Aalborg, 2005, contribution

Contribution to 8 Nordic Conference on Science Education, Aalborg, 2005

University and Engineering Physics Students' Understanding of Force and Acceleration - Can Amusement Park Physics Help?

Ann-Marie Pendrill,
Institute of Physics, Göteborg University, SE-412 96 Göteborg, Sweden, Ann-Marie.Pendrill@physics.gu.se

Abstract
Force and acceleration are fundamental physics concepts, known to be problematic to many students. Can amusement park projects be a way to deepen the understanding of these concepts? Pre- and post-testing was performed for first-year engineering and university physics students, using the well-established "Force Concept Inventory", which showed encouraging gains. However, as in earlier work, the results were found to exhibit considerable gender differences. In addition, a correlation with exam results showed the importance of force concepts, but also of other skills.

1. Introduction

Classical mechanics is a well studied area, both in physics and in physics education, and is known to cause problems for many students. The Aristotelian world view, where a force is needed to maintain a constant velocity and bodies fall with velocities depending on their mass, is a natural interpretation of years of continuous observations, and is given many years to develop before physics teachers try to interfere.

This study deals with first-year university and engineering physics students' understanding of fundamental concepts in mechanics. As one way to help students develop their understanding of force and acceleration, we have included amusement park projects in many courses. An amusement park can be seen as a large physics laboratory, where the thrills and excitement are created using Newton's laws. Acceleration, with all its vector character, is experienced throughout the body during the rides - although the connection is not necessarily made by the rider. The format of the amusement park project was designed to encourage challenging physics discussions among the students. By using a variety of learning situations, we aimed to let the students experience many different aspects of the concepts, and we also hoped to improve the learning outcomes for students with different learning preferences. Did the amusement park project help? Could any gender differences be observed?

As part of the evaluation, the Force Concept Inventory (Hestenes et al. 1992, Halloun et al. 1995) was used for initial diagnosis of the students and as a tool to evaluate the improvement of their understanding of force concepts. It was also used in a few other courses, to establish local references for characterizing the different student groups. Since the test is well documented, the results can be compared also to those of previously studied groups.

2. Method

We describe here in more detail the design of the university physics course, as well as the test used to monitor student understanding.

2.1. The introductory physics course at Göteborg University

The introductory physics course at Göteborg university in 2004 included a playground visit, student lecture demonstrations of physical phenomena and discussions about conceptual questions during lectures and problem solving classes. The students were also assigned an amusement park project, where each group of 6-8 students investigated one section of a roller- coaster and a swing, carousel or drop tower. All groups had different tasks that required them to relate the experience of the body in the ride to a mathematical description of the motion, as well as to data from electronic measurements of the g-forces experienced during the ride. The tasks were relatively open-ended. During the preparation for the visit the students had opportunities to discuss the projects with their teachers. The results of the investigations of the rides were presented in oral and written reports. Each group was also asked to work through the report of another group and to ask questions after the presentation. The amusement park project was first developed in the context of the educational programme "Problem Solving in Natural Sciences", described elsewhere in these proceedings (Hanson et al., 2006) and designed to widen recruiting to science educations. More details about the amusement park project can be found in previous work (Bagge & Pendrill 2002, 2004, Mårtensson-Pendrill & Axelsson 2000, Nilsson et al. 2004) and at the WWW-site, at http://fy.chalmers.se/LISEBERG/.

2.2. The force concept inventory

The Force Concept Inventory (FCI) is multiple-choice diagnostic test with 30 questions designed to probe students' conceptual understanding of force and related kinematics (Hestenes et al. 1992, Halloun et al. 1995). The answers in test are based on common student replies to open-ended questions. Hestenes and collaborators conclude that an FCI score of 60% can be regarded as the 'entry threshold' to Newtonian physics and a score of 85% as being Newtonian 'mastery threshold'. Hake (1998) performed a large survey study, including data from 62 high-school, college and entering university groups. He introduced a normalized gain defined as (class post-test average - class pre-test average)/ (100% - class pre-test average). and found that "conventional instruction" tends to give normalized gains around "1/4 of the possble gain, whereas the more interactive physics-education-research-based classes ... typically achieve twice as large fraction of the possible gain". The highest normalized gain in the survey was 0.69.

