BibSonomyburst/user/yish/mathematicsBibSonomy RSS feed for /user/yish/mathematics2012-02-16T15:16:43+01:00http://www.bibsonomy.org/bibtex/216d03a0e8ac507ce0f08605d713885f3/yishyish2012-02-01T13:07:34+01:00LDG design education learning mathematics practice representation representations teaching <span class="authorEditorList"><a href="/author/Herbst">Patricio Herbst</a>, <a href="/author/Chazan">Daniel Chazan</a>, <a href="/author/Chen">Chia-Ling Chen</a>, <a href="/author/Chieu">Vu-Minh Chieu</a>, and <a href="/author/Weiss">Michael Weiss</a> </span><em>ZDM</em> (<em>2011</em>)<em>10.1007/s11858-010-0290-5 . </em>Wed Feb 01 13:07:34 CET 2012ZDM10.1007/s11858-010-0290-591-103Using comics-based representations of teaching, and technology, to bring practice to teacher education courses432011LDG design education learning mathematics practice representation representations teaching This article situates comic-based representations of teaching in the long history of tensions between theory and practice in teacher education. The article argues that comics can be semiotic resources in learning to teach and suggests how information technologies can support experiences with comics in university mathematics methods courses that (a) help learners see the mathematical work of teaching in lessons they observe, (b) allow candidates to explore tactical decision-making in teaching, and (c) support preservice teachers in rehearsing classroom interactions.http://www.bibsonomy.org/bibtex/23f016373b6bc0d377320bbf5a8512ede/yishyish2012-01-12T21:47:06+01:00education learning lifelong literacies mathematics technomathematical vocational workplace <span class="authorEditorList"><a href="/author/Hoyles">Celia Hoyles</a>, <a href="/author/Noss">Richard Noss</a>, <a href="/author/Kent">Phillip Kent</a>, and <a href="/author/Bakker">Arthur Bakker</a> </span><em>Taylor &amp; Francis, </em>(<em>2009</em>)Thu Jan 12 21:47:06 CET 2012Improving mathematics at work: The need for techno-mathematical literacies2009education learning lifelong literacies mathematics technomathematical vocational workplace of mathematics in the workplace is evolving in the rapidly-changing context of new technologies and globalisation. Through a series of case studies from the manufacturing and financial service sectors, the authors argue that there has been a radical shift in the type mathematical skills required for work ' a shift not yet fully recognised by the formal education system, or by employers and managers.Examining how information technology has changed mathematical requirements, the idea of Techno-mathematical Literacies (TmL) is introduced to describe the emerging need to be fluent in the language of mathematical inputs and outputs to technologies and to interpret and communicate with these, rather than merely to be procedurally competent with calculations. The authors argue for careful analyses of workplace activities, looking beyond the conventional thinking about numeracy, which still dominates policy arguments about workplace mathematics. Throughout their study, the authors answer the following fundamental questions:What mathematical knowledge and skills matter for the world of work today?How does information technology change the necessary knowledge and the ways in which it is encountered?How can we develop these essential new skills in the workforce?With evidence of successful opportunities to learn with TmL that were co-designed and evaluated with employers and employees, this book provides suggestions for the development of TmL through the use of authentic learning activities, and interactive software design. Essential reading for trainers and managers in industry, teachers, researchers and lecturers of mathematics education, and stakeholders implementing evidence-based policy, this book maps the fundamental changes taking place in workplace mathematics.http://www.bibsonomy.org/bibtex/2a06a2585795fb274fe2d53c5552486ac/yishyish2012-01-09T22:47:45+01:00constructionism education learning logo mathematics programming <span class="authorEditorList"><a href="/author/Feurzeig">Wallace Feurzeig</a>, <a href="/author/Papert">Seymour Papert</a>, and <a href="/author/with a preface by Bob Lawler"> with a preface by Bob Lawler</a> </span><em>Interactive Learning Environments</em> <em>19(5):487-501</em> (<em>2011</em>)Mon Jan 09 22:47:45 CET 2012Interactive Learning Environments5487-501Programming-languages as a conceptual framework for teaching mathematics.192011constructionism education learning logo mathematics programming Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively to reduce formal barriers. This education can also be used to enable pupils to access an accurate understanding of some key mathematical concepts. In the field of heuristic knowledge for technical problem