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Computers & Education 50 (2008) 1128–1140 www.elsevier.com/locate/compedu

Physics students’ performance using computational modelling activities to improve kinematics graphs interpretation Ives Solano Araujo *, Eliane Angela Veit, Marco Antonio Moreira Physics Institute, UFRGS, Av. Bento Gonc¸alves, 9500 Porto Alegre, RS, Brazil Received 14 December 2005; received in revised form 9 November 2006; accepted 9 November 2006

Abstract The purpose of this study was to investigate undergraduate students’ performance while exposed to complementary computational modelling activities to improve physics learning, using the softwares Modellus. Interpretation of kinematics graphs was the physics topic chosen for investigation. The theoretical framework adopted was based on Halloun’s schematic modelling approach and on Ausubel’s meaningful learning theory. The results of this work show that there was a statistically significant improvement in the experimental group students’ performance when compared to the control group, submitted just to a conventional teaching method. Students’ perception with respect to the concepts and mathematical relations, as well as the motivation to learn, originated by the activities, have played a fundamental role in these findings. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Teaching/learning strategies; Interactive learning environments; Pedagogical issues; Simulation; Improving classroom teaching

1. Introduction Nowadays, physics teaching activities are permeated by didactical proposals involving personal computers using more and more elaborate softwares in order to facilitate students’ knowledge construction. However, there are few systematic studies about the influence of these software on the teaching/learning process. Among the more significant didactical proposals we remark four main modalities for computers in physics teaching (Araujo, Veit, & Moreira, 2004): tutorials (Interactive Journey Through Physics, The Particle Adventure, etc.); data acquisition (Science Workshop, Real Time Physics, VideoPoint, etc.); simulation (Interactive Physics, xyZET, Graphs and Tracks, Java applets, etc.) and modelling (Stella, Dynamo, PowerSim, Cellular Modelling System, Modellus, etc). Here we focus our attention on computer modelling tools, that is, computer softwares that allow users to create and explore computational models without knowledge of a computer programming language. We are particularly interested in the use of these tools to deal with physical models.

*

Corresponding author. E-mail address: [email protected] (I.S. Araujo).

0360-1315/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compedu.2006.11.004

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We consider physical models as simplified and idealized descriptions of either systems or physical phenomena, accepted by the scientific community, that involve elements such as external representation, semantic propositions, and underlying mathematical models. We understand modelling as a creative process, divided into five nonhierarchical stages: selection, construction, validation, analysis and model expansion, ‘‘where the middle three overlap and some of their steps can often be conducted concurrently’’ (Halloun, 1996). 2. Modellus software and interpretation of kinematics graphs Among the modelling tools now available, Modellus (Teodoro, Vieira, & Cle´rigo, 1997) stands out for allowing teachers and students to make conceptual experiments ‘‘. . . using mathematical models expressed as functions, derivatives, rates of change, differential equations and difference equations’’ (Teodoro, 1998) written in a straight form, that is, written as usual with pencil and paper without the need of symbolic metaphors, such as Forrester’s diagrams used to construct computational models with the software STELLA (Santos, Cho, Araujo, & Gonc¸alves, 2000). Another important feature provided through Modellus is the multiple representations, i.e., the user can create, see, and interact with analytical, analogous and graphical representations of mathematical objects (Teodoro, 1998, 2002). A powerful Modellus feature is its graphical outputs that can be seen simultaneously with animations. A graph allows us to compact a large quantity of information and easily recognize physical events data that in other ways would be more difficult to identify. For a scientist, to comfortably work with graphs is an indispensable skill. Kinematics graphs, i.e., position, velocity or acceleration versus time, generally are the first kind of graphs extensively used in a physics course. However, this subject is rarely well understood by the students. McDermott, Rosenquist, and van Zee (1987) analyzed the narratives made by students during the processes of elaboration and analysis of kinematics graphs and identified 10 main difficulties, classified into two categories. One category included five difficulties in connecting graphs to physical concepts: (a) to discriminate between the slope and height; (b) to interpret changes in height and slope; (c) to link one type of graph to another; (d) to match narrative information with relevant features of a graph; (e) to interpret the area under a graph. The other category included five difficulties in connecting graphs to the real world: (a) to represent continuous motion by a continuous line; (b) to separate the shape of a graph from the path of the motion; (c) to represent a negative velocity on a v versus t graph; (d) to represent constant acceleration on an a versus t graph; (e) to distinguish among different types of motion graphs. Murphy (1999) also studied this theme and identified graph-as-picture (GAP) interpretation, in which students expect the graph to be a picture of the phenomenon described, and slope/height confusion (SHC), in which students use the height of the graph at a point when they should use the slope of the line tangent to the graph at that point and vice-versa, as the two main difficulties when interpreting kinematics graphs. Beichner (1994) made an extensive study to verify students’ kinematics graphs understanding, using the Test of Understanding Graphs in Kinematics (TUG-K) developed by himself. He argues that physics teachers use graphs as a second communication language, assuming that their pupils can obtain a detailed description about a physical system through this type of representation. Unfortunately, his work showed that students do not share the vocabulary of such a language. The objectives and difficulties mapped by Beichner (1994) with the TUG-K test are shown in Tables 1 and 2. Table 1 Objectives of TUG-Ka Given

