@incollection{Mor03,
  added-at = {2011-02-04T12:44:42.000+0100},
  address = {Latvia},
  author = {Mor, Yishay and Sendova, Evgenia},
  biburl = {http://www.bibsonomy.org/bibtex/28392e8921413ba470274903d88938bb8/yish},
  booktitle = {History and Education in Mathematics and Informatics, Attracting Talent to Science; Proceedings of the International Congress MASSEE 2003, september 15-21, Borovets, Bulgaria},
  citeulike-article-id = {378268},
  editor = {Derzhanski, I. and Dimitrova, N. and Grozdev, S. and Sendova, Evgenia},
  interhash = {10d5ca8f993ec1e75bbaf13852891d09},
  intrahash = {8392e8921413ba470274903d88938bb8},
  keywords = {2004 cerme2005 cscl-2005 gmr guess-my-rule haifa-edtech ijceell06 ijtme2006 mathgamespatterns micromath my myown mythesis noe-kaleidoscope number polonsky sequences toontalk weblabs},
  priority = {0},
  publisher = {University of Latvia},
  timestamp = {2011-02-04T12:44:42.000+0100},
  title = {ToonTalking about Mathematics},
  url = {http://www.weblabs.eu.com/papers/ToonTalking_Mor_Sendova.pdf},
  year = 2003
}

@inproceedings{Mor05c,
  abstract = {This paper describes the iterative design of a web-based collaborative workspace used in
educational practice, called WebReports. The system’s unique feature is that it allows participants to
discuss mathematical and scientific concepts using programmed animated and interactive models of their
ideas. Rather than focusing on the specific features of the collaboration tool, we analyze it as part of a
constructionist activity system. We describe the context in which the system was developed and used and
compare our approach to previous research in the field. Further, we then present two scenarios which
demonstrate the system in action. Following that, we attempt to map our cases to an activity theory
framework. We highlight several issues in the process of the systems’ development, where the contradictions between the WebReports system and other elements in the activity system shaped its design, and comment on several issues which go beyond the activity theory framework.},
  added-at = {2011-02-04T12:44:11.000+0100},
  address = {Taipei, Taiwan},
  author = {Mor, Yishay and Tholander, Jakob and Holmberg, Jesper},
  biburl = {http://www.bibsonomy.org/bibtex/202dbc4c36ff5d259d0035992fed6ebee/yish},
  booktitle = {The 10th Computer Supported Collaborative Learning (CSCL) conference (2005)},
  citeulike-article-id = {378269},
  editor = {Koschmann, Timothy and Suthers, Daniel D. and Chan, Tak-Wai},
  interhash = {03b2e66b6177b29017115cbd8bcb8fca},
  intrahash = {02dbc4c36ff5d259d0035992fed6ebee},
  keywords = {activity collaboration constructionism cscl design experiment gmr haifa-edtech ijceell06 ijtme2006 iterative my myown mythesis noe-kaleidoscope sequences-ictmt7 theory thesis toontalk web-based weblabs webreports},
  pages = {450 - 459},
  priority = {0},
  publisher = {Lawrence Erlbaum Associates},
  timestamp = {2011-02-04T12:44:11.000+0100},
  title = {Designing for cross-cultural web-based knowledge building},
  url = {http://www.telearn.org/open-archive/browse?resource=238},
  year = 2006
}

