03. Learners' ideas about chemical bonding - Science-Education-Research

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Chapter 3 of Understanding Chemical Bonding: The development of A level students' understanding of the concept of chemical bonding

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Learners' ideas about chemical bonding

§3.0: The organisation of this review

In this chapter the literature concerning learners' understanding of chemical bonding will be reviewed. Before turning to consider studies directly concerned with the bonding topic it is appropriate to consider studies into learners' understandings in a number of other topics which may be considered to relate to the 'prerequisite knowledge' that might be expected in order to make sense of the idea of chemical bonds (see appendix 5).

The relevance of these related topics, 'matter, molecules and mechanics', to an understanding of bonding will be explained, and then a brief overview of the literature relating to learners' ideas in these topics will be presented. Some of the points of particular significance for the present study will be highlighted. (A more detailed review of the literature overviewed in this section may be found in appendix 7).

§3.1: Matter, molecules, mechanics: prerequisite knowledge for understanding chemical bonding

Although relatively little has been published about how learners understand chemical bonds, and how this understanding may develop, some of the literature relating to other science topics is relevant. The scientific concept of 'chemical bond' depends upon other assumed knowledge (see appendix 5, and also appendix 4). In particular three areas of prerequisite scientific knowledge may be identified: notions of matter and substance; the molecular model of matter; and notions of energy and force. For reasons of space the details of the literature for this section has been appended (appendix 7), and only an outline discussion is provided here.

§3.1.1: Learners’ notions of matter and substance

Scientists have a notion of 'matter', and usually classify it according to phases (i.e. most commonly solid, liquid and gas, although many substances have more than three phases). Materials may be composed of pure chemical substances, or mixtures of several such substances. For the chemist there is an important distinction between pure substances that are elements and those that are compounds. The existence of the phenomenon of electrostatic charge is also basic to understanding chemical bonding.

A number of studies report examples of alternative conceptions about matter (Bar and Travis, 1991; Briggs and Holding, 1986; Brook and Driver, 1989; Edwards and Mercer, 1987; Osborne and Cosgrove, 1983; Renström et al., 1990; Wightman et al., 1986; see appendix 7, §A7.1).

In particular, young children have difficulty recognising gas as substantive material. There are reports that air is only considered present when it can be felt (as when windy), and it is considered not to take up any space, nor to have any weight. Indeed sometimes air is thought to have negative weight. Youngsters may equate 'nothing' and 'just air' in an empty (sic) container. Hot air, and cold air are considered as distinct entities to one another and to normal air, and sometimes hot air is equated with heat.

There have been many alternative conceptions of state changes reported in the literature. The bubbles in boiling water have been variously identified with heat, air, oxygen, hydrogen and smoke, and the 'stuff' which leaves the water (not necessarily considered as related to the bubbles) may be seen as smoke, air, water or heat. Evaporation may be confused with boiling, but may also be thought to be a way of making milk 'thicker', or due to water passing through a surface. Water that has evaporated may be considered to cease to exist, or to become air, to spilt into hydrogen and oxygen, or to collect near ceilings. Condensation may be seen as due to oxygen and hydrogen combining, or water passing through a surface, or produced by coldness (directly, by acting with a surface, or reacting with heat). Condensation may be considered to be a distinct type of water, or even a kind of sweat. Studies also suggest that melting and dissolving may be seen as the same phenomenon.

For chemists the distinction between elements, compounds and mixtures is very significant, and this is another area where studies show learners have difficulties accepting the definitions, discriminations and models of science. Among the alternative conceptions of elements to be found in the literature are that they can be split up by chromatography, that they are a type of solid (and sometimes a type which releases a gas), that they can be split, that they give one product on electrolysis, that they make other elements, and that they are mixtures (but sometimes natural mixtures). It has also been reported that elements need oxygen to live. This is an example of animism, which will be discussed below (§3.1.4). Water is sometimes considered an element.

Compounds are thought to be mixtures by some learners, whilst others see the distinction between compounds and mixtures in terms of how many component elements are present. Compounds may be considered to have variable stoichiometry. Substances with more than one type of atom, such as oxides, may be seen as necessarily impure. For some learners the difference between a mixture and an impure substance is that the former is acceptable and the latter undesirable.

Although the distinction between elements, compounds and mixtures may be given in terms of molar definitions – a substance that can not be broken down into anything simpler by chemical means; a pure substance made up from more than one type of element; several types of pure substance mixed together – these are not sensible in the absence of a molecular model. (For example consider the difficulty of explaining how a pure substance can contain several elements, without using particle theory.)

§3.1.2: Learners’ notions of molecules

Scientists explain the observed behaviour of materials in terms of a well established and developed theory variously referred to in the school science curriculum as 'particle theory', 'atomic theory', or 'kinetic theory'. In a simple form this states that all chemical substances are made up from minuscule particles called molecules, and the macroscopic – or molar – behaviour of materials may be explained in terms of the properties of the microscopic – or perhaps better, sub-microscopic – molecules. It has been suggested that "the 'clumpiness' concept is, to a degree, an advance organizer for the entire field of chemical interactions" (Ault, Novak and Gowin, 1984, p.453).

Chemical bonding 'holds' the particles to one another, and so the concept of the chemical bond is meaningless without the concept of atomic-scale particles, which in turn are theoretical constructs that are only required and acquired in the context of the categories of substance and material.

Again there is much evidence in the literature that particle theory causes difficulties to learners (Ault, et al., 1984; Ben-Zvi et al., 1986; Briggs and Holding, 1986; Griffiths and Preston, 1992; Nussbaum and Novick, 1982; Renström et al, 1980; Wightman et al., 1986; see appendix 7, §A7.4).

In everyday parlance particle means a grain or drop, and many pupils appear to think in these terms, and think that molecules may be directly weighed, and seen under the microscope. It has also been shown that the whole notion of substances being comprised of particles is counter-intuitive, so that learners think in terms of the particles being embedded in the substance, or being made up from it. Sometimesmthe particles are thought to be infinitely divisible. Spaces between particles are often thought to be filled with the substance itself, or with other particles.

Even when learners appear to grasp the basic nature of molecules, they often apply the notions of the macroscopic world to them. This 'macro-micro' confusion means that particles such as individual molecules are often said to freeze, expand, soften, harden and so forth during phase change, so that the particles are seen as different (e.g. different weight, different size) in the different states of matter. Sometimes it may be the bonding which is said to melt. The particles may be said to individually have properties associated with the bulk substance such as conductivity, malleability, colour, odour (possibly correct!) and reactivity. The particles may be seen as 'solid' spheres, although they may also be considered as flat, or as different shapes designed to fit together. Other elicited possibilities are that the particles have the shape of the macroscopic object; or look like dots and circles (i.e. similar to textbook representations of atomic structures).

