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Correcting Students’ Misconceptions about Automobile Braking Distances and Video Analysis Using Interactive Program Tracker Peter Hockicko, Beáta Trpišová & Ján Ondruš

Journal of Science Education and Technology ISSN 1059-0145 Volume 23 Number 6 J Sci Educ Technol (2014) 23:763-776 DOI 10.1007/s10956-014-9510-z

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Author's personal copy J Sci Educ Technol (2014) 23:763–776 DOI 10.1007/s10956-014-9510-z

Correcting Students’ Misconceptions about Automobile Braking Distances and Video Analysis Using Interactive Program Tracker Peter Hockicko • Bea´ta Trpisˇova´ • Ja´n Ondrusˇ

Published online: 13 August 2014  Springer Science+Business Media New York 2014

Abstract The present paper informs about an analysis of students’ conceptions about car braking distances and also presents one of the novel methods of learning: an interactive computer program Tracker that we used to analyse the process of braking of a car. The analysis of the students’ conceptions about car braking distances consisted in obtaining their estimates of these quantities before and after watching a video recording of a car braking from various initial speeds to a complete stop and subsequent application of mathematical statistics to the obtained sets of students’ answers. The results revealed that the difference between the value of the car braking distance estimated before watching the video and the real value of this distance was not caused by a random error but by a systematic error which was due to the incorrect students’ conceptions about the car braking process. Watching the video significantly improved the students’ estimates of the car braking distance, and we show that in this case, the difference between the estimated value and the real value of the car braking distance was due only to a random error, i.e. the students’ conceptions about the car braking process were corrected. Some of the students subsequently performed video analysis of the braking processes of cars of various brands and under various conditions by means of Tracker that gave them exact knowledge of the physical quantities, which characterize a motor vehicle braking. Interviewing P. Hockicko (&)  B. Trpisˇova´ Department of Physics, Faculty of Electrical Engineering, University of Zˇilina, Zˇilina, Slovakia e-mail: [email protected] J. Ondrusˇ Department of Road and Urban Transports, Faculty of Operation and Economics of Transport and Communications, University of Zˇilina, Zˇilina, Slovakia

some of these students brought very positive reactions to this novel method of learning. Keywords Video analysis  Car braking distance  Misconceptions  Student’s t test

Introduction The dramatic increase in developing new technologies that we have been facing over the past decades has brought about invention of a number of new tools using of which in everyday life but also in the educational process in schools and universities is for young people very attractive. If studying physics is accompanied by using a computer, a new form of very attractive education arises (Hockicko 2010; Hodge et al. 2001). It is very important to use multimedia tools also in subjects other than physics to make science and technology more appealing and to address the scientific apathy of young people (Bussei and Merlino 2003). Online literature, online tutoring system, computer simulations and remote experiments can result in an online practical course that can be very useful in engineering studies and can be helpful for the engineering students throughout their academic studies and in their engineering career (Finkelstein et al. 2005; Wiesner and Lan 2004). E-learning platforms are especially useful when teaching science in general and physics in particular. They allow implementing tools of many kinds such as videos, mp3s, images or animations by means of which one can present dynamically many physical situations and concepts that are often difficult to apprehend using the traditional teaching methods (Martı´n-Blas and Serrano-Ferna´ndez 2009). Using computer to simulate and analyse various physical

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processes combined with games has proven to be very successful in teaching conceptual physics (Echeverrı´a et al. 2012), being an effective complement to traditional science education methods (Rutten et al. 2012). Poor qualitative understanding of physics the introductory physics students have has been investigated by a number of researchers (e.g. Halloun et al. 1985; Hestenes et al. 1992; Sokoloff and Thorton 1997). These authors pointed out that after attending traditional lectures, students did not exhibit any significant improvement on physics conceptual evaluation tests. The global test Force Concept Inventory (FCI) results demonstrated that the traditional teaching of the Newtonian mechanics in the early years of the university studies eliminates the wrong students’ perception of this subject acquired during the secondary school studies only to a small extent. One of the most important features of the FCI is that by subjecting the students to this test, the misconceptions they have when trying to apply the Newtonian mechanics ideas can be drawn forth (Martı´n-Blas et al. 2010). It has also been shown that traditional lectures or seminars help the students to acquire only basic knowledge without deeper understanding and ability of problem solving. The students do not have any conceptual understanding of the subject that should result from a sufficient number of solved quantitative tasks and from logically clear lectures (Redish 2003). It has also been argued (Felder and Brent 2003) that lectures based only on presentation slides do not result in optimum learning outcomes or in promotion of the development of transferable skills in the best possible way. Several innovative methods in physics education have been described and evaluated, and the impact of these methods on the learning outcomes of physics students has been investigated. The methods of this kind include PI (Peer Instruction), ILD (Interactive Lecture Demonstration), JiTT method (Just-in-time-teaching) (Mazur 1997; Schmidt 2011), etc. The nature of these methods lies mainly in the interactivity between the lecturer and the students who are actively involved in the individual stages of the teaching and learning process and actively participate in problem solving. This provides immediate feedback to the lecturer who can immediately respond to the incorrectly understood concepts (e.g. Sokoloff and Thorton 1997). We can also mention the learning method problembased learning (PBL). The students taught by this method quickly understood that the key skills required by industry, namely group work, time management and technical skills awareness, were enhanced. They convinced themselves that the main positive features of the PBL process were real application of the abovementioned skills and development of their teamwork and communication skills in the context of real-world problems (Gavin 2011). By means of the FCI

