See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/368962636

Characterising Features of Secondary Teachers’ Curriculum Scripts for

Geometric Similarity with Dynamic Mathematical Technology

Chapter · March 2023

DOI: 10.1007/978-3-031-05254-5_10

CITATIONS READS

0 181

4 authors:

Ali Simsek Nicola Bretscher

University of Missouri University College London
16 PUBLICATIONS 19 CITATIONS 24 PUBLICATIONS 120 CITATIONS

SEE PROFILE SEE PROFILE

Alison Clark-Wilson Celia Hoyles

University College London University College London
122 PUBLICATIONS 958 CITATIONS 258 PUBLICATIONS 7,735 CITATIONS

SEE PROFILE SEE PROFILE

All content following this page was uploaded by Ali Simsek on 04 March 2023.

The user has requested enhancement of the downloaded file.

Mathematics Education in the Digital Era

Volume 16

Series Editors
Dragana Martinovic, University of Windsor, Windsor, ON, Canada
Viktor Freiman, Faculté des sciences de l’éducation, Université de Moncton,
Moncton, NB, Canada

Editorial Board Members

Marcelo Borba, State University of São Paulo, São Paulo, Brazil
Rosa Maria Bottino, CNR – Istituto Tecnologie Didattiche, Genova, Italy
Paul Drijvers, Utrecht University, Utrecht, The Netherlands
Celia Hoyles, University of London, London, UK
Zekeriya Karadag, Giresun Üniversitesi, Giresun, Turkey
Stephen Lerman, London South Bank University, London, UK
Richard Lesh, Indiana University, Bloomington, USA
Allen Leung, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Tom Lowrie, University of Canberra, Bruce, Australia
John Mason, The Open University, Buckinghamshire, UK
Sergey Pozdnyakov, Saint Petersburg Electrotechnical University,
Saint Petersburg, Russia
Ornella Robutti, Dipartimento di Matematica, Università di Torino, Torino, Italy
Anna Sfard, University of Haifa, Haifa, Israel
Bharath Sriraman, University of Montana, Missoula, USA
Eleonora Faggiano, University of Bari Aldo Moro, Bari, Italy
The Mathematics Education in the Digital Era (MEDE) series explores ways in
which digital technologies support mathematics teaching and the learning of Net
Gen’ers, paying attention also to educational debates. Each volume will address one
specific issue in mathematics education (e.g., visual mathematics and cyber-­
learning; inclusive and community based e-learning; teaching in the digital era), in
an attempt to explore fundamental assumptions about teaching and learning
mathematics in the presence of digital technologies. This series aims to attract
diverse readers including researchers in mathematics education, mathematicians,
cognitive scientists and computer scientists, graduate students in education, policy-­
makers, educational software developers, administrators and teacher-practitioners.
Among other things, the high-quality scientific work published in this series will
address questions related to the suitability of pedagogies and digital technologies
for new generations of mathematics students. The series will also provide readers
with deeper insight into how innovative teaching and assessment practices emerge,
make their way into the classroom, and shape the learning of young students who
have grown up with technology. The series will also look at how to bridge theory
and practice to enhance the different learning styles of today’s students and turn
their motivation and natural interest in technology into an additional support for
meaningful mathematics learning. The series provides the opportunity for the
dissemination of findings that address the effects of digital technologies on learning
outcomes and their integration into effective teaching practices; the potential of
mathematics educational software for the transformation of instruction and
curricula; and the power of the e-learning of mathematics, as inclusive and
community-based, yet personalized and hands-on.
Submit your proposal: Please contact the Series Editors, Dragana Martinovic
(dragana@uwindsor.ca) and Viktor Freiman (viktor.freiman@umoncton.ca) as well as
the Publishing Editor, Marianna Georgouli (marianna.georgouli@springernature.com).
Forthcoming volume:
• The Evolution of Research on Teaching Mathematics: A. Manizade, N. Buchholtz,
K. Beswick (Eds.)
Alison Clark-Wilson • Ornella Robutti  
Nathalie Sinclair
Editors

The Mathematics Teacher

in the Digital Era
International Research on Professional
Learning and Practice

Second Edition
Editors
Alison Clark-Wilson Ornella Robutti
UCL Institute of Education Dipartimento di Matematica
University College London Università di Torino
London, UK Torino, Italy

Nathalie Sinclair
Faculty of Education
Simon Fraser University
Burnaby, BC, Canada

This work contains media enhancements, which are displayed with a “play” icon. Material in
the print book can be viewed on a mobile device by downloading the Springer Nature “More
Media” app available in the major app stores. The media enhancements in the online version
of the work can be accessed directly by authorized users.

ISSN 2211-8136     ISSN 2211-8144 (electronic)

Mathematics Education in the Digital Era
ISBN 978-3-031-05253-8    ISBN 978-3-031-05254-5 (eBook)
https://doi.org/10.1007/978-3-031-05254-5

1st edition: © Springer Science+Business Media Dordrecht 2014

2nd edition: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature
Switzerland AG 2022
This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether
the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of
illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and
transmission or information storage and retrieval, electronic adaptation, computer software, or by similar
or dissimilar methodology now known or hereafter developed.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication
does not imply, even in the absence of a specific statement, that such names are exempt from the relevant
protective laws and regulations and therefore free for general use.
The publisher, the authors, and the editors are safe to assume that the advice and information in this book
are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the
editors give a warranty, expressed or implied, with respect to the material contained herein or for any
errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional
claims in published maps and institutional affiliations.

This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Introduction

The eight intervening years between this second edition of The Mathematics Teacher
in the Digital Era and the first edition have seen increased attention on the role of
the teacher within technology-enhanced educational contexts, leading to a more
developed understanding of the components of related teacher education pro-
grammes and initiatives for both pre- and in-service teachers. The shock to the edu-
cation system caused by the global coronavirus pandemic simultaneously highlighted
the key role that teachers and lecturers play in the nurturing of generations of learn-
ers, alongside increased global attention to the role that (educational) technology
plays as a mediator of teaching and learning. Studies that have taken place during
the pandemic have provided insights into how teachers’ practices have had to
evolve, whilst also highlighting theoretical and methodological gaps in our under-
standing of the relatively new phenomena of “hybrid”, “at distance” or “remote”
teaching in school and university settings (Bretscher et al., 2021; Clark-Wilson
et al., 2021; Crisan et al., 2021; Drijvers et al., 2021; Maciejewski, 2021).
As we reflect on the academic impacts of the first edition of the book, the chap-
ters within have offered theoretical constructs and methodological approaches,
which have provided other researchers in the field with research tools that are con-
tinuing to advance our collective understandings of the field. In this second edition,
we invited all of the authors who had contributed to the first edition to submit new
research that evidenced advances in their experiences, knowledge and practices. We
also invited new authors, whose research had emerged in the intervening years, to
offer new critical perspectives that broaden the international commentary, with con-
tributions from Argentina, Australia, Canada, France, Germany, Hong Kong,
Iceland, Italy, Mexico, Turkey and the United Kingdom.