The Student will

(1) (2) (3) (4) (5) (6) (7)

Determine velocity Determine acceleration Determine displacement Determine change in velocity Select another corresponding graph Select textual description Select corresponding graph

a

Position–time graph Velocity–time graph Velocity–time graph Acceleration–time graph A kinematics graph A kinematics graph Textual motion description Adapted from Beichner (1994).

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Table 2 Students’ difficulties with kinematics graphsa Difficulties

Description

(1) Graph as picture error

The graph is considered to be like a photograph of the situation. It is not seen as an abstract mathematical representation, but rather a concrete duplication of the motion event Students often read values off the axes and directly assign them to the slope Students do not distinguish between distance, velocity, and acceleration. They often believe that graphs of these variables should be identical and appear to readily switch axis labels from one variable to another without recognizing that the graphed line should also change Students successfully find the slope of lines which pass through the origin. However, they have difficulty determining the slope of a line (or the appropriate tangent line) if it does not go through zero Students do not recognize the meaning of areas under kinematics graph curves Students often perform slope calculations or inappropriately use axis values when area calculations are required

(2) Slope/height confusion (3) Variable confusion

(4) Nonorigin slope errors (5) Area ignorance (6) Area/slope/height confusion a

Beichner (1994).

Several works (Brassel, 1987; Mokros & Tinker, 1987; Testa, Monroy, & Sassi, 2002) describe the development of successful proposals to improve kinematics graphs interpretation skills based on real time data acquisition using a personal computer (MBL proposals: ‘‘Microcomputer-Based Laboratory’’). One difficulty that frequently appeared in their work was students’ misunderstanding of graph-as-picture. The success of MBL activities seems to be related with this question. These activities allowed students to watch real time graphs drawn simultaneously with the experiment development. In some experiments, students used their own bodies like object of study in motion analysis. These motions were detected through sensors and the obtained data was used to draw kinematics graphs on the computer screen. It is likely that this interactivity was partly responsible for the improvement in graphs interpretation by MBL activities. Beichner (1990) proposed a study where the kinesthetic feedback was completely removed, only supplying students with visual replicas of motion situations. The graphs production was synchronized with the movement reanimation in order that students could see the object moving and simultaneously the drawing of kinematics graphs. The results obtained in this work indicate that this method does not supply an educational advantage compared with the traditional instructional method. The author argues that since Brassel (1987) and other researchers showed the superiority of MBL practices compared to conventional teaching, it should be considered another factor besides the visual juxtaposition. The factor that actually makes a difference, according to Beichner is the student’s interaction with the experiment. Based on Beichner’s results we assumed that the use of a computational tool that allows students to interact with the objects involved in the physical situation under study, and observe simultaneously the graphs related with their motion being displayed, could help students to overcome their difficulties to understand kinematics graphs. Modellus is a convenient software to explore this question especially because students are able to work with it either in the exploration or in the expressive mode very quickly. Our study was based on the use of complementary teaching activities involving computational models exploration and creation like an interaction process between student and experiment. The model exploration makes the student constantly wonder about the effects of his/her actions on the results generated by computational models. Normally this kind of questioning can be described in this way: - If I change ‘‘this’’ what happens with ‘‘that’’? This causal reasoning will be a background to promote the interactivity. The teaching activities were designed to motivate students’ questioning about the existing relationships among the kinematical concepts and the graphs of motion of a given moving body. 3. Meaningful learning Meaningful learning, the core of David Ausubel’s learning theory, is defined as a process where new information interacts with some relevant aspect of the individual’s knowledge structure. We can say that meaningful learning occurs when new information is assimilated through interaction with relevant subsuming concepts pre-existent in the learner’s cognitive structure (Ausubel, Novak, & Hanesian, 1978; Ausubel, 2000). Ausubel

