%0 Conference Paper %1 citeulike:481528 %A Carraher, David W. %A Earnest, Darrell %B Proceedings of the 27th International Conference for the Psychology of Mathematics Education %C Honolulu, HI %D 2003 %K games gmr gmx learning mathematics mathgamespatterns mythesis %T Guess My Rule Revisited %U http://www2.earlyalgebra.terc.edu/our_papers/2003/Carraher_EarnestPME2003.pdf %X We present classroom research on a variant of the guess-my-rule game, in which nine-yearl-old students make up linear functions and challenge classmates to determine their secret rule. We focus on issues students and their teacher confronted in inferring underlying rules and in deciding whether the conjectured rule matched the rule of the creators. We relate the findings to the tension between semantically and syntactically driven algebraic reasoning.

@inproceedings{citeulike:481528, abstract = {We present classroom research on a variant of the guess-my-rule game, in which nine-yearl-old students make up linear functions and challenge classmates to determine their secret rule. We focus on issues students and their teacher confronted in inferring underlying rules and in deciding whether the conjectured rule matched the rule of the creators. We relate the findings to the tension between semantically and syntactically driven algebraic reasoning.}, added-at = {2008-05-30T02:25:09.000+0200}, address = {Honolulu, HI}, author = {Carraher, David W. and Earnest, Darrell}, biburl = {https://www.bibsonomy.org/bibtex/223a821c366b42e64816d5fa6744e922f/yish}, booktitle = {Proceedings of the 27th International Conference for the Psychology of Mathematics Education}, citeulike-article-id = {481528}, comment = {"The Guess My Rule game suggested itself as a promising context for getting students to focus on written algebraic notation as an object of discussion because students would have to compare expressions written by the rule makers with those posed by the rule guessers and decide whether certain variations express the same or different underlying rules. The Guess-my-Rule game has often been used in mathematics education at different grade levels as a way to introduce children to linear functions (see, for example, Davis, 1967, 1985; Carraher, Schliemann, \& Brizuela, 2001, 2003; Schliemann, Carraher, \& Brizuela, 2003). This activity essentially provides students with values from a function's domain (input) and the corresponding value from the range (output); based on the data, students try to infer the function. In order to play the Guess My Rule game, students must accept that: 1) each input must result in a single output; and 2) a function is consistently used for all values of the solution set, that is, the rule cannot change. --- Analysis of the classes of rules chosen by students. --- "There was some evidence that third grade students from an urban public school with a prior background in early algebra activities based on functions and modeling could begin the transition from semantically driven to syntactically driven algebraic reasoning. We would hope to see students taking part in more prolonged and in depth debates about equivalent functions and identities. Furthermore, although students may initially find persuasive the fact that two rules produce the same output from a set of input values, eventually they need to abandon this approach and move towards proving the functions are equivalent. The discussion about ¥4 ¥5 simplifying to ¥20 exemplifies this sort of shift. But graphing the data may prove useful in lending meaning to the rules and (dis)proving their equivalence. Ultimately, we want students to be able to operate on equations in ways that preserve the solution set without having to resort to thinking about the original situations that gave rise to the equations. This does not mean that students should abandon, once and for all, semantically driven reasoning, for it may prove useful in other contexts, even some that entail the use of advanced mathematical reasoning. We look forward to encountering additional research that explores the transition and tension between semantically driven and syntactically driven mathematical reasoning."}, interhash = {137706fa4d50389288ede2b787e8114f}, intrahash = {23a821c366b42e64816d5fa6744e922f}, keywords = {games gmr gmx learning mathematics mathgamespatterns mythesis}, priority = {0}, timestamp = {2008-05-30T02:25:09.000+0200}, title = {Guess My Rule Revisited}, url = {http://www2.earlyalgebra.terc.edu/our_papers/2003/Carraher_EarnestPME2003.pdf}, year = 2003 }