Robyn Pierce

• PhD
• Professor (Associate) at University of Melbourne

This paper builds on our previous research and investigates how students’ fractional competence and reasoning can provide clear evidence of non-symbolic algebraic thinking and its progressive transition towards fully generalised algebraic thinking. In a large-scale study, 470 primary students completed a written paper and pencil test. This included...

Symbols are a cornerstone of the written language of mathematics and mathematical sciences. However, variations in their use pose a constant challenge to students. This paper reports data from first year undergraduate students studying mathematics, statistics and/or physics collected using surveys and interviews. It became clear that multiple uses...

In this follow-up article, the authors explain that when technology is integrated in an equitable manner and with due regard for professional learning, the affordances of Web 2.0 technology and interactive devices allow teachers to not only promote procedural fluency but also to develop students’ conceptual understanding, reasoning and problem-solv...

Undergraduate mathematics instructors often report that students make careless errors or have not previously learned key mathematical ideas and strategies. The purpose of this study is to explore evidence of an alternative explanation that at least some of these “errors” may result from students’ application of conceptions developed in the narrower...

The need for students to engage in critical thinking, collaboration, communication, and creativity when utilizing digital technologies is well established given the current push to prepare our students for future work expectations, often referred to as Industry 4.0. In this chapter, 54 Grade 5 students participated in online collaborative mathemati...

The current Australian Curriculum mandates that technology be utilised to support students to “investigate, create and communicate mathematical ideas and concepts” (ACARA, 2018). However, research reports suggest that use of digital technologies in Australian primary mathematics often focusses on the lower-order drilling of algorithms and basic fa...

The current Australian Curriculum mandates that technology be utilised to support students to “investigate, create and communicate mathematical ideas and concepts” (ACARA, 2018). However, research reports suggest that use of digital technologies in Australian primary mathematics often focusses on the lower-order drilling of algorithms and basic fac...

Fractional thinking with its interconnected constructs is key to understanding number and multiplicative thinking. Identifying students’ thinking and choosing questions to develop understanding and proficiency is a challenge for teachers. This paper examines the results of six tasks completed by 570 middle years’ students from Victorian schools. Th...

Lecturers and teachers lament over the difficulties their students have writing coherent mathematical statements. Students' habitual misuse of mathematical symbols, combined with an inability to explain what mathematical steps are being taken and why, is a concerning observation. At best this represents a lack of mathematical rigour and at worst, m...

School and university mathematics: do they speak the same language? Our university mathematics students come from amongst the successful school mathematics students but what difficulties with symbols do their lecturers and tutors observe? This paper reports on data from interviews with twenty-one first year lecturers and tutors from four universiti...

Online text discussion highlights “teachable moments”. A Bakhtinian lens is used to examine upper primary school students’ use of informal and formal language registers in mathematical problem solving in a Computer Supported Collaborative Learning (CSCL) environment. The authors argue that online discussion assists in the development of mathematica...

Online discourse draws attention to students’ use of a “transitional mathematical register” prompted by the dialogic nature of language development. A Bakhtinian lens is used to examine a case study of the use of informal and formal mathematics registers by primary school students engaged in mathematical problem solving while working in a Computer...

Although research shows that Computer Algebra Systems offer pedagogical opportunities, more than a decade later some teachers are reluctant to change established practices.

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,...

After more than a decade with CAS readily available and its use encouraged for teaching, learning and assessment, this paper considers the questions of (i) to what extent has CAS use been taken up by teachers as part of their classroom practice? and (ii) how much use are students making of CAS? From a wider survey on students’ perception of the use...

In this study we examine the use of cumulative and exploratory talk types in a year 5 computer supported collaborative learning environment. The focus for students in this environment was to participate in mathematical problem solving, with the intention of developing the proficiencies of problem solving and reasoning. Findings suggest that student...

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of ‘syntax template’ provides a theoretical framework to analyse undergraduate mathematics students’ written solutions, where we have identified several types of symbol-related error...

Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of ‘syntax template’ provides a theoretical framework to analyse undergraduate mathematics students’ written solutions, where we have identified several types of symbol-related error...

Low progression rates in the mathematical sciences are of national concern. Various programs providing student support have been implemented across the higher education sector and a number of researchers have analysed the teaching of specific topics with view to making recommendations for improvement. In this position paper we suggest that insight...

Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function, despite...

As a result of the growing use of state and national testing of literacy and numeracy among school students, there are increasing demands for teachers to interpret assessment data. In light of this, there is a need to provide benchmarks or a framework that identifies critical aspects of teachers' understanding that are needed to interpret data effe...

