The use of force’ notation to detect students’ misconceptions: Mutual interactions (3rd law) case

Ahcene Serhane Deparment of Physics E.N.S B.P N° 92 Vieux-Kouba, Algiers Algeria ahceneserhane@yahoo.com

Abstract: Since students start to learn, very early –in their educational age- how to represent forces –using arrows, letters and objects ect….-. The present preliminary research introduces and evaluates this method, as a technique pinpoint ting students’ misconceptions, namely those manifested trough notation or verbally explained by students themselves (the use of arrows & letters to represent forces, i.e. Conventional Notation of force = CNF). A sample of 102 students (boys & girls) preparing their Baccalaureate exam, were given a paper-and-pencil questionnaire, where several pictures in which two objects interact with each other, the two object were indicated by letters A & B, then the students were asked to represent the two interacting forces, using the usual notation (F A/B =- F B/A) as followed by teacher and text books). At the end of each situation we left a space for students to include a reason for their representation. Subsequent analysis of the participants’ displays yielded the following misconceptions: A-Mutual interaction understood, to be a sequence between two forces. B-Tendency to confuse letters indicating objects. C-Action and reaction are not always equal in magnitudes. D-Tendency to restrict mutual interaction to resting objects only. E-Difficulty to localize forces’ application points, especially in contact situations. G-The word ‘reaction’ referred to as in its colloquial form, rather than the scientific usage of reaction as simultaneous, exerted force, equal and opposite. K-Informal explanation in which the word “force” does not appear at all.

Keywords: mutual interactions, misconceptions, representations, forces. Introduction:

Students start using and manipulating combinations of arrows and letters to represent forces, in an early age of their education. Pozzer and Roth(2003) argue that “ pictures seem to be an extension of nature into the pages of the book … “( P. 1092). One may continue in this line of thinking and say that representing mutual interaction forces on those pictures may be an extension of the students internal world (in this case their knowledge in physics understanding) to the external world. The idea that methods could be used to elicit students’ understanding was inspired by Paivio’s (1986) Dual code theory. According to this theory, human cognition employs two different channels for processing and storing information, non-verbal (primarily the visual modality) and verbal. Consequently the learner constructs the meaning of the concept, its mental representation, using both channels. Therefore, in order to elicit what students hide in their minds regarding certain concepts, one has to urge students to show what is stored in both of the perceptual channels. It is not argued that other misconceptions detection methods such as interview or multiples choice test do not utilize the visual channel; indeed sometimes students are asked to explain phenomena described in pictures. This method (CNF) forces students to show their alternative conceptions either representatively and/or verbally (through the space left after each situation). And since the method requires the participants to represent the two interacting forces in each situation, this may force students to show their misconceptions themselves. Perhaps, it is worth to note that, one source of students’ misconceptions is the erroneous concepts propagated by teachers themselves Yip (1998). Indeed many studies have concluded that teachers/professionals evidence misconceptions as well (e.g. in physics: Galili and Hazan 2000; in physical chemistry: Gopal et al. 2004; in biology: Yip 1998). Misconceptions related to Newton’s third law: Misconceptions related to Newton’s third law have been the target of numerous studies; they were well known and documented. It should be noted, however, that the present study aims at introducing and testing the (CNF) method rather than exploring students’ conceptions focusing on Newton’s third law serves this purpose because a well documented subject, and therefore a good reference point. Moreover, the third law is suitable for the purpose of this research since on the one hand, it can easily be represented visually using pictures (presenting situations) of daily situations; which on the other hand, it is not a trivial law, as so many learners think. In fact there is no doubt that Newton’s third law is difficult to understand compared to other laws, and is even known to hide some of the last conceptions to be overcome in the transition to Newtonian viewpoint (Hestenes et al.1992). People; often admit doubt about the validity of Newton’s third law in all circumstances

