Developing a Framework for a Fine-Grained Computational Theory of Algebra Learning.
Peter Lochiel Glidden, Erin K. Fry · 1993
Theoretical tools from cognitive science were used to put together a framework for a fine-grained theory of how students learn elementary algebra in the classroom. Developing the framework included assessing the shortcomings of current models, evaluating whether unified theories of cognition can be adapted for learning mathematics in the classroom, and discussing the extension of these theories. Protocols were collected from an eighth-grade cla35 using the University of Chicago School Mathematics Project algebra text in an urban middle school. Audiotapes were made of student classroom conversations in working groups. Audiotapes from three students are quoted. Analyzing the data provides a framework for a fine-grained theory. Data suggest that in the initial stages of learning algebra, visual clues play a more important role than does syntactic or semantic understanding. Directly related is the importance of examples. Data also suggest that the more novel the problem, the more students are likely to rely on visual clues. Students in the early stages of learning tend to do mathematics problems based on how the symbols are arranged on the page, rather than syntactically deconstructing the expression or the underlying semantics. It is suggested that although a production system architecture is applicable to doing and learning mathematics in the classroom, students do not compose productions as quickly and easily as suggested by some theories. (Contains 25 references.) (SLD) *********************************************************************** Reproductions supplied by EDRS are the best that can be made from the original document. *********************************************************************** DEVELOPING A FRAMEWORK FOR A FINE-GRAINED COMPUTATIONAI THEORY OF ALGEBRA LEARNING Peter L. Glidden & Erin K. Fry University of Illinois at Urbana-Champaign Paper presented at 1993 AERA, Session 47.04 U.S. DEPARTMENT OF EDUCATION Office of Educahonal Research and Improvement EDUCATIONAL RESOURCES INFORMATION CENTER (ERIC) cD4hS document has been reproduced as reCe.ved Irons the person or organrzatron ongrnafing C Mnor chanpeS have been made to improve reprOductron cluably Ponts of sew Or Op.n.Ons staled ,ntntSCIOCu menl dO not necessardy represent otficra, OE RI posMon or pOt.Cy PERMISSION TO REPRODUCE THIS MATERIAL HAS BEEN GRANTED BY