Table Of ContentICME-13 Topical Surveys
Paul Drijvers · Lynda Ball
Bärbel Barzel · M. Kathleen Heid
Yiming Cao · Michela Maschietto
Uses of Technology
in Lower Secondary
Mathematics
Education
A Concise Topical Survey
ICME-13 Topical Surveys
Series editor
GabrieleKaiser,FacultyofEducation,UniversityofHamburg,Hamburg,Germany
More information about this series at http://www.springer.com/series/14352
Paul Drijvers Lynda Ball
(cid:129)
ä
B rbel Barzel M. Kathleen Heid
(cid:129)
Yiming Cao Michela Maschietto
(cid:129)
Uses of Technology in Lower
Secondary Mathematics
Education
A Concise Topical Survey
PaulDrijvers M.Kathleen Heid
Freudenthal Institute ThePennsylvania State University
UtrechtUniversity University Park, PA
Utrecht USA
TheNetherlands
Yiming Cao
Lynda Ball Schoolof Mathematical Sciences
MelbourneGraduate Schoolof Education Beijing NormalUniversity
TheUniversity of Melbourne Beijing
Melbourne, Victoria China
Australia
Michela Maschietto
BärbelBarzel Department ofEducation andHumanities
UniversitätDuisburg-Essen University of ModenaandReggio Emilia
Essen ReggioEmilia
Germany Italy
ISSN 2366-5947 ISSN 2366-5955 (electronic)
ICME-13 TopicalSurveys
ISBN978-3-319-33665-7 ISBN978-3-319-33666-4 (eBook)
DOI 10.1007/978-3-319-33666-4
LibraryofCongressControlNumber:2016939363
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Main Topics You Can Find in This ICME-13
Topical Survey
(cid:129) Topical study of the state of the art of the use of digital technologies in lower
secondary mathematics;
(cid:129) Comprehensive survey of research findings;
(cid:129) Future directions for the use of digital technologies in lower secondary
mathematics;
(cid:129) International perspectives integrated to provide a view on worldwide
developments.
v
Contents
Uses of Technology in Lower Secondary Mathematics Education. . . . . 1
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Survey on the State of the Art. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1 Evidence for Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Digital Assessment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Communication and Collaboration Through and
Of Technology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 Communication and Collaboration: Professional
Development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 Summary and Looking Ahead. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
vii
Uses of Technology in Lower Secondary
Mathematics Education
A concise topical survey
1 Introduction
Digitaltechnology1isomnipresentinsociety.Revolutionarytechnologicaldevelop-
ments change the character of professional environments, and therefore put new
demandsonworkers(Hoyles,Noss,Kent,&Bakker,2010).Consequently,thereare
newdemandsoneducationalsystemsinordertopreparestudentsforfutureprofessions.
Importantly, technology also offers opportunities for teaching and learning (see for
example, Clark-Wilson, 2010; Sacristán et al. 2010); exploiting these opportunities
requires rethinking educational paradigms and strategies. With the advent of such
technology, the question arises as to what the impact on education and teaching
practicesshouldbeinordertopreparethenextgenerationofstudentsforfuturecareers.
Both in professional practice and in personal life, it is particularly striking how
digitaltechnologiessuchassoftware-controlledengines,smartphones,tablets,and
GPSdevicesrelyonmathematicalalgorithmsthatareinvisibletotheuser,butplay
essential roles “under the hood”. Implications of these technology-rich environ-
ments have the potential to influence the nature of mathematics education and the
concepts and skills that future students will possess.
Roberts, Leung, and Lin (2013) comment on the complexity of the interplay
between technology, mathematics, and education, noting that this complexity
relatedtotheuseoftoolsinmathematicsisnotaphenomenonthatisduetocurrent
technologies, but one that has been evident whenever people use tools in mathe-
matics.Therapiddevelopmentofdigitaltechnologiesfeaturesnewcapabilitiesnot
evenconsideredpossibleinthepast.Despiteadvancesindigitaltechnologies,there
isstillstrongvalueinusingacombinationofphysicaltoolsanddigitaltechnologies
in mathematics education (Maschietto & Trouche, 2010). Different types of tech-
nologies are available for teaching mathematics, and different technologies are
appropriate for different purposes. General technologies for communication,
1To avoid constantly repeating the terms “digital technology” in this text we will often refer to
“technology”;whiledoingso,werefertodigitaltechnologyinmathematicseducation.
©TheAuthor(s)2016 1
P.Drijversetal.,UsesofTechnologyinLower
SecondaryMathematicsEducation,ICME-13TopicalSurveys,
DOI10.1007/978-3-319-33666-4_1
2 UsesofTechnologyinLowerSecondaryMathematicsEducation
documentation, and presentation are essential in order to support the exchange of
mathematical ideas. Mathematical technologies, such as spreadsheets, Computer
Algebra Systems (CAS), Dynamic Geometry Software (DGS), and applets, enable
teachers and students to investigate mathematical objects and connections using
differentmathematicalrepresentations,andtosolvemathematicalproblems(Zbiek,
Heid, Blume, & Dick, 2007).
