Chapter 6 of Understanding Chemical Bonding: The development of A level students' understanding of the concept of chemical bonding
An outline of the findings of the study
§6.0: The purpose and structure of this chapter
The findings of this research project are presented in the following five chapters. The present chapter is intended to act as an advance organiser to give the reader an overview of the material to follow.
The idea of progression – that has earlier been met in chapter 1 – is considered in relationship to the examination syllabus that the learners were following (§6.1). Two particular features are highlighted, that learners need to develop an understanding of bonding in electrostatic terms (§6.1.1), and that they must acquire new concepts relating to quantization: concepts such as orbital, energy level and electron spin (§6.1.2). The two case studies presented in chapters 7 and 8 are then previewed in the light of this perspective (§6.1.3).
In chapter 1 the notion of learning impediments was introduced. In this chapter it is suggested that the lack of appropriate experience or background knowledge makes quantization notions difficult to learn – an example of a null learning impediment (§6.2.1). It is also suggested that progression in understanding chemical bonding is affected by substantive learning impediments, and in particular alternative conceptions of electrostatics (§6.2.2), and a common alternative rationale used by students to explain bonding (§6.2.3).
§6.1: The notion of 'progression' as it relates to the findings of this research
In chapter 1, the notion of progression was discussed in terms of learners developing their conceptual toolbox (§1.7.2) to acquire the manifold models of chemistry (§1.7.1), and to overcome learning impediments (§1.7.3). In chapter 2 the constructivist approach to learning was considered (§2.1), as well as the notion that learners may be considered to undertake a cognitive apprenticeship (§2.8.5).
As the learners discussed in this thesis were enrolled on an examination course in chemistry the notion of their progression in understanding chemistry is related to the stipulations of the appropriate examination syllabus. The discussion will refer to the requirements of the Advanced Level Chemistry syllabus of the Associated Examining Board (syllabus number 0654). As the largest cohort of students interviewed took the examination in 1994, it is this edition of the syllabus – published in 1992 – which is quoted (A.E.B., 1992), and from which the key section has been reproduced in appendix 6.
Progression will therefore be understood in terms of the demands of this syllabus in relation to the level of understanding demonstrated by the learners before they were taught the relevant sections of the syllabus.
In this research it was found that at the beginning of an A level course learners tended to have simple models of the ionic and covalent classes of chemical bond (e.g. §11.6.1). Learners might also be aware that 'metallic' is also a category of chemical bond, but usually without knowing much more than it is bonding found in metals. The models of bonding that learners discussed at the beginning of their courses were based around the octet rule as an explanatory principle (§11.0, §11.2). These models gave little scope for the learners to develop the new categories of bonding required by their syllabus, and to develop the deeper understanding of bonding expected at this level.
§6.1.1: The adoption of Coulombic electrostatics
The examination syllabus followed required students to know about hydrogen bonding, and the Van der Waals' forces "responsible for bonding in molecular crystals" (A.E.B., 1992, p.4). These types of bond can not be explained from the explanatory principles elicited from the colearners when they started the course. An understanding of these categories of bond depended upon the adoption of electrostatic forces as an explanatory principle.
The syllabus required students to understand ionic bond formation in terms of "ionisation energy, electron affinity and lattice energy", and required students to be able to demonstrate "a qualitative appreciation of the effects of ionic charge and ionic radius on the magnitude of lattice energy for simple crystals" (A.E.B., 1992, p. 3), both of which required students to progress beyond the model of the ionic bond they had brought from earlier studies. Again the adoption of electrostatic forces as an explanatory principle was needed for learners to develop their understanding according to syllabus principles.
The syllabus also included a paragraph concerning polar bonding, and relatedconcepts,
"Bond polarity, electronegativity and inductive effect. Homolytic and heterolytic fission. Nucleophilic and electrophilic attack respectively, on positive and negative centres in molecules."
A.E.B., 1992, p.4
This was another area where learners could make little sense of the material from within their existing models of chemical bonds, and had to adopt explanations in terms of electrostatic forces.
The syllabus section on 'Structure and Bonding' (section 1, A.E.B., 1992, pp.3-4, see appendix 6) also included the requirements that students should study the shapes of simple molecules, and patterns of ionisation energies, both topics that required the application of electrostatic principles.
My analysis of the syllabus content in the light of the data collected (and considered in the subsequent chapters) leads to the conclusion that one aspect of progression in understanding chemical bonding depends upon the adoption of Coulombic electrostatics as an explanatory principle for bonding.
