Keith Jones

Keith Jones
University of Southampton · Southampton Education School

About

292
Publications
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Introduction
My research is in mathematics education and focuses on the teaching and learning of geometric and spatial reasoning, the teaching and learning of proof and proving (usually in geometry), and the use of digital technologies in mathematics education. Some project involve all three. I also research the initial and continuing professional development of mathematics teachers. My research spans all levels of education from elementary school, through secondary school, to university level. Latest news via Twitter: https://twitter.com/KeithJonesUoS
Additional affiliations
April 1992 - present
University of Southampton
Position
  • Professor (Associate)

Publications

Publications (292)
Book
Full-text available
This book brings together the development of a theoretical argument and its translation into an extensive empirical context as a result of the research work carried out by the Problem@Web project. Through the 3 years of the project, we studied youngsters engaged in mathematical problem-solving using digital technologies of their choice and to which...
Article
Full-text available
While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the struc...
Chapter
The chapter provides a comprehensive review of recent research in geometry education, covering geometric and spatial thinking, geometric measurement, and visualization related to geometry, as well as encompassing theoretical developments and research into teaching and teacher development. Studies examining the uses of forms of digital technology ar...
Book
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Big ideas in the mathematics curriculum for older school students, especially those that are hard to learn and hard to teach, are covered in this book. It will be a first port of call for research about teaching big ideas for students from 9-19 and also has implications for a wider range of students. These are the ideas that really matter, that stu...
Article
Full-text available
A key issue for mathematics education is how children can be supported in shifting from `because it looks right' or `because it works in these cases' to convincing arguments which work in general. In geometry, forms of software usually known as dynamic geometry environments may be useful as they can enable students to interact with geometrical theo...
Article
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This study focused on improving students’ learning mathematical of proofs and proving by using combinations of proof strategies that span different levels of understanding of proof structure; we refer to these as ‘level-spanning proof-production strategies’. We analysed the level-specific proof-production strategies evident in the lessons and class...
Article
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Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this activity...
Chapter
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The so-called 4th Industrial Revolution promises to enable people not only to consume more at a lower price and to live longer but also it is to transform education in general and the teaching and learning of mathematics in particular. The dangers of this so-called 'revolution' are already evident in terms of cyber-attacks, fake news, threats to da...
Conference Paper
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The award of the 2018 Fields Medal to Peter Scholze is acknowledgement of how his work is transforming arithmetic geometry and underlines the importance of what the renowned mathematician Hilbert immortalised as geometry and the imagination. Yet school geometry is not always experienced by pupils as valuing intuitive imaginings. This paper examines...
Article
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Digital tools have a potential to change significantly the form of mathematical learning taking place in classrooms, with research pointing to various affordances in comparison with physical tools such as paper-and-pencil environments. Nevertheless, there is a scarcity of research that has examined in-depth the interrelated roles these two types of...
Chapter
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The use of digital technologies is under increasingly intense scrutiny, with concerns growing over data security, cyberattacks, fake news, long-term exposure to wireless devices and digital screens, and the effect of using social media on mental health and well-being. Given the significant social and ethical dilemmas, this chapter examines key deba...
Article
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Given the important role played by students' spatial reasoning skills, in this paper we analyse how students use these skills to solve problems involving 2D representations of 3D geometrical shapes. Using data from in total 1357 grades 4 to 9 students, we examine how they visualise shapes in the given diagrams and make use of properties of shapes t...
Article
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This editorial considers possible future developments over the next 21 years of the journal Research in Mathematics Education (RME). One source of thinking about the future is to look at past trends and gaps. Over the period 2003–2017, gaps in research presented at BSRLM conferences include mathematics education and early years schooling, mathemati...
Conference Paper
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In this paper, we employ an analytical framework to examine the design features, teachers’ learning processes, and outcomes expected in three selected models of teachers’ collaboration and learning, namely the Action-Education model, the Learning Study model, and a Community-Centered model for teacher learning. Based on our analysis, we outline the...
Conference Paper
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In this short paper we focus on how a web-based open flow-chart proving system can support students’ level of understanding of proof structure. To study this, a teacher in a junior high school implemented the same lessons with and without technologies to two different classes with similar student attainment. We examined students’ written responses...
