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Probability-related naïve ideas across physics topics

“…or because 'results are never wrong'. (Rollnick et al, 2001) Particularly this latter view is consistent with assignment of measurement into the 'deterministic' ontology. In addition, some students report that a larger spread represents a better measurement set Sere et al, 2001), which is consistent with the idea discussed above that different parameters should be used before taking the mean.…”

“…Education researchers looking at student difficulties with measurement have commonly documented students who do not see the need to take multiple measurements, unless, of course, the instructor asks them to do so, or something obviously went wrong with the first measurement. (Abbott, 2003;Allie et al, 1998;Buffler et al, 2001;Davidowitz et al, 2001;Gott & Duggan, 1995;Hackling & Garnett, 1992;Heinicke, 2012;Rollnick et al, 2001;Sere et al, 1993) As an example, when Cauzinille-Marmeche et al had children test to see if container shape affects the time for a covered candle to extinguish itself, the children saw with the trial of two different containers that there was a difference in time. They did not repeat the experiment, however, as they did not expect that there could be a difference in time if the same container were used twice.…”

“…We might expect students with this view to recognise that readings will vary from measurement to measurement, and to attribute 'error' to this variance. However, when asked to identify such potential sources of error, we would not be surprised if these students tend to exclusively think about mistakes that they themselves might have made (a naïve idea documented by Goedhart and Verdonk (1991)), as they see the variation in the data as being due to personal mistakes (a view documented by Heinicke (2012), Leach et al (1998), Pillay et al (2008), andRollnick et al (2001)). We might further expect that such students would consequently repeat the experiment to get closer to a 'true value', thinking that they are increasing accuracy (whereas they are actually only increasing precision) (a naïve idea documented by Allie et al (1998), Evangelinos et al (2002), andSere et al (1993)).…”

“…(Austin et al, 1991;Deardorff, 2001;Gott & Duggan, 1995;Millar et al, 1994) Further aligned with what we would expect from students assigning measurement into the 'deterministic' ontology in this way, research has documented students who report only the last result, since that came after the most amount of 'practice' or who report the result that is a repeated value, since that is most likely to be the 'true value'. (Allie et al, 1998;Buffler et al, 2001;Davidowitz et al, 2001;Ibrahim, 2006;Pillay et al, 2008;Rollnick et al, 2001;Sere et al, 2001Sere et al, , 1993Warwick et al, 1999) Research has shown that, even when presented a data set and asked 'what value to report as the final result', students answer with a single value (as opposed to reporting a range). (Buffler et al, 2001;Volkwyn et al, 2008) Consistent with the student inclination to consider 'error' as comprised exclusively of experimenter mistakes, research has documented the student view that, given precise enough tools, a measurement with zero uncertainty can be obtained.…”

“…(Heinicke, 2012;Sere et al, 2001) Similarly, when asked whether two data sets with different means but overlapping spreads agree with each other or not, many of these students ignore data scatter and just use the arithmetic means (Abbott, 2003;Allie et al, 1998;Cauzinille-Marmeche et al, 1985;Davidowitz et al, 2001;Deardorff, 2001;Ibrahim, 2006;Leach et al, 1998;Lubben et al, 2001;Pillay et al, 2008;Rollnick et al, 2001;Sere et al, 2001Sere et al, , 1993 or individual data points. (Allie et al, 1998;Buffler et al, 2001;Davidowitz et al, 2001;Deardorff, 2001;Heinicke, 2012;Ibrahim, 2006;Rollnick et al, 2001;Sere et al, 2001;Volkwyn et al, 2008) This suggests that the correct answer on the original question with identical means may have come about for some reason other than deep conceptual understanding about spread. Students who do consider data spread in deciding whether two sets of data agree with each other or not will often say that the data agrees if the size of the spread is the same whether there is overlap or not.…”