FAVOURING THE UNDERSTANDING OF PARABOLIC
MOTION IN A VIDEO BASED LABORATORY
Louis Trudel1 and Abdeljalil Métioui2
1
Université d’Ottawa
2
Université du Québec à Montréal
Abstract: The parabolic motion concept was chosen since it is linked with the vector
nature of motion and it is likely that the students would harbour many alternative
conceptions with it. Our research objective consists in evaluating the effect of a video
based laboratory (VBL) on the high school students’ understanding of projectile motion.
A test of understanding based on SOLO taxonomy was used to measure students’
understanding of parabolic motion in a repeated measures research design. A repeated
measures analysis of variance shows that, during the implementation of the VBL, the
pupils’ understanding of parabolic motion increased in a significant way. Finally, we
conclude by specifying advantages and limits of our research, as well as
recommendations for subsequent research.
Key words: parabolic motion, computer assisted laboratory, learning sequence, secondary
school; conceptual understanding
INTRODUCTION
The world of physics phenomena can be a complex and unpredictable environment for
students. Students experience physical phenomena on a daily basis and naturally derive
preconceptions about their interactions with these phenomena. Students develop common
sense theories of the physical world that have proven time and time again to be
satisfactory for their day-to-day experiences (Knight, 2004). However, students’ prior
assumptions (often seen as misconceptions) are remarkably resistant to change and may
hinder the instructional effectiveness as well as the development of scientific literacy
(Knight, 2004) for two main reasons. Firstly, due to the complex nature of motion,
students experience difficulty to construct strong conceptual understanding of the
important differences between the key principles of kinematics: position or distance,
velocity, acceleration, and time in one or more dimensions (Aguirre, 1988). These
difficulties are compounded when they studied parabolic motion since it requires the
understanding of the various motion concepts used in one dimensional kinematics and, on
the top of that, how to combine them to understand properties of parabolic motion.
Consider for example the case of objects launched by firing or the case of objects
dropped from a moving carrier. In the first case, such as when a ball is given a horizontal
speed while approaching a cliff, students think that the ball will travel horizontally for
some time after going over the edge of the cliff before it begins to fall. In the second case,
the belief that an object carried along possess no impetus and that upon release, will fall
vertically, is shared by an important proportion of students (Dilbert, Karaman &
Duzgun). These last authors could explain these misconceptions and others about
parabolic motion by what they call a naïve theory of motion which is strikingly similar to
the medieval theory of impetus.
Secondly, students harbour many misconceptions when it comes to graphical
interpretation and representation. For them, graphs are seen as literal pictures of the
situation and not as indicators of which type of motion is occurring. Students may also
confuse the meaning of the slope of a line and the height of a point of the line (Beichner,
1994). It requires a great deal of conceptual understanding to correctly interpret the
graphical representation of an object’s position relative to time and translate that
understanding to the correct representation of the object’s velocity relative to time as well
as its acceleration relative to time graphs. These difficulties are compounded with
parabolic motion which involved the consideration (and their combination) of the various
kinematical quantities along the two components X and Y.
However, a hint about how to proceed to explain our students the subtleties of the
parabolic motion had already been proposed to us by Renaissance physicist Galileo
Galilei. Instead of studying the parabolic motion as a whole as would have done his
contemporaries, Galileo proceeded to separate the projectile motion into its main
components the constant speed horizontal motion and the free fall motion. One must
conclude then that the horizontal and vertical components of motion are independent and
that the trajectory of a projectile thrown at a certain speed, is the combination of these
two simpler motions (Knight, 2004). However, until recently, these cases about parabolic
motion were the subject of demonstrations or cookbook laboratories since they require
the use of complex equipment and lengthy calculations of speed and acceleration in the
two coordinates X and Y.
