Misconceptions re-conceived

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Why the effective teacher pays heed to the aufbau principle of learning

Taber, K. S. (2002) Misconceptions re-conceived: why the effective teacher pays heed to the aufbau principle of learning. A position paper for the virtual asynchronous RSC conference on 'What does a chemistry teacher need to know?' March 2002

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Abstract:

In this paper it is argued that there are three domains of knowledge that an effective teacher needs to call upon: knowledge of their subject; of the students; and of the pedagogy of the subject. The present paper focuses on a topic that links all three domains: alternative conceptions.

Introduction: three domains of knowledge

To teach effectively it is necessary for the teacher to have knowledge from at least three disparate areas, or domains. Obviously, perhaps, the teacher needs to know about the subject. To teach chemistry effectively it is important to have a good personal knowledge of chemistry. This may seem something that we should take for granted, but in the UK secondary system there is currently considerable concern that the policy of 'balanced science for all' up to age 16 is being serviced by a work-force that is increasing biased away from the physical sciences, and towards the life sciences in terms of degree background (and therefore, presumably, areas of specialised knowledge, and interest!)

The second domain is knowledge of the students themselves: their interests, motivations, aspirations, current levels of attainment, concentration span, prior knowledge, preferred learning styles and so forth. Again this may seem very obvious, at least to anyone with a teaching background.

The third domain is that of subject pedagogy: a knowledge of how to teach the subject. This has at least two components: a general knowledge of how learning occurs, and how it may best be facilitated, and a more specific aspect where these general ideas are applied in the context of the particular subject. The subject pedagogy provides insight into teaching order, appropriate pacing of topics, ways to approach topics, how to introduce and reinforce abstract concepts and so forth.

In my own view this key aspect of a teacher's professional knowledge is not always taken as seriously as it should be: at least not in the UK. There are many reasons for this. For one thing the science of learning theory is much less well developed than the science of chemistry (at least, the bits of chemistry considered at the level that relates to school science). Secondly most chemistry teachers are experts in chemistry, but – at best – enthusiastic amateurs in the psychology of learning. To some extent the same is true of their university tutors. This is not meant as a criticism: education is a rather broad discipline largely comprising of specialists from other fields who have moved into being educationalists with various degrees of professional training in the field! To be considered qualified to train teachers in the pedagogy of science: a background in science and the practice of teaching is seen essential, a knowledge of learning theory is merely an advantage!

There is perhaps some difference here between those teachers trained through degrees that prepared them as science teachers (and who are likely to have been taught by 'real' psychologists and other specialists), and those who graduated in their teaching subject (e.g. chemistry) before taking a separate teaching qualification. The latter are these days likely to be introduced to theories of how people learn by tutors who themselves have a limited background in psychology. Of course the current trend in teacher training in the UK is away from first degrees to post-graduate courses. The move to put most of the one year post-graduate teaching training time into schools rather than universities has only made this situation more extreme. Whilst many school-based mentors provide excellent induction into teaching practice, they are even further removed from an expertise in learning theory: often having little more than vague recollections of ideas they may have met during their own training.

This is a great shame, as if we wish our teachers to be critical and reflective practitioners it is essential that they should have access to a suitable knowledge base through which to interpret classroom observations, as well as the opportunity to observe and experience teaching. Of course, practising teachers will have their own tacit theories of teaching and learning, but research shows how limited and inappropriate these may be (Fox, 1983). The most astute and capable practitioners may spend time re-inventing and re-discovering the wheels of existing learning theory – while their less talented colleagues may often operate with a very impoverished theoretical underpinning for their practice.

What learning theory has to offer

There are a number of principles from (what we might term) the psychology of learning which inform teaching (Taber, 2002). Research into memory shows us the importance of reinforcing new ideas if we wish the learner to retain ideas met in lessons over a long period. That is, we cannot think of learning as a once-and-for-all action: rather it is a process that takes place over a considerable time period. Other research reminds us that learners are easily overloaded with new ideas and can only manage to hold a limited amount of new information in mind: too many ideas, or ideas that are too complex in relation to the learner's current understanding, will soon overload capacity. However, it is also clear that the apparent complexity of new information can not be judged in absolute terms: it depends on the way the material is conceptualised by learners. The key here is how new ideas are interpreted in terms of the learner's existing conceptual frameworks.

Indeed, the learner's prior knowledge is a key determinant of both the quality and quantity of learning that can be expected. Where a learner has full and accurate background knowledge for a topic, that is appropriately organised, then she is in a position to learn effectively from the teacher's presentation – as long as the links between new learning and prior knowledge are made clear. Where the learner has 'deficits' in the expected prior learning, is unable to perceive the links with previous learning, or holds alternative conceptions for key areas of knowledge, then any intended new learning becomes unlikely (Taber, 2001a).