(Gauld 1998). The third law is fundamental and essentially defines what counts as a force: a force is always involves an interaction between two objects. Brown (1989) explains that understanding Newton’s third law requires one to understand that forces arise from interaction. In this view, the third law actually underpins the other two laws (1st and 2nd) and several of common conceptions relating the 1st and the 2nd law can be attributed to the failure to apprehend the Newtonian view. There are at least five ideas should be taken in consideration, when we are dealing with Newton’s third law: 1st – A body cannot experience a force in isolation. 2nd –closely related to the above point is the fact that a body cannot exert a force in isolation. Body A cannot exert a force unless there is another body B to exert a force on A. We then say that A & B are mutually interacting. 3rd at all moments of time the force A exerts on B is of the same magnitude as the force B exerts on A. 4th An important implication of the above point is that neither force precedes the other one. 5th In the interaction of A and B, the force A exerts on B is in direction exactly opposite to the direction of the force which B exerts on A. The above points can be summarized as: if body A exerts a force on body B, body B simultaneously exerts on body A a force equal in magnitude and opposite in direction. In our daily life, however, we frequently observe non-symmetric situations. For instance, a crash of a small car with a lorry, a big ball hits a small one and so on, we usually tend to think that, the bigger, the faster or the stronger exerts a greater force than the smaller, the slower or the weaker. Interpreting the term interacting by a “conflict metaphor” (Hestenes et al.1992). Daily experiences, make it counter intuitive that, massive, rapidly moving body and small slowly moving body should exert the same forces on each other when they interact. Indeed, it make more sense (but wrong) to attribute the forces during the interaction to the active bodies and to believe that massive, rapidly bodies have large internal forces and consequently exert greater forces on other bodies while small, slowly bodies exert small forces. Newton’s third law as it was presented in static situations is hard to be comprehended or (digested). According to Brown, (1989) the conception of force, as a property of a single object rather than as arising from an interaction, can be observed in problems involving static situations. The above mentioned preconceptions make it evident that Newton’s third law provides excellent conditions to examine the sort of representations and explications the participants would produce, how they will represent the interacting forces-according to Newton’s third law-, and how they will clarify and explain confusing situations.

Aim: The aim of the present study was to show the efficiency of the (CNF) method as a misconceptions elicitation technique taking mutual interactions or traditionally speaking “Newton’s third law) as a research case. Given a paper, in which different pictures showing two interacting bodies (A & B), instructed to work individually, the participants were asked to represent, on each picture, the two forces involved between the interacting bodies using the usual notation followed by teachers and/or text books, namely (F A/B =- F B/A) –according to Newton’s 3rd law-a space was left after each situation in order to add a indication or clarification if it is necessary. Perhaps it is worth to note that the programs of the ministry of education (Algeria) focus generally on the educational principles, instructional methodology and teaching practice rather than emphasizing on the need to promote deeper understanding of the subject matter (Yip 1998). Analysis of students’ productions: To analyze data produced by students-representations of forces followed by explanations (not regularly). First, in order to formulate a tentative understanding, the participants productions were read and reread (3times), finally it was concluded that there were three categories of answers: A- completely correct representations (in total agreement with the Newtonian point of view). B- incomplete and /or imprecise representation e.g.(notations are not clear enough, one of the two forces is missing, it lacks some elements either forgotten or less attention, letters indicating objects are missing ect…) C-No representation displayed at all. In fact, research has mainly focused on contact situations: a book on table (terry et al, 1985; Hestenes et al. (Trumper 1996; parlmer2001), a man pushing a box (Brown 1989). Whereas the situations with object at a distance are comparatively rare, e.g. interaction between the earth and golf ball travelling (Kruger et al. 1990; Hestenes et al.1992), the earth and a ball that is dropped from a height (Suzuki 2005). In the research findings the following difficulties in comprehending Newton’s third law were identified as a result of process. 1-There is a consistent confusion between a contact situation and a situation at a distance; consequently, this leads to confuse not only forces at a distance and contact situations, but also difficulties in determining points of forces’ action. 2-In their explication, the word “reaction” used in a colloquial form-explanation which indicate a colloquial form of the word “reaction”as a response to an event, rather than the scientific usage of reaction as a simultaneous equal and opposite exerted force. 3- Difficulties to identify precisely points of forces’ action-they either do not

