Atom and molecule: upper secondary school French students' representations in long-term memory

Aytekin Cokelez and Alain Dumon
IUFM d'aquitaine, DAEST, Université Bordeaux 2, France
e-mail: alain.dumon@aquitaine.iufm.fr

Received 19 October 2004, accepted 30 June 2005

Abstract: The purpose of this study is to highlight collectively assimilated knowledge by upper secondary school French students (grades 10 to12) and to identify and describe the students' representations and misconceptions related to the concepts of 'atom' and 'molecule'. In order to understand assimilated knowledge better, the school science curricula and textbooks have been examined so as to identify the intended development of the conceptualisation of these concepts within the school curricula. This study is based on the written answers given by school students to four questions concerning these concepts, submitted a long time after the teaching has taken place. The analysis of the students' answers shows the various representations and misconceptions that concern the concepts of atom and molecule at each student level and allows us to see their evolution over these three years. [Chem. Educ. Res. Pract., 2005, 6 (3), 119-135]

Keywords:  didactical transposition, representation, misconception, model, atom, molecule.

Introduction

Students are presented with different models of atom and molecule during their schooling at secondary school level. These models originate from knowledge that has been gradually acquired by the scientific community during the development of science, and which we will name reference knowledge. The first task is to turn that knowledge into teaching objects: the knowledge to be taught as in Official Instructions and textbooks. Then teachers must bring this knowledge into use by devising class activities that are likely to support the students' learning. It will thus become school knowledge. Finally, the last stage of the student's work is to interpret the knowledge 'the way he can' during various steps which will lead him/her to transform it into acquired or assimilated knowledge in a particular context.

This personal learner's structured organisation of a system of knowledge has been called 'alternative framework' (Driver et al., 1978; Watts, 1983), 'children's science' (Gilbert et al., 1982) or 'alternative conception' (Gilbert et al., 1985). In reference to the models used by scientists to interpret the data obtained through the experiments and to predict events, such knowledge is also labelled 'mental model' by some. According to Vosniadou (1994) mental models refer to a specific mental representation or analogical representation, made up by an individual during his cognitive functioning. In francophone countries the term 'conception' has been used. Giordan and De Vecchi (1987) define a conception as a "unity of coordinated ideas and coherent clarifying images used by learners to reason when confronted with problem-situations". Later, Watts and Taber (1996) suggested the following distinction: "an alternative conception relates to particular phenomena, and the alternative framework concerns a web of ideas within a particular scientific topic". 

The purpose of this study is to highlight the assimilated knowledge collectively by students: which 'teaching models' of the atom and the molecule do they favour in a non-academic context? How does this representation of models develop from the grade 9 to the beginning of grade 12? 

Evolution of the presentation of the knowledge to be taught 

French Official Instructions don't prescribe any representation or reference model to be taught, just refer to the curricular model. Yet, in textbooks, the description of models is generally paired with a representation in the form of images or molecular models. Authors are therefore free to offer their representations in so far as they are compatible with the knowledge to be taught.

Grade 9 (age 14-15)
In grade 8, an atom is represented by a sphere; a molecule is made of assembled atoms and represented by space-filling molecular model. At this teaching level, an atom consists of a positively charged nucleus and of negatively charged electrons that move (revolve) around the nucleus: the electron suite. The nucleus of the atom contains as many positively charged units as there are electrons around it; the atom is neutral. 

• The set of electrons in an atom is labelled the electron suite.
• All electrons are identical, they bear the same mass (9.11x10^{-31 kg}) and the same charge (e = 1.6x10^-19 Coulomb).
• The mass of atom is essentially concentrated inside the nucleus.
• The diameter of an atomic nucleus is roughly 100 000 times as small as that of an atom: matter is mostly made of empty space.   

Thus, what must be taught is the neutral electric atom, and more precisely, the Rutherford atomic model. As far as molecules are concerned, at the end of grade 9, a student must be able to describe the molecular model of simple molecules: O₂, H₂O, CO₂, and CH₄ (that were met in grade 8).

In grade 9 textbooks, the representation of atoms is more diverse, but the model of the neutral atom (the number of negative charges of electrons equals to the number of positive charges of the nucleus) is that generally presented (Figure 1). In some textbooks, we can find a probabilistic representation of the electron cloud or the solar system model of atom.

Figure 1: Example of representation of a neutral atom model in textbooks

As far as the representation of molecules is concerned, textbooks present space-filling molecular models of the following molecules: H₂O, O₂, CO₂ and CH₄.

