BibSonomyburst/user/yish/postvivaBibSonomy RSS feed for /user/yish/postviva2012-02-16T03:55:08+01:00http://www.bibsonomy.org/bibtex/29b40aea813ff7f4db849707c231cc8da/yishyish2010-08-05T11:52:46+02:00design designresearch designscience eLPBookMor education jls10 learning mathematics postviva <span class="authorEditorList"><a href="/author/Lesh">Richard Lesh</a>, and <a href="/author/Sriraman">Bharath Sriraman</a> </span><em>ZDM - The International Journal on Mathematics Education</em> <em>37(6):490-505</em> (<em>2005</em>)Thu Aug 05 11:52:46 CEST 2010ZDM - The International Journal on Mathematics Education6490-505Mathematics Education as a Design Science372005design designresearch designscience eLPBookMor education jls10 learning mathematics postviva 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 sicence. 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/21168ad8da596915c223f2f159431342f/yishyish2010-08-05T11:52:34+02:00bruner eLPBookMor mathematics narrative postviva stories <span class="authorEditorList"><a href="/author/Sinclair">Natalie Sinclair</a>, <a href="/author/Healy">Lulu Healy</a>, and <a href="/author/Sales">Cassia Osorio Reis Sales</a> </span><em>ZDM - The International Journal on Mathematics Education</em> <em>41(4):441-452</em> (<em>2009</em>)Thu Aug 05 11:52:34 CEST 2010ZDM - The International Journal on Mathematics Education4441-452Time for telling stories: narrative thinking with dynamic geometry412009bruner eLPBookMor mathematics narrative postviva stories In his work on human cognition, Bruner (The culture of education, Harvard University Press, Cambridge, 1996) distinguishes between narrative and paradigmatic modes of thinking. While the latter is closely associated with mathematics, Bruner’s writings suggest that the former contributes non-trivially to the learning of mathematics. In this paper, we argue that the very nature of dynamic mathematical representations—being intrinsically temporal, occurring over time—offer very different opportunities for narrative thinking than do the static diagrams and pictures traditionally available to learners. Using examples from our research, we analyse these opportunities both in terms of their potential for enhancing understanding and for their relation to the kind of paradigmatic thinking that usually constitutes mathematical knowledge.http://www.bibsonomy.org/bibtex/2251f2f97a6c852022aa2957afef17d58/yishyish2010-08-05T11:52:24+02:00education learning limit mathematics postviva sequences theory <span class="authorEditorList"><a href="/author/Bergsten">Christer Bergsten</a> </span><em>ZDM - The International Journal on Mathematics Education</em> <em>40(2):189-199</em> (<em>2008</em>)Thu Aug 05 11:52:24 CEST 2010ZDM - The International Journal on Mathematics Education2189-199On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions402008education learning limit mathematics postviva sequences theory After an introduction on approaches, research frameworks and theories in mathematics education research, three didactical research studies on limits of functions with different research frameworks are analysed and compared with respect to their theoretical perspectives. It is shown how a chosen research framework defines the world in which the research lives, pointing to the difficult but necessary task to compare research results within a common field of study but conducted within different frameworks.http://www.bibsonomy.org/bibtex/24cd45be302c300e1bc294261cb85b9e3/yishyish2010-07-28T17:37:36+02:00Design activitysequences designpatterns eLPBookMor ims ims-ld jls10 lams learning postviva <span class="authorEditorList"><a href="/author/Dalziel">James R. Dalziel</a> </span><em>Sixth International Conference on Advanced Learning Technologies, </em><em>page 1101-1102. </em><em>IEEE, </em>(<em>2006</em>)Wed Jul 28 17:37:36 CEST 2010Sixth International Conference on Advanced Learning Technologies1101-1102Lessons from LAMS for IMS learning design2006Design activitysequences designpatterns eLPBookMor ims ims-ld jls10 lams learning postviva LAMS (the Learning Activity Management System) is a Learning Design system with a particular focus on sequencing of collaborative learning activities. This paper reviews a number of lessons learned from the development of LAMS, and their implications for both the existing IMS Learning Design specification, and its future scope and purpose. It proposes a number of areas for further development.http://www.bibsonomy.org/bibtex/2e9f5cd30484e8a2dc5ca5da4b8e36fb2/yishyish2010-07-28T17:35:40+02:00audittrail inquiry jls10 methodology methods postviva qualitative research validity <span class="authorEditorList"><a href="/author/Creswell">John W. Creswell</a>, and <a href="/author/Miller">Dana L. Miller</a> </span><em>Theory into practice</em> <em>39(3):124-130</em> (<em>2000</em>)Wed Jul 28 17:35:40 CEST 2010Theory into practice3124-130Determining validity in qualitative inquiry392000audittrail