@article{lesh2005med,
  abstract = {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).},
  added-at = {2010-08-05T11:52:46.000+0200},
  author = {Lesh, Richard and Sriraman, Bharath},
  biburl = {http://www.bibsonomy.org/bibtex/29b40aea813ff7f4db849707c231cc8da/yish},
  interhash = {7baad2b1c46f8d7f5a013845cfa71499},
  intrahash = {9b40aea813ff7f4db849707c231cc8da},
  journal = {ZDM - The International Journal on Mathematics Education},
  keywords = {design designresearch designscience eLPBookMor education jls10 learning mathematics postviva},
  number = 6,
  pages = {490-505},
  publisher = {Springer},
  timestamp = {2010-08-05T11:52:46.000+0200},
  title = {Mathematics Education as a Design Science},
  url = {http://www.springerlink.com/content/dp77p8189474017v/},
  volume = 37,
  year = 2005
}

@article{sinclair2009time,
  abstract = {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.},
  added-at = {2010-08-05T11:52:34.000+0200},
  author = {Sinclair, Natalie and Healy, Lulu and Sales, Cassia Osorio Reis},
  biburl = {http://www.bibsonomy.org/bibtex/21168ad8da596915c223f2f159431342f/yish},
  interhash = {4a8f6f751d29feec270867162c6d8141},
  intrahash = {1168ad8da596915c223f2f159431342f},
  journal = {ZDM - The International Journal on Mathematics Education},
  keywords = {bruner eLPBookMor mathematics narrative postviva stories},
  number = 4,
  pages = {441-452},
  publisher = {Springer},
  timestamp = {2010-08-05T11:52:34.000+0200},
  title = {Time for telling stories: narrative thinking with dynamic geometry},
  url = {http://www.springerlink.com/content/x03878218j163678/},
  volume = 41,
  year = 2009
}

@article{bergsten2008influence,
  abstract = {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.},
  added-at = {2010-08-05T11:52:24.000+0200},
  author = {Bergsten, Christer},
  biburl = {http://www.bibsonomy.org/bibtex/2251f2f97a6c852022aa2957afef17d58/yish},
  doi = {10.1007/s11858-008-0083-2},
  interhash = {d34e2c785ba7d168359e064f01ef1eba},
  intrahash = {251f2f97a6c852022aa2957afef17d58},
  journal = {ZDM - The International Journal on Mathematics Education},
  keywords = {education learning limit mathematics postviva sequences theory},
  number = 2,
  pages = {189-199},
  publisher = {Springer},
  timestamp = {2010-08-05T11:52:24.000+0200},
  title = {On the influence of theory on research in mathematics education: the case of teaching and learning limits of functions},
  url = {http://web.me.com/mario.sanchez/web/Blog/Entradas/2009/2/21_Uno_acad%C3%A9mico_files/Bergsten_2008_1.pdf},
  volume = 40,
  year = 2008
}

@inproceedings{dalziel2006lli,
  abstract = {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.},
  added-at = {2010-07-28T17:37:36.000+0200},
  author = {Dalziel, James R.},
  biburl = {http://www.bibsonomy.org/bibtex/24cd45be302c300e1bc294261cb85b9e3/yish},
  booktitle = {Sixth International Conference on Advanced Learning Technologies},
  interhash = {c9a5864e49defb65a512c96915ab8115},
  intrahash = {4cd45be302c300e1bc294261cb85b9e3},
  keywords = {Design activitysequences designpatterns eLPBookMor ims ims-ld jls10 lams learning postviva},
  pages = {1101-1102},
  publisher = {IEEE},
  timestamp = {2010-07-28T17:37:36.000+0200},
  title = {Lessons from LAMS for IMS learning design},
  url = {http://csdl.computer.org/comp/proceedings/icalt/2006/2632/00/263201101.pdf},
  year = 2006
}

@article{creswell2000dvq,
  abstract = {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.},
  added-at = {2010-07-28T17:35:40.000+0200},
  author = {Creswell, John W. and Miller, Dana L.},
  biburl = {http://www.bibsonomy.org/bibtex/2e9f5cd30484e8a2dc5ca5da4b8e36fb2/yish},
  interhash = {6e72982a2c9fc4c66f5a9154d7841f29},
  intrahash = {e9f5cd30484e8a2dc5ca5da4b8e36fb2},
  journal = {Theory into practice},
  keywords = {audittrail inquiry jls10 methodology methods postviva qualitative research validity},
  number = 3,
  pages = {124-130},
  publisher = {Routledge},
  timestamp = {2010-07-28T17:35:40.000+0200},
  title = {Determining validity in qualitative inquiry},
  url = {http://dx.doi.org/10.1207/s15430421tip3903_2},
  volume = 39,
  year = 2000
}