solving, experience of programming is no less valuable: it lends itself to promote a discussion of relations between formal procedures and the comprehension of intuitive problem solving and provides examples for the development of heuristic precepts (formulating a plan, subdividing the complexities, etc.). The knowledge gained in programming can also be used for the discussion of concepts and problems of classical mathematics. Finally, it can also facilitate the expansion of mathematical culture to topics in biological and physical sciences, linguistics, etc. The authors describe a programming language called 'Logo' adapted to objectify an enduring framework of mathematical experimentation. The paper reprinted below is the first published paper on the Logo programming language. It was written in 1968 by two of the three Logo language designers and presented at conference in Nice, France, in May 1968. It is important for several reasons. It clearly sets forth the objective of creating a language that is mathematically powerful yet accessible to little ones – easy enough for a third grade child to use for simple tasks. Its effectiveness for motivating students in posing and solving problems argues for Logo's educational power and utility. The heart of the language is set forth in this description of the genesis of Logo and its early form. Logo was designed to provide a conceptual foundation for teaching mathematical and logical ways of thinking in terms of programming ideas and activities. A rich variety of tasks that are interesting to children readily lend themselves to Logo programming. These may be drawn from mathematics, language, art, music, and other domains, in tasks of personal interest to students, often of their own choosing. They include such things as a variety of word games (finding words contained in words, writing words backwards, finding palindromes); question–answering and guessing games (e.g., Buzz, Twenty Questions); building semantic grammars for generating and producing poetry, jokes, or songs; making and breaking secret codes (e.g., substitution ciphers); designing and drawing patterns with a program controlled robot turtle; and developing strategies for a turtle with sensors to circumnavigate objects on an obstacle course. These projects introduce children to formal thinking procedures in the context of playful activities. There are many problems of this sort that children already know and like. A child thinks at first that he understands such problems perfectly because, with a little prodding, he can give a loose verbal description of his procedure. But he finds it impossible to make this description precise and general partly for lack of formal habits of thought and partly for lack of a suitably expressive language. The Logo environment provides students with an effective facility for actively constructing knowledge. Logo was expressly designed to embody the constructivist vision in mathematics, i.e. that learning is an active process of knowledge construction that gives rise to the production of publicly accessible artifacts. Here, they take the form of computer procedures that express the attempted solution of problems and that serve as a tangible means of thinking about and refining those solutions. Program descriptions are open to reflection and discussion, and procedures that fail can be examined, analyzed, and repaired. From the outset, Logo was intended to be a language for learning with ‘no threshold and no ceiling’. Later, when Papert took the Logo design as the basis of the MIT Logo Project, the language entered a period of further development and dissemination. Here, in the original Logo paper, you see the essence of the language and its generative ideas. Good reading!http://www.bibsonomy.org/bibtex/2be503c7be02eb83b90b0a51635edc5e6/yishyish2012-01-09T22:38:53+01:00constructionism education learning mathematics <span class="authorEditorList"><a href="/author/Feurzeig">Wallace Feurzeig</a>, <a href="/author/Papert">Symour Papert</a>, <a href="/author/Bloom">M. Bloom</a>, <a href="/author/Grant">R. Grant</a>, and <a href="/author/Solomon">C. Solomon</a> </span><em>SIGCUE Outlook</em> (<em>April 1970</em>)Mon Jan 09 22:38:53 CET 2012New York, NY, USASIGCUE OutlookApril13-17Programming-languages as a conceptual framework for teaching mathematics41970constructionism education learning mathematics http://www.bibsonomy.org/bibtex/29564263f38d2ceea8672ed857f7deef6/yishyish2012-01-05T12:01:17+01:00Europe Eurydice education mathematics report <span class="authorEditorList"><a href="/author/Eurydice"> Eurydice</a> </span><em>Education, Audiovisual and Culture Executive Agency EACEA P9 Eurydice, </em>(<em>2011</em>)Thu Jan 05 12:01:17 CET 2012Mathematics Education in Europe: Common Challenges and National Policies2011Europe