Once new ideas are met the learner will need time to appreciate just how they fit in with existing knowledge, and perhaps even require an adjustment to existing frameworks of knowledge. Those who are familiar with the work of Piaget may think in terms of new ideas being assimilated, leading to a dis-equilibrium where new ideas do not entirely fit with previous knowledge structures, and so requiring an accommodation. Where 'working memory' seems to be like RAM in a computer (and is easily extinguished), long-term memory traces are not readily erased (if at all) and altering established conceptual structures takes time. (Some observers have suggested that sleep may be a state where long term memory can be laid down, or at least, new learning can be better integrated with previous learning.)

Ideas such as these provide a perspective that can inform good teaching. The teacher who recognises the importance of prior learning, and appreciates the need to present material in a way that relates to existing knowledge, and at a pace that does not overload the learner is in a position to design effective teaching episodes. Even though misjudgements will still be made, increasing teaching experience allows a fine-tuning of the approach: the teacher is operating in a way that is informed by learning theory.

An aufbau model of learning

Jean Piaget (in many publications, e.g., 1929/1973) long ago presented a model of the child as naturally inquisitive: exploring the environment, making observations, and developing mental models of the world which might need to be modified in the face of future experiences. George Kelly (1955/1963) used the metaphor of man-as-scientist: that each of us develops our own personal (and unique) way of making sense of the world. Ideas such as these have informed science teaching, so that Driver wrote of the pupil as scientist – coming to class with a range of models and personal theories already in place (1983). However, these pupils were not 'ideal' scientists who would readily be rationally persuaded by the teacher's words, or their own observations, to change their minds. Rather, these pupils were more like the scientists described by Thomas Kuhn (1970) in that their thinking was constrained by their existing mental models, and – as Driver herself noticed – sometimes saw what their existing ideas predicted rather than what 'actually happened'. This is an important point when so much practical work is designed to help pupils appreciate the scientific models (and much more of an issue when an exploratory or 'discovery' heuristic is used in teaching!)

It is worth noting here, that none of this should be seen as meant to be critical of pupils, or of scientists for that matter! That humans have evolved and survived so long suggests that the way our brains operate can not be 'all bad'. The human brain is to some extent 'prepared' (or hard-wired) to develop in certain ways because this has been selected in human environments over many generations, but clearly not to the extent of having detailed scientific models built-in! We seem to have brains that readily pick up key patterns such as 'closer often means stronger' and 'more means more effect', but we are not born with the inverse square law or a definition of pH in place!

So, the human child, born with a mind that is hardly a tabula rasa, but largely lacking in useful models of the world, goes about constructing such models so that she can make sense of, and survive in, the world. (Not a blank slate, but a mental note pad with the lines and margins already in place perhaps?) The child observes the world, and acts in it, and notices patterns, and constructs models that help make predictions about future interactions. Where predictions fail, the models may need some adjustment. Occasionally they may need a complete overhaul or overthrow: but the benefits of building a new model may have to be balanced against the potential hazards of coping with operating without a model in the meantime. With both children and scientists there may be sensible reasons to sometimes hold on to an imperfect model until you are sure you have something better to replace it! (Thagard, 1992; Taber, 2001b).

This perspective on learning seems common sense. Children are not born knowing about the world. They come to know through experience. They draw generalisations from limited data, and sometimes draw the wrong generalisations. Starting virtually ab initio, the child has little choice than to construct knowledge of the world piecemeal and often haphazardly. This aufbau model of learning is called constructivism, and although much discussed, is surely based on common sense. (The controversies around constructivism are at the levels of the status that should be accorded to pupils' alternative models, and the extent to which teachers should actively direct the construction process.)

So far this account of the child building up their knowledge structures, or their 'cognitive structure', has ignored a very important factor: other people. Piaget is often criticised for seeming to ignore the role of others in the child's learning. For Piaget, others seemed to be just another aspect of the learners' environment. His contemporary Vygotsky however emphasised the importance of others (teachers and peers) in a child's learning (1978).

At first sight this may seem to suggest that my image of the lone learner trying to build up a model of the world will grossly over-estimate the likelihood of the pupil coming to class with beliefs about the natural world which are at odds with what they are to be taught. After all, humans are social creatures, and we have language to share culture. This is very true: but does not always solve the problem.

Children do negotiate meanings with those around them, but most of the early learning goes on in the presence of non-chemists, and in the absence of the chemistry teacher! Friends, siblings, parents etc., will certainly help the child to enter into the social world, but they cannot be assumed to either prioritise chemistry as a key area for discussion, nor to hold suitable expertise in the subject! As is well recognised, the versions of science that circulate in general society are often at odds with the authentic versions that scientists would recognise. Folk science can be a source of misinformation, just as the intuitive theories the child builds for herself.

