Uses of Technology in Lower Secondary Mathematics Education: A Concise Topical Survey PDF
Preview Uses of Technology in Lower Secondary Mathematics Education: A Concise Topical Survey
ICME-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 ©TheEditor(s)(ifapplicable)andTheAuthor(s)2016.Thisbookispublishedopenaccess. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland 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).
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