Keith S. Taber

& Royal Society of Chemistry

presented to the science SIG symposium

at the

British Educational Research Association Annual Conference, Cardiff Univesity, September 7-10 2000

Keith S. Taber © 2000

e-mail: kst24@cam.ac.uk

1. Introduction: Constructivism and alternative conceptions.

2. An alternative conceptual framework from chemistry education.

3. The origins of the 'octet' framework.

4. Notions of chemical stability.

5. The chemical stability probe.

6. Trainee teachers' responses.

7. The significance of the findings.

Constructivism is well accepted now as both a mainstream research programme in science education, and as a referent for teaching.

Very briefly, the basic idea is that each individual learner uses information from their environment - including, but by no means only including, teaching - as the raw material to construct their own representations of the world. Although in a classroom context the teacher's input is significant, the main criterion of what is learnt is what can be understood, or made to make sense; and this means that the main determinant of new learning is the existing structure of knowledge available to a learner (i.e., their cognitive structure).

The role of the teacher is to help support, or scaffold, the learners re-construction of knowledge to give representations that will lead to desired future behaviours: for example we want our pupils' understandings to match the teacher's understandings well enough for them to produce the examination answers that are judged 'correct'!

In fact when pupils and students are asked examination-type questions they often produce answers that are not considered correct. Sometimes this is due to a lack of ability to clearly express their thoughts, or even to comprehend what the question was meant to elicit. In these cases, perhaps, the learners does have a 'desired' sort of understanding of the concepts concerned - but the failure to 'perform' is due to other 'deficits'.

On other occasions the pupil concerned does not know the answer, or is confused about the topic, for whatever reasons. In a test, or when put-on-the-spot, some pupils may guess - or produce an answer apparently at random - whilst others will simply report that they do not know.

These are all situations that teachers often meet. But in recent decades a lot of attention has turned to another scenario, when the pupil thinks they do understand the concept and know the answer, but their thinking does not match the acceptable scientific version of knowledge.

In these cases we often refer to the pupil holding alternative conceptions or alternative frameworks for the concept area(1), as the pupils think they do understand - and they are often very successful in making sense (although not always the intended sense) of new information from their alternative perspective. This presents the teacher with a different pedagogical challenge to a pupil who agrees they do not know about a topic, or realises they are confused. Pupils can often develop highly complex alternative frameworks that are internally self-consistent and able to be widely applied: they just do not match the accepted scientific views of the world! These alternative conceptions are often also stable and resilient in the face of new information: pupils can be quite ingenious in reconstructing new knowledge into their existing frameworks!

Before a teacher is likely to be successful in teaching pupils with alternative conceptions the accepted school science models it is important that:

• the teacher is aware of the significance of alternative conceptions;

• the teacher is able to elicit the pupil's own way of understanding the topic;

• the pupil is made explicitly aware of their own conceptual frameworks.

Once this is achieved the teacher can present exercises and activities designed to persuade the pupil of the greater verisimilitude of the accepted scientific models over the pupils' alternatives. This may not be an easy task, but at least the teacher is made aware of the nature of the problem and is able to tackle it accordingly.

There is a vast literature on children's ideas in science(2), and although chemistry is somewhat under-represented, many alternative conceptions have been found(3). Some of these are quite 'contained' or discrete. Consider the following example:

research shows that many pupils\students believe that a salt produced by neutralisation must be neutral(4).

Leaving aside our sympathy for pupils who have somehow got the strange idea -

that: because materials that are neither acidic or basic are called neutral, then the process of neutralisation, by which an acid neutralises a base, will produce something neutral(5)

- this is quite a contained idea that effects just one part of their chemistry.

However, other ideas are more extensive and expansive, and deserve to be called alternative frameworks. One that I feel is particularly significant, that seems to be commonly adopted by pupils and students, is called the 'octet framework'.

Before I outline the framework, I should point out that as all learners are individuals, with somewhat idiosyncratic ideas, any talk of a 'common alternative framework' could be considered something of an oxymoron. Research that looks at pupils' alternative frameworks has to be in-depth detailed investigation, which produces something (the researchers' representation of the learners' representations!) that is unique for each learner.