Grade 10 (age 15-16)
Atom
The atom of mass A is made of a nucleus containing Z protons and (A-Z) neutrons and of an electron suite (or revolving electrons) that contains Z electrons.

• The nucleus of an atom is symbolised ^A_ZX; A is the number of nucleons (protons and neutrons); Z is the atomic number: it characterizes the element and represents the number of protons that the nucleus contains.
• Protons and neutrons have the same mass.
• The mass of the atoms virtually equals the sum of the mass of the nucleons that constitute it.
• Isotopes are atoms of one chemical element (identical Z) but with different numbers of neutrons.
• Electrons are distributed in shells, K, L, M that are further and further from the nucleus).
• The highest number of electrons in shells is 2 for K, 8 for L and 18 for M.
• The electronic structure of an atom or a monoatomic ion can be symbolized by K^XL^Y M^Z (for example, K²L⁴ for a carbon atom and K²L⁸ for Na⁺). 
• With the exception of helium, all atoms of noble gases bear 8 electrons on the outer shell.
• During chemical transformations, atoms change so as to acquire the electronic structure of the nearest noble gas in the periodic classification.   

Therefore, what must be presented is a mixed model composed of the Rutherford model completed by Chadwick, and of the chemists' model of shells (Lewis, Langmuir and Bohr).

Molecule
In a molecule, atoms are linked by covalent bonding. Each bond is formed by an electron pair that results from the sharing of two electrons, generally one from each of the linked atoms.

• Between two atoms one, two or three bonding electron pairs can be found.
• The electron pairs are represented by dashes.
• An electron pair of the outer shell that is not shared by two atoms is an unshared electron pair.
• The association of atoms within a molecule can be represented by Lewis representation: a planar formula of the molecule showing all the shared and unshared electrons.
• Shared and unshared electron pairs repel one another, and position themselves so as to be as far away from one another as possible.
  In commentaries, the curriculum authors make it clear that:
• The Lewis representation of atoms with electrons associated in electron pairs must not be used. 
• To establish the representation of a molecule, the use of systematic exploration is recommended: the electrons of outer shells in the atoms that make up the molecule are first numbered and then grouped in electron pairs; the electron pairs are then shared between atoms (bonding electron pair) or around atoms (unshared electron pair) so as to satisfy the rules of 'duet' and octet.   

In textbooks for grade 10, there exist only a few representations of the atomic model and when they are present, they are similar to the ones that are used in the textbooks of grade 9: neutral atoms and probabilistic representation. In this last representation the electron suite is generally identified, wrongly, with the electron cloud. No representation of the solar system model in shells is provided.

As far as molecules are concerned, the model of a covalent bond has been already introduced, and ball and stick models appear. Each stick between atoms can then be associated with a shared electron pair.
The interpretation of the geometry of some simple molecules is based on taking into account the repulsion of shared and unshared electron pairs around the central atom. 

Grades 11 and 12
In grade 11, the representation of molecules with the use of molecular models is generalized in organic chemistry. What is new is the introduction of the polar character of some bonds, and of polar molecules.

Lastly, it is only towards the end of the Physics curriculum in grade 12 that the Bohr model is introduced. It will thus not appear in our study.

Analysis of students' evolving representations of atoms and molecules 

Review of the literature
While very few studies have been carried out in this field in France, a lot of research has been conducted in Anglophone countries (UK, Australia, NZ, and Canada). Here, we present the main findings relevant to our work.

Conceptions of the atom
An atom is often described as round, solid, hard (Griffiths and Preston, 1992; Harrison and Treagust, 1996) and defined as a 'ball' or 'sphere' (Harrison and Treagust, 1996). Therefore, the water molecule consists of two or more solid spheres (Griffiths and Preston, 1992). 