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denotes these relevant concepts as subsumers. However, meaningful learning is not limited to a direct influence of subsumers on the elements of the new information. We should also consider the subsumers’ modifications and growth due to the interaction with the new material, because in this process the subsumer evolves, becoming more inclusive, more differentiated, and more able to assimilate new information. This means that the subsumers can present great variations from one individual to another. They could be wide and well differentiated or limited in amount and variety of elements, according to the learning experience of each person. Ausubel defines rote learning (or automatic) as that one in which the individual acquires new information with a few or no relationships with the existing subsumers in his/her cognitive structure. This knowledge is stored in a literal and arbitrary form, not linked to specific subsumers. Despite sharp differences between meaningful and rote learning, it is important to remark that Ausubel does not present the two types of learning as antagonistic, since he sees them as extremes of a continuum, i.e., there are different levels of meaningful and rote learning. Meaningful learning does not occur unless some knowledge elements relevant to new information in the same area exist in the learner’s cognitive structure and can serve as subsumers even though roughly elaborated. When learning begins to be meaningful, the subsumers become more and more elaborated and the individual more capable to assimilate new information. Ausubel proposes two basic conditions for meaningful learning: (a) the information that we want the student to learn should be potentially meaningful. He/She must have in his cognitive structure concepts relatable in a substantive and non-arbitrary way to the new knowledge to be learned. This one in turn should have logical meaning; (b) the learner should manifest a disposition to relate the new material to her/his cognitive structure in a substantive and non-arbitrary way. Even information potentially meaningful can produce just rote learning if the learner does not have a disposition to learn. Similarly, if the material is not potentially meaningful the process and the result will not be meaningful. The research hypothesis of this work is based on these conditions, which were also used as a guide to interpret the results. 4. Schematic modelling ‘‘Schematic modelling is an epistemological development theory based on cognitive research’’ (Halloun, 1996). In this framework it is admitted that models are major components of the human knowledge and that modelling is a cognitive process to construct and use knowledge in the real world. Halloun (1996) argues that when scientists propose to study a physical system, they focus on a limited number of the system’s features, built from a scientific conceptual model1 (e.g., a mathematical model) and/or a physical model (as a material artifact). Scientists analyze the built model and make inferences about the physical system it represents. The whole process is usually guided by some physical theory. Like in other scientific schemes (concepts, laws and other structures shared by scientists), the scientific models are schematic in the sense that they (a) use a limited number of basic features almost independent of the scientist’s individual idiosyncrasy, and (b) are developed and applied following generic modelling schemes. The first step in the process of schematic modelling consists of identifying and describing the composition of each physical system focused upon and the corresponding phenomenon. At the same time we should identify the proposal (e.g., the objectives of a textbook) and the validity of the expected outputs (including the results’ precision). Following these steps we select a suitable object model and build it. The model is then processed and analyzed while being validated continuously. ‘‘Following analysis, appropriate conclusions are inferred about the system in question, as well as about other referents of the model, and outcomes are justified in function of the modelling purpose and the required validity’’ (Halloun; Hestenes; apud Halloun, 1996). One important class of problems for the schematic modelling is the one of ‘‘paradigm problems’’. Halloun includes in this category problems that contain special features avoiding the direct application of numerical

1

Halloun denotes these models as scientific conceptual models and distinguishes them from ordinary models used by people.