Despite an emphasis on manipulative algebraic techniques in secondary school algebra, many tertiary mathematics students have mastered these skills without conceptual understanding. A significant number of students, with high tertiary entrance ranks, enrolled in first semester university mathematics were found to have misconceptions relating to pro...

Given the deluge of data that school principals and teachers receive as a result of student assessment it has become essential for them to have statistical literacy skills and understanding. Earlier work with primary and secondary teachers in Victoria revealed that, although most saw school statistical reports as valuable for planning and thought t...

Given the deluge of data that school principals and teachers receive as a result of student assessment, it has become essential for them to have statistical literacy skills and understanding. Earlier work with primary and secondary teachers in Victoria revealed that, although most saw school statistical reports as valuable for planning and thought...

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...

A strong understanding of the concept of function is vital for students studying calculus and has been seen as a unifying concept in mathematics and between mathematics and the real world. This paper reports on a pilot research on first year university students’ understanding of functions. Special attention has been given to students’ background on...

In Australia, as in other countries, school students participate in national literacy and numeracy testing with the resulting reports being sent to teachers and school administrators. In this study, the Theory of Planned Behaviour provides a framework for examining teachers' perceptions of factors influencing their intention to engage with these da...

This paper explores how four good teachers, who do not have a special interest in technology, meet the challenge of introducing the rapidly developing mathematics analysis software (e.g. spreadsheets, function graphers, symbolic algebra manipulation and dynamic geometry) into their classrooms. These teachers’ practice is viewed through the lens of...

Changes to students’ understanding of mathematical notation may be brought about by using technology within mathematics. Taking equality as a case study, the paper provides brief epistemological, historical, didactical, and computational reviews of its symbolic representation in pen-and-paper and technology-assisted mathematics, most especially in...

As a consequence of the increased use of data in workplace environments, there is a need to understand the demands that are placed on users to make sense of such data. In education, teachers are being increasingly expected to interpret and apply complex data about student and school performance, and, yet it is not clear that they always have the ap...

The growth in state-wide and national school testing in areas such a literacy and numeracy has led to the generation and dissemination of reports containing graphs and tables illustrating school and individual performance. These are intended to inform teachers, principals, and education organizations about student and school outcomes, so that the d...

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...

It is widely held that context is important in teaching mathematics and statistics. Consideration of context is central to statistical thinking, and any teaching of statistics must incorporate this aspect. Indeed, it has been advocated that real-world data sets can motivate the learning of statistical principles. It is not, however, a straightforwa...

The importance of beliefs as a factor affecting teaching and learning has long been established. In the field of statistics education, very little research has been conducted on the nature of teachers ’ beliefs, despite the likely impact these beliefs have on teachers ’ activities. This chapter first considers content-focused beliefs about statisti...

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...

In recent years the educational policy environment has emphasised data-driven change. This has increased the expectation for school personnel to use statistical information to inform their programs and to improve teaching practices. Such data include system reports of student achievement tests and socio-economic profiles provided to schools by vari...

Beliefs have long been known to affect teaching and learning. In statistics education, little research has been conducted on the nature of teachers’ beliefs, despite the likely impact these beliefs have on teachers’ activities. This chapter first considers content-focused beliefs about statistics, its relationship with mathematics, and its place in...

Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students’ learning requires carefully designed lessons. This paper reports on design re...

This chapter reports on the use of dynamic geometry to support the use of real world contexts to enhance the learning of mathematics in the middle secondary years. Dynamic geometry, either linked to real world images or used to create dynamic simulations, not only can provide opportunities for students to collect real or simulated data to make conj...

The use of mathematics analysis software (MAS) including handheld scientific and graphics calculators offers a range of pedagogical opportunities. Its use can support change in the didactic contract. MAS may become an alternative source of authority in the classroom empowering students to explore variation and regularity, manipulate simulations and...

Understanding linear functions is key to students developing a sound foundation for algebra. The common linear function rule y = mx + c presents students with the need to develop a conceptual understanding of both variables (x and y) and parameters (m and c) and to comprehend the different roles they play in the rule. Our Australian study explored...

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its avai...

In Victoria the use of technology in mathematics is strongly encouraged for years 7-10 (VCAA, 2008) and expected at year 11 and 12 (access to technology is assumed for some final secondary school assessment tasks, including examinations (VCAA, 2010)). The curriculum advice for teachers incorporates statements about use of technology for students' l...

The use of Computer Algebra Systems (CAS) in years9 and 10 classrooms as a tool to support learning or in preparation for senior secondary mathematics is controversial. This paper presents an analysis of the positive and negative aspects of using CAS identified in the literature related to these year levels, along with the perceptions of 12 experie...