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scores, it was shown that the conceptual comprehension of the students participating in the PBL classes was better than that of the students attending the traditional class (Sahin 2010). It has also been demonstrated that a modelbased introductory physics curriculum is much more effective in the students’ conceptual learning than a traditional lecture–laboratory type instruction (Liang et al. 2012). At last, we mention a not new and significant problem that the physics teachers encounter: the lack of the students’ ability to understand and interpret physics graphs. For instance, when studying mechanics, students generally have great difficulties interpreting kinematic graphs and understanding motion and force concepts (Beichner 1996; Hake 1998; Halloun et al. 1985; Hestenes et al. 1992). This problem cannot be ignored since many physical quantities (e.g. velocity, acceleration) are defined as slopes (gradients) of line graphs (Planinic et al. 2012). Interpretation of kinematic graphs is another type of physics problems that require high visual/spatial resources. Spatial visualization ability significantly influences effectiveness of physics instruction (Kozhevnikov and Thornton 2006), and as it is declared in Kozhevnikov et al. (2007), it plays a central role in conceptualization processes in physics and in scientific discoveries. Hence, using tools that visualize the examined physical processes in teaching and learning physics may significantly improve the level of the students’ understanding of these processes. This claim was supported, e.g., by (Beichner 1996) who did a post-instruction assessment of the students’ ability to interpret kinematic graphs with the result that groups which used video analysis tools generally performed better than students taught via traditional methods. In this paper, we present one of the new creative methods of teaching physics: video analysis using the interactive program Tracker (Open Source Physics) by means of which we analyse the process of a motor vehicle braking. To our knowledge, no one so far has done such a research, although the problem of the braking distance has been studied by a number of researchers. As examples, we give the works by Nagurnas et al. (2007), Wu et al. (2009), Ciubotariu and Neculaiasa (2011), Olson et al. (1984) and Lyubenov (2011). In Nagurnas et al. (2007), the authors verified by also performing experiments that the values of the parameters of the braking motion of various cars, especially the braking distance, calculated using the methods of mathematical statistics are in a good agreement with the real ones. The authors of Wu et al. (2009) present a method of how to calculate comfortable acceleration that means acceleration at which the braking does not cause discomfort to the passengers sitting in the car. Of course this acceleration depends on the initial speed m0 of braking, the braking (stopping) distance and also on the

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friction acting between the road and the tires of the car, when braking. We note that works such as this one are important for designing future intelligent traffic. The work by Ciubotariu and Neculaiasa examines the relationship between the parameters of braking and the nature of the car braking system. We find there also a formula for the calculation of the braking distance for braking with unblocked wheels. This depends on the initial speed, the deceleration of braking and the braking time. To find the braking distance using this formula, the authors suggest to determine these parameters experimentally. The reference (Olson et al. 1984) is an extensive report that studies the braking distance from all possible aspects and points of view such as the driver eye height, the obstacle height, the night-time visibility, road curvature, highway design and so on. In Lyubenov (2011), the braking distance under different road conditions is examined experimentally by means of a new device: the VBOX 3i 100 Hz GPS Data Logger. The author also gives a formula for calculation of the stopping distance that takes into account three main factors that affect it—the driver reaction time, the vehicle reaction time and the vehicle braking capability. The structure of the paper is the following: In ‘‘Motivation’’ section, we explain our motivation to analyse the students’ conceptions about the car braking distances, and in ‘‘Methodology’’ section, we describe the method we used in this analysis, i.e. we show why these conceptions are incorrect and how can they be corrected. Section ‘‘Video Analysis of Motor Vehicle Braking’’ contains some concrete examples of video analysis of a motor vehicle braking process using Tracker. In Section ‘‘Examples of Students’ Misconceptions and Selected Aspects of Braking’’, we discuss some of the misconceptions the students’ have about the length of the car braking distances and their dependence on the mass and the initial speed of the car and on the friction acting between the road and the tires of the vehicle. Section ‘‘Feedback’’ presents some of the students’ feedback to learning using Tracker, and we give evidence that teaching physics using this method brings better results than teaching via traditional methods. Our findings are summarized in ‘‘Summary’’ section.

Motivation The reason for the work part of which we present in this contribution has been a still large number of car accidents ending with injury or death happening on the roads every year. To illustrate this reality, we will now give a few facts. The evening’s TV News often reports about car accidents involving young people who overestimated their abilities or the capabilities of their motor vehicle. In many cases, these accidents end tragically and we are only informed that the driver has not adjusted his/her drive to the nature and the state of the road.

765 Table 1 Number of car accidents ending with injury or death and the corresponding numbers of victims that occurred in Slovak Republic in the shown time periods January–March of the year

Number of accidents ending with injury or death

Number of victims

2012

1,051

60

2013

899

43

2014

1,040

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It was not so long ago (January 2012) when the finalist of the first series of the Slovak Superstar driving BMW perished. His car in the course of overtaking a van and getting into its driving lane skidded, went off the road and at a speed of 140 km/h (as the witnesses claim) crashed on a tree. Due to this crash, the vehicle snapped off into three pieces and the body of one of the two victims who were instantly dead was catapulted several tenths of metres from the vehicle. According to the Federal Statistical Office of Germany in 2011 died as a consequence of car accidents 522 young people aged between 18 and 24 years. Young people usually drive older vehicles that are not equipped with modern safety systems. It often happens that they go off the road due to the loss of control of the vehicle. We just note that among the 18–24-year-old German drivers, there are two times more of those who do not fasten their seatbelts than among the rest of the drivers. Finally in Table 1, we present the numbers of car accidents that led to injury or death and the corresponding numbers of victims that occurred in Slovak Republic in the time periods of January–March of the years 2012, 2013 and 2014. The facts such as the ones just stated led us to start an investigation of the conceptions and the knowledge of young people who possess the driver’s licence about some aspects of the road traffic, particularly about the braking characteristics of motor vehicles. Are the young people sufficiently prepared concerning this area? Do they know what should be the speed of the car they are driving if it should be stopped at a sufficient distance from an obstruction and if they do not, what may be the possible ways to rectify this lack of knowledge? The present paper deals with the answers to these questions.

