%0 Conference Paper %1 brizuela2000mns %A Brizuela, Bárbara M. %A Carraher, David %A Schliemann, Analúcia D. %B Symposium paper, 2000 NCTM Research Pre-session Meeting %C Chicago, IL %D 2000 %K algebra drawing early learning mathematical mathematics mythesis notation semiotics sketching %T Mathematical notation to support and further reasoning ("to help me think of something") %U http://www2.earlyalgebra.terc.edu/our_papers/2000/Brizuela_et_all_NCTM2000.pdf %X Many researchers and educators now believe that elementary algebraic ideas and notation should be an integral part of young students' understanding of early mathematics. To support this change in thinking and practice, the field needs research on young learners' algebraic reasoning. In this study we take children's älgebraic reasoning" to refer to cases in which they express general properties of numbers or quantities. We believe that they can also express these properties and relations through written representation or notation, without having to treat conventional notation as a mere appendage to reasoning. The specific examples we focus upon refer to Sara, a student in the third grade classroom we taught in once every two weeks. Sara exemplifies, through her actions and her words, how notations can represent not only what was done while solving a problem and what happened in the context of the problem, but also how notations can become tools for thinking and reflecting about the relationships between quantities in the problem. In this way, we can begin to think about children's notations not only as tools for learners to represent their understanding and thinking about algebraic relations or as precursors of conventional algebra representation, but also as tools to further those understandings and that thinking.

@inproceedings{brizuela2000mns, abstract = {Many researchers and educators now believe that elementary algebraic ideas and notation should be an integral part of young students' understanding of early mathematics. To support this change in thinking and practice, the field needs research on young learners' algebraic reasoning. In this study we take children's "algebraic reasoning" to refer to cases in which they express general properties of numbers or quantities. We believe that they can also express these properties and relations through written representation or notation, without having to treat conventional notation as a mere appendage to reasoning. The specific examples we focus upon refer to Sara, a student in the third grade classroom we taught in once every two weeks. Sara exemplifies, through her actions and her words, how notations can represent not only what was done while solving a problem and what happened in the context of the problem, but also how notations can become tools for thinking and reflecting about the relationships between quantities in the problem. In this way, we can begin to think about children's notations not only as tools for learners to represent their understanding and thinking about algebraic relations or as precursors of conventional algebra representation, but also as tools to further those understandings and that thinking. }, added-at = {2008-05-30T01:54:02.000+0200}, address = {Chicago, IL}, author = {Brizuela, Bárbara M. and Carraher, David and Schliemann, Analúcia D.}, biburl = {https://www.bibsonomy.org/bibtex/2a490e366b58b512924bd9042de0d8209/yish}, booktitle = {Symposium paper, 2000 NCTM Research Pre-session Meeting}, interhash = {2cf08f6d1fac018ab5b0361aa75d8479}, intrahash = {a490e366b58b512924bd9042de0d8209}, keywords = {algebra drawing early learning mathematical mathematics mythesis notation semiotics sketching}, timestamp = {2008-05-30T01:54:04.000+0200}, title = {Mathematical notation to support and further reasoning ("to help me think of something")}, url = {http://www2.earlyalgebra.terc.edu/our_papers/2000/Brizuela_et_all_NCTM2000.pdf}, year = 2000 }