Publications by category
Books
Herbst P, Fujita T, Halverscheid H, Weiss M (2017).
The Learning and Teaching of Geometry in Secondary Schools: a Modeling Perspective. London, Routledge.
Abstract:
The Learning and Teaching of Geometry in Secondary Schools: a Modeling Perspective
Abstract.
Journal articles
Fujita T (2023). BSRLM day conference proceedings. Research in Mathematics Education, 25(3), 414-418.
Fujita T (2023). BSRLM day conference proceedings. Research in Mathematics Education, 25(2), 273-276.
Fujita T, Kondo Y, Kumakura H, Miyawaki S, Kunimune S, Shojima K (2023). Identifying Japanese students’ core spatial reasoning skills by solving 3D geometry problems: an exploration.
Asian Journal for Mathematics Education,
1Abstract:
Identifying Japanese students’ core spatial reasoning skills by solving 3D geometry problems: an exploration
Taking the importance of spatial reasoning skills, this article aims to identify “core” spatial reasoning skills which are likely to contribute to successful problem-solving in three-dimensional (3D) geometry. “Core” spatial skills are those which might be particularly related to students’ successful problem-solving in 3D geometry. In this article, spatial reasoning skills are malleable and can be improved with teaching/interventions with mental rotation, spatial orientation, spatial visualization, and property-based reasoning. To achieve the study aim, we conducted a survey in total of 2,303 Japanese Grade 4–9 students (10–15 years old). We take the following stages of the procedures in this article: (a) Descriptive statistics; (b) 2 parameter logistic model (2PLM) analysis; and (c) Experiments with the Pearson correlation coefficient. As a result, we identified that a set of a few tasks can be used to check if students have “core” spatial skills in 3D geometry. For both primary and secondary, rotating given representations mentally, and imagining and drawing 3D shapes, are important, and for secondary schools, property-based reasoning is also crucial for further problem-solving skills. Our findings and methodological approach have implications for mathematics education research and practice as our results provide clear, and promising principles for task/units/curriculum design for spatial reasoning in which more robust teaching intervention is necessary.
Abstract.
Melro A, Tarling G, Fujita T, Kleine Staarman J (2023). What Else can be Learned When Coding? a Configurative Literature Review of Learning Opportunities Through Computational Thinking.
Journal of Educational Computing Research,
61(4), 901-924.
Abstract:
What Else can be Learned When Coding? a Configurative Literature Review of Learning Opportunities Through Computational Thinking
Underpinning the teaching of coding with Computational Thinking has proved relevant for diverse learners, particularly given the increasing demand in upskilling for today’s labour market. While literature on computing education is vast, it remains unexplored how existing CT conceptualisations relate to the learning opportunities needed for a meaningful application of coding in non-Computer Scientists’ lives and careers. In order to identify and organise the learning opportunities in the literature about CT, we conducted a configurative literature review of studies published on Web of Science, between 2006 and 2021. Our sample gathers 34 papers and was analysed on NVivo to find key themes. We were able to organise framings of CT and related learning opportunities into three dimensions: functional, collaborative, and critical and creative. These dimensions make visible learning opportunities that range from individual cognitive development to interdisciplinary working with others, and to active participation in a technologically evolving society. By comparing and contrasting frameworks, we identify and explain different perspectives on skills. Furthermore, the three-dimensional model can guide pedagogical design and practice in coding courses.
Abstract.
Miyazaki M, Fujita T, Iwata K, Jones K (2022). Level-spanning proof-production strategies to enhance students’ understanding of the proof structure in school mathematics. International Journal of Mathematical Education in Science and Technology, 1-22.
Tarling G, Melro A, Kleine Staarman J, Fujita T (2022). Making coding meaningful: university students’ perceptions of bootcamp pedagogies. Pedagogies: an International Journal, 18(4), 578-595.
Shinno Y, Fujita T (2021). Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach.
International Journal of Mathematical Education in Science and TechnologyAbstract:
Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach
In this study we aim to characterize a way of proving which can be produced in a primary mathematics classroom and explore the factors that influence these processes and lead to changes in the way of proving. Assuming proving as a socially embedded activity, we conceptualize it as the interplay between ‘construction’ and ‘substantiation’ based on a well-established theoretical framework in mathematics education: the commognitive framework. A tangible proving task was designed, based on the idea of operative proofs, and implemented in a fifth-grade classroom in England. We analysed the construction and substantiation which fairly associated with discursive features (word use, visual mediator, narrative, and routine) during the proving process. The results show that the interplay between construction and substantiation developed progressively rather than in a straightforward manner, in which previously constructed narratives are reconstructed or substantiated in a more general context. This finding is relevant to understand the factors that might influence primary students to change the use of examples and the way of proving when used as a communicational means in proving. Our study has implications for possible continuity to proving activities in secondary schools, and thus contributes to advancing the research on proving in primary schools.
Abstract.
Fujita T, Doney J, Flanagan R, Wegerif R (2021). Collaborative group work in mathematics in the UK and Japan: use of group thinking measure
tests. Education 3-13: the professional journal for primary education, 49, 119-133.
Fujita T, Nakagawa H, Sasa H, Enomoto S, Yatsuka M, Miyazaki M (2021). Japanese teachers’ mental readiness for online teaching of mathematics following unexpected school closures. International Journal of Mathematical Education in Science and Technology, 54(10), 2197-2216.
Fujita T (2021). On Online Teaching and Learning of Mathematics: What Future Research can be Expected by Mathematics Education Research?. Hiroshima Journal of Mathematics Education, 14, 37-51.
Kazak S, Fujita T, Pifarre Turmo M (2021). Students’ informal statistical inferences through data modeling
with a large multivariate dataset. Mathematical Thinking and Learning, 25, 23-43.
Fujita T, Kondo Y, Hiroyuki K, Susumu K, Keith J (2020). Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9.