Charlet-Brehelin (1998) shows that only slightly over a third of students who have followed a traditional course of studies and have left Lower Secondary School (beginning in grade 10) have internalised the minimum formulation level required at the end of grade 9: an atom is made of a nucleus and electrons (electron suite). An identical observation is brought out by Harrison and Treagust, (1996). Students generally produce four categories of models: the atom as a sphere, solar system atom, neutral atom (positive charges of the nucleus equal to negative charges of the electrons), and the atom as a nucleus surrounded by an electron cloud. By the end of a traditional course of studies, the first two models are used by many students, 41% and 48% respectively (Charlet-Brehelin, 1998). According to Harrison and Treagust, (1996), many students represent an atom as a 'simple circle' within a large circle. Even after teaching, there remains among students a certain degree of confusion between the terms used: not only particle, atom, molecule, but also nucleus, proton, neutron and electron and their interrelationships (Osborne and Freyberg, 1985; Johnston, 1988). For some students, the number of electrons, protons and neutrons is the same for a given atom (Tsai, 1998). Keig and Rubba (1993) reveal that for many students (45%), electrons are pre-assembled in electron pairs within the atom. According to Taber (1998) and Robinson (1998), students use the rule of octet as a basic heuristic principle, to explain chemical bonding, chemical reaction and ion formation. An atom is said to be stable if its valence shell is filled, and is said to be unstable otherwise. The quantum model of the atom gives birth to the representation of the electron cloud. But the fact that the students are willing to use this representation at the end of grade 9 (Charlet-Brehelin, 1998) is no guarantee that they understand its meaning. Harrison and Treagust (1996 and 2000) show that, for students, the electron cloud is considered as a matrix in which electrons are embedded (as water drops in a cloud) and Tsaparlis and Papaphotis (2002) report that upper secondary Greek students' (grade 12) have greater difficulties in understanding the concept of 'atomic orbital'.

Conceptions of molecule
Atoms are generally grouped (Harrison and Treagust, 1996) and molecules are considered as groups of atoms rather than basic chemical entities (Taber, 1998) Such combination of atoms to form molecules is drawn by joining the circles or spheres that represent the atoms (Griffiths and Preston, 1992). As far as molecular models are concerned, three quarters of the students favour space-filling models to represent the molecule whereas the remaining quarter prefers the ball and stick model (Harrison and Treagust, 1996). For the drawn diagrams of molecules (more precisely H₂O), representations evolve, during the process of learning, from space filling model to structural formula (Pereira and Pestana, 1991). Three sorts of mistakes are identified: a) mistakes in representing bonds between atoms; b) mistakes in representing bond angles; c) bond orders (Pereira and Pestana, 1991; Keig and Rubba, 1993). The relative size of atoms is generally disregarded, and the length of the O-H bond increases when one goes from solid to gas state (Pereira and Pestana, 1991). Wrong understanding of the meaning of the formula that represents a molecule leads some students to have an additive misconception of the molecule (de Vos and Verdonk, 1987). The representation: H₂O is then interpreted as the association of one molecule of hydrogen (H₂) and one atom of oxygen (O), or of 'one oxygen atom and two hydrogen atoms (H₂) in the liquid state: O(g) + H₂(g) ? H₂O(l)', which leads to a wrongly drawn diagram of the molecule (Ben Zvi et al. 1988; Keig and Rubba, 1993).

Assimilated knowledge on the modelling of an atom

Methodology and results
The investigation was carried out with 930 students of various upper secondary schools: 239 grade 10 students (age 15-16), 422 grade 11 students (age 16-17), and 269 grade 12 students (age 17-18) of upper secondary schools. In order to collect the data, we asked them to complete a diagnostic questionnaire comprising four open questions. The tasks concerning the concept of atom were: 

• Draw a diagram of the hydrogen atom (grade 10), the oxygen atom (grades 11 and 12).
• Describe the hydrogen atom (grade 10), the oxygen atom (grades 11 and 12).   

The total number and percentage of answers given for each question, from each group is as follows:

• Drawing diagram: grade 10, 185 (77%); grade 11, 400 (95%); grade 12, 246 (91%).
• Description: grade 10, 172 (72%); grade 11, 364 (86); grade 12, 167 (62%).   

Different kinds of drawing diagrams have been identified in the students' answers:  
D 0: No answer or answer impossible to classify, biological cell, particle association, atom and molecule confused for one another.
D.1: Atom symbol and symbol and electron pairs for grade 11 and 12 students.
D.2: Sphere.
D.3: Composition atom model: varied representations where a nucleus and electrons are visible or representation of the neutral atom as in lower secondary school grade 9.
D.4: Solar system (2D or 3D).
D.5: Electron cloud.

Examples of such diagrams are given in Figure 2.

