Conceptual understanding of *functions in a multi-representational learning environment
Carol Jean Bell, The University of Texas at Austin, United States
The University of Texas at Austin . Awarded
The purpose of this study was to investigate whether students using the multi-representational software tool Function Probe™ develop a better conceptual understanding of functions than do students learning in a traditional classroom environment, while maintaining an equal proficiency in procedural skills. Function Probe™ was used in the investigation as a means to explore students' conceptual understanding of functions in a university pre-calculus course.
Quantitative data were collected and analyzed to compare students' ability to model real world problems, students' abilities to solve problems using Function Probe™ versus a graphing calculator, and students' proficiency in procedural skills using a nonequivalent control-group experimental design. The quantitative measures used included the College Board Entrance Examination on functions and graphs, called Functions and Graphs: Calculus Readiness Examination and diagnostic tests designed and used in a study by O'Callaghan (1995). The O'Callaghan (1995) exams consisted of questions that were categorized into one of four aspects of a conceptual knowledge of functions. These four aspects include (1) modeling, (2) interpreting, (3) translating, and (4) reifying functions.
The quantitative results indicated that there was no statistically significant difference between the experimental and control groups' proficiency in procedural skills, abilities to model real world applications, and abilities to solve problems using Function Probe™ versus a graphing calculator. The importance of this research is that it may help in understanding the effects of technologies on students' abilities to solve problems and whether learning in a multi-representational environment influences students' conceptual understanding of functions and their concept image of a function. This may then help in understanding the relationship between procedural and conceptual knowledge, and the transition from using procedural knowledge to using conceptual knowledge.
Bell, C.J. Conceptual understanding of *functions in a multi-representational learning environment. Ph.D. thesis, The University of Texas at Austin.
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