'Misconceptions' in science

The outcome of this wonderful learning process that every human child undergoes – largely unprovoked – is a rich and varied cognitive structure full of ideas about aspects of the world. Some aspects are highly integrated, coherent, and logically organised. Other features are not! Some ideas are strongly believed, but others are only tentative. Sometimes learners' cognitive structures are parsed in ways that seem odd: conflating concepts that we see as separate (such as having a notion of 'electricity' that is a mixture of what we would label current, potential difference, energy etc.), or storing separately items that we think of as linked. They may also have manifold conceptions for the 'same' item. This may be because they hold 'life-world' (everyday) versions in parallel to the version taught in school. or because they are in the process of building a new model that is not yet ready to take over from a previous version.

Physics and biology teachers may often find evidence of pupils' intuitive thinking in their classes. One of the best documented 'alternative conceptions' is the notion that a force will enable a body to move a certain distance, before the effect of the force is somehow 'used-up', and so the velocity of a body is proportional to the applied force (whereas in the absence of any other forces, an applied force will actually lead to a continuing increase in velocity). Teaching about Newtonian mechanics will be impeded by this belief, and the physics teacher needs to be aware, and to plan to persuade pupils of the scientific model. In a similar way, biology teachers explaining photosynthesis should take into account the common belief that a plant gets all its matter from the soil through the roots, rather than obtaining a significant amount from the carbon in the air.

Knowing about these common 'misconceptions' is an important part of the science teacher's pedagogic subject knowledge, and is as important when planning lessons as knowing the science in the curriculum. If pupils did present as tabula rasa then a good subject knowledge should be enough to plan the sequence and approaches of science teaching. However, in practice, pupils' minds are teeming with ideas of various degrees of match with the curriculum, and there is plenty of research evidence that an approach that ignores pupils' existing ideas is unlikely to bring about permanent changes in those ideas.

Alternative conceptions in chemistry

Although the central science, chemistry may not seem as central to everyday life as physics and biology. It is certainly there and important, but it does not usually have the same profile in 'folk science'. Nevertheless, there certainly are examples where pupils can brings ideas from their 'life-world' experience that can interfere with the learning of chemistry.

One example is the concept of acid, where pupils normally regard all acids as highly dangerous and corrosive, and take some convincing that pure rain, vitamin C, and fruits may be acidic.

To some extent this is an example of a technical word having a different meaning in everyday parlance (Watts & Gilbert, 1983). Other examples are the use of the words 'natural', and particularly 'pure'. Many products labelled pure (as in unadulterated) are certainly not pure substances in chemistry. Pure orange juice ceased to be pure when it is brought into the lab. (which perhaps may be another good reason for pupils not bringing food into science lessons!)

Linguistic cues can also be highly suggestive, when they are use to make inferences about new words (Schmidt, 1991). So neutralisation (a concept unlikely to be met in everyday life) is often assumed (quite reasonably, I would suggest) to always give a neutral product; and neutrons may be assumed to neutralise the effect of protons to stop them repelling each other out of the nucleus.

Being aware that pupils are likely to make such connections is important preparation for the teacher planning the lesson. Similarly, it is useful for the teacher preparing to teach the topic of isomerism to know that students commonly limit the notion to within a particular type of compound. Knowing this the teacher can emphasise examples that go across categories (e.g. ethers and alcohols) as well as within them (e.g. primary and secondary alcohols).

Alternative frameworks in chemistry

It would be possible to leave the theme at this point and summarise. After all, the point has been made that, firstly, pupils bring ideas from their 'life-world' knowledge, and make inferences from linguistic and other cues, which interfere with them learning the chemistry we try and teach; and, secondly, that being informed about such research findings can prepare the teacher to plan more effectively.

However, there is a further point to be made, that makes less pleasant reading, but is at least as important. This is that many alternative conceptions in chemistry derive, at least in part, from chemistry teaching. Whereas pupils come to class already 'knowing' about acids, they are unlikely to already have 'life-world' knowledge about neutralisation, neutrons and isomerism. And in the latter case, there is no obvious linguistic cue to send them in the wrong direction.

A more extreme case concerns the 'octet' framework: an alternative conceptual framework which has been found to be very common by the time pupils are about 16 (Taber, 1998). This is a connected set of ideas, at odds with chemistry, that are hardly likely to be brought to the classroom from everyday learning.