Figure 2. Examples of the student-drawn diagrams of an atom

In order to identify the characteristics of the model that were assimilated, as well as the misconceptions, a certain number of keywords have been picked from the written descriptions. They are shown in Table 1 (see Appendix) and they lead to the definitions of six levels of description:
L.0: Erroneous and no answer. 
L.1: An atom composed of a nucleus and an electron suite (or nucleus and electrons).
L.2: A neutral atom composed of a positive nucleus and an electron suite.
L.3: An atom composed of a nucleus that contains protons (Z) and neutrons, and an electron suite (or negative electrons).
L.4: An atom is composed of a nucleus that contains (Z) positive protons and an electron suite that contains (Z) negative electrons. The number of positive charges equals the number of negative charges. [For oxygen: 8 protons and 8 electrons].
L.5: An atom is composed of Z protons, A-Z neutrons and Z electrons.
L.6: An atom is composed of a nucleus that contains Z protons and A-Z neutrons, and of an electron suite (or circling electrons) that contain Z electrons (or Z negative electrons).

Remarks (in italics above) concern grade 11 and 12 curricula. We can consider level 1 as the minimum level judged acceptable for students at the end of grade 9 (Lower Secondary), level 2 is the curricular level of description in that class, level 3 is the minimum level judged acceptable in grade 10 (Upper Secondary) and level 6 corresponds to the curricular level of description in that class. 

Analysis of results
We recognise that a model can be represented in different ways, with the representations varying according to the aspects of the concept to be illustrated. From our questionnaire it is not possible to know the repertoire of representations that individuals may have. We can only identify the representations chosen by the students in response to the questions as they understood them. So, as the data from different grades does not refer to individuals, it is only possible to display an average evolution of understanding.

Drawing a diagram of an atom
The percentage of students who produced a representation of an atom was higher at the beginning of grade 11 and 12 than at the beginning of grade 10. Does this mean that the concept of the atom is more familiar to those older students? This is not necessarily so, indeed they are less and less likely to give a description with a diagram. The differences between the use of diagrams and words are: grade 10, -5%; grade 11, -9% and grade 12, -29%. These differences may be explained by the possibility that grade 12 students have forgotten the words used to describe the characteristics of the atom, or more probably, as we shall see later, by the greater emphasis placed on electron pairs that has diverted attention from these characteristics. Figure 3 allows for the comparison of the evolution of choice in the different drawing diagrams along Upper Secondary School. (See list on page 123)

Figure 3: Comparative study of the varieties of diagrams of the atom

For the majority of students entering grade 10, the atom is represented as a simple sphere (61% of diagrams; 63% if we add the key words sphere or ball as used in the descriptions of other models. If a remarkable decrease in the percentage can be noticed in the following two grades, one is surprised to find still around one-third of the students that remain on the same description in grade 11 (31% of diagrams; 35% diagrams + descriptions) and grade 12 alike (30% of diagrams; 35% diagrams + descriptions). This was already identified by Harrison and Treagust (1996). Moreover, for other representations of the models of atoms exist, a tendency that was already confirmed (Griffiths and Preston, 1992; Harrison and Treagust, 1996; Taber, 1998) to include them into a spherical envelope (around 9%). 

One should also consider the second favourite diagram of grade 11 and 12 students, the Lewis representation of the atom (symbol and electron pairs). Indeed, this mode of representation is forbidden by the new Official Instructions. Does this mean that some (older) teachers do not follow the instructions or that the representation is attractive due to its perception as a simplification when modelling the bonding in the molecule? Both are real possibilities, but the second is in agreement with the mental model of 'octet rule' proposed by Taber (1998). Students favour the representation of the eight electrons of oxygen in the form of four electron pairs around the symbol of the element (and this accounts for 13% and 10%), followed by the showing of the six outside electrons (10% and 7%).

The use of the atomic composition model, and more particularly that of 'neutral atom', reaches a maximum when students enter grade 11, whereas it accounts for a majority of representations in the textbooks of grade 9. It seems therefore, that its adoption, however low, is favoured in the teaching of the electronic structure and nucleus composition. A low percentage in the choice of electron cloud model can be seen among different grades, although it is the description that textbooks authors as well as curricula developers favour. Thus, as Harrison and Treagust (1996, 2000) showed in their work, such a model is not easily grasped by students.

Another interesting observation is that the use of the solar system model of atom increases from grade 10 to grade 12. Yet this model is not often used in textbooks, as it appears only in documents with historical contents. Moreover, although Official Instructions forbid the representation of the solar system model in shells in 2D, some students (8% in grade 10, 10% in grade 11 and 11% in grade 12) choose this diagram. Is that a consequence of school knowledge or is it the students' own conception to represent electronic shells?
Finally, as far as other representations are concerned, they can mainly be explained by the confusion between atom and molecule. One can regret that 5% of grade 12 students still remain at this level!