pay much attention to this problem or simply, they cannot do it properly. 4- The majority of students use repeatedly in their explications the expression «the force of….” Which supports the persistence of the conception of “ force as a property of objects”. 5- Action and reaction are considered as a temporal process, occurring trough time-the action comes first and then the reaction after which, of course, is wrong. Perhaps, this is due to some textbooks which continue to use the traditional words “action” and “ reaction” in presenting the third law, instead of mutual interaction. (Warren, 1979) suggests that the terms “action” and “reaction” imply a time-consequence. 6-Tendency to introduce irrelevant entities in their explications presenting irrelevant force exerting entities beside those involved in the interaction. 7-Tendency to restrict third law application to static situations only. 8- Tendency to confuse third law with the second law. 9- Informal explanation in which the word “force” is absent-displays which did not at all use the term “force” instead the words pull and push were used. 10-The context of situations influence highly students thinking- student may give answers which are consistent with the scientific view in one context while, at the same time their answers may be opposite or different than the scientifically accepted ones in another context (Montanero et al.2002; Tao and Gunstone 1999). The categories given above are not exclusive: a given display (representation + explanation) may suit more than one category (this is reflected in the percentages tables given below for each situation). From a methodological point of view it is very important, to note that the two categories: tendency to restrict the validity of third law to static/stationary situations, and the informal explanation in which the “force” is absent, reflect conceptual difficulties which cannot be inferred directly when considering a single display, but which become evident when considering the totality of the sample. The categories are further clarified and explanatory examples are provided in the result section. RESULTS: The analysis yielded a considerable number of difficulties and categories of responses, the percentages related to each situation are shown in tables below. Before detailing the tendencies and misconceptions categories, it is important to state that the percentages presented for each situation reflect the data collected from students’ (representations + explanations) for each situation, and are not representative of the participants degree of knowledge. It is very much possible that more of the participants hold one or another of the misconceptions, only that they do not happen to manifest in the proposed

situations. In fact, most of the situations were more or less familiar to students. However, a few of them Fig (2) may appear to be somehow unusual or a bit strange. Perhaps, the most peculiar and cumbersome one is Fig (2b) which illustrates an interaction between a finger and a pin, in two different ways: Fig (2 a), the finger presses a pin against a board (piece of wood say) in the usual way, i.e. the finger presses on the large surface of the pin. Fig (2b), The pin is turned up down and the finger presses it against the board on its pointed (sharpened) end, we expect the students to get some confusion or troubles answering this problem specially in case (b) and they may tend to attribute the pain felt by the finger to the force exerted by the pin on the finger being greater than the force exerted by the finger on the pin, on the same basis as attributing forces to objects as it was noted by (David Maloney 1984). Many students adopt a concept of force as an innate or a property of objects rather than arising from an interaction between objects. In all of the situations illustrated in in this research, there is an object which is more or less unambiguously smaller, massif, stronger, harmful, and generally more acting as an agent of causation than the other object. Students accustomed to the concept of force as an acquired property of object would be expected to respond that the massif, the heavier, the stronger, the harmful, etc, object (the object having more force) would exert a greater force, than the less massif one, the lighter one, the weaker one or the slowest one would or no force at all. The first picture of this study consisted of three interacting situations: (two are contact situations, the third one is a distant one) the first one was illustrated by the interaction of the floor with a table leg, in point A, Fig (1a). The second one shows a simple pendulum in which a ball is suspended by a wire at the point C Fig (1c). The third one by a magnetic needle near a magnet Fig (1b), they all were designed to obtain an all overview of students understanding of the third law, the students were asked to represent qualitatively and clearly the interacting forces involved in each situation, Perhaps it was not surprising that among the 102 students investigated, there were only 8 students who produced correct and precise representations of the interacting forces between the leg and the ground. Although the question was clear enough, most of the students tend to represent interaction between (table centre-Earth) instead of (leg-ground) this shows clearly the tendency to introduce irrelevant entities in their representations, the same misunderstanding was repeated in the situation N°1, Fig (1b), instead of representing interaction (Ball-wire i.e. (F w/B =- F B/w) they represented (Ball centre-Earth). Perhaps, we can explain this by students’ difficulties to identify the right forces involved in the interacting situation as well as the right objects on which the forces are exerted. While, nearly about half of the sample (48 students) gave confused, unclear, vague