Mathematics Education Research Journal,
32(2), 235-255.
Abstract:
Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9
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 to reason. We found that using either spatial visualisation or property-based spatial analytic reasoning is not enough for the problems that required more than one step of reasoning, but also that these two skills have to be harmonised by domain-specific knowledge in order to overcome the perceptual appearance (or “look”) of the given diagram. We argue that more opportunities might be given to both primary and secondary school students in which they can exercise not only their spatial reasoning skills but also consolidate and use their existing domain-specific knowledge of geometry for productive reasoning in geometry.
Abstract.
Miyazaki M, Nagata J, Chino K, Sasa H, Fujita T, Komatsu K, Shimizu S (2019). Curriculum development for explorative proving in lower secondary school geometry: Focusing on the levels of planning and constructing a proof. Frontiers in Education
Fujita T, Doney J, Wegerif R (2019). Students’ collaborative decision-making processes in defining and classifying quadrilaterals: a semiotic/dialogic approach.
Educational Studies in Mathematics,
101(3), 341-356.
Abstract:
Students’ collaborative decision-making processes in defining and classifying quadrilaterals: a semiotic/dialogic approach
© 2019, the Author(s). In this paper, we take a semiotic/dialogic approach to investigate how a group of UK 12–13-year-old students work with hierarchical defining and classifying quadrilaterals. Through qualitatively analysing students’ decision-making processes, we found that the students’ decision-making processes are interpreted as transforming their informal/personal semiotic representations of “parallelogram” (object) to more institutional ones. We also found that students’ decision-making was influenced by their inability to see their peers’ points of view dialogically, i.e. requiring a genuine inter-animation of different perspectives such that there is a dialogic switch, and individuals learn to see the problem “as if through eyes of another,” in particular collectively shared definitions of geometrical shapes.
Abstract.
Komatsu K, Fujita T, Jones K, Sue N (2018). Explanatory unification by proofs in a mathematics classroom. For the Learning of Mathematics, 38, 31-37.
Fujita T, Jones DK, Miyazaki M (2018). Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry.
ZDM,
50Abstract:
Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry
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-based proof learning support system. Through this analysis we illustrate the various errors they made, including using circular reasoning, which were related to their understanding of hypothetical syllogism as an element of the structure of mathematical proof. We found that, by using the computer-based feedback and, for some, teacher intervention, the learners started considering possible combinations of assumptions and conclusion, and began realising when their proof fell into logical circularity. Our findings raise important issues about the nature and role of computer-based feedback such as how feedback is used by learners, and the importance of teacher intervention in computer-based learning environments.
Abstract.
Norwich B, Fujita T, Adlam A, Milton F, Edwards-Jones A (2018). Lesson study: an inter-professional approach for Educational Psychologists to improve teaching and learning. Educational Psychology in Practice, 34, 370-385.
Fujita T (2018). “That Journal has a History”: Overview of the Technological Tools and Theories Studied in the International Journal for Technology in Mathematics Education. 2004-2018. International Journal for Technology in Mathematics Education, 25, 35-44.
Miyazaki M, Fujita T, Jones K, Iwanaga Y (2017). Designing a web-based learning support system for
flow-chart proving in school geometry. Digital Experiences in Mathematics Education, 3(3), 233-256.
Wegerif R, Fujita T, Doney J, Perez Linares J, Richards A, van Rhyn C (2017). Developing and trialing a measure of group thinking.
Learning and Instruction,
48, 40-50.
Abstract:
Developing and trialing a measure of group thinking
This paper offers a critical review of the issue of assessing the quality of group thinking, describes the development of a Group Thinking Measure that fills a gap revealed by the literature and illustrates the use of this measure, in combination with interpretative discourse analysis, as a way of distinguishing those behaviors that add value to group thinking from those behaviors that detract value. The Group Thinking Measure combines two tests of equal difficulty, one for individual use and one for use by triads. This enables a measure not only of how well groups are thinking together but also a correlation between individual thinking and group thinking. This innovation gives an indication of whether or not working in a group adds value and so the extent to which a classroom culture supports collaborative thinking.
Abstract.
Koutsouris G, Norwich B, Fujita T, Ralph T, Adlam A, Milton F (2017). Piloting a dispersed and inter-professional Lesson Study using technology to link team members at a distance.
Technology, Pedagogy and Education,
26(5), 587-599.
Abstract:
Piloting a dispersed and inter-professional Lesson Study using technology to link team members at a distance
This article presents an evaluation of distance technology used in a novel Lesson Study (LS) approach involving a dispersed LS team for inter-professional purposes. A typical LS model with only school teachers as team members was modified by including university-based lecturers with the school-based teachers, using video-conferencing and online video sharing. The aim was to examine the experiences of using video-conferencing and video transfer technology to support the use of LS procedures to connect team members between schools and university. The meetings from two LS teams (primary and secondary) were recorded and analysed using a discourse analysis framework, and team members were interviewed after the LS cycle. Despite some technical difficulties, the communication between the dispersed members of the teams was largely smooth and successful. Extending LS teams and practice to include non school teachers, using distance-linking technology, can more effectively support teachers, while reducing the practical constraints of bringing other professionals into the LS team.
Abstract.
Fujita T, Kondo Y, Kumamura H, Kunimune S (2017). Students’ geometric thinking with cube representations: Assessment framework and empirical evidence.
Journal of Mathematical Behavior,
46(2), 96-111.
Abstract:
Students’ geometric thinking with cube representations: Assessment framework and empirical evidence
While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In order to assess students’ thinking about 3D shapes, we constructed an assessment framework based on existing research studies and data from G7-9 students (aged 12-15). We then applied our framework to assess students’ geometric thinking in lessons. We report two cases of qualitative findings from a classroom experiment in which Grade 7 students (aged 12-13) tackled a problem in 3D geometry that was, for them, quite challenging. We found that students who failed to answer given problems did not mentally manipulate representations effectively, while others could mentally manipulate representations and reason about them in order to reach correct solutions. We conclude with the proposition that this finding shows the framework can be used by teachers in instruction to
assess their students' 3D geometric thinking.