vii
viii Introduction

A Journey Through the Text

The evolution of the research on technology in mathematics education has enabled

a more nuanced understanding of the teacher’s perspective to take account of their
trajectories of development from pre-service contexts through to in-service prac-
tices over time. Hence, we have chosen to loosely organise the text body in accor-
dance with teachers’ trajectories of experience with technology use. These
experiences concern those within: university undergraduate courses as learners of
mathematics; university-based pre-service teacher education courses; university-­
based teacher education courses and research projects with in-service teachers as
participants.
We begin with chapters by Thurm, Ebers and Barzel, and Bozkurt and Koyunkaya
that address more practical considerations regarding the provision of support and
training for both in-service and pre-service teachers of mathematics.
The growth of large-scale, online professional development initiatives aimed at
teachers has resulted in new research that seeks to develop theoretical understand-
ing of the design and impact of such initiatives alongside the development of appro-
priate methodologies to inform both aspects. The chapter by Thurm, Ebers and
Barzel addresses aspects of the design of professional development for mathematics
teachers in Germany with a particular focus on the role of the professional develop-
ment facilitators within a regional professional development programme for 30 par-
ticipants who are all such facilitators. The programme was conducted online (due to
the Covid-19 pandemic) and Thurm and colleagues’ findings focus on the impact of
a module of the programme that supported participants’ understanding (and use) of
video-based case studies of mathematics teaching that embed multi-representational
technology. They use Prediger, Roesken-Winter and Leuders’ Three-Tetrahedron
Model as a framework to highlight the complexities of PD design that has a class-
room level, teacher PD level and facilitators’ PD level (Prediger et al., 2019). Their
findings, which highlight aspects of facilitators’ noticing, emphasise the need for
carefully structured prompts to support the analysis of video-based activities that
serve the dual needs of the facilitators and the teachers with whom they are working.
A pre-service teacher education context in Turkey is the subject of the qualitative
action research reported by Bozkurt and Koyunkaya in which they study the impacts
of a redesigned practicum course informed by the Instrumental Orchestration model
(Drijvers et al., 2010; Trouche, 2004). The course design emphasises the pre-service
mathematics teachers’ (PSTs, n=4) developing use of a dynamic mathematics soft-
ware (GeoGebra) from the university setting (through micro teaching to their peers)
as their practices move to school classrooms. Their study adopts a cyclical research
method that draws on data from the PSTs’ lesson plans, supported by analyses of
their teaching and associated interviews. The research findings offer insights into
how the PSTs initially overlooked the exploitation modes for the technology in their
planning but became more systematic in their approach through both the processes
of micro teaching and during the practicum itself. Given that many pre-service pro-
grammes stop short of requiring PSTs to apply their learning about mathematical
Introduction ix

technologies within authentic teaching situations, this chapter provides valuable

insights on the design decisions taken by the teacher educators to develop such an
approach.
The majority of the remaining chapters in the book report studies that involve
in-service teachers as participants within a range of research settings, each with a
different focus. We order these chapters according to teachers’ trajectories of devel-
opment with novel to them technologies. We adopt this phrase from Ng and Leung
(Chap. 10) as it better reflects our experience and expectation that it is not possible
for all teachers to be cognisant of all available (and educationally relevant) tech-
nologies at any point in time, irrespective of how mature the wider community
considers these technologies to be.
The study by Bakos explores how a novel multi-touch tablet technology,
TouchTimes, is used by two primary teachers in British Columbia, Canada, through
a lens that considers the teacher, the tool and the mathematical concept as an ensem-
ble. Rooted in the instrumental approach, and in particular Haspekian’s elaboration
of double instrumental genesis (2011, 2014), Bakos uses her case studies to reveal
three new orchestration types alongside sharing insights on how the agency exerted
by the tool extends our existing understandings of the nature of multiplication, and
the role of haptic devices within young children’s development.
Ng, Liang and Leung’s study also focuses on a more novel technology, 3D pens,
which enable 3-dimensional models to be drawn as physical objects. The 3D pen
warms and extrudes a plastic filament to produce a model that then hardens as it
cools. Ng, Liang and Leung’s method adopts the use of video-aided reflection with
a group of four in-service secondary school teachers in Hong Kong to support their
realisations of the affordances of such technologies as a potential teaching tool. In
their findings, Ng, Liang and Leung provide evidence for how the videos operate as
a boundary object between the teachers and researchers in the study (Robutti
et al., 2019).
Although the concept of silent animated films to show mathematical concepts
dates back to the early twentieth century and was further developed in the 1950s by
Nicolet, the design-based research developed by Kristinsdóttir examines aspects of
their design and use in her case study in an upper secondary mathematics classroom
in Iceland. Kristinsdóttir describes silent videos as short (< 2 min) videos that do not
pose a mathematical problem to be solved but rather invite the viewer to wonder, to
experience dynamically changing mathematical objects such that they might dis-
cover something new or consolidate previous thoughts about the mathematics
shown in the video. Each associated silent video task invites students to work in
pairs to prepare and record a voice-over for the video clip, which is then shared with
the class during a whole-class discussion that is led by the teacher. Framed by a lens
that focuses on the formative assessment dimension of such discussions,
Kristinsdóttir adapted Schoenfeld’s Teaching for Robust Understanding framework
(2018) to identify opportunities and challenges associated with such discussions.
McAlindon, Ball and Chang’s study also explores an innovative technology-­
enhanced pedagogic approach, the flipped classroom, through a case study involving
an experienced teacher in an Australian secondary school. Defining the flipped
x Introduction

classroom as one in which the activities that would normally be conducted in the
classroom are flipped with those that would normally be conducted as homework,
they explore their case study teacher’s experiences and perceptions of a first imple-
mentation for the teaching of linear equations. This exploratory study, which involves
the teacher making qualitative comparisons with a parallel class that she taught using
her traditional approach, concludes positive outcomes such as improved student
engagement and improved formative assessment practices. Although the design pro-
cess for the teacher requires new technology skills and is time consuming, the authors
offer some guidelines to inform professional development initiatives that have the
goal to support mathematics teachers’ flipped classroom pedagogies.
Gueudet, Besnier, Bueno-Ravel and Poisard extend earlier research that featured
in the first edition of the book, which shone a theoretical lens on teachers’ classroom
practices at the kindergarten level from a Documentational Approach to Didactics
perspective (Gueudet et al., 2014). In the intervening years, evolutions of this theory
and its associated research methods have enabled the authors to consider a kinder-
garten teacher’s development as evidenced by both one of her documents (a micro
view) and the encompassing resource system (a macro view). The authors conclude
that both the micro and macro views are necessary to fully appreciate a teacher’s
design capacity within the context of long-term professional development concern-
ing digital technologies for education.
Staying in France, Abboud-Blanchard and Vanderbrouck report findings from a
study in France that explores the implementation of tablet computers in the French
primary school setting. Although tablets are no longer widely considered a new
technology, the authors’ contribution extends ideas reported in the first edition of
the book, which concludes three axes (cognitive, pragmatic and temporal) through
which to consider teachers’ adoption of new technologies within their mathematics
classrooms (Abboud-Blanchard, 2014). Abboud-Blanchard and Vanderbrouck
introduce the additional constructs of tensions and proximities, which they argue
align more specifically to classroom uses of tablet computers. In their chapter, the
authors articulate how these two new constructs evolve from Activity Theory, and
elaborations of Vygotsky’s and Valsiner’s respective Zone Theories.
Sandoval and Trigueros’ chapter is also situated in a primary school setting, this
time in Mexico. They offer new perspectives on the teaching of mathematics in
primary schools, with an emphasis on how two teachers integrate digital technolo-
gies to particularly meet the needs of learners from challenging socio-economic
contexts. In common with their contribution to the first edition of the book (Trigueros
et al., 2014), they adopt an enactivist approach to characterise teachers’ actions and
the resulting student activities that reveal high levels of participation in immersive
environments for learners who are commonly disenfranchised by education systems.
We move from primary school contexts to the secondary phase in the next two
chapters, which both follow teachers over a period of time with the aim to identify
aspects of their evolving practices. The first, by Simsek, Bretscher, Clark-Wilson
and Hoyles, is situated in England and focuses on three in-service teachers’ evolv-
ing use of a dynamic mathematical technology (Cornerstone Maths) for the teach-
ing of geometric similarity to 11–14 year olds over a period of months. The chapter
Introduction xi

extends the understanding of Ruthven and colleagues’ notion of curriculum script,

