Experience and Problem Representation in Statistics

Abstract

This research investigated experience level differences in problem representation in statistics. A triad judgment task was designed so that source problems shared either surface similarity (story narrative) or structural (inferential level) features (t test, correlation, or chi-square) with the target problem. Graduate students with varying levels of experience in statistics were asked to choose which source problem "goes best" with the target problem for each triad. Given a choice between a problem that shares surface-level characteristics and one that shares inferential-level characteristics, students who had taken 0 to 4 courses in statistics tended to represent problems on the basis of surface-level features. Students who had more than 4 courses did not consistently make choices on the basis of surface-level features, nor did they consistently rely on structural features. However, all students with statistics course backgrounds noticed structural features when competition between different types of features was eliminated. The role of surface and structural features in determining problem representations is discussed.

Effects of experience and surface-level distraction on ability to perceive ethical issues.

“…The results also supported the hypothesized competence-performance distinction for less ex perienced learners under conditions of distracting surface-level in formation, consistent with previous research (Hogan & Rabinowitz, 2009;Rabinowitz & Hogan, 2008). In summary, there were two main findings:…”

“…Al though the low response rate in this study (11%) is typical of other studies using the triad judgment task (e.g., Hogan & Rabinowitz, 2009;Rabinowitz & Hogan, 2008), as could be expected for a study recruiting college psychology samples on a voluntary no credit basis, caution is warranted for generalization of the results. In addition, as the e-mail invitation to participate was sent by a fellow psychology student, there may have been a response bias, in that students who are altruistic toward fellow students may have responded more than other students.…”

“…In the domain of statistics, for example, Rabinowitz and Hogan (2008) investigated experience-level differences in problem repre sentation. A triad judgment task was designed so that source problems shared either surface similarity (story narrative) or struc tural (inferential-level) features (t test, correlation, or chi square) with the target problem.…”

Teacher expertise and the development of a problem representation

“…The experimental design used in the present study drew upon methodologies examining problem representation in other domains including physics, mathematics, statistics, sports, and music (Chi et al 1981;Dufresne, Gerace, Hardiman, and Mestre, 1992;Hardiman et al, 1989;McPherson & Kernodle, 2007;Quilici & Mayer, 1996;Rabinowitz & Hogan, 2008;Wolpert, 1990); and analogical reasoning studies (Blanchette & Dunbar, 2000;Catrambone, Craig, & Neressian, 2006). The methodology included the development and administration of a triad judgement task to both expert and novice teachers.…”

“…Two features exist with one being surface in nature; best explained as pieces of information embedded in the problem narrative that provide a setting and/ or context, while the other feature consists of the deep, structural components delineated by the principles, concepts, and ideas rooted in the problem. Second, researchers (Adelson, 1981;Hogan & Rabinowitz, 2002;Novick, 1988;Rabinowitz & Hogan, 2008) are often interested in the relationship between experience in a domain and the features (surface and/or deep) used to define the problem mentally. Research conducted by Chi et al (1981) offers an example of how these two aspects, features of a problem and experience in a domain, have been studied.…”