Description of the atom 
A vast majority of students cannot produce a minimum level of description of the concept of atom required at the end of each grade. The differences observed between the three grades prove that if the teaching in grade 10 brings along a clearly positive evolution, the concept is not well absorbed. Indeed, whenever it is not the subject of teaching (i.e. in grade 11), its minimum characteristics appear to have been forgotten by the following year.
The minimum level judged acceptable at the end of grade 9, (L1) is only reached by 21% of grade 10 students, 47% of grade 11 students and down to 25% of students at the beginning of grade 12. As far as the minimal level acceptable at grade10 is concerned (L3), only 35% of grade 11 students and 15% of grade 12 students reach it. (The levels of description are described on p. 124.)

Figure 4: Comparison of the levels of description of the atom at different grades

From the diagrams and keywords, we have tried to discover what competences expected at the end of grade 10 appear in the students' answers at grades 11 and 12:

• Knowing the composition of atom - knowing that atom is electrically neutral. If 46% of grade 11 students and 47% of grade 12 make it clear that the number of protons equals that of electrons, only 9% and 4% of them state explicitly that the atom is electrically neutral. The composition of the nucleus of the oxygen atom (8 protons and 8 neutrons) is only explicitly referred to by 13% of grade 11 and 10% of grade 12 students;
• Discriminating between the electrons on the inside shells and electrons on the outer shells. 19% and 14% mention a clear organization of electrons in shells, but only 12% and 9% have a clear understanding of the right distribution of electrons in shells K and L (K² L⁶ for oxygen);
• Numbering the electrons of the outer shell. The presence of six electrons on the outer shell is clear in some representations (Lewis representation of the oxygen atom, K² L⁶, mentioning the six electrons in the description) among 22% of grade 11 students and 17% among grade 12 students.   

Considerations about the mass of atom being concentrated in the nucleus or about the atom as mainly constituted of empty space are only present in very few students' descriptions. Since the question did not explicitly ask that they write down everything they know about the structure of the atom, it is only possible to infer to their preferred representation, not to their total acquired knowledge on this concept. 

Students' misconceptions
The representation of atom by Lewis model is very often chosen by grade 11 and 12 students. It is present not only in diagrams but also in the descriptions of atom, either in written or symbolic forms, even when other representations are also used, with a percentage that reaches 46% in both classes. This result is in accordance with Keig and Rubba's work (1996). One may therefore assert with Taber (1995, 1998) and Robinson (1998) that the octet rule corresponds to a 'mental model' that the students have absorbed. Such a model leads them to a static conception of electrons within the atom; they are already grouped in electron pairs: "the atom is made of, consists of, possesses, contains,... electron pairs". And for some of the students, these electron pairs are already organized as bonding electron pairs or as bonds (3%, grade 11 and 10%, grade 12).

Other erroneous conceptions to be seen in diagrams and key words:

• Atom and molecule confused with each other (13%, grade10; 6%, grade 11; 5%, grade 12).
• A confusion between the different concepts used to describe atoms: proton - neutron, neutron - electron, ion - charged particle (respectively 4%, 3% and 2%), as already identified by Osborne and Freyberg (1985).
• Equating the total number of nucleons (16) with the number of electrons (3%, grade 11; 1%, grade 12).   

Assimilated knowledge of the modelling of water molecule
The same students, in the same questionnaire were asked to:
Draw a diagram of the water molecule;
Describe the water molecule.
The total number and percentage of answers given for each question, from each group is as follows:
Drawing a diagram: grade 10: 207 (87%); grade 11: 419 (99%); grade 12: 267(99%).
Description: grade 10: 178 (74%); grade 11: 419 (99%); grade 12: 222 (83%).
The analysis of the students' answers leads to various kinds of diagrams and levels of description, as happened for the atom. Key words appearing in the descriptions are presented in Table 2 (Appendix).

Different kinds of diagram:
D.0: Erroneous answer or no answer.
D.1: Space-filling model.
D.2: Ball and stick model.
D.3: Lewis structural formula model.
D.4: Lewis formula model.
Examples of such diagrams are given in figure 5.

Figure 5: examples of diagrams of the water molecule

Levels of description:
L.0: Erroneous description or no answer.
L.1: Water molecule is made of two atoms of hydrogen and one atom of oxygen.
L.2: Water molecule is made of two atoms of hydrogen linked to one atom of oxygen.
L.3: Water molecule is made of two atoms of hydrogen linked to one atom of oxygen by a covalent bond (or simple bond).
L.4: Water molecule is made of two atoms of hydrogen linked to one atom of oxygen by a covalent bond composed of two electrons (or linked electron pair).
L.5: Water molecule is made of two atoms of hydrogen linked to one atom of oxygen by a covalent bond. Each atom contributes one electron to make the bond.
Level 1 is required at the end of grade 9, level 3 is the minimum judged acceptable at the end of grade 10 and level 5 corresponds to the level of formulation in that class. 

