Surveying graduate students’ attitudes and approaches to problem solving

Students’ attitudes and approaches to problem solving in physics can profoundly influence their motivation to learn and development of expertise. We developed and validated an Attitudes and Approaches to Problem Solving survey by expanding the Attitudes toward Problem Solving survey of Marx and Cummings and administered it to physics graduate students. Comparison of their responses to the survey questions about problem solving in their own graduate-level courses vs problem solving in the introductory physics courses provides insight into their expertise in introductory and graduate-level physics. The physics graduate students’ responses to the survey questions were also compared with those of introductory physics and astronomy students and physics faculty. We find that, even for problem solving in introductory physics, graduate students’ responses to some survey questions are less expertlike than those of the physics faculty. Comparison of survey responses of graduate students and introductory students for problem solving in introductory physics suggests that graduate students’ responses are in general more expertlike than those of introductory students. However, survey responses suggest that graduate-level problem solving by graduate students on several measures has remarkably similar trends to introductory-level problem solving by introductory students.

Figure 1

Comparison of graduate students’ survey responses to 12 selected questions when considering introductory-level problem solving and graduate-level problem solving. The order of the questions in the histogram is such that the difference between the introductory-level problem solving (“Intro” in the figure) and graduate-level problem solving (“Graduate” in the figure) is largest for the first question [question (33)] and second largest for the second question [question (6)] etc. Error bars shown here (and in all other figures) are the standard errors. The responses to these questions are more favorable for introductory-level problem solving than for graduate-level problem solving. The neutral percent responses can be found by subtracting from 100, the percentage of favorable and unfavorable responses.

Figure 2

Histogram showing favorable (agree) and unfavorable (disagree) responses for survey question (6). The histogram shows that faculty were always aware of when they were wrong in problem solving but other respondents were less certain. Only about 50% of graduate students could tell that their answers were wrong in graduate-level problem solving. Graduate students-self and Graduate Students-intro refer to Graduate students’ response for graduate-level problem solving and introductory-level problem solving, respectively.

Figure 3

Histogram showing favorable (disagree) and unfavorable (agree) responses for survey question (11). The histogram shows that many more graduate students disagreed that they routinely use equations to calculate answers even if they are nonintuitive for introductory-level problem solving than graduate-level problem solving. Almost equal percentage of introductory physics students agreed and disagreed with the statement.

Figure 4

Histogram showing favorable (disagree) and unfavorable (agree) responses for survey question (5) about whether problem solving in physics is mainly an exercise in finding the right formula. The histogram shows that a large percentage of nonfaculty respondents from all groups agreed with the statement or were neutral.

Figure 5

Histogram showing favorable (agree) and unfavorable (disagree) responses for survey question (14). While the trend in the figure from introductory students to faculty may appear to be inconsistent with expectations, some faculty in individual discussions noted that they do not explicitly think about concepts that underlie the problem “while” solving problems because the concepts have become obvious to them. The introductory students often do not think about concepts because they believe in a plug and chug approach to problem solving in physics.

Figure 6

Histogram showing favorable (disagree) and unfavorable (agree) responses for survey question (30). The histogram shows that faculty and graduate students did not believe that it is more difficult to solve a physics problem with symbols than solving an identical problem with numerical answer but introductory physics and astronomy students often did.

Figure 7

Histogram showing favorable (agree) and unfavorable (disagree) responses for survey question (31). The histogram shows that faculty and graduate students preferred to solve a problem symbolically first and only plug in the numbers at the very end but less than half of the introductory physics and astronomy students agreed with them.

Figure 8

Histogram showing favorable (agree) and unfavorable (disagree) responses for survey question (2). The histogram shows that all faculty agreed that they often make approximations about the physical world but other respondents, including physics graduate students, were not always in agreement.

Figure 9

Histogram showing favorable (disagree) and unfavorable (agree) responses for survey question (12) about whether physics involves many equations each of which applies primarily to a specific situation. As we go from the introductory physics and astronomy students to faculty, the disagreement with the statement (favorable response) increases.

Figure 10

Histogram showing favorable (disagree) and unfavorable (agree) responses for survey question (3) about whether mathematics is the most important part of the problem solving process. The histogram shows that a large percentage of nonfaculty respondents from all groups agreed with the statement (unfavorable).

Figure 11

Histogram showing favorable (agree) and unfavorable (disagree) responses for survey question (20). The histogram shows that none of the groups had 80% individuals who agreed that they take the time to reflect and learn from the problem solutions after solving problems but the reasons for the lack of reflection varied across different groups.