Exploration of Students’ Misconceptions in Mechanics using the FCI

Veiw figure View Figure

View next figure

During year 2011-2012, only 14 students reached the threshold at the pre-test, and 16 at the post-test. During the three years, 279 notes were above the Newtonian threshold, among 850 pre-test and 957 post-test in all. Figure 1 shows the distribution of the notes for all the 3 years cumulated.

In order to understand the reasons of such a weak level, we decided to deepen the analysis of the FCI results and to analyze the answers question by question.

As signaled by Huffman and Heller ^[5], the authors of the FCI recommend the use of their test in three cases: firstly, as a diagnostic tool; secondly, for evaluating instruction and finally as a placement exam. In spite of Huffman and Heller criticism, it seemed to us that the inventory could still be used as a diagnostic tool and as a mean to evaluate instruction: Hestenes ^[2] says that a wrong answer is more significant than a good answer, and the answers were designed to capture misconceptions. Even if the test measures pieces of knowledge rather than a central concept of force ^[5], we thought that it could provide indications about how our students understand a given situation. Our minimal hypothesis was that the test provided information about their conceptions and misconceptions in Newtonian Mechanics.

Figure 2 shows the percentage of good answers to each question before (pre-test) and after (post-test) the course of mechanics between 2010 and 2013, all students and all teaching methods together.

Figure 2. Results of theFCI by question from 2010 to 2013

Download as

Veiw figure View Figure

View previous figure

View next figure

As the results of the pre-test and of the post-test were very close, which meant that the errors were quite the same before and after the course, we decided to cumulate answers to each question covering all 1807 takes (pre-test and post-test) during the three years before analyzing them in detail. Figure 3 shows the results for all takes cumulated.

Figure 3. Cumulated Results of the FCI by questions from 2010 to 2013

Download as

Veiw figure View Figure

View previous figure

View next figure

On figure 3, we have drawn a red and a green line dividing the scores into three subgroups according to the percentage of correct answers. The first group of questions is the one where the score is lower than 30%, the second comprises the questions with scores between 30% and 50% and the third group is composed of the questions which got a score above 50%.

3. Main Results

3.1. Analysis of the Answers for Scores Lower than 30%

Let start with the analysis of the group of questions having got scores under 30%. Include in this group are the questions n°2, 4, 5, 11, 13, 15, 17, 18, 20, 22, 25, 26 and 30. These are the questions where our students have most difficulties. The table from Hestenes and Jackson ^[3] mentioned above proposes a list of misconceptions related to each answer for each question.

This will be illustrated by an example. Question 15 read as follows: “a large truck breaks down out on the road and receives a push back into town by a small compact car. Having augmented its speed the car reaches its cruising speed, still pushing the truck” and this text is illustrated by an image showing a small car pushing a big lorry.

Five proposals are made to describe the situation:

A. the amount of force with which the car pushes on the truck is equal to that with which the truck pushes back on the car.

B. the amount of force with which the car pushes on the truck is smaller than that with which the truck pushes back on the car.

C. the amount of force with which the car pushes on the truck is greater than that with which the truck pushes back on the car.

D. the car's engine is running so the car pushes against the truck, but the truck's engine is not running so the truck cannot push back against the car. The truck is pushed forward simply because it is in the way of the car.

E. neither the car nor the truck exert any force on the other. The truck is pushed forward simply because it is in the way of the car.

The correct answer is A (Action – Reaction principle). According to Hestenes& al. ^[3], if the student validates the answer D, then he/she makes an error in the identification of active force. If he/she validates answer C then his/her conception is that the agent the most active produces the biggest force. If he/she validates answer B, the error concerns the influence of the mass on force.

For this question, the percentages of the different answers from our students are represented in Diagram 1.

Diagram 1. Answers to question 15

Download as

Veiw figure View Figure

View previous figure

We can see that 66.85% of the respondents make an error on the principle of action-reaction for a system moving at constant speed. For them, the solid which produces the movement has the biggest force while, in fact, the system composed by the truck and the car is in balance (First Newton's law) and while the action-reaction principle applies.