@inproceedings{Mor04b,
  abstract = {This paper proposes a narrative-oriented approach to the design of educational activities, as well as a CSCL system to support them, in the context of learning mathematics. Both Mathematics and interface design seem unrelated to narrative. Mathematical language, as we know it, is devoid of time and person. Computer interfaces are static and non-linear. Yet, as Bruner (1986; 1990) and others show, narrative is a powerful cognitive and epistemological tool. The questions we wish to explore are – • If, and how, can mathematical meaning be expressed in narrative forms – without compromising rigour? • What are the narrative aspects of user interface? How can interface design be guided by notions of narrative? • How can we harness the power of narrative in teaching mathematics, in a CSCL environment? We begin by giving a brief account of the use of narrative in educational theory. We will describe the environment and tools used by the WebLabs project, and report on one of our experiments. We will then describe our narrative-oriented framework, by using it to analyze both the environment and the experiment described.},
  added-at = {2011-02-04T12:44:02.000+0100},
  address = {Lausanne, Switzerland},
  author = {Mor, Yishay and Noss, Richard},
  biburl = {http://www.bibsonomy.org/bibtex/22b568b95028d4120d7411746160b4715/yish},
  booktitle = {proceedings of the 1st CSCL SIG Symposium},
  citeulike-article-id = {378265},
  interhash = {3e8b1597c3b2333eee5ab9dddb993b0b},
  intrahash = {2b568b95028d4120d7411746160b4715},
  keywords = {constructionism cscl-2005 gmr haifa-edtech ijtme2006 joe999 learning mathematics mathgamespatterns maths my myown mythesis narrative noe-kaleidoscope sequences sequences-esm toontalk weblabs webreports},
  priority = {0},
  timestamp = {2011-02-04T12:44:02.000+0100},
  title = {Towards a narrative-oriented framework for designing mathematical learning},
  url = {http://www.weblabs.eu.com/papers/KAL-CSCL04.MorNoss.pdf},
  year = 2004
}

@article{Mor06a,
  abstract = {This paper reports on a design experiment in the domain of number sequences conducted in the course of the WebLabs project. We iteratively designed and tested a set of activities and tools in which 10-14 year old students used the ToonTalk programming environment to construct models of sequences and series, and then shared their models and their observations about them utilising a web-based collaboration system. We report on the evolution of a design pattern (programming method) called “Streams” which enables students to engage in the process of summing and “hold the series in their hand”, and consequently make sophisticated arguments regarding the mathematical structures of the sequences without requiring the use of algebra. While the focus of this paper is mainly on the design of activities and its epistemological foundations, we include some illustrative examples of one group of students' work, which indicate the potential of the activities and tools for expressing and reflecting on deep mathematical ideas.},
  added-at = {2011-02-04T12:43:34.000+0100},
  author = {Mor, Yishay and Noss, Richard and Hoyles, Celia and Kahn, Ken and Simpson, Gordon},
  biburl = {http://www.bibsonomy.org/bibtex/2f7705204cb381d4853cffcde77b6a57a/yish},
  citeulike-article-id = {387332},
  interhash = {44ee2fd1011d1d8cf560e3f4a53b51b3},
  intrahash = {f7705204cb381d4853cffcde77b6a57a},
  journal = {the International Journal for Technology in Mathematics Education},
  keywords = {CiHB ILE KalDesignResearch PlanetMakingStuffTogether algebra cerme6 constructionism design gmr haifa-edtech ijtme2006 learning mathematics maths my myown mythesis noe-kaleidoscope number polonsky selected sequences sequnces toontallk top weblabs webreports},
  number = 2,
  pages = {65-78},
  priority = {0},
  timestamp = {2011-02-04T12:43:34.000+0100},
  title = {Designing to see and share structure in number sequences},
  url = {http://telearn.noe-kaleidoscope.org/open-archive/browse?resource=237},
  volume = 13,
  year = 2006
}

@inproceedings{Hoyles05,
  added-at = {2011-02-04T12:43:11.000+0100},
  address = {Bristol},
  author = {Hoyles, Celia and Kahn, Ken and Mor, Yishay and Noss, Richard and Sendova, Evgenia and Sacristán, Ana I. and Simpson, Gordon},
  biburl = {http://www.bibsonomy.org/bibtex/24ffcafc1a0a5cd62c996450cdf197b16/yish},
  booktitle = {the 7th International Conference on Technology in Mathematics Teaching},
  citeulike-article-id = {378254},
  comment = {THE WEBLABS PROJECT: BUILDING NEW FORMALISMS FOR MATHEMATICAL AND SCIENTIFIC IDEAS Richard Noss WEBBING CONNECTIONS BETWEEN STUDENTS’ UNDERSTANDINGS OF POSITION AND VELOCITY GRAPHS Gordon Simpson, Celia Hoyles, Richard Noss A MULTIPLE-REPRESENTATION APPROACH TO EXPLORING SEQUENCES AND CONVERGENCE Yishay Mor, Richard Noss MAKING INFINITY CONCRETE BY PROGRAMMING NEVER-ENDING PROCESSES Ken Kahn, Evgenia Sendova, Ana Isabel Sacristan, Richard Noss},
  interhash = {e397ec0a6399f5a97bc13516dc5a425a},
  intrahash = {4ffcafc1a0a5cd62c996450cdf197b16},
  keywords = {cardinality convergence gmr graph guess haifa-edtech ijtme2006 my myown mythesis noe-kaleidoscope sequences sequences-ictmt7},
  priority = {2},
  timestamp = {2011-02-04T12:43:11.000+0100},
  title = {The WebLabs Project: Building New Formalisms for Mathematical and Scientific Ideas},
  year = 2005
}