Analysis of results
Diagram of the water molecule
The percentage of total answers to this second question is higher than that to the questions on the atom. Students seem more familiar with the water molecule than with the atom. Yet it is puzzling to note that the difference between these two percentages is higher for grade 12 students (-16%) than for grade 10 (-13%) although the description of water molecule is taught in grade 10 and 11 curricula.

As Pereira and Pestana (1991) and Harrison and Treagust (1996) showed, Figure 6 shows an evolution in the drawing of diagrams along Upper Secondary School. When entering grade 10, the majority of students (68%) choose the model that was introduced at Lower Secondary level: the space-filling model. In grades 11 and 12, they mainly rely on Lewis formula model, which was studied in grade 10 (37%). In grade10, ball and stick models of molecule are also used to represent molecules. Therefore, it may be remarked that a space-filling model is favoured by a quarter of grade 11 and 12 students and the use of this model decreases from grade 10 to grade 12.

Figure 6: Comparative study of the kinds of drawing diagram of water molecule

As stressed by Griffiths and Preston (1992), 70% of grade 10 students choose a space-filling model where they put hydrogen atom and oxygen atoms together (diagram 1 in Figure 5), whereas the students in the later grades produce a more acceptable representation: hydrogen atoms are 'integrated' into the oxygen atom (diagram 2 in Figure 5). Lastly, the representation in the guise of angled geometry of these different models increases noticeably from grade 10 (71%) to the higher grades (84%).

Let us note that in grade 11, 3% of the students feel it necessary to represent the molecule by the representation of each constitutive atom with the use of the solar system model in 2D.

Description of water molecule 
Figure 7 shows clearly that students seem more familiar with the concept of the molecule than with that of the atom since the percentage of unacceptable descriptions is lower in all grades. Nevertheless, it is surprising to see that grade 12 students are no better than grade 10 students as far as the description of the molecule is concerned. If we consider the minimum level expected at the end of grade 9, it is reached or exceeded by 58% of grade 10 students, 74% of grade 11 students and only 57% of grade 12 students. As far as the minimum level judged acceptable at the end of grade 10 is concerned, only 15% of grade 11 students and 13% of grade 12 students reach it.

As we can see in Table 2 (Appendix), the idea of chemical bonding appears, implicitly (with the use of a verb: attached, jointed, joined, connected, etc.) or explicitly, in few grade 10 students' descriptions (12%); this is not surprising, as it is not in the curriculum at that level. Yet, the idea of bonding, explicitly or implicitly formulated is present in around one-third of the students' answers in the later grades; understandably, since covalent bonding is studied in grade 10. The percentage of students who mention covalent bonding between hydrogen and oxygen atoms is very low: 7% in grade 11 and 5% in grade 12.

Figure 7: Comparative study of the levels of description of water molecule

In some descriptions of the water molecule, the following can be observed: 

• The notion of the polarity of the molecule (11% of grade 11 students), The idea is introduced at the beginning of grade 11, at the same time as the students answer the questions. In grade 12, only 2% of the students refer to it. 
• An explicit mention of the angle between the O-H bonds (5%, grade 11 students; 10%, grade 12). The accurate value is not often given.            

Students' misconceptions 
As noted by Pereira and Pestana (1991), when dealing with the diagrams of molecules with the help of space-filling models and ball and stick models, students do not always show the respective size of atoms: 33%, grade 10; 7%, grade 11; 15%, grade 12. The radiuses of the circles that represent oxygen and hydrogen atoms are generally equal. 

Some students confuse atom and molecule in the description: "the water molecule consists of two molecules of hydrogen and one of oxygen" (12%, grade 10; 3%, grade 11 and 8%, grade 12). In grade 10, they also sometimes refer to dihydrogen or dioxygen to name atoms (7%), thus showing confusion in their conceptions. 

Attributing colour to atoms in the description of water molecule (for example: "one red circle and two white circles")remains from grade 10 to grade 12 (6%, 3%, 5%) and 8% of grade 12 students still think that the molecule possesses macroscopic properties. These students thus seem to have difficulty in distinguishing model from reality. Indeed, the colour code for atoms was developed when the representation of molecules relied on the use of molecular models. 