Abstract.
Norwich B, Koutsouris G, Fujita T, Ralph T, Adlam A, Milton F (2016). Exploring knowledge bridging and translation in Lesson Study using an inter-professional team.
International Journal of Lesson and Learning Studies,
5(3), 180-195.
Abstract:
Exploring knowledge bridging and translation in Lesson Study using an inter-professional team
Purpose – it is argued that the issues of translating basic science, including knowledge from neuroscience, into relevant teaching are similar to those that have been experienced over a long period by educational psychology. This paper proposes that such a translation might be achieved through Lesson Study (LS), which is an increasingly used technique to stimulate teacher enquiry. To explore these issues, this paper presents the findings from a modified LS approach that involved psychologists and mathematics lecturers working together with school-based teachers to prepare a series of lessons on mathematics.
Design/methodology/approach – the LS team review and planning meetings and subsequent interviews were recorded and analysed for common themes, with reference to patterns of knowledge bridging. Particular attention was paid to translational issues and the kind of knowledge used.
Findings – Overall, there was some successful bridging between theory and practice, and evidence of translation of theoretical knowledge into relevant teaching practice. However, the analysis of the team’s interactions showed that relatively little involved a useful applied neuroscience/neuropsychology element, whereas other psychological knowledge from cognitive, developmental, educational and clinical psychology was considered more relevant to planning the LS.
Originality/value – This study illustrates how reference to brain functioning has currently little specific to contribute directly to school teaching, but it can arouse increased interest in psychological processes relevant to teaching and learning. This approach reaffirms the central role of teacher-led research in the relationship between theory and practice. The findings are also discussed in relation to the SECI model of knowledge creation.
Abstract.
Kazak S, Fujita T, Wegerif R (2016). Students' informal inference about the binomial distribution of "Bunny hops": a dialogic perspective.
Statistics Education Research Journal,
15(2), 46-61.
Abstract:
Students' informal inference about the binomial distribution of "Bunny hops": a dialogic perspective
The study explores the development of 11-year-old students’ informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic ideas. Findings from the study suggest that dialogic talk facilitated students’ reasoning as it was supported by the use of simulation tools available in the software. It appears that the interaction of using simulation tools, talk between students, and teacher prompts helps students develop their understanding of probabilistic ideas in the context of making inferences about the distribution of random bunny hops.
Abstract.
Miyazaki M, Fujita T, Jones K (2016). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223-239.
Kazak S, Wegerif R, Fujita T (2015). Combining scaffolding for content and scaffolding for dialogue to support conceptual break throughs in understanding probability.
ZDM: the International Journal on Mathematics Education,
47(7), 1269-1283.
Abstract:
Combining scaffolding for content and scaffolding for dialogue to support conceptual break throughs in understanding probability
In this paper, we explore the relationship between scaffolding, dialogue and conceptual breakthroughs, using data from a design-based research study into the development of understanding of probability in 10-12 year old students. Our aim in the study was to gain insight into how the combination of the scaffolding of content using technology and scaffolding for dialogue in the expectation that this would facilitate conceptual breakthroughs. We analyse video-recordings and transcripts of pairs and triads talking together around TinkerPlots software with worksheets and teacher interventions, focusing on moments of conceptual breakthrough. The dialogue scaffolding promoted both dialogue moves specific to the context of probability and dialogue in itself. This paper focuses on an episode of learning that occurred within dialogues (framed and supported by the scaffolding. We present this as support for our claim that combining scaffolding for content with scaffolding for dialogue can be effective. This finding contributes to our understanding of both scaffolding and dialogic teaching in mathematics education by suggesting that scaffolding can be used effectively to prepare for conceptual development through dialogue.
Abstract.
Miyazaki M, Fujita T, Jones K (2015). Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs.
ZDM: the International Journal on Mathematics Education,
47(7), 1211-1224.
Abstract:
Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs
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 lower secondary school can be designed to scaffold students’ initial understanding of geometrical proofs. In order to scaffold the process of understanding the structure of introductory proofs, we show how flow-chart proofs with multiple solutions in ‘open problem’ situations are a useful form of scaffold. We do this by identifying the ‘scaffolding functions’ of flow-chart proofs with open problems through analysis of classroom-based data from a class of Grade 8 students (aged 13-14 years old) and quantitative data from three classes. We found that using flow-chart proofs with open problems supported the students’ development of a structural understanding of proof by giving them a range of opportunities to connect proof assumptions with conclusions. The implication is that such scaffolds are useful to enrich students’ understanding of introductory mathematical proofs.
Abstract.
Kazak S, Wegerif R, Fujita T (2015). The importance of dialogic processes to conceptual development in mathematics.
Educational Studies in Mathematics,
90(2), 105-120.
Abstract:
The importance of dialogic processes to conceptual development in mathematics
We argue that dialogic theory, inspired by the Russian scholar Mikhail Bakhtin, has a distinct contribution to the analysis of the genesis of understanding in the mathematics classroom. We begin by contrasting dialogic theory to other leading theoretical approaches to understanding conceptual development in mathematics influenced by Jean Piaget and Lev Vygotsky. We argue that both Piagetian and Vygotskian traditions in mathematics education overlook important dialogic causal processes enabling or hindering switches in perspective between voices in relationship. To illustrate this argument, we use Piagetian-, Vygotskian- and Bakhtinian-inspired approaches to analyse a short extract of classroom data in which two 12-year-old boys using TinkerPlots software change their understanding of a probability problem. While all three analyses have something useful to offer, our dialogic analysis reveals aspects of the episode, in particular the significance of the emotional engagement and the laughter of the students, which are occluded by the other two approaches.