§6.1.2: The acquisition of novel concepts related to quantization
In principle a full understanding of chemical bonding at A level would be expected to include an appreciation of the concepts of atomic and molecular orbitals. The examination syllabus section on bonding and structure (A.E.B., 1992, pp.3-4) included references to "elementary treatment of quantum numbers and atomic orbitals", energy levels ("the line spectrum of atomic hydrogen as evidence for electron energy levels"), and sub-shells ("plot of standard molar first ionisation energies against atomic number to introduce sub-shells").
In addition the syllabus required candidates to be able to explain the shapes of molecules in terms of "repulsion between bonding and non-bonding electron pairs", and "the covalent bond considered as electron pairing or as the overlap of atomic orbitals". The notion of electron pairs is one which makes no sense from a purely electrostatic perspective, and requires the introduction of the concept of electron (quantum-mechanical) spin.
Learners were also required to know something of delocalised bonding (in benzene and metals), which again makes little sense in the absence of the molecular orbital concept.
These concepts (orbitals, quantum numbers, energy levels, sub-shells, electron pairs, delocalisation) are all notions that do not feature in pre-A level courses (i.e. the requirements for G.C.S.E. science or chemistry) and it would not be expected that students commencing A level should be familiar with them. The data collected in the present research supports this contention, and therefore leads to the conclusion that one aspect of progression in understanding chemical bonding depends upon the acquisition of novel concepts related to quantization.
§6.1.3: Progression in the case studies
Models of cognitive change (§2.10) might also suggest that an analysis of progression in understanding chemical bonding could relate to the level of integration of electrostatic and quantum (i.e. orbital) concepts. However, I have discussed earlier how this is problematic as curriculum science does not present a coherent model of the chemical bond which readily integrates these two sets of ideas (§1.7.1). I have suggested, rather, that it might be appropriate to consider learning in terms of the analogy of acquiring a conceptual toolkit (§1.7.2). In the present research there was evidence that an apparent lack of coherence in the models being learnt did not seem to be necessarily problematic for learners, who were open to the manifold nature of the models of chemistry. This will be illustrated in some detail through the case of colearner Tajinder, who it will be shown was able to recognise that he selected from three competing explanatory principles: each of which he apparently viewed as a partial but incomplete truth (§8.4.5).
Indeed although analysis of the data was undertaken in terms of categories that separately considered aspects of what I will term 'electrostatic thinking' and 'orbital thinking', this scheme in part evolved from the analysis itself (through the principle of grounded theory, §4.4) and reflects the data.
In the subsequent chapters two case studies are used to illustrate progression. In the case of Annie (chapter 7) there is evidence of progression in terms of both the acquisition of new 'tools' being added to her conceptual 'tool box', and the increasing sophistication of her preexisting concepts (§7.1). However, Annie's case also demonstrates how progression may be limited by both aspects of a learner's existing cognitive structure (§7.21, §7.2.2), and by an ignorance of the tacitly assumed prerequisite electrostatic principles of A level chemistry course (§7.2.3, c.f. §3.1.3). The case also illustrates how an alternative conception (labelled deviation charges) may become well established in cognitive structure and may prove stable despite being apparently incongruous with the material being presented to a learner (§7 .2.2).
Annie's case also illustrates how a learner may apparently have available at one time two disparate explanatory schemes, and switch between them (§7.3). Early in her course Annie explained chemical bonding in terms of an explanatory principle based on full electron shells (labelled the stable shells explanatory principle), and although she learnt to use an alternative principle based on electrostatic forces (the electrostatic forces explanatory principle) this did not immediately replace her existing explanatory principle.
This theme is explored further in the second case considered in depth, that of Tajinder (chapter 8). In Tajinder's case three alternative explanatory principles were elicited (§8.1). Like Annie, Tajinder used an explanatory principle based on the octet rule (labelled the octet rule explanatory principle) as the basis for forming many explanations (§8.2.1). Again like Annie, he learnt to develop arguments based on a second explanatory principle derived from electrostatic considerations (which I have labelled the coulombic forces explanatory principle, §8.3.1), and, once again like Annie, this supplemented rather than replaced his use of octet thinking (§8.4.4). As with Annie, Tajinder's application of accepted electrostatic principles to chemistry was impeded by an alternative conception (labelled conservation of force, §8.2.5). Tajinder also demonstrated the use of a third explanatory principle, based on the tendency for systems to evolve to minimum energy, which he used to complement his octet rule and Coulombic forces explanatory principles (labelled the minimum energy explanatory principle, §8.3.3).
In the discussion of this case it is shown how Tajinder's developing understanding of chemical bonding is related to his acquisition of the additional (i.e. Coulombic forces and minimum energy) explanatory principles to complement his original octet rule explanatory principle (§8.4.3). Evidence is also presented to show how these alternative explanatory principles were concurrently available in Tajinder's cognitive structure over an extended period of time, giving him plural explanatory schemes to select from when discussing chemical bonding (§8.4.5).