Sometimes learners fail to understand the basic similarity of molecules of a single substance, so that different particles may be assumed to have different sizes, shapes or weights. The particles in a pure substance may be assumed to contain different elements or atoms. Conversely, other pupils think that all particles in a substance must move at the same speed, or even that all atoms are the same size and weight.

The relationship between elements, compounds, atoms and molecules is another area of difficulty for learners, so that elements may be seen as part of an atom, and atoms as larger than molecules. If all the molecules in a substance are the same it may be identified as an element, whilst other learners report that all the atoms in a compound are the same.

The work of Renström, Andersson and Marton (1980) demonstrates that the acquisition of the scientific notion of molecules can be a slow process: with molecules seen variously by learners at different stages in developing their understanding of the model as only part of the substance; made up from the substance; and surrounded by the substance.

So, as Ault and co-workers propose, "the basic proposition that 'everything is made of molecules' needs the added emphasis 'and nothing else'" (Ault et al., 1984, p.459). This brief survey of the literature relating to learner's understanding of the molecules concept may perhaps best be summarised by a comment of Ault, Novak and Gowin,

"The 'molecule concept' is of nearly limitless complexity. … children have the capacity of grasping the abstract meaning of molecules at some level, though often in terms of imaginative, unconventional conceptual patterns."

Ault et al., 1984, p.460

§3.1.3: Learners’ notions of force and energy

According to physics, objects are bound together by forces, and so the chemical bond must be a force (or rather an equilibrium of forces). Later in this chapter it will be reported that learners' notions of bonding as involving force are often vague or non-existent (§3.2.2), and this is somewhat reflected in the results to be reported from the present research (see in particular chapter 10). Wightman, reflecting on the findings from her case studies on students' learning about particle theory, asks "what basis can there be for understanding bonding without previous knowledge of forces generally, forces acting at a distance, and the existence of attraction and repulsion forces?" (Wightman et al., 1986, p.268).

The literature on learners' notions in mechanics is particularly rich, and appendix 7 (§A7.7) discusses a number of studies which present learners' alternative conceptions for aspects of the force and energy concepts (Brook and Driver, 1984, 1986; Gilbert and Zylbersztajn, 1985; McCloskey, 1983; Solomon, 1992; Viennot, 1985a; Watts, 1982, 1983a, 1983b; Watts and Gilbert, 1983; Watts and Zylbersztajn, 1981).

Physics only recognises (at least in our cosmic epoch) four fundamental types of force – the strong nuclear force, the electromagnetic force, the weak force, and gravitation – so chemical bonds would be expected to be derived from one (or more) of these types of interaction. Basically the chemical bond is viewed as electrostatic in origin (i.e. deriving from the electromagnetic force).

A number of key principles from mechanics would be expected to apply to molecular interactions, including 'Newton's third law' – or Newton-3 as it will be abbreviated – that if a body A exerts a force on a body B, then the body B exerts a force on A which is equal in magnitude, anti–parallel in direction, and acts along the same line of action. Yet this seems counter intuitive to many learners who feel that a larger object will exert a larger force (reflected in the data presented in chapter 10). The electrostatic force between two charges can be attractive (if the charges are 'opposite') or repulsive (if they are of the same sign charge). The magnitude of this force is given by Coulomb's law, that the force between two charged particles is directly proportional to the product of their charges, and inversely proportional to the square of their separation. It may be noted that the force acts on both charges, and is of the same size, and must be either attractive for both particles (when it has a negative value from Coulomb's law), or repulsive for both (when positive) In these respects Coulomb's law may be seen as a case of Newton-3 (see above).

Balanced forces lead to equilibrium situations: so that a stationary system (or indeed a non-accelerating one) is either subject to no forces, or to forces that balance, and whose effect would therefore cancel (this is known as Newton's first law, or Newton-1). Where a net force acts on a body it will be accelerated as long as the force acts. Yet research into learners' notions of motion shows that this is counter-intuitive for most learners. Indeed one of the most established findings in the literature on alternative conceptions is that most people (children, adolescent students, and adults) often tend to intuitively apply an alternative notion of force and motion that is closer to the historical impetus theory (that a moving object's push gets used up) and are more likely to relate applied force with velocity than with acceleration.

The nature of our universe is such that balanced forces are very common as matter on a molecular scale often interacts in such a way as to give 'stable equilibria' – that is systems where moderate perturbation in either direction leads to a restoring force which returns the system to equilibrium. However this stability is not absolute, as large perturbations may lead to a resultant force between the particles that reinforces the disturbance, and the system undergoes a change in configuration to a new equilibrium. (In other words negative feedback acts on small inputs to ensure stability, but positive feedback from larger inputs ensures change is also possible.) The particular combination of fundamental constants and cosmic starting conditions that has led to a Universe with these properties – without which there would be no materials, let alone life – has been the focus of much speculation (e.g. Barrow and Tippler, 1986; Breuer, 1991 {1981} ; Gale, 1981.)

The research literature suggests that learners often have difficulties identifying balanced forces: they may not distinguish force from net force, and may not pay equal heed to all forces acting in a system. Watts (1983a) has identified eight distinct alternative frameworks (n.b. alternative frameworks2, c.f. §2.4.) for school children's understanding of force, and some learners may hold several of these (c.f. §2.5.2, §2.9). The single physicists' concept of force may be related to different types of phenomena to learners: something passed between bodies, something indwelling in some bodies (for example moving objects); something maintaining a status quo, etc. (§A7.7). One of Watts' frameworks for force was labelled designated forces where the "force seems to reside within the objects" and is 'immanent', 'indwelling' or 'inherent' (1983a, p.222). The forces were associated with (designated to) the perceived agent causing action, so that "some objects were seen as 'having' force, others were not" (p.223). Another framework of particular relevance to the present study was that of configuration forces, where learners construed an object restrained in a fixed position to "have force' (p.221). In this framework the force is seen as a bonding without which objects would move apart. This framework might be considered a suitable 'intermediate conception' (§2.3.10) to curriculum science as it associates force and bonding: however this framework does identify an equilibrium situation with a force rather than with balanced forces.

