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• W1510229335 abstract "The fragmentation of strategies that distinguishes the more successful elementarygrade students from those least successful has been documented previously. Thisstudy investigated whether this phenomenon of divergence and fragmentation of strategieswould occur among undergraduate students enrolled in a remedial algebracourse. Twenty-six undergraduate students enrolled in a remedial algebra course useda reform curriculum, with the concept of function as an organizing lens and graphingcalculators during the 1997 fall semester. These students could be characterized asvictims of the proceptual divide, constrained by inflexible strategies and by priorprocedural learning and/or teaching. In addition to investigating whether divergenceand fragmentation of strategies would occur among a population assumed to be relativelyhomogeneous, the other major focus of this study was to investigate whether studentswho are more successful construct, organize, and restructure knowledge in waysthat are qualitatively different from the processes utilized by those who are least successful.It was assumed that, though these cognitive structures are not directly knowable,it would be possible to document the ways in which students constructknowledge and reorganize their existing cognitive structures.Data reported in this study were interpreted within a multi-dimensional frameworkbased on cognitive, sociocultural, and biological theories of conceptual development,using selected insights representative of the overall results of the broad datacollection. In an effort to minimize the extent of researcher inferences concerning cognitiveprocesses and to support the validity of the findings, several types of triangulationwere used, including data, method, and theoretical triangulation. Profiles of thestudents characterized as most successful and least successful were developed.Analysesof the triangulated data revealed a divergence in performance and qualitatively differentstrategies used by students who were most successful compared with studentswho were least successful.The most successful students demonstrated significant improvement andgrowth in their ability to think flexibly to interpret ambiguous notation, switch theirtrain of thought from a direct process to the reverse process, and to translate amongvarious representations. They also curtailed their reasoning in a relatively short Periodof time. Students who were least successful showed little, if any, improvement duringthe semester. They demonstrated less flexible strategies, few changes in attitudes, andalmost no difference in their choice of tools. Despite many opportunities for additionalpractice, the least successful were unable to reconstruct previously learned inappropriateschemas. Students' concept maps and schematic diagrams of those maps revealedthat most successful students organized the bits and pieces of new knowledge into abasic cognitive structure that remained relatively stable over time. New knowledgewas assimilated into or added onto this basic structure, which gradually increased incomplexity and richness. Students who are least successful constructed cognitivestructures which were subsequently replaced by new, differently organized structureswhich lacked complexity and essential linkages to other related concepts and procedures.The bits and pieces of knowledge previously assembled were generally discardedand replaced with new bits and pieces in a new, differently organized structure." @default.
• W1510229335 created "2016-06-24" @default.
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• W1510229335 date "1998-04-01" @default.
• W1510229335 modified "2023-09-28" @default.
• W1510229335 title "Cognitive Units, Concept Images, and Cognitive Collages: An Examination of the Processes of Knowledge Construction" @default.
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