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formulas and including open questions that allow the students to contemplate their own conceptions about the physical systems. The resolution of this type of problems occurs in five nonhierarchical stages: selection, construction, validation, analysis and expansion. The three intermediate stages overlap, and some of these steps can be conducted at the same time. In each stage, the modeller wonders to herself or himself about specific questions and tries to answer them systematically. In this framework we define our understanding of computational modelling applied to physics teaching as the modelling process proposed by Halloun (1996) added to the use of the computer as a cognitive tool to help the execution of the nonhierarchical stages of the model’s construction, validation, analysis and expansion. We would like to stress that in this study we considered a physical model not only as a material artifact (Halloun’s definition), but as stated by Greca and Moreira (2002): ‘‘When the statements of the theory are concerned with a simplified and idealized physical system or phenomenon, the resulting description is a physical model’’. 5. Method 5.1. Subject and research hypothesis This study investigated the combined use of exploratory and expressive activities, presented as problem-situations and developed with Modellus as an instructional complement to help students understand kinematics graphs. The problem-situations mentioned here are linked to questions formulated from well-defined physical situations. Initially, the students were asked to express their answers in a traditional way (pencil and paper) and later on they had to compare their results with those obtained with computer models, looking cautiously in order to justify possible discrepancies among them. Many times these questions were presented as a ‘‘challenge’’. Our research hypothesis was that the experimental treatment would promote students’ motivation to learn, connecting the new information with their cognitive structure in a substantive and non-arbitrary way. This would provide conditions for meaningful learning that would result in a better score in a posttest about the topic studied. 5.2. Research design We chose to work with kinematics graphs because we believe that the ability to deal with graphs is a basic student skill to follow a physics course and we were conscious of students’ difficulties in this subject (Agrello & Garg, 1999; Beichner, 1990, 1994; Brassel, 1987; McDermott et al., 1987; Mokros & Tinker, 1987; Murphy, 1999; Testa et al., 2002). This study was developed according to a non-equivalent control group research design, because the available schedule of the students involved in this study did not allow an equivalent control group. The quasiexperimental design adopted is shown in Table 3 with Campbell and Stanley’s notation (1963). The participants were 52 freshmen undergraduate college physics students of the Federal University of the Rio Grande do Sul (UFRGS), Brazil, in the first semester of 2002. They were equally divided into experimental (submitted to the treatment) and control group, both non-randomly assigned. The experimental group worked weekly in a computer laboratory during four weeks while the control group did not have any extra class activities. All students enrolled in this research had been exposed to the study of kinematics before

Table 3 Research designa Design Experimental group Control group

O1 O1

O1, initial test; X, treatment (computational activities); O2, final test. a Adapted from Campbell and Stanley (1963).