which is one of the five Structuring Features of Classroom Practice that was
described and critiqued in the first edition of the book (Ruthven, 2014). Simsek and
colleagues’ chapter contributes a case example of such a curriculum script for the
teaching of a specific mathematics topic, highlighting aspects of more productive
teaching practices which are often difficult to notice.
Villareal’s chapter, in which she describes research in Argentina, follows a sec-
ondary school mathematics teacher from her pre-service teacher education pro-
gramme into her role as a novice in-service teacher. The research dually categorises
the teacher’s evolving relationships with technology, which adopts Goos’ taxonomy
of sophistication (master, servant, partner and extension of self (Goos, 2000), along-
side Ruthven’s five Structuring Features of Classroom Practice (Ruthven et al.,
2009). These two frameworks offer an interesting and novel perspective for cate-
gorising the evolution of teachers’ classroom practices that have implications for
the design of teacher education programmes and initiatives.
A university in Canada is the setting for the research reported by Buteau, Muller,
Santacruz Rodriguez, Mgombelo, Sacristan and Gueudet, which expands research
understanding on the long-term development for a faculty-wide integration of pro-
gramming technologies within undergraduate-level courses for both mathematics
students and future mathematics teachers. Situated in the same context as the earlier
study by Buteau and Muller (2014), the instrumental orchestration framework is
used to examine the 20-year trajectory of this integration from the perspective of the
faculty members. The authors’ analysis of the course instructors’ and selected stu-
dents’ schemes concludes an orchestration and genesis alignment model that high-
lights the complexities of the instructor’s role as both policy maker and teacher with
responsibility for orchestrating the students’ instrumental geneses.
The Covid-19 pandemic provides the context for the research study that features in
the chapter by Sánchez Aguilar, Esparza Puga and Lezama. Set in South America, the
authors conducted a survey (n = 179) across five Latin American Countries (Argentina,
Chile, Colombia, Mexico and Uruguay) that aimed to elicit teachers’ perceptions of
the abrupt integration of digital technologies into their practices, triggered by wide-
spread and mandatory school closures in the first six months of 2020. This was framed
within a methodology that aims to capture the lived experience of teachers by giving
them a voice to express the obstacles that they faced. The study captures the broad
range of technologies in play, extending beyond solely mathematical technologies
(i.e., calculators, dynamic geometry software or spreadsheets) to include more general
technologies such as videoconferencing software and learning management plat-
forms. The findings revealed six categories of obstacles that capture both what they
did and how they felt as they worked to overcome the challenges that they faced.
The penultimate two chapters of the book offer theoretical contributions.
In the first edition of the book, the chapter by Arzarello, Robutti, Sabena, Cusi,
Garuti, Malara and Martignone introduced a new theoretical model, Meta-Didactical
Transposition (MDT), which was developed to respond to the need to consider the
complexity of teacher education with respect to the institutions in which teaching
operates, alongside the relationships that teachers must have with these institutions
xii Introduction

(Arzarello et al., 2014). The original MDT model (now referred to as MDT.1), an
extension of Chevallard’s Anthropological Theory of Didactics (1985, 1992, 1999),
describes the evolution of teachers’ education over time by analysing the different
variables involved: components that change from external to internal (internalisa-
tion); brokers who support teachers interacting with them; and dialectic interactions
between the community of teachers and researchers. The chapter by Cusi, Robutti,
Panero, Taranto and Aldon presents an evolution of MDT, namely, Meta-Didactical
Transposition.2 (MDT.2), which offers a deeper insight into the process of inter-
nalisation that captures the way in which the actors within the teachers education
programme develop shared praxeologies over time through the introduction of the
external (and, in some cases digital) components.
The final chapter, by Sinclair, Haspekian, Robutti and Clark-Wilson, charts the
development of theories that frame research on teaching mathematics with technol-
ogy from both a historical perspective and an epistemological one. Building directly
on Ken Ruthven’s chapter in the first edition of this book, it aims to highlight the
evolution of the relevant theories since 2014 and highlights trends in the ways that
these have been operationalised in recent studies. Furthermore, the authors seek to
make explicit the philosophical roots of the commonly adopted theories to provoke
the reader to consider what each might reveal—or conceal—concerning aspects of
teaching mathematics with digital technologies.

Alison Clark-Wilson
 Ornella Robutti
 Nathalie Sinclair

References

Abboud-Blanchard, M. (2014). Teachers and technologies: Shared constraints, common responses.

In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital
era: An international perspective on technology focused professional development
(pp. 297–317). Springer.
Arzarello, F., Robutti, O., Sabena, C., Cusi, A., Garuti, R., Malara, N., & Martignone, F. (2014).
Meta-didactical transposition: A theoretical model for teacher education programmes. In
A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era:
An international perspective on technology focused professional development (pp. 347–372).
Springer.
Bretscher, N., Geraniou, E., Clark-Wilson, A., & Crisan, C. (2021, November). Learning from the
pandemic: Capitalising on opportunities and overcoming challenges for mathematics teaching
and learning practices with and through technology (Part 3). Paper presented at the British
Society for Research into Learning Mathematics.
Buteau, C., & Muller, E. (2014). Teaching roles in a technology intensive core undergraduate
mathematics course. In A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics
teacher in the digital era: An international ­perspective on technology focused professional
development (pp. 163–188). Springer.
Chevallard, Y. (1985). La transposition didactique. La Pensée Sauvage.
Chevallard, Y. (1992). Concepts fondamentaux de la didactique: perspectives apportées par une
approche anthropologique. Recherches en Didactique des Mathématiques, 12(1), 73–112.
Introduction xiii

Chevallard, Y. (1999). L’analyse des pratiques enseignantes en théorie anthropologique du didac-