In both cases then, progression, at least to the extent to which it was judged to have occurred, has been related to the acquisition of additional explanatory principles which supplemented, but during the period of the learners' courses did not replace, existing explanatory schemes.
§6.2: Impediments to progression in understanding chemical bonding
When the data collected for this study is considered in terms of the view of progression presented above, the major findings of this research may be summarised:
- Learners may experience difficulty in appreciating aspects of the 'orbital' concept used in chemistry.
- Learners exhibit beliefs about the interactions of charged particles which are inconsistent with Coulombic electrostatics, and may therefore act as a barrier (a substantive learning impediment, see chapter 1, §1.5.3) to the learning of curriculum science models.
- Learners exhibit beliefs constructed from an explanatory principle derived from the octet rule, which provides them with an alternative rationale for the formation of chemical bonding, before they are introduced to the model taught at A level.
Although these finding are to some extent illustrated through the discussions of the case studies of Annie and Tajinder presented in chapters 7 and 8, they are considered in depth in the thematic chapters 9, 10 and 11 respectively. Before the detailed evidence is considered in those chapters, the main features of each of these three findings will be outlined.
§6.2.1: Learners may experience difficulty in appreciating aspects of the 'orbital' concept used in chemistry.
In the present research it was found that some aspects of the orbital concept gave learners difficultly. The uncertainty about the meaning of electron spin (§9.2.6), and the identification of orbital probability envelopes with 'boundaries' (§9.2.4) were not judged to be be serious impediments to progress, but it was also found that
- learners commonly confused hybridised atomic orbitals with molecular orbitals (§9.3.2);
- had difficulty remembering the designation of atomic orbitals, and understanding the relationship between orbitals, sub-shells and energy levels (§9.2).
This theme is considered, in chapter 9, in less depth than the other two main findings considered below. In part this is because there is less data to discuss as generally the learners did not tend to answer questions in the interviews in terms of orbital concepts. However, I have also chosen to focus more on the other aspects of my results, as I believe they are of more significance. Learners tended to find orbital ideas abstract and unfamiliar, and – in the case of orbital labels – arbitrary. However learners seemed to experience little interference from existing knowledge when learning these ideas (that is they tend to experience null learning impediments, rather than substantive learning impediments). By contrast the two other main findings concern competition between preexisting knowledge and the desired learning outcomes. It is these areas, where learning is heavily a matter of accommodation rather than just assimilation (§2.10.1), where I believe this study can offer insights of pedagogic significance (see chapter 12, §12.5).
§6.2.2: Learners exhibit beliefs about the interactions of charged particles which are inconsistent with Coulombic electrostatics
As progression was found to be related to the adoption of electrostatic principles as the basis of explaining bonding phenomena, learners' notions about electrostatic forces are of central importance to the research.
It was found in this study that most of the chemistry learners interviewed exhibited notions about the interactions between charged particles which were inconsistent with curriculum science. This is discussed in detail in chapter 10. The following features were found amongst one or more of the colearners in the study,
- an interpretation of charge as a deviation from full electron shells, rather than a deviation from electrical neutrality (§7.2.2).
- forces were seen to act from one charged particle onto another, without reciprocity as required by Newton's third law (§10.4). The 'reaction' forces might be absent, considered as negligible, of the wrong sign (i.e. an attraction paired with a repulsion), or wrong magnitude (i.e. the greatest force acting on the smaller particle).
- systems were considered to be in equilibrium without forces being balanced; or to be non-equilibrium systems when forces would cancel (§10.3).
- nuclei were considered to give rise to a fixed amount of attraction – depending upon charge – which would be shared amongst the electrons available to receive it (§10.5).
These alternatives to conventional electrostatic principles were found to varying extents (for example the deviation charges notion was only elicited from Annie, but the notion of the effects of a charge being shared seemed to be common). Some learners were found to apply different variants of physical principles in contexts that were equivalent from a curriculum science perspective (c.f. §2.4.2). Similarly the meanings that learners appeared to give to words such as 'force' and 'attraction' did not always match the curriculum science definitions (c.f. §3.2.1).
§6.2.3: Learners exhibit beliefs constructed from an explanatory principle derived from the octet rule, which provide them with an alternative rationale for the formation of chemical bonding
The adoption of electrostatic principles to explain bonding phenomena was found to be inhibited by colearners' preexisting notions. It was generally found that the colearners involved in the research commenced their A level studies with an existing rationale for chemical bonding which was based around a heuristic used in curriculum science called the 'octet rule'. This is discussed in more detail in chapter 11 (§11.0). Arguments constructed from this explanatory principle were elicited from learners at all stages of the A level course.