inquiry jls10 methodology methods postviva qualitative research validity WRITING ABOUT VALIDITY IN QUALITATIVE inquiry is challenging on many levels. Multiple perspectives about it flood the pages of books (e.g., Lincoln & Guba, 1985; Maxwell, 1996; Merriam, 1998; Schwandt, 1997) and articles and chapters (e.g., Altheide & Johnson, 1994; Lather, 1993; Maxwell, 1992). In these texts, readers are treated to a confusing array of terms for validity, including authenticity, goodness, verisimilitude, adequacy, trustworthiness, plausibility, validity, validation, and credibility. Various authors have constructed diverse typologies of validity (e.g., Maxwell’s five types, 1992; Lather’s four frames, 1993; and Schwandt’s four positions, 1997). It is little wonder that Donmoyer (1996), who wrote an editorial on validity in the Educational Researcher, commented on the diverse perspectives of validity by contrasting Miles and Huberman’s (1994) “traditional conception of validity” with Lather’s (1993) “ironic validity” (p. 21). Novice researchers, in particular, can become increasingly perplexed in attempting to understand the notion of validity in qualitative inquiry.http://www.bibsonomy.org/bibtex/2e50d48715e47b1b7d6d44b432ae9a80d/yishyish2010-07-06T18:27:11+02:00designapproaches designresearch jls10 phd postviva <span class="authorEditorList"><a href="/author/Bannan-Ritland">B. Bannan-Ritland</a>, and <a href="/author/Baek">JY Baek</a> </span><em>Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teaching, </em><em>Routledge, </em><em>New York, NY, </em>(<em>2008</em>)Tue Jul 06 18:27:11 CEST 2010New York, (NY)Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teachingInvestigating the act of design in design research2008designapproaches designresearch jls10 phd postviva http://www.bibsonomy.org/bibtex/2088f835551a710ac777eb8552c93cd60/yishyish2010-07-06T18:23:28+02:00designapproaches designresearch jls10 methodology phd postviva <span class="authorEditorList"><a href="/author/Cobb">Paul Cobb</a>, and <a href="/author/Gravemeijer">K. Gravemeijer</a> </span><em>Handbook of Design Research Methods in Education, </em><em>Routledge, </em><em>New York, NY, </em>(<em>2008</em>)Tue Jul 06 18:23:28 CEST 2010New York, {NY}Handbook of Design Research Methods in EducationExperimenting to support and understand learning processes2008designapproaches designresearch jls10 methodology phd postviva http://www.bibsonomy.org/bibtex/2e38078bbccdf7bf0a3db8e32730e10f2/yishyish2009-11-25T16:49:00+01:00design designpatterns epistemology learning methodology patterns postviva <span class="authorEditorList"><a href="/author/Kohls">Christian Kohls</a>, and <a href="/author/Panke">Stefanie Panke</a> </span><em>Proceedings of the 16th Conference on Pattern Languages of Programs, </em>(<em>2009</em>)Wed Nov 25 16:49:00 CET 2009Proceedings of the 16th Conference on Pattern Languages of ProgramsIs that true? Thoughts on the epistemology of patterns.2009design designpatterns epistemology learning methodology patterns postviva This paper presents a theoretical perspective on patterns derived from epistemology and theory of science. We argue that patterns are specific kinds of theories and that the process of pattern mining is similar to scientific discovery. Exploring the concepts induction, deduction and abduction with respect to patterns, we reflect upon common methods of pattern mining in the pattern community. This allows for a critical discussion of the level of confidence and corroboration of patterns. We suggest new research questions on the mining and evaluation of patterns.http://www.bibsonomy.org/bibtex/20e49267e8de040788a28ed2110481ee7/yishyish2009-10-30T21:22:24+01:00education ethics justice mathematics philosophy postviva social <span class="authorEditorList"><a href="/author/Ernest">Paul Ernest</a> </span><em>Philosophy of Mathematics Education</em> (<em>2007</em>)Fri Oct 30 21:22:24 CET 2009Philosophy of Mathematics EducationWhy Social Justice?212007education ethics justice mathematics philosophy postviva social http://www.bibsonomy.org/bibtex/26906546d4c93165a1d83b14206df73fd/yishyish2009-10-30T19:58:17+01:00education empowerment ethics justice learning mathematics philosophy politics postviva social <span class="authorEditorList"><a href="/author/Sriraman">Bharath Sriraman</a>, and <a href="/author/Steinthorsdottir">Olof Steinthorsdottir</a> </span><em>Information Age Publishing, Incorporated, </em>(<em>2009</em>)Fri Oct 30 19:58:17 CET 2009Critical Issues in Mathematics Education319–336Social Justice and Mathematics Education: Issues, Dilemmas, Excellence and Equity 2009education empowerment ethics justice learning mathematics philosophy politics postviva social This article explores reasons for educational research and practice in social justice from evolutionary, ideological and philosophical viewpoints. The tension between nihilistic and empathetic tendencies within our history is used to