tique. Recherches en Didactique des Mathématiques, 19(2), 221–266.
Clark-Wilson, A., Bretscher, N., Crisan, C., Geraniou, E., Gono, E., Neate, A., & Shore, C. (2021).
Learning from the pandemic: Capitalising on opportunities and overcoming challenges for
mathematics teaching and learning practices with and through technology (Part 2). Paper pre-
sented at the British Society for Research into Learning Mathematics June 2021.
Crisan, C., Bretscher, N., Clark-Wilson, A., & Geraniou, E. (2021). Learning from the pandemic:
Capitalising on opportunities and overcoming challenges for mathematics teaching and learn-
ing practices with and through technology. Paper presented at the British Society for Research
into Learning Mathematics March 2021.
Drijvers, P., Doorman, M., Boon, P., Reed, H., & Gravemeijer, K. (2010). The teacher and the tool:
Instrumental orchestrations in the technology-rich mathematics classroom. Educational
Studies in Mathematics, 1–22. https://doi.org/10.1007/s10649-­010-­9254-­5
Drijvers, P., Thurm, D., Vandervieren, E., Klinger, M., Moons, F., van der Ree, H., … Doorman,
M. (2021). Distance mathematics teaching in Flanders, Germany, and the Netherlands during
COVID-19 lockdown. Educational Studies in Mathematics, 108(1), 35–64. https://doi.
org/10.1007/s10649-­021-­10094-­5
Gueudet, G., Bueno-Ravel, L., & Poisard, C. (2014). Teaching mathematics with technology at the
Kindergarten level: Resources and Orchestrations. In A. Clark-­Wilson, O. Robutti, & N. Sinclair
(Eds.), The mathematics teacher in the digital era (pp. 213–240). Springer.
Haspekian, M. (2011). The co-construction of a mathematical and a didactical instrument. In
M. Pytlak, T. Rowland, & E. Swoboda (Eds.), Proceedings of the seventh congress of the euro-
pean society for research in mathematics education (pp. 2298–3007). University of Rzeszów.
Haspekian, M. (2014). Teachers’ instrumental geneses when integrating spreadsheet software. In
A. Clark-Wilson, O. Robutti, & N. Sinclair (Eds.), The mathematics teacher in the digital era:
An international perspective on technology focused professional development (pp. 241–276).
Springer.
Maciejewski, W. (2021). Teaching math in real time. Educational Studies in Mathematics, 108(1),
143–159. https://doi.org/10.1007/s10649-­021-­10090-­9
Prediger, S., Roesken-Winter, B., & Leuders, T. (2019). Which research can support PD facilita-
tors? Strategies for content-related PD research in the Three-­Tetrahedron Model. Journal of
Mathematics Teacher Education, 22(4), 407–425. https://doi.org/10.1007/s10857-­019-­09434-­3
Robutti, O., Aldon, G., Cusi, A., Olsher, S., Panero, M., Cooper, J., … Prodromou, T. (2019).
Boundary objects in mathematics education and their role across communities of teachers and
researchers in interaction. In G. M. Lloyd & O. Chapman (Eds.), (Vol. International handbook
of mathematics teacher education: Volume 3, pp. 211–240). Brill.
Ruthven, K. (2014). Frameworks for analysing the expertise that underpins successful integration
of digital technologies into everyday teaching practice. In A. Clark-Wilson, O. Robutti, &
N. Sinclair (Eds.), The mathematics teacher in the digital era: An international perspective on
technology focused professional development (pp. 373–394). Springer.
Ruthven, K., Deaney, R., & Hennessy, S. (2009). Using graphing software to teach about algebraic
forms: A study of technology-supported practice in secondary-­school mathematics. Educational
Studies in Mathematics, 71(3), 279–297.
Schoenfeld, A. H. (2018). Video analyses for research and professional development: The teaching
for robust understanding (TRU) framework. ZDM, 50(3), 491–506. https://doi.org/10.1007/
s11858-­017-­0908-­y
Trigueros, M., Lozano, M.-D., & Sandoval, I. (2014). Integrating technology in the primary school
mathematics classroom: The role of the teacher. In A. Clark-­Wilson, O. Robutti, & N. Sinclair
(Eds.), The mathematics teacher in the digital era: An international perspective on technology
focused professional development (pp. 111–138). Springer.
Trouche, L. (2004). Managing the complexity of human/machine interactions in computerized
learning environments: Guiding students’ command process through instrumental orchestra-
tions. International Journal of Computers for Mathematical Learning, 9, 281–307.
Contents

Professional Development for Teaching Mathematics

with Technology: Fostering Teacher and Facilitator Noticing ��������������������    1
Daniel Thurm, Patrick Ebers, and Bärbel Barzel

Using the Instrumental Orchestration Model for Planning
and Teaching Technology-­Based Mathematical Tasks
as Part of a Restructured Practicum Course������������������������������������������������   31
Gülay Bozkurt and Melike Yiğit Koyunkaya
An Ensemble Approach to Studying the Teaching
of Multiplication Using TouchTimes��������������������������������������������������������������   65
Sandy Bakos
Using First- and Second-Order Models to Characterise
In-Service Teachers’ Video-Aided Reflection on Teaching
and Learning with 3D Pens ����������������������������������������������������������������������������   95
Oi-Lam Ng, Biyao Liang, and Allen Leung
Opportunities and Challenges That Silent Video Tasks
Bring to the Mathematics Classroom������������������������������������������������������������ 119
Bjarnheiður Kristinsdóttir
Teaching Linear Equations with Technology:
A Flipped Perspective�������������������������������������������������������������������������������������� 149
Andrew McAlindon, Lynda Ball, and Shanton Chang

Tensions and Proximities in Teaching and Learning Activities:
A Case Study of a Teacher’s Implementation of Tablet-­Based Lessons������ 181
Maha Abboud and Fabrice Vandebrouck
Digital Resources in Kindergarten Teachers’ Documents
and Resource Systems: A Case Study in France ������������������������������������������ 211
Ghislaine Gueudet, Sylvaine Besnier, Laetitia Bueno-Ravel,
and Caroline Poisard

xv
xvi Contents

Analysis of Primary School Teachers’ Roles in the Dynamics

of Mathematics Lessons That Integrate Technology
Resources in Challenging Socio-economic Contexts������������������������������������ 235
Ivonne Sandoval and María Trigueros
Characterising Features of Secondary Teachers’
Curriculum Scripts for Geometric Similarity
with Dynamic Mathematical Technology������������������������������������������������������ 263
Ali Simsek, Nicola Bretscher, Alison Clark-Wilson, and Celia Hoyles
Instrumental Orchestration of the Use of Programming
Technology for Authentic Mathematics Investigation Projects ������������������ 289
Chantal Buteau, Eric Muller, Joyce Mgombelo,
Marisol Santacruz Rodriguez, Ana Isabel Sacristán,
and Ghislaine Gueudet
Researching Professional Trajectories Regarding
the Integration of Digital Technologies: The Case of Vera,
a Novice Mathematics Teacher ���������������������������������������������������������������������� 323
Mónica E. Villarreal and Cristina B. Esteley

The Abrupt Transition to Online Mathematics Teaching
Due to the COVID-­19 Pandemic: Listening to Latin American
Teachers’ Voices ���������������������������������������������������������������������������������������������� 347
Mario Sánchez Aguilar, Danelly Susana Esparza Puga,
and Javier Lezama
Meta-Didactical Transposition.2: The Evolution of a Framework
to Analyse Teachers’ Collaborative Work with Researchers
in Technological Settings �������������������������������������������������������������������������������� 365
Annalisa Cusi, Ornella Robutti, Monica Panero, Eugenia Taranto,
and Gilles Aldon
Revisiting Theories That Frame Research
on Teaching Mathematics with Digital Technology�������������������������������������� 391
Nathalie Sinclair, Mariam Haspekian, Ornella Robutti,
and Alison Clark-Wilson

Index������������������������������������������������������������������������������������������������������������������ 419
Contributors

Maha Abboud is a professor and researcher in Mathematics Education in France.

She is the head of the LDAR lab (Laboratoire de Didactique André Revuz), the larg-
est science and mathematics education laboratory in France. Her research interests
focus on teachers’ activities with digital technologies. She also studies the practices
of teacher educators and their impact on the teaching and learning of mathematics
and, more broadly, within STEM education. Her professional interests aim at
improving teachers’ professional development in the light of technological change.
She has supervised eight doctoral theses related to these topics. Her theoretical con-
cerns focus on conceptualising teacher and student activities in technology-based
lessons that aim to enhance students’ mathematical thinking. As leader of her
research team, she initiates and participates in the development and refinement of
concepts and methods in educational investigation of the daily life of the mathemat-
ics/science classroom. She teaches mathematics and didactics at the Master’s degree
level at the universities of Cergy and Paris Cité.

Mario Sánchez Aguilar is the Head of the Mathematics Education Program of the
National Polytechnic Institute of Mexico. He serves as an Associate Editor of the
research journals Educación Matemática and Implementation and Replication
Studies in Mathematics Education. He is a visiting professor at the University of
San Carlos of Guatemala. He obtained his PhD in Mathematics Education from
Roskilde University in Denmark in 2010. He is interested in the use of digital tools
in the teaching and learning of mathematics.

Gilles Aldon is now retired after a career as a mathematics teacher and then as a
researcher at the French Institute of Education (Ecole Normale Supérieure de Lyon)
where he was head of the EducTice research team until his retirement. His main
research topic is the use of technology in mathematics teaching and learning.
Particularly, he is interested in the issues of the modifications of teaching and learn-
ing in the digital era, the contribution of technology in the experimental part of
mathematics, and the problem solving processes. The research methodology that
was developed in the EducTice team rests upon design-based research and the

xvii
xviii Contributors

collaborative research where teachers and researchers are involved in both the
research description and the methodology. He is also the president of the International
Commission for the Study and Improvement of Mathematics Teaching (CIEAEM in
French), which investigates the conditions and the possibilities for the development
of mathematics education, taking into account both teachers’ and researchers’
experiences.

