Arthur Bakker

University of Amsterdam, Faculty of Social and Behavioural Sciences, Faculty Member

Followers

1,325

Following

Co-authors

Public Views

Professor of STEM Education and Curriculum, leading the Research Centre Curriculum Studies (slo.nl/rccs). Research interests: design research, boundary crossing, mathematics education, statistics education, learning theories, translanguaging, inclusion and equity

less

George K. # Zarifis

Aristotle University of Thessaloniki

Dr Mervat Mahdy

Benha University

H.Eray Çelik

Yuzuncu Yil University

Sam Rocha

University of British Columbia

Marc Champagne

Kwantlen Polytechnic University

David Seamon

Kansas State University

Louis de Saussure

University of Neuchâtel

Roe Fremstedal

Norwegian University of Science and Technology

Simon McIntyre

The University of New South Wales

Armando Marques-Guedes

UNL - New University of Lisbon

InterestsView All (18)

Uploads

Books by Arthur Bakker

Publications Arthur Bakker

Networking theories in design research: An embodied instrumentation case study in trigonometry. I... more

Download

Editorial

Educational Studies in Mathematics, 2019

Educational Studies in Mathematics (ESM) has reached a special point in its history. Some 50 year... more

Download

Design principles in design research: A commentary

Unterrichtsentwicklung macht Schule, 2019

Bakker, Arthur (2019). Design principles in design research: A commentary. In Angelika Bikner-Ahs... more

The Learning Potential of Boundary Crossing in the Vocational Curriculum

The Wiley Handbook of Vocational Education and Training, 2019

Vocational education and training (VET) is a heterogeneous field, which is organized in diverse w... more Vocational education and training (VET) is a heterogeneous field, which is organized in diverse ways in different countries. Part of VET is school‐based: Students are at school most of the time and do an internship at the end of their vocational education. Part of VET is work‐based: Employees work most of the time, but receive training to qualify better for their current or future work. Both school‐based education and work‐based training have been studied a lot, but far less is known about the transitions that students and employees make between school and work. Yet these transitions are crucial. If learners cannot connect
what they learn in different settings, it is very likely that what they have learned in educational settings remains inert. What they have learned in an internship or regular work may not be enriched by what they gained in education or training. It is therefore crucial to think through what implications follow for curriculum and pedagogy in VET when we ask how to support VET learners to make such transitions and connections. Such transitions and making connections have been conceptualized in terms of boundary crossing.

bakker2019designprinciplescommentary.pdf

In the context of this book, innovation is about achieving desirable goals in domain-specific edu... more In the context of this book, innovation is about achieving desirable goals in domain-specific education. The various contributions to the second part of the book provide knowledge about how to achieve something worthwhile in a particular domain, and all do so in the form of design principles as a result from design research. Such principles are popular in design research and other approaches to innovate educational practice, but education and educational research would benefit from further reflection on what they are and how they are grounded in research and practice. My commentary therefore reflects on design principles in design research. For the various chapters, I analyze whether the design principles as formulated are values, criteria, predictions, advice, or heuristics. I argue that design research would benefit from more clarity of the nature of design principles, and what counts as empirical support. Moreover, I reflect on how design principles could be communicated in a succinct form so that they can inspire others to use them wisely in educational practice.

Download

Design Research in Education: A Practical Guide for Early Career Researchers

Design Research in Education is a practical guide containing all the information required to begi... more Design Research in Education is a practical guide containing all the information required to begin a design-research project. Providing an accessible background to the methodological approaches used in design research as well as addressing all the potential issues that early career researchers will encounter, the book uniquely helps the early career researcher to gain a full overview of design research and the practical skills needed to get their project off the ground. Based on extensive experience, the book also contains multiple examples of design research from both undergraduate and postgraduate students, to demonstrate possible projects to the reader.