Eurydice education mathematics report Competence in mathematics is integral to a wide range of disciplines, professions and areas of life. This Eurydice report reveals crucial elements of the policies and practices that shape mathematics instruction in European education systems, focusing on reforms of mathematics curricula, teaching and assessment methods, as well as teacher education. The report also explores how countries tackle low achievement and increase students’ motivation to learn mathematics. It is based on an extensive literature review on mathematics education, main findings from the international surveys PISA and TIMSS and includes the results of a Eurydice pilot survey (SITEP) on the content of initial teacher education programmes. It covers 31 countries (all EU Member States, plus Iceland, Liechtenstein, Norway and Turkey) and takes the reference year 2010/11. http://www.bibsonomy.org/bibtex/2dbb6b9f88022346507ec4f6f9f61054b/yishyish2011-11-16T13:31:33+01:00abduction education learning mathematics <span class="authorEditorList"><a href="/author/Reid">D.A. Reid</a> </span><em>Proceedings of the CERME, </em><em> 3, </em>(<em>2003</em>)Wed Nov 16 13:31:33 CET 2011Proceedings of the CERMEForms and uses of abduction32003abduction education learning mathematics This paper offers first steps towards a typology of forms and uses of abductive reasoning in mathematics education. It organises several descriptions of abductive reasoning found in the literature in terms of their logical forms, the relation between specifics and generalities found in them, and the uses suggested for abductive reasoning. Examples are then given of abductive reasoning in mathematics classrooms, and these examples are described making use of the typology developed.http://www.bibsonomy.org/bibtex/2f6fbd2f838e379dcfe474386368c50d3/yishyish2011-11-16T13:30:05+01:00abduction education mathematics proof <span class="authorEditorList"><a href="/author/Mariotti">M.A. Mariotti</a> </span><em>Handbook of research on the psychology of mathematics education: Past, present and future</em> (<em>2006</em>)Wed Nov 16 13:30:05 CET 2011Handbook of research on the psychology of mathematics education: Past, present and future173--204Proof and proving in mathematics education2006abduction education mathematics proof http://www.bibsonomy.org/bibtex/25eb3b0324dcaaa99f09421f04fd6fa32/yishyish2011-11-16T13:25:42+01:00Argumentation Toulmin abduction education induction learning mathematics proof <span class="authorEditorList"><a href="/author/Pedemonte">Bettina Pedemonte</a> </span><em>Educational Studies in Mathematics</em> <em>66(1):23 - 41</em> (<em>2007</em>)Wed Nov 16 13:25:42 CET 2011Educational Studies in Mathematics123 - 41How can the relationship between argumentation and proof be analysed?.662007Argumentation Toulmin abduction education induction learning mathematics proof The paper presents a characterisation about argumentation and proof in mathematics. On the basis of contemporary linguistic theories, the hypothesis that proof is a special case of argumentation is put forward and Toulmin’s model is proposed as a methodological tool to compare them. This model can be used to detect and analyse the structure of an argumentation supporting a conjecture (abduction, induction, etc.) and the structure of its proof. The aim of the paper is to highlight the importance of structural analysis between argumentation and proof. This analysis shows that although there are clear cases of continuity between argumentation supporting a conjecture and its proof, there is often a structural distance between the two (from an abductive argumentation to a deductive proof, from an inductive argumentation to a mathematical inductive proof). [ABSTRACT FROM AUTHOR]http://www.bibsonomy.org/bibtex/26b915ff7fa0d5848fb68605dcc33e4de/yishyish2011-11-08T17:05:42+01:00design designpatterns designresearch education learning mathematics my myown patterns thesis <span class="authorEditorList"><a href="/author/Mor">Yishay Mor</a> </span><em>Institute of Education - University of London, </em>(<em>2010</em>)Tue Nov 08 17:05:42 CET 2011A Design Approach to Research in Technology Enhanced Mathematics Education2010design designpatterns designresearch education learning mathematics my myown patterns thesis This thesis explores the prospect of a design science of technology enhanced mathematics education (TEME), on three levels: epistemological, methodological and pedagogical. Its primary domain is the identification of scientific tools for design research in TEME. The outputs of this enquiry are evaluated by a demonstrator study in the domain of secondary school mathematics. A review of existing literature establishes a need for a design perspective in TEME research, but at the same time suggests a need for a consensual