Many pupils hold a sub-set, if not the full range, of these ideas: reactions occur between substances which are always in the form of atoms, reactions occur so that atoms can obtain full shells (something they want, and need); when covalent bonds break the electrons always return to 'their own' atoms; ionic bonds only occur between atoms which have had an electron transferred between then (so much for precipitation reactions!), so atoms can only form ionic bonds with the same number of other atoms as their valency allows; species with full shells (which is taken to mean eight electrons in period 3 and above) are more stable than those without (so that Na^7- is more stable than the Na atom), etc.

Even if this framework is not actually, intentionally, 'taught' in science classes, it is clearly learnt there – for pupils are hardly likely to hear discussions of ionic bonding at the breakfast table, or exchange stories of electronic configurations in the playground. This common alternative framework (which has proved very hard to overcome when students study at College level for A levels) has been inferred from science teachers and the textbooks used in schools. Here is an area where teachers need to understand the consequences of what they are teaching, and use this to inform more effective instruction.

Teaching informed by the three domains of knowledge

This brings me back to my starting point. Teaching chemistry effectively requires the teacher to draw upon three distinct domains of knowledge. Clearly the teacher's own chemical knowledge should reflect accepted scientific ideas, and should provide a suitable basis for teaching. Just as important, the teacher needs enough pedagogic knowledge to appreciate how the subject is structured, and how to relate this to what we know about the psychology of learning. The teacher needs to be able to interpret the curriculum science at the 'optimum level of simplification' (Taber, 2000) that makes it meaningful and manageable for pupils, but provides authentic models that support later progression. In particular, the teacher needs to know about the common alternative conceptions that pupils tend to bring to class, and the common habits of mind (Andersson, 1986; Watts & Taber, 1996) which so often lead to pupils drawing inappropriate inferences in chemistry classes.

In the abstract such knowledge can be classed as 'pedagogic' knowledge. However, it is of course essential to bear in mind the learners as well! As well as having different aptitudes, learning styles and motivations, different pupils also arrive with different levels of background knowledge, different repertoires of alternative conceptions, and different tendencies in interpreting teaching. Exploring prior learning is therefore an key, and time-effective activity. As every learner is a unique individual, effective teaching means using knowledge of the learners to customise a general plan (base upon subject and pedagogic knowledge) to produce a specific lesson for the particular pupils in this class. The effective chemistry lesson is informed by the science, knowledge of how chemistry is learnt, and knowledge of what the pupils already think they know about the chemistry.

References:

Andersson, B. (1986) The experiential gestalt of causation: a common core to pupils' preconceptions in science, European Journal of Science Education, 8 (2), pp.155-171.
Driver, R. (1983) The Pupil as Scientist?, Milton Keynes: Open University Press.
Fox, D. (1983) Personal theories of teaching, Studies in Higher Education, 8 (2), 1983, pp.151-163.
Kelly, G. (1963) A Theory of Personality: The Psychology of Personal Constructs, New York: W. W. Norton & Company (taken from The Psychology of Personal Constructs, first published 1955).
Kuhn, T. S. (1970) The Structure of Scientific Revolutions (2nd edition), Chicago: University of Chicago.
Piaget, J. (1973) The Child's Conception of The World, St. Albans, U.K.: Granada (first published in Great Britain by Routledge & Kegan Paul, 1929).
Schmidt, H-J. (1991) A label as a hidden persuader: chemists' neutralization concept, International Journal of Science Education, 13 (4), pp.459-471.
Taber, K. S. (1998) An alternative conceptual framework from chemistry education, International Journal of Science Education, 20 (5), pp.597-608.
Taber, K. S. (2000) Finding the optimum level of simplification: the case of teaching about heat and temperature, Physics Education, 35 (5), pp.320-325.
Taber, K. S. (2001a) The mismatch between assumed prior knowledge and the learner's conceptions: a typology of learning impediments, Educational Studies, 27 (2), 159-171.
Taber, K. S. (2001b) Shifting sands: a case study of conceptual development as competition between alternative conceptions, International Journal of Science Education, 23 (7), 731-753.
Taber, K. S. (2002) Misconceptions in chemistry: prevention, diagnosis and cure?, London: Royal Society of Chemistry.
Thagard, P. (1992) Conceptual Revolutions, Oxford: Princeton University Press.
Vygotsky, L. S. (1978) Mind in Society: The development of higher psychological processes, Cambridge, Massachusetts: Harvard University Press.
Watts, D. M. & Gilbert, J. (1983) Enigmas in school science: students' conceptions for scientifically associated words, Research in Science and Technological Education, 1 (2), 1983, pp.161-171.
Watts, M. and Taber, K. S (1996) An explanatory gestalt of essence: students' conceptions of the 'natural' in physical phenomena, International Journal of Science Education, 18 (8), pp.939-954.