Another related concept is that of energy. Stable configurations of systems are associated with low potential energy. Systems tend to proceed to states of lower potential energy (and in the present research this was found to be an explanatory principle that A level chemistry students do adopt, see chapter 8, §8.3.3). The term 'chemical potential energy' is sometimes used in relation to chemical systems, although this form of energy can also be conceptualised as electrostatic potential. The energy changes associated with chemical reactions are seen by chemists as very significant. The free energy change of a process is seen as a measure of its tendency to occur, and consequently knowledge of the energy changes involved in the 'steps' of the reaction allow predictions to be made about viable chemical reactions. (For the purpose of analysis the reaction process is divided into a series of steps which may relate sequentially to the hypothesised mechanism the molecules undergo, but is unlikely to correspond to discrete processes at the bench – if only because the different molecules will not be passing through the steps at the same time.) The energy involved in breaking specific bonds is calculated (although quoted per mole), along with ionisation energies, electron affinities, lattice energies, solvation energies etc.

The research literature shows that, as with force, learners' notions of energy may be very different from a physicist's. To learners, energy may be intimately tied to movement, or to vitality, or to food or good health.

The concepts of force and energy are fundamental in physics, and may be understood at various levels of sophistication. However Ault, Novak and Gowin have made the point that 'energy' and 'force' must be considered as "high level" concepts when integrated into molecular-level explanations (1984, p.452). In contrast the research literature shows that learners may have a variety of alternative conceptions for force and energy, and that indeed for many school pupils concepts that physicists consider to be distinct (energy, force, momentum, power, speed, strength, velocity, work, etc.) are either not distinguished, or are not discriminated between through the same lines of demarcation.

§3.1.4: Learners’ animistic and anthropomorphic references

Piaget (§2.2.1) had noted how children imbue inanimate objects with characteristics of living things (1973 {1929} , see §A7.6 for a brief discussion). The literature on children's understanding of particle theories provides a number of examples of animistic and anthropomorphic references to atoms and molecules (Driver, 1983; Wightman, et al., 1986; §A7.6). Anthropomorphic language has also been found in learners' notions of macroscopic phenomena (Viennot, 1985a; Watts, 1982, 1983a, 1983b; Watts and Zylbersztajn, 1981) so that objects may be said to try to overcome gravity, or to need energy (§A7.7.7).

As well as direct comments that atoms are alive, particles have been said to jump, reproduce, move anywhere they want, and hold hands. Thermal expansion has been explained in terms of particles and substances getting away from the heat, liking being cool, needing more room, or not wanting to be too close together.

§3.1.5: Scientists’ animistic and anthropomorphic references

Anthropomorphic and animistic language may be used in a quite explicit way in science, as when Millikan referred to an oil drop having an electron "sitting on its back", or by virtue of using words such as 'want' and 'need' which we associate with human desires. When Robert Boyle referred to two slabs of marble falling apart in a vacuum "wanting that pressure of air, that had formerly held them together" he presumably did not literally intend to suggest that minerals had preferences, any more than Millikan meant to imply that electrons can literally sit down, or that an oil drop has a backbone (both quotations are taken from Wolpert, 1992; p.96 and p. 95 respectively). These examples are historical, but Wolpert himself refers to cells in the developing embryo which "make the decision to become a humerus" (p.137), and in another recent 'popular science' book – with the anthropomorphic title of 'Taming the Atom' – von Baeyer refers to "the intimate act of molecular mating" (1992, p.121).

It is in a metaphorical sense that the learner's knowledge has foundations and scaffolding (c.f. §2.1.2, §2.2.2). When Darwin presented natural selection in anthropomorphic language he was not suggesting that nature is alive in the same sense as an individual ape: it was an extended metaphor, and he believed that "everyone knows what is meant and is implied by such metaphorical expressions" (quoted in Beer, 1986). Similarly Lovelock's Gaia (1979) is an organism in a metaphorical sense: it is by definition supra-organismic. When Rose refers to bacteria collecting near a source of glucose behaving as if they knew the glucose was there, he believes this analogy will communicate his meaning effectively (1992, p. 164). The philosopher and chemist Polanyi once commented that "our conception of science should not be one which strives at the logically impossible, self- destructive ideal of completely explicit statements" (Kirschenbaum and Henderson, 1990).

It should be noted that, as Benfey (1982) has pointed out, there is a historical tradition of 'organicist' concepts in chemistry. Benfey has suggested that one may consider molecules in terms of their biographies,

"entities with a life–history, from their birth when they adopt the structure that determines their identity, through their life span with all the buffeting they receive which rotates, vibrates, stretches, bends and excites [sic] them, to their final farewell when they are fragmented, substituted, absorbed, or metamorphosed to enter the life history of another chemical species. Here we are very close to the language commonly used in the description of organisms."
Benfey, 1982, p.397

Benfey was explicitly using this language metaphorically. Schrödinger himself once asked "do electrons think?" (Moore, 1989, p.448). For him it was a rhetorical question, the idea was ridiculous and showed (in his view) the inadequacies of the Copenhagen interpretation of quantum mechanics, whereas it is not clear that this is the case when school pupils and students make such references (see §11.3.3 for a discussion of the extent of learners' awareness of their anthropomorphic language in the present study).

It has been argued that anthropomorphic and animistic thinking can be very valuable in increasing the appeal of school science, especially amongst girls and young women (Watts and Bentley, 1994). It is well established that in general boys and girls already have different science interests on entering secondary education (e.g. Taber, 1991) and gender-related attitudes to science are believed to be at least partially to do with different preferred modes of relating to the world (see Smail's analysis of 'characteristics of children and science education', 1987, p.83). The under- representation of women in science is a serious matter, and anything that can be done to make science curricula better match the interests, cognitive styles, and aspirations of females is to be encouraged, even if it means challenging the 'masculine' nature of science as it is normally practised (Bentley and Watts, 1987). Watts and Bentley (1994), working from a constructivist perspective, have discussed the merits of anthropomorphic and animistic language in humanising and feminising school science. The possible value of anthropomorphic language to students in the present study is considered in chapter 12 (§12.4.4).