reflexively examine the origins and causes of inequity with emphasis on the works of giants such as Paolo Freire, John Dewey, Karl Marx, and Vivekananda. Finally we address one particular issue in depth, namely the tension between excellence and equity in talent development in schools, east and west.http://www.bibsonomy.org/bibtex/29d3f6e1a121170b3c35356102c610a0a/yishyish2009-10-30T18:16:40+01:00education empowerment epistemological learning mathematics philosophy postviva social <span class="authorEditorList"><a href="/author/Ernest">Paul Ernest</a> </span><em>Philosophy of Mathematics Education Journal</em> (<em>2002</em>)Fri Oct 30 18:16:40 CET 2009Philosophy of Mathematics Education JournalEmpowerment in mathematics education152002education empowerment epistemological learning mathematics philosophy postviva social In this paper I explore the meaning of empowerment in the teaching and learning of mathematics. The main part of the paper is devoted to distinguishing three different but complementary meanings of empowerment concerning mathematics: mathematical, social and epistemological empowerment. Mathematical empowerment concerns gaining the power to use mathematical knowledge and skills in school mathematics. Social empowerment is the ability to use mathematics for social betterment. Epistemological empowerment means confidence and personal power over the use, creation and validation of knowledge. After analysing what these three interpretations of empowerment mean, I relate them to the theme of equity.http://www.bibsonomy.org/bibtex/2187484fb4987efc20373b9fdf3809e58/yishyish2009-10-26T20:54:06+01:00MIT constionism education educationalprogramming haifa-games-course language learning papert postviva programming scratch software <span class="authorEditorList"><a href="/author/Resnick">Mitchel Resnick</a>, <a href="/author/Maloney">John Maloney</a>, <a href="/author/Monroy-Hernández">Andrés Monroy-Hernández</a>, <a href="/author/Rusk">Natalie Rusk</a>, <a href="/author/Eastmond">Evelyn Eastmond</a>, <a href="/author/Brennan">Karen Brennan</a>, <a href="/author/Millner">Amon Millner</a>, <a href="/author/Rosenbaum">Eric Rosenbaum</a>, <a href="/author/Silver">Jay Silver</a>, <a href="/author/Silverman">Brian Silverman</a>, and <a href="/author/Kafai">Yasmin Kafai</a> </span><em>Communications of the ACM</em> <em>52(11):60-67</em> (<em>2009</em>)Mon Oct 26 20:54:06 CET 2009Communications of the ACM 1160-67Scratch: Programming for All522009MIT constionism education educationalprogramming haifa-games-course language learning papert postviva programming scratch software When Moshe Y. Vardi, Editor-in-Chief of Communications, invited us to submit an article, he recalled how he first learned about Scratch: "A colleague of mine (CS faculty)," he said, "told me how she tried to get her 10-year-old daughter interested in programming, and the only thing that appealed to her was Scratch." That's what we were hoping for when we set out to develop Scratch six years ago. We wanted to develop an approach to programming that would appeal to people who hadn't previously imagined themselves as programmers. We wanted to make it easy for everyone, of all ages, backgrounds, and interests, to program their own interactive stories, games, animations, and simulations, and share their creations with one another.http://www.bibsonomy.org/bibtex/2cadf3625b40d529071872458d599ac2b/yishyish2009-10-26T20:38:13+01:00AI AIED ITS analysis collaborative convsation cscl design discourse education language learning postviva social <span class="authorEditorList"><a href="/author/Rickel">Jeff Rickel</a>, <a href="/author/Lesh">Neal Lesh</a>, <a href="/author/Rich">Charles Rich</a>, <a href="/author/Sidner">Candace L. Sidner</a>, and <a href="/author/Gertner">Abigail Gertner</a> </span> (<em>2001</em>)Mon Oct 26 20:38:13 CET 2009Proceedings of Tenth International Conference on AI in Education592--594{Building a bridge between intelligent tutoring and collaborative dialogue systems}2001AI AIED ITS analysis collaborative convsation cscl design discourse education language learning postviva social Our research objective is to develop computer tutors that collaborate with students on tasks in simulated environments. Towards this end, we seek to integrate two separate but related research threads: intelligent tutoring systems (ITS) and collaborative dialogue systems (CDS). Research on ITS [10] focuses on computer tutors that adapt to individual students based on the target knowledge the student is expected to learn and the presumed state of the student’s current knowledge. Research on CDS (e.g., [5]), with an equally long history, focuses on computational models of human dialogue for collaborative tasks. Unfortunately, there has been a surprising lack of cross-fertilization between these two research areas. Work on tutorial dialogue for ITS has not leveraged general models of collaborative dialogue. Similarly, research