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Students’ preconceptions of three vector quantities

University of British Columbia

This study was directed towards the identification and analysis of students' intuitive ideas or preconceptions about three kinematic vector quantities — vector position, displacement, and velocity. A list of ten implicit vector characteristics derived from a task analysis of these three vector quantities, served as the framework for the development of the interview protocols used in the study and the subsequent analysis of the data. The study proceeded in two phases; in the first, clinical-type interviews were conducted with twenty grade ten students using two tasks which involved describing the movement of a boat on a lake and a river; in the second phase, a group interview protocol (G.I.P.) requiring a written response was developed (based upon the tasks and the results of the first phase) and administered to 8 classes of grade ten students, producing a total sample of 176 subjects. Analysis of the results from the first phase yielded a small but variable number (2 to 5) number of inferred rules for each of the ten implicit vector characteristics dealt with in the individual interviews. These 'inferred rules' are hypothesized sets of beliefs (preconceptions) or cognitive structures used by the subjects to explain a problem situation posed by the interviewer. Further categorization yielded three broad types of preconceptions — scalar, transitional, and vectorial — which were based in part upon criteria derived from the current physics perspective. The overall results from the first phase indicated that most students possessed fairly consistent preconceptions regarding the directional and distance components involved in the description of the movement of a boat on a lake. For example, all students recognized the necessity of using a reference point and a frame of reference, however, they employed different 'inferred rules' in the selection of these references. Overall, for four vector characteristics, most of the subjects used vectorial type 'inferred rules' (where they considered the quantitative aspects of the variables involved, e.g., direction and distance); for three of the vector characteristics, a high percentage of subjects made use of scalar-type 'inferred rules' which corresponded to fairly primitive notions (where they considered only one qualitative or quantitative variable); for the remaining three vector characteristics, most of the subjects demonstrated transitional-type 'inferred rules' (which consisted in some combination of the two prior extreme categories). The results from the second phase of the study, in general, corroborated the findings from the first phase. While some new 'inferred rules' were identified, about 80 percent of the inferred rules used were common to those discovered in the interview sample. Hence, it would seem that the results were neither an artifact of the interview procedure, nor limited to a small group of grade ten students In summary, the study illustrated the application of a particular analytical technique to generate sets of 'inferred rules' which were hypothesized to account for the way that grade ten subjects intuitively approached a problem situation involving a directional as well as other components By developing a group questionnaire, the general validity of the approach and results were enhanced by finding similar response patterns in a larger more heterogeneous group of subjects. The educational implications of both the rational task analysis, which yielded the list of implicit vector characteristics, and the substantive results, expressed in terms of the various sets of 'inferred rules', were discussed in terms of their applicability to classroom teachers and curriculum developers.

Text

2010-03-30

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http://hdl.handle.net/2429/23046

Mathematics Education

University of British Columbia

Graduate