X

O2 O2

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the beginning of our research and they continued with the regular physics lessons in other topics during the whole period in which the experiment was performed. Hence, the computational modelling activities were complementary to their traditional lessons. 5.3. Treatment We elaborated a series of modelling activities2 using Modellus in order to help students to overcome their difficulties to understand kinematics graphs, especially those shown in Table 2. Our goal in developing them was to help students to achieve the objectives presented in Table 1. Two kinds of activities were developed: exploratory and expressive (Bliss & Ogborn, 1989). In an exploratory activity, students use Modellus models built by us to observe and analyze their essential features, and try to understand some relationships between the mathematics underlying the model and the physics phenomenon studied. In this kind of activity students interact with the model by changing the initial values or the parameter’s model to answer the questions formulated as driven queries or ‘‘challenges’’. Some resources such as ‘‘scroll bars’’ and ‘‘buttons’’ are provided to facilitate this task. In an expressive activity, students build the whole model, from its mathematical structure to the evaluation of the final results, and create ways of representing it. In this kind of activity qualitative as well as quantitative information is given and some questions are proposed to motivate the elaboration of a model that would describe well the phenomenon in focus. Students are free to choose their own approach to the problem, to interact with the model as much as they want to, and to rebuild the model how many times they need. We would like to emphasize that in both kinds of activities the interaction between the students and the computer models was mediated by the teacher/researcher, both in terms of technical support to work with the software and in explaining some aspects of the physics and/or mathematics involved in the model development. Another point that we would like to stress is that the activities set elaborated was complementary to traditional lessons and did not intend to replace them. In order to build this auxiliary material we assumed that it would be used in a short, but effective, interaction of the student with the activities. 6. Procedures The treatment was performed in a weekly session lasting 2 h 15 min in a computer lab where the experimental group developed the modelling activities set that were planned to help students to overcome the difficulties listed in Table 2, and to achieve the objectives enumerated in Table 1. Students worked individually or in pairs according to their own choice. All students occasionally interacted with their adjacent classmates, even those who had chosen to work alone. The instructional media consisted of Modellus models and a printed guide to help them with the activities. This guide contained instructions on how to explore and construct the models as well as questions that they should try to answer to accomplish their tasks. 7. Instruments 7.1. Elaboration, validation and applications of initial test The purpose of an initial test for experimental and control groups was to check the difficulties presented in Table 2 and to serve as a covariate in the analysis of the final test results. In order to have this initial test we adapted to Portuguese the Test of Understanding Graphs in Kinematics (TUG-K), consisting of 21 multiple-choice questions designed by Beichner (1994). We knew of a Portuguese version of Beichner’s test (Agrello & Garg, 1999), however we preferred to make our own version because we did not find reference to its validity and also because the original Beichner’s test has some statements which are not rigorous enough.

2

These activities can be found in Araujo and Veit (2002), in Portuguese.

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The content validation was made by submitting our test version for examination by six experts, all of them doctors in physics. Their suggestions were incorporated into the initial test and then we applied it to a group formed by 37 freshmen Electrical Engineering3 students of UFRGS in April 2002 in order to get the Cronbach’s alpha coefficient which measures the reliability of this kind of instrument. Reliability is an indicator of how precisely we make the measurement. The students performed the initial test in at most one hour. As soon as the initial test was validated we applied it to 88 freshmen physics majors at UFRGS in their first week of classes. Just after the test application, but before scoring their tests, we asked the students if they were interested and had readiness to take part in the experimental group. So, from a total of 88 students, 26 were volunteers for the experimental group and 26 others formed the control group. 7.2. Elaboration, validation and application of final test In order to evaluate the effectiveness of the treatment it was necessary to assess the performance of both groups, the experimental group after treatment and the control group after traditional instruction, and then to compare them. To do this we prepared a final test reordering the 21 questions of the initial test and adding four more questions of the same kind. These additional test items were built from problems proposed by McDermott et al. (1987) following the same objectives shown in Table 1. We submitted these items to the same specialists who evaluated the initial test for content validation purposes. The final test was applied to a group formed by 35 freshmen Civil Engineering students (UFRGS), in April 2002, in order to measure the reliability of the final test, through Cronbach’s alpha coefficient. The test application took approximately 1 h. After the treatment the final test was applied to the same group of 88 students, which was subjected to the initial test. The students performed the final test in at most one hour and a half. In the last meeting with the experimental group we asked the students to make an anonymous written testimony about their feelings with respect to the treatment including criticisms, comments and suggestions. Later on we conducted semi-structured interviews with six volunteers from this group, aiming for a better comprehension about students’ ‘‘motivation to learn’’ provoked by the computation modelling activities performed with Modellus. 8. Results and discussion 8.1. Reliability analysis of initial and final tests As mentioned before, the initial and final tests were applied to pilot groups in order to evaluate the reliability coefficient of these instruments before they were employed with the experimental and control groups. The Analysis of Internal Consistency (AIC) was then performed according to Cronbach (1967, apud. Moreira & Silveira, 1993). The main AIC results are shown in Table 4. This analysis included the total score alpha coefficient calculation as well as each individual question correlation coefficient to the total test score. 8.2. Comparison between experimental and control groups The final and the initial test scores are shown in Table 5. The final score is in general greater then the initial one for both groups. As can be seen in Table 6, the experimental and control group mean scores are not the same in the initial test and an Analysis of Variance and Covariance (ANOVA/ANCOVA) had to be done to correct the final test scores. This procedure adjusts by regression the final test scores, matching the students to each other in their initial test scores, in other words, it evaluates by regression which would be the final test mean scores if there were not differences between the individuals in the initial test. 3 The initial test was validated for freshmen engineering students and was applied to freshmen physics’ students supposing that both populations are similar. Such supposition is necessary because the instrument’s validity is related to situations where it is applied (Moreira & Silveira, 1993, p. 83).