and imprecise representations (e.g. one or two elements of representations are missing), the remainder, more than third of the sample (43) did not produce any representation at all. In the second diagram the students were shown a magnet needle and a magnet with their north poles close to each other (fig 1b). Once again the subjects were told to concern themselves only with “representing qualitatively & correctly” the two forces, the objects (the needle & the magnet) exert on each other. Only 11 students gave a clear and precise representations for this situation, more than third of the sample gave confused and vague representations, curiously, 52 of the subjects (more than half of the sample) returned blank paper, with no representation at all, three students interpreted the interacting forces in a way contrary to the conventional representation followed by textbooks and teachers. The third Fig (1c) shows a ball attached in wire in point C. Once again, there were only 7 students who gave correct representations, this indicates a clear difficulty for students in interpreting these situations in terms of a pair of forces, in other words, identifying contact from distant situations.

Situation N° 1

Fig (1a) Fig (1b) Fig (1c)

Percentages of categories of representations of forces (Fig 1a)

Percentages of categories of representations of forces (Fig 1b)

%of responses

N of responsesTypes of reponses

7.84%8Correct responses50.00%51 Incomp&Impr respo42.16%43No responses100%102Total

%of responses

N of responsesTypes of reponses

10.78%11Correct responses38.24%39 Incomp&Impr respo50.98%52No responses100%102Total

Percentages of categories of representations of forces (Fig 1c)

Situation N° 2

Fig 2b Fig 2a

The second situation was presented to students in two figure-diagrams, fig (2a) and fig (2b) as it was mentioned above, the subjects were asked to represent, as before, the two pair forces, the finger and the pin exert on each other in both cases. At the end of each question a space was left and the subjects were urged to include a reason or an explanation for their answers. Data and statistical analysis show that in Fig (1a) 22 subjects gave correct answer i.e. representations that are compatible with Newtonian theory, whereas in Fig (1b)–which seems to be unfamiliar or unusual for students- Only 16 students produced correct representations, whereas nearly half of the participants in both cases produced incomplete and unclear representations, the majority of the remainder give no representations at all. More than fifth of sample in both cases did not make any attempt and contented themselves with white answers. As it was shown in the percentages table below, the remaining did not give any representation. Curiously, among those who produced correct representations, there were explanations and statements which seemed to be in total opposition to their representations. The fact that they represent correctly this situation can probably be attributed to the blindly memorization

%of responses

N of responsesTypes of reponses

17.65%7Correct responses56.86%58 Incomp&Impr respo36.27%37No responses100%102Total

of Newton’s third law. We may note that similar categories of responses are very close to each other in both cases.

Table of percentages corresponding to situation N° 2

Type of responses Fig(1a) Fig(1b)Correct responses 22 21.57% 16 15.68%

Impre&incomp resp

54 52.94% 63 61.76%

No responses 26 %25.50 23 22.55%total 102 100%

%100102 100%

The third picture, shows a wagon attracted by a fixed electric motor on the floor, through a wire, again the students were told to represent correctly- according to Newton’s third law- the two interacting forces (motor-wagon). This problem again showed large results for a predictable misconception, students still hold; the students’ interpretation of the problem is, if the motor makes the wagon move, that means the later (the motor) exerts a greater force than the wagon does, and they did not see the need to analyse the situation further, i.e. look the interaction of the (motor-ground) and (wagon-ground), it seemed very clearly difficult for the majority of them to imagine the two forces on the string joining the two objects to be equal. Only 18 students (nearly 18%) gave correct and precise representations, 28% displayed confused and imprecise answers, the rest of the participants (56) did not content themselves to produce any answer. Curiously, among those who produced correct representations (the magnitudes are equal and opposite), using the usual notations (F A/B =- F B/A) a considerable number of them presented statements and comments in contradiction with their answers, we paraphrased this as: the motor exerts a greater force on the wagon than the wagon does, the reason, why the wagon moves, this kind of problems showed how this common misconception is still persistent with the majority of students

Table of percentages corresponding to situation N°3

Situation N°3

Fig (3)