§3.2: The literature on learners’ ideas about chemical bonding

"Most students enter their first chemistry course with little or no feeling for chemical phenomena at the molar level. They do not come with a set of organized observations and questions for which they desire a theoretical rationale. In addition most have no fundamental understanding of electricity and magnetism. Yet, by Chapter 2 or 3, most chemistry textbooks have launched into a theoretical explanation of chemical phenomena at the electrical level. This I think is the fundamental paradox of the modern general chemistry course:

"we are basically engaged in forcing students to absorb a set of theoretical answers at the electrical level, which they do not understand, to a set of questions at the molar level, which, from their point of view, do not exist."
Jensen, 1995, p.71

As outlined in chapter 1 (§1.1), bonding is a key topic in the study of chemistry at all levels. Considering its centrality to chemistry it is perhaps surprising that there have not been a greater number of studies into the learning of this topic. The research in the literature tends to be concerned with identifying misconceptions, rather than considering how understanding develops. One of the reasons conjectured to explain this oversight (§1.3.3) is that this topic relies on prerequisite knowledge in other science topic areas, i.e. as reviewed above (§3.1). As we have seen, and as Jensen suggests in the motto above, student understanding of prerequisite concepts may be limited.

§3.2.1: Chemical bonding

A chemical bond is "the linkage between atoms in molecules and between molecules and ions in crystals" (Penguin Dictionary of Chemistry, Sharp, 1983). Without chemical bonds there would be no condensed matter, and indeed most common gases – those that are molecular such as oxygen, nitrogen, carbon dioxide, etc. – would not exist.

In other words, from the scientific world view there is no a priori reason to expect atoms to stick together, unless there is some form of force attracting the particles together. The scientific model of the atom, as containing positive and negative charges, however leads to an expectation that atoms will be attracted together, due to electrostatic forces. In general the expectation is that there will be an equilibrium distance between two atoms where attractions and repulsions balance: at lesser distances there will be a resultant repulsion; at greater distances a resultant attraction.

From the scientific viewpoint then

atoms would not be expected to be linked unless there is some form of physical (i.e. in terms of the laws of physics) bond;
there are net forces between atoms which at most separations would tend to attract them together;
this electrostatic force is the physical basis of the chemical bond.

In practice chemists do not talk of a single kind of chemical bond, but a variety of types. The most significant distinction is in terms of strength: some types of chemical bond are only disrupted at very high temperatures (e.g. in diamond), whilst others are overcome at extremely low temperatures (e.g. in neon.) This is explained in terms of the detail of atomic structure, and in particular as a result of quantum effects. Electrons in atoms occupy specific orbitals, and have quantum- mechanical spin. The orbitals are arranged in what may be simplistically seen as concentric shells, and the number and type of orbitals in each shell is limited by strict rules. The energy associated with different orbitals in the atomic system varies, and each orbital can only be occupied by up to two electrons. The atomic structure, in orbital terms, may in principle be seen to arise from a solutions to a mathematical model of the physical system (i.e. the Schrödinger equation).

When atoms interact the system then consists of several nuclei, and the configuration of all the electrons, and in principle the molecule or crystal, could also be calculated from the same mathematical model. In practice the mathematics is too difficult to solve precisely for all but the simplest systems,

"though the newer quantum mechanics certainly had implications for chemistry, the compositional and structural aspects of the electrical revolution [in chemistry], which had already emerged in the two decades before the advent of matrix mechanics in 1925 and wave mechanics in 1926, had far more impact for the average chemist"
Jensen, 1995, p.89

However various approximations are possible, and qualitative arguments based on the overlap of the atomic orbitals often give satisfactory predictions for many cases. These rules are used to explain the basis of the periodic table, and give different atoms different valencies – the number of strong bonds formed – and lead to the different bond properties perceived. So on this model:

the numbers of (strong) bonds formed by an atom – and therefore the stoichiometry of stable molecules – is determined by physical principles of electrostatics and quantum theory;
the varying nature of the bonds in different substances may also be explained.

In practice chemists use a range of intermediate level concepts and rules to 'explain' bonding ideas (see chapter 1, §1.7, and the analysis of the chemistry student's conceptual toolbox in appendix 4). An example would be electronegativity. Differences in electronegativity 'explain' bond polarity. As electronegativity itself may be explained in terms of electrostatics, this concept may be seen as analogous to a 'sub- routine', or a mathematical theorem, that once proved may be taken as given, and used without repeating the derivation each time. In studies to age 16, bond polarity tends to be ignored, and covalent and ionic bonds are taught as apparently distinct phenomena. In post-16 courses, such as the G.C.E. Advanced level chemistry course followed by the colearners in this study, the notion of bond polarity (and therefore electronegativity) becomes of major importance. As Lewis and Waddling have suggested "the key concepts at this level, in a study of group and period trends, are those of polarisation and mixed linkage" (1986, p.22).

Other examples of this 'sub-routine' approach would include categories of bond, such as hydrogen bonds. The hydrogen bond concept may be understood in terms of electrostatics and quantum-mechanics; but in practice chemists have criteria for the hydrogen bond (e.g. the system must include a hydrogen atom bonded to an electronegative atom), and a range of phenomena that they associate with it (e.g. higher than otherwise expected boiling temperature), so that they can operate with the concept without keep relating it back to first principles.

In this sense many of the concepts applied in chemistry are used heuristically. A particularly important example in the context of the present study is the octet rule, which was known by chemists well before it was understood in terms of quantum mechanics. It is a rule of thumb that can often be successfully used to predict stable molecular stoichiometries, and charges on many common ions (e.g. the chloride ion will be Cl-, where the magnesium ion will be Mg2+). However, it is a limited rule. For example carbon monoxide does not match the rule, and nor does the sulphate ion, to give two common chemical species. The significance of this rule to the present research will be demonstrated in chapter 11.

§3.2.2: Bonding as the result of physical forces

Griffiths and Preston asked grade-12 students (16-18 years) to sketch molecules of ice. They report that typical diagrams showed the molecules touching each other without spaces between, and they conjectured for these learners the concept of bonding might have little to do with forces of attraction (1992, p.620). For some students in their sample molecules were not bound due to inherent interactions between atoms, but were held together by "something external to the molecules".

In a French study of first year undergraduate science students Cros et al. (1986), looked at two topics, acids and bases (which is not considered here) and the atom. The research had three stages: 40 unstructured interviews; 50 semi-structured interviews; and then 400 students at two Universities were surveyed by questionnaires before starting their lecture courses. (So although University students, these learners were at an equivalent stage of their scientific education as the colearners in the present study at the end of their A level course.) Cros and coworkers found that the interactions between atoms in molecules were often unknown (38%) or poorly known (18%) (pp.308-309), and that often students were not even aware that such interactions existed (p.311). It would seem that some students did not perceive the need for physical forces to hold the atoms and molecules together. So although most students could name the constituents of an atom (p.311), 21% of the students thought there were no interactions between the components of the atomic nucleus (and a further 40% did not respond to this item – so that the majority of students were not able to suggest any type of interaction). A follow-up study found that after one year of University study the electrostatic model was better understood (Cros et al., 1988, p.332), although 16% still thought there were no interactions between nucleons, with 31% not responding to this item (p.332).