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Table 4 Synthesis of the internal consistence analysis of initial and final tests applied to pilot and research groups Group

Test

N

Average (total score)

Standard deviation (total score)

Items

Cronbach’s alpha

Pilot

Initial Final

37 35

14.60 16.89

4.13 4.89

21 25

0.81 0.84

Research

Initial Final

52 52

12.25 18.00

4.63 5.36

21 25

0.83 0.88

Initial–final correlation coefficient

0.64

Table 5 Experimental and control groups performance on the initial and final tests common items Objectives

4 2 6 3 1 2 2 6 7 4 5 7 1 5 5 4 1 3 7 3 6

Initial test item number

Final test item number

Experimental group Right answer % (initial test)

Right answer % (final test)

Control group Right answer % (initial test)

Right answer % (final test)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

4 5 20 21 1 2 3 6 7 8 10 9 11 12 14 13 15 16 17 18 19

19 73 69 19 81 50 35 65 23 27 62 85 35 73 31 27 35 54 50 69 50

62 89 85 81 96 85 54 81 65 58 65 89 50 81 65 62 65 89 69 89 58

46 88 81 54 88 46 58 85 15 42 62 81 46 73 65 38 50 69 85 100 81

50 92 92 73 81 62 54 92 73 46 73 92 73 92 77 46 50 85 92 96 85

Table 6 Comparison between the averages of experimental and control groups in the initial and final tests Group

Experimental Control

Initial test (21 items)

Final test (25 items)

Mean total score

Standard deviation

Right answer %

Mean total score

Standard deviation

Right answer %

10.65 13.85

4.24 4.51

51 66

17.88 18.12

6.23 4.45

73 75

Initial–final correlation coefficient

0.72 0.64

The adjusted final test averages for both groups are shown in Table 7, as well as the F ratio for the difference between both means and the statistical significance level of this difference (Finn, 1997). From Table 7 we can see that the experimental group had a larger mean than the control group and that we can discard the null hypothesis4 at a level of significance smaller than 0.05. 4

According to the null hypothesis the average student performance would be the same with or without the treatment.

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Table 7 Comparison between experimental and control groups on final test through adjusted means Group

Adjusted mean final test

F

Statistical significance level

Experimental Control

19.21 16.79

4.08

0.049

Table 8 Comparison between the experimental and the control group in terms of the objectives linked to common questions in the initial and in the final test

Experimental group Control group Mann–Whitney’s U-test

Mean gain Objective 1

Mean gain Objective 2

Mean gain Objective 3

Mean gain Objective 4

Mean gain Objective 5

Mean gain Objective 6

Mean gain Objective 7

0.62 0.19 0.065

0.69 0.15 0.039

1.15 0.31 0.002

1.08 0.15 0.008

0.46 0.42 0.877

0.27 0.27 0.715

0.31 0.46 0.688

Continuing our analysis, the 21 questions of the initial test were grouped according to their objectives (Table 1), forming groups of three questions (Table 5). We compared, then, the performance of the experimental and of the control group in terms of their means relative to each of the objectives, as shown in Table 8. The statistical significance level of the comparison between the gains was measured through the Mann–Whitney’s U-test (a non-parametric test equivalent to the t-test for the difference between means). In Table 8 we can observe that where the results are statistically significant, the experimental group had a better performance. This happens in the first four objectives, relating to the interpretation of the meaning of the concepts of height, slope and area below the curves of the graphs. As for objectives 5, 6 and 7, involving

Fig. 1. Illustrative screen of the first computational activity performed by the students.