epistemic infrastructure for the field: a shared set of rules, processes and representations which bound and support its scientific discourse. Three constructs are proposed towards such an infrastructure: design narratives, design patterns, and the cycles of design research in which they are embedded. The first two are representations of domain design knowledge; the latter is a description of a design-centred scientific process. The three constructs identified at the epistemological level are operationalised as a methodological framework by projecting them into a specific research setting of the demonstrator study. Appropriate methods and procedures are identified for collecting data, organising and interpreting them as design narratives, and extracting design patterns from these narratives. The methodological framework is applied in the demonstrator domain to the question of learning about number sequences. A review of the educational research on number sequences identifies challenges in this area related to the tension between learners’ intuitive concept of sequences and the dominant curricular form. The former appears to be recursive in nature and narrative in form, whereas the latter is a function of index expressed in algebraic notation. The chosen design approach combines construction, collaboration and communication. It highlights the need for representations and activities which lead learners from intuitive concepts to formal mathematical structures. Three interleaved themes connect the primary and the demonstrator domains: narrative, systematisation and representation. Narrative emerges as a key element in the process of deriving knowledge from experience. Systemisation concerns the structured organisation of knowledge. The tension between the two calls for representations which support a trajectory from the intuitive to the structural. The main outcome of this study is a methodological framework for design science of TEME which combines design narratives and design patterns into structured cycles of enquiry. This framework is supported both theoretically and empirically. Inter alia, it is used to derive a contribution towards a pedagogical pattern language of construction, communication and collaboration in TEME.http://www.bibsonomy.org/bibtex/2b3472592beb8966d17ce788688d7c753/yishyish2011-10-04T15:44:06+02:00algebra cultural culture education learning mathematics representation semiotics <span class="authorEditorList"><a href="/author/Radford">Luis Radford</a> </span><em>Research in Mathematics Education</em> <em>12(1):1-19</em> (<em>2010</em>)Tue Oct 04 15:44:06 CEST 2011Research in Mathematics Education11-19Algebraic thinking from a cultural semiotic perspective122010algebra cultural culture education learning mathematics representation semiotics In this article, I introduce a typology of forms of algebraic thinking. In the first part, I argue that the form and generality of algebraic thinking are characterised by the mathematical problem at hand and the embodied and other semiotic resources that are mobilised to tackle the problem in analytic ways. My claim is based not only on semiotic considerations but also on new theories of cognition that stress the fundamental role of the context, the body and the senses in the way in which we come to know. In the second part, I present some concrete examples from a longitudinal classroom research study through which the typology of forms of algebraic thinking is illustrated.http://www.bibsonomy.org/bibtex/2e00c252c75c77c91d2de3a0f3755335c/yishyish2011-08-03T16:00:25+02:00geometry learning mathematics maths mlearning mobile <span class="authorEditorList"><a href="/author/Spikol">D. Spikol</a>, and <a href="/author/Eliasson">J. Eliasson</a> </span><em>The 6th IEEE International Conference on Wireless, Mobile, and Ubiquitous Technologies in Education, </em><em>page 137--141. </em><em>IEEE, </em>(<em>2010</em>)Wed Aug 03 16:00:25 CEST 2011The 6th IEEE International Conference on Wireless, Mobile, and Ubiquitous Technologies in Education137--141Lessons from Designing Geometry Learning Activities that Combine Mobile and 3D Tools2010geometry learning mathematics maths mlearning mobile http://www.bibsonomy.org/bibtex/27437a448c9479bb241eee56993467fc5/yishyish2011-08-03T15:55:42+02:00learning mathematics maths mlearning mobilemath <span class="authorEditorList"><a href="/author/Wijers">Monica Wijers</a>, <a href="/author/Jonker">Vincent Jonker</a>, and <a href="/author/Drijvers">Paul Drijvers</a> </span><em>ZDM</em> (<em>2010</em>)Wed Aug 03 15:55:42 CEST 2011ZDM1--11MobileMath: exploring mathematics outside the classroom2010learning mathematics maths mlearning mobilemath Computer games seem to have a potential for engaging students in meaningful learning, inside as well as outside of school. With