Methodology Testing of Students’ Conceptions About Car Braking Distances As Ebersbach et al. (2010) note, examining students’ correct or incorrect beliefs about physical phenomena is not

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Pre-test (N = 515)

220 200 180 160

braking distance [m]

only relevant for the domain of developmental psychology but it is also of central importance for education as these beliefs often serve as a basis for the acquisition of formal knowledge. If the concepts the students have when entering their university studies are not in line with physical laws, the acquisition of the correct ones might be impeded since misconceptions are highly resistant to change even if conflicting evidence is provided. For the purposes of our investigation, we tested the conceptions about the car braking distances of the first-year students of the Faculty of Operation and Economics of Transport and Communications and the Faculty of Civil Engineering at the University of Zˇilina. These students were taking the course on mechanics, and the testing was done just after covering kinematics and dynamics in the traditional lectures. The task imposed on the students was the following: Find the braking distances of the automobile Sˇkoda Octavia 1.6 LX that begins to brake when moving at speeds 20, 40, 60, 80 and 100 km/h along an asphalt road. The car is driving on summer tires, and the driver is braking by totally flooring the brake pedal. We add that the roadway surface was a little wet after a small rain. Since the vehicle did not have the system ABS, the measured braking distance corresponded to braking in slide (video was prepared by Karlubı´k 2010). The testing of the students was performed two times: before and after watching a video that contained recordings of the braking of Sˇkoda Octavia 1.6 LX starting at the above-mentioned initial speeds. We call this a pre-test and a post-test, respectively. The students also had to answer the questions whether they drove a car and whether they already had been involved in a car accident with the following result: 78 % of the students drive a car, and 23 % have been already directly involved in a car accident. The pre-test and the post-test were performed on a sample of 515 students. As it is obvious, from each student we collected ten answers—five initial braking distances estimates for each of the above given initial speeds and five final braking distances estimates for each of these initial speeds. In this way, we obtained ten files of 515 values each—five files in case of the pre-test and five files in case of the posttest. These data are depicted by means of box graphs in Figs. 1, 2. Here, the median was calculated as the mean value of the obtained braking distances that were arranged in a nondescending progression, and the extreme values, i.e. the values loaded with a nonrandom error, were identified using the Grubbs’s test of extreme values. If among the student’s answers such an extreme braking distance value was found at least once, the data corresponding to his/her answers were excluded from all five (pre-test or post-test) of our data files. This resulted in (five) sample files of 492 values each in case of the pre-test and (five) sample files of 492 values each in case of the post-test.

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Median 25%-75% Extent of nonoutlying Outlying Extremes

140 120 100 80 60 40 20 0 20

40

60

80

100

initial velocity [km/h]

Fig. 1 Box graphs of the initial estimates of the car braking distances, i.e. the estimates made before watching a video recording of braking of Sˇkoda Octavia 1.6 LX

These sample files were then subjected to further statistical processing that is described in the next section. Statistical Analysis of the Sets of Answers Obtained from the Tests If there is a difference between the students’ car braking distances estimates and the true values of these quantities, then our aim is using the collected data to find out whether this difference is caused only by a random error, in which case the students’ conceptions about the car braking distances are correct, or also by a systematic error, i.e. these conceptions are incorrect. To fulfil this task, we used our sample data files to perform the Student’s t test (in the following text just ‘‘t test’’) (Snedecor and Cochran 1989). This test is used when one wants to determine the population mean of some quantity in case we have data only from a sample or several samples selected out of the whole population that are much smaller than this population. Thus, these data form sample data files of much shorter length than would be the length of a file corresponding to the whole population. Obviously, we have only one sample data file representing the whole population for a particular initial speed obtained from the pre-test or the post-test. However, the t test can be applied only in case when one can reasonably expect the population distribution of the investigated quantity to be normal (in the following text, we will just use the phrase ‘‘the population is

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180

braking distance [m]

160

H 0: l = d y:

Post-test (N = 515)

220 200

767

Median 25%-75% Extent of nonoutlying Outlying Extremes

H1:l = dy:

140

The true value of the distribution of the car braking distances estimates for the whole population is equal to the expected braking distance. The true value of the distribution of the car braking distances estimates for the whole population is not equal to the expected braking distance.

120 100 80 60 40 20 0 20

40

60

80

100

initial velocity [km/h]

Fig. 2 Box graphs of the final estimates of the car braking distances, i.e. the estimates made after watching a video recording of braking of Sˇkoda Octavia 1.6 LX

normal’’) (Taylor 1997) or when the sample files are large, i.e. the number of data in a sample file is n C 30. Then, the distribution of the means of the sample files around the true value of the investigated quantity is also normal and that is what one needs to be able to use the t test. In our case, we ‘‘measure’’ many times the same quantity—the car braking distance at some initial speed either before or after watching the video. Thus, it is reasonable to assume that our population (e.g. all university students in Slovakia) is normal, i.e. our measurement is subject to a random error. When our population is not normal but our sample files contain data loaded with a random error and are large (which is true in our case), one can use the central limit theorem and the law of large numbers to justify the application of the t test to these data. But our data can also be loaded with a systematic error, which would manifest itself by a shift of the whole bell-shaped Gauss distribution in case our population is normal or of the distribution for the case when our population is not normal but our sample is large. This would mean that the true value of the population distribution of the student’s car braking distances estimates is not equal to the expected value of this quantity. Armed with the above stated ideas, we can now describe the procedure of applying the t test to our data. We test the null hypothesis H0 against the two-sided alternative hypothesis H1 at the significance level a = 5 % for each of our ten files of the braking distances values:

