Does constructivism exclude direct instruction?

The mathematics guidelines assert that “while direct instruction is very important in mathematics children also need to develop their own learning strategies”

(NCCA 1999, p. 4). Direct instruction may appear to be in direct conflict with the earlier claim made in the guidelines that cognitive development is a product

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of social interaction between partners who solve problems together. If direct instruction is so important the issue arises as to how children can also be given opportunities to develop their own learning strategies. Direct instruction has always been popular in mathematics teaching. Indeed the very influential Cockcroft Report (1982), subtitled Mathematics Counts, stated that mathematics teaching at all levels should include exposition by the teacher. However, Cockcroft sought balance by also stressing the need for other forms of interaction such as discussion, practical work, consolidation of skills, problem- solving and investigational work. Cockcroft also concluded that there was one aspect of exposition, which was insufficiently appreciated; this aspect was questioning.

Questions and answers should constitute a dialogue. There is a need to take account of, and to respond to, the answers which pupils give to questions asked by the teacher as the exposition develops….. exploration of a pupil’s incorrect or unexpected response can lead to worthwhile discussions and increase awareness for both teacher and pupil of specific misunderstandings or misinterpretations.

(Cockcroft 1982, p. 72)

It follows that not only pupils’ errors but teachers’ errors also could bring about valuable learning experiences. It can be seen that Cockcroft took a very sophisticated view of what exposition by the teacher should entail. His view is more complex than the standard, closed three-part sequence of teacher Initiation, student Response and teacher Evaluation (IRE) of which Cazden (2001) writes. Cazden describes this pattern of discourse as being the oldest, “with a long and hardy life

through many decades of formal Western-type schooling” (Cazden 2001, p. 30). Cockcroft’s dynamic type of dialogue through questioning is essentially social

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constructivist in that both parties; teacher and pupil, are engaged in the negotiation of meaning.

However, are there any circumstances in which simply telling pupils information could be compatible with social constructivist pedagogy? Love and Mason (1995) state that there are many circumstances in which it is not only proper and effective, but essential to tell people things. For instance, Love and Mason (1995) suggest that “telling people something, in expository or explanatory mode, can be of positive

assistance, as long as what is said or explained is at the edges of what the pupils can do for themselves, rather than in the core” (Love and Mason 1995, p. 58). This is consistent with a social constructivist pedagogy in that the pupils in question may have misconceptions of which the teacher is aware or may have turned down a blind alley in their thinking and as a result the teacher attempts to help the pupils work at their zo-ped or at what Skemp (1995) terms their ‘frontier zone’ (Skemp 1995, p. 197). As Jaworski (1994, p. 62) cautions, “There has to be recognition of where a student stands and where she might reasonably reach”. In such cases the teacher’s dilemma can be summarised as ‘to tell or not to tell’. Love and Mason (1995) point out that “it makes sense to tell people things when they are in a state to be able to

hear, to relate to, to make connections with, and to assimilate what is being said and yet not be able to work it out quickly for themselves” (Love and Mason 1995, p. 34).

To tell or not to tell is a real dilemma for teachers when they are under curricular and time constraints. In such situations, it makes sense to tell pupils information, which hopefully cultivates further clarity in their thinking. Indeed, it may be essential in maintaining the pupils’ motivation and helping them avoid frustration. So far I have advocated ‘telling’ in situations where scaffolding has failed and the

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in classrooms where teachers espouse social constructivist principles pupils have to be organised so that they will work cooperatively and productively in groups. Through experience, a teacher knows which pupils will work best with one another. For instance, the teacher may be aware of personality clashes among pupils. A teacher may decide that a particular pupil would work better in one group than another. This may involve ‘telling’ the pupil that he would work better in an alternative group and discussing why so that the pupil can see the rationale behind his being moved. Another fundamental aspect of ‘telling’ occurs in the issuing of instructions to groups. Pupils have to be told of the nature of their activity, what equipment they may need and where they will be working. Such aspects of ‘telling’ may seem trivial but without the establishment of such routines or habits the classroom atmosphere becomes chaotic. Skemp (1995) describes habits as forming “an essential sub-structure of our daily life, since they free our conscious attention

for the non-routine and problematic” (Skemp 1995, p. 82). ‘Telling’ pupils clearly what they have to do in their groups ensures a productive use of time and enables pupils to devote their energies to higher-order tasks such as problem solving.

Even within problem solving activities there may be occasions when a teacher will ‘tell’ a pupil what to do. Let me give an example from my teaching experience. One

of my pupils was calculating the area of a floor 4.25m by 7.3m as part of a textbook problem solving exercise. My main objective for this pupil was to see if he understood the positioning of the decimal point in the answer. The pupil, not knowing his tables (basic number facts) very well, had written 5+5+5+5+5+5+5 to calculate 7X5. This twelve-year-old pupil had a legitimate but laborious strategy for calculating the tables. The dilemma I faced was whether or not to tell him the basic number facts as he worked through the computation. I decided to tell him the

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answers to the computations he found difficult as time was an issue and I wanted to see where he would position the decimal point. As I suspected, he did not realise that tenths multiplied by hundredths led to an answer in thousandths with three digits after the decimal point. Further scaffolding was needed at that point so I would argue that my ‘telling’ of the tables preceded and was subordinate to my scaffolding of the place-value concept.

What I am suggesting here is that “low road transfer is also necessary in

mathematics, so that the basic skills are automated in order to release the learner to use higher-order skills” (Open University, 1995, p. 120). Here I have illustrated ‘telling’ as the routinisation of the basic number facts. This aspect of ‘telling’

ensured the child and I had time to explore his understanding of the place-value concepts involved in decimal multiplication; such understanding being the primary objective of the lesson. Brophy (2006) puts it well when he states:

It appears that transmission techniques are best used for efficiently communicating canonical knowledge (initial instruction establishing a knowledge base) and social constructivist techniques are best used for constructing knowledge networks and developing processes and skills (synthesis and application).

(Brophy 2006 p. 534)

It may be that ‘low road’ knowledge, such as basic number facts, has to be regarded as a tool or even a cultural artefact, which can be used to release the pupil to engage in higher order cognitive processes such as problem solving. Furthermore, Hyslop- Margison and Strobel (2008) state that, in some circumstances, it is pedagogically acceptable to simply teach by lecturing, and lecture should not be entirely written out of a constructivist teacher’s repertoire. They suggest that “lecture, or direct

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instruction, is especially effective in classrooms where students already possess considerable subject knowledge” (Hyslop-Margison and Strobel 2008 p. 74).

Although the authors appear to be writing about adolescent students the point is still the same – there are times when it is appropriate to tell students information. I believe it is important to state that practicalities, such as time constraints, dictate that it is impossible to set up group learning situations for all aspects of knowledge acquisition. It is therefore essential to rationalise which aspects of knowledge need telling and which need negotiation in group contexts.

In this section I have suggested that ‘telling’ is justifiable in certain contexts. It may succeed scaffolding when the teacher believes she has no option but to tell. However, it can also precede scaffolding in situations involving the establishment of classroom routines, such as grouping, in the automation of basic number facts and, in general terms, the promotion of low road transfer to free the mind for higher order

processing. I leave my last words of qualification to Love and Mason (1995): For some reason, the idea of pupils making sense for themselves is often seen as

incompatible with telling them things… they are in fact entirely compatible. The point about telling people things is to choose carefully what to tell and when to tell it.

(Love and Mason 1995, p. 34)