Taking advantage of pedagogical opportunities afforded by new technology requires appropriately designed lessons. This article reports on the use of ‘lesson study’ to research principles for the design of a lesson aiming to take advantage of multiple representations. The lesson, for year 10 students who had personal access to TI-Nspire, focused on...

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...

Technology is available and accessible in many mathematics classrooms. Adopting technology to support teaching and learning requires teachers to change their teaching practices. This paper reports the responses of a diverse cohort of 92 secondary mathematics teachers who chose to respond to an Australian state-wide survey (Mathematics with Technolo...

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...

The degree to which statistics teaching focuses on rules or on critical thinking depends on teachers’ perceptions of and knowledge of statistics, along with their pedagogical content knowledge. This paper reports findings from a brief study with 27 pre-service primary teachers. The teachers completed a survey and planned a lesson for a grade six cl...

This paper reports on the effectiveness of an intervention designed to improve nursing students' conceptual understanding of decimal numbers. Results of recent intervention studies have indicated some success at improving nursing students' numeracy through practice in applying procedural rules for calculation and working in real or simulated practi...

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...

Massively multiplayer online role-playing games (MMORPGs) are emerging in the computer game industry as a very popular genre. These games have existed since the late 1990s, but in the last few years the market has become increasingly strong. This relatively new genre is attracting a widespread audience, bringing together those who previously enjoye...

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...

The Mathematics and Technology Attitudes Scale (MTAS) is a simple scale for middle secondary years students that monitors five affective variables relevant to learning mathematics with technology. The subscales measure mathematics confidence, confidence with technology, attitude to learning mathematics with technology and two aspects of engagement...

In today's world, where the volume of knowledge everyone must deal with is increasing exponentially, many educators agree that schools must focus on developing skills for life-long learning. But what does that mean for an area such as algebra? Teachers' goal in school algebra should be to guide students to "work smarter" with algebraic symbols and...

Computer algebra systems (CAS) were originally designed for mathematicians, scientists, and engineers, and their implementation into education, and especially into schools, is still very much in its infancy. This situation is reflected in the research on CAS and hence our ability to describe the influence of CAS on student learning in algebra. This...

Those who market people or products choose their images very carefully. They create positive associations in the public's mind by photographing their clients with sporting heroes or national icons. In this paper we present a variety of evidence to show that a major and overlooked reason for teachers' use and choice of real world problems is to take...

Using a computer algebra system (CAS) in the classroom provides many opportunities for improving student learning. However, to take advantage of such a powerful instrument as CAS requires changes to many aspects of the classroom. The different ways in which three pioneering Australian teachers adapted their teaching to use CAS are described (see al...

Computer Algebra Systems (CAS) performs algorithmic processes quickly and correctly. Concern is commonly expressed that students using CAS will merely be pushing buttons but this paper indicates that, while CAS may assist students, this facility impacts on only one section of the mathematical modeling process: CAS may be used to help find mathemati...

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...

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 article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS techn...

This study analyses some of the consequences of adopting a functional/modelling approach to the teaching of algebra. The teaching of one class of 17 students was observed over five weeks, with 15 students undertaking both pre- and post-tests and 6 students and the teacher being interviewed individually. Use of graphics calculators made the predomin...

Computer Algebra Systems (CAS) can perform routine algebraic manipulations quickly and correctly using inbuilt algorithms. An application called Symbolic Math Guide (SMG) can be added to a TI89 to enable the CAS to be used to help students learn how to perform step-by-step algebraic manipulation. SMG supports students when learning to "do the same...

The ability to recognize equivalent algebraic expressions quickly and confidently is important for doing mathematics in an intelligent partnership with computer algebra. It is also a key aspect of algebraic expectation, the algebraic skill that parallels numeric estimation. The progress in this ability of 50 students learning mathematics with CAS o...

Computer Algebra Systems (CAS) potentially offer students a powerful tool. However the mere availability of CAS does not enhance teaching and learning; students (and teachers) need to use it effectively. This paper presents a framework for components of Effective Use of CAS and illustrates its use as a guide for monitoring the progress of students....

In this paper we will explore the challenge of making statistics more meaningful to future nurses. In the fast moving undergraduate student world the expectations we place upon nursing students are considerable. Typically they experience high class-contact hours in addition to their clinical placements. Compounding the problem, undergraduate nursin...

This paper describes the construct 'algebraic insight', a subset of symbol sense especially required for the use of computer algebra systems. The first aspect is 'algebraic expectation', needed to work within the symbolic mode. It is an algebraic parallel to number sense or estimation in the use of a four function calculator. There are three elemen...

This paper reports on the responses of students using DERIVE, a computer algebra system, in an introductory calculus course at undergraduate level. There was strong evidence that the use of this technology was a catalyst for students to use three learning strategies which the literature links to enhanced learning outcomes: regularly using multiple...