However, there are sometimes striking similarities between the ideas of different learners. (This is to be encouraged when those ideas closely reflect what the teacher is trying to teach{!}, but are often also found with alternative conceptions.) In presenting a common alternative framework one has two basic choices: to discuss a particular learner's ideas, but point out that these were reflected in other cases; or to produce a type of amalgam or aggregate representation.

The 'octet framework' presented here (see appendix A) is of the latter form, and was developed through a grounded theory approach, starting with detailed individual case studies, and gradually building a more general model. This, then, is a model of a conceptual structure that represents no one individual learner in all its details, but is matched to varying degrees by many chemistry students. Most of the research leading to this model was undertaken with A level students, but (those parts that are relevant) are also reflected in data from KS4 pupils as well.

The basis of octet thinking is the 'full shells explanatory principle':

This principle is the basis of a complex of related notions(10), such as,

• One way atoms can obtain full outer shells is to donate (give away) electrons (but they can only do this if another atom accepts them).

• One way atoms can obtain full outer shells is to accept (take) electrons form another atom.

• An ionic bond is (/is formed by) the transfer of electrons.

• If atoms overlap their outer shells then electrons in the overlap count towards the outer shells of both.

• An atom can therefore obtain an 'octet' by sharing electrons with another atom.

• A covalent bond is a pair of electrons shared between atoms.

A number of logically related features were identified in the research as being associated with 'octet thinking'(11):

• an atomic ontology

• use of anthropomorphic language

• significance given to electronic history

• electrovalency as the determinant of the number of ionic bonds formed.

• a dichotomous classification of bonding.

• demarcation between bonds, and 'just forces'.

 

Although the research which uncovered this way of thinking had focused on the concept of chemical bonding, the octet framework is more widely significant. For example, it effects students' thinking about patterns of ionisation energy, so that some students think that electrons can only be stripped from an atom until it has a 'full shell'. Perhaps most significantly, it is the basis for explanations about why chemical reactions occur.

It has been found, for example, that when chemistry students are asked why hydrogen reacts with fluorine, they will commonly suggest it is because through the reaction the fluorine and hydrogen atoms are able to get full shells:

"Fluorine is a halogen and has 7 outer electrons. To be stable it would like 8 electrons in its outer shell. By covalently bonding with the hydrogen atom which would like 2 electrons in its outer shell they form hydrogen fluoride which is stable"

This response was provided by an A level student from a school sixth form, despite having been given the equation:

and a diagram (figure 1) showing the molecules of reactants.

And this response was not unusual: most of the students in that sixth form chemistry group gave similar responses!

Given that:

This alternative conceptual framework is clearly very significant to the teaching of the subject.

The octet framework then is potentially a major impediment to the learning of accepted ideas about the subject. Research suggests that this type of 'octet thinking' is not only widespread, but tends to be tenaciously held onto despite formal teaching,

It is therefore of some interest to know where the idea originates. Some common alternative conceptual frameworks are believed to arise from early life experience. For example, it is found that children (and adults) commonly have a naive theory of motion along the lines of the pre-Newtonian impetus theories: i.e., when an object is given a push, the push will get it so far before it runs out. This 'intuitive physics' is considered to largely derive from early experiences of pushing objects, which then only get so far before they stop. Clearly, in the absence of any knowledge of frictional forces, this is not an unreasonable deduction!

The alternative neutralisation conception referred to earlier, that all products of neutralisation will be neutral, will not have derived from early childhood experience of playing with acids and alkalis! Its origin is, presumably, due to over-interpretation of linguistic clues when the topic is first studied in school. If something that is neither acidic nor basic is called 'neutral', and if in a 'neutralisation' the acid 'neutralises' the base, and vice versa, then it is not unreasonable to expect a neutral product! Indeed this is a very sensible deduction in the absence of a clear understanding of the difference between the strength of an acid/alkali and its concentration.