The fourth problem was concerned with a walker; the picture showed a person walking on the ground from right to left and the subjects were asked to draw the interacting forces, in terms of Newton’s third law, between the person’s foot and the ground fig (4). Only 7 students of the sample managed to present a correct and complete force diagram representation i.e. (the 2 forces were equal in magnitude, opposite, exerted on two different bodies and acting on the same line), 74 considered a distant interaction rather than a contact interaction between the person’s and earth center (There seem to be a great majority, among students that hold a persistent confusion between contact and distant situations' interactions), the remainder (21) gave no answers. The goal of this diagram is to urge students to show their point of view and/or their comprehensions (à propos) related to the mechanism of a walker, and consequently their conceptions and difficulties. In fact, the construction and argumentation of diagrams modeling interactions between a walker and the ground, is not as simple as we may think, but it requires more attention and further analysis. According to studies (Caldas & saltiel, 1995) students confuse always friction forces, they have unclear idea about frictions forces, they hold the wrong conception, that is , friction forces are always opposing motion, for example, the walker exerts a force on the ground to accelerate or to brake (decelerate)- we consider only one foot, since the other one is in the air- the

%of responses

N of responsesTypes of reponses

17.65%18Correct responses27.45%28Incomp&Impr respo54.90%56No responses100%102Total

understanding of this matter or more exactly (the mechanism of walking) statics and kinetic friction allow the students to deal with more complex situations, such as the interactions between the ground and a wheel drive or not of a car in accelerating or braking situation.

Situation N°4

Fig (4)

Table of percentages corresponding to situation N°4

Types of responses N of Responses % of responses Correct responses 7 6.86%Incom&impre resp 74 72.55%No responses 21 20.59%Total 102 100%

The construction and argument of forces diagram modeling the interaction between the walker and the floor is not as simple matter as we may think, but it requires much more attention and further analysis. According to studies by (Saltiel and Caldas, 1995) (13 ) students confuse always the laws governing statics and kinetic friction. As a result of these studies the majority of students believe that the friction forces are always opposite direction to the direction of movement of the object in question, therefore very few of them accept the idea that a frictional force can be also a motor or propulsion force. For instance, the walker exerts a force on the ground to accelerate or to brake (decelerate)- we consider only one foot, since the other one is in the air-

understanding the mechanism of walking allows students to deal with more other complex situations, such as the interactions between the ground and the wheel drive or not of a car in accelerating or braking situation. The fifth question, showed a situation of a big truck and a small car about to make a crash (collision), the aim of this question was to examine students understanding of interactions forces between two objects of different masses. As it was indicated in the table of responses, only 9 students responded correctly this question, i.e. the two forces were clearly represented (equal

magnitudes, opposite, exerted on the car and the truck, on the same line of action and using usual notation followed by text book and teachers (F C/V =- F V/C)), 40 persons displayed imprecise and/or incomplete answers, more than 50% did not answer the question. Some of those who gave imprecise representations followed their answers with statements indicating that the truck exerts a greater force than the car does at the collision. Percentages of responses are shown below.

Fig (5)

Table of percentages corresponding to situation N°5

Types of responses N of Responses % of responsesCorrect responses 9 8.82%Incomp&impr resp 40 39.26%No responses 53 51.97%total 102 100%

The sixth question is quite similar to the fourth one (the walker), it showed a motorcycle with a driving wheel background in a state of acceleration, the purpose of this situation is to lead students to identify their conceptions arguing, diagrams modeling the interactions between the two wheels and the floor. The students were asked to represent the two interacting forces between

the ground and the two wheels, again only 8 persons of the sample succeeded to display correct representations, nearly half of the population (49) presented unclear and vague representations, the remainder (45) did show any attempt, probably they find the problem so difficult. In addition to the lack of accuracy and clarity of the answers in the second category, on the representation of the forces of interaction between the wheels and the ground, the majority of the answers, represent frictional forces in the opposite direction of the movement, they do not accept the idea that a frictional force can also be in the same direction of movement, this may suggest that the vast majority of them believe that the frictional forces are always opposite to the direction the body movement, and a few of them only accept the idea that frictional forces can also help movement rather than hinder it.