Tussen opleiding en beroepspraktijk: Het potentieel van boundary crossing

by Arthur Bakker and Ilya Zitter

Improving mathematics at work: The need for techno-mathematical literacies

Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2010). Improving mathematics at work: The need for ... more

Design research in statistics education: On symbolizing and computer tools

Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Ut... more

Download

Papers by Arthur Bakker

The Role and Nature of Knowledge in Vocational Programmes

An important issue in the design of vocational education is the positioning of the knowledge comp... more An important issue in the design of vocational education is the positioning of the knowledge component of occupations in the curriculum. The underlying question here is what knowledge contents students come across during their education in order to develop their personal knowledge base for professional performance. The knowledge contents of occupations are not unambiguous. In the literature, a distinction is made between different types of knowledge. The first type is codified knowledge that is related to disciplinary knowledge such as language and mathematics but also mechanics, physiology, nutrition, economy, et cetera. Occupational knowledge refers to the specific manifestations of this discipline knowledge. The second type of occupational knowledge refers to distributed and embodied knowledge that can be partly explicated in procedures.

Tussen opleiding en beroepspraktijk

Word problems versus image-rich problems

The Learning Potential of Boundary Crossing in the Vocational Curriculum

The Wiley Handbook of Vocational Education and Training, 2019

Vocational education and training (VET) is a heterogeneous field, which is organized in diverse w... more Vocational education and training (VET) is a heterogeneous field, which is organized in diverse ways in different countries. Part of VET is school‐based: Students are at school most of the time and do an internship at the end of their vocational education. Part of VET is work‐based: Employees work most of the time, but receive training to qualify better for their current or future work. Both school‐based education and work‐based training have been studied a lot, but far less is known about the transitions that students and employees make between school and work. Yet these transitions are crucial. If learners cannot connect what they learn in different settings, it is very likely that what they have learned in educational settings remains inert. What they have learned in an internship or regular work may not be enriched by what they gained in education or training. It is therefore crucial to think through what implications follow for curriculum and pedagogy in VET when we ask how to support VET learners to make such transitions and connections. Such transitions and making connections have been conceptualized in terms of boundary crossing.

Designing an instrument to measure the development of techno-mathematical literacies in an innovative mathematics course for future engineers in STEM education

ZDM – Mathematics Education

Techno-mathematical Literacies (TmL), which are defined as a combination of mathematical, workpla... more Techno-mathematical Literacies (TmL), which are defined as a combination of mathematical, workplace and ICT knowledge, and communicative skills, are acknowledged as important learning goals in STEM education. Still, much remains unknown about ways to address them in teaching and to assess their development. To investigate this, we designed and implemented an innovative course in applied mathematics with a focus on Techno-mathematical Literacies for 1st-year engineering students, and we set out to measure the learning effect of the course. Because measuring TmL is an uncharted terrain, we designed tests that could serve as pre- or posttests. To prevent a test learning effect, we aimed to design two different but equally difficult tests A and B. These were assigned randomly to 68 chemistry students, as a pretest, with the other one serving as posttest after the course. A significant development in TmL was found in the B-pre group, but not in the A-pre group. Therefore, as a follow-up ...

Download

Teacher's Scaffolding over the Year to Develop Norms of Mathematical Inquiry in a Primary Classroom

Mathematics Education Research Group of Australasia, 2015

Developing mathematical inquiry practices requires that teachers are explicit about classroom nor... more Developing mathematical inquiry practices requires that teachers are explicit about classroom norms that support these practices. In this study, we asked: How can a teacher scaffold the development of norms and practices in mathematical inquiry over time? Analysis of classroom video over a year showed that the teacher constantly diagnosed classroom norms and responsively used strategies to improve them. By the end of the year, there was evidence of inquiry norms and practices independent of the teacher's presence.