The poor understanding of what the chemical formula, H₂O, represents (Ben-Zvi et  al. 1988; Keig and Rubba, 1993) leads some students to produce an erroneous description or drawing diagram of the water molecule: H and 2O (or H₂ and O): 5%, 4%, 7%. 

Lastly, 5% of grade 11 and 4% of grade 12 students believe that the bond between atoms is of the ionic type (molecule consisting of ions or bonding resulting from an exchange of electrons between atoms). 

Conclusions 

The results of the present study show: 

• That the model the students favour through their years of study is that of the spherical atom. Nevertheless, the choice of such drawn diagrams decreases from grade 10 to grade 12 in favour of the Lewis representation (symbol and electron pairs). But, for many students who rely on that representation, electrons are 'pre-assembled' in electron pairs within the atom. 
• That for the representation of the water molecule, they move from a strong use of the space-filling model (where all atoms are put side by side) to the diagram according to the Lewis formula as taught in grade 10. But it should be noted that students seldom mention covalent bonding between atoms when describing the water molecule. 
• That the levels of assimilation of the concepts of atom and molecule are much lower than those required at the end of the different grades. 
• That from grade 10 to grade 12, for some students, confusion remains between atom and molecule and between model and reality. 
• The students' conceptualisation of microscopic models of atom and molecule is therefore really problematic. Attempts at interpreting the origins of such difficulty were suggested by Barlet and Plouin (1997), Tsaparlis (1997) and Taber (2004):  
• The concepts involved are abstract and cannot be related to everyday experience. Their understanding requires a high level of abstraction from the students, which seems to be the case for only some 50% of them when entering university; 
• Real training cannot take place unless students manage to give a meaning to the new knowledge they are presented with. To do so, they rely on the knowledge available in their long-term memory. Whenever such knowledge is not available or wrongly structured, the result leads to superficial, mechanical learning.            

Therefore, it is no surprise that in the first confrontation with complex knowledge, students cannot easily absorb it. This is demonstrated by the fact that, after thorough teaching of the models, a positive evolution can be observed in the students' answers. When the topic is not studied any longer, many students go back to their initial levels of drawn diagram and integration. On this subject, Taber (2004) writes: "It is conjectured that recently acquired knowledge - though accessible in response to direct questioning - may not be available in a form suitable to act as the foundation for new learning, not having yet been fully integrated into conceptual schemes".  

How can we make the students progress in the appropriation of these abstract concepts? It is not a question of the curriculum, since our observations are in agreement with those carried out in various Anglo-Saxon countries. Our hypothesis is that the possibility of progress is based on activities that allow students to rationalize the organisation of conceptual knowledge. Our first proposal is to work on historical models. Classroom discussion based on arguments/counterarguments on the possibilities and limits of each model can facilitate the students' conceptual understanding (Justi and Gilbert, 2000; Laugier and Dumon, 2000; Niaz et al., 2002). A second proposal is to help students to discern that each representation of one model is a 'purpose-built model' linked to the question asked (Harrison and Treagust, 2000). ). Finally, inquiry based teaching sequences engaging students to make inferences about the atomic realm can be a good strategy to help them in linking the domains of macroscopic observation, sub-microscopic particles, and symbolic representation (Toomey et al., 2001). 