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Table 9 First computational activity in detail General description

Next to the horizontal (vertical) reference system there is a red (blue) sphere, the position of which is assigned by x(y), in such a way that it can move only in one dimension. Running the model and moving the spheres with the mouse, the graph position versus time to each one of them is drawn simultaneously to their movement

Objectives to be achieved Learning difficulties

   

Activity statement

Move the red sphere horizontally and observe the graph of x versus time (a) What kind of trajectory does the red sphere describe? (b) In which circumstance does the graph of x versus time present a horizontal line? (c) Describe the displacement done by the red sphere, analyzing the graph of x versus time. Move the blue sphere vertically and observe the graph y versus time (d) Notice that the trajectory of the blue sphere is straight. How come that the graph of y versus time is not a straight line? (e) Describe the displacement done by the blue sphere, analyzing the graph of y versus time

Given the graph position versus time, the student should be able to determine the speed Given any kinematic graph, the student should be able to describe the displacement textually Perception of graphs as a picture of the movement Confusion between kinematic variables

the textual description and a comparison between graphs of different kinematic variables as function of time, it is not possible to state that the experimental group had a superior performance. However, in spite of the last results not having shown statistical significance, we considered important to search for reasons that would allow us to understand why the performance of the experimental group was better than that of the control group in relation to objectives 1–4, but not in relation to 5–7. For that, we present two of the proposed activities wich also serve to illustrate the common elements in our plan to develop potentially meaningful materials to achieve our objectives. The set of activities include several situations in which the students – through the displacement of objects, insertion of values and creation of models – interacted with the computer in the search for answers to the presented questions.

Fig. 2. Illustrative screen of the tenth computational activity performed by the students.

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Table 10 Tenth computational activity in detail General description

Objectives to be achieved Learning difficulties Activity statement

Running this model, the student can use the mouse to move a vertical bar in red associated to the acceleration of a certain moving object; the kinematic graphs of the displacement produced are shown simultaneously, however, in none of them the magnitude represented is showed in the vertical axis  Given the graph position versus time, the student should be able to determine the velocity  Given the graph velocity versus time, the student should be able to determine the acceleration  Confusion between height and slope  Confusion between kinematic variables An object is in the origin of the coordinate system with zero velocity and acceleration 1 m/s2 in the positive orientation of the axis. Vary its acceleration in the vertical bar and identify which is the corresponding graph of the position, of the velocity, and of the acceleration versus time. In particular, try to produce line segments in the graphs: (a) velocity versus time (b) position versus time (c) a positive velocity variation (d) a negative velocity variation (e) a zero velocity variationWhat conclusions can you extract from your attempts?

The first activity performed by the students, illustrated in Fig. 1 and described in Table 9, is an example of how objectives 5–7 were approached. In this activity, the students had ample freedom to move the little balls – as long as in one-dimensional motion – and, most of the time, they were constructing graphs to which a textual description was hard to get. As result, the confrontation of their answers with those of the other groups was not viable and only turning to the researcher–teacher they had hints about his performance. In other activities involving textual descriptions, the confrontation of results was possible, but, even so, according to our observations, the students did not seem motivated by the proposed exercises. This may have been one of the main reasons for the failure of objectives 5–7. Regarding objectives 1–4, we show, as an example, the tenth activity illustrated in Fig. 2 and described in Table 10 – in which the answers could be expressed in a few words or even in screen produced graphs through the direct manipulation of cursors and insertion of numerical values. In this case, the motivation of the students in each challenge they overcame was clearly noticed. The feedback, supplied by the computational simulation, linked to the student’s own actions seem to have been the differential factor which allowed the proposed objectives to be achieved. This finding agrees with those obtained by Beichner (1996). Next, we present a few personal accounts, given by students, on their work with computational activities. 9. Interview and opinions analyses We looked for additional support for our research hypothesis analyzing the data collected on semi-structured interviews with six students of the experimental group and on 26 anonymous written testimonies of this same group. Based on this analysis we believe the conditions for meaningful learning became more favorable because the computational modelling activities allow students to perceive the relevance of the mathematical relations underlying the physical models and to think about the role of graphs on the motion’s study. In the students’ words: ‘‘. . . I could learn what the ‘‘drawing’’ of a graph is, what it shows and what it is representing. Before I used to try ‘to flee’ from a problem that had graphs, now I perceive how I can extract much useful information from it.’’ (Student 1) ‘‘. . . playing with one slide bar back and forth I can observe how this affects the motion under study. As the change in the slide bar represents change in the value of some variable in an equation, we can know what the variable represents in the motion and in the graphs.’’ (Student 3) ‘‘I thought Modellus was very interesting and I have used it already in other situations, for instance my father works in an environmental area and wants to make some graphs. I had to think a little bit,