on collaborative dialogues has focused on modeling conversations between peers or between an expert and novice, but has rarely addressed tutorial issues.http://www.bibsonomy.org/bibtex/2c7082cc8cb99c52cc0d527da5474ba3b/yishyish2009-10-13T16:46:55+02:00concept definition didactics education formal limit limits postviva university <span class="authorEditorList"><a href="/author/Przenioslo">Malgorzata Przenioslo</a> </span><em>Educational Studies in Mathematics</em> <em>60(1):71--93</em> (<em>September 2005</em>)Tue Oct 13 16:46:55 CEST 2009Educational Studies in Mathematics#sep#171--93Introducing the Concept of Convergence of a Sequence in Secondary School602005concept definition didactics education formal limit limits postviva university My purpose in this paper is to present a didactic tool – a set of specially designed problems and questions for discussion – that can help making students better aware of the various aspects of the formal notion of limit of a sequence. The didactic tool will be justified using results from my own and other authors' research on students' naïve or erroneous conceptions of limit of a sequence. ER -SpringerLink - Journal Articlehttp://www.bibsonomy.org/bibtex/238d5f9b2203204278d229350c0b1440a/yishyish2009-10-13T16:42:43+02:00college convergence learning limit limits mathematics postviva university <span class="authorEditorList"><a href="/author/Roh">Kyeong Hah Roh</a> </span> (<em>2007</em>)Tue Oct 13 16:42:43 CEST 2009An Activity for Development of the Understanding of the Concept of Limit2007college convergence learning limit limits mathematics postviva university This study examines how college calculus students develop and accommodate their conceptual understanding of the limit of a sequence. The ε−strip activity was specially designed to examine students’ understanding of the formal definition of the limit of a sequence. This study focuses on a student’s conception of limit and her understanding of the relation between error bounds and indices in the formal definition of limit. The results show that the student improved her understanding of the concept of limit as well as her understanding of the formal definition of the limit of a sequence since engaging in the ε−strip activity.http://www.bibsonomy.org/bibtex/2dd3e5e3d763c1eb8dc93b43b3321f6e1/yishyish2009-10-13T16:39:31+02:00learning limit limits mathematics postviva proof sequences <span class="authorEditorList"><a href="/author/Burn">Bob Burn</a> </span><em>Educational Studies in Mathematics</em> <em>60(3):269--295</em> (<em>November 2005</em>)Tue Oct 13 16:39:31 CEST 2009Educational Studies in Mathematics#nov#3269--295The Vice: Some Historically Inspired and Proof-Generated Steps to Limits of Sequences602005learning limit limits mathematics postviva proof sequences This paper proposes a genetic development of the concept of limit of a sequence leading to a definition, through a succession of proofs rather than through a succession of sequences or a succession of εs. The major ideas on which it is based are historical and depend on Euclid, Archimedes, Fermat, Wallis and Newton. Proofs of equality by means of inequalities precede the notion of limit. For example, the determination of the volume of a pyramid precedes the definition of limit. The algebraic details given here are anachronistically modern, and the notion of a vice between two inequalities which provides the distinctive perspective of this paper would not have been recognized in this form by any of the named mathematicians since it presumes the existence of negative numbers and their comparability in a modern sense with positive numbers. ER -SpringerLink - Journal Articlehttp://www.bibsonomy.org/bibtex/28fe97e8c081768e8c964b0efc7318b4f/yishyish2009-10-13T13:31:56+02:00algebra learning limit mathematics postviva reasoning <span class="authorEditorList"><a href="/author/Bergsten">Christer Bergsten</a> </span><em>Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education, </em><em> 2, </em><em>page 153-160. </em><em>Prague, Czech Republic July 16-21, </em>(<em>2006</em>)Tue Oct 13 13:31:56 CEST 2009Prague, Czech Republic July 16-21Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education153-160Trying to reach the limit--The role of algebra in mathematical reasoning22006algebra learning limit mathematics postviva reasoning In this paper the role of algebra in students’ mathematical reasoning about limits of functions in undergraduate mathematics is analysed, considering the students’ educational setting. Data from a video study where six students worked in pairs to solve problems on limits of functions, and an analysis of their calculus lectures, indicate that algebra is at the same time a key and a lock to reach the limit in these problems. This double effect is related to the mathematical organisation taught, as well as the students’ sense of authority as internal or