Download

Tussen opleiding en beroepspraktijk : het potentieel van boundary crossing

Leren en werken goed laten aansluiten? Een complex vraagstuk! Studenten en startende werknemers z... more Leren en werken goed laten aansluiten? Een complex vraagstuk! Studenten en startende werknemers zijn vaak niet optimaal voorbereid, opleiders weten niet goed wat er op de werkvloer speelt en praktijkbegeleiders hebben weinig zicht op wat stagiairs al op de opleiding hebben geleerd. Daarnaast zijn er vanuit Human Resources Development vragen over het Leven Lang Leren van hun werknemers op en buiten de werkplek zodat organisaties kunnen inspelen op actuele ontwikkelingen. Leren in een formele, schoolse context staat meestal op gespannen voet met leren op de werkplek. Vaak worden de verschillen tussen opleiding en beroepspraktijk als hinderlijk ervaren terwijl die verschillen juist ook leerzaam kunnen zijn. In Tussen opleiding en beroepspraktijk wordt aan de hand van een theoretisch kader over boundary crossing en vele praktijkvoorbeelden beschreven hoe het leerpotentieel op de grens tussen opleiding en de beroepspraktijk, tussen professionaliseringstrajecten en leren op het werk, kan worden aangeboord. De beschikbare wetenschappelijke en ervaringskennis op het gebied van boundary crossing is gebundeld en toegankelijk gemaakt voor opleiders van beroepsopleidingen (mbo en hbo) en professionaliseringstrajecten in organisaties. Tussen opleiding en beroepspraktijk biedt inzichten en inspiratie voor de innovatie van opleidings- en professionaliseringsactiviteiten, voor zelfstudie en ook voor het vormgeven van formele opleidingen. Dit boek is geschikt voor mbo- en hbo-docenten en studenten aan masteropleidingen zoals Leren en Innoveren, Onderwijskunde, Professioneel Meesterschap of Expertdocent Beroepsonderwijs. Bent u docent en wilt u het boek voorschrijven aan uw studenten van een van deze opleidingen, dan kunt u hier een docentexemplaar aanvragen. 'Tussen opleiding en beroepspraktijk' is daarnaast interessant voor managers, adviseurs, beleidsmedewerkers en HRD’ers in onderwijs of bedrijfsleven.

The Emergence of Proportional Reasoning from Embodied Interaction with a Tablet Application: An Eye-Tracking Study

Embodied cognition is emerging as a promising approach in educational technology. This study is b... more Embodied cognition is emerging as a promising approach in educational technology. This study is based on the conjecture that a potentially powerful methodology for researching embodied mathematics design would be to gather empirical data on children's shifting visual attention as they learn to operate the technological devices so as to solve the situated problems. The aim of the study is to gain insight into the role of visual attention in the emergence of new sensorimotor schemes underlying mathematical concepts, especially proportion tasks. The research question is: How does visual attention change in the emergence of sensorimotor schemes during proportional reasoning tasks? An exploratory study was conducted amongst eight 5 th-and 6 th-grade students (age 10-12 years). Based on the original Mathematical Imagery Trainer for Proportion (MIT-P) designs for Wii and iPad (Abrahamson), a new tablet app has been developed. While students completed the hands-on proportion tasks, a Tobii x2-30 and an external camera were used for real-time processing and storage of both video and gaze data, resulting in integrated videos of hand-and eye movements. Data analysis revealed cross-participant variation in exploration path, progress rate, and inferences. Yet across all participants insight coincided with a shift from: (a) random finger movements accompanied by gazing at salient figural contour; to (b) new bimanual coordinations accompanied by gazing at new non-salient figural features. The study thus supports classical constructivist claims that mathematical concepts are grounded in operatory schemes. In particular, the data literally show the dynamical emergence of attentional anchors for situated problem solving as mediating the development of mathematical concepts. Thus new research methodologies stand to validate claims from embodiment.

Download

Contextualising Vocational Knowledge: A Theoretical Framework and Illustrations From Culinary Education

Vocations and Learning, Dec 8, 2015

The nature of knowledge in vocational education is often described in dichotomies such as theory ... more The nature of knowledge in vocational education is often described in dichotomies such as theory versus practice or general versus specific. Although different scholars now acknowledge that vocational knowledge is more than putting bits of theoretical and practical knowledge together, it is still unclear how vocational knowledge should be theorised instead. In this article we theorise the idea of contextualising vocational knowledge to understand the nature of vocational knowledge and illustrate this process of contextualising with empirical examples from culinary education. We adopt an activity-theoretical focus on contextualising that involves both particularising and providing coherence. We posit a cognitive process of meaning making where meaning derives from seeing the relationships of parts to the whole. The aspects of the nature of coherence and the relation between concepts and actions seem rather underdeveloped in vocational education theory. To characterise this process at a micro-level, we enhance the activity-theory approach with an inferentialist one. Inferentialism offers a way to focus on reasons and inferential relations between concepts and actions that provides coherence in vocational knowledge. To characterise the broad spectrum of processes relevant for vocational knowledge, we propose the terms Bconceptualising^and Bconcretising^. Conceptualising involves inferring what follows from understanding a