@incollection{bannan2008investigating,
  added-at = {2010-07-06T18:27:11.000+0200},
  address = {New York, (NY)},
  author = {Bannan-Ritland, B. and Baek, JY},
  biburl = {http://www.bibsonomy.org/bibtex/2e50d48715e47b1b7d6d44b432ae9a80d/yish},
  booktitle = {Handbook of design research methods in education: Innovations in science, technology, engineering, and mathematics learning and teaching},
  interhash = {6651910779b5d0e45897cd603b3b8ecf},
  intrahash = {e50d48715e47b1b7d6d44b432ae9a80d},
  keywords = {designapproaches designresearch jls10 phd postviva},
  publisher = {Routledge},
  timestamp = {2010-07-06T18:27:11.000+0200},
  title = {Investigating the act of design in design research},
  year = 2008
}

@incollection{CobbGravemeijer08,
  added-at = {2010-07-06T18:23:28.000+0200},
  address = {New York, {NY}},
  author = {Cobb, Paul and Gravemeijer, K.},
  biburl = {http://www.bibsonomy.org/bibtex/2088f835551a710ac777eb8552c93cd60/yish},
  booktitle = {Handbook of Design Research Methods in Education},
  editor = {Kelly, Anthony E. and Lesh, Richard A. and Baek, John Y.},
  interhash = {f587fa0371bf1200ea56f9e0622ae9cd},
  intrahash = {088f835551a710ac777eb8552c93cd60},
  keywords = {designapproaches designresearch jls10 methodology phd postviva},
  publisher = {Routledge},
  timestamp = {2010-07-06T18:23:28.000+0200},
  title = {Experimenting to support and understand learning processes},
  year = 2008
}

@inproceedings{KohlsPanke09,
  abstract = {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.},
  added-at = {2009-11-25T16:49:00.000+0100},
  author = {Kohls, Christian and Panke, Stefanie},
  biburl = {http://www.bibsonomy.org/bibtex/2e38078bbccdf7bf0a3db8e32730e10f2/yish},
  booktitle = {Proceedings of the 16th Conference on Pattern Languages of Programs},
  interhash = {a0ccd242309b53c987b94d00d8b4f26e},
  intrahash = {e38078bbccdf7bf0a3db8e32730e10f2},
  keywords = {design designpatterns epistemology learning methodology patterns postviva},
  timestamp = {2009-11-25T16:49:00.000+0100},
  title = {Is that true? Thoughts on the epistemology of patterns.},
  url = {http://www.hillside.net/plop/2009/papers/People/Is%20that%20true....pdf},
  year = 2009
}

@article{ernest07,
  added-at = {2009-10-30T21:22:24.000+0100},
  author = {Ernest, Paul},
  biburl = {http://www.bibsonomy.org/bibtex/20e49267e8de040788a28ed2110481ee7/yish},
  interhash = {5c311de63f325effbc08a8f9c2164b65},
  intrahash = {0e49267e8de040788a28ed2110481ee7},
  journal = {Philosophy of Mathematics Education},
  keywords = {education ethics justice mathematics philosophy postviva social},
  timestamp = {2009-10-30T21:22:24.000+0100},
  title = {Why Social Justice?},
  url = {http://people.exeter.ac.uk/PErnest/pome21/Ernest%20%20Why%20Social%20Justice.doc},
  volume = 21,
  year = 2007
}

@incollection{sriraman2009social,
  abstract = {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.},
  added-at = {2009-10-30T19:58:17.000+0100},
  author = {Sriraman, Bharath and Steinthorsdottir, Olof},
  biburl = {http://www.bibsonomy.org/bibtex/26906546d4c93165a1d83b14206df73fd/yish},
  interhash = {da66a0d48bdcc5fbb7bdc386ed722a89},
  intrahash = {6906546d4c93165a1d83b14206df73fd},
  journal = {Critical Issues in Mathematics Education},
  keywords = {education empowerment ethics justice learning mathematics philosophy politics postviva social},
  pages = {319–336},
  publisher = {Information Age Publishing, Incorporated},
  timestamp = {2009-10-30T19:58:17.000+0100},
  title = {Social Justice and Mathematics Education: Issues, Dilemmas, Excellence and Equity
},
  url = {http://www.umt.edu/math/reports/sriraman/Sriraman_18_2009.pdf},
  year = 2009
}