@inproceedings{Matos05,
  added-at = {2011-02-04T12:22:25.000+0100},
  address = {Sant Feliu de Guíxols, Spain},
  author = {Matos, João Filipe and Mor, Yishay and Noss, Richard and Santos, Madalena},
  biburl = {http://www.bibsonomy.org/bibtex/21e53996c8c7994f17938350efb409cd8/yish},
  booktitle = {Fourth Congress of the European Society for Research in Mathematics Education (CERME-4)},
  citeulike-article-id = {378260},
  interhash = {be14dd3cb7f193831a6096555075db81},
  intrahash = {1e53996c8c7994f17938350efb409cd8},
  keywords = {IJCEELL communities cscl-2005 gmr gmx haifa-edtech mathgamespatterns my myown mythesis noe-kaleidoscope of polonsky practice sequences weblabs webreports},
  priority = {2},
  timestamp = {2011-02-04T12:22:25.000+0100},
  title = {Sustaining Interaction in a Mathematical Community of Practice},
  url = {http://telearn.noe-kaleidoscope.org/open-archive/browse?resource=533},
  year = 2005
}

@article{mornoss06,
  abstract = { This paper describes a narrative-oriented approach to the design and the analysis of a computational system and a set of activities for mathematical learning. Our central contention is that programming can offer a key to resolving the tension between the different representational structures of narrative and mathematical formalism. In the course of describing our
approach, we make a distinction between the epistemic-cognitive elements of narrative and the social, cultural and affective elements. We then elaborate the theoretical grounds of the individual epistemic facets of narrative. We propose a link between narrative theories of learning and constructionist traditions, specifically the notion of situated abstraction. This link suggests the possibility of further dialogue between the two academic communities },
  added-at = {2011-02-04T12:21:34.000+0100},
  author = {Mor, Yishay and Noss, Richard},
  biburl = {http://www.bibsonomy.org/bibtex/2b54f884125d439beee1afeab9c3ca6fa/yish},
  interhash = {63536356a52ca6953ab75efc57c03285},
  intrahash = {b54f884125d439beee1afeab9c3ca6fa},
  journal = {International Journal of Continuing Engineering Education and Life-Long Learning  (IJCEELL)},
  keywords = {KalDesignResearch TEL cerme6 constructionism eLPBookMor gmr haifa-edtech learning maths my myown mythesis narrative polonsky programming selected sequences top},
  number = 2,
  pages = {214-233},
  timestamp = {2011-02-04T12:21:34.000+0100},
  title = {Programming as Mathematical Narrative},
  url = {http://telearn.noe-kaleidoscope.org/open-archive/browse?resource=493},
  volume = 18,
  year = 2008
}

@article{Mor04,
  added-at = {2011-02-04T12:21:18.000+0100},
  author = {Mor, Yishay and Hoyles, Celia and Kahn, Ken and Noss, Richard and Simpson, Gordon},
  biburl = {http://www.bibsonomy.org/bibtex/235e51249bb837622b3192f1ef9228188/yish},
  citeulike-article-id = {378263},
  interhash = {e1ad973316c6fa060625df13f8cb51c6},
  intrahash = {35e51249bb837622b3192f1ef9228188},
  journal = {Micromath},
  keywords = {GmX IJCEELL cerme2005 cscl-2005 gmr haifa-edtech ijtme2006 mathgamespatterns my myown mythesis noe-kaleidoscope sequences-ictmt7 weblabs webreports},
  number = 2,
  pages = {17-23},
  priority = {2},
  timestamp = {2011-02-04T12:21:18.000+0100},
  title = {Thinking in Progress},
  url = {http://www.lkl.ac.uk/kscope/weblabs/papers/Thinking_in_process.pdf},
  volume = 20,
  year = 2004
}