Conference Paper
Full-text available
In this paper, we focus on research that has examined what teachers need to know in order to teach geometry. In particular, we focus on the extent to which research on teacher ‘content knowledge’ (CK) and teacher ‘pedagogical content knowledge’ (PCK) for geometry teaching is able to distinguish between geometry CK and geometry PCK. We do this by an...
Chapter
Counterexamples play a crucial role in the disciplinary practice of mathematics, and experiences with their use can enhance students’ engagement with mathematical practice and their learning of mathematical content. Although it is known that students encounter difficulties in producing and addressing counterexamples, and while there is evidence tha...
Chapter
This study explores how a proving task with technology can be designed to develop students’ strategic knowledge of how to construct alternative proofs to the same problem, and how the designed task enriched their strategic knowledge in proving in the context of geometrical proof. The designed task had three components; open problem with flow-chart...
Conference Paper
Full-text available
In this short paper we focus on the introduction of deductive proof in Japanese junior high school mathematics textbooks. Using two major authorized textbooks with over 70% of national share of classroom use, we examined all proofs in the 8th grade textbooks where a mathematical proof was introduced. In doing so, we analysed the relationships betwe...
Article
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A key aim of mathematics teaching is for children to develop appropriate and efficient strategies for solving tasks. The analysis presented in this paper moves beyond the exploration of changes in the strategies that children employ to solve tasks and extends to observation and exploration of changes that occur when their overall solving approach r...
Article
The professional development of teachers in China takes place, to a large extent, in Teaching Research Groups (TRG) that exist in all schools. Though there are diverse models of TRG activities, these might, on the surface, appear to resemble forms of Action Research (AR) or include elements that might resemble AR. In conducting a Lesson Design Stud...
Conference Paper
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This working group paper introduces a new initiative to bring together research on proof and proving and research on international comparison. While the past two decades has seen a strong increase in research into proof and proving in mathematics education, much has been conducted in single national and cultural contexts. There are four areas in wh...
Article
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This issue of Research in Mathematics Education (RME) marks a special point in the history of the journal; it marks 21 years of RME. As an international journal with the explicit aim of being informative and relevant to researchers in the field world-wide, RME is the official journal of the British Society for Research into Learning Mathematics (BS...
Article
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Task design is increasingly recognised as crucial for enhancing student learning of mathematics. Even so, and despite the significance of mathematical activity related to proofs and counterexamples in school mathematics, the task design principles underpinning students’ success in proof-related activity remains under-explored in mathematics educati...
Conference Paper
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This paper presents an analysis of data from two qualitative microgenetic studies that aimed at examining changes in the verbal reports of 5-6 year old children solving an additive task and 9-10 year old children solving partitive quotient problems. In each of the two studies, children participated in a sequence of task-based interviews. The analys...
Conference Paper
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In this overview of CERME11 Working Group 4 on geometry teaching and learning, three themes are identified: how space intervenes in ‘doing geometry’; learning geometry from cognitive and didactical points of view; teaching of geometry, including problem solving, manipulation with tools (including drawings), visualization, and proof. Considered as t...
Chapter
In mathematical problem-solving, the emphasis is often on the classroom use of so-called open problems. According to some, problem-solving is best stimulated by providing open-ended mathematical tasks. Not only that, it is also argued that openness of problems is more conducive to students’ mathematical creativity compared to using closed tasks. In...
Chapter
Across the world, problem-solving remains a key element of the mathematics curriculum and a central aim of mathematics teaching and learning. In order to embrace innovative ways of thinking and working, mathematical problem-solving in school classrooms is being challenged by the increasingly widespread use of digital technologies, the promotion of...
Book
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The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education,...
Chapter
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Globalization, and the internationalization of universities, brings both opportunities and dilemmas for university researchers in general, and for researchers in the Educational Sciences in particular. International collaboration has been shown to have a positive effect on the productivity of researchers in terms of the number of publications autho...
Article
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The use of digital technologies in mathematics classroom continues to increase. Yet even when well-planned, such use is not unproblematic; indeed, uncertainties are inherent. In this article, we use analyses of teachers’ activity in two classrooms, a French one and an English one, when technology in general, and dynamic geometry software in particu...
