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

University and Engineering Physics Students' Understanding of Force and Acceleration

Ann-Marie Pendrill,
Institute of Physics, Göteborg University, SE-412 96 Göteborg, Sweden

Force and acceleration are fundamental physics concepts, known to be problematic to many students. In this work first-year physics students' understanding of mechanics has been probed in many different ways. The Force Concept Inventory has been for initial diagnosis, and in some cases also for post-testing. As part of the course, the students were assigned tasks relating the mathematical description of the motion in amusement park rides to the experience of the body. The results, as well as the gains exhibit considerable gender differences.

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. In this study, first-year physics students' understanding of mechanics has been probed in different ways. The Force Concept Inventory has been used for initial diagnosis of the students in the Göteborg university physics programme, as well for engineering physics students at Chalmers. An amusement park visit was one of the activities included in the course to help student develop their understanding of force and acceleration. The presentations of their investigations often lead to challenging physics discussions.

2 The force concept inventory

The Force Concept Inventory (FCI) is multiple-choice test designed to monitor students' conceptual understanding of force and related kinematics (Hestenes et al. 1992, Halloun et al 1995). Hestenes and collaborators conclude that an FCI score of 60% can be regarded as the 'entry threshold' to Newtonian physics and 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. The cumulative graphs in Figure 1 shows the distribution of individual pre-test scores and give 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 group has a very high average FCI score, 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%.

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 below.

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 maximum number of points at 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 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 post-test score for the second-year students (F2, N=55), but also to post-test scores for the university students (N=31).

2.1 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. 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 score 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 progess to investigate these difficulties in more detail (Adawi et al, 2005).

Figure 2Comparison of 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.

2.2 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. 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%. The pre-test gender differences were even more marked for the entering university physics students, as discussed in more detail below. We first look into the response patterns the different FCI questions for engineering physics students and, for comparison, include also the fraction of correct responses for second-year engineering physics students.

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 considering the importance of 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 response 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).

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 introductory mechanics course 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. Each group investigated one section of a roller-coaster and one other ride attraction. All groups had different tasks that involved relating the experience of the body in amusement park rides 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 amusement park projects with their teachers. The results of the investigations, which were performed in groups of 6-8 students, 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 and Nyman). More details about the amusement park project can be found in previous work (Bagge and Pendrill 2002, 2004, Mårtensson-Pendrill and Axelsson 2000, Nilsson et al 2004) and at the WWW-site, at

The intentions behind the design of the course included student involvement and a wide variation of taskts to accommodate different learning styles and to help students to connect different aspects of physics knowledge. 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 is thus widened for the post-test, with the female post-test average comparable to the pretest average for the male students. This widening gender gap is a cause for concern and calls for closer investigation. A possible interpretation is that the female students took on a larger responsibility for coordinating the group work.

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 number used to evaluate the normalized gain.
Group Pre-test (%) Post-test (%) 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

3. Discussion

Although our new physics students often have a reasonably good grasp of force concepts, and are able to work out forces in one-dimensional situations, we have found that they often lack an appreciation of the vector character of both force and acceleration. Gender differences are a cause of concern. Amusement park investigations may help develop a more complete understanding, but the rides do not by themselves radiate knowledge. Discussion and follow-up, including challenging students' descriptions, are important to help students focus on important features of force and acceleration.
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. Partial funding for this work was provided by CSELT - Chalmers strategic effort in learning and teaching.

Adawi T., Ingerman Å. and Pendrill, A-M. (2004), How mathematical is conceptual understanding?, Contribution to Physics Teaching in Engineering Education (PTEE) 2005, Brno

Bagge, S. and Pendrill, A.-M.(2002), Classical physics experiments in the amusement park, Physics Education 37, 507-511

Bagge, S (2003), Learning Physics by Experiment - An investigation of extramural learning (licentiate thesis, Göteborg University)

Bagge, S. and Pendrill, A.-M.(2004), Extramural learning at Liseberg. In E.K. Henriksen and M. Ødegaard (Ed.) Naturfagenes didaktik - en displin i forandring? - Proc. 7th nordic research symposium about science in school, Høgskolen i Agder.

Hestenes, D., Wells, M. and Swackhamer, G. (1992), "Force Concept Inventory",

Halloun I, Hake R, Mosca E and Hestenes D (1995), Force Concept Inventory, password protected at The Physics Teacher 33,141-158

Mårtensson-Pendrill, A-M and Axelsson, M., (2000), Science at the Amusement Park, CAL-laborate Volume 5, available at

Nilsson, P., Pendrill, A-M. and Pettersson, H. (2004), Learning physics with the body, IOSTE IX.

Rennie, L. J. and Parker L H (1998) Equitable measurement of achievement in physics: high school students' responses to assessment tasks in different formats and contexts J. Women and Minorities in Sci. Eng. 4 (2-3), 113-127 (1998).

McCullough, L. E. and Foster, T., A Gender Context for the Force Concept Inventory, AAPT Announcer 30(4), 105 (2000) see also

McCullough L E and Meltzer, DE (2001) Differences in male/female response patterns on alternative-format versions of FCI items available at href=