DESIGNING LEARNING SEQUENCES ABOUT
PRE-QUANTITATIVE PARTICLE MODELS

Martine Méheut
LDPES, Université Denis Diderot, Paris, France
 

1 INTRODUCTION

To teach some notions about the particle structure of matter from the first years of secondary schooling (or even earlier) seems nowadays unavoidable. This can be related to the increase in everyday-life of linked technologies, such as "electronics" or "nuclear" power for example, and to the diffusion through the media of particular words and images.

In such teaching, we have to be careful with the "concrete" character of these models and to pay attention to their theoretical contents. The need for caution has been shown by evaluations of the results of teaching in this field, and didactical research (Dow, Auld & Wilson, 1978 ; Novick & Nussbaum, 1978 ; Pfundt, 1981 ; Méheut, 1982 ; Brook, Briggs & Driver, 1984), which have brought to light some difficulties and misconceptions relative to

- the existence of vacuum,

- the separation between the sensible properties of matter and the mechanical properties of atoms.

These difficulties can be easily understood if we recall some specific features of the historical development of atomic models. The particle theories of the structure of matter developed from a philosophical assertion rather than from empirical evidence, namely the immutability of matter under transformations and its unity under various aspects. Atomist philosophers considered sensations as misleading ; they asserted that reality remains concealed and can be reached by reason, rather than by direct perceptions. So, matter can be coloured, fluid, compressible, combustible, and so on, whilst atoms have invariable shape, have dimensions, and can only move, collide and aggregate.

" Atoms have no more phenomenological qualities than heaviness, size, shape (...). Because all qualities can change, the atoms can't change anyway (...)" or " They have nothing of the changing nature ; they have necesarily permanent mass and shape.". (Epicure, quoted by Bensaude-Vincent & Kounelis, 1991)

Errors and misconceptions revealed by didactical research indicate that students are rather reluctant to agree with such "arbitrary" hypotheses. Let us remember the objections that these viewpoints encountered, either in the early stages of atomism or at various moments of its development (Kubbinga, 1983, Bensaude-Vincent & Kounelis, 1991 ; Pullman, 1995). Let us give only as an echo of these debates some words of Ostwald just before atomism was accepted by the international scientific community.

"Everywhere it is repeated, as an axiom, that only the mechanics of atoms can give the key of physical world. Matter and motion are the two concepts to which the most complex natural phenomena are reduced in final analysis (...). Nobody usually takes care to note how much this point of view, so widespread, is quite hypothetical, quite metaphysical." or " Then, one will say, if we have to accept atoms, or mechanics, what image of the reality will we keep ? But we don't need any image, any symbol (...). To establish relationships between realities, that is tangible, measurable variables, (...), this is the task of science and science doesn't fulfil it when concluding with a more or less hypothetical image." (Ostwald, quoted by Bensaude-Vincent & Kounelis, 1991)

Similarly, there is Boltzmann's answer, justifying atomism as a powerfull instrument for thinking, on the grounds of its capacity to offer unifying descriptions and predictions of observable phenomena, and not as truth devoid of any arbitrariness or hypothesis.

"And to elaborate images to represent facts so that they make it possible to predict the course of similar phenomena, this is the first aim of any exact science (...). Images will be modified and completed so that they will suffice to describe old and new phenomena. To conclude, I will not hesitate to support, albeit with some reservations, that to contain some arbitrary elements comes from the intrinsically figurative nature of images and that to go beyond the observed facts is indeed unavoidable if one wants to explain even one additional fact " (Boltzmann, quoted by Bensaude-Vincent & Kounelis, 1991)

Designing teaching-learning sequences, we tried to put into play some of the following characteristic features of particle models of matter:

- rational rather than empirical origins,

- "instruments for thinking" rather than "observable reality",

- mechanical properties which make concretization easy.

The aim is to develop models as cognitive tools in order to unify descriptions and then to predict physical phenomena, the models getting more and more precise in relation with the questions. In this approach, we did not suppose that students would be able to infer a particulate nature of matter by observation and interpretation of some experimental facts (Nussbaum & Novick, 1982 ; Johnston, 1990).

