Information Course Syllabi Philosophy of Mathematics Education Links

Seward's Philosophy on the Teaching of Mathematics
Mathematical competence is acquired through a careful balance of conceptual understanding, problem solving, and logical proofs. The drill of skills should receive decreased attention and mathematical proofs should not be used as the most important method of fostering understanding. Rather, more emphasis should be placed on conceptual clarity and creative problem solving in order to develop a mature mathematical competence.

In this manner, the teacher must be simultaneously a transmitter of the knowledge and a coach, in order to motivate students and their problem solving skills. Effective mathematics teaching should involve active student participation during class time as a very important component of the teaching strategy.

As implied earlier in my philosophy of education, problem solving is especially important for the students studying mathematics. The teacher must use problem solving strategies (i.e. the scientific method) that require persistence, the ability to recognize wrong assumptions, analyze a situation through the use of trial and error, modeling graphing, and drawing conclusions.

Further, through the guidance of the mathematics teacher, students must be taught to apply inductive and deductive reasoning techniques to construct mathematical arguments. They must be able to develop conjectures on the basis of intuition and test these conjectures by using logic and deductive and inductive proof. Additionally, students must be taught to judge the validity of mathematical arguments.

Finally, the mathematics teacher should make consorted efforts to ensure that students are taught the skills necessary to read, write, and speak mathematics, and relate and connect mathematics to real-world applications and across the curriculum. In this manner, the mathematics teacher should demonstrate to students that mathematics is a growing subject interrelated with many other disciplines.


  Last updated: January 8, 2012
  Copyright 2012