As it is clear from Table 2, the quantity dy which was obtained by means of the video analysis using the program Tracker represents the theoretical (expected) value of the car braking distance. By means of the one-sample t test, we wanted to find out whether this theoretical value is consistent with the students’ observations. To this end, we calculated for each of our ten sample data files a 95 % twotailed confidence interval for the true value l if the parameter r2, i.e. the square of the standard deviation of the distribution of the car braking distances estimates for the whole population, is unknown according to the prescription (Markechova´ et al. 2011)   Sn Sn Xn  ta;n1 : pffiffiffi ; Xn þ ta;n1 : pffiffiffi ð1Þ n n where ta,n-1 is the critical value of the Student’s t distribution with n - 1 degrees of freedom with the same true value l as it has the distribution of the car braking distances for the whole population. These critical values for the significance level a = 5 % we evaluated in Excel. They can also be found on the World Wide Web. Obviously, in the above formulas, n = 492 in case of an initial estimates sample file, and n = 492 in case of a final estimates sample file. The quantity n 1X Xn ¼ Xi ð2Þ n i¼1 is the sample mean and the quantity S2n ¼

n 1 X ðXi  Xn Þ2 n  1 i¼1

ð3Þ

is the square of the sample standard deviation. We note that this formula represents the most commonly used estimator of r2, and at the same time, it is the unbiased estimator of the variance of the normal distribution. Both upper and lower limits of the confidence intervals (1) for each of our ten sample data files in case of a = 5 %, i.e. in case we have 95 % confidence intervals, are given in Table 2. The statement ‘‘95 % confidence interval’’ means that if we calculated many such confidence intervals using many sample files that would represent the measurement of the same quantity, 95 % of these intervals would contain the true value l of the distribution of this quantity. We stress that our two quintuples of the sample data files

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Table 2 Sample mean values, squares of sample standard deviations, lower and upper bounds of the confidence intervals (1) for a = 5 % and initial speeds and braking distances obtained by means of Tracker for automobile Sˇkoda Octavia 1.6 LX

initial speed (tachometer)

20 km/h

40 km/h

60 km/h

80 km/h

100 km/h

X n [m] (pre-test)

3.00

6.78

13.13

20.70

31.28

2.43

5.10

10.37

16.32

25.02

2.78

6.33

12.21

19.26

28.64

3.21

7.23

14.05

22.15

33.07

2

Sn [m] lower bound of the confidence intervals (1) for α = 5% [m] upper bound of the confidence intervals (1) for α = 5% [m] braking distances dy found using video analysis [m]

X n [m] (post-test) 2

Sn [m] lower bound of the confidence intervals (1) for α = 5% [m] upper bound of the confidence intervals (1) for α = 5% [m] initial speeds found using video analysis [km/h]

2.25±0.02 7.14±0.10 21.27±0.24 43.02±0.47 73.12±0.58

2.11

7.01

20.82

41.96

73.16

0.66

2.49

8.29

17.91

33.02

2.05

6.79

20.09

40.37

70.24

2.17

7.24

21.56

43.54

76.09

19.19±0.19 34.57±0.41 55.87±0.42 75.44±0.55 93.98±0.58

corresponding to the pre-test and the post-test each represent a measurement of a different quantity. Thus, our population for each of the ten cases is represented only by one sample file. Subjecting our data to the t test means the following: in case that dy falls within the limits of our 95 % confidence interval, the hypothesis H0 is confirmed, i.e. at the 5 % significance level, the difference between the true value of the braking distance and the braking distance found from the students’ estimates is due to only a random error, and thus, the students’ conceptions about this quantity are correct. In the opposite case, i.e. when dy does not assume a value from our 95 % confidence interval, the hypothesis H0 is rejected at the significance level of 5 % and the hypothesis H1 is accepted. This means that the difference between the true value of the car braking distance and the braking distance found as the mean of the students’ estimates is caused by a systematic error since the whole interval (1) is shifted with respect to the theoretical value of the car braking distance dy. Thus, in this case, the students’ conceptions about the car braking distances are incorrect. Applying the above ideas to our concrete data, we see n of looking at Table 2 that in case of the initial estimates X the car braking distances, the expected value dy (turquoise, underline) in four cases out of five does not fall into the 95 % confidence interval for the true value l (red, italic). Hence, we reject the hypothesis H0 and accept the hypothesis H1 meaning that the students’ estimates of the car braking distances are loaded with a systematic error, i.e. their conceptions about these quantities are incorrect.

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On the other hand, we can see in Table 2 that in case of the n made by the students car braking distances estimates X after watching the video, the theoretical value dy in four out of five cases falls within the limits of the 95 % confidence intervals for the true value l (yellow, bold). Hence, we accept the hypothesis H0, i.e. we can state that in this case, our data are loaded only with a random error, which means that the conceptions of the students about the car braking distances are correct after watching the video.

Video Analysis of Motor Vehicle Braking As it follows from the above results, watching a video recording of the car braking process in a positive manner affects the students’ conceptions about the car braking distances. This means that applying innovative methods in teaching physics is one of the ways how to increase the level of the students’ knowledge (Krupova´ 2009; Krisˇˇta´k et al. 2014). This fact motivated us to prepare in collaboration with the students and the faculties of the University of Zˇilina more video recordings of braking of cars of various brands under various conditions. By analysing these videos using Tracker, we could compare the car braking distances for cases when the car is driving on summer or winter tires and when it is braking on a wet or a dry road. The automobiles recorded on these videos were Sˇkoda Felicia 1.3 LX and Fabia Monte Carlo 1.2 TSI, Volkswagen Polo, Citroe¨n C6 3,0i V6, Renault Thalia and Mazda 3. We made the recordings at the airport with

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Fig. 3 An example of a video problem posted on the World Wide Web. The video records the braking of Sˇkoda Felicia 1.3 LX, and the braking started at a speed of about 40 kmh-1 as commented in the above text

asphalt surface that is located in the township Rosina near the town Zˇilina. One of the video problems posted on the World Wide Web prepared on the basis of these recordings

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is given in Fig. 3 (Hockicko 2013, http://hockicko.uniza. sk/Priklady/video_tasks.htm). The results of the analyses of these video recordings performed using Tracker are illustrated in Figs. 4, 5 and 8. Figures 3, 4 and 5 refer to the braking of Sˇkoda Felicia 1.3 LX and the initial speed, i.e. the speed at which the car started to brake, m0 = 40 kmh-1. This was the speed the driver of the car tried to keep before starting braking. However, as we will see below, by analysing the corresponding video recording using Tracker and by direct measurement using the device called XL meter, we obtained initial speed of about 37 kmh-1. Figure 4 shows the recording of the process of braking of Sˇkoda Felicia 1.3 LX and the time dependencies of the distance and the speed in the course of braking as obtained by Tracker. Figure 5 depicts how Tracker by means of fitting of the dependence of the speed on time determines the deceleration and the initial speed of the motion, as well as the braking distance that is equal to the area of the grey triangle. Clearly, this braking process is a motion at constant acceleration. In this case, we get using extrapolation the initial speed 11.64 ms-1, that is, 41.9 kmh-1, the deceleration 4.47 ms-2 and the braking distance 11.91 m. We bring to your attention, though, that this initial speed corresponds to time t = 0. However, in reality, the car started braking at t = 0.3 s, when the initial speed was 10.28 ms-1, i.e. about 37 kmh-1.