As neutralisation is commonly taught in school chemistry, but acid strength not discussed until sixth form level, this alternative conception is surely very likely to be adopted unless the original presentation of material on neutralisation is deliberately planned to avoid this.

There is nothing the science teacher can do to stop children coming to class with an impetus framework for forces and movement, but the adoption of the alternative neutralisation conception is largely a result of teaching (of the way in which we order the presentation of topics). I have distinguished these two types of case by referring to them as ontological and pedagogic (or epistemological) learning impediments(12).

As with neutralisation, bonding is a topic which pupils do not (usually) think about until they are taught science formally, so the octet framework must be considered to be a pedagogic learning impediment. This is helpful, as it means it may be avoided if we plan our teaching differently!

One interesting aspect of the octet framework is that many explanations of chemical bonding given in school text books easily lend themselves to fitting the alternative framework. Indeed, some seem to be explicitly using it! For example, many diagrams supposedly showing bond formation start from isolated atoms, although there are very few chemical reactions where this would be the case. I have suggested some possible reasons for this(13):

"Three possibilities are:

1: The diagrams are not meant to represent chemical processes of our world, but the primeval formation of molecular matter in some previous cosmological epoch.

2: Diagrams of this form are used because this is the way the authors were taught, and it has not occurred to them that they are misleading.

3: The authors are aware of the inaccuracy of the diagrams, but chose to use them because they are consistent with the (invalid) explanation of chemical processes in terms of achieving full shells."

I described the first possibility as "rather obscure", and suggested that "the third possibility would seem to suggest a somewhat cynical attitude on the part of authors who are aware they are presenting misleading information, but chose to develop the deceit rather than find a more intellectually valid approach."

However the second option was perhaps more worrying - that those who were meant to be in the know also held the alternative conceptions. And if this was possible with textbook authors, who are often teachers, it could also be the case with other classroom practitioners.

Yet, one would imagine, by the time someone has made the transition from pupil through science graduate to teacher, they will have adopted the accepted scientific models? There is some evidence to suggest that this may not be the case.

For example, table 1 gives a comparison of the way the ionic bond is understood in orthodox science, compared with the 'molecular' interpretation which is common used when students apply the octet framework(14):

Oversby asked a small group of trainee chemistry teachers about this 'molecular framework' for ionic bonding. A majority (6/11) of the group believed that this alternative framework was "an adequate representation of ionic bonding"(15).

It is therefore sensible to explore the chemical understandings of teachers and teachers-in-training to find out if they hold, and would therefore explicitly teach, alternative conceptions of chemistry. In this paper an example of such enquiry is given: a consideration of student teachers' responses to a probe about chemical stability.

Something is stable if it does not tend to change. In chemistry, the opposite to stable is unstable! Stable and unstable are 'thermodynamic' terms, in the sense that they relate to the relative 'energy' levels of the system. (Total energy is always conserved - so here we are referring to chemical potential energy: basically the electrostatic energy of the configurations of atomic cores and valence electrons.) If a system can evolve to a lower energy state, it is unstable, and will change.

Figure 2 shows a hypothetical molecular rearrangement where the products would be at a higher energy than the reactants: so the reactants are stable with respect to this change - it will not happen. (To be pedantic, at equilibrium, the mole ratio products:reactants is a very small number.)

Figure 3 shows an unstable chemical system, where the energy state of the products is lower than that of the reactants, and energy can be 'released' by the reactants evolving to products:

However, although unstable systems do change, the rate of reaction can vary enormously. So I understand that diamonds will in time change to another allotrope of carbon, graphite, which is much more useful as a lubricant, or in making pencils. Diamonds are not forever. However, they will outlast their owners by some considerable degree. Although diamonds are technically unstable, they are inert as the energy barrier to reaction is very high (figure 4). Diamonds will also burn in oxygen, but again the energy barrier is so high that there is little danger of jewellery undergoing spontaneous combustion at normal temperatures!

