12. Discussion

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Chapter 12 of Understanding Chemical Bonding: The development of A level students' understanding of the concept of chemical bonding

Discussion

§12.0: Overview of this chapter

In this final chapter I intend to draw together the major themes of this thesis. In particular I will summarise what I have learnt about the developing understanding of chemical bonding among A level students, and consider the implications of my study.

The chapter commences with a brief overview of my findings and the identification of the key feature of students' developing understanding of the chemical bond (§12.1). The major learning impediments that have been uncovered in this research are reviewed (§12.2). It is then argued that one of these impediments, students' use of octet thinking, should be ascribed the status of an alternative conceptual framework that represents common aspects of student thinking (§12.3). Student progression in the topic is then considered in terms of models of the understanding of a typical [sic] A level 'fresher'; the 'ideal' A level examination candidate; and the two colearners Annie and Tajinder at the time they sat their A level examinations (§12.4.1). This provides the basis for considering a question introduced in chapter 1 (§1.7.5): whether students' alternative conceptions should be considered as metaphorical barriers or bridges in the learning process (§12.4.2); and in particular whether octet thinking is a 'stepping stone' on an appropriate conceptual trajectory (§12.4.3). One aspect of octet thinking, anthropomorphic language, is considered to have a potential role as a mediator between the highly abstract and the familiar (§12.4.4). Then, in view of the difficulty learners have passing beyond octet thinking, an alternative conceptual trajectory to understanding chemical bonding is considered (§12.4.5). I then turn to consider what others can learn from this research. I offer advice to teachers and those responsible for the curriculum, based on my consideration of the learning impediments discussed in this thesis (§12.5). I also provide a list of potentially fruitful avenues of further research that follow from work reported (§12.6). Finally, on a personal note, I explain the most important lesson I have drawn from this study.

§12.1: Understanding chemical bonding

In this thesis I have suggested that an understanding of chemical bonding at the level of G.C.E. Advanced level (A level) syllabuses requires the acquisition and use of conceptual tools based upon Coulombic and quantum principles. The 'A level chemist' would not be expected to develop a full appreciation of quantum mechanics, but certain key orbital ideas are important at this level (see appendices 4 and 6). Electrostatic (Coulombic) ideas are part of the assumed background knowledge widely applied in explaining facets of chemistry at this level (see chapter 3 and appendix 5).

It is widely accepted that quantum ideas are non-intuitive (§9.1), and there was much evidence that some orbital ideas were difficult to learn (see chapter 9), for example distinguishing between orbitals and energy levels, and the three-fold distinction between ground state atomic orbitals, rehybridized atomic orbitals and molecular orbitals. However, besides making a transition from thinking in terms of shells to orbitals, and perhaps learning to ignore the normal meaning for 'spin', the orbital ideas these learners met could largely be classed as a novel conceptual domain, and not replacements for specific existing conceptions. Therefore the main barrier to acquiring these ideas was their abstract and complex nature, rather than strongly held contradictory notions. In terms of the typology suggested in chapter 1 (§1.5), students may experience a deficiency learning impediment because they do not have any direct experience of the quantum world.

Whereas A level chemistry students would not be expected to have any knowledge of orbitals at the beginning of their course – and indeed this was generally true for the colearners in the present project – some basic electrostatic ideas would be an expected prerequisite for A level chemistry (appendix 5). All the colearners in the study had some notions of electrostatic interactions when they were first interviewed, although these were not necessarily seen to be relevant to chemical bonding. Indeed the development of an electrostatic conceptual framework for chemical bonding was generally impeded by two types of substantive learning impediments (§1.5.3). The first was the nature of the colearners' existing conceptions of electrostatics (see chapter 10), and the second was the existence of an alternative explanatory principle for explaining chemical bonds (see chapter 11). The former conceptions were largely consistent with those previously reported in the literature (§3.1.3), and which are often considered as 'intuitive theories' or preconceptions. In my typology they would be best labelled as ontological learning impediments (§1.5.4). In contrast, the common use of a full shells explanatory principle (§11.2) was 'alternative' to an acceptable understanding of chemistry at A level, but was based on taught rather than intuitive ideas. Thus, the presence of this principle in a

learner's cognitive structure may be considered to be an epistemological learning impediment (§1.5.5), and may suggest that the teaching of some aspects of chemistry in schools needs to be rethought. Although not all the colearners held exactly the same set of ideas, the evidence from this study is that the presence of an explanatory principle based on the octet rule may be very common among chemistry students commencing A level (§11.2). I have presented a model of the way such an explanatory principle based on the octet rule may become the basis for a range of common features in learners utterances and written statements. These features have been referred to as octet thinking (chapter 11).

It is argued here, based on the analysis presented earlier, that:

  • the major theme for progression in understanding chemical bonding during an A level course may be characterised as the construction of an explanatory scheme based on electrostatic principles.

§12.2: Learning impediments to progression in understanding chemical bonding

The main substantive learning impediments to developing understanding of chemical bonding revealed in this research related to

(i) learners' alternative notions of forces between charges, and
(ii) the common preexisting rationale for bonding developed from the octet rule heuristic.

§12.2.1: Alternative electrostatics

Among the alternative conceptions (i.e. conceptions alternative to curriculum science) of electrostatics uncovered were:

  • alternative ideas about equilibrium and non-equilibrium (§10.3), or newton-1 errors as I have labelled them:
  • if a zero net force is acting on an object, it is stationary (rather than not accelerating), and if an object is moving it must experience a net non-zero force.
  • a stable structure (i.e. configuration of several particles) is held together by a net attractive force (rather than a zero net force).
  • alternative ideas about the reciprocal nature of forces between bodies (§10.4), or newton-3 errors, as I have labelled them:
  • a larger body attracts a smaller body, but the smaller body does not attract the larger body.
  • a larger body attracts a smaller body with a larger force than the smaller body attracts the larger body.
  • if one body attracts a second body, the second body repels the first body.
  • a notion that a charge (by itself) gives rise to a set amount of attraction regardless of other charges that it may be interacting with – a conception that I have tagged as conservation of force (§10.5).

There was evidence that the conservation of force conception was widely used by colearners and so it is considered to have the status of a key explanatory principle (§10.5.4).

Another alternative conception uncovered was colearner Annie's interpretation of charge symbols ('+', '-') as deviation charges (§7.2.2). This was very significant for her developing understanding of chemical bonding, but was not found with any of the other colearners.

Newton-1 errors. The literature reviewed in chapter 3 suggested that learners commonly have alternative notions to Newtonian mechanics. According to the curriculum science perspective chemical reactions occur – that is chemical bonds break, and other chemical bonds form – as a result of systems of forces that are not in equilibrium; whereas the forces acting in stable structures are in equilibrium. Although this point is not often explicitly made in the explanations given in textbooks, it is an implicit assumption. A student who does not tend to consistently apply Newton's first law will find some of the arguments used at chemistry at this level nonsensical. The research carried out for this study reflects the literature (§3.1.3) in finding that learners do not always recognise the conditions for equilibrium or non-equilibrium situations (§10.3).

