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- W2425442876 abstract "Students' graphical representations of statistical associations are explored through analyses of responses from 97 students in grades 4, 5, and 6. The task involved representing (a) the association People grow taller as they get older, (b) this association with age modifier, and (c) this association with sex differences. Three levels of representing bivariate associations and of representing multivariate associations are described: unsuccessful, partial, and complete. Issues for developing student representations are discussed. Graphs are commonly used to convey at a glance large amounts of statistical data, particularly data involving bivariate and multivariate associations, which are otherwise difficult to convey without reporting fonnal statistics such as t-tests or regression lines. Graphs produced by students may convey not only statistical data, but also how students understand statistical data, and how they understand bivariate- and multivariate-associations. Although many studies have explored students' interpretations of graphs (for a review, see Leinhardt, Zaslavsky, & Stein, 1990), it is only recently that students' representations have begun to receive attention by mathematics education researchers (e.g., Mevarech & Kramarsky, 1997; Moritz, 1999; Moritz & Watson, 2000; Watson, 2000). Mevarech and Kramarsky (1997) asked 92 grade 8 students to represent the following four claims of association between time studying and achievement grades in school: 1. [increasing function] the more she studies, the better her grades; 2. [constant function] no matter how long she studies, she always gets the same grade; 3. [curvilinear function] up to three hours, the longer she studies the better her grades, but beyond three hours, she becomes tired and her grades become lower; and 4. [ decreasing function] when she studies more, her grades decrease. Approximately 55% of students appropriately represented claims 1, 2, and 4 using a labelled two-axis graph, whereas the curvilinear function of claim 3 was correctly represented by only 38% of students. About 10% of students represented generalised ideas of graphs or represented relations between the variables in idiosyncratic way. Three common alternative conceptions were evident in responses that represented (a) only a single point in a graph, (b) only one factor in each of a series of graphs, and (c) increasing function irrespective of task requirements. These conceptions were evident in approximately 20%, 20%, and 10% of students' responses respectively (students could exhibit more than one conception). The first two conceptions involve eliminating variable data to reduce complexity of the representation. The last conception indicates that constant, curvilinear, and decreasing functions may be more difficult for students, for example involving appreciating that as one measure changes, the other measure may remain constant, and thus representing a repeated value on that measure. A number of studies (Moritz, 1999; Moritz & Watson, 2000; Watson, 2000) have reported on responses from students in grades 6 to 11 to represent in a graph an almost perfect relationship between the increase in heart deaths and the increase in the use of motor vehicles, as claimed in a newspaper extract and presented in a written survey task. Moritz and Watson (2000) described a framework of four levels according to degree of success in representing the association. At each level, different categories of response were evident. At" @default.
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- W2425442876 date "2000-01-01" @default.
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- W2425442876 title "Graphical Representations of Statistical Associations by Upper Primary Students" @default.
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