Download

Eye-Tracking Piaget: Capturing the Emergence of Attentional Anchors in the Coordination of Proportional Motor Action

Human Development, 2015

The combination of two methodological resources-natural user interface and multimodal learning an... more The combination of two methodological resources-natural user interface and multimodal learning analytics-is creating opportunities for educational researchers to empirically evaluate theoretical models accounting for the emergence of concepts from situated sensorimotor activity. Seventy-six participants (9-14 years old) solved tabletbased presymbolic manipulation tasks designed to foster grounded meanings for the mathematical concept of proportional equivalence. Data gathered in task-based semistructured clinical interviews included action logging, eye-gaze tracking, and videography. Analysis of these data indicates that successful task performance coincided with spontaneous emergence of stable dynamical gaze path patterns soon followed by multimodal articulation of strategy. Significantly, gaze patterns included unmanipulated, non-salient screen locations. We present cumulative evidence that these gaze patterns served as ''attentional anchors'' mediating participants' problem solving. By way of further contextualizing our claim, we also present case studies from the various experimental conditions. We interpret the findings as enabling us to revisit, support, refine, and perhaps elaborate on seminal claims from Piaget's theory of genetic epistemology and in particular his insistence on the role of situated motor-action coordination in the process of reflective abstraction.

Download

Authentic practices as contexts for learning to draw conclusions from correlated data

Introduction and research question Many researchers aim to improve science and mathematics educat... more

Publications Arthur Bakker

Networking theories in design research: An embodied instrumentation case study in trigonometry. I... more

Download

Editorial

Educational Studies in Mathematics, 2019

Educational Studies in Mathematics (ESM) has reached a special point in its history. Some 50 year... more

Download

Design principles in design research: A commentary

Unterrichtsentwicklung macht Schule, 2019

Bakker, Arthur (2019). Design principles in design research: A commentary. In Angelika Bikner-Ahs... more

The Learning Potential of Boundary Crossing in the Vocational Curriculum

The Wiley Handbook of Vocational Education and Training, 2019

bakker2019designprinciplescommentary.pdf

Download

Design Research in Education: A Practical Guide for Early Career Researchers

Tussen opleiding en beroepspraktijk: Het potentieel van boundary crossing

by Arthur Bakker and Ilya Zitter

Improving mathematics at work: The need for techno-mathematical literacies

Hoyles, C., Noss, R., Kent, P., & Bakker, A. (2010). Improving mathematics at work: The need for ... more

Design research in statistics education: On symbolizing and computer tools

Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. Ut... more

Download

The Role and Nature of Knowledge in Vocational Programmes

Tussen opleiding en beroepspraktijk

Word problems versus image-rich problems

The Learning Potential of Boundary Crossing in the Vocational Curriculum

The Wiley Handbook of Vocational Education and Training, 2019

Vocational education and training (VET) is a heterogeneous field, which is organized in diverse w... more Vocational education and training (VET) is a heterogeneous field, which is organized in diverse ways in different countries. Part of VET is school‐based: Students are at school most of the time and do an internship at the end of their vocational education. Part of VET is work‐based: Employees work most of the time, but receive training to qualify better for their current or future work. Both school‐based education and work‐based training have been studied a lot, but far less is known about the transitions that students and employees make between school and work. Yet these transitions are crucial. If learners cannot connect what they learn in different settings, it is very likely that what they have learned in educational settings remains inert. What they have learned in an internship or regular work may not be enriched by what they gained in education or training. It is therefore crucial to think through what implications follow for curriculum and pedagogy in VET when we ask how to support VET learners to make such transitions and connections. Such transitions and making connections have been conceptualized in terms of boundary crossing.