Newton-3 errors. As reported in chapter 3, the literature suggests that Newton's third law is commonly counter-intuitive to learners (§3.1.3). In the present study A level students were found to assume that the larger body must be exerting the larger force (§10.4.4). This assumption was made by students in contexts of everyday phenomena (such as falling apples), astronomical systems (such as earth-moon) and systems at the molecular level. The finding that learners commonly expected a nucleus to attract an electron more than the electron attracted the nucleus would seem to be a more abstract example of the same principle that leads to their expectation that the earth would pull on an apple more than the apple would pull on the earth.

Conservation of force. The specific finding that chemistry learners in this study commonly held a notion of conservation of force (i.e. that a given nuclear charge can – or will – give rise to a set amount of force, to be shared amongst the electrons present), would seem to be an original discovery (§10.5).

However, it is consistent with some of the results of previous workers, as discussed in chapter 3 (§3.1.3). For example, it is known that for some learners the concept of force is not clearly distinguished from momentum or energy, so perhaps a conflation with charge should not be surprising. Possibly even more significant is the way that the literature suggests that learners commonly talk of the force of a body, rather than the force between two bodies. Watts' designated forces framework (1983a) may be particularly important here, as in the present study learners commonly designated forces to nuclei. Perhaps this is an example of the common Gestalt suggested by Anderson, the experiential gestalt of causation (§2.4.4), where the the nucleus was the agent, acting on the object (an electron) through the instrument of its force.

§12.2.2: Octet thinking

The second category of substantial learning impediment (impeding the colearners from acquiring an effective electrostatic conceptual framework for explaining chemical bonding that largely matched curriculum science), was the existence of a range of ideas which I have interpreted as linked through the use of an explanatory principle based on the octet rule (see chapter 11).

The summary of octet thinking, as set out below, is not from any one student, but is a model which has some features that match utterances from each of the colearners. Indeed, in terms of this model, some of the colearners would best be considered to have been in transition between octet and electrostatic complexes at the start of their A level courses. Nevertheless each of the colearners matched the model in some parts.

The core conceptions are:-

  • atoms want full outer shells;
  • atoms form bonds to obtain full outer shells;
  • atoms may form bonds by sharing or transferring electrons;
  • a covalent bond is the sharing of electrons;
  • shared electrons 'count' (for 'full shell' purposes) towards the shells of both atoms sharing them;
  • an ionic bond is the transfer of electrons between atoms;
  • atoms are stable if, and only if, they have full outer shells.

Subsidiary conceptions that may also be present are:

  • electrons belong to atoms;
  • in a covalent bond each of the bonding electrons is more strongly attracted to its own atomic nucleus;
  • when a covalent bond breaks the electrons return to their own atoms;
  • in an ionic lattice there is a distinction between the interaction between the specific ions which were formed by a particular electron transfer event, and the interactions between other counter-ions;
  • in sodium chloride ion-pairs are (or are like) molecules;
  • the true structure of sodium chloride contains two distinct adjacent cation-anion separations;
  • the species solvated in salt solutions are atoms, as transferred electrons return to their own atoms as the lattice is broken up.

§12.3: An alternative conceptual framework: the octet rule framework

In chapter 2 I presented a discussion of the terms used in the literature to label learners' ideas elicited in research (§2.4). In particular, the term conceptual framework was considered, and it was pointed out that this term was used in different ways by different researchers (§2.4.1).

Some workers have used the term framework to describe the thinking of an individual learner, and there has been criticism of (composite) alternative frameworks presented in the literature, as not adequately reflecting to thinking of specific learners (§2.4.2). In my results section I have attempted to avoid this potential source of ambiguity by discussing the explanatory principles that colearners Annie and Tajinder appeared to be applying, and how these might lead to complexes of ideas.

I propose that – in the sense of one common use of the term – octet thinking in chemistry represents an alternative conceptual framework. However, this suggestion is indeed open to the criticism that my model of octet thinking does not entirely match the thinking of my colearners in all details. I wish to make clear therefore that on the basis of my research I am proposing an alternative conceptual framework in the sense of what I labelled in chapter 2 as alternative framework2 i.e., in Gilbert and Watts' 1983 terms, "thematic interpretations of data, stylised, mild caricatures of the responses".

Features of the octet rule alternative conceptual framework2:

  • considering atoms as the basic ontological entities of chemistry, and electrons as parts of (specific) atoms;
  • the full shells explanatory principle used as the reason for chemical reaction and bond formation;
  • discussing bonding phenomena in anthropomorphic terms, as if atoms were sentient actors;
  • imbuing previous states as being significant, in the sense of electrons having 'memories' of their origins, and tendencies to act accordingly;
  • construing the ionic bond through a molecular model where the bond is defined in terms of electron transfer, and thus the number of bonds is limited to the electrovalency, giving a molecular entity (whether in name or not);
  • bonding is construed in terms of the ionic and covalent models that 'make sense' according to octet thinking, so that bonds are construed as ionic or covalent (e.g. when they would more appropriately described as polar); or as like ionic or covalent (e.g. the metallic bond may be seen as like an ionic bond);
  • interactions that can not be classed as ionic or covalent are considered not to be proper bonds, but just forces.

In developing this alternative framework2, I have started from interpretations of the thinking of individuals – and have presented my own interpretations of the complexes (individual conceptual frameworks) of Annie and Tajinder: that is their alternative frameworks1.

However – although I believe that case studies are of intrinsic interest, and are important in following the progression of student thinking – there is a sense in which they may be seen to be largely of academic interest. No other chemistry teacher will have Annie or Tajinder in his or her class for A level chemistry, and therefore aspects of my findings which are idiosyncratic to these individuals have limited value in informing the teaching of other practitioners.

For example, Annie's deviation charge conception (§7.2.2) is of interest as an example of how a learner can misinterpret curriculum science , yet still manage to build up a scheme for making sense of the subject based on an alternative conception of a fundamental point. It was also of great significance in her own understanding of A level chemistry, and had I interpreted Annie's comments earlier in the study I may have been able to offer a more effective input as a teacher. (Conversely, if Annie had not been a colearner in my study, then it seems likely she would have passed through the entire course with her alternative conception never diagnosed; and would have had no opportunity for the remedial feedback provided before her examination.)

However, no evidence was found in the study, that Annie's deviation charges had direct parallels in the cognitive structures of other chemistry learners. Probably the general notion of deviation charges is not unique to Annie, but it would seem to be a rare alternative conception, and there is little point advising other teachers to be vigilant in spotting it amongst their students.

On the other hand, Tajinder's conservation of force explanatory principle did seem to have close parallels among the thinking of other learners in the study, and my description of this aspect of Tajinder's thinking (§8.2.5) would seem to match a common alternative conception (§10.5). It does seem appropriate to inform other chemistry teachers that some of the students in their classes will be interpreting their teaching about topics such as ionisation energy in terms of notions that are closely described by my model of the conservation of force explanatory principle .