Fig (6)

Interaction moto (roue motrice)/sol

Table of percentages corresponding to situation N°6

Types of responses N of Responses % of responses Correct responses 8 7.84%Incom&impr respo 49 48.40%No responses 45 44.12%Total 102 100%

Discussion: The principal goal of this study was to introduce and evaluate the efficiency of the (CNF) method, for probing students’ misconceptions in physics. The method relies on the basic terminology and conventional (usual) notations used at school to represent physical quantities, namely forces. In this research, the (CNF) method was taken in the context of a special physics subject, that to say reciprocal actions or traditionally speaking “Newton’s third law”. It is my view that comprehending physical laws includes the knowledge how them to

real situations. One outcome of his method is that, it has demonstrated the ability to determine whether or not students are indeed able to apply abstract physical laws to real phenomena. In fact all the situations proposed to students were relevant to the third law. However, few students only succeeded to represent correctly the interacting forces in each situation. This may be to the difficulty of bridging the world of physics taught in class, to the world outside the classroom. In this context, Cajas (1999) argues that connecting school science with students’ everyday life-and this includes students’ abilities to use scientific knowledge in real, everyday life situations, rather than merely solving contrived text problems-is a complex task. Mayon and knutton’s (1997) systematic work on school science and students’ out-of-school experience to students’ out-of-school experience. However, although pictures situations are at the centre of the (CNF)method, the fact that students look at the situation displayed in the picture trough science vision and represent it according to conventional notation (using vectors) or verbally (using expressions) forces them to reveal the view of how the real and the abstract come together. The importance of this method, it revealed some undocumented misconceptions and tendencies: the misconceptions that the third law describes a sequence of events; the tendencies to introduce irrelevant entities in representations, and the use of the word ‘reaction’ in its colloquial sense. It also reaffirmed some known misconceptions, such as those connected with the tendency to restrict the application of 3rd law stationary or static situations. The fact that new misconceptions were revealed trough the use of (CNF) might suggest that it has some unique potential from other misconception elicitations methods. It should be noted that the (CNF) did not elicit all of the misconceptions documented in the literature. Perhaps we should have proposed more situations to reveal other misconceptions. Summarizing, we say that the (CNF) method does has its unique benefits, the method is very simple and practical and can be easily used by teachers as an integral part of their instructions, the method can also provide the students with an interesting and authentic way to connect’ (to bridge) their out-of-class daily experiences with their physics learning. As was already mentioned the purpose of this study was to proof the efficacity of the (CNF) method. The results showed that the (CNF) method has the ability to bring to the fore students’ lack of solid

understanding of Newton’s 3rd law, this lack of understanding, suggests that we should be more concerned about the problem. According to Hellingman (1992),” we face the undeniable fact, hard as it is to believe, that not only students but also professional physicist to quite a large extent do not have a full understanding of the concept of force” (p 112). Furthermore, the (CNF) method also revealed two categories of students regarding the language used in their displays, the first category evidenced an almost complete lack of using the abstract physics term “force” , and instead, using everyday language (push, pull, ram…ect ), the other one (few compared with the first one), did use the term ‘force’. Differences in terms and expressions such as these should not be taken seriously. Vygotsky, for example, considered language as the principal of all higher mental functions (see Vygotsky 1934/1986) and, therefore as virtually a sin qua non of mental growth as is well known. Indeed, using scientific terms indicates that, for students who had reached a higher level of thinking and understanding, it was more natural to describe the real world using physical terminology. Being aware that language plays a crucial role in the process of conceptual growth, it is important that teacher will use and encourage students to use formal terms when explaining real situations involving the third law. This makes the explanation more accurate and therefore lead to a better understanding of the law and its applicability in real situations. In this context, it is worth noting that text books, sadly, still use (continue to use) an old fashion formulation of 3rd law in terms of action/reaction instead of force. Mayer and Gallini (1990), in their famous paper, “When is an illustration worth ten thousand words?” “…tools and techniques for enhancing students’ visual learning of scientific information present a relatively untapped potential for improving instructions” (p715). It is my hope that this method, along with other endeavors, looking for innovative ways to bring life and color to the study of physics, are making the first step in the right direction. I hope that this modest work would be another brick added to the field of science education, and effective way within the reach of teachers and researchers to upgrade and improve education in general and physics in particular.

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