes, topics covered, participants' reflections and further actions taken. The paper reveals the social and learning outcomes experienced by adults who participated in the computer clas...