Wightman undertook two case studies with classes of 13-14 year old being taught about particle theory. Bonding ideas were referred to when an explanation of the different states of matter was needed. In one of the case study classes one of the students had transferred from another school where he had apparently previously undertaken some work on atomic structure and bonding, although he had found it "a bit difficult to believe". His recall of the details was hazy. He had covered,

"what it's been made up out of, like the protons and neutrons and electrons and things and er, the way that they're joined together, and the electrons help to form, one electron'll go to the other two and – – them both, kind of."
'Eric', quoted in Wightman et al., 1986, p.107

Another student interviewed envisaged the forces between particles to be like elastic,

"it seems to me that there's a sort of force banging the particles together and this can be er stretched a bit, like – if it's a solid it's a lot stronger force, and if it's a liquid it's not as strong and you can stretch it more. … [The force is] binding the particles together … sort of like, there's elastic holding them together and it can stretch and contract to pull the particles back together again."
'Guy', quoted in Wightman et al., p.106

Although this student recognises the role of forces, he seems to envisage the force itself to be material, something that can be stretched. Guy was still able to operate with this theory, and later he is reported as using his ideas to explain what happens when butter is left out of the 'fridge', when "the bonds between [the particles] … aren't as strong, and so it makes it softer" (p.159).

In the case study class a group of pupils had brain-stormed their own model of chemical bonding before the teacher had formally introduced particle ideas. This model included electrostatic notions, but augmented by material linkage. As 'Suzanne' explained,

"we were thinking that some [of the 'atoms'] were positive and some were negative. … we did a little drawing. Say that all the positive ones had little holes in them all the way round – all the negative ones had things sticking out of them – and when they're solids they were linked together – the things sticking out went in the holes – and they came out when they were in a liquid."
Wightman et al., 1986, p.198

The teacher in this case study used the analogy of magnetism to help the pupils understand why atoms should stick together (although pointing out that the force was actually more like static electricity, a topic that had not yet been covered, p. 214). Two of the pupils had difficulty with this explanation (pp.214-6): one could not understand why the atoms should separate in gases, and another wanted to know why the "magnetification" did not cause the 'atoms' in a gas to "stick together" when they collided. The teacher in the case study was reduced to sidestepping the issue as "something to do with chemistry" (p.216). Clearly understanding bonding as a physical force is an insufficient concept unless it is accompanied by some idea of how energy and force are related (see earlier in this chapter for a review of student ideas in these areas, §3.1.3). As Brook has pointed out in a review, when senior secondary pupils were asked about the behaviour of particles in a block of ice, as its temperature rose, very few referred to bonding. Even where pupils did refer to the forces between the particles, and the motion of the particles they did not relate the two (1986, p.36). In view of Ault et al.'s point (reported above in §3.1.3) that 'energy' and 'force' must be considered as "high level" concepts when integrated into molecular-level explanations (1984, p.452), it is not surprising that,

"there was no evidence that any students were thinking in terms of a 'potential well', from which particles could escape if energy was supplied to them."
Brook, 1986, p.36

When a group of the students in Wightman's case study were later asked about how they imagined the bonding, one still suggested a material link – "like string between the atoms sort of holding it all together" (p.291). Others remembered the teacher's explanation and suggested "magnetism. Some sort of force", "static electricity or something like that" (p.291), but the apparently selective nature of the bonding was still problematic,

"I suppose if it was hot, then it wasn't magnetised as much or something, and then when it was cold it magnetises more."

"When they are hot they vibrate more, so the static isn't as strong"

"What I thought was … when they stop vibrating it might be a liquid"

"When they cool down, the bonding will be increased so they won't be able to move around as much."
student comments reported in Wightman et al., 1986, pp.291-292

As one of the students commented, "the point is, how do we get the bonding back?" (p.292). A resolution of sorts was reached with the suggestion that the bonding was "ever present", but had not always "got a chance to like grip, grip [the particles] … and keep them together". It was suggested that when the particles slowed down the bonding was then able to "get to grips" with the particles as it is "a bit easier to keep slower things together" (p.292). For other students the bond remained a material entity, and one conjectured that as the bonding was "like glue" thermal expansion might be because "the bondings get thicker" (p.305).

§3.2.3: Atomic structure and the orbital concept

One of the most important consequences of quantum mechanics in understanding chemical bonding is the introduction of the orbital concept into chemistry. The electrons in atomic systems are located in orbitals: chemical bonding may be conceptualised as due to the interaction of the atomic orbitals to form molecular orbitals at lower energy levels. (That is, the solutions to the mathematical model are molecular orbitals when several nuclei contribute.) In a sketchily reported study, Cervellati and Perugini (1981) asked 290 first year University students 'what an atomic orbital is' as part of a written instrument. The main categories in their analysis of responses were

an energy level (34%);
a portion of space (33.5%);
a trajectory (16%);
a mathematical function (3%).

(The percentages are of those answering: just over 30% of the sample did not respond to this question.) In a small scale study of Advanced level physics students in three schools in England Mashhadi found that about a quarter of his sample held a 'mechanistic' conception of the atom with "fast moving electrons in definite orbits, similar in some ways to the planetary model of the atom" (1994, p.6). Just less than a quarter of the sample demonstrated a 'random motion' picture, that is, "involving random movement within a bounded region or at different energy orbits: e.g. an electron "moves randomly but in the shape of a certain shell" (p.7).

Of these perspectives, the notion of a trajectory is the least appropriate as it refers to a model of the electron in an atom (following a specific path) that has largely been superseded in advanced work. However, Cros and coworkers, found "in [fresher University] students' minds the dominant model of the atom is that of Bohr" (Cros et al., 1986, p.308). In their follow-up study after one year of University work this model was said to have receded somewhat, but without students having acquired a clear understanding of the interactions within an atom (Cros et al., 1988, p.332). They concluded that although the students had followed courses involving extensive study of the Bohr and Schrödinger models of the atom there had been very little change in their ideas (p.333). Cros and coworkers concluded from interviews that "the persistence of the Bohr model is remarkable even to the point where the answer to a question on the atom is given by a circular motion of the hand, showing the planetary system, before any word is spoken!" (p.333).

Each of the other three Cervellati and Perugini answer categories has some merit. The Penguin Dictionary of Chemistry defines orbital as a term "loosely used to describe the geometrical figure which describes the most probable location of an electron. More accurately an allowed energy level for electrons" (Sharp, 1983, p.288).