In a similar way, the octet rule framework that I am presenting here is a model that represents aspects of the thinking of the all of the colearners interviewed, and was found to be reflected in other data collected from a wider range of chemistry learners. As there is no reason to suspect that the learners concerned are atypical of the wider population of A level chemistry students, the octet rule framework is of considerable significance to chemistry teachers. Indeed, as octet thinking was shown to be present at the start of an A level course, and to still be in evidence at the end, this is an alternative conceptual framework that has consequences for teachers of school science, A level chemistry, and University chemistry.

§12.4: Progression in understanding chemical bonding

In this research a view of progression in learning chemistry has been taken (§1.7) which has allowed me to accept that learners' cognitive structures may include a range of conceptual tools of varying degrees of coherence which may be used to construct explanations in chemistry which are integrated to varying extents. (This was related to the state of chemistry itself as a discipline – §1.3.1, §1.7.1.)

In the following section I will discuss the progression in understanding chemical bonding that might be expected for an 'ideal' student, and compare this with what was found in the present research. The complexes of ideas about chemical bonding elicited from Annie and Tajinder will be represented diagrammatically in a form similar to Venn diagrams used to show sets. These diagrams (figures 12.4 and 12.5) will emphasis how colearners were found to be able to construct largely distinct complexes of ideas built around alternative explanatory principles, which they used to answer questions about chemical processes. So Tajinder could explain bond formation in terms of minimising energy, forming octets or the action of electrostatic forces. In chapter 2 the phenomenon of 'multiple frameworks' was considered (§2.5.2). Whereas some commentators had dismissed multiple frameworks as evidence of researchers attempting to fit learners' ideas to their preconceived and inadequate categories, I suggested that from a Kellyan perspective the possibility of an individual holding several incommensurate versions of a concept area in cognitive structure was quite plausible. The longitudinal nature of my research has demonstrated that Tajinder's alternative explanatory principles for explaining bonding were stable and theory-like, and could not be explained away as minitheories (c.f. Claxton, §2.6). Moreover, although I have emphasised the inadequacy of octet thinking, Tajinder's octet rule explanatory principle meets Solomon's criteria of 'scientific knowledge' (table 2.1), and can not be assigned to a distinct 'life-world' system of knowledge (c.f. §2.7). My research suggests that multiple frameworks may reflect genuine aspects of learners' cognitive structures, and that – at least in a topic area where curriculum science can not offer a single coherent explanatory model (§1.7.1) – learners such as Tajinder can accept this ambiguity without apparent problem (see appendix 29).

§12.4.1: Representing colearner progression in understanding chemical bonding

In chapter 2, figure 2.3 presented a schematic model of the colearner seen as a system of components (such as perceptual and processing units and aspects of cognitive structure). Figure 12.1 reproduces the main features.

In chapter 1 some basic working assumptions about cognitive structure and the learning process were made (§1.4) – including the notion that it is possible to devise models of a learner's conceptual structure that may be judged by their utility in explaining data.

In figure 12.1 the box labelled 'resources of cognitive structure' is shown as having two types of component – conceptual tools, and complexes. This is a simplistic division, and it may well be that there is a continuum of scales within an individual's conceptual structure. It may also be the case that as the complexes include the conceptual tools it is an artificial distinction. It is beyond the scope of this study to attempt to determine whether this is the case, but the arguments concerning conceptual change discussed in chapter 2 (§2.10) suggest that several frameworks may exist in parallel that include 'the same' concepts. The model that has been adopted assumes that cognitive structure may be treated as if it contains concepts that may be used as components in constructing arguments (and building higher order concepts); and also complexes of conceptions that incorporate (copies of) those concepts.

In terms of such a model it is possible to consider progression in understanding the chemical bond. Figure 12.2 uses this form of schematic to consider the case of an 'ideal' candidate for the A level chemistry examination. This individual has a wide selection of conceptual tools from curriculum science related to bonding to use in answering examination questions relating to chemical bonding. Figure 12.2 also suggests that the 'ideal' candidate may have developed two complexes of conceptions from these conceptual tools so that explanations do not need to be constructed ab initio: one based around the principles of quantum theory (Q), and the other Coulombic forces (C). Moreover these two complexes are integrated to some extent.

In this research it was found that on commencing an A level course students were more likely to reflect the level of cognitive resources shown in figure 12.3. For one thing, at this stage the learner has many fewer conceptual tools relevant to the topic area. (And even those concepts that are available will not match the 'versions' of the concept in figure 12.2, so that – for example – the concept ionic bond may mean something quite different in the two cases.)

At least as significant is the absence of the complexes 'Q' and 'C'. At this stage the student is unlikely to have any notions of orbitals or other quantum concepts. The complex labelled 'E' represents electrostatic ideas. Typically the learner will use the ideas of attractions and repulsions between charges in some of his or her explanations for chemical phenomena. However, this complex is not strictly 'Coulombic' (although it may be developed to become similar to 'C'), as it is likely to incorporate alternative notions to the Coulombic electrostatics of curriculum science (such as conservation of charge).

The A level inductee (fig.12.3) typically uses 'E' much more sparingly than the ideal examination candidate uses 'C' (fig.12.2). Instead most explanations about bonding are constructed from the alternative octet rule framework (O). Figure 2.3 may stand as a general model for the colearners in this study when they began their A level courses, although the details would vary from one individual to another.

The role of the A level chemistry teacher could be seen as guiding the learner by providing the scaffold of experience that facilitates progression from the type of structure represented in figure 12.3 to that in figure 12.2. Tajinder provides an example of a real student, who obtained the top grade in the A level chemistry examination. Yet the research shows that he did not develop his cognitive structure to match figure 12.2. In his case figure 12.4 would be a better representation of this aspect of his cognitive structure by the end of his course,

Tajinder demonstrated that he had acquired a full range of conceptual tools relating to chemical bonding (§8.4.1); however he did not develop the type of unified 'Q/C' framework suggested in figure 12.2. Rather he operated with three largely discrete explanatory principles (§8.4.5). 'E' reflects an electrostatic framework, that may be understood to be a developed version of the corresponding component (E) in figure 12.3. Similarly, the 'O' in figure 12.4 may be seen as being largely unaltered from that shown in figure 12.3. Although octet thinking dominated Tajinder's explanations much less at the end of his course when he had alternative explanatory principles, it remained a major component of his thinking (§8.4.4).

'M' represents a framework of ideas constructed around Tajinder's minimum energy explanatory principle and using the conceptual tools of 'orbitals' and 'energy levels'. This developed some way towards 'Q' in figure 12.2, but did not become integrated with his electrostatic framework.

However, the most significant difference between figures 12.2 and 12.4 is the presence of 'O' in Tajinder's cognitive structure. If similar figures were drawn for the other colearners at the end of their courses they would also include frameworks of this type, and in most cases they would be major components of the student's cognitive structure. It would seem that – at least in the cases studied – acquiring additional conceptual tools is easier than dismantling existing explanatory frameworks. Indeed the analysis of chemical knowledge presented in chapter 1 suggests that – in general – it would not be appropriate to completely discard chemical tools (c.f. §1.7.2). Usually new conceptual tools supplement rather than substitute existing ones.