References 

Barlet R. and Plouin D. (1997), La dualité microscopique-macroscopique: un obstacle sous-jacent aux difficultés en chimie dans l'enseignement universitaire, ASTER, 25, 143-173. 
Ben-Zvi R., Eylon B. and Silberstein J. (1988), Theories, principles and laws, Education in Chemistry, 25, 89-92 
Charlet-Brehelin D. (1998), Contribution à l'enseignement - apprentissage du concept d'atome au collège, Thèse, Université Montpellier II. 
De Vos, W. and Verdonk A.H. (1987), A new road to reaction. Part 4. The substances and its molecules, Journal of Chemical Education, 64, 692-695. 
Driver R. and Easley J., (1978), Pupils and paradigms: a review of literature related to concept development in adolescent science students, Studies in Science Education, 5, 61-84. 
Gilbert J.K. and Swift D.J., (1985), Towards a Lakatosian analysis of the Piagetian and the alternative conceptions research programs, Science Education, 69, 681-696.  
Gilbert J.K., Osborne R.J. and Fensham P.J., (1982), Children's science and its consequences for teaching, Science Education, 66, 623-633.  
Giordan A. and De Vecchi G. (1987), Les origines du savoir, Delachaux and Niestlé, Neuchâtel - Paris. 
Griffiths K. A. and Preston R. K., (1992), Grade-12 students' misconceptions relating to fundamental characteristics of atoms and molecules, Journal of Research in Science Teaching, 29, 611-628. 
Harrison A.G. and Treagust D.F., (1996), Secondary students' mental models of atoms and molecules: implications for teaching chemistry, Science Education, 80, 509-534. 
Harrison A.G. and Treagust D.F., (2000), Learning about atoms, molecules, and chemical bonds: a case study of multiple-model use in grade 11 chemistry, Science Education, 84, 352-381. 
Johnston K., (1988), Learning and teaching about the particulate theory of matter: a report on a teaching scheme in action, in proceeding of a bi-national UK-Israel seminar: Learning difficulties in chemistry, Jerusalem, 55-79. 
Justi R. and Gilbert J., (2000), History and philosophy of science through models: some challenges in the case of 'the atom', International Journal of Science Education, 22, 993-1009. 
Keig F.P. and Rubba A.P., (1993), Translation of representations of the structure of matter and its relationship to reasoning, gender, spatial reasoning, and specific prior knowledge, Journal of Research in Science Teaching, 30, 883-903. 
Laugier A. and Dumon A., (2000), Histoire des sciences et modélisation de la transformation chimique, Bulletin de l'Union des Physiciens, 826, 1261-1284. 
Niaz M., Aguilera D., Maza A. and Liendo G., (2002), Arguments, contradictions, resistances and conceptual change in students' understanding of atomic structure, Science Education, 86, 505-525. 
Osborne, R. and Freyberg P., (1985), Learning in science: the implications of children's science, Auckland:Heineman. (in Griffiths and Preston, 1992, p. 612 ).  
Pereira M.P. and Pestana M.E.M., (1991), Students' representations of models of water, International Journal of Science Education, 13, 313-319. 
Robinson W.R., (1998), An alternative framework for chemical bonding, Journal of Chemical Education, 75, 1074. 
Taber K.S., (1998), An alternative conceptual framework from chemistry education, International Journal of Science Education, 20, 597-608. 
Taber, K. S., (2003), The atom in the chemistry curriculum: fundamental concept, teaching model or epistemological obstacle?, Foundations of Chemistry, 5, 43-84. 
Taber K.S., (2004), Learning quanta: barriers to stimulating transitions in student understanding of orbital ideas, Science Education, 89, 94-116. 
Toomey R., DePierro E. and Garafalo F., (2001), Helping students to make inferences about the atomic realm by delaying the presentation of atomic structure, Chemistry Education Research and Practice, 2, 129-144. 
Tsai C.C., (1998), An analysis of Taiwanese eighth graders' science achievement, scientific epistemological beliefs and cognitive structure outcomes after learning basic atomic theory, International Journal of Science Education, 20, 413-425. 
Tsaparlis G., (1997), Atomic and molecular structure in chemical education, Journal of Chemical Education, 74, 922-925. 
Tsaparlis G. and Papaphotis, G., (2002), Quantum-chemical concepts: are they suitable for secondary students? Chemistry Education Research and Practice, 3, 129-144. 
Vosniadou S., (1994), Capturing and modelling the process of conceptual change, Learning and Instruction, 4, 45-49. 
WattsM., (1983), A study of schoolchildren's alternative frameworks of the concept of force, European Journal of Science Education, 5, 217-230. 
WattsM. and Taber K., (1996), An explanatory gestalt of essence: students' conceptions of the 'natural' in physical phenomena, International Journal of Science Education, 18, 939-954. 

Official Instructions :  

B.O.E.N. - N° 5 du 9 mars 1995, Programmes du cycle central des collèges 
B.O.E.N. -H.S. N° 4 du 22 juillet 1999, Programmes des 3ème des collèges 
B.O.E.N. -H.S. N° 6 du 12 août 1999, Programme de la classe de seconde 
B.O.E.N. -H.S. N° 7 du 31 août 2000, Programme de la classe de 1ère, série scientifique 
B.O.E.N. -H.S. N° 4 du 30 août 2001, Programme de la classe de terminale, série scientifique

Appendix. Summaries of the students' descriptions of the atom and the water molecule 

The tables below show, the keywords picked from the written descriptions and classified into different categories. A description of one student may contain more than one keyword. So the total number of the key-words is greater than the total number of students' answers (in parentheses), and the total of percentage is greater than 100%.  

Table 1.  Summary of the students' descriptions of the atom 

Table 2: Summary of the students' descriptions of the water molecule.