Abstract.
Fujita T, Jones K (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81-91.
Jones K, Fujita T (2013). Interpretations of National Curricula: the case of geometry in textbooks from England and Japan.
ZDM: the International Journal on Mathematics Education,
45(5), 671-683.
Abstract:
Interpretations of National Curricula: the case of geometry in textbooks from England and Japan
This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.
Abstract.
Kazak S, Wegerif R, Fujita T (2013). I’ve got it now!: Stimulating insight about probability through talk and technology. Mathematics Teaching(235), 29-32.
Fujita T (2012). Learners' level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon.
Journal of Mathematical Behavior,
31(1), 60-72.
Abstract:
Learners' level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon
This paper reports on data from investigations on learners' understanding of inclusion relations of quadrilaterals, building on the ideas from our earlier study (Fujita & Jones, 2007). By synthesising past and current theories in the teaching of geometry (van Hiele's model, figural concepts, prototype phenomenon, etc.), we propose a theoretical model and method to describe learners' cognitive development of their understanding of inclusion relations of quadrilaterals, and in order to investigate the topic, data are collected from trainee teachers and lower secondary school students. The findings suggest that in general more than half of above average learners are likely to recognise quadrilaterals primarily by prototypical examples, even though they know the correct definition, and this causes them difficulty in understanding the inclusion relations of quadrilaterals. © 2011 Elsevier Inc.
Abstract.
Fujita T (2012). Reimagining Japanese education: borders, transfers, circulations, and the comparative.
JOURNAL OF EDUCATION FOR TEACHING,
38(1), 107-109.
Author URL.
Fujita T, Jones K (2011). The Process of Re-designing the Geometry Curriculum: the case of the Math Assoc in England in Early XX Century. International Journal for the History of Mathematics Education, 6, 1-23.
Fujita T, Yamamoto S (2011). The development of children's understanding of mathematical patterns through mathematical activities.
Research in Mathematics Education,
13(3), 249-267.
Abstract:
The development of children's understanding of mathematical patterns through mathematical activities
In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on the Fibonacci sequence (Bamboo numbers) used in the context of a Substantial Learning Environment (SLE), which is designed to be mathematically rich, have a clear purpose and give opportunities to utilise mathematical thinking. The flexible nature of the SLEs makes it possible for teachers and children to explore various mathematical patterns. To capture children's activities when working within SLEs, we make particular reference to Pegg and Tall's work in 2005, and consider a theoretical framework based on the SOLO taxonomy (Biggs and Collis 1982) and the developmental process of understanding mathematical concepts. It was found that the key progression to be made through learning using our Bamboo number-based SLEs is from Multi-structural to Relational levels. It was also suggested that it is difficult for many children to understand the structural aspects of number patterns. © 2011 British Society for Research into Learning Mathematics.
Abstract.
Fujita T, Jones K (2007). Learners' understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
Yamamoto S, Fujita T (2006). A brief history of the teaching of geometry in Japan. Paedagogica Historica: international journal of the history of education, 42(4&5), 541-545.
Fujita T, Jones K (2003). The place of experimental tasks in geometry teaching: Learning from the textbooks design of the early20th Century. Research in Mathematics Education, 5(1), 47-62.
Fujita T (2001). The order of theorems in the teaching of Euclidean geometry: Learning from developments in textbooks in the early 20th Century. ZDM: the International Journal on Mathematics Education, 33(6), 196-203.
Chapters
Komatsu K, Fujita T (2023). Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning. In (Ed) Handbook of Digital Resources in Mathematics Education, Springer International Publishing, 1-29.
Komatsu K, Fujita T (2023). Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning. In (Ed) Handbook of Digital Resources in Mathematics Education, Springer International Publishing, 1-29.
Miyazaki M, Fujita T, Jones K (2019). Web-Based Task Design Supporting Students’ Construction of Alternative Proofs. In Hanna G, Reid D, de Villiers M (Eds.)
Proof Technology in Mathematics Research and Teaching, Spinger, 291-321.
Abstract:
Web-Based Task Design Supporting Students’ Construction of Alternative Proofs
Abstract.
Miyazaki M, Fujita T, Jones K (2019). Web-Based Task Design Supporting Students’ Construction of Alternative Proofs. In (Ed) Proof Technology in Mathematics Research and Teaching, Springer International Publishing, 291-312.
Miyazaki M, Fujita T (2015). Proving as an Explorative Activity in Mathematics Education. In Sriraman S (Ed) The First Sourcebook on Asian Research in Mathematics Education China, Korea, Singapore, Japan, Malaysia and India, Information Age Publishing.
Fujita T, Hyde R (2013). Approaches to learning mathematics. In (Ed)
Mentoring Mathematics Teachers: Supporting and Inspiring Pre-Service and Newly Qualified Teachers, 42-58.
Abstract:
Approaches to learning mathematics
Abstract.
Fujita T, Hyde R (2013). Approaches to learning mathematics. In Rosalyn H, Edwards J-A (Eds.) Mentoring in Mathematics Education, Routledge Kegan & Paul, 43-58.
Conferences
Fujita T, Jones K, Kunimune S (2010). STUDENTS' GEOMETRICAL CONSTRUCTIONS AND PROVING ACTIVITIES: a CASE OF COGNITIVE UNITY?.
Author URL.
Publications by year
2023
Fujita T (2023). BSRLM day conference proceedings. Research in Mathematics Education, 25(3), 414-418.
Fujita T (2023). BSRLM day conference proceedings. Research in Mathematics Education, 25(2), 273-276.
Fujita T, Kondo Y, Kumakura H, Miyawaki S, Kunimune S, Shojima K (2023). Identifying Japanese students’ core spatial reasoning skills by solving 3D geometry problems: an exploration.