The following table (Table 1) shows the answers made by our students to the questions in this first group with scores under 30%. The correct answer to the question is in green, the yellow represents the highest percentage(s) of answers. Sometimes, two answers have quite similar scores and are considered equally.

The misconceptions provided by Hestenes & al. ^[3] which correspond to the highest percentage(s) of errors made by our students are presented in the second table (Table 2).

Table 1. Answers for scores under 30%

Download as

Veiw figure View Table

Table 2. Misconceptions according to Hestenes& al. for scores under 30%

Download as

Veiw figure View Table

If we follow Hestenes and his colleagues (misconceptions indicated in Table 2), it seems that there is no dominant conceptual error among our students. But if we look carefully at the phrasing of the answers which have got the highest scores, things change, and we can identify three misconceptions, some of them being recurrent in spite of the type of problem (Table 3).

Out of 13 questions, 8 concern the force applied to a solid in motion. We can make the hypothesis that our students do not correctly understand what is happening when there are several forces applied to a solid in motion. It seems that their recurrent point of failure is that they consider that there must be a force in the direction of the movement: some questions revealed it explicitly, since their favorite answers includes a force in the direction of the movement (5, 11, 18); others are more implicit: for the students, there is a resulting force in the direction of the movement, even if there are no force applied or if the only forces in presence are action and reaction of two bodies against each other (13, 15, 17, 25, 30). Another recurrent misconception is that the weight or the mass has an impact on the trajectory of a falling object (2, 4); and a third one reveals confusion between acceleration and velocity (20, 22, 26).

Table 3. Our students’ misconceptions (1)

Download as

Veiw figure View Table

These notionsare widely covered by the program through exercises on Newton’s first law and third law, and it is the same for the principle of action-reaction. If the students make a mistake concerning these mechanical concepts before the course, it could be considered as normal, because many of them are not familiar with mechanics. But, when they commit these errors after the course, whatever the teaching method used, it becomes problematic, and this raises a lot of questions!

3.2. Analysis of the Answers for Scores between 30% and 50%

Questions for which the score is between 30% and 50% are n° 1, 3, 8, 9, 10, 14, 16, 21, 23 and 28. The answers are presented with the same color convention as before in Table 4 below.

Table 4. Answers for scores between 30% and 50%

Download as

Veiw figure View Table

Table 5. Misconceptions according to Hestenes& al. for scores between 30% and 50%

Download as

Veiw figure View Table

Then, we compare the results of the students with the misconceptions provided by Hestenes& al. ^[3] (Table 5). When two wrong answers have similar scores (i.e. within an interval lower than 5%), we consider them equally.

In Table 5, we see that one misconception “the last force to act determines motion” appears more often than others, and that the other errors just appear once. This misconception is part of the one identified previously: the movement is driven by the last force applied.

Again, if we look carefully at the answers which have got the highest scores, we can identify three misconceptions already spotted in the previous set of questions, together with a new one (Table 6).

Table 6. Our students’ misconceptions (2)

Download as

Veiw figure View Table

The same misconceptions as in the previous set are the following: weight or mass have an impact on the trajectory of a falling object (1) or on the intensity of the force (28); some confusion between acceleration and velocity (3, 10, 21, 23-2) is still influencing the answers, and finally, the idea that there is a driving force in the direction of the movement of an object is again underpinning the answers to several questions (8, 9-2, 16, 23-1). It seems that there is also a misconception related to the vector nature of velocity, which causes wrong answers to questions 9(a) and 14…

3.3. Analysis of the Answers in the Upper Part (Score above 50%)

Table 7. Answers for scores over 50%

Download as

Veiw figure View Table

Table 8. Misconceptions according to Hestenes & al. for scores over 50%

Download as

Veiw figure View Table

Questions getting scores over 50% are n° 6, 7, 12, 19, 24, 27 and 29. The answers to these questions are presented in Table 7. There are still significant percentages of wrong answers to these questions, so we can repeat the same exercise as before applied to these questions (Table 8), taking into consideration the highest score(s) among the wrong answers.

Again, there is no dominant misconception appearing in Table 8. But, if we do the same exercise as previously, we can identify from their responses some misconceptions, which are presented in Table 9 below.

Table 9. Our students’ misconceptions (3)

Download as

Veiw figure View Table