Fig. 4 Video recording of the process of braking of the car Sˇkoda Felicia 1.3 LX on wet asphalt road, and the corresponding speed and distance time dependencies obtained by Tracker. The video recording is the same as that used in the video problem depicted in Fig. 3

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Fig. 5 Analysis of the braking process of the car Sˇkoda Felicia 1.3 LX by means of Tracker that allows for determining deceleration, initial speed and braking distance. The analysed video recording is that shown in Figs. 3 and 4

There exist several commercial devices (Duda´cˇek, and Ondrusˇ 2010) that are able to accurately and instantaneously determine the braking distances, the initial speeds, the time of braking and the average deceleration during braking (Rievaj et al. 2013). Figure 6 depicts an output from such a device called the XL meter—direct measurements of the time dependencies of the instantaneous acceleration, the instantaneous speed and the distance gone by the car Sˇkoda Felicia 1.3 LX on wet road. This output refers to the motion whose braking part recording is used in the video problem displayed in Fig. 3 and analysed in Figs. 4 and 5. As it can be seen, the initial speed obtained by this method was about 37 kmh-1, which is basically the same as that determined by analysing the braking part of this motion using Tracker. Hence, Tracker and XL meter are in a very good agreement in this case. We also point out that on the basis of the graphs shown in Fig. 6, it is possible to determine times at which the driver changed gears and the magnitude of the average acceleration at a certain gear. To give more evidence that the analysis of our video recordings using Tracker is really correct, we performed more direct measurements using XL MeterTM. In Fig. 7, we then compare the braking distances as functions of initial speed obtained on both wet and dry asphalt road for Citro¨en C6 by means of these two methods. As it is clear, we basically got identical results.

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At the end of this section, we mention two works that are concerned with train braking distances. These distances should be such that safe and for the passengers comfortable stopping of the train be possible. To this end, Kim et al. (2010) present an analytical method by means of which the relationship between the brake and adhesion forces of the disc brake system can be estimated. In Pugi et al. (2013), a modular tool is presented that allows for accurate prediction of train braking performance and thereby of the train braking distance on the basis of main train features. Clearly, such knowledge may be very useful for train designers.

Examples of Students’ Misconceptions and Selected Aspects of Braking In this section, we give some selected misconceptions the students had about the car braking process, explain why are these opinions incorrect and show how the correct conceptions can be acquired by watching video recordings of vehicle braking and performing video analysis of these videos by means of Tracker. We also discuss the dependence of the braking distance on the initial speed and mass of the vehicle and friction acting between the tires and the road.

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Fig. 6 Analysis of the whole drive of Sˇkoda Felicia 1.3 LX, i.e. accelerating, moving at a constant speed and braking using XL MeterTM. The measurements shown correspond to the motion whose braking part recording is a part of the video problem given in Fig. 3 and is analysed in Figs. 4 and 5

Fig. 7 Comparison of braking distances as functions of initial speed determined using XL MeterTM and Tracker for various initial speeds in case of Citro¨en C6 driving on wet and dry asphalt road

M1 M2

A car with an initial speed of 100 km/h is able to stop on a distance smaller than 25 m. The braking distance depends linearly on the initial speed.

The fact that the students really possess wrong ideas about the length of the braking distance and its dependence

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on the initial speed is clearly demonstrated in Fig. 1—more than 50 % of them think that the braking distance corresponding to the initial speed of 100 kmh-1 is shorter than 25 m and majority assumes a linear increase of the length of the braking distance with increasing initial speed. It was interesting to watch the reactions of the tested students during playing of the video recordings of a vehicle braking process. Already when the video depicting the braking for the initial speed of 60 kmh-1 was played, almost all of them were surprised (they laughed, were astonished). Many of them alleged (and this was the case each year when the videos were presented at the lectures) that they did not expect such a long braking distance; especially, surprised were those who had estimated the braking distance to be 5 m and less. Some of them explained this answer by mistaking the braking distance for time. To correct these wrong conceptions, we let the students watch video recordings of braking of cars of various brands for various initial speeds and analyse these recordings by means of Tracker. From the obtained data, they could plot graphs representing the dependence of the braking distance s on the initial speed of braking m0. They found that this dependence was quadratic (Haugland 2013) as illustrated in Fig. 7 and given in the first approximation by the equation s ¼

v20 ; 2gl

ð4Þ

where g is the standard acceleration due to gravity, and l represents the coefficient of either static or kinematic friction depending on whether the wheels are turning in the course of braking or whether the automobile is braking in slide, respectively. We remark that relation (4) is also used in Wu et al. (2009) for determining comfortable acceleration of braking as we commented in ‘‘Introduction’’ section. From the data plotted in the above-mentioned graphs, the students also determined by fitting and according to (4) the coefficients of static friction acting between the tires of Citro¨en C6 on both dry and wet asphalt road. The obtained values were 0.98 and 0.63, respectively. To illustrate what are roughly the real values of the deceleration and the braking distance for braking from the initial speed of about 100 kmh-1, we show in Fig. 8 another analysis of the braking motion using Tracker. This analysis was done using a video recording of braking of Citroe¨n C6 at the initial speed of 103 kmh-1. As can be seen, the braking distance amounted to 45.21 m, which was the shortest braking distance we recorded at this initial speed for all cars. The braking deceleration had a value of about 9.28 ms-2. We note that the maximum deceleration at which braking is still safe is about 10 ms-2. We again note that the initial speed was not 31.14 ms-1, i.e. 112.1 kmh-1, as obtained from the extrapolation of the fit

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Fig. 8 Video analysis of the braking motion of Citroe¨n C6. The initial speed amounts to 28.61 ms-1 = 103 kmh-1

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since the car did not start braking at t = 0, but at a later time (about t = 0.23 s, v0 = 28.61 ms-1). The length of the braking distance markedly depends on the mass of the vehicle.