@incollection{pratt2009,
  abstract = {There has been a growing recognition of the educational potential of computer games. However, it is recognised that the process of designing and deploying technology-enhanced resources in general and games for mathematical learning in particular is a difficult task. This chapter reports on the use of patterns, referred to as p-d patterns, to address this challenge. Based on a review of the literature, a set of typologies of the domain was generated which formed the springboard for the development of over a hundred p-d patterns. These patterns are hierarchical by nature and constitute a pattern language that could be mobilised to facilitate pattern-specific communication and knowledge sharing between communities. Such patterns are, for example, shown to incorporate recurrent themes, such as scaffolding and reflection, instantiated in patterns across both design and deployment. Finally, we will set out how the patterns approach could be consolidated to become the stimulus for a much needed breakthrough in the articulation of how design needs and functionalities constitute theory in the field of designing for learning.},
  added-at = {2009-08-29T17:24:49.000+0200},
  author = {Pratt, Dave D. and Winters, Niall and Cerulli, Michele and Leemkuil, Henny},
  biburl = {http://www.bibsonomy.org/bibtex/2f43bab0e07f697bf2f42e58c67410e77/yish},
  booktitle = {Technology-Enhanced Learning},
  editor = {Balacheff, Nicolas and Ludvigsen, Sten and de Jong, Ton and Lazonder, Ard and Barnes, Sally},
  interhash = {010e8686cde02ecaa42db8f0c6ee9026},
  intrahash = {f43bab0e07f697bf2f42e58c67410e77},
  keywords = {design designpatterns education games gmr gmx learning mathematics mathgamespatterns patterns},
  pages = {215-232},
  publisher = {Springer},
  timestamp = {2009-08-29T17:24:49.000+0200},
  title = {A Patterns Approach to Connecting the Design and Deployment of Mathematical Games and Simulations},
  url = {http://www.springerlink.com/content/v63v2g2012032220/?p=3ab869de11664ad89a0bfc657f802013},
  year = 2009
}

@article{santos:016601,
  added-at = {2009-08-18T15:02:49.000+0200},
  author = {Santos, T. S. and Lee, J. S. and Migdal, P. and Lekshmi, I. C. and Satpati, B. and Moodera, J. S.},
  biburl = {http://www.bibsonomy.org/bibtex/21556420f08672ff4273a3b07b49aaead/stared},
  description = {Room-Temperature Tunnel Magnetoresistance and Spin-Polarized Tunneling through an Organic Semiconductor Barrier},
  doi = {10.1103/PhysRevLett.98.016601},
  eid = {016601},
  interhash = {7005b59bb5c80d77cdff57ffdc472529},
  intrahash = {1556420f08672ff4273a3b07b49aaead},
  journal = {Physical Review Letters},
  keywords = {gmr imported spin tunneling},
  number = 1,
  numpages = {4},
  pages = 016601,
  publisher = {APS},
  timestamp = {2009-08-18T15:02:49.000+0200},
  title = {Room-Temperature Tunnel Magnetoresistance and Spin-Polarized Tunneling through an Organic Semiconductor Barrier},
  url = {http://link.aps.org/abstract/PRL/v98/e016601},
  volume = 98,
  year = 2007
}

@article{Stanton-2007,
  added-at = {2009-04-03T15:00:14.000+0200},
  author = {?},
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	dOUy5rZXlzWk5TLm9iamVjdHOAB6ISE4ACgAOiFRaABIAGWWFsaWFzRGF0YVxyZWxhdGl2ZVBhd
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	yMDA3LnBkZgAADgAiABAAUwB0AGEAbgB0AG8AbgAtADIAMAAwADcALgBwAGQAZgAPABgACwBNAE
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	DIANwA6AD8AQQBTAFwAYgBpAHAAeACDAIUAiACKAIwAjwCRAJMAnQCqAK8AtwC5AqsCsAK5AsQC
	yALWAt0C5gMsAzEDNAAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAANB},
  biburl = {http://www.bibsonomy.org/bibtex/2f39ba202cf6d1cbb6fc1fb2d4273f792/gdurin},
  date-added = {2008-09-24 15:57:45 +0200},
  date-modified = {2008-09-24 15:59:23 +0200},
  description = {Domain wall dynamics in nanowires},
  interhash = {efaa6bd8a9b46ba00edd3070ca9fbf75},
  intrahash = {f39ba202cf6d1cbb6fc1fb2d4273f792},
  journal = {IEEE TRANSACTIONS ON MAGNETICS},
  keywords = {GMR JEMS08, measurements},
  month = {JUNE},
  number = 6,
  pages = 2767,
  timestamp = {2009-04-03T15:00:14.000+0200},
  title = {A Portable Technique for the Contactless Measurement of Magnetoresistance
	Using Infrared Fiber Optics},
  volume = 43,
  year = 2007
}