Sandy Bakos achieved her PhD in mathematics education at Simon Fraser

University, Canada. Prior to this, she taught elementary school (K–6) for 15 years in
Alberta, Canada, and also spent a year teaching grades 4/5 in Victoria, Australia.
Her research examines how elementary school teachers implement digital technolo-
gies for teaching and learning mathematics. Sandy’s work has primarily focused on
teachers’ adoption and use of TouchTimes as a pedagogical tool, how this particular
digital technology shapes their own understanding of multiplication, and how teach-
ers then use it to build student understanding.

Lynda Ball is a senior lecturer in Mathematics Education at the Melbourne

Graduate School of Education at the University of Melbourne. Her doctoral study
and subsequent research focuses on teaching and learning secondary mathematics
with technology. Her early research focused on the use of Computer Algebra
Systems (CAS) for teaching, learning and assessment in senior secondary mathe-
matics, with particular interest in the evolution of written communication of exami-
nation solutions in the presence of CAS. Teacher beliefs and experiences in teaching
with technology were also a focus. Recent research collaborations, including those
with research students, are in the area of STEM education, flipped learning, online
diagnostic assessment systems, technology-assisted guided discovery, communica-
tion with technology and computer algebra systems in mathematics. The evolution
of teacher practices and opportunities to improve student learning with technology,
as well as teacher professional development, are ongoing research interests.

Bärbel Barzel is a full professor of Mathematics Education at the University of

Duisburg-Essen. Her research focuses on the meaningful use of technology in the math-
ematics classroom and the professionalisation of teachers to orchestrate and manage this
successfully. She is a leading member of the German Centre for Mathematics Teacher
Education (DZLM), a nationwide centre that researches and develops professional
development (PD) courses and materials for teachers and PD facilitators.

Sylvaine Besnier is a kindergarten teacher in Rennes (France). She has been a

member of the Center for Research for Education, Learning and Didactics (CREAD)
since 2012. In 2016, she defended a PhD on the documentation work of kindergar-
ten teachers in mathematics, with specific attention to their use of digital resources
and its consequences in terms of professional development. Her work focuses on the
resources and professional knowledge of teachers. She is particularly interested in
the teaching of numbers at kindergarten level and in digital resources. In terms of
theory, her research uses the documentational approach to didactics and the notion
of orchestration.
Contributors xix

Gülay Bozkurt is an assistant professor in the Department of Mathematics

Education at İzmir Demokrasi University, Turkey. She received both her MPhil
degree in Educational Research (2012) and her doctoral degree in Education (2016)
from the University of Cambridge. She also holds an MSc degree in Mathematics
Education (2010) from the University of Warwick. Additionally, she has extensive
experience as a secondary school teacher of mathematics in Turkey and is thus
aware of the practical world of school teaching. Her research interests centre around
the use of digital technologies in mathematics education and, in particular, the
development of pre-service and in-service mathematics teachers’ professional
knowledge for teaching with technology.

Nicola Bretscher is a lecturer in Mathematics Education at UCL Institute of

Education. Her research interests centre around the use of (digital) technology in
mathematics education and, in particular, how mathematics teachers integrate tech-
nology into their classroom practice and their mathematical knowledge for teach-
ing. She is also interested in the use of quantitative and mixed methods in
mathematics education research. These research interests inform her teaching on
initial teacher education, Master’s programmes as well as doctoral supervision.
Nicola first became interested in the use of technology in the teaching and learning
of mathematics as a pre-service teacher during her training year. As a secondary
school mathematics teacher, she developed this interest through her Master’s dis-
sertation, focusing on the development of teaching techniques for using dynamic
geometry software in her own classroom practice. Her doctoral research focused on
mathematics teachers’ knowledge and how it is involved in interacting with technol-
ogy, as a means of exploring technology integration further. She is a statistician for
the SMART Spaces project, an evaluation of an intervention based on spaced learn-
ing in science education funded by the Education Endowment Foundation.

Laetitia Bueno-Ravel is an associate professor of Mathematics Education at the

University of Brest and a member of the Center for Research for Education, Learning
and Didactics (CREAD). Her PhD (defended in 2003, University of Grenoble,
France) concerned the place given to algorithmics by teachers in high school math-
ematics education. The use of new technologies by teachers has always been a cen-
tral theme in her research. For several years, she has been reorienting her research
work towards the integration of new technologies in the teaching of mathematics
and the documentary work of teachers at primary school level, focusing on the
teaching of number construction, numeration and calculation. From 2012 to 2018,
Laetitia was a member of COPIRELEM, a French association of primary school
teacher trainers promoting research in mathematics education to the community of
teacher trainers, in particular through the annual organisation of conferences.

Chantal Buteau is a full professor in the Department of Mathematics and Statistics

at Brock University (Canada). Since she joined Brock in 2004, Chantal has been
progressively involved in education research with a main focus on the integration of
digital technology for (university) mathematics learning, including programming,
xx Contributors

CAS, and epistemic mathematics (computer) games. Over the years, Chantal has
taken part in various collaborative research projects funded by the Canadian Social
Sciences and Humanities Research Council (SSHRC), such as “Computer Algebra
Systems (CAS) in University Instruction: An International Research Study on CAS
Usage and Sustainability”, and leads the research under which this chapter falls.
Chantal recently conducted research work for the Ontario Ministry of Education
(Canada) on the teaching and learning of elementary coding and secondary school
computer studies. She is Co-director of the Mathematics Knowledge Network
(http://mkn-rcm.ca) that brings together diverse mathematics education stakehold-
ers from across Ontario (Canada), and Lead of its Computational Modelling com-
munity of practice. In terms of teaching related to this chapter, Chantal has been
directly involved in her department in the teaching of the programming-based math-
ematics MICA courses. In 2018, she also introduced a MICA III course section
specifically designed for future teachers.

Shanton Chang is a professor of Information Behavior at the School of Computing

and Information Systems, the University of Melbourne. He is an Associate Dean
(International) at the Faculty of Engineering and Information Technology. He is
also the co-chair of the Digital Access and Equity Program at the Melbourne Social
Equity Institute. His research focuses on examining information needs and online
behaviours in education, health and business contexts. Shanton has published exten-
sively in this field. He is also the co-author of Digital Experiences of International
Students: Challenging Assumptions and Rethinking Engagement (2020) as part of
the Routledge Series on Internationalization in Higher Education. He is also co-­
editor of the Journal of Studies in International Education Special Issue on
“Digitalization of International Education”. He was also recognised by the
Australian Computer Society as Information Communication Technology (ICT)
Educator of the Year in 2017.

Annalisa Cusi graduated in Mathematics from Modena and Reggio Emilia

University, where she also obtained a PhD in Mathematics. She worked as a research
fellow at Torino University from 2014 to 2016, within the European Project
FaSMEd, aimed at investigating the role played by digital technologies in support-
ing formative assessment processes. She is an associate professor of Mathematics
Education at the Department of Mathematics of the Sapienza University of Rome,
where she is involved in pre-service and in-service teacher education programmes.
Her main research interests are: (1) early algebra and innovative approaches to the
teaching of algebra; (2) analysis of teaching/learning processes, with a focus on the
role played by the teacher during classroom discussions; (3) methodologies for pre-
and in-service teacher education; (4) analysis of the dynamics that characterise
teachers’ and researchers’ interactions within communities of inquiry; (5) formative
assessment practices in mathematics within technology-enhanced classrooms; and
(6) design and use of digital tools and resources to foster individualisation at univer-
sity level.
Contributors xxi

Patrick Ebers is a PhD student in Mathematics Education at the University of

Duisburg-Essen. In his PhD thesis he is analysing how video cases can be used to
improve teachers’ noticing regarding how students use technology. He is an external
member of the German Centre for Mathematics Teacher Education (DZLM) and he
also works as a secondary school mathematics and physics teacher.

