%0 Book Section %1 Mason96 %A Mason, John %B Approaches to Algebra: Perspectives for Research and Teaching %C Dordrecht %D 1996 %E Bednarz, Nadine %E Kieran, Carolyn %E Lee, Lesley %I Kluwer Academic Publishers %K algebra ch2 generalization gmr ijtme2006 mythesis patterns sequences sequences-ictmt7 %P 65--86 %T Expressing generality and roots of algebra %U http://print.google.com/print?id=koZG1cmE2nAC&pg=PA65

@incollection{Mason96, added-at = {2006-03-07T17:56:12.000+0100}, address = {Dordrecht}, author = {Mason, John}, biburl = {https://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 = {2008-04-27T02:42:22.000+0200}, title = {Expressing generality and roots of algebra}, url = {http://print.google.com/print?id=koZG1cmE2nAC\&pg=PA65}, year = 1996 }