@article{ernest2002empowerment,
  abstract = {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.},
  added-at = {2009-10-30T18:16:40.000+0100},
  author = {Ernest, Paul},
  biburl = {http://www.bibsonomy.org/bibtex/29d3f6e1a121170b3c35356102c610a0a/yish},
  interhash = {d3e5364dfbe891b01932504b01a469a2},
  intrahash = {9d3f6e1a121170b3c35356102c610a0a},
  journal = {Philosophy of Mathematics Education Journal},
  keywords = {education empowerment epistemological learning mathematics philosophy postviva social},
  timestamp = {2009-10-30T18:16:40.000+0100},
  title = {Empowerment in mathematics education},
  url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.4.9516&rep=rep1&type=pdf},
  volume = 15,
  year = 2002
}

@article{resnick-scratch,
  abstract = {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.},
  added-at = {2009-10-26T20:54:06.000+0100},
  author = {Resnick, Mitchel and Maloney, John and Monroy-Hernández, Andrés and Rusk, Natalie and Eastmond, Evelyn and Brennan, Karen and Millner, Amon and Rosenbaum, Eric and Silver, Jay and Silverman, Brian and Kafai, Yasmin},
  biburl = {http://www.bibsonomy.org/bibtex/2187484fb4987efc20373b9fdf3809e58/yish},
  doi = {10.1145/1592761.1592779},
  interhash = {97f8bd2a9129f17aa5250ff91684a1e5},
  intrahash = {187484fb4987efc20373b9fdf3809e58},
  journal = {Communications of the ACM  },
  keywords = {MIT constionism education educationalprogramming haifa-games-course language learning papert postviva programming scratch software},
  number = 11,
  pages = {60-67},
  timestamp = {2009-10-26T20:54:06.000+0100},
  title = {Scratch: Programming for All},
  url = {http://cacm.acm.org/magazines/2009/11/48421-scratch-programming-for-all/},
  volume = 52,
  year = 2009
}

@article{rickel2001building,
  abstract = {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.},
  added-at = {2009-10-26T20:38:13.000+0100},
  author = {Rickel, Jeff and Lesh, Neal and Rich, Charles and Sidner, Candace L. and Gertner, Abigail},
  biburl = {http://www.bibsonomy.org/bibtex/2cadf3625b40d529071872458d599ac2b/yish},
  booktitle = {Proceedings of Tenth International Conference on AI in Education},
  interhash = {6e0f049b40b4d16676a9033d810afa51},
  intrahash = {cadf3625b40d529071872458d599ac2b},
  keywords = {AI AIED ITS analysis collaborative convsation cscl design discourse education language learning postviva social},
  pages = {592--594},
  timestamp = {2009-10-26T20:38:13.000+0100},
  title = {{Building a bridge between intelligent tutoring and collaborative dialogue systems}},
  url = {http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.28.9400&rep=rep1&type=pdf},
  year = 2001
}

@article{malgorzata2005introducing,
  abstract = {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  -},
  added-at = {2009-10-13T16:46:55.000+0200},
  author = {Przenioslo, Malgorzata},
  biburl = {http://www.bibsonomy.org/bibtex/2c7082cc8cb99c52cc0d527da5474ba3b/yish},
  description = {SpringerLink - Journal Article},
  interhash = {f7d90cd0759fa84ab73d9d3d606e0466},
  intrahash = {c7082cc8cb99c52cc0d527da5474ba3b},
  journal = {Educational Studies in Mathematics},
  keywords = {concept definition didactics education formal limit limits postviva university},
  month = {#sep#},
  number = 1,
  pages = {71--93},
  timestamp = {2009-10-13T16:46:55.000+0200},
  title = {Introducing the Concept of Convergence of a Sequence in Secondary School},
  url = {http://dx.doi.org/10.1007/s10649-005-5325-4},
  volume = 60,
  year = 2005
}

@article{roh2007activity,
  abstract = {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.},
  added-at = {2009-10-13T16:42:43.000+0200},
  author = {Roh, Kyeong Hah},
  biburl = {http://www.bibsonomy.org/bibtex/238d5f9b2203204278d229350c0b1440a/yish},
  interhash = {75ef1915e5ca575d6de3e7288b04e38c},
  intrahash = {38d5f9b2203204278d229350c0b1440a},
  keywords = {college convergence learning limit limits mathematics postviva university},
  timestamp = {2009-10-13T16:42:43.000+0200},
  title = {An Activity for Development of the Understanding of the Concept of Limit},
  url = {http://ftp.fi.muni.cz/pub/muni.cz/EMIS/proceedings/PME31/4/104.pdf},
  year = 2007
}