To show that the above statement is incorrect, we also recorded the braking motion of the truck mixer MAN for various initial speeds of braking and performed direct measurements using the XL MeterTM. The mass of this vehicle is about 22,000 kg which means that it is significantly heavier than a passenger vehicle whose mass is about 1,000–2,000 kg. From among the students who we asked about the relationship between the braking distances of these two kinds of vehicles, 85 % thought that the braking distance of the truck would be markedly longer than that of the passenger vehicle, and 15 % thought the opposite. No one thought that the braking distances of the passenger vehicle and the ten to twenty times heavier truck mixer would be comparable, which is the correct answer as justified by Eq. (4) according to which in the first approximation the braking distance does not depend on mass. This fact is demonstrated in Fig. 9 where we plot the dependencies of the braking distance measured using the XL MeterTM on the initial speed for the truck mixer MAN and for the passenger vehicle Mazda3 of mass 1,381 kg on dry asphalt road. Clearly, the braking distances of these two automobiles are comparable and so are the coefficients of static friction lMAN = 0.72 and lmazda = 0.70 calculated using Eq. (4).

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braking distance [m]

M3

Mazda3 MAN

70 60 50 40

y = 0.0055x 2+ 0.0323x

30

R²= 0.9949

20 2

y = 0.0056x - 0.0162x

10

R² = 0.9996

0 0

10

20

30

40

50

60

70

80

90

100 110 120

initial speed [km/h]

Fig. 9 Comparison of braking distance as function of initial speed on dry asphalt road determined using XL MeterTM for MAN (triangles) and Mazda3 (squares)

Hence, by Eq. (4) as far as a bicyclist, a passenger car, a truck or a bus have tires of the same quality, they will brake along the same road with the same deceleration since their braking distances are the same for the same initial speed. Thus, when, e.g, a bicycle is riding behind a truck at a small distance from him, the bicyclist must not assume that he/she comes to a stop in a shorter time than the truck because although the much more heavier truck possesses much larger inertia due to its large mass, the frictional force acting on its tires is much larger. Hence, braking distances of the bicycle and the truck should be comparable.

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We have to point out that the braking distance corresponding to a certain initial speed is in reality larger than that given by equation (4). This is due to the fact that the braking distance also depends on the reaction time of the driver and the car since neither the driver nor the braking system can react instantaneously. For example, the reaction time of a concentrated driver is about 0.6 s that of a tired or a sick driver is about 2.4 s. By Eq. (4), the braking distance corresponding to a certain initial speed is indirectly proportional to the coefficient of friction. That means the braking distance increases with decreasing l. This is illustrated in Fig. 7 that clearly demonstrates that the braking distances are larger for a wet road compared to the ones for a dry road. This is caused by larger friction acting between the tires of the vehicle and a dry road compared to the one acting between the tires and a wet road resulting in larger values of the coefficient of friction in case of the dry road compared to the ones for the wet road. As we already stated above, in case of Citro¨en C6 and an asphalt road, these values determined by fitting the data obtained using Tracker, i.e. the plots displaying the dependence of the braking distance on the initial speed, and comparing this fit with Eq. (4) were 0.98 and 0.63, respectively. Obviously, this is consistent with the above statements. The fact that the coefficient of friction is larger in case of a dry asphalt road than in case of a wet asphalt road is also confirmed in Brada´cˇ et al. (1997) who give the range of values of the coefficient of static friction (the wheels are turning) for a dry asphalt road from about 0.6 to about 0.9 and for a wet asphalt road from about 0.3 to about 0.8. The coefficient of kinematic friction (braking in slide) for a wet asphalt road assumes significantly lower values than the corresponding coefficient of static friction—from about 0.3 to about 0.4. On an icy road is the value of the coefficient of kinematic friction even smaller—about 0.1 (Hockicko 2013).

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Fig. 10 The dependence of the speed of a train on time before its entry to a train station

experimental groups, i.e. those who worked with Tracker (n = 90), revealed that students found the lectures presented also by means of video analysis and simulations more interesting, and they increased understanding of the studied physical phenomena and showed the interconnection between physical theory and daily practice. Using computer and video analysis made physics a more popular and interesting subject. We observed that students liked these new interactive methods of teaching and learning as using them made it possible to immediately apply their skills and knowledge acquired in studying mathematics and physics. We give a few reactions of the students who worked with Tracker to illustrate the above stated facts • • • •

• Feedback The students who took part in our tests about the automobile braking distances expressed their impressions, e.g. by following comments • • • •

There should be more videos like this. Really? A great video! WOW, I didn’t expect the braking distances to be so large! From now on I’m driving slower.

Students’ feedback has become an important element in teaching and learning, and it is a useful tool for development of new course teaching methods (Nair et al. 2011). The informal interviews with the students of the

Thanks the video analysis I have understood some points that haven’t been clear to me so far. I really liked analysing videos by means of a computer program. I have understood the physics better, the dependences of the speed and the distance on time. This is a very good way of using physics in practice. Since we repeatedly used certain formulas, I remembered them better. Also studying physics was for me easier since I could try out how it worked. I gained knew knowledge in physics.

