Causal i nferen ce grap hical re p rese ntat ion raw

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Causal I nferen ce Grap hical Re p rese ntat ion Raw Nu me rical D ata Grap h P rodu ction Associatio n S tate ment ÒLevel of nois e is relat ed to number of pe ople Ó OR ÒClas srooms wit h m ore people make l ess n oise Ó Causal Statem ent ÒMo re pe o ple in the classroom cause a lowe r level o f n oiseÓ Grap h Interpreta tion Figure 1 . Forms of representing statistical association and skills of correlational reasoning to translate them.
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40 10.2. TASKS Students were provided with brief contexts of data collection involving at least two variables, and were given verbal statements of association to represent graphically: Q1(a). "People grow taller as they get older". Q1(b). "People do grow taller. But when you are 20 years old, you stop growing”. Q1(c). “For 10 year olds, girls and boys are about the same height. But men usually grow to be taller than women.” Q2. “People who studied for more time got lower scores.” Q3. "An almost perfect relationship between the increase in heart deaths and the increase in use of motor vehicles”. These tasks were intended be more informative of student understanding of association than asking students to judge whether a given graph represents an association. Q1 was based on Mevarech and Kramarsky (1997) who observed students' difficulties with linear relation of zero slopes. 10.3. SURVEY RESPONSES Responses from previous research have been coded into 3 levels for Q1 (Moritz, 2000) and 4 levels for Q3 (Moritz & Watson, 2002). For this study, a total of 184 student surveys (grades 3, 5, 7, and 9) were gathered. Coding responses to Q2 was discussed with respect to causal reasoning about the topic context and beliefs about the direction of the association (see Figure 2). Figure 2 . Student responses to Q2: (left) causal, grade 7; (middle) direction, grade 5; (right) direction, grade 7. 10.4. INTERVIEW DIALOGUE In videotaped individual interviews, 34 students in grades 3, 5, 7, and 9 were first asked to explain their graphs, in particular how the graphs show the information and why they chose to represent the verbal statement the way they did. In an attempt to create cognitive conflict to explore how students might learn from new ideas, interviewees then were shown graphs drawn by other students, and asked to compare the different responses to decide which better represented the verbal statement. Selected extracts of dialogue illustrated how some students ignored the specifications of the survey task in order to represent what they believed about the topic context. REFERENCES Mevarech, Z. R. & Kramarsky, B. (1997). From verbal descriptions to graphic representations: Stability and change in students’ alternative conceptions. Educational Studies in Mathematics , 32, 229-263. Moritz, J. B. (2000). Graphical representations of statistical associations by upper primary students. In J. Bana & A. Chapman (Eds.), Mathematics education beyond 2000. Proceedings of the 23rd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 440-447). Perth: MERGA.
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