To overcome these difficulties in the understanding of parabolic motion and propose
more genuine investigation of its properties, the use of technology would make easier the
data collecting and analysis while supporting the student in his investigation (Jonassen,
Strober, & Gottdenker, 2005). In this approach, called 'video-based laboratory' or VBL,
the parabolic motion of objects are recorded as videos, treated by softwares allowing the
measure of the horizontal and vertical positions of objects according to time, while these
objects undergo various parabolic trajectories, and the organization of these data in tables
and graphs. Such an approach has several advantages: 1) it allows the pupil to focus on
the generation of hypotheses and the interpretation of results, two skills not much
developed in traditional laboratories; 2) it allows the pupil to generate and to prove
several hypotheses much faster, by making easier strategies of variation of parameters
necessary for the formulation of hypotheses regarding the properties of parabolic motion;
3) in physical situations where it is necessary to come back on the results of an
experience to check the accuracy of the results obtained or possibly to change the original
hypothesis, the VBL can allow the traditional laboratory to become iterative in spite of
the school constraints with respect to time or equipment. In effect, it is often necessary
for the pupil to come back on the results of an experience to study the reasons of the gap
between his ideas and his experimental results, thus favouring conceptual change in
sciences (Lin, 2007).
Consequently, our research pursues two main goals. The first one is to design a learning
sequence that takes into account the alternative conceptions of students on parabolic
motion and allow them to verify their hypothesis in a video-based laboratory. The second
one is to evaluate the effect of such a strategy on the high school students’ understanding
of parabolic motion. We will in the next section describe the conception and
implementation of the VBL and in the following sections the methods used to evaluate its
effect on students’ understanding of parabolic motion.
CONCEPTION AND IMPLEMENTATION OF THE VIDEO-BASED
LABORATORY
As regards the activities of conceptual change of kinematics phenomena, we conceived
them in order to study the characteristics of parabolic motion. To allow the pupils to work
in small groups of four or five persons, we conceived a guide to supervise the steps of the
pupils. The guide introduces two cases of parabolic motion to study different aspects of
this type of motion. With respect to these two cases, the first one intends to have students
focus on what happened when they compare the X component of constant speed motion
with parabolic motion respectively. The second one asks the students to compare the Y
component of motion of a ball in free fall and in parabolic motion.
Describing the first case presented to students, two balls, say A and B, are released at the
same time from the same height from the top of two parallel inclined planes so that, at the
bottom of the inclined plane, they pursue their journey at the same constant speed on two
horizontal tracks put on a table. Reaching the edge of the cliff of the table, one of the ball
A follows through its motion on the same horizontal plane whereas the other ball B
leaves the table undergoing a projectile motion. Describing the second case, one of the
ball, say A, is thrown at constant speed on a horizontal track put on a table while the
other ball, say B, is suspended to an electromagnet. When ball A reaches the edge of the
cliff of the table, it strikes a lever that induces the electromagnet to release ball B. Thus in
the second case, ball A follows a projectile motion while ball B follows a free fall
motion. For both two cases, the guide proposes students activities (questions, graphics to
draw, etc.) which guide the modelling process of the pupils. The process of conceptual
change is structured as a POE task (Prediction> Observation> Explanation) (Russell,
Lucas & McRobbie, 2004).
Every POE task takes place in the following way. For each case, the physical situation
represented under a concrete form by a physical set-up is explained to the pupils in the
guide. Questions linked to each of the two cases ask the student to predict what is going
to arrive if experience is to be performed and to write their predictions in their notebook.
Once written, they compare their predictions with their peers in small group discussions
to reach a general agreement. Upon agreement, each group send their representative to
present their predictions to the whole class. In this step, teacher acts as a facilitator,
asking questions to get pupils clarify their ideas. Then, when all teams have presented
their ideas, the teacher demonstrates the phenomenon in front of the pupils and records it
under video form with the help of pupils’ volunteers. The video in then downloaded in
USB keys that are distributed to each team.
Before actually letting students proceed with the data collecting and analysis with their
computer, the teacher draw their attention to the main features of the phenomena by
viewing and replaying the actual experiment as shown in the video (cases 1 and 2 above).
As such the observation of the real phenomena of parabolic motion demonstrated in front
of the students is important to help them identify the critical aspects of the experimental
set up, before actually proceed to the data collecting and analysis, while mobilizing
different learning modalities. Hence, the students could see for example in case 1 the two
balls traveling together horizontally as well as hearing the unique sound of the two balls
striking the wood board. The same can be said with respect to case 2 where students
could see the two balls being at the same vertical positions at the same time or hitting the
bottom.