Asian Journal for Mathematics Education,
1Abstract:
Identifying Japanese students’ core spatial reasoning skills by solving 3D geometry problems: an exploration
Taking the importance of spatial reasoning skills, this article aims to identify “core” spatial reasoning skills which are likely to contribute to successful problem-solving in three-dimensional (3D) geometry. “Core” spatial skills are those which might be particularly related to students’ successful problem-solving in 3D geometry. In this article, spatial reasoning skills are malleable and can be improved with teaching/interventions with mental rotation, spatial orientation, spatial visualization, and property-based reasoning. To achieve the study aim, we conducted a survey in total of 2,303 Japanese Grade 4–9 students (10–15 years old). We take the following stages of the procedures in this article: (a) Descriptive statistics; (b) 2 parameter logistic model (2PLM) analysis; and (c) Experiments with the Pearson correlation coefficient. As a result, we identified that a set of a few tasks can be used to check if students have “core” spatial skills in 3D geometry. For both primary and secondary, rotating given representations mentally, and imagining and drawing 3D shapes, are important, and for secondary schools, property-based reasoning is also crucial for further problem-solving skills. Our findings and methodological approach have implications for mathematics education research and practice as our results provide clear, and promising principles for task/units/curriculum design for spatial reasoning in which more robust teaching intervention is necessary.
Abstract.
Komatsu K, Fujita T (2023). Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning. In (Ed) Handbook of Digital Resources in Mathematics Education, Springer International Publishing, 1-29.
Komatsu K, Fujita T (2023). Intertwined Use of Physical and Digital Tools in Mathematics Teaching and Learning. In (Ed) Handbook of Digital Resources in Mathematics Education, Springer International Publishing, 1-29.
Melro A, Tarling G, Fujita T, Kleine Staarman J (2023). What Else can be Learned When Coding? a Configurative Literature Review of Learning Opportunities Through Computational Thinking.
Journal of Educational Computing Research,
61(4), 901-924.
Abstract:
What Else can be Learned When Coding? a Configurative Literature Review of Learning Opportunities Through Computational Thinking
Underpinning the teaching of coding with Computational Thinking has proved relevant for diverse learners, particularly given the increasing demand in upskilling for today’s labour market. While literature on computing education is vast, it remains unexplored how existing CT conceptualisations relate to the learning opportunities needed for a meaningful application of coding in non-Computer Scientists’ lives and careers. In order to identify and organise the learning opportunities in the literature about CT, we conducted a configurative literature review of studies published on Web of Science, between 2006 and 2021. Our sample gathers 34 papers and was analysed on NVivo to find key themes. We were able to organise framings of CT and related learning opportunities into three dimensions: functional, collaborative, and critical and creative. These dimensions make visible learning opportunities that range from individual cognitive development to interdisciplinary working with others, and to active participation in a technologically evolving society. By comparing and contrasting frameworks, we identify and explain different perspectives on skills. Furthermore, the three-dimensional model can guide pedagogical design and practice in coding courses.
Abstract.
2022
Miyazaki M, Fujita T, Iwata K, Jones K (2022). Level-spanning proof-production strategies to enhance students’ understanding of the proof structure in school mathematics. International Journal of Mathematical Education in Science and Technology, 1-22.
Tarling G, Melro A, Kleine Staarman J, Fujita T (2022). Making coding meaningful: university students’ perceptions of bootcamp pedagogies. Pedagogies: an International Journal, 18(4), 578-595.
2021
Shinno Y, Fujita T (2021). Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach.
International Journal of Mathematical Education in Science and TechnologyAbstract:
Characterizing how and when a way of proving develops in a primary mathematics classroom: a commognitive approach
In this study we aim to characterize a way of proving which can be produced in a primary mathematics classroom and explore the factors that influence these processes and lead to changes in the way of proving. Assuming proving as a socially embedded activity, we conceptualize it as the interplay between ‘construction’ and ‘substantiation’ based on a well-established theoretical framework in mathematics education: the commognitive framework. A tangible proving task was designed, based on the idea of operative proofs, and implemented in a fifth-grade classroom in England. We analysed the construction and substantiation which fairly associated with discursive features (word use, visual mediator, narrative, and routine) during the proving process. The results show that the interplay between construction and substantiation developed progressively rather than in a straightforward manner, in which previously constructed narratives are reconstructed or substantiated in a more general context. This finding is relevant to understand the factors that might influence primary students to change the use of examples and the way of proving when used as a communicational means in proving. Our study has implications for possible continuity to proving activities in secondary schools, and thus contributes to advancing the research on proving in primary schools.
Abstract.
Fujita T, Doney J, Flanagan R, Wegerif R (2021). Collaborative group work in mathematics in the UK and Japan: use of group thinking measure
tests. Education 3-13: the professional journal for primary education, 49, 119-133.
Fujita T, Nakagawa H, Sasa H, Enomoto S, Yatsuka M, Miyazaki M (2021). Japanese teachers’ mental readiness for online teaching of mathematics following unexpected school closures. International Journal of Mathematical Education in Science and Technology, 54(10), 2197-2216.
Fujita T (2021). On Online Teaching and Learning of Mathematics: What Future Research can be Expected by Mathematics Education Research?. Hiroshima Journal of Mathematics Education, 14, 37-51.
Kazak S, Fujita T, Pifarre Turmo M (2021). Students’ informal statistical inferences through data modeling
with a large multivariate dataset. Mathematical Thinking and Learning, 25, 23-43.
2020
Fujita T, Kondo Y, Hiroyuki K, Susumu K, Keith J (2020). Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9.
Mathematics Education Research Journal,
32(2), 235-255.
Abstract:
Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9
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 to reason. We found that using either spatial visualisation or property-based spatial analytic reasoning is not enough for the problems that required more than one step of reasoning, but also that these two skills have to be harmonised by domain-specific knowledge in order to overcome the perceptual appearance (or “look”) of the given diagram. We argue that more opportunities might be given to both primary and secondary school students in which they can exercise not only their spatial reasoning skills but also consolidate and use their existing domain-specific knowledge of geometry for productive reasoning in geometry.
