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ELEMENTARY SCHOOL PRE-SERVICE TEACHERS’ UNDERSTANDINGS OF ALGEBRAIC GENERALIZATIONS



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TMME vol6 nos 1 2 p 201 ELEMENTARY SCHOOL PRE SERVICE TEACHERS UNDERSTANDINGS OF ALGEBRAIC GENERALIZATIONS Jean E Hallagan1 Audrey C Rule Lynn F Carlson State University of New York Oswego Abstract It is critical for all students to learn algebra including the ability to generalize to function in our increasingly complex world This pretest intervention posttest study of preservice elementary teachers N 63 in their math methods course assessed their knowledge of writing and applying algebraic generalizations using instructor made rubrics along with analysis of work samples and reported insights Initially although most subjects could solve a specific case they had considerable difficulty determining an algebraic rule After a problemsolving based teaching intervention students improved in their ability to generalize however they encountered more difficulty with determining the algebraic generalization for items arranged in squares with additional single items as exemplified by x2 1 than with multiple sets of items as exemplified by 4x Keywords algebra generalizations intervention pre service elementary teachers Overview It is critical for all school aged students to learn algebra including the ability to generalize to function in our increasingly complex world National Council of Teachers of Mathematics NCTM 2000 RAND 2003 Preservice elementary teachers play a critical role in initiating and developing algebraic reasoning in grades K 6 however the research base of teachers knowledge regarding algebraic instruction is rather limited Doerr 2004 Kieran 2006 Many call for increased attention to algebraic reasoning in the elementary grades to ease the transition from arithmetic and build understanding of the abstract concept of variables Kieran 1992 Kaput 2000 At the same time teachers weak conceptual understanding of essential subject matter knowledge is well known Ma 1999 The transition from a procedural approach in arithmetic to a structural understanding of algebra does



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