These videos are then transferred to USB keys and distributed to every team. Having
inserted these sequences of pictures in the REGAVIi software, the students of every team
can then, with the aid of a cursor, take measures of the successive horizontal or vertical
positions of the two balls according to time. These measures are automatically put in
tables by REGAVI. Later, these tables can be transferred for analysis to the REGRESSIii
software (Durliat & Millet, 1991). This last software possesses functions allowing the
pupil to produce different graphs of position and speed along both coordinate axis X and
Y according to time. As such, REGRESSI makes easier the discovery of relations
between variables by providing means to compare the adjustment of different curves
(linear, quadratic, exponential, etc.) in gathered data. At last, the pupils try then to explain
the gaps, if need be, between their predictions and their results.
The role of the teacher in the VBL is to introduce activities to the pupils, to allocate roles
to the pupils during small group discussions, to perform the demonstration of every case
of motion in front of the pupils, to record these movements under video form and to
distribute them to the pupils and, finally, to make easier exchanges between the pupils
during whole class discussion. In order to do so, we planned a training period of two
hours duration, conducted by the main researcher, where the two teachers could master
the elements of the VBL and practice the skills to conduct discussions efficiently. As
regards the adaptation of the approach to the schoolroom, both the main researcher and
the teachers met, throughout research, to undertake adjustments requested according to
the evolution of pupils’ understanding. Besides, two supplementary meetings prior to the
implementation allowed the teachers to gain knowledge of the approach and the main
researcher to add modifications in order to adapt the activities to the context of the school
and to the characteristics of the pupils.
Activities took place in the classroom of the physics teachers. It is to note that each
physics teacher taught in the same class but at different times. Therefore, the following
description is valid in either case. The classroom was suitable for our research, because it
had several mobile tables that could be regrouped in small islets where the pupils could
work in small teams. An interactive Smartboard situated in front of the classroom allows
the teachers to present to their students demos that have been created in order to
familiarize their students to the use of the software REGAVI and REGRESSI. A unique
set up allowing the demonstration of the cases of motion was located at the back of the
class on a long and fixed table at short distance from the islets. This last feature allows
the teacher to let the various setups in position once they have been built so that they
could be used the following day if needed to be.
METHODOLOGY
Context and research protocol
Our study consisted of two classes of 21 and 24 French-speaking pupils respectively,
attending a physics course in a high school of the province of Ontario in Canada. These
two classrooms were following an optional introductory course in physics at the 11th
grade at a high school in the province of Ontario in Canada.
The first group was composed mainly of students who have chosen a special orientation
toward science offered by the school so that it is reasonable to assume that they were
interested by science in general and physics in particular. The second group was
composed of regular students and a small number of students with learning disabilities.
The teacher of the first group was of femine gender and had five years of experience in
teaching science. The teacher of the second group was of masculine gender and had
twenty years of experience in teaching science and mathematics. Both teachers held
bachelor degree in science and a teaching certificate in science teaching.
Research took place at the beginning of the second semester. It is to note that the school
where took place the research had adopted a calendar where lessons, which normally
stretch over all school year, were condensed in one semester. Consequently, the lessons
of the first semester differed from the lessons of the second semester. To study the
implementation of the VBL, the main researcher held a research diary where he recorded
his observations on the sequence of events, the critical details regarding the introduction
of the VBL by the teacher, comments of the teacher in meetings with the main researcher,
and links that the main researcher could establish between his observations and the
theoretical framework of the present research (Altrichter & Holly, 2005). During the
experimentation, the main researcher or one of his research assistants were present at
each of the periods to observe the unfolding of the events and take the measures of
pupils’ understanding. The main researcher or one of his assistants also played the role of
monitor of laboratory, to solve the difficulties which may arise with the experimental set
up or the use of data and analysis software by the pupils.
The VBL described in the previous paragraph was implemented in the 11th grade physics
course during four successive periods of one hour and quarter close to the beginning of
the second semester, but after students have seen the motion in one dimension. In each of
these periods, the pupils had to answer a question taken haphazardly in a bank of problem
during the first five minutes of the period. Moreover, there were supplementary measures
of understanding immediately before and after the implementation of the approach.