Cristina B. Esteley was a mathematics teacher who worked in several secondary

schools in Córdoba, Argentina. She has a Master’s degree in mathematics education
from the City University of New York (USA). She has a PhD in Education Sciences
from the National University of Córdoba (UNC). She has taught mathematics and
mathematics education at several Argentine universities. She conducts research
focused on professional trajectories of teachers or future teachers of mathematics
when they are involved with mathematical modelling activities in contexts that pro-
mote collaborative work and the use of technologies. She participates or has partici-
pated as a researcher in charge of research projects and as advisor of PhD theses or
others graduate works on topics related to her research. She is a member of the
Science and Technology Education Group (GECYT) of FAMAF and of the editorial
committee of Revista de Educación Matemática published at UNC since 1979. She
collaborates and has collaborated with colleagues in the framework of the
International Commission on Mathematical Instruction. Such collaborations focus
on inquiries, analyses and evaluations of research on mathematical modelling and
on collaborative work among mathematics teachers.

Ghislaine Gueudet has been a full professor of Mathematics Education at the

University Paris-Saclay, France since September 2021 and was previously a profes-
sor at the University of Brest (France). Her PhD (defended in 2000, University of
Grenoble, France) concerned university Mathematics Education, and she is still
researching this theme. She is Co-editor-in-chief of the International Journal for
Research in Undergraduate Mathematics Education. Since 2006 she has been
developing a new research direction on the design and use of educational resources
(including digital resources). Concerning these resources, she has introduced in a
joint work with Professor Luc Trouche, then with Professor Birgit Pepin, the docu-
mentational approach to didactics, analyzing teachers’ interactions with resources
and the consequences of these interactions in terms of professional development.
The documentational approach is now used in studies concerning teaching practices
and teachers’ professional development at all school levels and in teacher education
programmes. Ghislaine has been involved as Co-editor for several collective books
on university mathematics education and/or teaching resources and the documenta-
tional approach, and is author or co-author of more than fifty articles and book
chapters.

Mariam Haspekian is a researcher in Mathematics Education at the EDA labora-

tory, and a senior lecturer in Didactics of Mathematics at University of Paris Cité,
where she is the head of the three-year Bachelor’s degree (Licence) in “Educational
Sciences” programme. She completed her thesis in 2005 under the direction of
xxii Contributors

Michèle Artigue, on the integration of spreadsheets for algebra teaching. Since then,
her work, within diverse national and international projects, has concerned the
teaching of mathematics in digital environments and is oriented along two direc-
tions: the networking of theoretical frames in mathematics education, and the analy-
sis of instrumented teaching practices. Contributing to the Instrumental Approach in
didactics, her work seeks to develop tools for studying the mathematical practices
implemented by teachers in new situations. To analyse these, she introduced and is
working on the concepts of distance from practices, didactic reference points and
double instrumental genesis of the teacher. She has participated in the organisation
of many international conferences (ICME, CERME, EMF). In France, she is a
member of the Committee of the ARDM (Association for Research in Didactics of
Mathematics, part of the French Commission for Mathematics Teaching-CFEM).

Celia Hoyles taught mathematics in London schools from the late 1960s before
moving into higher education, becoming a professor at the Institute of Education,
University of London, in 1984. She was inspired by the vision of Seymour Papert to
use digital technology to open access to mathematics, and has led many research
and development projects to promote this aim with a range of colleagues, notably
Richard Noss. Celia worked to change the public face of mathematics by co-­
presenting a popular TV mathematics quiz show in the UK, Fun and Games, which
topped the prime-time ratings between 1987 and 1990. She was the first recipient of
the International Commission of Mathematics Instruction (ICMI) Hans Freudenthal
medal in 2004, and the Royal Society Kavli Education Medal in 2011. She was the
UK Government’s Chief Adviser for mathematics (2004–07) and the director of the
National Centre for Excellence in the Teaching of Mathematics (2007–13). Celia
gave a keynote speech at the International Congress on Mathematical Education
(ICME, 11), Monterrey, Mexico in 2008. Celia was President of the Institute of
Mathematics and its Applications (IMA) (2014–15) and she was made an Officer of
the Order of the British Empire in 2004 and a Dame Commander in 2014.

Melike Yiğit Koyunkaya is an associate professor in the Department of

Mathematics Education at Dokuz Eylul University, Turkey. She received her doc-
toral degree in Curriculum and Instruction with a focus on Mathematics Education
from Purdue University in 2014. She also holds Bachelor’s and Master’s degrees in
Mathematics from Ege University, Turkey. Her research interests concern geometry
education from a constructivist theoretical approach and the professional develop-
ment of pre-service mathematics teachers in relation to teaching with technology.

Bjarnheiður Kristinsdóttir works as an adjunct lecturer at the University of

Iceland. She holds a BSc degree in Mathematics from the University of Iceland, a
Dipl. Math. (MSc) degree in Applied Mathematics from the Freiberg University of
Mining and Technology in Germany, and a PhD in Mathematics Education from the
University of Iceland. Her doctoral project on the definition, development and
implementation of silent video tasks was conducted in close collaboration with
mathematics teachers in upper secondary schools in Iceland. Before and during her
Contributors xxiii

doctoral studies, Bea worked for eight years as a licensed mathematics teacher at
upper secondary school level. Her research focus is on mathematics teaching prac-
tices and task design, especially involving practices that require students to think,
the use of dynamic geometry software and videos, formative assessment, and the
orchestration of classroom discussion. Bea has been active within the Nordic-Baltic
GeoGebra Network since 2012 and has collaborated on research projects with
Professor Zsolt Lavicza and his team at the Johannes Kepler University Linz School
of STEM Education in Austria since 2016, most recently on task design for the EU
project <colette/> (https://colette-­project.eu/), which aims to develop a computa-
tional thinking learning environment for teachers and students in Europe.

Allen Leung is a professor of Mathematics Education at Hong Kong Baptist

University. He received his PhD in Mathmatics from the University of Toronto,
Canada. His research interests include geometric reasoning in dynamic geometry
environments, development of mathematics pedagogy using variation, tool-based
mathematics task design, and integrated STEM pedagogy. Allen has published in
major international mathematics education journals, books and conference proceed-
ings. He was involved in ICME 11, 12 and 13 as a Topic Study Group organising
member, a presenter of a Regular Lecture and a member of an ICME survey team.
He has contributed to two ICMI Studies and was an IPC member of the 22nd ICMI
Study: Task Design in Mathematics Education. He co-edited the Springer book
Digital Technologies in Designing Mathematics Education Tasks – Potential and
Pitfalls (Mathematics Education in the Digital Era Book Series) (2016). Allen is an
associate editor of the Springer journal Digital Experiences in Mathematics
Education.

Javier Lezama has a PhD in Mathematics Education from the research centre
CINVESTAV in Mexico City. He is a member of the National System of Researchers
of Mexico, Level 1. He is one of the founders of the Mathematics Education Program
of the National Polytechnic Institute of Mexico. Javier also created the social network
“DocenMat” aimed at mathematics teachers from all over Latin America. He is a
visiting professor at the Autonomous University of Guerrero in Mexico. His research
interests are connected to the area of mathematics teacher education and development.