external.http://www.bibsonomy.org/bibtex/21de3e4c93525437a00608bdfedadf673/yishyish2009-10-13T13:26:44+02:00algebra geometry learning limit mathematics postviva <span class="authorEditorList"><a href="/author/Elia">Iliada Elia</a>, <a href="/author/Gagatsis">Athanasios Gagatsis</a>, <a href="/author/Panaoura">Areti Panaoura</a>, <a href="/author/Zachariades">Theodosis Zachariades</a>, and <a href="/author/Zoulinaki">Fotini Zoulinaki</a> </span><em>International Journal of Science and Mathematics Education</em> <em>7(4):765-790</em> (<em>August 2009</em>)Tue Oct 13 13:26:44 CEST 2009International Journal of Science and Mathematics Educationaugust4765-790GEOMETRIC AND ALGEBRAIC APPROACHES IN THE CONCEPT OF "LIMIT" AND THE IMPACT OF THE "DIDACTIC CONTRACT"72009algebra geometry learning limit mathematics postviva The present study explores students’ abilities in conversions between geometric and algebraic representations, in problem- solving situations involving the concept of “limit” and the interrelation of these abilities with students’ constructed understandingof this concept. An attempt is also made to examine the impact of the “didactic contract” on students’ performance throughthe processes they employ in tackling specific tasks on the concept of limit. Data were collected from 222 12th-grade highschool students in Greece. The results indicated that students who had constructed a conceptual understanding of limit werethe ones most probable to accomplish the conversions of limits from the algebraic to the geometric representations and thereverse. The findings revealed the compartmentalized way of students’ thinking in non-routine problems by means of their performancein simpler conversion tasks. Students who did not perform under the conditions of the didactic contract were found to be moreconsistent in their responses for various conversion tasks and complex problems on limits, compared to students who, as aconsequence of the didactic contract, used only algorithmic processes.SpringerLink - Journal Articlehttp://www.bibsonomy.org/bibtex/2196cd967ca3ffd5d05cfc87567a67992/yishyish2009-10-13T12:59:02+02:00Infinite application curiculum limit mathematics postviva sequences sum university visualization <span class="authorEditorList"><a href="/author/Nardi">Elena Nardi</a>, <a href="/author/Biza">Irene Biza</a>, and <a href="/author/González-Martín">Alejandro González-Martín</a> </span> <em>28(3):84-89</em> (<em>2008</em>)Tue Oct 13 12:59:02 CEST 2009Proceedings of the Conference of the British Society for Research into the Learning of Mathematics384-89Introducing the concept of infinite sum: Preliminary analyses of curriculum content282008Infinite application curiculum limit mathematics postviva sequences sum university visualization In this paper we report the first phase of a study that aims to analyse curriculum content, pedagogical practice and student perceptions of the complex, often counter-intuitive but significant mathematical concept of infinite sum (aka series in Calculus). Sources of student difficulty with the concept identified in previous, not very extensive, research include: certain student perceptions of infinity; limited exposure to visualisation, contextualisation and applications of infinite sums; and, teaching through reduction to an algorithmic approach. Here we report preliminary analyses regarding curriculum content and, in particular, the initial phases of a three-dimensional analysis (cognitive, epistemological, didactical) of mainstream texts used to introduce the concept to undergraduates in the UK.http://www.bibsonomy.org/bibtex/23315068315375ac16211ce3e492089fa/yishyish2009-10-13T12:56:16+02:00Asymptotes Images Limits Sequences cognition definitions learning limit mathematics postviva sequences teaching visual visualization <span class="authorEditorList"><a href="/author/Roh">Kyeong Hah Roh</a> </span><em>Educational Studies in Mathematics</em> <em>69(3):217--233</em> (<em>2008</em>)Tue Oct 13 12:56:16 CEST 2009Educational Studies in Mathematics3217--233Students' images and their understanding of definitions of the limit of a sequence692008Asymptotes Images Limits Sequences cognition definitions learning limit mathematics postviva sequences teaching visual visualization There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been conducted on how students’ understanding of the rigorous definition of limit is influenced by the images of limit that the students have constructed through their previous learning. This study explored how calculus students’ images of the limit of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews, students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on activity, called the ɛ–strip activity. This paper illustrates how these students’ understanding of definitions of the limit of a sequence was influenced by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching and learning the concept of limit, as well as on research in mathematics education, are also discussed.