AN UNIFYING MODEL FOR PHYSICAL TRANSFORMATIONS OF MATTER

Characterizing the model

The experimental field and the functions of the model

During a first sequence, we proposed to students that they could interpret physical phenomena (compression of a gas, mixing of gases by diffusion, change of state) as changes of the spatial organization of immutable particles. The models thus elaborated remain quite rough : they provide a coherent interpretation only of the conservation of matter in these phenomena. Using such models one needs to separate space and matter in order to be consistent with the existence of vacuum and the immutability of particles. We also expected that students would propose permanent and multi-directional motion of particles in order to explain the mixing by diffusion of two gases.

The "concretization" of the model

We introduced this sequence through the production and the discussion of iconic representation. This method of representation implies constraints due to its static nature ; on the other hand, the students are given a great share of initiative in the choice of the significant features that they use. One can thus make a variety of the possible representations appear and elicit the pertinent variables of the model by discussing the meaningful or meaningless nature of the different aspects of the representations made by the pupils. Some samples of working sheets are presented in the annex.

The didactical experiment conditions

We were able to repeat this experiment in each of two years with about three hundred 13-14 year old third formers, viz eleven forms. The learning took place for an hour and a half per week over a six week period, in the usual form groups and in the normal time table. Frequent meetings with our teaching colleagues taking part in the experiment allowed us to work out a precise protocol and to take into account the students' cognitive skills and the normal operating routines of the school.

We defined an accurate protocol with the teachers in order to collect the data during the classes. The data were the pupils' written productions (in every tested form) and tape recordings of the teachers' interventions and of the discussions of several groups of students (in three forms). After the sequence, we assessed by means of written questionnaires various aspects of the individual model building evolved during the learning sequence.

Some results

The invariance of particles

We have chosen to impose invariance as a guide line in the elaboration of the model. This constraint is generally well respected by pupils, who were found to be sensitive to a contradiction.

In the course of this sequence the pupils used the particle shape as a parameter of the model, so allowing the modelling of different substances. The answers to the final questionnaires show that a vast majority of pupils (about 80%) then prove able to establish the idea of invariant shape. Yet one can remark that a low percentage (about 10%) of pupils misinterpret the increase of volume during a thermal expansion process as being a swelling of the particles ; a majority (about 60%) interpret it properly as an augmentation of the distances between particles.

Separating space and matter

The variability of interparticulate distances makes it possible to separate mass variations from volume variations. It is put forward by a great number of pupils in order to explain the compression of a gas sample. It's then used again not only as an explanation of the greater or lesser compressibility of gases, liquids and solids, but also of the miscibility of gases and liquids.

It seems, however, that some pupils were somehow reluctant to conceive of a region devoid of matter. So, in order to model a gas they draw contiguous particles, with no interstitial space (4%), or particles superimposed upon a continuous background (7%). Later on, in order to model a solid they focus on the properties of non compressibility, cohesion, or non miscibility of solids in order to avoid accepting the existence of such empty spaces (15%).

To what extent did the sequence help to achieve a better dissociation of the two concepts of mass and volume ? We can compare the answers given, before and after the sequence, to questions about a thermal expansion process, a phenomenon that was not interpreted during the sequence (see figure 1). There is a noticeable progress in the affirmation of the mass invariance and in the dissociation of the mass and volume concepts. A third of the pupils use particle arguments exclusively in order to justify this invariance of mass.
 

 
 
 
 
  Expansion of water    Expansion of copper 
Mass Before (N=113)  After (N=151   Before (N=113)  After (N=164
increases 19%  4%    28%  7% 
           
decreases 8%  1%    9%  1% 
           
no variation 68%  93%    59%  91% 
           
no answer 5%  2%    4%  1% 
 Conservation of mass during an expansion process; the evolution of pupils' answers
Figure 1: An unifying model for physical transformations
 

 

Motion

We also expected that students would propose a permanent and multi-directional motion of particles in order to explain the mixing by diffusion of two gases. Only a few pupils (less than 1%) met this expectation. About one quarter of them evoked the mobility of particles, without specifying the conditions and the nature of such a motion.