This would suggest the first of Cervellati and Perugini's four options is the most precise.

However the Hutchinson Dictionary of Science defines the term as the "region around the nucleus of an atom (or, in a molecule, around several nuclei) in which an electron is most likely to be found" (Lafferty and Rowe, 1994, p.421) and the Penguin Dictionary of Science defines orbital as, "the space containing all the points in an atom or molecule at which the wave function of an electron (two electrons may be present if they have opposite spins) has an appreciable magnitude" (Uvarov, et al., 1979, p.298), which would suggest the second option is closer to the scientific meaning.

Chambers Science and Technology Dictionary offers the following entry for 'orbital', which is consistent with this approach,

"The properties of each electron in a many-electron atom may be reasonably described by its response to the potential due to the nucleus and to the other electrons. The wave function, which expresses the probability of finding the electron in a region, is specified by a set of four quantum numbers and defines the orbital of the electron. The state of the many-electron atom is given by defining the orbitals of all the electrons subject to the Pauli exclusion principle."
Walker, 1991, p.632, italics added

Then again, the Penguin Dictionary of Physics defines atomic orbital as "an allowed wave function of an electron in an atom obtained by a solution of Schrödinger's wave equation" (Pitt, 1977, p.30), i.e. as a mathematical function. It is clear from the various dictionary definitions presented, that deciding whether learners' definitions of chemical concepts are appropriate is not always straightforward. Such lack of consensus over definitions reflects Kuhn's observation that in science "definitions were seldom taught, and [the] occasional attempts to produce them often evoked pronounced disagreements" (1977, p.xix).

Jones has argued that the failure to attempt to teach quantum mechanics (described as "the most successful tool ever invented for understanding nature") in some form from early in the science curriculum means that by the time students are introduced to quantum theory they are already so familiar with classical mechanics that they develop "an uneasy hybrid" of the two perspectives (1991, p.93). Jones suggests that this leads to "half-baked and incorrect conceptual models which stunt understanding and the development of interest" (p.93). Students' familiarity with classical mechanics, and the usual approach of introducing quantum theory through the models of the first two decades of the century (when the scientists themselves were trying to move beyond their classical notions) acts – in the typology introduced in chapter 1 – to an epistemological learning impediment. Shiland suggests

that "the presentation of sophisticated atomic theory (quantum mechanics) in secondary chemistry texts is not accompanied by sufficient evidence or applications to promote its rational acceptance as determined by a model of conceptual change (1997, p.535). One of Mashhadi's sample of Advanced level students explained that they had been taught about electrons as particles from early in secondary school, and about light as being a wave from even earlier, and "you have a long time to think of one thing before it is even mentioned that it is possible that may not be completely true" (1991, p.8).

§3.2.4: The covalent bond

In their French study Cros and coworkers found that although 85% of freshers knew molecules were made up from atoms, 38% were not able to suggest what the interactions between atoms might be. Only a third mentioned covalency (25%) or electron-sharing (8%) (Cros et al., 1986, pp.308-309). After one year of University science non-response to this item had dropped to 2%, and 63% were able to give an appropriate response (Cros et al., 1988, p.334).

Peterson, Treagust and Garnett describe the development and use of an instrument to diagnose grade-11 and -12 students' concepts of covalent bonding and structure after teaching had taken place (Peterson et al., 1989). Their research was carried out in South Australia, with 15-17 year olds electing to take chemistry. They developed a 15 item 'two-tier' multiple choice test – each item had two parts, the first asking student to select responses to a 'content' questions, and the second asking them to select a reason for their answer in the first part. The covalent bonding and structure diagnostic instrument, covered bond polarity, molecular shape, polarity of molecules, lattices, intermolecular forces and the octet rule. The topic area had been defined through a concept map and 33 propositional statements, verified by 6 'science educators'.

Peterson and coworkers initially identified relevant conceptions through "regular classroom teaching" (p.302), then carried out unstructured interviews, and asked students to prepare concept maps, and to answer open-ended written tests. 159 grade 11, and 84 grade 12, students from five schools were involved. These students had taken 6-7 months of chemistry instruction, including the topic being investigated. Peterson and coworkers concluded that "students may have acquired accurate content responses without an adequate understanding of the concepts involved" (p.308). In particular they identified thirteen 'misconceptions' (p.310). These were:-

Bond polarity:

Equal sharing of electron pairs occurs in all covalent bonds.
The polarity of a bond is dependent on the number of valence electrons in each atom involved in the bond. • Ionic charge determines the polarity of the bond.

Molecular shape:

The shape of a molecule is due to equal repulsion between the bonds.
Bond polarity determines the shape of a molecule.
The V-shape in a molecule of the type SCl2 is due to repulsion between the non-bonding electron pairs [only].

Intermolecular forces:

Intermolecular forces are the forces within a molecule.
Strong intermolecular forces exist in a continuous covalent solid. (The authors note that this "may be a case of mistaken terminology rather than a conceptual misunderstanding" p.311.)
Covalent bonds are broken when a substance changes shape.

Polarity of molecules:

Non-polar molecules [only] form when the atoms in the molecule have similar electronegativities.
•Molecules of the type OF2 are polar as the non-bonding electrons on the oxygen form a partial negative charge.

Octet rule:

Nitrogen atoms can share 5 electron pairs in bonding.

Lattices:

High viscosity of some molecular solids is due to strong bonds in the continuous covalent lattice.

Peterson and coworkers concluded that "following instruction of the topic, students in this sample have not developed the appropriate conceptual understanding of covalent bonding and structure that is an integral part of the grade-11 and -12 chemistry course in South Australia." (p.312). They also comment on the use of the term "shared" to denote electrons in polar bonds,

"Our supposition is that although in chemistry we can describe a "shared electron pair" to mean that the electron pair exists in some space between the atoms in a molecule, in the everyday English language "to share" means "to possess or use or endure jointly" (Pocket Oxford Dictionary, 1964, p.759)."
Peterson et al., 1989, p.313

It is notable that polar bonds seem to be taken as a sub-category of covalent bonds, rather than a class of bonds intermediate to covalent and electrovalent (see §11.6).

