@article{Noss97, title = {The Construction of Mathematical Meanings: Connecting the Visual with the Symbolic}, author = {Richard Noss and Lulu Healy and Celia Hoyles}, journal = {Educational Studies in Mathematics}, number = {2}, pages = {203-233}, url = {http://www.lkl.ac.uk/rnoss/MA/Mathsticks.doc}, volume = {33}, year = {1997}, biburl = {http://www.bibsonomy.org/bibtex/2dcc7eb49adf07d481e46a8689b26e8c9/yish}, abstract = {In this paper, we explore the relationship between learners‘ actions, visualisations and the means by which these are articulated. We describe a microworld, Mathsticks, designed to help students construct mathematical meanings by forging links between the rhythms of their actions and the visual and corresponding symbolic representations they developed. Through a case study of two students interacting with Mathsticks, we illustrate a view of mathematics learning which places at its core the medium of expression, and the building of connections between different mathematisations rather than ascending to hierarchies of decontextualisation.}, comment = {"While most students are able to identify a great variety of patterns (Stacey, 1989), many of these patterns do not readily lend themselves either to the expression of a functional relationship or to an algebraic representation in any straightforward way (Lee and Wheeler, 1987). Indeed, students who are able to apply a correct method to any number of specific cases often cannot articulate a general pattern or relationship in natural language (see, for example, MacGregor and Stacey, 1992), and expression in algebraic symbolism is still more problematic. There is also a question mark over the status of the algebraic expression even if it is successfully constructed by the student. Lee and Wheeler (1987) suggest that it is rare for those students who do produce algebraic representation to check these expressions - even empirically by substituting in particular examples. Stacey (1989) found that only a small proportion of students responded to requests for explanation by providing mathematical justification and, similarly, Arzarello (1991) pointed to students' difficulties in providing mathematically valid justification of their suggested algebraic rules. Taken together, the evidence suggests that algebraic formulation is often disconnected from the activity which precedes it, a meaningless extra that neither illuminates the problem nor provides a means for validating its solution. Algebra is viewed as an endpoint, a problem solution in itself rather than a tool for problem solving." p 204}, keywords = {abstraction construction ijceell06 ijtme2006 matchsticks mathematical meanings mythesis situated symbolic visual } } @article{citeulike:154630, title = {Designing a programming-based approach for modelling scientific phenomena}, author = {Gordon Simpson and Celia Hoyles and Richard Noss}, journal = {Journal of Computer Assisted Learning}, month = {April}, number = {2}, pages = {143-158}, publisher = {Blackwell Publishing}, url = {http://dx.doi.org/10.1111/j.1365-2729.2005.00121.x}, volume = {21}, year = {2005}, biburl = {http://www.bibsonomy.org/bibtex/23d82349dd3082ec040f4861b2624681e/yish}, abstract = {We describe an iteratively designed sequence of activities involving the modelling of one-dimensional collisions between moving objects based on programming in ToonTalk. Students aged 13–14 years in two settings (London and Cyprus) investigated a number of collision situations, classified into six classes based on the relative velocities and masses of the colliding objects. We describe iterations of the system in which students engaged in a repeating cycle of activity for each collision class: prediction of object behaviour from given collision conditions, observation of a relevant video clip, building a model to represent the phenomena, testing, validating and refining their model, and publishing it – together with comments – on our web-based collaboration system, WebReports. Students were encouraged to consider the limitations of their current model, with the aim that they would eventually appreciate the benefit of constructing a general model that would work for all collision classes, rather than a different model for each class. We describe how our intention to engage students with the underlying concepts of conservation, closed systems and system states was instantiated in the activity design, and how the modelling activities afforded an alternative representational framework to traditional algebraic description.