Designing an instrument to measure the development of techno-mathematical literacies in an innovative mathematics course for future engineers in STEM education

ZDM – Mathematics Education

Download

Teacher's Scaffolding over the Year to Develop Norms of Mathematical Inquiry in a Primary Classroom

Mathematics Education Research Group of Australasia, 2015

Download

Tussen opleiding en beroepspraktijk : het potentieel van boundary crossing

The Emergence of Proportional Reasoning from Embodied Interaction with a Tablet Application: An Eye-Tracking Study

Download

Contextualising Vocational Knowledge: A Theoretical Framework and Illustrations From Culinary Education

Vocations and Learning, Dec 8, 2015

Download

Eye-Tracking Piaget: Capturing the Emergence of Attentional Anchors in the Coordination of Proportional Motor Action

Human Development, 2015

Download

Authentic practices as contexts for learning to draw conclusions from correlated data

Introduction and research question Many researchers aim to improve science and mathematics educat... more

Towards a framework for understanding students' informal statistical inference and argumentation

The aim of our current collaboration has been to explore concepts for an emerging framework desig... more The aim of our current collaboration has been to explore concepts for an emerging framework designed to better understand the relationship between learners&amp;amp;amp;amp;amp;amp;amp;#x27; inferential reasoning in statistics and their processes of argumentation embedded mostly in context. The concepts we will present grow out of our reading of philosophy, the literature in different fields on argumentation and inference, and our experiences over several years with a wide range of students and adults involved in drawing statistical inferences. This preparatory ...

Grensanalyses : op zoek naar leerpotentieel

Effects of innovative science and mathematics teaching on student attitudes and achievement: A meta-analytic study

Educational Research Review, Nov 1, 2016

DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

Download

Interesses en studiekeuze van jongeren met bètatalent: Onderzoek naar leerlingen van Junior College Utrecht en U-Talent Academie

Draijer, J., Bakker, A., Tromp, S., & Akkerman, S. F. (2017). Interesses en studiekeuze van j... more

Contextualising vocational knowledge

The Multidimensional Structure of Interest

Frontline Learning Research, 2020

There is increasing attention for interest as a powerful, complex, and integrative construct, ran... more There is increasing attention for interest as a powerful, complex, and integrative construct, ranging in appearance from entirely momentary states of interest to longer-term interest pursuits. Developmental models have shown how these situational interests can develop into individual interests over time. As such, these models have helped to integrate more or less separate research traditions and focus the attention of the field more on the developmental dynamics. This, however, also raises subsequent questions, one being how development can be understood in terms of interest structure. The developmental models seem to suggest that development occurs roughly along the line of six dimensions, which we summarize as the dimensions of historicity, value, agency, frequency, intensity, and mastery. Using an experience sampling method that was implemented in a smartphone application, we prompted 94 adolescents aged 13 to 16 (60% female) to rate each interest they experienced during two week...

Download

Supporting Students to Develop Concepts Underlying Sampling and to Shuttle Between Contextual and Statistical Spheres

The Teaching and Learning of Statistics, 2016

To stimulate students' shuttling between contextual and statistical spheres, we based tasks on pr... more To stimulate students' shuttling between contextual and statistical spheres, we based tasks on professional practices. This article focuses on two tasks to support reasoning about sampling by students aged 16-17. The purpose of the tasks was to find out which smaller sample size would have been sufficient for making reliable inferences. The research question addressed is: How can students be supported to develop concepts underlying sampling and to shuttle between contextual and statistical spheres? Design research was carried out to test whether the tasks had the potential to support students' concepts underlying sampling and to find indications of what teachers should do to use this potential. Analysis of video recordings indicates that the students showed a balanced development of the concepts underlying sampling. They seemed aware of the purposes of the tasks and were able to apply their statistical knowledge, but tended to forget to shuttle back.

Download

Eye-Tracking the Emergence of Attentional Anchors in a Mathematics Learning Tablet Activity

Advances in educational technologies and instructional design book series, 2017

Little is known about micro-processes by which sensorimotor interaction gives rise to conceptual ... more Little is known about micro-processes by which sensorimotor interaction gives rise to conceptual development. Per embodiment theory, these micro-processes are mediated by dynamical attentional structures. Accordingly this study investigated eye-gaze behaviors during engagement in solving tablet-based bimanual manipulation tasks designed to foster proportional reasoning. Seventy-six elementary-and vocational-school students (9-15 yo) participated in individual task-based clinical interviews. Data gathered included action-logging, eye-tracking, and videography. Analyses revealed the emergence of stable eye-path gaze patterns contemporaneous with first enactments of effective manipulation and prior to verbal articulations of manipulation strategies. Characteristic gaze patterns included consistent or recurring attention to screen locations that bore non-salient stimuli or no stimuli at all yet bore invariant geometric relations to dynamical salient features. Arguably, this research validates empirically hypothetical constructs from constructivism, particularly reflective abstraction.