Two of these authors report quantitative results from the the covalent bonding and structure diagnostic instrument (Peterson and Treagust, 1989) based on the data from the 84 grade-12 students in the sample. Eight of the misconceptions were found to be commonly chosen by these students:

nonpolar molecules [only] form when the atoms in the molecule have similar electronegativities (34%);
strong intermolecular forces exist in a continuous covalent (network) solid (33%);
bond polarity determines the shape of a molecule (27%);
the shape of molecules is due only to the repulsion between thel bonding electron pairs (25%);
equal sharing of the electron pair occurs in all covalent bonds (23%);
intermolecular forces are the forces within a molecule (23%);
the shape of molecules is due only to the repulsion between the
nonbonding electron pairs (22%);
nitrogen atoms can share five electron pairs in bonding (20%).

The abstract nature of this topic area has been acknowledged by Staver and Halstead, who used a post-test to investigate 84 students' understanding of chemical bonding and geometry after instruction, in one U.S. high school (Staver and Halstead, 1985). The published report does not give details of the questions, nor consideration of the specific difficulties students may have had. The authors do conclude however that,

"The results indicate clearly that reasoning capacity influences post-test performance as expected. Molecular geometry, shape and polarity are abstract concepts that require formal reasoning [i.e. Piagetian stage] to fully comprehend. … Shape and geometrical concepts, however, also require spatial reasoning…"
Staver and Halstead, 1985, p.442

§3.2.5: Crystal lattices

In their study of students entering University to study science, Cros and coworkers found that crystals "remained a mystery for most" (Cros, et al., 1986, p.309). When asked about the interactions in a crystal 42% of the students did not reply, and 15% gave incorrect or completely inadequate information. Only 27% of the students referred to a clearly defined arrangement of atoms or ions" (p.309). After one year of University study the interactions within the crystal were described as "somewhat less mysterious" to the students (Cros et al. 1988, p.344) as there was some mention of ionic bonds between the constituents (19%), and an increased mention of electrostatic interactions, although only from 8% to 18%" (p.334).

§3.2.6: The ionic bond

Butts and Smith (1987) undertook research to follow up a survey finding that the difference in properties between ionic compounds and molecular compounds had been rate as a difficult topic by 29% of students asked. Butts and Smith interviewed 26 high school chemistry students about this topic. They found that most of those surveyed associated sodium chloride with ionic bonding, which is appropriate, but that the students often also volunteered a description of the electron transfer event (i.e. from sodium atom to chlorine atom) which could result in the formation of the bond (Butts and Smith, p.196). In other words, it appeared that their thinking about ionic bonding was focussed on the process of ion formation, rather than the nature of the bond itself.

Ten of the students (almost 40% of this small sample) referred to molecules of NaCl (p.196). In the NaCl lattice each ion is bonded by electrostatic forces to six nearest neighbours (of opposite charge), and this symmetry leads to a giant ionic structure. From a curriculum science perspective it is not considered appropriate to conceptualise any discrete sub-units of the crystal lattice, above the level of the ions themselves. (The notion of the unit cell is used by crystallographers to represent the various lattice parameters economically, but this is not seen as a discrete structural unit.) The molecule concept is inappropriate in this context, as it implies a structurally significant sub-unit, such as NaCl ion pairs. It would only be meaningful to discuss the lattice structure as composed of ion pairs if the interactions within specific pairs differed from those between pairs, which is not the case in a perfectly symmetrical lattice. Four of the students interviewed actually proposed such a distinction: either that the 'NaCl molecules' had internal covalent bonds, but were ionically bonded to other molecules, or vice versa (p.196).

Some related conceptions were uncovered when the students were shown 'ball and stick' models. In such a model each ion is represented by a ball, and is attached to each of its six counter-ion neighbours by a wire, which could be seen to represent the electrostatic interaction (but also functions to hold the model together). In this model, the ionic bonding is the overall effect of all the wires (electrostatic forces) linking the lattice of balls (ions). Again this was not always appreciated: one student thought that the six wires represented one ionic bond, and five "physical" bonds (p. 196). Another student expected seven wires "because chlorine has seven electron in its outer shell" (p.196).

Butts and Smith reported that some of the students did not think there were ions in the solid (e.g. that "solid sodium chloride doesn't conduct because it is in separate molecule") – but that the ions were formed on dissolving. Two of the students believed that dissociation only occurred if electricity was applied (p.196).

In chapter 11 results from the present research will be presented which reflect some aspects of this literature: the close association between ion formation and bonding (§11.2.2); the number of bonds being limited by valency (§11.5); and reference to ionic molecules (§11.4.3).

§3.2.7: Intermolecular bonding

Three of the students interviewed by Butts and Smith did not appreciate the nature of a molecular solid, where discrete molecules are held in lattice positions by intermolecular forces, which are weaker than the intramolecular bonding. These students thought a grain of sugar was a single molecule (c.f.§3.1.2), and had a giant structure like diamond (Butts and Smith, 1987, p.196).

In their study of Canadian students (at 'sixth form' level) Griffiths and Preston reported that some thought that the molecules in ice were not bonded in any particular pattern (Griffiths and Preston, 1992).

§3.2.8: Bond energy

Bond formation is an exothermic (energy-releasing) process, and bond breaking is endothermic. Indeed the 'driving force' for chemical processes is often said to be the free energy change (which must be negative for a feasible process), and bond enthalpies are often the major contributor. The greater the bond enthalpy, the more energy required to 'break' the bond, and the greater is said to be the 'bond strength'.

Hapkiewicz (1991) has commented on two common 'misconceptions' found in high school students (her evidence is a combination of the anecdotal, and a consideration of text-book treatments). The main focus of her article is the notion of 'energy rich' bonds. This is usually met in biology when the function of ATP in metabolism is considered. The conversion of ATP to ADP is used to provide the cell with an energy source: and thus the broken bond is often referred to as an 'energy rich phosphate bond', which implies that energy is released on bond fission. As Holman (1986) comments "confusion is reflected in, and compounded by, the tendency one still sometimes meets to describe ATP as containing a high energy bond" (p.49). In fact energy is required to break this bond (as indeed any bond), and the misconception may arise from not considering the net effect of all the bond fission and bond formation steps that are part of the chemical reaction.

Hapkiewicz also notes that students may believe double bonds are easier to break than single bonds. This notion arises from the higher reactivity of many organic compounds with double bonds – for example alkenes readily undergo addition reactions. The difficulty here is that the double bond need to be understood as comprised as two components: the sigma (s) bond, and the pi (π) bond. The pi bond is relatively readily disrupted, and addition reactions involve electrophilic 'attack' at this site. However the sigma bond is not broken during these reactions. The bond enthalpy for the double bond would refer to the fission of both components, and is therefore greater than for a single bond – although not usually twice as large.

