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Approaches of PCK: verbal, visual, artefacts and actions

This writing draws together the descriptions of the various narrative metaphor approaches described by teachers and those used in computing text books. The full pyramid now reflects that the narrative metaphor represents pedagogic content knowledge by some 16 different approaches.

It is now proposed that those approaches can be placed on a spectrum or construct. The value of doing this is to better explain to teachers the significance of the characteristics of each of the approaches and thus indicating when the strategy might most profitably be used.

    

Construct of approaches: cognitive to physical

An important aspect of the theoretical narrative metaphor is visual representation. The importance of the visual image in pedagogic content knowledge in general has been established (Hill, 1997; Sowa, 1984; Turner-Bisset, 2001; Vile and Polovina, 1998) but the rôle in computing appears to be dominant.

Is that dominance of the visual narrative metaphor coincidental with the image schema metaphor that is representative of cognition?

The following table matches curriculum topics to diagrammatic approaches and the diagrammatic approaches are matched to image schema.

Pedagogic blending

The blending of pedagogic approaches is an important element of pedagogic content knowledge. Its importance is reflected in the fact that teachers note that they use more than one strategy to support the students’ learning. Blending is the simultaneous use of more than one strategy. Two examples were presented when considering the curriculum topic “recursion”. The approach adopted in the text book Understanding Computer Science (Bradley, 1999: 387-392) blends the algorithmic and kinaesthetic. The concept of recursion is described using a Tower of Hanoi toy. The physical placing of one block upon another is complemented with a stated algorithm. The playing of the game seeks to minimise the number of moves. Playing the games enables students to develop a repeated pattern of moves. That pattern of moves is equivalent to the procedure that is called recursively.

 (Bradley, 1999: 387 fig 18.9)

Figure 39 blending algorithm and kinaesthetic - Tower of Hanoi

The textbook then explains the process through the use of pseudocode. The Tower of Hanoi metaphorically represents the computer program being executed (upon).

An alternative approach is to begin with the recursive algorithm that is then applied to the Tower of Hanoi. The Tower of Hanoi, in the same way, is representative of the processes of the computer - the program (Green, 2003). This blending of the kinaesthetic (moving of the discs from one pin to another) and the algorithmic combines features that complement the kinaesthetic and visual learner. The third example of this blending also supports the auditory learner. Interview 11 reports “recursion; yes, I use the Tower of Hanoi. I find that they spend a lot of time "playing" with the discs. I get them to think of a pattern that they repeat. I encourage them to chant the pattern. They discover the small unit of code that is repeated within it”.

Pseudocode recursion

John Woollard (February 2004)