Colearners were found to use this principle,
- when they had no alternative rationale to explain why bonds formed; but also,
- after they had been taught about bonding from an electrostatic perspective; and,
- after they had demonstrated they were able to apply arguments based on electrostatic principles; and even
- to examples where the principle was invalid in its own terms.
By considering one case study in detail it will be demonstrated that colearner Tajinder was able to maintain and apply arguments based on several apparently inconsistent explanatory principles (§8.4.5). Tajinder was not only found to switch between arguments based on these different principles, but he also came to demonstrate an awareness and acceptance of the manifold nature of his mental models (a finding which it will be argued is particularly significant for the issue of the validity of 'multiple frameworks' as discussed earlier).
Although when considered in detail each colearner interviewed had a somewhat distinct set of notions about the explanatory power to be derived from the octet rule, it will be suggested that there are sufficient common aspects to justify the presentation of a model of octet thinking.
The basis of octet thinking is the full shells explanatory principle:
The full shells explanatory principle
Atoms form bonds in order to achieve stable electronic configurations – variously referred to as octets, full outer shells or noble gas (electronic) configurations/structures.
This principle is the basis of a complex of related notions, 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 from 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 nanother 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':
- an atomic ontology (§11.1)
- use of anthropomorphic language (§11.3)
- significance given to electronic history (§11.4)
- electrovalency as the determinant of the number of ionic bonds formed (§11.5)
- dichotomous classification of bonding (§11.6)
- distinguishing between bonds, and 'just forces' (§11.7)
Each of these features will be briefly described here, before being illustrated in more detail with evidence from the data base in chapter 11. In the discussion section (chapter 12) it will be suggested that it is appropriate to refer to this complex of ideas as a common alternative conceptual framework (§12.3).
An atomic ontology: atoms as the units of matter
The research suggests that atoms are ascribed a special ontological significance by learners, so that chemical systems tend to be conceptualised in terms of combinations of atoms, although this may not always be the most useful and appropriate approach. The notion of electrons belonging to atoms (see below) may be associated with this tendency to perceive discrete neutral atoms as some sort of 'natural' unit of matter
The use of anthropomorphic language
Whereas an electrostatic explanatory principle defines a mechanism for chemical processes to occur, i.e. electrostatic forces, the full shells explanatory principle is not associated with any particular type of force. Colearners tended to give explanations based on this principle in language that was anthropomorphic, that is, atoms were spoken of as if they were sentient actors that had perceptions and desires, and were able to act accordingly. Such language may represent either anthropomorphic thinking on the part of the learner (thinking in terms of the atom being a sentient actor), or alternatively, a metaphorical description where the best way the learner can find to explain their thinking is to speak as if atoms were conscious agents (see §12.4.4).
The history conjecture: significance given to electronic history
Another aspect of learners' thinking identified in the interviews was the implicit suggestion that the history on an electron is significant. This could be seen as closely related to the notion of electrons belonging to atoms: for if electrons belong to particular atoms then it might be important to identify which atom an electron came from, and therefore belonged to. One consequence of the history conjecture is an assumption that when a bond breaks atoms get 'their own electrons back'. The history conjecture may also lead to the ionic bond being defined in terms of the donation and acceptance of an electron between atoms, rather than an interaction between ions.
The valency conjecture: electrovalency as the determinant of the number of ionic bonds formed
When an electron transfer event is seen as an integral part of the ionic bond, such that ionic bonds can only occur where there has been electron transfer, then the number of ionic bonds that an atom may form is determined by the number of electrons it will donate or accept in reaching an octet state, i.e. by the electrovalency, rather than by its coordination number in a structure.
A dichotomous classification of bonding
The full shells explanatory principle readily accommodates covalent and ionic bonding, but the research suggest that learners cannot readily explain other bonding classes from this perspective. Therefore for a learner applying octet thinking anything that is recognised as bonding will tend to be classified in terms of the dichotomous classification ionic-covalent.
The just forces conjecture: distinguishing between bonds, and 'just forces'
Some forms of interaction that are accepted as examples of chemical bonding within curriculum science may be labelled as 'just forces' by a student who understands bonding in terms of the full shells explanatory principle. For example interactions such as hydrogen bonding that do not lead to octet configurations may be discounted as bonds. When considering ionic materials, application of the valency conjecture will limit the number of bonds an ion is seen to form, and application of the history conjecture will allow a specific interaction to be identified as the ionic bond so that the other interactions between counter ions may be considered to be just forces. Similarly, if a learner classifies bonds using the covalent- ionic dichotomy, then interactions that can not be understood as either covalent nor ionic may be discounted from consideration as 'proper' bonds.
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