Download

Designing an instrument to measure the development of techno-mathematical literacies in an innovative mathematics course for future engineers in STEM education

by Arthur Bakker and Nathalie van der Wal

ZDM – Mathematics Education

Download

Applying Contemporary Philosophy in Mathematics and Statistics Education: The Perspective of Inferentialism

The aim of this discussion group was to put contemporary philosophy to work (cf. Cobb, 2007). Inf... more The aim of this discussion group was to put contemporary philosophy to work (cf. Cobb, 2007). Inferentialism is an example of contemporary philosophy (Brandom, 2000) that increasingly receives interest in mathematics and statistics education. It can be considered an orienting framework that provides epistemological foundations for conceptualizing and analyzing knowledge, learning, communication, and reasoning in the fields of mathematics and statistics. Inferentialism avoids a represen-tationalist perspective on knowledge and learning by focusing on reasoning and inferences (Bakker & Derry, 2011). The Discussion Group (DG) brought together researchers who are interested in the role and use of inferentialism or other contemporary philosophies in mathematics and statistics education. It gave the attendants the opportunity to share perspectives, to question, to discuss, and to make joint efforts in answering the posed key issues. The DG format at ICME provided the opportunity to discuss the significance and the restrictions of the perspective of inferentialism and other contemporary philosophies on the learning and teaching of mathematics and statistics.

Download

Towards argumentative grammars of design research

Design research is considered a valuable but demanding methodological framework that continues to... more Design research is considered a valuable but demanding methodological framework that continues to generate theoretical and methodological reflection. An important topic to address is that of argumentative grammar, the logic guiding a method and supporting warranted claims, because critics consider it a weak spot of design research. With reference to the history of logic, I challenge these critics' demand of an argumentative grammar that relies solely on structure rather than also on content. The purpose of this paper is to think through what argumentative grammars of design research could look like. Because the literature is so limited on this topic, I draw on interviews with experts in design research to evaluate and discuss my own attempt to formulate an argumentative grammar in relation to possible research questions. One conclusion is that design research requires multiple argumentative grammars depending on the design and the research focus.

Download

Introduction to the papers of TWG17: Theoretical perspectives and approaches in mathematics education research

by Arthur Bakker and Mariam Haspekian

Since CERME4 in 2005, theoretical approaches and perspectives have been the topic of an ongoing C... more Since CERME4 in 2005, theoretical approaches and perspectives have been the topic of an ongoing CERME working group. The idea of the networking of theories emerged at CERME 4 and was explored in the subsequent conferences. At CERME 5 (Arzarello et al., 2007), the diversity of theories in the field of mathematics education was regarded as a source of richness, and the networking of theories as a multi-theoretical approach which preserves theoretical identity but also while allowing to bridge the boundaries of theories for a better understanding of teaching and learning. Thereby, the effort was made to make hidden assumptions and relationships of theoretical approaches visible. Principles and heuristics of handling the diversity of theories in empirical research were explored as a new possibility to better grasp the complexity of empirical situations of teaching and learning mathematics, such as the interplay between the individual and the social. Typical heuristics to network theories were to relate different approaches based on research: bottom-up on the one hand and starting from theoretical views top-down on the other, but also mixed types were presented. One interesting result was that not only theoretical principles may be hidden in the use of theories but also the view on the nature of mathematics can be an implicit but relevant feature in the specific theoretical approach.