§3.2.9: Bond formation and chemical change

Chemical processes – 'reactions' – involve the reorganisation of systems of atomic cores (i.e., a core being the nucleus plus inner electrons) and valence electrons. In other words, reactions involve changes in bonds. Understanding of chemical bonds is therefore closely related to an understanding of chemical change – and the explanations given for why reactions occur.

Some previous research has suggested that learners may have alternative conceptions regarding chemical change. Pfundt found that in a sample of thirty 8 – 13 years olds substances involved in chemical processes were commonly considered either to retain their identity, although changing their properties, or to be destroyed (reported in Briggs and Holding, 1986, p.7). This compares with a scientific view that reacting substances are changed into different substances, but the matter from which they are comprised is conserved.

This scientific perspective is based on conceptualising substances in terms of molecular particles, that in turn are made up from smaller units. The substance is defined by the molecules it is comprised of. As the molecules are changed in chemical processes, new substances are produced. Conservation occurs at the level of the molecular sub-units: these retain their integrity, but reorganise into new configurations. It is conventional to consider the conserved units to be the atoms, although this is not strictly correct (§12.4.5, §12.5).

Clearly, although scientists have a powerful model for explaining chemical change in terms of conserved entities, it is an abstract scheme. Learners who have not mastered the particle model of matter could not be expected to appreciate the scientific meaning of 'pure substance', nor understand what it is that changes ('is destroyed'), and what retains its integrity ('its identity') during chemical reactions. Pfundt's findings are therefore not surprising if the appropriate theoretical constructs (such as those discussed earlier in this chapter, §3.1) are not available to learners.

Briggs and Holding (1986) analysed a sample of responses to an A.P.U. (Assessment of Performance Unit) survey item on chemical change. 15 year olds were given a description and diagrams to show what happened when some material was heated in a test tube. The students were asked to give observations that supported a view that a chemical change had taken place. The information given showed that after heating (and allowing to cool) the contents of the test tube had changed in four ways: an increase in volume, a decrease in mass, a change in colour, and the the

material no longer appeared granular. Of 277 scripts examined, 45% gave only observations, and 41% related these to ideas about chemical change (although it should be noted only observations were specifically requested in the question). Of these, more of the responses were categorised as giving alternative ideas than accepted (scientific) ideas (23%, c.f. 18%, p.60). Alternative, or ambiguous, notions included:

a change of state was presented as evidence of chemical change by "one in ten of all responses" (p.63).
the substance had "disolved" [sic] (p.64) – although it was not clear what the solvent might be. Again a physical change is suggested as evidence of a chemical process. Briggs and Holding found the notion of dissolving was also used to describe the reaction of zinc and sulphur in responses to another A.P.U. question (pp.76-77.)
the amount of chemical increased, there was more of the chemical after heating (p.64.) This probably refers to volume, whereas chemists would consider amount of a substance in moles, or in terms of mass. A change in density is interpreted by respondents as more chemical.
the particles [granules?] had broken up and made more (p.64). This almost seems a magical explanation. (The same respondent went on to refer to "the juice of the orange" rising up the tube, perhaps misinterpreting what was meant by an orange chemical (p.59) in the question.
the material expanded and/or changed colour due to the heat (p.65), i.e., again a physical change was envisaged – although this should have been reversed on cooling. (It might be more correct to suggest that these respondents lack the distinction between physical and chemical changes.)
the material was richer before heating, and weakened on expansion (p. 65) – here terms (richer, weakened) seem to be used in some metaphorical sense, although it is not possible to be confident of such an interpretation. In response to another question one student wrote that "the sulphur is obviously a more powerful substance than zinc", and again it is unclear quite what the student meant.
the decrease in mass was used to make the change (p.65.)

Just as learners might be expected to have difficulties with notions of substances changing in chemical reactions, it is also difficult for learners to conceptualise how and why chemical processes occur without the scientific particle model. Schollum (reported in Briggs and Holding, 1986, p.8) interviewed 11 to 18 year-olds to find out their ideas about chemical change, and found alternative conceptions which were categorised as

the conglomerate view, in which all the reactants merely join up rather like pins to a magnet;
the 'favourable circumstance' view: this maintains the idea that the reaction products were really hiding there all along and when conditions were right they revealed themselves;
the 'it's magic' view, in which anything could happen once the chemicals set each other off.

§3.2.10: Consequences for the present study

Although a number of studies relating to learners' ideas about chemical bonding have been found in the literature, the body of work discussed is limited. For one thing none of these studies have reported the results of working closely with individual learners to assess the progression of their thinking.

The literature reported is based on curricula in a number of countries. The French work reported by Cros and coworkers (1986, 1988) is of interest, although it is difficult to believe that such a small number of post A-level Chemistry students in the U.K. would refer to ionic bonding. The different curricula in the two countries would seem to emphasise the boding topic to a different extent. (In the British system however, some students entering University to study physics, or mathematics may well not have studied chemistry post-16; where in France the baccalauréat system ensures a common background for science students.)

The literature reveals a number of 'misconceptions' about chemical bonding, although simply listing these does not illuminate their origin, nor suggest how teachers can best avoid/overcome them. It has been pointed out that bonding is an abstract topic. Zoller reviews a number of topics that give College freshers difficulty in chemistry, including the quantum model of atom; Lewis acids and bases; and electrophiles and nucleophiles; the reactivityof multiple bonds; and inductive and mesomeric effects in aromatic substitutions. These are topics which either relate directly to bonding, or are described and explained in terms of the same underlying models and principles (electrostatics, orbitals, etc.) Zoller makes the point that the difficulty of chemistry is not just due to its abstract nature, but to the range of – what I have referred to above (§1.3.1) as – concepts formed by bootstrapping one on another,

"The relatively large number of difficulties and student misunderstandings and misconceptions in freshman chemistry are probably due to the many abstract, nonintuitive concepts which are not based on, and/or derived from, and/or interrelated logically with one another, at least not in a simple and straightforward sense. Furthermore, the lack of one common denominator or a simple integrating conceptual scheme for all these complex concepts and subconcepts, and the consequent difficulty in the use of the same approach for different cases and different systems, call for different, specifically designed teaching strategies for coping with the difficulty and misunderstanding in each case."
Zoller, 1990, p.1063, italics in original

I hold a similar perspective to Zoller (§1.3.1, §1.7.1), and it is this feature of chemistry that makes the exploration of learners' ideas, and how they develop, important for those hoping to illuminate the learning and teaching of chemistry.

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