Battleground Schools Summary

In reading this article I have formed several thoughts. Firstly the relation of mathematics education to politics. I find this particularly unsettling... as I have always viewed mathematics as transcendent beyond all corporeal concepts including politics, religion, culture, etc. Perhaps this view point regarding mathematics is apt it is apparently not so apt when applied to mathematics education. Throughout the past century educators have grappled between traditionalist approaches to mathematics education and progress approaches to mathematics education.

In regards to the New Math era it seems that the mantra of the epoch was to model all mathematics education in the style of Carl Friedrich Gauss, whose book Disquisitiones Arithmeticae set the tone and style for advanced mathematics textbooks until the modern age, which is to present mathematics neatly as beginning with a set of axioms, then proceeding to state and prove simple results known as propositions, then build up various theorems using propositions and lemmas proved, and a few pithy comments spread throughout to keep the reader in check. Modern textbooks would also have a few exercises in each chapter. This is strongly influenced by Gauss's personality as a perfectionist. Gauss was famous for destroying the scratch work he did before proving a result as to show the world only the 'perfect' mathematics. This is counter to how mathematics is actually done or learned however, and I believe this attributed to the failure of the New Math program.

Another key factor leading to the collapse of the New Math program is the 'golden age' effect. In essence, it comes to policy makers who are usually very gifted and skilled in the subject area, remembering that when they went through the lower grades of school that they were not challenged. They then inferred that adding a few 'simple' additions to the mix that 'anyone' can understand and learn would greatly improve education overall. These assumptions are not valid of course, as they usually use themselves (probably in the top 1-3% of the population) as the 'norm'.

In the current curricular reforms the battle between traditionalist and progress views again associates inflammatory politics into mathematics education. I personally feel that quantitative literacy is key to the longevity of a liberal democracy. As such it is certain that high quality mathematics education to all adults of society is crucial to the continued success of our democratic society. In particular all students need to be taught to not only carry out rote exercises but to interpret mathematical data, models, and statistics as to inform themselves about the current state of affairs in the economy and politics. Thus the conception that mathematics ought to be taught only to a few academic elites and then disseminated to the masses as needed is as outdated as the concept that only a few people ought to be literate and everyone else can get their information from those educated elites. Thus, reform in mathematics education is urgently needed.