If the energy barrier in an unstable system is very low, then the system is labile, and will evolve to a lower energy state very quickly (figure 5):

These figures all represent abstract generalised contexts. In reality it makes little sense to ask, for example, 'is this stick of sulphur stable' without giving the physical and chemical conditions. At a high enough temperature sulphur will undergo a change of allotrope between rhombic and monoclinic forms; when a little hotter it will melt; on further heating it may burn, reacting with atmospheric oxygen: but not if it is being heated in an inert atmosphere with no oxygen present!

In terms of atoms, some are considered more stable than others. The inert gases have monatomic molecules, which means they are found as discrete atoms. Most elements (even those found native, like sulphur) are not found as isolated atoms, but in molecules (e.g. S₈).

An atom of neon would be considered stable, whereas an atom of sulphur would be expected to readily interact with other atoms. However, this can only happen if there are other atoms around! If there were discrete atoms of oxygen, or hydrogen, or iron etc. adjacent to an isolated atom of sulphur, we would expect it to interact with them.

However, in the absence of such potential chemical partners, the atom would be stable. It would not spontaneously decompose! So discussion of stability without a context seems rather an empty notion.

Yet research evidence suggests that among many pupils and students, the octet alternative conceptual framework dominates thinking to such an extent that chemical stability is often judged, without consideration of a wider context, in terms of whether the atom has the 'desired' octet/full outer shell configuration. For example, over one hundred A level students completed an exercise called 'the truth about ionisation energy diagnostic instrument' which asked them to judge the truth of a set of statements about a sodium atom(16).

Although nearly all of these students thought that "energy is required to remove an electron from the atom", a majority (56%) also agreed that "if the outermost electron is removed from the atom it will not return because there will be a stable electronic configuration", and three quarters of respondents (75%) agreed that "the atom would be more stable if it 'lost' an electron".

An even more significant finding was that, incredibly, over four-fifths (83%) of respondents agreed that "the atom would become stable if it either lost one electron or gained seven electrons". It would seem that these students were overwhelmingly suggesting that not only would Na⁺ (electronic configuration, 2.8) be stable, but so would the species Na^7- (electronic configuration, 2.8.8), which is highly unstable from an orthodox scientific perspective.

This finding seemed dubious, and so a separate question was prepared based on three diagrams of the two relevant sodium ions and the sodium atom (figure 6).

The diagrams were followed by three multiple choice questions, each asking respondents to compare the stability of two of the species. (For example to chose between A being more stable, equally stable or less stable than B, with a 'do not know' option available.) Then there was a free-response question asking them to explain their reasoning.

The draft instrument was presented to two first year A level chemistry groups(17). One group of sixteen students had studied A level topics such as chemical bonding, and ionisation energies. Ten of these students - a majority - responded that the neutral atom was less stable than the Na^7- ion. The other group of students were given the same question as part of their induction to A level chemistry. An even larger proportion (eleven of thirteen) thought that the neutral atom was less stable than the Na^7- ion.

Students in both of these groups argued that the anion would be stable because of its electronic configuration, i.e. due to the octet of electrons in the outer shell. For example one of the students who had studied ionisation energy wrote that "[the anion] also has a full outer shell making it stable, whereas [the atom] is unstable with its one outer electron".

It was therefore concluded that the 83% support for the statement that "the atom would become stable if it either lost one electron or gained seven electrons" (in responses to 'the truth about ionisation energy diagnostic instrument') reflected a genuine belief that the octet of electrons in a species such as the Na^7- anion can provide stability despite (or perhaps rather without consideration of) its large electrostatic charge.

The 'chemical stability' question seemed to be an effective probe for eliciting this way of thinking. The probe has been developed since its initial use. In particular, the free-response part of the exercise would have been difficult to analyse with large samples because some respondents attempted to give a single rationale for their overall responses, whilst others gave three separate answers: one for each of the multiple-choice questions. The format of the page was changed to give space for a reason next to each of the three multiple choice parts.

Other versions of the question, using different atoms, have since been written, but were not used with the trainee teachers.