Abstract.
2019
Miyazaki M, Nagata J, Chino K, Sasa H, Fujita T, Komatsu K, Shimizu S (2019). Curriculum development for explorative proving in lower secondary school geometry: Focusing on the levels of planning and constructing a proof. Frontiers in Education
Fujita T, Doney J, Wegerif R (2019). Students’ collaborative decision-making processes in defining and classifying quadrilaterals: a semiotic/dialogic approach.
Educational Studies in Mathematics,
101(3), 341-356.
Abstract:
Students’ collaborative decision-making processes in defining and classifying quadrilaterals: a semiotic/dialogic approach
© 2019, the Author(s). In this paper, we take a semiotic/dialogic approach to investigate how a group of UK 12–13-year-old students work with hierarchical defining and classifying quadrilaterals. Through qualitatively analysing students’ decision-making processes, we found that the students’ decision-making processes are interpreted as transforming their informal/personal semiotic representations of “parallelogram” (object) to more institutional ones. We also found that students’ decision-making was influenced by their inability to see their peers’ points of view dialogically, i.e. requiring a genuine inter-animation of different perspectives such that there is a dialogic switch, and individuals learn to see the problem “as if through eyes of another,” in particular collectively shared definitions of geometrical shapes.
Abstract.
Miyazaki M, Fujita T, Jones K (2019). Web-Based Task Design Supporting Students’ Construction of Alternative Proofs. In Hanna G, Reid D, de Villiers M (Eds.)
Proof Technology in Mathematics Research and Teaching, Spinger, 291-321.
Abstract:
Web-Based Task Design Supporting Students’ Construction of Alternative Proofs
Abstract.
Miyazaki M, Fujita T, Jones K (2019). Web-Based Task Design Supporting Students’ Construction of Alternative Proofs. In (Ed) Proof Technology in Mathematics Research and Teaching, Springer International Publishing, 291-312.
2018
Komatsu K, Fujita T, Jones K, Sue N (2018). Explanatory unification by proofs in a mathematics classroom. For the Learning of Mathematics, 38, 31-37.
Fujita T, Jones DK, Miyazaki M (2018). Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry.
ZDM,
50Abstract:
Learners' use of domain-specific computer-based feedback to overcome logical circularity in deductive proving in geometry
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-based proof learning support system. Through this analysis we illustrate the various errors they made, including using circular reasoning, which were related to their understanding of hypothetical syllogism as an element of the structure of mathematical proof. We found that, by using the computer-based feedback and, for some, teacher intervention, the learners started considering possible combinations of assumptions and conclusion, and began realising when their proof fell into logical circularity. Our findings raise important issues about the nature and role of computer-based feedback such as how feedback is used by learners, and the importance of teacher intervention in computer-based learning environments.
Abstract.
Norwich B, Fujita T, Adlam A, Milton F, Edwards-Jones A (2018). Lesson study: an inter-professional approach for Educational Psychologists to improve teaching and learning. Educational Psychology in Practice, 34, 370-385.
Fujita T (2018). “That Journal has a History”: Overview of the Technological Tools and Theories Studied in the International Journal for Technology in Mathematics Education. 2004-2018. International Journal for Technology in Mathematics Education, 25, 35-44.
2017
Miyazaki M, Fujita T, Jones K, Iwanaga Y (2017). Designing a web-based learning support system for
flow-chart proving in school geometry. Digital Experiences in Mathematics Education, 3(3), 233-256.
Wegerif R, Fujita T, Doney J, Perez Linares J, Richards A, van Rhyn C (2017). Developing and trialing a measure of group thinking.
Learning and Instruction,
48, 40-50.
Abstract:
Developing and trialing a measure of group thinking
This paper offers a critical review of the issue of assessing the quality of group thinking, describes the development of a Group Thinking Measure that fills a gap revealed by the literature and illustrates the use of this measure, in combination with interpretative discourse analysis, as a way of distinguishing those behaviors that add value to group thinking from those behaviors that detract value. The Group Thinking Measure combines two tests of equal difficulty, one for individual use and one for use by triads. This enables a measure not only of how well groups are thinking together but also a correlation between individual thinking and group thinking. This innovation gives an indication of whether or not working in a group adds value and so the extent to which a classroom culture supports collaborative thinking.
Abstract.
Koutsouris G, Norwich B, Fujita T, Ralph T, Adlam A, Milton F (2017). Piloting a dispersed and inter-professional Lesson Study using technology to link team members at a distance.
Technology, Pedagogy and Education,
26(5), 587-599.
Abstract:
Piloting a dispersed and inter-professional Lesson Study using technology to link team members at a distance
This article presents an evaluation of distance technology used in a novel Lesson Study (LS) approach involving a dispersed LS team for inter-professional purposes. A typical LS model with only school teachers as team members was modified by including university-based lecturers with the school-based teachers, using video-conferencing and online video sharing. The aim was to examine the experiences of using video-conferencing and video transfer technology to support the use of LS procedures to connect team members between schools and university. The meetings from two LS teams (primary and secondary) were recorded and analysed using a discourse analysis framework, and team members were interviewed after the LS cycle. Despite some technical difficulties, the communication between the dispersed members of the teams was largely smooth and successful. Extending LS teams and practice to include non school teachers, using distance-linking technology, can more effectively support teachers, while reducing the practical constraints of bringing other professionals into the LS team.
Abstract.
Fujita T, Kondo Y, Kumamura H, Kunimune S (2017). Students’ geometric thinking with cube representations: Assessment framework and empirical evidence.
Journal of Mathematical Behavior,
46(2), 96-111.
