The introduction to Bill Higginson's "On the Foundations of Mathematics Education" begins with reference to Gulliver's travels, remarking on the far-reaching societies that Gulliver encounters on his voyages. A quoted passage discusses how a math educator attempted to teach his pupils by giving to them a wafer to eat, upon which the theories they were to learn were written. From this passage, I imagine that Higginson will begin to discuss how math education is often conducted en masse, in a one-size-fits-all style, where the teacher is the keeper of the knowledge to be transferred to the pupil. The teacher will offer up their wisdom for the students to nourish themselves on, with hopes that they will be able to digest the offering. Higginson, I imagine, will discuss how math education treats the students who find these offering “too nauseous” to be able to digest, and will offer alternative ways of approaching math education instead of this top-down approach, where the teacher is the purveyor of wisdom.
On further reading, Higginson reveals his thesis statement: “We will not begin to make significant progress in dealing with [the difficulties of learning mathematics] until we more fully acknowledge the foundations of our discipline.” Higginson’s goal in this article is to broach a model of mathematics education called the MAPS-tetrahedral model, where MAPS stands for mathematics, philosophy, psychology, and sociology. He hopes that developing this model as the foundation for math education will help educators better understand their subject, and approach its teaching. Higginson concludes the article in a fascinating, humbling way, claiming that even if this model is shown to be “incomplete, logically flawed, or of very limited use” its ulterior motive, regarding the value it might contribute to help stimulate discussion between educators concerning the foundations of math education, will remain.
I agree with Higginson that mathematics education is highly interdisciplinary, but I wouldn't place much emphasis on the role of philosophy. I would instead place a greater emphasis on the impact of mathematics education on society.
ReplyDeleteThe article I read on research programs in mathematics is very much in the same spirit as the Higginson article, in that it tries to lay a foundation for mathematics education.
This certainly sounds good to me: I do think math education might benefit from being placed in a larger, more interdisciplinary sphere. The article I read focused more on the connections between people involved in math education, that is the practitioners and the theorists. I suppose these are not mutually exclusive ideas.
ReplyDelete(I also really like the Higginon ending)