Wednesday, 4 August 2010

Abstraction

This blog is a reflection on teaching abstraction using variation theory. Marton, Runesson, and Tsui (2003, p 6) have said that when teaching using variation theory, the teacher will use contrast, generalisation, separation, and fusion. Contrast helps identify specific features of the phenomenon. Generalisation helps identify similar phenomena or other phenomenon that are identical. Separation helps identify specific features or aspects of the phenomenon. Fusion is about simultaneous awareness and should help see the phenomenon as a whole.

When we look at abstraction, we are looking to move away from specific phenomenon to something that categorises a set of phenomena. This means identifying features that are common to the phenomena. Generalisation is seen as part of the process of identifying abstractions. This is looking for features that are common to the phenomena to which the generalisation is to apply. However, fusion also plays an important part in the sense of forming the abstraction. Seeing how the common factors work together to form the new entity, the abstraction.

From the perspective of cognitive processes, the emphasis with respect to abstraction is synthesis. That is exemplifying, classifying, and summarising. Anderson et al. (2001, p 276) define synthesis as putting together elements and parts so as to form a whole. I see it as making connections between ideas.

Abstraction is also about making connections in order to reduce complexity. Some details are ignored because they are either irrelevant or they belong to a specialisation of the abstraction.

My contention is that in order to teach abstraction, we need to help students see the commonalities, that is those things that are common to the phenomena, and to see or put aside those that are unique, or find ways to handle the unique features so that there is a common extension mechanism.

This process means that we need to highlight the similarities in part by contrasting them with what changes. Some of these will be easy to spot. Others will require some manipulation.

References

Marton, F., Runesson, U., & Tsui, A. B. M. (2003). The space of learning. In F. Marton & A. B. M. Tsui (Eds.), Classroom discourse and the space of learning (pp. 3-40). Mahwah, NJ; London: Lawrence Erlbaum Associates, Publishers.

Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., . . . Wittrock, M. C. (Eds.). (2001). A taxonomy for learning and teaching and assessing: A revision of Bloom's taxonomy of educational objectives Addison Wesley Longman.

No comments: