On the Foundations of Mathematics Education

Author: William Higginson

Source: For the Learning Mathematics. Vol. 1, No.2 (Nov., 1980), pp. 3-7

In this paper, Higginson explores to elucidate what foundational dimensions in mathematics education as a discipline. He suggests and verifies that mathematics education is composed of four dimensions: Mathematics, Philosophy (arbitrary), Psychology, and Sociology. Mathematics concerns the contents in mathematics learning, philosophy concerns the context of mathematical concepts, psychology concerns the context of individual learning in mathematics, and sociology concerns students’ learning environments in mathematics. These disciplines form one tetrahedral model and are related to each other as an edge, thus this model is termed “MAPS-Tetrahedral model”. It invites mathematics educators to think that mathematics education is not an individual discipline and have insights from multiple perspectives.

MAPS-Tetrahedral model

Response:
I totally agree with Higginson's idea that mathematics education consists of multiple dimensions as a discipline. Because each people has different backgrounds as well as the societies, mathematics educators are required to find and adopt their own approaches to fit their leaners. For instance, the teaching approaches and methods in the United States did not work well in some developing countries when some U.S. teachers were dispatched there as an international cooperation program, and those leaners mathematical knowledge was not improved by the U.S. teachers. This fact supports Higginson's main idea. However, since mathematics education is organic, the foundational dimension of mathematics education could be changeable with the times. As the author acknowledges the flaw of his MAPS model, I believe current mathematics education has more dimensions other than MAPS. For example, "technology" impacts on mathematics education nowadays, regardless positive or negative, and it connects to other disciplines.

Question:
Do you agree with the idea that MAPS model is still working in current mathematics education? If not, what kind of foundational dimension/discipline should be added/removed?
And I have another question!
One of the main mathematics educators should be mathematics teachers at schools who are directly teaching their students. What can they do to adopt the multi-perspectives of foundational dimensions at their classes?