To give also some quantitative evidence of the positive features of the interactive teaching and learning using Tracker, we present the answers of the students who were taught by traditional methods and the students of the experimental group to one of the questions of the test to which they were subjected at the beginning and at the end of the semester. The test question was the following The graph in the figure (Fig. 10) shows the dependence of the speed of a train on time before its entry to a train station. What was the magnitude of the acceleration of the train during braking? (A) (B) (C) (D)

30/8 ms-2 30/12 ms-2 30/10 ms-2 40/12 ms-2

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Fig. 11 Percentage of answers to a test question given by students taught by traditional methods and students who worked with Tracker at the beginning (pre-test) and at the end (post-test) of the semester

The graphs in the following Fig. 11 give the percentage of the answers to all four possibilities. As it can be seen, at the end of the semester the percentage of the correct answers (red, (A)) is larger than that at the beginning of the semester. But more importantly it is clear from the graphs that while at the beginning of the semester, the percentage of the correct answers is about the same for the students taught by traditional methods and those belonging to the experimental group; at the end of the semester, the percentage of the correct answers of the students belonging to the experimental group is significantly larger than that of the students taught by traditional methods. We also performed various surveys at other technical universities. These surveys confirmed that using video analysis and simulations in the educational process results in enhanced knowledge compared to that gained through teaching by traditional methods (Hockicko 2012; Hockicko et al. 2014). Our research also showed that active learning develops student’s communication and cooperation. We observed that the class attendance and the students’ participation in the learning process were significantly higher when using active learning methods compared to the traditional teaching-based classes. We found out that the students taught using interactive methods liked teamwork and enhanced their communication skills; we felt a stronger motivation and a good learning atmosphere in the class (Hockicko 2012). Finally, we must add that an important element in active learning is discussion. As Oliveira and Oliveira (2013) state, it allows for immediate clarification of doubts and verification of the correct understanding of the concepts, thus also promoting the teacher–student interaction. To summarize, our experiments clearly demonstrated that interactive methods, i.e. in our case videos and video analysis, made it possible for the students to gain more effectively knowledge of better quality. The use of these tools increases the demonstration of the curriculum, increases students’ attention, forces them to work and think

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independently and helps to reduce misconceptions gained during elementary school and high school education.

Summary As stated in the above text, about 78 % of students drive a car and about 23 % of them were already involved in a car accident. One of the possible causes of the numerous car accidents caused by young people may be incorrect students’ conceptions about the car braking distances. In this contribution, we have shown by means of statistical processing of data obtained by testing a sample group of students that the deviation of the students’ braking distance estimates from the real values of this quantity is not caused by a random but by a systematic error. As we have seen, however, after watching videos recording braking of cars of various brands, the students’ car braking distances estimates became consistent with the real values meaning that the deviations of these estimates from the real values were caused only by a random error. Some of the tested students also performed video analysis of the process of braking recorded on the videos by means of the interactive program Tracker. By watching the student’s reactions to the results of this analysis and also by directly interviewing some of them, we found that the students liked this method of learning and they found it very interesting. We could see that their understanding of the fundamental physical laws became deeper compared to that the students attending a traditional class had. The students taught interactively liked the teamwork, the possibility to discuss immediately the results of the video analysis, and we also felt a very good atmosphere in the class. To conclude the present paper has demonstrated that watching videos recording the process of braking and subsequently performing the video analysis using these videos in an appropriate and attractive way forms correct students’ conceptions about the car braking distances. We

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saw that using videos and other multimedia aids affected in a positive manner the level of the students’ knowledge and their understanding of physical phenomena. We do not have any evidence that motor vehicle braking is a part of the teaching process at the schools and the drivers’ schools in Slovakia. However, giving the young people the correct knowledge about the braking distances of their cars can make them drive in a more responsible manner and consequently may save their life and also the lives of other road traffic participants. Moreover, Tracker is free and video analyses such as those presented in this contribution can be done not only at universities but also by the high school students. On the basis of the arguments just given, we think that the research presented in this paper is important and is one of the steps to be done on the way to lower the car accident rate. Acknowledgments This work was supported by the Slovak Grant Agency KEGA on the basis of the agreements No. 035ZˇU-4/2012 and by Foundation Volkswagen Slovakia (No. 052/12). It was written within the project from Operational Programme Education called Development of culture quality at the University of Zˇilina based on the European standards of higher education, ITMS code 26110230060 and Centre of excellence for systems and services of intelligent transport, ITMS 26220120028 supported by the Research & Development Operational Programme funded by the ERDF.

References Beichner RJ (1996) The impact of video motion analysis on kinematic graph interpretation skills. Am J Phys 64(10):1272–1277 Brada´cˇ A et al (1997) Judicial engineering, Academic Publisher CERM, s. r. o., Brno, ISBN 80-7204-057-X Bussei P, Merlino S (2003) European workshop on multimedia in physics teaching and learning. Europhys News 34(3):116–117 Ciubotariu D, Neculaiasa V (2011) Contributions regarding the study of the braking system of cars. J Eng Stud Res 17(2):37–44 Duda´cˇek J, Ondrusˇ J (2010) Results of measurements of the braking characteristics of the passenger automobile Citroe¨n C6. Exper Road Traffic Electr Eng Mech Eng Other Tech Fields 11(1):27–30. ISSN 1335-1133. ISSN 0031-921X Ebersbach M, Van Dooren W, Verschaffel L (2010) Knowledge on accelerated motion as measured by implicit and explicit tasks in 5 to 16 year olds. Int J Sci Math Educ 9(1):25–46 Echeverrı´a A, Barrios E, Nussbaum M, Ame´stica M, Leclerc S (2012) The atomic intrinsic integration approach: a structured methodology for the design of games for the conceptual understanding of physics. Comput Educ 59(2):806–816 Felder RM, Brent R (2003) Learning by doing. Chem Eng Educ 37(4):282–283 Finkelstein ND, Adams WK, Keller CJ, Kohl PB, Perkins KK, Podolefsky NS, Reid S, LeMaster R (2005) When learning about the real world is better done virtually: a study of substituting computer simulations for laboratory equipment. Phys Rev Spec Top Phys Educ Res 1(1):1–7 Gavin K (2011) Case study of a project-based learning course in civil engineering design. Eur J Eng Edu 36(6):547–558 Hake RR (1998) Interactive-engagement versus traditional methods: a six-thousand-student survey of mechanics test data for introductory physics courses. Am J Phys 66(1):64–74