This article documents a change in the use of a Computer Al-gebra System, (CAS), with a group of first year, undergradu-ate, mathematics students. CAS was initially used as an as-sistant for doing mathematics, enabling students to solve dif-ficult problems. During the period of the study it came to be used as an assistant for learning mathematics,...

An important component of the algebra needed to do mathematics with a computer algebra system (CAS) is symbol sense, analogous to 'number sense' in arithmetic with a four function calculator. This paper presents an assessment of a component of symbol sense: algebraic expectation. We describe the results of 169 Year 11 students including interesting...

Refining mathematical understanding through the use of multiple representations and negotiation of meaning has been considered important for students. This paper reports on an observational study of students using a Computer Algebra System in an introductory calculus unit at undergraduate level. There was strong evidence that the use of this techno...

Computer Algebra Systems (CAS) are powerful tools for both doing and learning mathematics. They may be used to perform algorithmic routines both quickly and correctly but harnessing this power in a manner which is effective for promoting learning is not trivial. Research undertaken with both secondary school and undergraduate students clearly indic...

Will this material be on the exam? Why do I need to know this stuff? These are the sorts of questions that have been regularly asked by our mathematics students. Pre-service mathematics teachers often suggest that they do not need to learn anything that they do not have to teach. Generally, these students appear to have very little aesthetic apprec...

The study of linear functions is important as it provides students with their first experience of identifying and interpreting the relationship between two dependent variables. This paper, which builds on previous research, reports a study undertaken with 64, year 9 students from two Australian schools. Linear functions were introduced to these stu...

In this study more than 40% of the 355 student nurses who completed a pre-test, involving comparisons of decimal numbers, made errors that indicate an incomplete or incorrect conceptual understanding. This includes students who are sometimes able to achieve 100% on drug calculations tests. Seven test items with error rates of between 10% and 26% fo...

In this paper we propose that 'lesson study' may be adapted from its primary use as a professional development strategy for use as a valuable research strategy, especially to identify principles of good lesson design. We report on a project undertaken in two Australian schools where lesson study research was used to investigate the design of a less...

Details are provided of simple algebraic items which can be used to detect two particular ways students think about the numerical meanings of letters (in contrast to non-numerical thinking). The data from Year 7 students (n=228) and Year 8 students (n=139) on these items is analysed using response patterns to probe student thinking. Less than 10% o...

It is not uncommon for students with limited school mathematics backgrounds to decide to study mathematics as a second subject area for teaching. This paper reports on a de-tailed study of a group of such students who, in 1998, undertook a course in introductory calculus using the Computer Algebra System DERIVE. This learning style bene ted some st...

1 Abstract Using CAS in the ,classroom ,provides ,many ,opportunities for improving student learning. However, to take advantage of such a powerful instrument as CAS requires changes,to many aspects of the classroom. The different ways in which three pioneering Australian teachers adapted their teaching to use,CAS are described. Two ofthe,teachers...

Integrating a powerful instrument such as CAS into requires changes to many aspects of the classroom, which teachers will make from the base of their prior teaching styles and their beliefs about mathematics and how it should be taught. The paper describes the different ways in which two pioneering Australian teachers adapted their teaching to use...

Real-world data can be used in the classroom to stimulate the learning of important statistical principles. A recent study with pre-service primary/elementary teachers highlighted that even when teachers were supplied with a suitable statistically rich example, some did not identify its affordances, and struggled to bring out the significant ideas...

As part of an investigation into statistical literacy for the teaching workplace, this research paper uses a framework for professional statistical literacy to examine teachers' perceptions of the complexity and value of such reports. Although teachers identified aspects of the data as useful for their work, many features were described as being di...

Introduction The use of Computer Algebra Systems (CAS), like DERIVE, for teaching and learning mathematics has raised many questions. This paper reports on a small-scale study that focused on two questions: firstly, does level of algebraic insight relate to students' use of CAS? Secondly, does algebraic insight improve in a mathematics course taugh...

Animated graphics can provide a basis for discussion of calculus concepts. This paper reports analysis of the responses from nineteen undergraduate mathematics students who were asked to write a work sheet based on a simple animation linking the graph of a function with its gradient function. Their responses were benchmarked against those of experi...

Introduction In early 2008 researchers from the University of Melbourne's New Technologies for Teaching Mathematics project created a lesson for the Year 10 students at their Victorian research schools.

Mathematics Analysis Software' (MAS) encompass computer software or calculators capable of performing the algorithmic processes necessary to carry out routine mathematical procedures from any branch of mathematics, including any or all of arithmetic calculations, symbolic algebra manipulations, statistics calculations and data display, graph plotti...