@inproceedings{citeulike:481528,
  abstract = {We present classroom research on a variant of the guess-my-rule game, in which nine-yearl-old students make up linear functions and challenge classmates to determine their secret rule. We focus on issues students and their teacher confronted in inferring underlying rules and in deciding whether the conjectured rule matched the rule of the creators. We relate the findings to the tension between semantically and syntactically driven algebraic reasoning.},
  added-at = {2008-05-30T02:25:09.000+0200},
  address = {Honolulu, HI},
  author = {Carraher, David W. and Earnest, Darrell},
  biburl = {http://www.bibsonomy.org/bibtex/223a821c366b42e64816d5fa6744e922f/yish},
  booktitle = {Proceedings of the 27th International Conference for the Psychology of Mathematics Education},
  citeulike-article-id = {481528},
  comment = {"The Guess My Rule game suggested itself as a promising context for getting students to focus on written algebraic notation as an object of discussion because students would have to compare expressions written by the rule makers with those posed by the rule guessers and decide whether certain variations express the same or different underlying

rules.





The Guess-my-Rule game has often been used in mathematics education at different

grade levels as a way to introduce children to linear functions (see, for example, Davis, 1967, 1985; Carraher, Schliemann, \& Brizuela, 2001, 2003; Schliemann, Carraher, \& Brizuela, 2003). This activity essentially provides students with values from a function's domain (input) and the corresponding value from the range (output); based on the data, students try to infer the function. In order to play the Guess My Rule game, students must accept that: 1) each input must result in a single output; and 2) a function is consistently used for all values of the solution set, that is, the rule cannot change.

---

Analysis of the classes of rules chosen by students.

---

"There was some evidence that third grade students from an urban public school with a

prior background in early algebra activities based on functions and modeling could begin

the transition from semantically driven to syntactically driven algebraic reasoning. We

would hope to see students taking part in more prolonged and in depth debates about

equivalent functions and identities. Furthermore, although students may initially find

persuasive the fact that two rules produce the same output from a set of input values,

eventually they need to abandon this approach and move towards proving the functions

are equivalent. The discussion about ¥4 ¥5 simplifying to ¥20 exemplifies this sort of

shift. But graphing the data may prove useful in lending meaning to the rules and

(dis)proving their equivalence. Ultimately, we want students to be able to operate on

equations in ways that preserve the solution set without having to resort to thinking about

the original situations that gave rise to the equations. This does not mean that students

should abandon, once and for all, semantically driven reasoning, for it may prove useful

in other contexts, even some that entail the use of advanced mathematical reasoning. We

look forward to encountering additional research that explores the transition and tension

between semantically driven and syntactically driven mathematical reasoning."},
  interhash = {137706fa4d50389288ede2b787e8114f},
  intrahash = {23a821c366b42e64816d5fa6744e922f},
  keywords = {games gmr gmx learning mathematics mathgamespatterns mythesis},
  priority = {0},
  timestamp = {2008-05-30T02:25:09.000+0200},
  title = {Guess My Rule Revisited},
  url = {http://www2.earlyalgebra.terc.edu/our_papers/2003/Carraher_EarnestPME2003.pdf},
  year = 2003
}

@article{Weigand91,
  added-at = {2008-05-30T01:00:20.000+0200},
  author = {Weigand, Hans G.},
  biburl = {http://www.bibsonomy.org/bibtex/29304403554988e421ed22aa85cf7d658/yish},
  citeulike-article-id = {532472},
  comment = {focus on iteration sequences, a_n = f(a_n-1), and providing alternative graphical representations for them.},
  interhash = {8efaa6524691adc5dcc01abe961b2471},
  intrahash = {9304403554988e421ed22aa85cf7d658},
  journal = {Educational Studies in Mathematics},
  keywords = {gmr have ijtme2006 iteration mythesis paper scalar-functional sequences},
  number = 1,
  pages = {411-437},
  priority = {2},
  timestamp = {2008-05-30T01:00:20.000+0200},
  title = {Iteration Sequences and their Representations},
  volume = 22,
  year = 1991
}

