%0 Journal Article %1 Mor06a %A Mor, Yishay %A Noss, Richard %A Hoyles, Celia %A Kahn, Ken %A Simpson, Gordon %D 2006 %J the International Journal for Technology in Mathematics Education %K 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 %N 2 %P 65-78 %T Designing to see and share structure in number sequences %U http://telearn.noe-kaleidoscope.org/open-archive/browse?resource=237 %V 13 %X 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.

@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 = {https://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 = {2011-07-28T13:19:30.000+0200}, 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 }