Download

PROMOTING TEACHERS' SCAFFOLDING OF STUDENTS' MATHEMATICAL LANGUAGE IN A PROFESSIONAL DEVELOPMENT PROGRAMME

by Arthur Bakker and Fokke Munk

To promote students' acquisition of language required for mathematical learning, the employment o... more To promote students' acquisition of language required for mathematical learning, the employment of language-supporting scaffolding strategies (Smit, 2013) has proven to be effective. So far, little is known about how this teaching approach can be upscaled in educational practice. This study investigates the features of a professional development programme focused on teachers' scaffolding of students' mathematical language. In design-based implementation research seven professional development sessions for two professional learning communities in different parts of the Netherlands (consisting of 5 and 10 teachers) were shaped and enacted by four researchers-educators. Over time, all participants (researchers, educator, and teachers) collaboratively identified both process and product features of the professional development programme. Besides insights into these features, this study also yielded professionalized language-oriented primary teachers and a course programme that these teachers and others can employ to further upscale the language-oriented approach in primary mathematics classrooms.

Download

PROMOTING TEACHERS' SCAFFOLDING OF STUDENTS' MATHEMATICAL LANGUAGE IN A PROFESSIONAL DEVELOPMENT PROGRAMME

by Arthur Bakker and Fokke Munk

Download

Evidence for Reflective Abstraction: Seeing (Eye-Tracking Data) is Believing

by Dor Abrahamson and Arthur Bakker

76 volunteering students aged 9-14 participated in a design-based research study investigating re... more 76 volunteering students aged 9-14 participated in a design-based research study investigating relations between perception, action, and cognition in the context of evaluating an experimental activity for learning the mathematical topic of proportions. In individually administered task-based interviews, participants manipulated a touchscreen tablet, trying to solve a micro-choreography problem involving a " mystery " bimanual coordination. Interface interactions were logged, all screen actions and multimodal utterance were videotaped, and eye-gaze pathways were recorded. For data analysis, eye-tracking pathways were superimposed onto the video data, so we could see where the participants were looking as they moved the virtual objects on the screen. To our surprise, concurrent with improved performance new eye-gaze path patterns emerged that were either static or dynamical but included screen locations bearing no apparent stimuli. Verbal and gestural input suggests that these spontaneous patterns served the participants as " steering wheels " for enhancing their control of the environment. We submit that the process of students exploring, discovering, and articulating these " steering wheels " bears a striking correspondence to Piaget's hypothetical process of reflective abstraction: interiorization, coordination, encapsulation, and generalization. This study is perhaps the first to go beyond clinical data so as to corroborate a theoretical construct key to Piaget's genetic epistemology.

Download

Exposing Piaget’s scheme: Empirical evidence for the ontogenesis of coordination in learning a mathematical concept

by Dor Abrahamson, Shakila Shayan, Arthur Bakker, and Marieke Van Der Schaaf

The combination of two methodological resources—natural-user interfaces (NUI) and multimodal lear... more The combination of two methodological resources—natural-user interfaces (NUI) and multimodal learning analytics (MMLA)—is creating opportunities for educational researchers to empirically evaluate seminal models for the hypothetical emergence of concepts from situated sensorimotor activity. 76 participants (9-14 yo) solved tablet-based non-symbolic manipulation tasks designed to foster grounded meanings for the mathematical concept of proportional equivalence. Data gathered in task-based semi-structured clinical interviews included action logging, eye-gaze tracking, and videography. Successful task performance coincided with spontaneous appearance of stable dynamical gaze-path patterns soon followed by multimodal articulation of strategy. Significantly, gaze patterns included uncued non-salient screen locations. We present cumulative results to argue that these 'attentional anchors' mediated participants' problem solving. We interpret the findings as enabling us to revisit, support, refine, and elaborate on central claims of Piaget's theory of genetic epistemology and in particular his insistence on the role of situated motor-action coordination in the process of reflective abstraction.

Download

Networking theories as an exampleof boundary crossing

This review essay first discusses a book authored by the Networking TheoriesGroup and argues that... more This review essay first discusses a book authored by the Networking TheoriesGroup and argues that the strategies for networking of theories are very similar to the learningmechanisms identified in the literature on boundary crossing. I propose that these twotheoretical perspectives may be put into a fruitful dialogue.

Arthur Bakker

Uploads

Books by Arthur Bakker

Papers by Arthur Bakker

Log In