Abstract:
Students’ geometric thinking with cube representations: Assessment framework and empirical evidence
While representations of 3D shapes are used in the teaching of geometry in lower secondary school, it is known that such representations can provide difficulties for students. In order to assess students’ thinking about 3D shapes, we constructed an assessment framework based on existing research studies and data from G7-9 students (aged 12-15). We then applied our framework to assess students’ geometric thinking in lessons. We report two cases of qualitative findings from a classroom experiment in which Grade 7 students (aged 12-13) tackled a problem in 3D geometry that was, for them, quite challenging. We found that students who failed to answer given problems did not mentally manipulate representations effectively, while others could mentally manipulate representations and reason about them in order to reach correct solutions. We conclude with the proposition that this finding shows the framework can be used by teachers in instruction to
assess their students' 3D geometric thinking.
Abstract.
Herbst P, Fujita T, Halverscheid H, Weiss M (2017).
The Learning and Teaching of Geometry in Secondary Schools: a Modeling Perspective. London, Routledge.
Abstract:
The Learning and Teaching of Geometry in Secondary Schools: a Modeling Perspective
Abstract.
2016
Norwich B, Koutsouris G, Fujita T, Ralph T, Adlam A, Milton F (2016). Exploring knowledge bridging and translation in Lesson Study using an inter-professional team.
International Journal of Lesson and Learning Studies,
5(3), 180-195.
Abstract:
Exploring knowledge bridging and translation in Lesson Study using an inter-professional team
Purpose – it is argued that the issues of translating basic science, including knowledge from neuroscience, into relevant teaching are similar to those that have been experienced over a long period by educational psychology. This paper proposes that such a translation might be achieved through Lesson Study (LS), which is an increasingly used technique to stimulate teacher enquiry. To explore these issues, this paper presents the findings from a modified LS approach that involved psychologists and mathematics lecturers working together with school-based teachers to prepare a series of lessons on mathematics.
Design/methodology/approach – the LS team review and planning meetings and subsequent interviews were recorded and analysed for common themes, with reference to patterns of knowledge bridging. Particular attention was paid to translational issues and the kind of knowledge used.
Findings – Overall, there was some successful bridging between theory and practice, and evidence of translation of theoretical knowledge into relevant teaching practice. However, the analysis of the team’s interactions showed that relatively little involved a useful applied neuroscience/neuropsychology element, whereas other psychological knowledge from cognitive, developmental, educational and clinical psychology was considered more relevant to planning the LS.
Originality/value – This study illustrates how reference to brain functioning has currently little specific to contribute directly to school teaching, but it can arouse increased interest in psychological processes relevant to teaching and learning. This approach reaffirms the central role of teacher-led research in the relationship between theory and practice. The findings are also discussed in relation to the SECI model of knowledge creation.
Abstract.
Kazak S, Fujita T, Wegerif R (2016). Students' informal inference about the binomial distribution of "Bunny hops": a dialogic perspective.
Statistics Education Research Journal,
15(2), 46-61.
Abstract:
Students' informal inference about the binomial distribution of "Bunny hops": a dialogic perspective
The study explores the development of 11-year-old students’ informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic ideas. Findings from the study suggest that dialogic talk facilitated students’ reasoning as it was supported by the use of simulation tools available in the software. It appears that the interaction of using simulation tools, talk between students, and teacher prompts helps students develop their understanding of probabilistic ideas in the context of making inferences about the distribution of random bunny hops.
Abstract.
Miyazaki M, Fujita T, Jones K (2016). Students’ understanding of the structure of deductive proof. Educational Studies in Mathematics, 94(2), 223-239.
2015
Kazak S, Wegerif R, Fujita T (2015). Combining scaffolding for content and scaffolding for dialogue to support conceptual break throughs in understanding probability.
ZDM: the International Journal on Mathematics Education,
47(7), 1269-1283.
Abstract:
Combining scaffolding for content and scaffolding for dialogue to support conceptual break throughs in understanding probability
In this paper, we explore the relationship between scaffolding, dialogue and conceptual breakthroughs, using data from a design-based research study into the development of understanding of probability in 10-12 year old students. Our aim in the study was to gain insight into how the combination of the scaffolding of content using technology and scaffolding for dialogue in the expectation that this would facilitate conceptual breakthroughs. We analyse video-recordings and transcripts of pairs and triads talking together around TinkerPlots software with worksheets and teacher interventions, focusing on moments of conceptual breakthrough. The dialogue scaffolding promoted both dialogue moves specific to the context of probability and dialogue in itself. This paper focuses on an episode of learning that occurred within dialogues (framed and supported by the scaffolding. We present this as support for our claim that combining scaffolding for content with scaffolding for dialogue can be effective. This finding contributes to our understanding of both scaffolding and dialogic teaching in mathematics education by suggesting that scaffolding can be used effectively to prepare for conceptual development through dialogue.
Abstract.
Miyazaki M, Fujita T, Jones K (2015). Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs.
ZDM: the International Journal on Mathematics Education,
47(7), 1211-1224.
Abstract:
Flow-chart proofs with open problems as scaffolds for learning about geometrical proofs
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 lower secondary school can be designed to scaffold students’ initial understanding of geometrical proofs. In order to scaffold the process of understanding the structure of introductory proofs, we show how flow-chart proofs with multiple solutions in ‘open problem’ situations are a useful form of scaffold. We do this by identifying the ‘scaffolding functions’ of flow-chart proofs with open problems through analysis of classroom-based data from a class of Grade 8 students (aged 13-14 years old) and quantitative data from three classes. We found that using flow-chart proofs with open problems supported the students’ development of a structural understanding of proof by giving them a range of opportunities to connect proof assumptions with conclusions. The implication is that such scaffolds are useful to enrich students’ understanding of introductory mathematical proofs.
Abstract.
Miyazaki M, Fujita T (2015). Proving as an Explorative Activity in Mathematics Education. In Sriraman S (Ed) The First Sourcebook on Asian Research in Mathematics Education China, Korea, Singapore, Japan, Malaysia and India, Information Age Publishing.