@article{miyazaki,
  added-at = {2008-01-31T23:53:26.000+0100},
  author = {Miyazaki, T. and Tezuka, N.},
  biburl = {http://www.bibsonomy.org/bibtex/2f65441194fea4c82ee328e68ba2c5435/srd27},
  date = {Issue 3, 2 January 1995},
  interhash = {7c2f16632a4f3741296bfe33c48befab},
  intrahash = {f65441194fea4c82ee328e68ba2c5435},
  journal = {Journal of Magnetism and Magnetic Materials},
  keywords = {GMR},
  number = 3,
  tech = {Pages L 231-L 234 T. Miyazaki and N. Tezuka},
  timestamp = {2008-01-31T23:53:26.000+0100},
  title = {Giant magnetic tunneling effect in Fe/Al2O3/Fe junction},
  volume = 139,
  year = 1995
}

@article{Hoyles91,
  abstract = {This paper presents some findings of research into the discussion between pupils in computer and non-computer environments. The research was concerned with analysing the processes whereby pairs of pupils came to make mathematical generalizations in three environments, LOGO, spreadsheet and paper and pencil. Critical decisions in the generalization process were identified in order to allow comparisons to be made across environments. The analysis reveals differences in the effects of task environment on the negotiation of the mathematical generalization particularly in relation to the part played by formalization.},
  added-at = {2006-06-05T02:47:21.000+0200},
  author = {Hoyles, Celia and Healy, Lulu and Sutherland, Rosamund},
  biburl = {http://www.bibsonomy.org/bibtex/223764ea6b804494d735b4e2f87311bf6/yish},
  citeulike-article-id = {396766},
  comment = {patterns in the descriptive / analytic sense},
  interhash = {ecc387af176f9bd0e30e064ad73a7093},
  intrahash = {23764ea6b804494d735b4e2f87311bf6},
  journal = {Journal of Computer Assisted Learning},
  keywords = {aided computer education gmr gmx instruction learning logo mathematics mathgamespatterns need problem read solving spreadsheets},
  number = 4,
  pages = {210--228},
  priority = {2},
  timestamp = {2006-06-05T02:47:21.000+0200},
  title = {Patterns of discussion between pupil pairs in computer and non-computer environments},
  volume = 7,
  year = 1991
}

@incollection{Mason96,
  added-at = {2006-03-07T17:56:12.000+0100},
  address = {Dordrecht},
  author = {Mason, John},
  biburl = {http://www.bibsonomy.org/bibtex/20972426ba1c32f09551479c9e17fa701/yish},
  booktitle = {Approaches to Algebra: Perspectives for Research and Teaching},
  citeulike-article-id = {379239},
  comment = {"Generalization is the heartbeat of mathematics, and appears in many forms. If teachers are unaware of its presence, and are not in the habit of getting students to work at expressing their own generalizations, then mathematics is not taking place." "The reason for emphasizing expression of generality in number patterns is only to provide experiences which highlight the process." p. 65 Identifies four principle roots of algebra: Expressing generality Possibilities and constraints (supporting awareness of variable) Rearranging and Manipulating (seeing why different expressions for the same thing do in fact give the same answer) Generalized Arithmetic (traditional letters in place of numbers to express the rules of arithmetic) (p 66) ME: all these are manifested in GmR.},
  editor = {Bednarz, Nadine and Kieran, Carolyn and Lee, Lesley},
  interhash = {b1c1d081c98e2f41f2c76f36b6cee0b6},
  intrahash = {0972426ba1c32f09551479c9e17fa701},
  keywords = {algebra ch2 generalization gmr ijtme2006 mythesis patterns sequences sequences-ictmt7},
  pages = {65--86},
  priority = {2},
  publisher = {Kluwer Academic Publishers},
  timestamp = {2006-03-07T17:56:12.000+0100},
  title = {Expressing generality and roots of algebra},
  url = {http://print.google.com/print?id=koZG1cmE2nAC\&pg=PA65},
  year = 1996
}