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but we were successful. We can use Modellus in areas other than physics; it is a very useful tool.’’ (Student 7) We believe that the treatment has generated a student’s disposition to learn because the modelling activities allow students to review concepts and problems seen previously in a conventional form. Through this new perspective they can observe and interact with their study object without limiting the teaching/learning of physics processes to find the correct formula and apply it to solve problems. In the students’ words: ‘‘I like very much the software. Sometimes I don’t have any tasks to do and I want to know, wondering, how would be the graph of this or that specific motion.’’ (Student 1) ‘‘Modellus is amazing! We can see the numbers changing within a graph or even directly in the motion. Its cool.’’ (Student 3) ‘‘I liked very much the modelling activities. Sometimes I applied Modellus even to solve problems presented in the General Physics classes to see whether my results were correct or not.’’ (Student 4) These findings suggests that it is worth using complementary modelling activities with Modellus to promote meaningful learning in physics in the area of interpretation of kinematics graphs. 10. Conclusion The advent of educational software in physics teaching requires research on its effective contribution to the learning process. In spite of the increasing use of these new resources there are few research studies in this area so far. Among the various possibilities to use computers in physics teaching we chose computer schematic modelling because it allows students to interact with the construction process and scientific knowledge analysis, promoting a better understanding of physical models. We chose to investigate the possibility that computer modelling might help students to understand kinematics graphs because the ability to work with graphs is fundamental to follow most physics courses. Of course, computational modelling can be used in very different contexts to describe the dynamic nature of physical phenomena. Further research about the benefits of computational modelling in others contexts would be necessary to improve physics learning. Our goal in this study was to investigate possible gains in students’ meaningful learning in physics when exposed to complementary computational modelling activities applied in lab situations during a short time period. These activities were developed considering two important factors: the difficulties commonly experienced by students in the interpretation of kinematics graphs (Table 1) and the objectives that they should achieve to improve this interpretation (Table 2). The findings of this study indicate that the experimental group attained a better mean performance than the control group. Such results suggest that the use of modelling activities, through Modellus, can help students to improve their ability to understand kinematics graphs. It is important to notice that we did not intend to judge whether the software is ‘‘useful’’ or not to teaching in an absolute way. We believe that it makes no sense to evaluate a tool as an end in itself, because its efficiency will depend directly on where, when and how it will be used. Another relevant aspect to be pointed out is the student learning motivation fostered by the treatment. Besides the natural interest of most students in the use of microcomputers, the results suggest that the application of modelling activities exerts a positive influence on the individual’s predisposition to learn physics. This occurs when students perceive the relevance of some mathematical relations and concepts during the interaction with the conceptual models. Subjects which previously seemed to be very abstract for them turned out to be familiar and more concrete. To conclude, we stress the importance of research studies to investigate the benefits provided by computers to the learner to connect and understand physical concepts and how to get the maximum benefits from this kind of tool. It is not enough to employ innovative materials and methods. Without knowing how students assimilate all of these, we risk misemploying valuable resources and reinforcing thoughts and attitudes we are just trying to overcome.

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