}, issn = {0266-4909}, citeulike-article-id = {154630}, priority = {2}, doi = {10.1111/j.1365-2729.2005.00121.x}, keywords = {1d ILE collision constructionism design education ijceell06 ijtme2006 mythesis physics weblabs webreports } } @article{Mor04, title = {Thinking in Progress}, author = {Yishay Mor and Celia Hoyles and Ken Kahn and Richard Noss and Gordon Simpson}, journal = {Micromath}, number = {2}, pages = {17-23}, url = {http://www.lkl.ac.uk/kscope/weblabs/papers/Thinking_in_process.pdf}, volume = {20}, year = {2004}, biburl = {http://www.bibsonomy.org/bibtex/235e51249bb837622b3192f1ef9228188/yish}, priority = {2}, citeulike-article-id = {378263}, keywords = {GmX IJCEELL cerme2005 cscl-2005 gmr ijtme2006 mathgamespatterns my mythesis noe-kaleidoscope sequences-ictmt7 weblabs webreports } } @article{simpson06, title = {Exploring the mathematics of motion through construction and collaboration}, author = {Gordon Simpson and Celia Hoyles and Richard Noss}, journal = {Journal of Computer Assisted Learning}, number = {2}, pages = {114-136}, url = {http://www.blackwell-synergy.com/doi/abs/10.1111/j.1365-2729.2006.00164.x}, volume = {22}, year = {2006}, biburl = {http://www.bibsonomy.org/bibtex/218e587a4a9d49017c60eca4464daeb7e/yish}, abstract = {In this paper we give a detailed account of the design principles and construction of activities underlying a model-based approach to learning about the relationships between position, velocity and acceleration, and corresponding kinematics graphs. In these activities, students controlled the movement of objects in a programming environment, recording the motion data and plotting corresponding position-time and velocity-time graphs. They shared their findings on a specially-designed web-based collaboration system, and posted cross-site challenges to which others could react. We present learning episodes that provide evidence of students making discoveries about the relationships between different representations of motion. We conjecture that these discoveries arose from their activity in building models of motion and their participation in classroom and online community.}, citeulike-article-id = {490065}, priority = {2}, keywords = {PlanetMakingStuffTogether communication computer constructionism game ijtme2006 learning lunarlander mathematics mathgamespatterns modelling mythesis programming science weblabs webreports } } @article{TMMKTCR, title = {The Microevolution of Mathematical Knowledge: The Case of Randomness}, author = {David Pratt and Richard Noss}, journal = {Journal of the Learning Sciences}, number = {4}, pages = {453-488}, url = {http://www.leaonline.com/doi/abs/10.1207/S15327809JLS1104_2}, volume = {11}, year = {2002}, biburl = {http://www.bibsonomy.org/bibtex/25823c499fc30baf7e96127cea1f85370/yish}, abstract = {In this article, we explore the growth of mathematical knowledge and in particular, seek to clarify the relation between abstraction and context. Our method is to gain a deeper appreciation of the process by which mathematical abstraction is achieved and the nature of abstraction itself, by connecting our analysis at the level of observation with a corresponding theoretical analysis at an appropriate grain size. In this article, we build on previous work to take a further step toward constructing a viable model of the microevolution of mathematical knowledge in context. The theoretical model elaborated here is grounded in data drawn from a study of 10 to 11 year olds' construction of meanings for randomness in the context of a carefully designed computational microworld, whose central feature was the visibility of its mechanisms-how the random behavior of objects actually "worked." In this article, we illustrate the theory by reference to a single case study chosen to illuminate the relation between the situation (including, crucially, its tools and tasks) and the emergence of new knowledge. Our explanation will employ the notion of situated abstraction as an explanatory device that attempts to synthesize existing micro- and macrolevel descriptions of knowledge construction. One implication will be that the apparent dichotomy between mathematical knowledge as decontextualized or highly situated can be usefully resolved as affording different perspectives on a broadening of contextual neighborhood over which a network of knowledge }, keywords = {Boxer KalDesignResearch mathematical mythesis randomness } } @book{citeulike:493437, title = {Windows on Mathematical Meanings : Learning Cultures and Computers}, address = {Dordrecht}, author = {Richard Noss and Celia Hoyles}, howpublished = {Hardcover}, month = {June}, publisher = {Kluwer Academic}, url = {http://www.amazon.fr/exec/obidos/ASIN/0792340736/citeulike04-21}, year = {1996}, biburl = {http://www.bibsonomy.org/bibtex/224490771b2cdaed75b12c9218ac9ec7b/yish}, abstract = {{Why are mathematical ideas so hard? Is mathematics an unassailable peak, which only the few can ever hope to conquer? Or can mathematics be broadened to be accessible to the many? Noss and Hoyles have written a book which challenges some of the conventional wisdoms on the learning of mathematics. They use the computer as a window onto mathematical meaning-making, drawing together the threads of their individual and collaborative research over more than a decade. The pivot of their theory is the idea of webbing, which explains how someone struggling with a new mathematical idea can draw on supportive knowledge, and reconciles the individual's role in mathematical learning with the part played by epistemological, social and cultural forces.