Conference Paper
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This case study of a university teacher of calculus1, based on data from a questionnaire, semi-structured interview, and observation, illustrates how the teacher used their knowledge of calculus teaching to sequence the building blocks of mathematical theories (BBMT) of the concepts of calculus.
Conference Paper
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This paper proposes a conceptualization of an expert teacher’s expertise by coordinating a subject-based behaviour/cognitive analysis and a social-culturally situated analysis. Data from our Lesson Design Study in Shanghai, China, included lesson plans, transcripts of the video-recorded lessons, and transcripts of commentary on the lessons by the e...
Conference Paper
Full-text available
Research on the reading of proofs is an important area of proof research in mathematics education. As one aspect of the reading of proofs, we focus on 'proof appraisal' by students (that is, students' judgements about given proofs) and explore how students appraise different proofs of an identical statement. Using a simple proof and a gen-eralisabl...
Chapter
This chapter concludes the collection of chapters, each of which expands on the papers presented during the Topic Study Group on the teaching and learning of secondary school geometry at ICME-13. In articulating a vision for where the field of secondary school geometry could go in the near future, the chapter revisits issues of methodologies for da...
Chapter
This chapter introduces the book by providing an orientation to the field of research and practice in the teaching and learning of secondary school geometry. The introduction then outlines the chapters in the book, each of which expands on the papers presented during the Topic Study Group on the teaching and learning of secondary school geometry at...
Book
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This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry i...
Article
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Much remains under-researched in how learners make use of domain-specific feedback. In this paper, we report on how learners’ can be supported to overcome logical circularity during their proof construction processes, and how feedback supports the processes. We present an analysis of three selected episodes from five learners who were using a web-b...
Article
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Kitcher’s idea of ‘explanatory unification’, while originally proposed in the philosophy of science, may also be relevant to mathematics education as a way of enhancing student thinking and achieving classroom activity that is closer to authentic mathematical practice. There is, however, no mathematics education research treating explanatory unific...
Chapter
In this commentary we provide an analytical look at the four studies reported within this theme of the volume and we discuss related issues and insights that we obtained from these studies. We offer a focused view of each study in the same order as presented in the four preceding chapters, and we conclude that these studies not only provide new ins...
Article
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As international research confirms, many secondary school students can find it difficult to construct mathematical proofs. In this article, we explain the pedagogical and technological underpinnings of a web-based learning support system for students who are just starting to tackle deductive proving in geometry. We show how the system was designed...
Conference Paper
Full-text available
In this paper we present a framework for describing mathematical activity in which mathematical knowledge is developed through proofs and refutations. The framework is constructed by adding the component generation of mathematical knowledge to our previous framework of conjecturing (or working on given statements), proving, and refuting (e.g. disco...
Article
This book, Approaches to Qualitative Research in Mathematics Education: Examples of Methodology and Methods, edited by Angelika Bikner-Ahsbahs, Christine Knipping, and Norma Presmeg, is a timely and valuable addition to the research literature in mathematics education. Across 18 chapters written by more than 30 prominent researchers, the book offer...
Chapter
Full-text available
This is a summary report of the ICME-13 survey on the theme of recent research in geometry education. Based on an analysis of the research literature published since 2008, the survey focuses on seven major research threads. These are the use of theories in geometry education research, the nature of visuospatial reasoning, the role of diagrams and g...
Article
Proof validation is important in school mathematics because it can provide a basis upon which to critique mathematical arguments. While there has been some previous research on proof validation, the need for studies with school students is pressing. For this paper, we focus on proof validation and modification during secondary school geometry. For...
Conference Paper
Full-text available
Given that understanding a proof entails students breaking the proof into components or modules and then specifying the logical relationship between each of the modules, in this paper we focus on what proof modules can be identified during the process of learning deductive proving in school geometry. Through an analysis of observations of grade 8 g...
Conference Paper
Full-text available
This study addressed the use of dynamic geometry environments in students’ mathematical activity related to proofs and refutations. Using a framework of student interpretation of diagrams, we analysed a task-based interview where a triad of Japanese secondary school students (16–17 years old) tackled tasks related to conjecturing, proving, and refu...