In the present study, the FCI was given to entering students in the engineering physics programme at Chalmers and in the Göteborg university physics program, as well as to second-semester students at the biotechnology programme at Chalmers. Most students have provided their names, enabling us to assess also possible gender differences, both for the total score and for individual questions. In addition, we have considered the correlation between exam result and FCI score for the engineering physics students.

A post-test has been given to a few of the student groups and the improvement for the university students is analysed in some more detail.

3. Results and Discussion

We present in this section results for a number of investigations of different student groups, and consider various aspects of the FCI test results. First, the characterization of different student groups is presented in 3.1. In section 3.2 we consider the relation to exam results. Gender differences are presented and discussed in sections 3.3-3.5, first for total results and then for individual questions, and finally, for the normalized gain between pre- and post-test scores in a project-oriented course.

3.1. Test scores for different student groups

The results on the FCI test exhibit large differences between different student groups. The cumulative graphs in Figure 1 show the distribution of individual pre-test scores, giving a visual characterization of the groups.

The engineering physics programme (F) is highly competitive and attracts students with a general strong interest in physics and mathematics. The engineering physics students groups have very high average FCI scores, 77% and 79%, respectively for the students entering 2003, and 2004. Figure 1 includes also results of a post-test performed some time after the second mechanics courses for students entering 2002, with a marginally higher average score, 82%. It should be noted that the engineering physics students entering before 2004 did not take part in the amusement park project.

The physics programme at Göteborg university (GU) accepts a smaller number of students, but in practice all applicants who are formally qualified are enrolled, leading to a much wider distribution of scores and a lower average, 56%. A post-test was given, unannounced, during class the week before the exam. The 31 students who participated achieved an average of 83%. The normalized gain for this group of students was 0.57, with large differences between male and female students as discussed in section 3.5.

Figure 1. Cumulative graph showing, on the horizontal axis, the percentage of students having at least the FCI score given on the vertical axis, where 30 is the number of questions in the test. Each point corresponds to one individual student. The lower curve is the pre-test score for university physics students(GU, N=59), whereas the upper curves refer to the first year engineering physics students starting in the years 2003 and 2004 (F1,03 and F1,04, with 110 and 111 students participating, respectively) and to the post-test score for the second-year students (F2, N=55), but also to post-test scores for the university students (N=31).

3.2. Test scores and exam results

The good scores of the engineering physics students were encouraging, not least in the view of reports about declining mathematics skills (e.g., Helenius & Tengstrand 2005). However, the results on the mechanics exam did not meet expectations. Figure 2 shows the correlation between individual exam results and initial FCI score. A first look may give the impression that the FCI scores is irrelevant for the exam result. A closer investigation of the diagram shows a remarkable lack of points in the upper left triangle. This can be taken as an indication that a good understanding of force concepts is a necessary, but not sufficient, condition for passing the exam. During the grading of the exam problems it was clear that lacking mathematical skills, as well as ability to apply them in a physics context, often raised obstacles for the students. An interview study is in progress to investigate these difficulties in more detail (Adawi et al., 2005).

Figure 2. Comparison of the FCI score and exam results in the for the engineering students entering in 2003. Each point corresponds to one individual. The maximum number of points at the exam was 60, and the pass limit was lowered from 30 to 24.

3.3. Gender differences

For all student groups we have tested, we have found that the subgroup of female students had lower FCI scores, although it must also be noted that some female students were among the top scorers in all groups. The total pre-test score was 78% for the male engineering physics students and 67% for the female students entering in 2003. Since relatively few female students choose engineering physics, we wanted to investigate if the gender difference could be a possible effect of students choice of education programme. The test was thus given also to new students in the biotechnology program at Chalmers. This is also a highly competitive program, but, with the emphasis on biotechnology, rather than physics, it attracts are larger number of female students. The average pre-test score was 54%, with the female students scoring an average 51% compared to 60% for the male students. The post-test average was 78%, corresponding to a normalized gain of 52%. (Too few students gave their name in the post test to make a gender comparison meaningful.) The pre-test gender differences were even more marked for the entering university physics students, as discussed in more detail below. In section 3.4 we look into the response patterns for the different FCI questions for engineering physics students and, for comparison, include also the fraction of correct responses for second-year engineering physics students.

Gender differences have been observed also in previous work, and we are now trying out a version where the FCI questions are put in alternative contexts (McCullough & Foster, 2000, and McCullough & Meltzer, 2001).

