Connecting symbolic difficulties with failure in physics

American Journal of Physics

Volumn 79, Issue 1, 2011, Pages 133-140

  Torigoe, Eugene T ^a   Gladding, Gary E ^b  

^a ALLEGHENY COLLEGE   (United States)

^b University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650758456     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.3487941     Document Type: Article

References (22)

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6. The examples shown are from Ref. 4.
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12. See supplementary material at for all ten numeric and symbolic pairs of questions used in this study.
13. Question 4 was created by modifying an existing symbolic question. When numbers were introduced to create the numeric version, one of the symbolic options corresponded to an imaginary quantity. To ensure the similarity of all of the options, only the magnitude of this quantity was displayed in the numeric version. Two of the other five options for this question do not agree between the versions, but each of these options was chosen by 2% or less of the students.
14. The p-value represents the likelihood that such a difference can be observed under the assumption that the null hypothesis is true (see Ref. 15).
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16. Some questions were common between the two versions of the final exam.
17. The discrimination of multiple-choice questions is most commonly measured using the point biserial coefficient of correlation because the result of a multiple-choice question is most commonly dichotomous. The multiple-choice questions in this study were analyzed using the Pearson correlation coefficient r, because students were given partial credit for multiple selections. As a result a student could receive a score of 0, 0.33, 0.5, or 1 on each question.
18. The error of the mean difference shown in Table is less than what one would calculate if the errors for the top and bottom groups were combined in quadrature. To calculate the error shown, we took advantage of the fact that the difference in score between the top and bottom groups could be determined for each question. The error in the mean difference for the equation priority questions was determined by calculating the variance of the distribution of differences for the 40 equation priority questions. This process of pairing data is analogous to how one would calculate gains on the FCI by pairing the each precourse and postcourse score by student, rather than finding the mean difference between the average precourse score and the postcourse score for the class as a whole.
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