As Tajinder was a successful student, it might be appropriate to compare his case with that of Annie (who obtained a lower grade in the A level examination: D c.f. A). She also acquired some new conceptual tools related to bonding during her course (§7.1). Like Tajinder, she retained octet thinking through her course (§7.3.1). Although – like Tajinder – she acquired an electrostatic explanatory principle, this was less developed by the end of her course (§7.3.2). One factor here is that at the start of her course Annie did not seem to use conventional electrostatic notions. Although she talked of charges, and used them in her explanations, for Annie these were her deviation charges (D, §7.2.2), which were already a key part of her stable shells explanatory principle (O).

So for Annie, not only did she commence A level – like most of her peers – without the components needed to construct a framework such as 'Q', but she also lacked the basis to form a framework such as 'C'. Whereas most of the colearners at least had a relevant electrostatic explanatory principle on which to build (figure 12.3), Annie did not (figure 12.5).

Annie may be considered to have commenced A level studies with a double handicap: her stable shells explanatory framework acted as a substantial learning impediment (shared with the other colearners) so that she did not see the need for the explanations of curriculum science; and her ignorance of conventional electrostatics meant that there was a null learning impediment (that the other colearners did not share) so that she had little relevant structure to relate to electrostatic explanations she met. (In addition the notion of deviation charges acted as an additional substantial learning impediment to acquiring the conventional notions of charge).

§12.4.2: Barriers or bridges: stepping stones revisited

In chapter 2 it was pointed out that whilst some researchers seem to view learners' alternative ideas in science as necessarily 'barriers' to the learning of curriculum science, the constructivist view focuses on the importance of current cognitive structure as resources for learning, and sees alternative conceptions as potential bridges to desired learning (§2.3.9). Although the present research has been undertaken within a constructivist frame, it has taken a pragmatic stance that it is necessary to model progression in understanding chemical bonding, and to diagnose common learning impediments to that progression whether the alternative ideas elicited are to be considered as obstacles to be demolished or to be seen as the foundations for constructing new knowledge.

Although this study investigated some of the individual colearners' thinking over a period of two academic years, this was not long enough to give a clear idea of whether some of the alternative ideas elicited were best seen as stepping stones to curriculum science.

It would certainly be possible to analyse elicited alternative conceptions to compare them with their curriculum science 'targets'. For example, Annie's deviation charges may be compared to the electrostatic charges of curriculum science:

conception:deviation chargeelectrostatic charge
status:alternativecurriculum science
label:chargecharge
types:positive & negativepositive & negative
action:opposite – attract similar – repelopposite – attract similar – repel
charge on atoms changed byaddition or removal of electronsaddition or removal of electrons
atom made more positive by:given extra electronremoval of electron
defined by:deviation from desired electronic configurationbasic ontological category
charge found on:most atomsions
uncharged:stable ions,
noble gas atoms, atoms with extra octets atoms with missing octets		atoms (not ions)
table 12.1

Annie's deviation charge conception compared with curriculum science
Table 12.1 shows that there were a number of ways in which Annie's use of 'charge' matched the accepted meaning. Yet it seems clear from the case study that Annie's deviation charge notion was not helpful as an intermediate conception on a conceptual trajectory (§2.3.10) to understanding electrostatic charge (see §7.2.2). Indeed, it was the similarities of Annie's conception with the curriculum version which allowed her to make sense (i.e. form a coherent alternative interpretation) of explanations from the curriculum science perspective given by teachers and texts, and thus helped reinforce her alternative meanings (c.f.2.3.6).

Conversely, Tajinder's minimum energy explanatory principle, certainly could be considered as an intermediate conception on a potential conceptual trajectory (§2.3.10) to understanding chemical processes. Like Annie's deviation charges, this explanatory principle has similarities and differences with orthodox science.

Tajinder's notion was not identical to the curriculum science version because it was not integrated with his ideas of force and equilibrium. Yet it was basically a sound principle. It might have acted as an epistemological learning impediment had Tajinder's use of this principle excluded his thinking in other terms. Yet Tajinder's acceptance of plural explanatory schemes (§8.4.5) meant that he could explain a phenomenon in terms of minimising energy, then re-examine the phenomenon from a different perspective (such as the effect of forces).

Although Annie eventually learnt about electrostatic charges, her deviation charges tended to come to mind first, and the two meanings were mutually exclusive (§7 .2.2).

In Tajinder's case, knowledge of his minimum energy explanatory principle could inform a teacher hoping to provide a scaffold (§2.2.2) to facilitate the eventual integration of this principle with his coulombic forces explanatory principle. The teacher aware of this cognitive resource could use it as the basis of constructing knowledge. In Annie's case, the deviation charges conception was not a useful resource for learning about chemistry.

In both cases the diagnosis of the learner's ideas was important: in one case to identify the conceptual foundations in place, in the other case to identify a notion that would need to be challenged (c.f. §2.8.3).

§12.4.3: The octet rule framework as a stepping stone?

The full shells explanatory principle is not valid as a scientific explanation of why bonding occurs. However the present research suggests that it provides a rationale that is readily adopted by learners. This principle undoubtedly acts as a substantive learning impediment which interferes with learning of the models of curriculum science (as is documented in detail in chapter 11).

One possibility is that the full shells explanatory principle acts as a totally unnecessary epistemological learning impediment that could be avoided by appropriate changes to pedagogic practice. This possibility is considered below, where advice is given on how teachers can avoid their students developing octet thinking (§12.5).

However, application of the octet rule framework does demonstrate that students have an understanding of the basic chemical idea of substance, and also hold a fairly detailed version of atomic theory (understanding the relationship between atoms and elements; appreciating sub-atomic structure, and the notion of electronic configuration; distinguishing atoms, molecule and ions). Chapter 3 (particularly §3.1.1 and §3.1.2) reported how many learners have great difficulty with these abstract concepts. So while use of the octet rule framework may be an impediment to conceptual development at one level, it also demonstrates that a range of difficult scientific ideas have been learnt.

It is certainly true that the progression from ignorance of the chemical ontology of elements, compounds and mixture, to an understanding of chemical substances and processes in the terms represented in figure 12.2 represents a vast degree of conceptual development. This present research project has only investigated a small part of this development, yet the case studies presented in chapters 7 and 8, as well as the supporting evidence from other learners presented in chapters 9 through 11, demonstrate the long-term nature of such conceptual growth.

It may be that the gap between complete ignorance of atomic ideas and the type of understanding expected of the 'ideal' A level candidate represents a chasm in cognitive structure that few learners could effectively cross by age 18 (when the A level examination is most commonly taken). Perhaps this 'chasm' acts as a deficiency learning impediment so vast that progression is only possible for most learners when appropriate stepping stones are available (§2.3.10). The orthodox scientific rationale may be so alien to learners' intuitions that alternative intermediate conceptions are required that learners can more easily relate to.

If this is the case, the full shells explanatory principle may be taking on this role. Perhaps some aspects of the octet rule framework have particular appeal to learners (such as the sea of electrons metaphor, §11.6.4). Perhaps there is a gestalt for dichotomising experience (§11.6, c.f. Kelly's bipolar construct systems, §2.2.4).

