November 14, 2007

Historical "Parallelism

Thomaidis and Tzanakis (2007, Educ Stud Math 66:165-183) conducted research about "historical evolutions and students' conception of the order relation on the number line".  They take this as the opportunity to discuss the "controversial relation between the historical evolution of mathematical concepts and the process of their teaching and learning". Is it possible then to follow this "genetic" approach instead of the formal axiomatic one? They cite Harper (1987) who appears to believe that the first approach is possible since the learning route is parallel to the historic one. They also cite Sierpinska (1994), who, on the other hand, believes that the similarities (Harper's parallel roads) are just that (similarities); there is nothing beyond some coincidences that emerge because of the use of language or because of specific mechanisms used when learning. Brousseau (1983) does not argue against using historical approach, but is completely against reproducing whole historic situations; this could be, not only confusing, but also uneconomic (timewise). Herscovics (1989) also finds common aspects between the procedure of learning and the historic evolution but since the modern learning enviroments are so different this "parallelism" should not be taken too literally, as it is asserted.

After presenting their research results, Thomaidis and Tzanakis elaborate the previous opinions a bit further and suggest that, one could exploit these similarities between the learning procedure and the historical development "to  foresee possible persistent difficulties of the students;  and to make teachers more tolerant towards their students' errors, by increasing their awareness that these errors and difficulties do not simply mean that the student hasn't studied enough, but may have deeper epistemological roots which should be explored and understood thoroughly".

What I see through this article, is once again the need for the maths teachers to be educated about the history of the discipline that they teach. In this case, being aware of difficulties encountered in the past, they may actually get to understand students' weakenessess and be more able to help with it. If they are completely unaware of how a notion evolved, they will have their own experience alone to guide them throught the teaching of this notion. Students, moreover, need to know that they do have someone to rely upon, when things just make no sense.

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