However, two versions of the 'sodium' exercise were prepared, with the multiple choice options presented with slightly different word order(18). The two variants were printed on different coloured paper, and when administered were given out to alternate students in the group to randomise the distribution. (When analysing the responses the scripts were numbered b1-19 and p1-19 according to the colour of the paper: the numbers just identify individual responses, and represent only the order in which each response was read.)

The two versions of the exercise used in the present study are presented as appendices B and C.

The respondents in the present study were graduates training to be science teachers, enrolled on the Post-Graduate Certificate in Education course. The group were the part of the PGCE Science cohort who had identified themselves as being biology specialists. They were preparing to work in schools teaching biology to university entry level, but also teaching chemistry topics to at least KS3, and usually to KS4 (i.e. school leaving level, at age 16). The students were near the end of the first term of their course, and had undertaken some 'methods' work in chemistry earlier in the term. Most would have had little experience of teaching any chemistry at this stage of their training.

There were 38 students present on the afternoon that the exercise was undertaken. The context was a session on 'probing understanding' designed to introduce students to techniques (other than formal tests) that could be used to explore pupils' thinking.

Much of the two hour session was concerned with being introduced to the rationale and process of techniques, and to examples of the kind of data that could be obtained. However, some activities were introduced, including pairs of students trying out a simple construct repertory test exercise with diagrams of different animals.

The exercise was administered to the students as part of the session, in part to provide variety of activity, and in part to get the students to experience how their pupils might feel when subject to classroom exercises exploring their understanding. However, this particular exercise was selected because I was genuinely interested in seeing their answers.

The responses, in terms of selections in the multiple choice parts of the exercise, are given in tables 2-4.

Although tables 2-4 show that the response percentages showed some variation with word order (i.e. the two versions of the instrument), the overall pattern was similar, and the responses have been pooled to give a sample size of 38.

Table 2 shows that over two thirds of this group of trainee science teachers judged the sodium cation as more stable than the neutral atom, as is shown in figure 6, below.

As would be expected, there was variety in the way the responses were justified. One trainee pointed out that "Na is found more as A than B" (b1), which is certainly a valid point. The figure presented to students showed isolated chemical species, but as the isolation was not specified in the question it is not unreasonable for the student to contextualise their response.

A few other respondent made similar points: that Na⁺ was "the naturally occurring ion" (b7), that "Metallic Na is more reactive" (p5), and that the "Na⁺ ion exists in solution" (p9). A few of the justifications made little sense {"It has an even number of atoms [sic] in its outer shell" (b17) and "A is more reactive because it has an extra ion" (b6)}.

However most (22 students) made specific reference the A's full outer shell, or to B's lack of such a pattern. A few of these responses justified this explanation further. So one trainee pointed out that "B has a free electron which more readily bonds to another atom than the outer electrons in A" (p3), and another suggested the cation was more stable "As 'A' has full outer shell (Hund's Rule)." (b12). (Of course, Hund's rules do not apply to comparisons between systems with different numbers of electrons, so this is not a valid justification!)

Most, however, seemed to feel that reference to the full shells was sufficient explanation, giving answers such as "Full outer electron shell in A not in B" (b18), or "A has a full outer shell, whereas B needs to lose an electron to become stable" (p19).

Had these trainees been thinking in terms of ionisation energies, and been suggesting that the cation was more stable in terms of the energy required to remove an electron, then the popularity of this choice would have been readily understood: however, most seemed to be thinking of the species in isolation, and considered the atom would be more stable simply by emitting an electron: "B [the sodium atom] needs to loose the electron from its outer shell in order to be stable" (b3), whereas "...A [the sodium cation] has "lost" one and become more stable" (b14).

A few of the trainee teachers demonstrated one of the characteristics that had previously been reported when pupils apply the octet conceptual framework: anthropomorphic thinking. So they reported that the "outer electron shell prefers a certain no. of electrons..." (p15), and as "B [the sodium atom] has one electron on its outer shell, and therefore will want to try + lose it" (b5). As "...B [the sodium atom] wants to lose one" (b13), the sodium atom would "...try to create Na ions by bonding" (b7).

Almost two fifths of this group thought that the sodium anion was more stable than the neutral atom, as is shown in figure 7 below.