3.4. Problem-dependent gender differences

Figure 3 shows a comparison between the fraction of correct answers for the 2003 first-year male and female students in the engineering programme, and also includes the results of the second-year students. For many questions, there are insignificant differences between the groups. For others, e.g. questions 4, 5, 13 and 18 the main difference is between first- and second-year students, whereas for the questions 14, 15, 17, 25, 26 and 30 a notably smaller fraction of the female students give the correct answer.

Rennie and Parker (1998) considered the gender difference related to real-life problems and gender-adapted versions of the test have been designed (e.g. McCullough and Foster, 2000). McCullough L E and Meltzer (2001) have investigated the gender-adapted test, and found significantly modified response patterns for a few items. E.g. the original FCI item 14 includes an airplane dropping a packet. When changed to a bird dropping a fish, the fraction of correct responses from female students in her sample changed from 22% to 55%. Item 22 and 23 concerns a rocket, during and after using the engines. When the rocket was replaced by a person on ice, accidentally turning on a fire extinguisher the fraction of correct responses for female students on question (a straight-line motion) was improved from 10% to 48%. However, McCullough and Meltzer also found a remarkable decrease, from 47% to 18%, in fraction of correct answers for male students for question 22, considering the accelerated motion of the rocket/person.
Figure 3. Fraction of correct responses for the different items in the FCI test, for the first- and second-year engineering physics students. For the first-year students, the results of male (N=84) and female (N=16) students are presented separately. (The results refer to the students starting in 2003. 16 questionnaires were handed in anonymously).

3.5. Gender-dependent gain in a project-oriented course

Table I shows the pre- and post-test results for male and female students in the University physics programme, as well as the normalized gain. The gender difference was very pronounced in the beginning of the course, where only a quarter of the female students, compared to three quarters of the male students, scored 50% or more.

The intentions behind the design of the course included student involvement and a wide variation of tasks to accommodate different learning styles and to help students to connect different aspects of physics knowledge. This is often considered as one way to improve the learning situation for less traditional student groups. The results indicate that the invitations to active engagement in the course have given significant improvement on the FCI test scores. Still, male students seem to have benefited more from the course, in terms of FCI score gain. The large gender difference in the pre-test was found to be widened for the post-test, with the female post-test average comparable to the pretest average for the male students. A possible interpretation is that the female students took on a larger responsibility for coordinating the group work. The widening gender gap for FCI scores after the course is a cause for concern and calls for closer investigation. As one part of this investigation, we are now trying the alternative FCI format by McCullough & Meltzer (2001).

Group	Pre-test (%)	Post-test (%)	Normalized gain
Table I. Fraction correct answers in the pre and post-test FCI scores for entering university physics students. The pre-test was taken by 59 students. The pre-test scores in parentheses correspond to 31 identifiable students that took both the pre and post-test and are the numbers used to evaluate the normalized gain.
Male, N=35(20)	69 (70)	91	0.72
Female, N=24(11)	41 (44)	67	0.41
All, N=59(31)	56 (61)	83	0.57

4. Conclusion

The inclusion of the amusement park project and other activities, that encourage students to discuss important concepts, was found to give a gain comparable to the best "interactive engagement methods" included in the comparison by Hake (1998). The force concept inventory is an easily administered test, which can provide a helpful initial characterization of different student groups, and their possible problems concerning fundamental aspects of mechanics. The results are known to indicate relatively large gender differences, which were found also in this work and the widening gender gap between pre- and post-test is a cause of concern. Investigations are underway investigate the context-dependence of the replies to the test questions as well as possible pre-selection gender effects for the students in our different education programmes.

The correlation with exam results illustrates the importance of force concepts, but also of other skills, to solve exam problems in mechanics. The conceptual nature of the test means that mathematical skills, which are needed for the exam, play a relatively small role for the test score. In addition, the test gives relatively few challenges to the understanding of the vector character of force and acceleration, which are in focus during studies of forces in roller coasters and swings. An analysis of results on tests focusing more directly on these aspects is underway.

Acknowledgements

The author was the examiner of the introductory physics course at Göteborg university. I am grateful to the teachers who provided access to the other students, in particular to Tomas Carlsson who administered and graded the test for the Biotechnology students. Partial funding for this work was provided by CSELT - Chalmers strategic effort in learning and teaching.

References

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