During the period immediately preceding the beginning of research, fifteen minutes had
been dedicated at the end of the period to introduce the research to pupils. It is to note
that two weeks before the actual experiment, students has already experiment a similar
strategy with two cases of constant motion (Trudel & Metioui, 2012).
Data collection instruments
To measure the evolution of understanding according to the number of periods dedicated
to the use of the video based laboratory, we conceived a test of parabolic motion after a
literature review on the subject according to SOLO taxonomy (Biggs & Collis, 1982).
Indeed, to measure the level of understanding , Masters and Mislevy (1993) suggest,
firstly, that the test items contain a series of questions designed to reveal different ways
of understanding of students and, secondly, that these ways of understanding are then
compared to a framework that allows to order them. One type of items that meets the first
criterion Master and Mislevy (1993) is called a super- item. A super item is constructed
in two parts. The first part, called the core, involves the wording of a statement describing
a situation involving some selected physical properties of parabolic motion. The second
part is to write a series of questions in order to identify the different ways of
understanding the students about the physical situation described in the core (Hattie &
Purdie, 1998). Since our test covers parabolic motion, the core of each super -item
involves different concepts of parabolic motion.
Data analysis
Since every pupil is measured at several occasions, conditions in which these
measurements are taken may vary, that it is in the day of the week, the hour during day,
etc. So, a student may not get the same result in answering questions of identical
difficulty because he is tired or irritated during a particular occasion. In such a case,
where the temporal dimension is important, the choice of an item response theory model
(IRT model) must take into account the variations in the course of the time of the answers
of the pupils. As such, the model with facets developed by Linacre (Bond & Fox, 2007)
allows considering the influence of these different factors or 'facets' on the measure of
understanding. To determine if the VBL had an effect on the understanding of the
students, a repeated measures analysis of the variance was performed of the computed
values by the IRT model. This analysis allows us to compare the results of the pupils
between the different occasions of measure and to determine if one of these results differs
significantly from the others. This comparison can take a specific form called contrast
(Howell, 2008). To evaluate the effect of VBL on students’ understanding of projectile
motion, it is necessary to determine if the increase of their understanding according to the
number of periods of the implementation of the VBL is linear. As such, it is possible,
with the aid of orthogonal polynomials to separate the contributions from the linear
tendencies and higher polynomials (linear, quadratic, cubic, etc). Besides, these elements
of variance being independent to each other, they can be separately tested (Howell,
2008).
PRESENTATION AND ANALYSIS OF THE RESULTS
Results of group 1
The figure 1 presents the average values, as computed by the IRT model used, of the
understanding acquired by the students of group 1 at every time measure. By studying the
figure 1, one must note that, although there are some variations, there is an upper linear
trend of the understanding of the motion of projectile among students of group 1. The
repeated measures variance analysis confirms that the positive linear tendency of group 1
students’ understanding of projectiles is statistically significant (see Table 1). Moreover,
we also notice the presence of a significant tendency of order 5 that may be explained by
variations from day to day measurement.
1.5
1.0
.5
0.0
-.5
-1.0
-1.5
1
2
3
4
5
6
Time (number of periods)
Figure 1. Evolution of average understanding of group 1 students
Table 1
Repeated measures variance analysis of group 1 students understanding with number of
periods
Source
UNDERSTANDING
Error
UNDERSTANDING
Contrast
Linear
Quadratic
Cubic
Order 4
Order 5
df
1
1
1
1
1
F
15.540**
.973
3.378
.003
16.186**
Linear
Quadratic
Cubic
Order 4
Order 5
20
20
20
20
20
(.526)
(2.815)
(1.251)
(2.482)
(2.327)
Note. Values included in parentheses represent mean square errors
**p<0.01
Power
.963
.156
.417
.050
.969
Results of Group 2
The figure average values of the understanding of projectiles acquired by the students of
group 2 at every time measure follow, although some variations, an upper trend in a way
similar to the group 1. Due to space limitation, the graph of these results won’t be shown
here. Similarly, a repeated measures variance analysis confirms that the positive linear
tendency of group 2 students’ understanding of projectiles is statistically significant (p<
0.01). There is also a significant tendency of order 4 that may be explained by day to day
variation (p<0.01).