Biyao Liang is a postdoctoral fellow sponsored by the Hong Kong Research Grants
Committee’s (RGC) Research Fellowship Scheme and supervised by Dr Oi-Lam Ng
at the Chinese University of Hong Kong. She obtained her BSc in Mathematics from
South China Normal University (China) and a PhD in Mathematics Education from
the University of Georgia (USA). Her research programme is at the intersections of
mathematical cognition, social interactions and teacher education. Specifically, her
research draws on radical constructivism and Piagetian theories to characterise stu-
dents’ and teachers’ ongoing constructions of mathematical knowledge through social
interactions and to design educational opportunities, tools and materials that can sup-
port learning through interactions. She has diverse classroom experiences in Mainland
xxiv Contributors

China, Hong Kong, Kansas and Georgia, and has been teaching content and pedagogy
courses for pre-service secondary mathematics teachers since 2019.

Andrew McAlindon is a secondary school teacher of Mathematics and integrated

Science Technology Engineering and Mathematics (STEM) in Victoria, Australia.
His doctoral research centred on the efficacy of the flipped classroom in secondary
school mathematics, with a focus on student outcomes and teacher perspectives.
Andrew has an ongoing focus on educational improvement in school contexts, with
teacher professional development in pedagogical approaches within mathematics
and STEM being an ongoing research interest.

Joyce Mgombelo is an associate professor of Mathematics Education at Brock

University, Ontario, Canada, where she teaches courses and supervises graduate
students in mathematics education and cognition. Her research interests are in the
areas of mathematics/STEM education, teacher education (in-service and pre-­
service) and curriculum studies. Her research programme focuses on mathematics
cognition, identity and ethics, based on principles of human cognition. This work is
developed from the theoretical perspectives of enactivism, complexity science and
psychoanalysis. Joyce’s most recent research includes the Canadian Social Sciences
and Humanities Research Council (SSHRC)-funded collaborative research projects
“Educating for the 21st Century: post-secondary students learning ‘progmatics’
(computer programming for mathematical investigation, simulation, and real-world
modeling)” and “Advancing research methodology in mathematics education for
collective learning systems” as well as the Canada Global Affairs collaborative
development project “Capacity Development for mathematics teaching in rural and
remote communities in Tanzania”.

Eric Muller is a professor emeritus in the Department of Mathematics and Statistics

at Brock University and a fellow of the Fields Institute for Research in Mathematical
Sciences. He has published in the areas of theoretical physics, operations research
and mathematics education. He continues to collaborate in research that focuses on
the use of programming technology in project-based courses in undergraduate
mathematics. Eric completed an MSc in 1963 in the area of Calculus of Variations
under Professor Hanno Rund at the University of Natal in Durban. He then briefly
taught at Rhodes University in Grahamstown before moving to the University of
Sheffield where he completed a PhD in the area of Thermal Conductivity under
Professor Norman March. He joined the Department of Mathematics at the fledg-
ling Brock University in 1967 and retired in 2004. Thereafter he spent time with
Pacific Resources for Education and Learning located in Honolulu and visited
mathematics departments in colleges on isolated islands dispersed over the North
Pacific.

Oi-Lam Ng is an assistant professor in the Department of Curriculum and

Instruction at the Chinese University of Hong Kong. Her research interests include
technology innovations in mathematics education, language and mathematics
Contributors xxv

discourse, mathematics teacher noticing, and STEM education. Particularly, she is

interested in advancing a Papert-inspired conception of “learning as making” and
the new opportunities it entails for engaging learners in constructionist practices
with emergent technologies (3D printing, coding, etc). Oi-Lam’s research has been
funded by the Research Grant Councils of Canada and Hong Kong respectively, and
her funded research is entitled “The effects of implementing a ‘learning as Making’
pedagogy on school mathematics learning: Primary students’ inquiry-based Making
with 3D Printing Pens”. Her work has been published in Educational Studies in
Mathematics, ZDM: International Journal on Mathematics Education, and the
British Journal of Educational Technology. Oi-Lam teaches mathematics and
STEM education courses. She received her PhD from Simon Fraser
University, Canada.

Monica Panero holds a PhD in Mathematics and is a lecturer and researcher in

Mathematics Education in the Dipartimento formazione e apprendimento of the
Scuola universitaria professionale della Svizzera italiana. Her main research foci
are on formative assessment, technology in mathematics education, attitudes
towards mathematics and its teaching, and mathematics teacher education. In her
recent publications she interrelates such interests by investigating the role of tech-
nology formative assessment, during her postdoctoral research within the European
project called FaSMEd (2014–16); by studying design principles for fostering and
assessing involvement and collaboration in MOOCs for mathematics teachers; and
by analyzing the evolution of pre-service primary school teachers’ attitudes towards
mathematics and its teaching. She is part of the executive board of the International
Commission for the Study and Improvement of Mathematics Teaching, and part of
the scientific committee of the open access semestral journal Didattica della
matematica. Dalla ricerca alle pratiche d’aula.

Caroline Poisard is an associate professor of Mathematics Education at the

University of Brest and a member of the Center for Research for Education, Learning
and Didactics (CREAD). Her research concerns the resources for teaching and
learning mathematics at primary school. It has three axes: world languages as a
resource for doing mathematics; material and virtual resources for teaching (calcu-
lating instruments, the Chinese abacus); and mathematical workshops in the class-
room (manipulations and games).

Marisol Santacruz Rodriguez is an assistant professor at the Faculty of Education

and Pedagogy of Universidad del Valle (Cali, Colombia). Her specialty is geometric
education using digital resources. Her research focuses on the study of the student’s
activity using digital technologies, the teacher’s documentational work and the anal-
ysis of the professional knowledge involve in the geometry classroom. For many
years, Marisol also taught mathematics at elementary school level. At present, she
is more focused on mathematics teacher education and the use of programming for
teaching mathematics.
xxvi Contributors

Ana Isabel Sacristán is a full researcher in the Department of Mathematics

Education of the Centre for Research and Advanced Studies (Cinvestav) in Mexico
City, where she has worked since 1989. Her main area of research is the teaching
and learning of mathematics through digital infrastructures. She is particularly fond
of the constructionism paradigm as a basis for the design of learning environments
where students can explore, and build ideas and concepts through computer pro-
gramming activities. She has published many academic papers in that area, but has
also developed tasks and authored materials for the Mexican Ministry of Education,
in particular those for the national “Teaching Mathematics with Technology” pro-
gramme, on the use of computer programming activities for mathematical learning.
She has trained teachers across Mexico and has co-led nationwide research and
evaluation on the use of technological tools in Mexican classrooms. She has also
been part of many international committees, including the International Programme
Committee of the 17th ICMI Study on “Mathematics Education and Technology—
Rethinking the Terrain” and has been a visiting professor in several countries,
including at the Institute of Education, University of London in England; Université
du Québec à Montréal in Canada; and the French Institute of Education at Lyon-­
ENS in France. More recently she has collaborated with Canada’s Brock University.

Ivonne Sandoval has been a teacher and researcher at the National Pedagogical
University, Mexico City (Mexico), since 2008. She is a member of the National
System of Researchers of Mexico, Level 1. Her research focuses on designing and
implementing digital technologies and other resources for mathematics education.
Due to this interest, she has co-authored mathematics textbooks for elementary and
middle school students in Mexico. She also participated in a Mexican National proj-
ect dealing with the integration of digital technologies in elementary schools. Ivonne
also has an interest in research related to the development of spatial reasoning. She
is concerned with elaborating STEM tasks in different cultural contexts through
using various resources for students and teachers at elementary school level, specifi-
cally in socioeconomically disadvantaged contexts. In this case, she is concerned
with studying students, teachers and resources. She also investigates mathematics
teaching specialised knowledge, and for this reason, she belongs to the Iberoamerican
network for Mathematics Teaching Specialized Knowledge (MTSK) recognised by
the Iberoamerican Universities Postgraduates Association (AUIP) since 2019. Her
main contributions to mathematics education knowledge have focused on teachers’
use of technology and geometry. She has also participated in research with several
national and international groups in Mexico, Spain, Colombia, the United States
and Canada.