Whatever 'stepping stones' may be needed to allow learners to develop the highly abstract concepts of chemistry would need to bridge with their existing experience of the world. One candidate for such a bridge would be the anthropomorphic language of the octet rule framework which allows a learner to think about atomic systems in analogy with the more familiar social context.

§12.4.4: Anthropomorphic language

The phenomenon of students using anthropomorphic language to describe the 'behaviour' of particles such as molecules and electrons is reported in the literature (§3.1.4). In the present study this type of language was found to be common amongst the utterances of A level students (§11.3). Indeed I have proposed that anthropomorphic language is an integral part of the octet rule framework. The implication of my research is that such language stands in place of appropriate scientific explanations.

However, I would argue that anthropomorphic language need not necessarily be a undesirable thing in learning science. If one accepts that the human conceptual system largely develops through analogy (§2.4.4), then it could be argued that anthropomorphism may be seen as a means of making unfamiliar systems comprehendible by comparison with the familiar behaviour of people. Indeed, anthropomorphism may be seen to have been used for pedagogic purposes by scientists. It was pointed out in chapter 3 (§3.1.5) that anthropomorphic and animistic language may be used in a quite explicit way in science, and that it has been seen as valuable in increasing the appeal of school science.

Explanation and understanding. In science explanation tends to be most valued if in terms of causality: effects are explained by their causes; good theories explain a large range of phenomena in terms of a small number of fundamental causes. Often a sufficient 'cause' at one level of explanation is itself a phenomenon that needs to be explained at a more fundamental level. For the active scientist explanation is likely to be in terms of mechanism and logical reasoning.

Few scientists – cosmologists excepted – are searching for the ultimate cause, and this is often illustrated with the idea that the biologist uses the ideas of the chemist who in turn uses the ideas of physics. Despite being an extreme simplification there is indubitably some truth is this idea: when Crick, Franklin, Wilkins and Watson 'solved' the D.N.A. structure 'problem', they became widely celebrated: Crick and Watson especially. They were no less scientists for having to take as given a considerable amount of knowledge about keto-enol tautomerism, X-ray diffraction techniques, hydrogen bonding etc., without deriving such ideas from 'first principles'. Perhaps what scientists, but not necessarily our students, do is think at several levels at once (e.g. D.N.A. as a functioning unit carrying a code in heredity, D.N.A. as a macro-molecule composed of sub-units of bases and sugars, D.N.A. as comprised of atoms bonded together, D.N.A. as a structure which can be investigated by physical techniques, D.N.A. as a substance found in chromosomes, etc.), and use description at one level to explain a phenomenon at another.

In school and college science we are concerned with developing understanding. Ultimately we want our students to be able explain phenomena in a logical manner – but understanding is not an all or nothing process. The learner constructs meaning, and construction tends to be a piecemeal process that requires good foundations, and may require the use of temporary scaffolding and supports – to be removed later when the structure is complete (c.f. §2.2.2). Understanding may often start at a 'descriptive' level, and only when the description is familiar can causes be considered (or different levels of explanation be developed – in the terms of the paragraph above). Teachers (and scientists) communicate meaning through the use of analogy and metaphor, to compare the novel phenomenon with ideas familiar to the audience (§3.1.5).

It would follow from such considerations that metaphorical anthropomorphism is to be encouraged. We should approve when students use such language as part of their early attempts to make sense of aspects of science. Nuclei, electrons and bonds are small and abstract compared to the objects of direct experience of young people. Appropriate analogies can act as an introduction to this microworld.

Two classes of anthropomorphism. Metaphorical anthropomorphism, or perhaps 'weak' anthropomorphism, is seen as a virtue. If Jagdish is well aware that atoms do not want, realise, feel or experience happiness, but uses such terms to communicate her ideas about the sodium atom in analogy with a social being, then this is a healthy stage between ignorance of the atomic world and being able to express her ideas in the more physical (and alas perhaps less poetic) language of energy and forces, and solutions to the Schrödinger equation (§11.3.3). But if Jagdish thinks a sodium atom literally experiences its world through feelings and emotions much like hers, then it is but a short step to explaining chemistry through the feelings of atomic species. (So, for example, sodium atoms react with chlorine molecules because they want to.) When Schrödinger asked if electrons think (§3.1.5) it was a rhetorical question, but the findings from the present study suggest that perhaps such questions are not rhetorical for some students. This 'strong' version of anthropomorphism is teleological, in that it allows phenomena to be explained in terms of the (non-existent) desires of atomic species to achieve the end-state.

I am suggesting that strong anthropomorphism is being used when bonding is seen to enable atoms to 'achieve' or 'attain' a full outer shell. Some students interpret the 'full outer shell' as a sufficient explanation for chemical reactions – atoms react to form molecules or ions because they want, or need, to achieve a full outer shell. If the student considers that such teleological anthropomorphism is a sufficient cause of the chemical change, then he or she has no reason to seek other levels of explanation (say in terms of potential energy and electrical fields). For this reason I suggest that such 'strong' anthropomorphic thinking could actually be an impediment to further learning.

However, it could also be argued that perhaps strong (teleological) anthropomorphic language is the first stage in developing understanding, allowing the learner to obtain a descriptive level of understanding of atomic-level phenomena through mental role-play and empathy. Maybe as the abstract atomic world becomes familiar through such 'social' modelling the learner is able to move past the descriptive level (but perhaps retaining anthropomorphic language to be used metaphorically, or simply as habit). So it is possible that even strong (teleological) anthropomorphism may be a stepping stone on an appropriate conceptual trajectory (§2.3.10).

Such uncertainty suggests that more work should be undertaken to investigate children and young people's use of anthropomorphic language (see §12.6).

§12.4.5: An alternative conceptual trajectory?

To summarise my argument: the octet rule framework represents a complex of related ideas that were demonstrated to differing extents by chemistry students in the study, and which were based around the full shells explanatory principle. This principle seems to be a common alternative conception, in that it was used to some extent by all the colearners interviewed. In that

(a) the full shells explanatory principle offers an alternative rationale to the explanations of curriculum science, and

(b) that the octet rule framework is not consistent with the 'target' level of understand of chemical bonding desired at A level,

these aspects of student thinking may be considered to be substantive learning impediments.

However, given that the curriculum science models of bonding are very abstract and based on a range of prerequisite topics that are known to present difficulties, it may be that the octet rule framework acts as a stepping stone to bridge between a student's ignorance of atomic and sub-atomic phenomena and the desired understanding.

Yet even if the octet rule framework is seen in this light, the present research suggests that progression from octet thinking to applying curriculum science models is unlikely to be complete by the end of an A level course. Tajinder was a well motivated and able student who achieved the highest grade in his A level examination. He had supplemented his A level studies with his participation in the research. The long sequence of in-depth interviews where his Z.P.D. (§2.2.2) was probed through the scaffolding of relentless questioning might be expected to closely match the conditions where learning was most likely to occur (§2.2.3). Yet even Tajinder's conceptual development fell short of the target understanding.

