%0 Journal Article %1 carraher2001cys %A Carraher, D. %A Schliemann, A. %A Brizuela, B. %D 2001 %J Proceedings of the XXV Conference of the International Group for the Psychology of Mathematics Education %K algebra drawing early learning mathematics mythesis notation semiotics sketching %P 130--140 %T Can young students operate on unknowns %U http://www2.earlyalgebra.terc.edu/our_papers/2001/Carraher_et_all_PME2001.pdf %V 1 %X Algebra instruction has traditionally been delayed until adolescence because of mistaken assumptions about the nature of arithmetic and about young students' capabilities. Arithmetic is algebraic to the extent that it provides opportunities for making and expressing generalizations. We provide examples of nine-year-old children using algebraic notation to represent a problem of additive relations. They not only operate on unknowns; they can understand the unknown to stand for all of the possible values that an entity can take on. When they do so, they are reasoning about variables.

@article{carraher2001cys, abstract = {Algebra instruction has traditionally been delayed until adolescence because of mistaken assumptions about the nature of arithmetic and about young students' capabilities. Arithmetic is algebraic to the extent that it provides opportunities for making and expressing generalizations. We provide examples of nine-year-old children using algebraic notation to represent a problem of additive relations. They not only operate on unknowns; they can understand the unknown to stand for all of the possible values that an entity can take on. When they do so, they are reasoning about variables.}, added-at = {2008-02-17T17:41:13.000+0100}, author = {Carraher, D. and Schliemann, A. and Brizuela, B.}, biburl = {https://www.bibsonomy.org/bibtex/21159e6c3c3b62af5897a449354c3791a/yish}, interhash = {ba590bbdf3d36eaaee861cc7802fb805}, intrahash = {1159e6c3c3b62af5897a449354c3791a}, journal = {Proceedings of the XXV Conference of the International Group for the Psychology of Mathematics Education}, keywords = {algebra drawing early learning mathematics mythesis notation semiotics sketching}, pages = {130--140}, timestamp = {2008-04-27T15:58:15.000+0200}, title = {{Can young students operate on unknowns}}, url = {http://www2.earlyalgebra.terc.edu/our_papers/2001/Carraher_et_all_PME2001.pdf}, volume = 1, year = 2001 }