Conference Paper
Full-text available
In this short paper, our focus is on how secondary school students work with diagrams during proving activity in geometry. Using data from a project investigating the design of dynamic geometry software (DGS) tasks that facilitate students’ proving activity, we found that the students’ discussion settled on various versions of the diagram. Out of s...
Conference Paper
Full-text available
Although the mathematical activity of proofs and refutations is widely recognised as significant in school mathematics, much remains under-explored about ways of facilitating such activity in the classroom. In this paper, we address this issue by focusing on task design in dynamic geometry environments. In particular, we formulate three principles...
Chapter
This chapter focuses on the process of teacher change and, in particular, how a Chinese expert teacher in Shanghai used the idea of teaching with variation (to support a junior teacher with three years of teaching experience) to develop certain ways of reflecting on her teaching. We identified the expert teacher’s significant guidance in the follow...
Conference Paper
Microgenetic research designs entail highly-concentrated observation of learners’ behaviour within specific domains, contexts and periods of time, aiming at capturing change in learning as it occurs. Microgenetic analyses enable researchers to scrutinise various forms of data and explore differences in the process of change within and across indivi...
Conference Paper
Full-text available
In Japan, ‘model lessons’ are often provided by expert teachers during ‘Lesson study open house’ when expert teachers open their lessons to other teachers. A challenge for observing teachers is how to ‘transform’ such model lessons into their own practice. In this paper, with our focus on the planning phase of lesson study, we analyze four lesson p...
Conference Paper
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This paper focuses on the aspects of ‘noticing expertise’ can be identified in the geometry lessons taught by an expert teacher of school mathematics at grades 7 and 8. From an analysis of ten successful lessons we identified the following components of ‘noticing expertise’ relating to productive geometrical reasoning: a) selecting different types...
Article
This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span fro...
Article
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This paper introduces a special journal issue presenting selected papers from the 12th International Conference on Technology in Mathematics Teaching (ICTMT12), hosted by the Faculty of Sciences and Technology of the University of Algarve, in the city of Faro, from 24-27 June 2015. With the overall theme of re-visioning teaching and learning with t...
Article
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Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the ‘design’ of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to it. Whilst t...
Chapter
Today’s youngsters are growing up in an era of rapidly advancing digital technologies. While young people in this generation are undoubtedly active users of digital technologies, the issue of whether their digital competency levels are necessarily well developed is a topic of debate. This chapter provides an introduction to, and an overview of, the...
Chapter
Over several years of the SUB12 and SUB14 online mathematical competitions, we became aware of the technological fluency of many of the young participants. We draw on quantitative data from a survey that was administered online by inviting all participants to respond. The data show how the participants describe themselves in terms of their experien...
Chapter
This chapter develops around two fundamental ideas, namely, that (1) the perception of the affordances of a certain digital tool is essential to solving mathematical problems with that particular technology and that (2) the activity thus undertaken stimulates different mathematising processes which, in turn, result in different conceptual models. L...
Chapter
The final chapter summarises the overall findings of the Problem@Web project and considers the implications of the findings in terms of how the youngsters of today tackle mathematical problems and communicate their mathematical problem-solving. With data from the youngsters’ participation in two online mathematical problem-solving competitions that...
Chapter
Given that solving mathematical problems entails developing ways of thinking and expressing thoughts about challenging situations where a mathematical approach is appropriate, this chapter unveils a theoretical framework that aims to guide a better interpretation of students’ capability to solve mathematical problems with digital technologies, in t...
Chapter
This chapter offers the perspectives of teachers on youngsters solving mathematical problems with technology during the SUB12 and SUB14 mathematics competitions. Drawing on a series of interviews with teachers who have supported the participation of their students over several editions of the competitions, we identified what they see as the competi...
Chapter
In this chapter, we describe and analyse a number of examples of 7th and 8th graders showing diverse ways of expressing their mathematical thinking in solving algebraic word problems with a spreadsheet. Different youngsters’ approaches to situations where quantity variation is involved are characterised. The problems require finding an unknown valu...
