Figure 2 student graph of weight in kg leading to

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Figure 2. Student graph of weight in kg leading to discussion of’ bumps’. REFERENCES Cobb, P., Gravemeijer, K. P. E., Bowers, J. & McClain, K. (1997). Statistical minitools . Vanderbilt University, TN. Programmed and revised (2001) at the Freudenthal Institute, Utrecht University, Netherlands. ARTHUR BAKKER Freudenthal Institute Postbus 9432, 3506 GK Utrech Netherlands
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36 6. ‘VARIATION’ FROM A STUDENT’S PERSPECTIVE CHRIS READING University of New England, Australia [email protected] As statistics is the methodology needed to make decisions under uncertainty and variation is the source of this uncertainty, the understanding and analysis of variation is critical to students’ reasoning in statistics. Although a number of global questions were posed relating to how students dealt with variation in different situations and some factors affecting their responses, the two questions deal with in most detail were: How is this variation described by students? and Is there an hierarchy of understanding of variation? During the session a variety of student responses, which had been collected from a number of different sources, were used to help build up a Matrix of Description and Understanding of Variation (summarized in Table 1). This matrix, which gradually unfolded as the session progressed, is only in an embryonic form with no column headings as yet. The student responses, in italics, may help to elaborate on the titles of each cell in the matrix. First, examples of the language used by students when asked to describe variation in general terms were examined and allocated to three cells forming the beginning of the matrix. Second, examples of any variation- related aspects of responses to open-ended general questions in various areas of statistics were presented and added to the matrix, creating some new cells. Third, variation-related aspects of student responses to a variation in sampling problem were slotted into the matrix. Fourth, and final, video excerpts of students working on the same sampling problem, but in a small group situation, were viewed and appropriate response segments added to the matrix. Table 1. Summary of suggested Matrix of Description and Understanding of Variation SUBSTITUTE ANOTHER WORD different changing variety MOVE FROM ONE VALUE TO THE NEXT drop or go higher from high to low and back up again IDENTIFY EXTRANEOUS SOURCE OF VARIATION I might get less than my friends might pick all over the place CONCERN WITH MIDDLE VALUES size of the numbers doesn’t matter just have to be different CONCERN WITH EXTREMES minimum and maximum varies from 2- 7 stay out of the extremes INDIRECTLY IDENTIFY SOURCE OF VARIATION not pick 7 – have got other colours in there LOOK FOR A PATTERN no regular eating habits overall are gradually increasing CONCERN WITH EXTREMES AND WHAT HAPPENS BETWEEN most …and least …and on average … DIRECTLY IDENTIFY SOURCE OF VARIATION depends on what day it is for different ages DISCUSS CHANGE COMPARED TO SOMETHING come close to most of the non-extreme values DISCUSS CHANGE COMPARED TO
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