DISCUSSION AND CONCLUSION
Our research is inspired by the constructivist approach, where the pupil constructs his
knowledge by interacting with his environment. Given the difficulties pupils encountered
in the physics course to gain conceptual understanding of kinematics concepts, we
conceived a video-based laboratory (VBL), a specialized version of the usual computerassisted laboratory, allowing the pupils to generate and prove hypotheses with the help of
data collection and analysis softwares while discussing in small groups about videos of
objects in motion. The approach introduced here use the capacities of the computer so
that the student can, from a common sense conception of properties of motion, of a
qualitative nature, make the transition to a mathematical representation in the form of
position-time and speed-time graphs in both coordinates X and Y.
In our experiment, it appears that the visual-based laboratory had a significant impact on
group 1 and 2 understanding. Although these results appear promising, one must note that
the maximum value of understanding of students in group 1 does not exceed 1.5 logit for
group 1 and 0.5 for group 2. According to the curve of probabilities of transition between
SOLO levels, these results means that on average the students could not reach the
relational level of SOLO taxonomy (Trudel, Parent, & Auger, 2008). One possible
explanation would be, as suggested by one of the teacher, that the VBL used here did not
include problem-solving activities that would have helped students make the links
between their understanding of the properties of the phenomena studied in the VBL and
the various contexts where these properties come into play. As such, the students stayed
at the multi-structural level (SOLO taxonomy). Another possible explanation is that the
variations observed are part of a regular pattern of conceptual development as
exemplified by Granott (2002).
Concerning the implementation of the VBL, the comments gathered at the end of
research during interviews with the pupils and the teacher show that these activities were
advantageous to the pupils in their understanding of the different aspects of parabolic
motion. Some pupils appreciated the concrete character of activities which they preferred
to lectures. In the same vein, they could make links with mathematical notions such as
the production and the interpretation of Cartesian coordinates as well as the calculus of
the slope of a line. Moreover they familiarize themselves with the use of data collection
and analysis softwares in the physics laboratory. Besides, it seems that the presentation
format of motion phenomena as demonstrations did not prevent the pupils from
considering these activities as laboratories (Roth, McRobbie, Lucas, & Boutonné, 1997).
However, improvements remain to be made with respect to the tutorials aimed to
familiarize pupils to the collection and analysis software, notably by increasing their
easiness of use. In this respect, the teacher suggested to introduce the pupils in the
handling of the softwares by giving them a prior training of around thirty minutes with
the aid of a bank of activities already recorded under video. Perhaps one of the main
obstacles to be overcome is the perception of the pupils regarding these activities. Indeed,
the emphasis put on the discussion of hypotheses between pupils runs opposite to pupils’
conceptions of the role of laboratory in physics courses that mainly attempt to verify
theories (Larochelle & Désautels, 2007).
This study undertaken with two groups of students cannot pretend to formulate
conclusions that can be generalized to all high school pupils. As a result, these
conclusions have a speculative character and are to be considered in the light of the
exploratory aim of our study. This research adopts the perspective that the usage of
computer science in the physics laboratory is revolutionizing the education of this
discipline. However, computer-assisted experimentation is too often dedicated to the
technical side of the data collecting and organization in form of tables and graphs. This
emphasis on the technical precision of measurements, in spite of his rigor, risks of
making us forget that it is often necessary for the pupils to develop their qualitative
reasoning as well as their quantitative counterpart. However, it is not a question of
leaving out the mathematization of the properties of phenomena but to consider it only
when the essential elements of problem are qualitatively understood by the pupils.
Researches undertaken with several groups of pupils may help to confirm results obtained
in the present study (Slavin, 2007).
NOTES
i
The REGAVI software allows data collection from a video of a moving object as an
AVI file. This software contains functions for measuring successive positions of the
object it organizes in tables. It is possible thereafter to transfer the data in the Regressi
file for analysis (see the following site:
www.micrelec.fr/equipelabo/pics_art/pdf/M0314G26.pdf • PDF file).
ii
The REGRESSI software performs Cartesian graphs of data transferred from collection
software as Regavi. The Regressi software also contains functions to calculate new
variables (speed, acceleration) and from measurements of position and time to find the
best curve of a set of data points, etc. (Durliat & Millet, 1991).
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