Chapter
Co-variational reasoning has received particular attention from researchers and mathematics educators because it is considered of paramount importance for the understanding of concepts such as variable, function, rate of change, derivative, etc. Some of the critical issues that have been identified in several studies consist of the difficulty in in...
Chapter
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Whilst students in Shanghai were top-ranked internationally in the 2009 and 2012 PISA (Programme for International Student Assessment) studies, much less is known about Shanghai students’ attitudes towards mathematics and how this varies across the 11–15 age range. This chapter reports on a study of attitudes towards mathematics of Shanghai student...
Article
Full-text available
Recent research on the scaffolding of instruction has widened the use of the term to include forms of support for learners provided by, amongst other things, artefacts and computer-based learning environments. This paper tackles the important and under-researched issue of how mathematics lessons in junior high schools can be designed to scaffold st...
Conference Paper
Full-text available
The MC squared project (http://www.mc2-project.eu) aims to design and develop a new genre of authorable e-book, which the project calls the ‗c-book‘ (c for creative), extending e-book technologies to include diverse interactive components, learning analytics and collective design. As a research lens, literature from communities of interest (CoI) is...
Conference Paper
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This paper reports on an expert teacher’s ideas and practice of teaching with variation that underpin her guidance of junior teachers in lesson design study in a research project in Shanghai, China. The data we analysed included the teacher’s lesson plan, teaching references, classroom materials, together with the video of the lesson and its transc...
Conference Paper
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The European ‘MC-squared’ project is fostering several so-called ‘Communities of Interest’ (CoI) in a number of European countries. These communities work on designing and developing digital, interactive, creative, mathematics textbooks, called c-books. The c-books are made in the online digital authoring environment in which authors can construct...
Conference Paper
Full-text available
This paper focuses on the pedagogical underpinnings of the design of a web-based learning support system for lower secondary school pupils who are just beginning to learn how to tackle deductive proving in geometry. In particular, we explain how the key features of our web-based system can scaffold learners’ learning of congruency-based proofs in g...
Chapter
Full-text available
The teaching of geometry, especially the teaching of proof in geometry, is central to mathematics education in China at the lower secondary school level. This chapter uses a case study of how an expert mathematics teacher in Shanghai taught geometrical theorems to a class of Grade 8 students (aged 13-14 years) to illustrate the ‘shen tou’ (‘permeat...
Article
In Japan it is in Grades 7–9, and primarily in geometry, that school students are introduced to the significance and methodology of proof in mathematics. As textbooks play a central role in everyday lessons in Japan, this paper presents an analysis of the geometry chapters of a selected mathematics textbook currently in common use with students age...
Conference Paper
Full-text available
In a study of open flow-chart proving, we report possible effects and limitations by examining, from a theoretical perspective, the features of this approach such as visualising proof structures and promoting the construction of different proofs. We conclude that the use of open flow-chart proving can contribute to a) helping students develop their...
Chapter
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The use of mathematics textbooks by pre-service teachers in English schools is an under-researched area. While systematic research exists in other countries (see, for example, Nicol and Crespo 2006), there is only anecdotal evidence, albeit significant, to suggest that the use of mathematics textbooks in English secondary schools is underpinned by...
Conference Paper
Full-text available
The European ‘MC-squared’ project has a number of Communities of Interest’ (CoI) (Fischer, 2001) in European countries that work on digital, interactive, creative, mathematics textbooks, called cBooks. A community of interest consists of several stakeholders from various ‘Communities of Practice’ (Wenger, 1998). In this paper we outline the creatio...
Chapter
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According to TIMSS data, the use of textbook in mathematics classrooms in England is relatively low in comparison to other countries. Although the reasons for this might be varied, the pronouncements of Ofsted, the official body for inspecting schools in England, might have an influence. This paper reports on a text analysis of almost 10,000 public...
Chapter
Full-text available
The EU-funded ‘MC-squared’ project is working with a number of European communities to develop digital, interactive, creative, mathematics ‘textbooks’ that the project calls ‘cBooks’. The cBooks are authored in a Digital Mathematics Environment in which participants can construct books with various interactive ‘widgets’. This paper provides an outl...