%0 Book Section %1 citeulike:379347 %A Balacheff, Nicolas %A Kaput, James J. %B International Handbook of Mathematics Education %C Dordrect, NL %D 1996 %E Bishop, Alan J. %E Keitel, Christine %E Kilpatrick, Jeremy %E Laborde, Colette %I Kluwer academic publishers %K CnE07 ILE ai algebra arithmetic artificial calculus collaborative computation computers curriculum distance education geometrystatistics gmx intelligencemodeling learning mathematics mathgamespatterns microworlds mythesis proof review tel transposition %P 469-504 %T Computer-Based Learning Environments in Mathematics %U http://www.simcalc.umassd.edu/downloads/internhandbook.pdf %X Computer-Based Learning Environments in Mathematics Nicolas Balacheff & James J. Kaput This chapter attempts to set a perspective on where interactive technologies have taken us and where they seem to be headed. After briefly reviewing their impact in different mathematical domains, including arithmetic, algebra, geometry, statistics, and calculus, we examine what we believe to be the sources of technology's power, which we feel is primarily epistemological. While technology's impact on daily practice has yet to match expectations from two or three decades ago, it's epistemological impact is deeper than expected. This impact is based in a reification of mathematical objects and relations that students can use to act more directly on these objects and relations than ever before. This new mathematical realism, when coupled with the fact that the computer becomes a new partner in the didactical contract, forces us to extend the didactical transposition of mathematics to a computational transposition. This new realism also drives ever deeper changes in the curriculum, and it challenges widely held assumptions about what mathematics is learnable by which students, and when they may learn it. We also examine the limits of Artificial Intelligence and microworlds and how these may be changing. We close by considering the newer possibilities offered by the internet and its dramatic impact on connections among learners, teachers, and the immense resources that are becoming available to both. Our conclusion is that we are very early in the technological transformation and that we desperately need research in all aspects of teaching and learning with technology.

@incollection{citeulike:379347, abstract = {Computer-Based Learning Environments in Mathematics Nicolas Balacheff \& James J. Kaput This chapter attempts to set a perspective on where interactive technologies have taken us and where they seem to be headed. After briefly reviewing their impact in different mathematical domains, including arithmetic, algebra, geometry, statistics, and calculus, we examine what we believe to be the sources of technology's power, which we feel is primarily epistemological. While technology's impact on daily practice has yet to match expectations from two or three decades ago, it's epistemological impact is deeper than expected. This impact is based in a reification of mathematical objects and relations that students can use to act more directly on these objects and relations than ever before. This new mathematical realism, when coupled with the fact that the computer becomes a new partner in the didactical contract, forces us to extend the didactical transposition of mathematics to a computational transposition. This new realism also drives ever deeper changes in the curriculum, and it challenges widely held assumptions about what mathematics is learnable by which students, and when they may learn it. We also examine the limits of Artificial Intelligence and microworlds and how these may be changing. We close by considering the newer possibilities offered by the internet and its dramatic impact on connections among learners, teachers, and the immense resources that are becoming available to both. Our conclusion is that we are very early in the technological transformation and that we desperately need research in all aspects of teaching and learning with technology.}, added-at = {2008-05-30T01:21:02.000+0200}, address = {Dordrect, NL}, author = {Balacheff, Nicolas and Kaput, James J.}, biburl = {https://www.bibsonomy.org/bibtex/2eec581c8c1df985827fe97833f2923d8/yish}, booktitle = {International Handbook of Mathematics Education}, citeulike-article-id = {379347}, comment = {page 21: describe a game called "parade" which has many similarities with guess my graph. Students use a simulation environment to generate motion graphs, then exchange these with peers across the internet. The challange is to reproduce the graph generated by the other group.}, editor = {Bishop, Alan J. and Keitel, Christine and Kilpatrick, Jeremy and Laborde, Colette}, interhash = {b292e8929e02e478080763f934b1c514}, intrahash = {eec581c8c1df985827fe97833f2923d8}, keywords = {CnE07 ILE ai algebra arithmetic artificial calculus collaborative computation computers curriculum distance education geometrystatistics gmx intelligencemodeling learning mathematics mathgamespatterns microworlds mythesis proof review tel transposition}, pages = {469-504}, priority = {5}, publisher = {Kluwer academic publishers}, timestamp = {2008-05-30T01:21:03.000+0200}, title = {Computer-Based Learning Environments in Mathematics}, url = {http://www.simcalc.umassd.edu/downloads/internhandbook.pdf}, year = 1996 }