Where does motivation come from? Person's motivation may be a personal treat but is also nurtured by the prevailing culture. The argument that the progress of technology necessitates deeper understanding and better mastery of mathematics does not and can't work well with the students in so far as it does not correspond to the observable reality. Children watch their successful parents that did well mostly oblivious of the development of mathematics.
Nancy Rosenberg (1970) describes the lack of credibility and the power of conviction in the common arguments:
- The study of mathematics develops orderly thinking habits and a disciplined mind.
- Surely educated people should have some understanding of the mathematics that makes all this possible (from designing aircraft to predicting the weather.) And facility with numbers is a practical necessity. Without it we cannot balance our budget, compute our taxes, or understand what we read in the newspapers.
Writes she:
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Neither of the arguments had much appeal for the students, because neither related directly to their experience.
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More than that, children's every day experience directly contradicts both arguments. This was true three decades ago as much as it is today. These arguments did not work in the belligerent world of antiquity. We all know that the Romans were not interested in science notwithstanding the incredible feasts perpetuated by Archimedes in defense of Syracuse.
On the other hand, history affords us examples when changing attitude, the prevailing culture did successfully lead to flourishing of mathematics and mathematics education. Take, for instance, Germany of the first half of the 19th century. "Between 1800-1820 there was only one really important mathematician in Germany - Carl Friedrich Gauss - and young mathematicians used to go to Paris for more advanced studies. But only ten years later, the situation changed drastically ... the centre of mathematical activity had shifted to Germany" [Fauvel et al]. Among other reasons for the decisive change: "The education system became central in society, and teachers became the central agents. Secondary school teachers were given high social prestige - they stood for scientific values and took up the status of scholars." Kummer and Weierstrass became university professors after having careers as schoolteachers.
And more (p10): "The belief was unique to Germany at that time that the function of a professor was not only to pass the knowledge, but to create it too. The kind of mathematics promoted within these structures tended towards what we would call 'pure' mathematics. There was turning away from the old-style involvement of mathematics with practical and empirical problems..."
References
- Nancy Rosenberg, How to Enjoy Mathematics with Your Child, Stein and Day, 1970
- Möbius and his band, ed. J.Fauvel, R.Flood and R.Wilson, Oxford University Press, 1993