the growing availability of mobile handheld technology (HHT), a number of location-based games for handheld mobile phones with GPS have been designed for educational use. The exploitation of this potential for engaging students into meaningful learning, however, so far remains unexplored. In an explorative design research, we investigated whether a location-based game with HHT provides opportunities for engaging in mathematical activities through the design of a geometry game called MobileMath. Its usability and opportunities for learning were tested in a pilot on three different secondary schools with 60 12–14-year-old students. Data were gathered by means of participatory observation, online storage of game data, an online survey and interviews with students and teachers. The results suggest that students were highly motivated, and enjoyed playing the game. Students indicated they learned to use the GPS, to read a map and to construct quadrilaterals. The study suggests learning opportunities that MobileMath provides and that need further investigation.http://www.bibsonomy.org/bibtex/25a491831fe94b76d4130dade8f3e76ee/yishyish2011-08-03T15:49:33+02:00education games learning mathematics maths mlearning mobile <span class="authorEditorList"><a href="/author/Wijers">M. Wijers</a>, <a href="/author/Jonker">V. Jonker</a>, and <a href="/author/Kerstens">K. Kerstens</a> </span><em>Proceedings of the European Conference on Game Based Learning, Barcelona, </em><em>page 507--516. </em>(<em>2008</em>)Wed Aug 03 15:49:33 CEST 2011Proceedings of the European Conference on Game Based Learning, Barcelona507--516MobileMath: the Phone, the Game and the Math2008education games learning mathematics maths mlearning mobile Computer games appear to be able to engage students in meaningful learning, inside as well as outside of school. Mobile games, especially location-based games played on mobile phones with GPS, integrate the player's position into the game-play and thus support situative learning. This type of games can augment the reality by adding 'virtual elements' to it. In this paper we discuss the results of a pilot study on MobileMath, a location-based mobile game that integrates concepts from mathematics and geography. MobileMath is played on a mobile phone with a GPS receiver. It is designed to investigate how a modern, social type of game can contribute to students engagement in learning mathematics. Teams compete on the playing field by gaining points by covering as much area as possible. They do this by constructing squares, rectangles or parallelograms by physically walking to and clicking on each vertex (point). The shapes they construct are virtual elements added to the real world. As the game proceeds the free playing space gets smaller. It is possible to 'hinder' other teams and to deconstruct the shapes they made, points are gained by this also. During the game, in real-time the locations of all teams and all finished quadrilaterals are visible on each mobile phone. The game data are stored online and can be viewed back and discussed later. In this pilot study the usability of MobileMath was tested with three different secondary schools. Four one-hour games, each with seven or eight teams of two students (n=60), were played around the schools. Data were gathered by means of (participatory) observation, analysis of the games played, a survey and interviews with students and teachers. The results show highly motivated students, who enjoyed playing the game. Students indicated they learned to use the GPS, to read a map and how to construct quadrilaterals. http://www.bibsonomy.org/bibtex/27a7554ed5cf7ee93bebfc7c0c9f19c3f/yishyish2011-08-03T15:47:40+02:00education learning mathematics maths mlearning mobile school smartphones teaching <span class="authorEditorList"><a href="/author/?"> ?</a> </span><em>Mlearn2010 - 9th world conference on mobile and contextual learning, </em><em>page 9-16. </em>(<em>October 2010</em>)Wed Aug 03 15:47:40 CEST 2011Mlearn2010 - 9th world conference on mobile and contextual learning109-16MobiMaths: An approach to utilising smartphones in teaching mathematics2010education learning mathematics maths mlearning mobile school smartphones teaching The teaching of mathematics at second level is well known to be a challenging issue. An overemphasis on didactic teaching, lack of encouragement to explore possible alternative solutions to problems, an overemphasis on procedure and the separation of mathematical procedures from real world problems are just some of the factors which are put forward as contributing to the difficulties in math education. Through its inherent ability to support collaboration, and contextualised learning, mobile technology offers the potential to address at least some of the issues in mathematics