Ali Simsek has primary research interests in secondary school mathematics educa-
tion in general with a particular focus on the use of dynamic mathematical technolo-
gies (DMTs) in the classroom. In his four-year teaching experience in Turkey, Ali
developed a keen interest in the use of DMTs to enhance his students’ mathematical
learning. This led to him pursuing postgraduate studies in the field of Educational
Technologies in Mathematics Education. Having been awarded a competitive
Contributors xxvii

scholarship from the Turkish government, he completed an MA degree at University

College London (UCL)’s prestigious Institute of Education (IOE) in England in
2016. Following this, he then completed a PhD at the same university in 2021 under
the supervision of Professor Dame Celia Hoyles, Professor Alison Clark-Wilson
and Dr Nicola Bretscher. In his PhD research, he investigated lower secondary
mathematics teachers’ actual classroom practices as they used DMTs in the class-
room to promote their students’ understanding of the mathematical domain of geo-
metric similarity (GS). The findings of his PhD research revealed salient differences
and some commonalities between the teachers, pointing to key characteristics of
classroom practice involving DMTs for teaching GS. Ali now works as a national
educational expert at the Ministry of National Education in Turkey.

Danelly Susana Esparza Puga obtained a Bachelor’s degree in mathematics from

the Autonomous University of Ciudad Juárez (UACJ) in 2011. In 2014 she received
a Master’s degree in Mathematics Education from the UACJ and obtained her PhD
in Mathematics Education from the National Polytechnic Institute of Mexico in
2018. She is a member of the National System of Researchers of Mexico, and her
research interests focus on the use of digital tools in the teaching and learning of
mathematics.

Eugenia Taranto holds a PhD in Pure and Applied Mathematics and is a postdoc-
toral researcher at the University of Catania, where she is also a lecturer in
Mathematics Education for a graduate-level course. Her research fields include
MOOCs (Massive Open Online Courses) for mathematics teacher education, in par-
ticular, she collaborated on the design and delivery of five Italian MOOCs and she
is the instructional designer of an international MOOC and technologies to mediate
the teaching and learning of mathematics (dynamic geometry systems, MathCityMap,
learning videos, serious games). She is the author of papers and chapters in various
prestigious journals and books.

Daniel Thurm is an assistant professor of Mathematics Education at the University

of Siegen in Germany. His research focuses on professional development for teach-
ing mathematics with technology as well as on digital formative assessment. He is
a member of the German Centre for Mathematics Teacher Education (DZLM), a
nationwide centre that researches and develops professional development (PD)
courses and materials for teachers and PD facilitators.

Maria Trigueros is an invited professor in the Mathematics Education Department

at the Benemérita Universidad Autónoma de México. She was a professor in the
Department of Mathematics at Instituto Tecnológico Autónomo de México for forty
years. She received her PhD in Education from Universidad Complutense de Madrid
in Spain and her degree and MSc in Physics from the Universidad Nacional
Autónoma de México (UNAM). She is a member of the Mexican Academy of
Sciences and of the Mexican National Researchers’ System. Her research focuses
on advanced mathematics teaching and learning, and on the use of technology in the
xxviii Contributors

teaching and learning of mathematics at elementary and middle school level. Her
main contributions to mathematics education knowledge have focused on teachers’
use of technology, algebra, linear algebra and calculus. Maria has received several
awards, among them the Luis Elizondo Prize, and has participated in national proj-
ects on the use of technology in mathematics teaching. She has developed instruc-
tional materials for students at elementary and middle school level and has served
as editor for several Mexican and international mathematics education research
journals. She has also participated in research with several national and interna-
tional groups in Mexico and other countries.

Fabrice Vandebrouck is a professor at Université Paris Cité and member of the

LDAR lab (Laboratoire de Didactique André Revuz). He is Co-director of the doc-
toral school Savoirs Sciences Education. He defended his PhD thesis in Mathematics
in 1999 before moving into the mathematics education field. He teaches mathemat-
ics to undergraduate students at the university and didactics at Master’s level. His
research concerns the transition from high school to tertiary level alongside the
integration of technologies in the teaching of mathematics. Fabrice has supervised
eight theses on these topics. He is one of the main contributors to the development
of activity theory in didactics of mathematics, alongside Maha Abboud, Aline
Robert and Janine Rogalski. He is editor of the book Mathematics Classrooms:
Students’ Activities and Teachers’ Practices (2013), and presented an invited lecture
at the 13th International Congress on Mathematical Education entitled “Activity
Theory in French Didactic Research”.

Mónica E. Villarreal has a degree in Mathematics from the Universidad Nacional

de Córdoba (UNC) (Argentina). She holds a PhD in Mathematics Education from
the Universidade Estadual Paulista (Brazil). She is a professor at the Faculty of
Mathematics, Astronomy, Physics and Computer Sciences (FAMAF) of UNC and
researcher at the National Council of Scientific and Technical Research (CONICET)
of Argentina. Mónica is a member of the Science and Technology Education Group
(GECYT) of FAMAF. She is involved in the initial education of mathematics teach-
ers. She has conducted and continues to conduct research on the professional devel-
opment of pre-service and in-service mathematics teachers, mathematical modelling,
and the use of digital technologies in educational contexts, directing research proj-
ects and theses on these topics. Mónica has numerous national and international
publications in co-authorship, and has participated in many congresses and invited
conferences. Since 2017 she has been Associate Editor of the Revista de Educación
Matemática published at UNC since 1979. She was a member of the International
Program Committee for the organisation of ICME 13 in Hamburg (2016). Mónica
is the Argentinean representative for the International Commission on Mathematical
Instruction (ICMI).
About the Editors

Alison Clark-Wilson is a professorial research fellow at UCL Institute of

Education (Faculty of Education and Society), University College London. Alison’s
research spans aspects of designing, implementing and evaluating educational digi-
tal technologies with a particular interest in mathematics education. This includes
theoretical contributions (the hiccup theory), alongside design-based research inter-
ventions and evaluation studies (Cornerstone Maths, TI-Nspire/TI-Navigator).
Between 2017 and 2021 Alison led the European Society for Research in
Mathematics Education’s working group on “Teaching mathematics with technol-
ogy and other resources”. As a former school mathematics teacher and teacher edu-
cator, Alison has particular empathy for the challenges faced by teachers as they
seek to stay abreast of technological developments, often with little systemic sup-
port and few professional incentives. Alison is the lead editor of the book
Mathematics Education in the Digital Age (2021) and presented the invited lecture
at the 14th International Congress on Mathematical Education in 2021 entitled
“(Re)Assessing Mathematics: Retaining the Integrity of Mathematics as a Human
Activity in the Digital Age”.

Ornella Robutti is a full professor of Mathematics Education in the Department of

Mathematics “G. Peano” of the University of Torino. Her fields of research are stu-
dents’ cognitive processes in mathematical activities; teaching mathematics within
technological environments; teachers’ work as individuals and in communities,
when teaching mathematics, when learning in professional development pro-
grammes, and when designing tasks for students; meanings of mathematical objects
in institutional and social contexts; mathematics students’ and teachers’ identities;
and boundary objects and boundary crossing between communities. She is the
author of articles/chapters in mathematics education and a team leader/lecturer/par-
ticipant in many international congresses (ICMI Study, ICME, PME, CERME,
ICTMT). In Italy she has been a member of CIIM (the scientific commission for
mathematics teaching of the Italian Mathematics Association), and in charge of in-­
service and pre-service teachers’ professional development programmes.

xxix
 xxx About the Editors

Nathalie Sinclair is a distinguished university professor in the Faculty of Education

at Simon Fraser University. She is the founding editor of Digital Experiences in
Mathematics Education and has written several books, including Mathematics and
the Body: Material Entanglements in the Classroom (2014). She directs the Tangible
Mathematics Project, which has created the multitouch applications TouchCounts
and TouchTimes.

View publication stats