Now as Na^7- would be a highly unstable species, which presumably would require the application of a very intense external electric field to stop it spontaneously emitting electrons; and as sodium is well know as a metal, i.e. an element that forms cations; and as trainees are unlikely to have ever encountered Na^7- in any form in their studies; it is of some interest that a significant minority thought this would be more stable than the neutral atom.

One trainee suggested that "B is less stable because it is an atom and will be more likely to bond" (b6). This is an interesting response, as if the Na^7- species did exist, it would presumably form ionic bonds very readily with any cations in its vicinity. {However, as was discussed above (see table 1), the formation of ionic bonds is often identified with the process of electron transfer, i.e. ion formation, rather than with existing ions being bound together.}

The other explanations for why trainees thought the anion might be more stable than the neutral atom referred to either the single electron of the atom:

"It has 1 electron in the outer shell available to bond with other atoms" (b17)

"because B [the atom] does not have a full outer shell of electrons" (p7)

or to the 'full shell' of the anion:

"because C [the anion] has a full outer shell of electrons" (p16)

or both:

"again C [the anion] has a full outer shell of electrons and so is less likely to give e^- [electrons] up than B [the atom], which will want to give away an e^- to get a full outer shell" (p14).

Most the trainees making this selection, referred to the "full outer shell of electrons" (p10). In fact, despite this conviction that "the 3rd shell is full in C [the anion], but in B [the atom] it is not a complete shell" (B13), neither species actually had a full outer shell of electrons. Even the one respondent who seemed to realise this referred to there being "...nearly a full electron shell in C..." (b7).

In fact, although the sodium anion C (with its electronic configuration of 2.8.8), had an octet of electrons in its outer shell - it was ten electrons short of having a full outer shell (2.8.18). (Not only was the octet configuration not stable in this case, but the species that would have had the full outer shell, the Na^17- anion, would not have been the ground electronic state for that highly charged species!)

Almost a third of those trainees who expressed a view thought that the anion would be more stable than , or as stable as the cation (see figure 8).

The responses of those trainees who thought that the anion was more stable than the cation seemed to be somewhat confused. One trainee suggested that this was "because the 3rd electron shell is further away from the centre" (b7) without further explaining why this would make the species more stable.

Some of the responses from trainees suggesting that the two ions would be equally stable also seemed vague - "Both ions of sodium" (p17) - or confused:

"...The nucleii are the same, and when they are bonded in a compound they should be stable. Probably. Oh dear!" (p18).

However, there were a number of references to the (perceived) equally full shells of the two species: that is, that "both have full outer shells" (p6).

The study reported here represents the opportunistic collection of data from one group of trainee science teachers in one university, using a simple pen-and-paper instrument. It is clearly not possible to know how representative this group is of trainee teachers, let alone science teachers, nationally. The students had not completed their training, and may well have considerably developed their conceptual understanding during the rest of the year, particularly when they had increasing experience of teaching chemical topics.

This group of trainees were biology specialists, and perhaps a different pattern of responses might have been obtained from chemistry specialists. However, much teaching of physical science topics in schools is undertaken by science teachers who consider themselves stronger on the life-science side of the curriculum, so this does not negate the relevance of the study. Indeed the issue of 'teaching outside one's strengths' may be considered a major one is science education today(20)!

This limited study then suggests that an alternative conceptual framework which has been claimed to be widespread among pupils - 'octet thinking' - may also be influencing the thinking of trainee teachers (and therefore, perhaps also practising teachers). This supports the observations of Oversby, and perhaps provides a clue to the predominance of chemically irrelevant diagrams supposedly representing bond formation in many text books.

Previous research(21) suggests that 'octet thinking' may often co-exist alongside more conventional scientific thinking, and so the level of references to 'full shells' in the present exercise may not closely match the extent to which such explanations might be used in other contexts. However, it is clear that many of these student teachers imbued octet/full shell structures with a degree of stability that was not justified scientifically.

More work is clearly needed to explore the extent and consequences of such thinking among teachers