Discussion

Our students worked on modelling physical phenomena by immutable particles. In this first step, only some limited aspects of these transformations were taken into account. Nevertheless students were given the opportunity to discuss necesary complements to the initial hypothesis : the existence of vacuum, the variability of distances and of arrangements of particles. The analysis of data (Chomat & al., 1988 ; Méheut & Chomat, 1990a ; 1990b) makes clear that more specific learning sequences have to be developed in order that students put into play kinetic, dynamic and thermodynamic aspects of particle models, which are necesary for more effective modelling of physical phenomena.

A PREDICTIVE MODEL FOR THERMOELASTIC PROPERTIES OF GASES

Characterizing the model

The "concretization" of the model

We developed a computer simulation in order to introduce and explore the kinetic and dynamic aspects of particle models. This program generates images of moving entities in a rectangular box (see figure 2). Entities move according to the kinetic theory of gases, except for some procedures related to the low number of entities (about one hundred particles) and the discrete treatment of some variables (position, speed : magnitude and direction) (Chomat, Larcher & Méheut, 1990). The dimensions of the frames are modifiable. It is possible to obtain two boxes with a common side ; this side can, if desired, move in relation to the impacts of the particles. The user can set the number and the "speed" (mean square speed) of the particles in each frame. He can also choose to display the values of parameters of the simulation and of some variables : the number of particle impacts against a side of the box (for the whole length of the side or by unit of length) for a given duration and, when the common side is moving, the position of this side at any insteant, and the mean position of this side for a given length of time.
 

"Concretization" of the model; a screen copy
Figure 2 : A predictive model for thermoelastic properties of gases
 

The experimental field and the functions of the model

During this second sequence, our aims were to help students to develop kinetic and dynamic particle models. The expected ways of thinking require the use of relationships between the number of particles, the occupied space, the speed of particles, the frequency and the "force" of impacts. Such models make possible the explanation and the pediction of phenomena related to the thermoelastic properties of gases ; they give an interpretation of relationships between the volume, the temperature and the pressure of a gas.

We chose the phenomena and the questions so that students could be in a position to bring into play progressively more and more variables of the model. We also took into account some results of didactical research about teaching pressure (Séré, 1985) and specific ways of causal linear reasoning in elementary thermodynamics (Rozier & Viennot, 1990 ; see also part C, chapter 3 in this book). Moreover we wanted to ensure that during this sequence models could be used to make predictions. That is the reason why we searched for phenomena about which students at this age have difficulties making predictions or explanations. So we opted for making the students work first with phenomena without variations of temperature ; the variables of the model are therefore the dimensions of the frames, the number of entities in each box, and the frequency of impacts of particles on the sides of the boxes. Phenomena with variations of temperature are then proposed in order to put students into a position to bring into play more kinetic and dynamic aspects of the models : the speed of entities and the "force" of impacts.

We used an unsophisticated device (see figure 3) in order to make the relationship between the elements of the experimental device and those of the simulation as easy as possible. This device is made of two syringes (containing air) connected by a length of rubber tubing ; a drop of coloured water is placed in this tubing. This tubing can be blocked with a clip or a tap ; the plungers of the syringes can be locked. The experiments consist of creating a difference of pressure between the two quantities of air (the tubing staying blocked) and then letting the system evolve towards a new equilibrium by removing the clip. The difference of pressure can be created by shifting a plunger (compression experiment) or by heating one syringe (heating experiment).
 

The device and experimental situations
Figure 3: A predictive model for thermoelastic properties of gases
 
 

For each phenomenon, pupils were asked to predict first, then to observe and to explain the features they observed, without any use of the model ; the questions concerned the shifting, and the stopping of the coloured drop.

1. What will happen if the tap is opened ?

2. Will the drop move ?

O yes O no O I don't know

Why ?

3 . Why did the drop move ?