education. This paper describes the approach we are following to create a set of tools, learning applications and teacher supports, which exploit smartphone technology to aid in the teaching and learning of mathematics. The work is underpinned by a social constructivist pedagogy with an emphasis on collaborative problem solving and the contextualisation of learning. This paper discusses issues in mathematics education before going on to describe the broad approach being followed in our research. The underlying technical architecture is described along with the first two activities we have developed. The preliminary results from a user evaluation study are reported upon.http://www.bibsonomy.org/bibtex/22a92995485e45d76aa61b70df65b1b94/yishyish2011-06-28T00:15:21+02:00asld-book dbr design designapproaches education ldg learning learningdesigngrid mathematics research science <span class="authorEditorList"><a href="/author/Lesh">Richard Lesh</a>, and <a href="/author/Sriraman">Bharath Sriraman</a> </span><em>ZDM</em> <em>37(6):490-505</em> (<em>2005</em>)Tue Jun 28 00:15:21 CEST 2011ZDM6490-505Mathematics education as a design science372005asld-book dbr design designapproaches education ldg learning learningdesigngrid mathematics research science We propose re-conceptualizing the field of mathematics education research as that of a design science akin to engineering and other emerging interdisciplinary fields which involve the interaction of “subjects”, conceptual systems and technology influenced by social constraints and affordances. Numerous examples from the history and philosophy of science and mathematics and ongoing findings of M& M research are drawn to illustrate our notion of mathematics education research as a design science. Our ideas are intended as a framework and do not constitute a “grand” theory (see Lester, 2005, this issue). That is, we provide a framework (a system of thinking together with accompanying concepts, language, methodologies, tools, and so on) that provides structure to help mathematics education researchers develop both models and theories, which encourage diversity and emphasize Darwinian processes such as: (a) selection (rigorous testing), (b) communication (so that productive ways of thinking spread throughout relevant communities), and (c) accumulation (so that productive ways of thinking are not lost and get integrated into future developments).http://www.bibsonomy.org/bibtex/2ae47b13e31f4c1eeec27a29e99f26479/yishyish2011-04-06T22:05:40+02:00curriculum design education evaluation evidence framework learning mathematics research <span class="authorEditorList"><a href="/author/Clements">D.H. Clements</a> </span><em>Journal for Research in Mathematics Education</em> <em>38(1):35</em> (<em>2007</em>)Wed Apr 06 22:05:40 CEST 2011Journal for Research in Mathematics Education135Curriculum Research: Toward a Framework for "Research-based Curricula"382007curriculum design education evaluation evidence framework learning mathematics research Government agencies and members of the educational research community have petitioned for research-based curricula. The ambiguity of the phrase "research-based", however, undermines attempts to create a shared research foundation for the development of, and informed choices about, classroom curricula. This article presents a framework for the construct of research-based curricula. One implication is that traditional strategies such as market research and research-to-practice models are insufficient; more adequate is the use of multiple phases of the proffered Curriculum Research Framework.http://www.bibsonomy.org/bibtex/29c4bd8d909e22d1f79a2f3991ad7802d/yishyish2011-03-21T18:03:15+01:00education games haifa-games-course learning mathematics mathgamespatterns <span class="authorEditorList"><a href="/author/Bragg">Leicha Bragg</a> </span><em>Mathematics education research journal</em> <em>19(1):29-44</em> (<em>2007</em>)Mon Mar 21 18:03:15 CET 2011Mathematics education research journal129-44Students' conflicting attitudes towards games as a vehicle for learning mathematics: A methodological dilemma192007education games haifa-games-course learning mathematics mathgamespatterns Mathematics games are widely employed in school classrooms for such reasons as a reward for early finishers or to enhance students’ attitude towards mathematics. During a four week period, a total of 222 Grade 5 and 6 (9 to 12 years old) children from Melbourne, Australia, were taught multiplication and division of decimal numbers using calculator games or rich mathematical activities. Likert scale surveys of the children’s attitudes towards games as a vehicle for learning mathematics revealed unexpectedly high proportions of negative attitudes at the conclusion of the research. In contrast, student interview