One possible conclusion is that, as far as understanding chemical bonding is concerned, the requirements of A level chemistry syllabuses are unrealistic for the vast majority of learners. However, an alternative approach would be to ask if there is another conceptual trajectory which might more effectively allow learners to progress to the target understanding. Figure 12.6 illustrates this idea.

figure 12.6: two conceptual trajectories towards understanding chemical bonding

In this figure it is assumed that a learner needs to progress from an ignorance of relevant curriculum science ideas, to an understanding of chemical bonding which matches the A level chemistry syllabus.

The learner would need to (1) adopt the chemistry ontology of substance (elements, compounds mixtures) which it is known is counter-intuitive to most young children (§3.1.1). The learner would also need to (2) accept the basic premise of the particle model of matter. This would include appreciating the properties of bulk matter are explained by particle theory, but that the particles themselves do not possess macroscopic attributes – another difficult idea for learners (§3.1.2). Even with these prerequisite foundations in place, a great deal of conceptual development (A) is required to reach an understanding of chemical bonding that satisfied A level syllabus requirements. For meaningful learning to take place, this development would need to proceed by manageable steps, allowing the learner to assimilate or accommodate (§2.10.1) each novel concept before the subsequent step is taken.

At present (path B), a learner's first introduction to particle theory could involve the use of terms such as atoms and molecules without any clear distinctions being drawn (see appendix 7, §A7.4.2, §A7.5). However, in chemistry instruction the emphasis is likely to be on atoms as the basic constituents and building blocks of matter. It follows from this that molecules and lattices will be conceptualised as combinations of atoms, and ions will be seen as altered atoms. In explanations of these combinations and alterations of atoms, the learner will meet the octet rule. Although the octet rule may be presented in terms that are perfectly valid from a curriculum science perspective (but may not be, see appendix 33, §A33.11), the evidence from this study suggests that overwhelmingly learners will adopt the full shells explanatory principle to explain chemical reactions and chemical bonding. It was not possible in this research – when the learners already held this principle – to know the extent to which the explanatory principle may be explicitly taught or implied by teachers and texts, or is personally constructed from the octet rule by individual learners, or may be formed as part of the social consensus developed between pupils trying to make sense of their school lessons. However, it was found that the learner will develop a range of ideas related to this explanatory principle, which collectively I have modelled as the octet rule framework.

From this position the octet rule framework may act as a stepping stone to the required understanding, although the conceptual change needed for this step may require more time than is available in an A level course. My own research would suggest that the octet rule framework is too different from the curriculum science perspective to allow a ready transformation, and it is quite likely that instead it may be retained in cognitive structure as one of a number of multiple frameworks for the topic.

Given that even if the octet rule framework can be seen as a stepping stone, it does not seem to be a particularly effective one, it seems sensible to consider an alternative trajectory. One possibility is included on fig.12.6. In this path (C), there is no discussion of atoms until other material has been learnt. The learner is taught about Coulombic electrostatics. At the present time this may be assumed prerequisite knowledge, and implicit in explanations given to students, but this research demonstrates that learners may not share curriculum science electrostatics, and – in any case – often do not see its relevance to chemical explanations).

Once learners are familiar with Coulombic electrostatics they are presented with an ontology of the basic building blocks of chemistry being charged particles: nuclei and electrons. These entities would be understood in terms of their Coulombic interactions.

The next step would be to introduce the orbital concept as restricting the possible locations of electrons in any system so that the configurations that nuclei and electrons take up when they interact are subject to additional constraints superimposed on the electrostatic considerations.

Only then would the atom be formally introduced. The learner would first be introduced to systems of nuclei, and shells of electrons making up 'atomic cores'. Then further systems of cores and electrons would be considered. An atom is a system of a single atomic core plus sufficient electrons for the charge on the electrons to balance that of the core. Ions and (polynuclear) molecules are other possible systems.

Chemical change can then be explained as changes in the configurations of cores plus electrons brought about by unbalanced forces. Bonds may be understood as stable configurations of cores plus electrons that require a significant energy input to disturb them from equilibrium. The learner would then have appropriate knowledge to apply to the content of the A level syllabus.

It may prove that such a trajectory is not feasible within the time available for most learners, as the concepts involved are too abstract. Yet this present research suggests that although learners readily adopt the octet rule framework, they then have difficulty progressing beyond octet thinking even when it cannot explain the phenomena they are asked to consider. An alternative trajectory more closely tied to the target understanding (such as path C in fig.12.6) might be more effective as long as the teaching sequence explicitly supplies the required knowledge in a logical order, and in manageable steps.

§12.5: Advice to teachers, teacher educators, textbook authors and curriculum planners

As a result of the research reported here it is possible to offer advice about the teaching of chemistry. My main recommendations would be:

✪ Introduce electrostatics early.

✪ Avoid over-emphasis of the octet rule, octets, full shells etc.

✪ Present an ontology based on systems of nuclei and electrons.

1. Introduce electrostatics early. The development of octet thinking is tied to a perception of the octet rule as the cause of chemical bond formation. It seems likely that this is at least partly because of a null learning impediment:

(a) learners do not have an awareness of basic electrostatics (a deficiency learning impediment), or

(b) they do not see the relevance of electrostatics to chemistry (a fragmentation learning impediment).

I would recommend that from the time that atoms and molecules are first taught, the electrostatic nature of the interactions between sub-atomic particles is made clear, and emphasised.

I would conjecture that if learners had reason to perceive electrostatic forces as the 'cause' of chemical interactions, then they would not feel a need to adopt the octet rule as an inappropriate explanatory principle. It would be useful for further research to be undertaken to explore the effectiveness of this recommendation.

2. Avoid over-emphasis of the octet rule, octets, full shells etc. In the present research no attempt was made to observe teaching, to find out if learners' acquisition of an octet rule explanatory principle was truly a misconception of what their teachers had said, or perhaps in some cases the result of the teacher him/ herself using octet thinking. However, some introductory text books certainly lend themselves to interpretations which would support octet thinking (see appendix 33, §A33.12). Firstly, they may treat the terms octet and full outer shell as synonyms, and thus give students incorrect information about electronic configurations for heavier elements (which is not a problem at the intended level, i.e. up to G.C.S.E., but requires 'unlearning' at A level).

The 'octet rule' is really concerned with the stability of noble gas electronic configurations. The term octet means a set of eight electrons, and therefore is technically inappropriate for period 1 (hydrogen and helium). For periods 1 and 2 the noble gas electronic configuration is equivalent to having electrons shells that are all either full or empty, thus the term 'full outer shell'. However for period 3 and beyond noble gas structures do not involve full outer shells. Argon is ten electrons short of a full outer shell, and Xenon is not only 24 electrons short of a full outermost shell, it is also 14 electrons short of a full outermost-but-one shell. Yet elementary text book authors ignore these complications, and tell their young readers that atoms are stable if they have full shells (§11.2.6 and appendix 33, §A33.12).