4. Explain why it stopped . (Where did it stop ? Under what conditions ?)

A second step included the use of the computer program in order to build a model of the system and to simulate the observed phenomena. For this purpose, we asked pupils to discuss the validity of a simulation proposed by the teacher. The aim of these first questions was to put pupils into a position to consider and to choose the values of the parameters of the model : the number of entities in each frame, the dimensions of the frames, and the speed of the entities in each frame in relation to the macroscopic parameters : quantities of gas in each syringe, volumes and temperatures.

1. Does this simulation represent the situation adequately , before the tap is opened?

O yes O no O I don't know

- If you say "yes", please explain why it is well adapted.

- If you say "no", please explain what must be changed, and why.

2. Is the simulation adapted to representing the situation immediately after the drop stops ?

O yes O no O I don't know

- If you say "yes", please explain why it is well adapted

- If you say "no", please explain what must be changed, and why.

After obtaining a suitable simulation, pupils were asked to explain the shifting and the stopping of the drop with the help of this simulation.

3. According to the simulation, why did the common side (representing the drop) move?

4. Explain why it stopped. (Where did it stop ? Under what conditions ? )

Teachers could then opt for displaying the number of impacts or for using a simulation with a moving side in order to help pupils to develop the expected relationships between the variables of the model.
 
 

The didactical experiment conditions

The aims of the experiment are on the one hand to obtain information on the feasibility and the effectiveness of this learning process and on the other hand to test the hypotheses underlying the choice of phenomena and questions. The experiment included several stages. The first stage consisted of interviews of five pairs of students ; these interviews were divided into two sequences of nearly three quarters of an hour each and they were tape recorded. The second stage was the implementation of a nine hour learning sequence in sixteen 2nd year classes in French secondary schools. We gathered data all along the sequence by written work : nine sheets for each student. The analysis concerned the work of ten randomly selected students out of each class (ie 160 students). In a third stage, two years after the development of this learning sequence, we gathered some additional information for two purposes. The first was to ascertain and to clarify some results obtained by the analysis of the data gathered during the interviews and the classroom sequence ; the second was to assess the long-term effects of this learning process.

Some results and discussion

The analysis of the data collected during interviews provides information about the way students took into account the different variables of the model in relation to the phenomena and the questions (Chomat & al., 1990 ; Méheut & al., 1994).

- About the compression experiment, students seemed interested first in representing density variations and differences ; let us give an example.

Jonathan and Stanislas

J: I should like to reduce the dimensions of the box.

S: And to divide it approximately into two parts.

...

S: With small particles more closed up than the others.

...

J: The right one more reduced than the left one and equal numbers of particles in both boxes.

To explain the shifting of the drop, some of them considered the impacts of particles against the sides of the boxes ; they explained the shifting and the stopping of the drop by comparing the frequencies of impacts on both sides.

Olivier and Pascal

- the shifting

I: And on the screen, how is the push of the air represented ?

O: The air, it rebounds ; the small points rebound against the wall, here more because they have less room so they collide more against the walls.

P: We say, as they have less room, they rebound more against all the walls and as they move with the same speed, they collide more against the walls.

- the stopping

O: They will collide as much because they will have as much space.

- About the heating experiment, all the students managed to translate an increase of the temperature of the air into an increase of the speed of particles. So, this was suggested by some students before the interviewer asked them to work with the computer simulation (see for exampleOlivier and Pascal) . It was accepted by the other students after trying other possibilities : particles expanding, multiplying, repulsive forces between particles.

Olivier and Pascal

They seem to feel first some difficulty in predicting what will happen. Pascal then makes a good prediction by using an idea of expansion.

P: The air will expand and then, when one opens it, it will push ; it will push the drop more than ...

After observing, he went from this idea to an increase of the speed of the particles.

P : The air was more ... The particles were more distant in the same place, they collided much more quickly.

...

P: What ! They collide much more quickly. It isn't exactly that they are more distant but ... They collide much more quickly, they move much more quickly.

...

P: By heating, one speeded up the moving of particles.