775 Halloun I, Hestenes D (1985) The initial knowledge state of college physics students. Am J Phys 53(11):1043–1055 Haugland OA (2013) Car stopping distance on a tabletop. Phys Teach 51(5):268 Hestenes D, Wells M, Swackhamer G (1992) Force concept inventory. Phys Teach 30(3):141–158 Hockicko P (2010) Nontraditional approach to studying science and technology. Communications 12(3):66–71 Hockicko P (2012) Attractiveness of learning physics by means of video analysis and modeling tools. In: Proceedings of the 40th SEFI annual conference engineering education 2020: meet the future, 2012, Thessaloniki, Greece Hockicko P (2013) Video-analysis based tasks in physics. University of Zˇilina, EDIS, Zˇilina. http://hockicko.uniza.sk/Priklady/video_ tasks.htm Hockicko P, Krisˇˇta´k Lˇ, Neˇmec M (2014) Development of students’ conceptual thinking by means of video analysis and interactive simulations at technical universities. Eur J Eng Educ (in press). doi:10.1080/03043797.2014.941337 Hodge H, Hinton HS, Lightner M (2001) Virtual circuit laboratory. J Eng Educ 90(4):507–511 Karlubı´k A (2010) Video-measurements in physics teaching (thesis). Bratislava, p. 61 Kim Y.-M, Kim Y.-G, Kim S.-W, Park C.-K, and Park T.-W (2010) Estimation of the adhesion force for a disk brake in a skid control condition. Int J Automot Technol 11(5):673–680 Kozhevnikov M, Thornton R (2006) Real-time data display, spatial visualization ability, and learning force and motion concepts. J Sci Educ Technol 15(1):111–132 Kozhevnikov M, Motes MA, Hegarty M (2007) Spatial visualization in physics problem solving. Cogn Sci 31(4):549–579 Krisˇˇta´k Lˇ, Neˇmec M, Danihelova´ Z (2014) Interactive method of teaching physics at technical universities. Inf Educ 13(1): 51–71 Krupova´ I (2009) The development of natural science literacy in pupils in the first stage of basic school using the method of managed discovery. Pedagogika LIX-2009(3):259–268. ISSN 0031-3815 Liang LL, Fulmer GW, Majerich DM, Clevenstine R, Howanski R (2012) The effects of a model-based physics curriculum program with a physics first approach: a causal-comparative study. J Sci Educ Technol 21(1):114–124 Lyubenov D (2011) Stopping distance. Deceleration. VBOX 3i. GPS Data Logger. In: Proceedings of the III international scientific conference transport problems 2011, Katowice, Poland, 2011, p 199–205 Markechova´ D, Stehlı´kova´ B, Tirpa´kova´ A (2011) Statistical methods and their applications. Constantine the Philosopher University in Nitra, p 534 (in Slovak) Martı´n-Blas T, Serrano-Ferna´ndez A (2009) The role of new technologies in the learning process: moodle as a teaching tool in physics. Comput Educ 52(1):35–44 Martı´n-Blas T, Seidel L, Serrano-Ferna´ndez A (2010) Enhancing force concept inventory diagnostics to identify dominant misconceptions in first-year engineering physics. Eur J Eng Educ 35(6):597–606 Mazur E (1997) Peer instruction. A user’s manual. Prentice Hall, New York Nagurnas S, Mitunevicˇius V, Unarski J, Wach W (2007) Evaluation of veracity of car braking parameters used for the analysis of road accidents. Transport 22(4):307–311 Nair CS, Patil A, Mertova P (2011) Enhancing the quality of engineering education by utilising student feedback. Eur J Eng Educ 36(1):3–12 Oliveira PC, Oliveira CG (2013) Using conceptual questions to promote motivation and learning in physics lectures. Eur J Eng Educ 38(4):417–424

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Author's personal copy 776 Olson PL, Cleveland DE, Fancher PS, Schneider LW (1984) Parameters affecting stopping sight distance. The University of Michigan Transportation Research Institute Planinic M, Milin-Sipus Z, Katic H, Susac A, Ivanjek L (2012) Comparison of student understanding of line graph slope in physics and mathematics. Int J Sci Math Educ 10(6):1393–1414 Pugi L, Malvezzi M, Papini S, Vettori G (2013) Design and preliminary validation of a tool for the simulation of train braking performance. J Mod Transport 21(4):247–257 Redish EF (2003) Teaching physics. Wiley, New York Rievaj V, Vra´bel J Huda´k A (2013) Tire inflation pressure influence on a vehicle stopping distances. Int J Traffic Transport Eng 2(2):9–13. ISSN 2325-0062 Rutten N, van Joolingen WR, van der Veen JT (2012) The learning effects of computer simulations in science education. Comput Educ 58(1):136–153 Sahin M (2010) Effects of problem-based learning on university students’ epistemological beliefs about physics and physics learning and conceptual understanding of newtonian mechanics. J Sci Educ Technol 19(3):266–275

123

J Sci Educ Technol (2014) 23:763–776 Schmidt B (2011) Teaching engineering dynamics by use of peer instruction supported by an audience response system. Eur J Eng Educ 36(5):413–423 Snedecor GW, Cochran WG (1989) Statistical methods, 8th edn. Ames, Iowa State University Press Sokoloff DR, Thorton RK (1997) Using interactive lecture demonstrations to create an active learning environment. Phys Teach 35(6):340–347 Taylor JR (1997) An introduction to error analysis. University Science Books, Sausalito Tracker (program). http://www.cabrillo.edu/*dbrown/tracker Wiesner TF, Lan W (2004) Comparison of student learning in physical and simulated unit operations experiments. J Eng Educ 93(3):195–204 Wu Z, Liu Y, Pan G (2009) A smart car control model for brake comfort based on car following. IEEE Transp Intell Trans Syst 10(1):42–46