@article{bob2005historically,
  abstract = {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  -},
  added-at = {2009-10-13T16:39:31.000+0200},
  author = {Burn, Bob},
  biburl = {http://www.bibsonomy.org/bibtex/2dd3e5e3d763c1eb8dc93b43b3321f6e1/yish},
  description = {SpringerLink - Journal Article},
  interhash = {98a01aaa6b037d22116d4b90bfe12038},
  intrahash = {dd3e5e3d763c1eb8dc93b43b3321f6e1},
  journal = {Educational Studies in Mathematics},
  keywords = {learning limit limits mathematics postviva proof sequences},
  month = {#nov#},
  number = 3,
  pages = {269--295},
  timestamp = {2009-10-13T16:39:31.000+0200},
  title = {The Vice: Some Historically Inspired and Proof-Generated Steps to Limits of Sequences},
  url = {http://dx.doi.org/10.1007/s10649-005-7923-6},
  volume = 60,
  year = 2005
}

@inproceedings{bergsten-trying,
  abstract = {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.},
  added-at = {2009-10-13T13:31:56.000+0200},
  address = {Prague, Czech Republic July 16-21},
  author = {Bergsten, Christer},
  biburl = {http://www.bibsonomy.org/bibtex/28fe97e8c081768e8c964b0efc7318b4f/yish},
  booktitle = {Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education},
  interhash = {fce73dea52c0843b428602d6f2b088e7},
  intrahash = {8fe97e8c081768e8c964b0efc7318b4f},
  keywords = {algebra learning limit mathematics postviva reasoning},
  pages = {153-160},
  timestamp = {2009-10-13T13:31:56.000+0200},
  title = {Trying to reach the limit--The role of algebra in mathematical reasoning},
  url = {http://eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/29/8c/0d.pdf#page=161},
  volume = 2,
  year = 2006
}

@article{iliada2009geometric,
  abstract = {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.},
  added-at = {2009-10-13T13:26:44.000+0200},
  author = {Elia, Iliada and Gagatsis, Athanasios and Panaoura, Areti and Zachariades, Theodosis and Zoulinaki, Fotini},
  biburl = {http://www.bibsonomy.org/bibtex/21de3e4c93525437a00608bdfedadf673/yish},
  description = {SpringerLink - Journal Article},
  interhash = {be43812913ba545f7787792de8dfb82c},
  intrahash = {1de3e4c93525437a00608bdfedadf673},
  journal = {International Journal of Science and Mathematics Education},
  keywords = {algebra geometry learning limit mathematics postviva},
  month = {august},
  number = 4,
  pages = {765-790},
  timestamp = {2009-10-13T13:26:44.000+0200},
  title = {GEOMETRIC AND ALGEBRAIC APPROACHES IN THE CONCEPT OF "LIMIT" AND THE IMPACT OF THE "DIDACTIC CONTRACT"},
  url = {http://dx.doi.org/10.1007/s10763-009-9149-z},
  volume = 7,
  year = 2009
}

@article{nardi2008introducing,
  abstract = {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.},
  added-at = {2009-10-13T12:59:02.000+0200},
  author = {Nardi, Elena and Biza, Irene and González-Martín, Alejandro},
  biburl = {http://www.bibsonomy.org/bibtex/2196cd967ca3ffd5d05cfc87567a67992/yish},
  booktitle = {Proceedings of the Conference of the British Society for Research into the Learning of Mathematics},
  interhash = {2d5f8ea4b32b9b216c0fbfb410e6732f},
  intrahash = {196cd967ca3ffd5d05cfc87567a67992},
  keywords = {Infinite application curiculum limit mathematics postviva sequences sum university visualization},
  number = 3,
  pages = {84-89},
  timestamp = {2009-10-13T12:59:02.000+0200},
  title = {Introducing the concept of infinite sum: Preliminary analyses of curriculum content},
  url = {http://www.bsrlm.org.uk/IPs/ip28-3/BSRLM-IP-28-3-15.pdf},
  volume = 28,
  year = 2008
}

@article{roh2008students,
  abstract = {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.},
  added-at = {2009-10-13T12:56:16.000+0200},
  author = {Roh, Kyeong Hah},
  biburl = {http://www.bibsonomy.org/bibtex/23315068315375ac16211ce3e492089fa/yish},
  interhash = {44f2efd9c0511eae64a9e04185518d46},
  intrahash = {3315068315375ac16211ce3e492089fa},
  journal = {Educational Studies in Mathematics},
  keywords = {Asymptotes Images Limits Sequences cognition definitions learning limit mathematics postviva sequences teaching visual visualization},
  number = 3,
  pages = {217--233},
  publisher = {Springer},
  timestamp = {2009-10-13T12:56:16.000+0200},
  title = {Students' images and their understanding of definitions of the limit of a sequence},
  url = {http://www.springerlink.com/content/r08p62229u377k24/},
  volume = 69,
  year = 2008
}