It might be argued that it is acceptable to introduce the idea of full outer shells as a general notion, provided that when period 3 elements are considered the idea is developed. Yet the texts reviewed included specific references to the third shell being full when it held eight electrons, and chlorine and neon atoms were described as having full shells. One book that did acknowledge that the third shell was not full when it held an octet justified treating it as a full shell on the basis that eight electrons in the third shell behaved like a full shell (appendix 33, §A33.12). (This is circular logic: the stability that is found to be associated with an outer-shell s2p6 configuration is inappropriately regarded as being due to a full shell. Then when it is acknowledged that the stable configuration is not necessarily a full shell, it can be considered to behave like a full shell because it exhibits the stability – inappropriately – associated with full shells, but actually inherent in the configuration.)

More significantly some introductory texts I have consulted seem to use the octet rule as an explanatory principle, rather than as a heuristic. Although the idea may be initially presented as an observed correlation between certain electronic structures and chemical stability, subsequent text may imply that stability is therefore explained by noble gas configurations (see appendix 33, §A33.11).

Having an octet does not intuitively suggest stability, but the catchy phrase "full outer shell" may well do – even though it is technically suspect. Once the notion of full shells being stable is established, it may then be used to explain the 'purpose' of bonds. Further, as bonds are formed during chemical reactions the 'explanatory principle' may be extended to explain the reactions themselves.

What is ignored when such statements are made is that in chemical reactions bonds are broken as well as made, so that although the octet rule could 'explain' why atomised materials would 'react', it has little relevance to the chemistry that is met in school, industry or everyday life.

3. Present an ontology based on systems of nuclei and electrons. The present study found that the A level chemistry learners investigated appeared to operate with an ontology of the sub-microscopic world based on the atom as the unit of matter (§11.1).

In practice two objections may be made to this, one in terms of quantum mechanical (orbital) thinking, and one in more general terms. In quantum mechanical terms it may be argued that the atom as conceptualised in elementary textbooks is an idealisation which does not exist in the real world. Our concept of an atom is of a discrete structure which comprises of a nucleus and one or more electrons in atomic orbitals. In the sense of this theoretical construct the atom certainly exists: evidence may be found in books, examination papers, pupils' exercise books and so forth. Our concept of the atom also has the feature that atomic orbitals have infinite extent, and that when the atomic orbitals of two different atoms overlap they interact to form molecular orbitals. It follows logically that it is not possible for a discrete atom to exist, unless it was the only atom in the universe. In our universe the atoms must perturb each other to some extent, and therefore they are no longer – strictly speaking – distinct atoms, but rather part of some immense 'molecular' structure.

However, although the universe could not contain entities that totally match the theoretical concept, it is often sensible to consider that discrete atoms do exist. This is appropriate when one system of a nucleus and electrons is so little perturbed by others that we can ignore the interactions. I will call this the atomic approximation, justified as a 'first approximation' in many systems, providing we accept that we are simplifying, which always involves the loss of some detail.

My second point is that the chemical community has a historically rooted ontological commitment to the atom as the building block of matter (c.f. §1.6). The original notion of atom was something atomos, indivisible. The last 100 years has shown that not only is the atom not a candidate, but that it is the very divisibility of atoms that gives us chemistry at all. Yet the atom is still presented as the basic unit in which to discuss chemistry. I believe that this ontological commitment may be seen in the way in which chemical bonding is usually described 'historically' in terms of bond formation between atoms (and indeed taking up Benfey's point about molecular life– histories, see §3.1.5, this might be related to the high incidence of anthropomorphism discussed above, §12.4.4). I would argue that such an approach is mythical: in our physical environment, during the present cosmological epoch, chemistry seldom occurs between atoms. Indeed, most atoms are relatively unstable, and those that tend to be stable (i.e. the noble gas atoms) do not have much chemistry – they do not tend to form bonds readily.

The implication that common materials are formed from atomised matter. Chemical reactions of importance in the real world consist of processes involving relatively stable materials. This is even true for reactions such as binary syntheses that have little relevance in industry, the environment or biology, but

which are considered useful as illustrations in the school or college laboratory.

molecular frameworkelectrostatic framework
statusalternative framework2curricular science
role of moleculesion-pairs are implied to act as molecules of an ionic substanceionic structures do not contain molecules – there are no discrete ion-pairs in the lattice
focusthe electron transfer event through which ions may be formedthe force between adjacent oppositely charged ions in the lattice
valency conjectureatomic electronic configuration determines the number of ionic bonds formed
(e.g.: a sodium atom can only donate one electron, so it can only form an ionic bond to one chlorine atom)		the number of bonds formed depends on the coordination number, not the valency or ionic charge (e.g.: the coordination is 6:6 in NaCl)
history conjecturebonds are only formed between atoms that donate / accept electrons
(e.g.: in sodium chloride a chloride ion is bonded to the specific sodium ion that donated an electron to that particular anion, and vice versa)		electrostatic forces depend on charge magnitudes and separations, not prior configurations of the system (e.g.: in sodium chloride a chloride ion is bonded to six neighbouring sodium ions)
'just forces' conjectureions interact with the counter ions around them, but for those not ionically bonded these interactions are just forces
(e.g.: in sodium chloride, a chloride ion is bonded to one sodium ion, and attracted to a further five sodium ions, but just by forces – not bonds)		a chemical bond is just the result of electrostatic forces – ionic bonds are nothing more than this (e.g. the forces between a chloride ion and each of the neighbouring sodium ions are equal)
Table 12.2: A comparison of the molecular framework and curriculum science explanations of ionic bonding


If sodium chloride is required it will be found in natural deposits. If we require a laboratory preparation we might chose a neutralisation process. If we wished to demonstrate binary synthesis of sodium chloride our reagents would be metallic sodium and molecular chlorine as these are the elemental forms. Yet again examination of some elementary textbooks revealed that the reaction between sodium and chlorine was described and illustrated as if between individual atoms of sodium and chlorine, which undergo electron transfer to form ion pairs (appendix 32, §A32.5). Such a presentation clearly reflects the 'molecular' framework for understanding ionic bonding (see appendix 2, §A2.0) which includes a number of common aspects of octet thinking described in chapter 11.

Table 12.2, above, presents a comparison between the molecular and conventional curriculum science interpretations of ionic bonding, as discussed in appendix 2. It will be noted that the components of the alternative conceptual framework2 make up a subset of the octet rule framework discussed above.

Similar presentations were found in text book descriptions of the reactions between hydrogen and chlorine, hydrogen and fluorine, magnesium and chlorine, hydrogen and carbon, and hydrogen and oxygen (see appendix 32, §A32.5). In the latter cases isolated atoms were drawn even when several 'molecules-worth' of reactant atoms were required for the reaction! So these strangely irrelevant diagrams cannot be explained as representing real chemical processes, nor as due to some kind of graphical economy. 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.

The first option would seem to be rather obscure, unless there is some presupposition that the 'natural state' of matter (i.e. that which does not need to be explained, see the discussion of the explanatory gestalt of essence in chapter 2, §2.4.4) consists of atoms; and materials in our world do need to be derived from such a starting point. That is, that the authors are following an atomic ontology. This is perhaps not completely fanciful as the notion of elemental atoms predates the science of Dalton, Rutherford and Bohr by many centuries.