Olivier says very little until this moment. Commenting on a picture, he develops the idea that particles expanded.

O : (before heating) There are as many particles in each syringe and they collide as much ; they collide both as much against the same wall, so the wall keep still and , in the second situation (after heating), particles expand , so when they collide against the wall, it makes a bigger collision than when small particles collide against the wall.

Pascal then recalls the hypothesis of immuability of particles. Olivier then agrees with Pascal's explanations.

This question of interpreting an increase of temperature comes back when using the computer simulation.

P : We should have to try to heat, what !

...

P: We should have to try to recreate when heating.

O: On the computer, would it be possible to represent when heating ?

The interviewer sends back this question to the students.

I: How would it be possible to do that ?

P: If what I said is right, we would have to be able to speed up the particles in this one (box).

This relation was more or less used according to the group. Some students related the speed of particles and the frequency of impacts, but didn't consider the force of impacts ; so they explained the equilibrium by the equality of the frequencies of impacts on both sides. Other students succeded in considering both the frequency and the force of the impacts.

Jonathan and Stanislas

J: As it goes faster on the left, the "force de frappe" if we can call it in this way, is higher than this one on the right. But, as it's hitting the wall more from the left, everything is balanced.

Jean- Michel and Florence

JM: The impacts are more violent because molecules are faster.

I: So, when do you think the wall should stop ?

JM: For example, if an impact of a blue molecule has a value of ten and there are ten impacts, and if an impact of a blue molecule has a value of five, it should be twenty impacts of black molecules for ten impacts of blue molecules ; then the wall will stop.

The analysis of the data collected during the classroom sequences gives some information about the short-term and the longer-term efficiency of this learning sequence. For example, in order to assess the efficiency of the particle model built by students as the outcome of this sequence, we gave students experiments that were a little different from those they simulated during the sequence. For both experiments, the number of students reasoning in a particulate way was a little more than a half. Among these, the greatest number (34%) compared the frequencies of impacts. The predictions were correct for a great majority of students (more than 80%). Two years later, students who attended this learning sequence used a particle model more than students who did not attend it.

Analysis of the data can provide evidence about the hypotheses underlying the choice of phenomena and questions. For instance, in choosing the questions, we formulated the hypothesis that students will take into account and compare actions exerted by two systems more for a stopping than for a shifting. The analysis of the data are in accordance with this first hypothesis (table 1).
 

 
 
Table 1 : Testing H1 hypothesis
 
Situation  compression 

N= 145 

heating 

N= 160 

Explaining 

Taking into account 

the shifting the stopping the shifting the stopping
one sample of gas 96 %  69 % 88 % 56 % 
both samples of gas 4 %  28 % 10 % 37 % 
no answer  0 % 3 %  2 % 7 %
 

In choosing the phenomena, we made the hypothesis that phenomena related to temperature were more problematic than elastic properties, when temperature is not put into play. This second hypothesis can be seen as preliminary to a third one, that the model will seem more useful to students for thermoelastic properties and then they will use it more than for elastic properties. The analysis of the data is in accordance with the second hypothesis (table 2), but we didn't observe the expected effect related to the third hypothesis. We now consider that the questions we chose were not sufficient for students to feel the need of such a model and use it more than alternative phenomenological types of explanation. We have to remember that a major quality of the particulate model is its unifying power. Establishing this characteristic on a secure basis is a long process !
 
 

Table 2 : Testing H2 hypothesis
 
Situation 

Prediction 

compression 

N= 79 

expanding 

N= 77

heating 

N= 79

cooling 

N= 77 

right direction shifting 77%  53% 22%  21%
no shifting 11%  12% 39%  40%
wrong direction shifting 11%  31% 22%  25%
no answer 0 %  4% 17%  14% 
 
 

CONCLUSION

In order to design these teaching sequences, we took into account some specific features of atomic models and some students' misconceptions and ways of reasoning. For both sequences, we chose the "theoretical" content of the model in close connection with the phenomena and the questions. The didactical experiments enabled us to test the hypotheses underlying the design of these "didactical structures" (Lijnse, 1994) and provided precise information about the effectiveness of the expected learning process. Thus, they threw light on some limitations of these structures in relation to our expectations and suggested some directions for improving the design of such sequences.