Kazak S, Wegerif R, Fujita T (2015). The importance of dialogic processes to conceptual development in mathematics.
Educational Studies in Mathematics,
90(2), 105-120.
Abstract:
The importance of dialogic processes to conceptual development in mathematics
We argue that dialogic theory, inspired by the Russian scholar Mikhail Bakhtin, has a distinct contribution to the analysis of the genesis of understanding in the mathematics classroom. We begin by contrasting dialogic theory to other leading theoretical approaches to understanding conceptual development in mathematics influenced by Jean Piaget and Lev Vygotsky. We argue that both Piagetian and Vygotskian traditions in mathematics education overlook important dialogic causal processes enabling or hindering switches in perspective between voices in relationship. To illustrate this argument, we use Piagetian-, Vygotskian- and Bakhtinian-inspired approaches to analyse a short extract of classroom data in which two 12-year-old boys using TinkerPlots software change their understanding of a probability problem. While all three analyses have something useful to offer, our dialogic analysis reveals aspects of the episode, in particular the significance of the emotional engagement and the laughter of the students, which are occluded by the other two approaches.
Abstract.
2014
Fujita T (2014). Paired Book Review: Robert Recorde: the life and times of a Tudor mathematician and Mathematical expeditions: exploring word problems across the ages. History of Education, 43(5), 713-716.
Fujita T, Jones K (2014). Reasoning-and-proving in geometry in school mathematics textbooks in Japan. International Journal of Educational Research, 64, 81-91.
2013
Fujita T, Hyde R (2013). Approaches to learning mathematics. In (Ed)
Mentoring Mathematics Teachers: Supporting and Inspiring Pre-Service and Newly Qualified Teachers, 42-58.
Abstract:
Approaches to learning mathematics
Abstract.
Fujita T, Hyde R (2013). Approaches to learning mathematics. In Rosalyn H, Edwards J-A (Eds.) Mentoring in Mathematics Education, Routledge Kegan & Paul, 43-58.
Jones K, Fujita T (2013). Interpretations of National Curricula: the case of geometry in textbooks from England and Japan.
ZDM: the International Journal on Mathematics Education,
45(5), 671-683.
Abstract:
Interpretations of National Curricula: the case of geometry in textbooks from England and Japan
This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.
Abstract.
Kazak S, Wegerif R, Fujita T (2013). I’ve got it now!: Stimulating insight about probability through talk and technology. Mathematics Teaching(235), 29-32.
2012
Fujita T (2012). Learners' level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon.
Journal of Mathematical Behavior,
31(1), 60-72.
Abstract:
Learners' level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon
This paper reports on data from investigations on learners' understanding of inclusion relations of quadrilaterals, building on the ideas from our earlier study (Fujita & Jones, 2007). By synthesising past and current theories in the teaching of geometry (van Hiele's model, figural concepts, prototype phenomenon, etc.), we propose a theoretical model and method to describe learners' cognitive development of their understanding of inclusion relations of quadrilaterals, and in order to investigate the topic, data are collected from trainee teachers and lower secondary school students. The findings suggest that in general more than half of above average learners are likely to recognise quadrilaterals primarily by prototypical examples, even though they know the correct definition, and this causes them difficulty in understanding the inclusion relations of quadrilaterals. © 2011 Elsevier Inc.
Abstract.
Fujita T (2012). Reimagining Japanese education: borders, transfers, circulations, and the comparative.
JOURNAL OF EDUCATION FOR TEACHING,
38(1), 107-109.
Author URL.
2011
Fujita T, Jones K (2011). The Process of Re-designing the Geometry Curriculum: the case of the Math Assoc in England in Early XX Century. International Journal for the History of Mathematics Education, 6, 1-23.
Fujita T, Yamamoto S (2011). The development of children's understanding of mathematical patterns through mathematical activities.
Research in Mathematics Education,
13(3), 249-267.
Abstract:
The development of children's understanding of mathematical patterns through mathematical activities
In this paper we report how children (aged 8) developed their mathematical understanding through number tasks based on the Fibonacci sequence (Bamboo numbers) used in the context of a Substantial Learning Environment (SLE), which is designed to be mathematically rich, have a clear purpose and give opportunities to utilise mathematical thinking. The flexible nature of the SLEs makes it possible for teachers and children to explore various mathematical patterns. To capture children's activities when working within SLEs, we make particular reference to Pegg and Tall's work in 2005, and consider a theoretical framework based on the SOLO taxonomy (Biggs and Collis 1982) and the developmental process of understanding mathematical concepts. It was found that the key progression to be made through learning using our Bamboo number-based SLEs is from Multi-structural to Relational levels. It was also suggested that it is difficult for many children to understand the structural aspects of number patterns. © 2011 British Society for Research into Learning Mathematics.
Abstract.
2010
Fujita T, Jones K, Kunimune S (2010). STUDENTS' GEOMETRICAL CONSTRUCTIONS AND PROVING ACTIVITIES: a CASE OF COGNITIVE UNITY?.
Author URL.
2007
Fujita T, Jones K (2007). Learners' understanding of the definitions and hierarchical classification of quadrilaterals: Towards a theoretical framing. Research in Mathematics Education, 9(1), 3-20.
2006
Yamamoto S, Fujita T (2006). A brief history of the teaching of geometry in Japan. Paedagogica Historica: international journal of the history of education, 42(4&5), 541-545.
2003
Fujita T, Jones K (2003). The place of experimental tasks in geometry teaching: Learning from the textbooks design of the early20th Century. Research in Mathematics Education, 5(1), 47-62.
2001
Fujita T (2001). The order of theorems in the teaching of Euclidean geometry: Learning from developments in textbooks in the early 20th Century. ZDM: the International Journal on Mathematics Education, 33(6), 196-203.