In the context of lower secondary mathematics with current technologies,
mathematical procedures have the potential to be outsourced to powerful mathe-
matical technologies (such as graphing tools, spreadsheet software, statistical
packages,and ComputerAlgebra Systems) challenging current curricula goals and
teachingandassessmentpractices.Thequestionariseswhetherornotthepotential
changetogoalsandpracticescometofruitionintherealclassroom.Inastudywith
sevenclassesofYear8–10students,overaperiodofthreeyears,Fuglestad(2009)
found that most students developed the digital competence to make good choices
about the mathematical technology (such as different technologies like DGS,
spreadsheet,andfunctionplotter)tosuittheirpreferredapproacheswhensolvinga
given task. Zehavi and Mann (1999) reported an early trial of the use of DERIVE
with 13–14-year-old students in which the use of technology changed the organi-
zationoftheclassroom.Technologyfosteredachange fromteacherdemonstration
followed by student practice of problems, to student control of the modelling
process and class discussion following students’ work on teacher-prepared com-
puterized tutorials. In a review of studies on integration of Computer Algebra
Systemsinschools,Barzel(2012)alsofound that therole ofteachersandstudents
changed in the presence of technology.
This topical survey establishes an overview of the current state of the art in
technology use in mathematics education, including both practice-oriented expe-
riencesandresearch-basedevidence,asseenfromaninternationalperspective.We
now discuss three core themes related to technology in mathematics education:
Evidence for effect; Digital assessment; Communication and collaboration.
(cid:129) Theme 1: Evidence for effect
What are the research findings about the benefits of the integration of digital
tools in lower secondary mathematics education for student learning?
(cid:129) Theme 2: Digital assessment
What are the features of effective digital assessment in the context of both
summative and formative assessment and in the delivery offeedback?
(cid:129) Theme 3: Communication and collaboration
Howcantechnologybeusedtopromotecommunicationandcollaborativework
between students, between teachers, and between students and teachers? What
are the potential professional development needs of teachers integrating digital
technologies into their teaching, and how can technology act as a vehicle for
such professional development activities?
In the final section of the survey we offer suggestions for future trends in
technology-rich mathematics education and provide a research agenda in light of
1 Introduction 3
these trends. We predict what lower secondary mathematics education might look
like in 2025, with respect to the place of digital tools in curricula, teaching, and
learning,andexpresssomeideastopromoteadeepunderstandingofmathematics.
The issues and findings presented in this topical survey provide an overview of
currentresearch,lookingforwardtoapositionofeffectiveintegrationoftechnology
to support mathematics teaching and learning in lower secondary.
2 Survey on the State of the Art
In this section we present the state of the art on the use of technology for teaching
and learning mathematics in lower secondary education, as well as the research in
this field. First, we summarize the quantitative and qualitative evidence of effect
(Sect. 2.1)andthendigitalassessmentisaddressed (Sect. 2.2).Finally, wediscuss
the options for communication, collaboration and teachers’ professional develop-
ment (Sect. 2.3).
2.1 Evidence for Effect
Over thepast decades, there has been considerable research on the impact of tech-
nology in learning and teaching mathematics (Blume & Heid, 2008; Clements,
Bishop,Keitel,Kilpatrick,&Leung,2013;Drijvers,Barzel,Maschietto,&Trouche,
2006; Heid & Blume, 2008; Hoyles & Lagrange, 2010). For many teachers, edu-
cators, and researchers, new advances in technology and increased access to tech-
nologyinmathematicseducationprovidedopportunitiesfornewperspectivesonthe
developmentofstudents’understanding.Manyclaimshavebeenmadeconcerning
the potential for change in mathematics education as a result of the availability of
technology and the subsequentbenefits for studentlearningoutcomes.
One may wonder, however, whether the potential changes and improved
learning outcomes have been realized. If research findings suggest benefits for
students´ learning through the integration of technology in mathematics education,
this provides an imperative to address the limited use of technologies in lower
secondarymathematicscoursesreportedbyPISA2012(OECD,2015).Limiteduse
oftechnologymaybeduetopracticalconsiderations,butitalsoraisesthequestion
ofwhethertheresearchfindingsareconvincingenoughwithrespecttothebenefits
for student learning of the integration of digital tools in lower secondary mathe-
matics education. To investigate whether digital technology improves student
learning, we first revisit some review studies, focusing mainly on quantitative
research(Sect.2.1.1).Next,weaddresstheroleoftheteacherasanimportantfactor
(Sect. 2.1.2). To address the question of why technology might improve student
learning, this section closes with important results from qualitative research
(Sect. 2.1.3).