If the second possibility were to be correct it would certainly support the notion of the full shells explanatory principle as an (epistemological) learning impediment, and suggests its efficacy is so great as to effect generations of learners.

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.

The present study suggests that chemistry learners may adopt similar approaches, producing diagrams (see chapter 11 and appendix 35) similar to those textbook figures I criticise here.

Yet where the chemical 'history' of substances are known, they have not originated from isolated atoms of the elements. Where the history of substances is not known, curriculum science informs us that it is irrelevant: a substance with a given chemical formulae has properties that do not depend upon how it was prepared (for example copper oxide, CuO, should be the same if prepared by heating copper in oxygen, or by thermally decomposing copper carbonate). The assumption that one starts with isolated atoms of the elements is then incorrect, and should be an irrelevance. Yet this simple error provides the justification for raising the octet rule to the status of an explanatory principle. The octet rule does indeed provide an effective heuristic for predicting stable chemical structures, but can provide no rationale for the vast majority of chemical processes of interest, where both reactants and products 'obey' the rule.

My own recommendation would be to give the highest status to different species in the sub-microscopic ontological zoo: electrons and nuclei. Although nuclei are not immutable, their reactions are the domain of physics. In chemical processes nuclei and electrons retain their integrity.

I would recommend that when it is judged learners are ready to tackle the theoretical models of sub-microscopic particles they are introduced to nuclei and electrons as the basic 'building blocks' of chemical systems. Atoms, ions and molecules may then be given equal status as a higher level of structure. At an advanced level the notion of atomic cores (nuclei plus 'inner' shells of electrons) may be emphasised, with the core taken as an important sub-system which with valency electrons makes up atoms, molecules, and ions. These structures should be explained in terms of the electrostatic attractions and repulsions acting between the nuclei and electrons in the system. Chemical processes should be explained as rearrangements of the system.

I would also recommend that these re-arrangements need to be taught in terms of electrostatic forces, (electrostatic) potential energy, and quantum shells (with a maximum number of electrons allowed). I would argue that if these ideas cannot be presented in some intellectually valid way that learners can understand, then these learners are not ready to learn about chemistry at the sub-microscopic level.

The alternatives to this are are to provide an invalid basis, or no rationale at all, for chemical systems and chemical change. In the latter case, the present research suggests, learners will develop their own reasons for chemical reactions. In either case the learners are likely to develop ideas that do not provide a suitable basis for advanced work, and interfere with the later acquisition of the accepted curriculum science models.

§12.6: Suggestions for further research

The limited scope of the present study means that there are many avenues of work which could build on this research. Some of these are:

1. It would be possible to survey the occurrence of some of the learners' alternative ideas presented in this study: the conservation of force conception, and aspects of the octet rule framework. (This could build on the provisional work reported in appendices 2 and 3.)

2. Where learners study both chemistry and physics it would possible to investigate whether the same alternative ideas about electrostatics are elicited in both subjects – or whether this knowledge is compartmentalised according to perceived subject boundaries (c.f. Paminder's comment (§A3.2) that "I can't think about physics in chemistry, I have to think about chemical things in chemistry").

3. It would be possible to investigate the extent to which the octet rule framework is a construction of students, and to what extent is it actually taught in lower school classes? If it is taught by some teachers, it would be interesting to relate this to subject specialism and scientific background. (That is, for example, do physics graduates teach chemical bonding topics differently to chemistry or biology graduates.)

4. It is possible to prepare teaching schemes based upon the recommendations made in this thesis, and investigate their effectiveness in promoting more effective learning.

5. More research should be undertaken to find the extent to which both alternative frameworks, and anthropomorphic and figurative language, may act as barriers to the required learning, or as bridges between ignorance and desired learning outcomes. In particular, if alternative frameworks can take on both roles, can useful frameworks be readily distinguished from others, and their development encouraged by teachers? Work could be undertaken to investigate children and young people's use of anthropomorphic language, to find out the extent to which it is used in a poetic or teleological sense, and in particular to answer the questions:

• how aware are learners of their anthropomorphism, do they realise the implications of their language, and what do they intend such terms to convey?
• do most (all) learners pass through a 'strong (teleological) anthropomorphic' stage in understanding atomic phenomena?
• do some learners not pass beyond such a stage, being limited to understanding the atomic world in terms of the intentions and deliberate actions of atoms etc.?
• does weak (metaphorical) anthropomorphic language develop from strong (teleological) anthropomorphism, or is it a separate phenomena?

6. Research could be undertaken to find out the appropriate age to start teaching students about chemistry in terms of particle models, without requiring omissions or distortions which may hinder later learning by acting as epistemological learning impediments.

7. Finally it would be possible to investigate chemistry students and prospective science teachers in higher education to find out the extent to which octet thinking is retained as learners become more familiar with curriculum science models and are exposed more to the quantum mechanical approach to the subject.

§12.7: Epistemological learning impediments: a personal coda

On a personal note, I have learnt a great deal from undertaking this research. As a teacher of a particular subject at a particular level (i.e. A level chemistry) I have developed a detailed insight into the way students' ideas develop, and where they falter.

However, the most significant lesson I have learnt from this study applies to all my teaching practice – whatever the subject and level. Unlike some of those researchers and commentators cited in chapter 2 (§2.5), my research experience – sequences of in-depth interviews carried out over many months – has convinced me that that learners' alternative ideas in science can be very stable, and coherent enough to be effective competitors with curriculum science. A learner such as Tajinder presents much more than clusters of minitheories (§2.6). Further – again unlike some of the workers cited – I am personally convinced of the reality of learners holding multiple frameworks, so that the student's learning of the teacher's models supplements rather than replaces any preexisting notions. In the context of my research this can not be explained in terms of different domains of knowledge (§2.7): although the octet rule framework may be influenced by 'life-world' knowledge (such as comparisons with social actions), it is clearly an alternative abstract conceptual framework within the scientific domain.

In time the learning of a curriculum science model that explains more, perhaps with less arbitrary assumptions, may lead to a student using an alternative conception less: but when students have found their alternative schemes effective they will certainly not give them up within the time span of a few years. As future learning depends on current cognitive structure, alternative frameworks will surely have a long-term influence on a learner's thinking.

Where a student's alternative conceptions act as ontological learning impediments the teacher has to accept and work with – or around – them. However, where alternative conceptions are epistemological learning impediments they could have been avoided. Those G.C.S.E. text book authors who suggest that chemical reactions take place so that atoms may obtain full outer shells may feel they are simplifying a difficult and abstract topic. They may also be putting into place a learning impediment that will interfere with the students' later progression in the subject.

As a teacher I have learnt from this research that I should think very carefully before I simplify. It is never possible to tell the whole story, and in chemistry in particular our models are of limited precision and application. But I believe there is one question a teacher must try to answer about any partial explanation given:

is this simplification likely to provide a fertile cognitive resource for a fuller understanding, or will it be an impediment to further progression?

If I can bear that question in mind in my professional practice, then the time and effort put into this research should pay dividends for my future students.

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