data revealed positive associations between games and mathematical learning. This paper reports on the methodological dilemma of resultant conflicting attitudinal data related to game-playing. Concerns arising from the divergence in the results are raised in this paper. Implications based on the experience of this study may inform educational researchers about future methodological choices involving attitudinal research.http://www.bibsonomy.org/bibtex/2ed67685c7e301429b9892dffa6b29970/yishyish2011-02-08T12:53:52+01:00abstraction contel11 education genesis instrumental instrumentation learning mathematics situated sociocultural technologies <span class="authorEditorList"><a href="/author/Hoyles">Celia Hoyles</a>, <a href="/author/Noss">Richard Noss</a>, and <a href="/author/Kent">Phillip Kent</a> </span><em>International Journal of Computers for Mathematical Learning</em> <em>9(3):309--326</em> (<em>2004</em>)Tue Feb 08 12:53:52 CET 2011International Journal of Computers for Mathematical Learning3309--326On the integration of digital technologies into mathematics classrooms92004abstraction contel11 education genesis instrumental instrumentation learning mathematics situated sociocultural technologies Trouche‘s (2003) presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche‘s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student‘s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics.http://www.bibsonomy.org/bibtex/2c4eb1a315c533f6257bad44ad70ab5df/yishyish2011-02-08T01:14:08+01:00education haifa-mlearning learning math4mobile mathematics maths mlearning mobile <span class="authorEditorList"><a href="/author/Botzer">Galit Botzer</a>, and <a href="/author/Yerushalmy">Michal Yerushalmy</a> </span><em>International Conference on Cognition and Exploratory Learning in Digital Age, </em>(<em>2007</em>)Tue Feb 08 01:14:08 CET 2011International Conference on Cognition and Exploratory Learning in Digital AgeMobile application for mobile learning2007education haifa-mlearning learning math4mobile mathematics maths mlearning mobile The paper presents a pilot case study intended to examine how socio-cultural and situated learning aspects are reflected in learning experiences within a novel mobile learning environment, Math4Mobile, a cellular application for mathematics learning. The case study focused on four students in a mathematics methods course who were engaged in a mathematics project based on the cellular applications. We found that use of the cellular environment enhanced the participants’ engagement in the modeling of real life scenarios and contributed to collaboration between participants. These effects can be attributed to the mobility, flexibility, and availability of cellular tools, and they point to a possible contribution of mobile tools to mathematics education. http://www.bibsonomy.org/bibtex/27a90700f4dab0594735876ea4dffd6f1/yishyish2011-02-08T01:10:46+01:00education haifa-mlearning learning math4mobile mathematics maths mlearning mobile <span class="authorEditorList"><a href="/author/Daher">Wajeeh Daher</a> </span><em>Australasian Journal of Educational Technology</em> <em>26(1):85-104</em> (<em>2010</em>)Tue Feb 08 01:10:46 CET 2011Australasian Journal of Educational Technology185-104Building mathematical knowledge in an authentic mobile phone environment262010education haifa-mlearning learning math4mobile mathematics maths mlearning mobile Although many researchers have examined knowledge building in traditional settings and distance learning, few have examined middle school students' building of mathematical knowledge using mobile phones. The present study uses two well-known models of knowledge building to carry out the examination: the interactive analysis model of knowledge building phases developed by Gunawardena, Lowe and Anderson (1997) and the six themes model of knowledge building characteristics developed by Scadamalia and Bereiter (2006). The findings show that the middle school students participating in this research went through all the knowledge building phases suggested by Gunawardena, Lowe and Anderson (1997). They further experienced other knowledge building phases that fit the authentic context in which they learned. Participants advanced their knowledge of ideas as a community, collaborating to carry out authentic activities using mobile phones. They demonstrated constructive and critical use of information in general and of authoritative information in particular. Participants worked as mathematicians, especially during the second part of the experiment, when they suggested real world phenomena to explore using the mobile phone. My conclusion suggests learning mathematics by carrying out authentic activities using mobile phones, to encourage and enrich the mathematics knowledge building of students in K-12.