}}, citeulike-article-id = {493437}, priority = {2}, isbn = {0792340736}, keywords = {CiHB ILE KalDesignResearch PlanetMakingStuffTogether abstraction constructionism ijceell06 ijtme2006 mathgamespatterns microworlds mythesis situated } } @book{noss2005, title = {Entwicklungsorientiertes Technologie-Management}, address = {Kovaÿéc}, annote = {XI, 396 S}, author = {{Christian} Noss}, howpublished = {Hamburg}, url = {http://gso.gbv.de/DB=2.1/CMD?ACT=SRCHA&SRT=YOP&IKT=1016&TRM=ppn+484939092&sourceid=fbw_bibsonomy}, year = {2005}, biburl = {http://www.bibsonomy.org/bibtex/2925cfb31d88bb3d7e46e89b66f7200e3/fbw}, description = {imported}, isbn = {3-8300-1831-2}, keywords = {imported } } @techreport{webreports, title = {Technical Infrastructure: The WebReports site}, author = {Gordon Simpson and Yishay Mor and Jesper Holmberg and Richard Noss and Jakob Tholander and Ken Kahn and Celia Hoyles}, institution = {London Knowledge Lab}, type = {project report}, url = {http://telearn.noe-kaleidoscope.org/open-archive/browse?resource=335}, year = {2007}, biburl = {http://www.bibsonomy.org/bibtex/26ba056ca751e97c19c9fca45e1447425/yish}, abstract = {The WebReports website allows children to create text-based and interactive content that is accessible on line and to comment on each other’s work, thereby being provided with opportunities to collaboratively build knowledge around a range of different learning domains. In this document we first summarise our key findings. We then provide an account of the evolution of the system during the three years of the project, giving the rationale for our major changes. Finally, we describe the functionality and architecture of the final version of the WebReports system. Project web site: http://www.lkl.ac.uk/kscope/weblabs/ See also: Yishay Mor, Jakob Tholander and Jesper Holmberg (2005) Designing for cross-cultural web-based knowledge building (http://telearn.org/open-archive/browse?resource=238_v1). The 10th Computer Supported Collaborative Learning (CSCL) conference Yishay Mor, Richard Noss, Celia Hoyles, Ken Kahn and Gordon Simpson (2006). Designing to see and share structure in number sequences (http://telearn.org/open-archive/browse?resource=237_v1). the International Journal for Technology in Mathematics Education, (13)2:65-78, Gordon Simpson, Celia Hoyles and Richard Noss. Exploring the mathematics of motion through construction and collaboration (http://telearn.org/open-archive/browse?resource=202_v1). Journal of Computer Assisted Learning, (22)2:114-136}, keywords = {infrastructure learning mythesis technical weblabs webreports } } @incollection{KaputNossHoyles02, title = {Developing new notations for a learnable mathematics in the computational era}, address = {London}, author = {James J Kaput and Richard Noss and Celia Hoyles}, booktitle = {Handbook of International Research in Mathematics Education}, editor = {L English}, pages = {51-75}, publisher = {Lawrence Erlbaum}, url = {http://www.lkl.ac.uk/rnoss/papers/DevelopingNewNotations.pdf}, year = {2002}, biburl = {http://www.bibsonomy.org/bibtex/2f0f560b7ec45dfb2ba2e5c3a5ab3eb8d/yish}, abstract = {Not for the first time we are at a turning point in intellectual history. The appearances of new computational forms and literacies are pervading the social and economic lives of individuals and nations alike. Yet nowhere is this upheaval correspondingly represented in educational systems, in classrooms, or in school curricula. As far as mathematics is concerned, the massive changes to mathematics that characterize the late twentieth century—in terms of the way it is done, and what counts as mathematics—are almost invisible in the classrooms of our schools and, to only a slightly lesser extent, our universities.}, keywords = {IJCEELL computational constructionism learning mathematics mythesis notation representation } } @inproceedings{conf/ct/GoldsteinKNP01, title = {Building Rules.}, author = {Ronnie Goldstein and Ivan Kalas and Richard Noss and Dave Pratt}, booktitle = {Cognitive Technology}, crossref = {conf/ct/2001}, editor = {Meurig Beynon and Chrystopher L. Nehaniv and Kerstin Dautenhahn}, pages = {267-281}, publisher = {Springer}, series = {Lecture Notes in Computer Science}, url = {http://link.springer.de/link/service/series/0558/bibs/2117/21170267.htm}, volume = {2117}, year = {2001}, biburl = {http://www.bibsonomy.org/bibtex/295d26ec13ef82d5e190b7c1a17a44870/yish}, abstract = {This paper reports on aspects of the Playground project in which young children (age 6 to 8) are writing and sharing their own computer videogames. We discuss how structures in the kernel language influenced the design of one of the project’s playgrounds and in turn children’s thinking and use of rules. One feature of the paper is the range of children’s responses to the task of translating their ideas for games into formal rules; kernel features, such as object orientation and the use of events, at times support and at other times constrain those responses.}, date = {2002-01-03}, isbn = {3-540-42406-7}, keywords = {building constructionism design education games learning playground } }