References

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Brooks, A., Briggs, H., & Driver, R. (1984). Aspects of secondary students' understanding of the particulate nature of matter . The University of Leeds.

Chomat, A., Larcher, C., & Méheut, M. (1988). Modèle particulaire et activités de modélisation en classe de quatrième . Aster,9, 143-184..

Chomat, A., Larcher, C., & Méheut, M. (1990). Modèle particulaire et démarches de modélisation . Paris : LIREST.

Dow, W.M., Auld J., & Wilson, D.J. (1978). Pupils' concepts of gases, liquids, solids . Dundee : College of Education.

Kubbinga, H. (1983). Le développement historique du concept de "molécule " dans les sciences de la nature jusqu'à la fin du 18ème siècle. Thèse de troisième cycle. Paris : EHESS.

Johnston, K. (1990). Students' responses to an active learning approach to teaching the paticulate theory of matter. In P.L.Lijnse et al. (Eds.), Relating macroscopic phenomena to microscopic particles . (pp. 247-265).Utrecht : CDß Press.

Lijnse, P.L. (1994). La recherche-développement : une voie vers une "structure didactique" de la physique empiriquement fondée. Didaskalia, 3, 93-108.

Méheut, M. (1982). Combustions et réaction chimique dans un enseignement destiné à des élèves de sixième. Thèse de troisième cycle. Université Paris 7.

Méheut, M., & Chomat, A. (1990a). The bounds of children atomism ; an attempt to make children build up a particulate model of matter. In P.L.Lijnse et al. (Eds.), Relating macroscopic phenomena to microscopic particles . (pp. 266-282).Utrecht : CDß Press.

Méheut, M, & Chomat, A. (1990b). Les limites de l'atomisme enfantin ; expérimentation d'une démarche d'élaboration d'un modèle particulaire par des élèves de collège. European journal of psychology of education, 5,4,417-437.

Méheut, M., Chomat, A., & Larcher, C. (1994). Construction d'un modèle cinétique de gaz par des élèves de collège : jeux de questionnement et de simulation. In M. Caillot (Ed.), Actes du quatrième séminaire national de la recherche en didactique des sciences physiques. (pp. 53-71). Amiens : IUFM de Picardie.

Novick, S., & Nussbaum, J. (1978). Junior high school pupils' understanding of the particulate nature of matter : an interview study. Science education, 62, 273-281.

Nussbaum, J., & Novick, S. (1978). Alternative frameworks, conceptual conflict and accomodation : toward a principled teaching strategy. Instructional Science, 11, 183-200.

Pfundt, H. (1981). The final link in the division process or the first building block ? Pre-instructional conceptions about the structure of substances. Chimica didactica, 7, 75-94.

Pullman, B. (1995). L'atome dans l'histoire de la pensée humaine. Paris : Fayard.

Rozier, S., & Viennot, L. (1990). Students reasoning in thermodynamics. In P.L.Lijnse et al. (Eds), Relating macroscopic phenomena to microscopic particles . (pp. 36-49). Utrecht : CDß Press.

Séré, M. G. (1985) Analyse des conceptions de l'état gazeux qu'ont les enfants de 11 à 13 ans, en liaison avec la notion de pression, et propositions de stratégies pédagogiques pour en faciliter l'évolution. Thèse d'état. Université Paris 6.
 
 
 
 
APPENDIX:
 
A UNIFYING MODEL FOR PHYSICAL TRANSFORMATIONS OF MATTER
Some working sheets
 
Figure 1a: Interpretation of the compression of a gas
 
Figure 2a: Discussing the interpretation of the compression of a gas
 
Figure 3a: Interpretation of change of state
 
 
*********************

Section E3,  Designing learning sequences about pre-quantitative particle models  from: Connecting Research in Physics Education  with Teacher Education
An I.C.P.E. Book © International Commission on Physics Education 1997,1998
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