Philosophy of Mathematics

The combination of all the subjects taught in schools is intended to transform children into responsible, contributing, self-sufficient, confident citizens.  The process of schooling gives students the knowledge, skills, and attitudes needed to secure the self-efficacy and self-worth necessary to effectively contribute to society.  When students feel confident that they can affect change, they are more likely to go ahead and do so.  The study of mathematics contributes to this confident attitude.  By having a firm foundation of mathematical thinking, students have the necessary tools to solve not only simple everyday problems, but also have the foundational skills to tackle more complicated mathematical challenges.  Because math surrounds us in everyday life, being able to successfully complete tasks involving math carries a crucial importance.  Having a lack of mathematical skill can not only lead to unproductive, even hopeless everyday living, but it can also lead to scrutiny from peers.  To preserve the egos of our students, we teach them to think mathematically so they can function and prosper as contributing members of society.

Students learn mathematics in their own personal ways.  Therefore, teaching math is somewhat a system of trial and error; multiple approaches should be used to guarantee that all students in the class have been exposed to an approach that corresponds with their learning style.  This means that a variety of resources should be made available to students at all times: pencils, paper, computers, manipulatives, calculators, space to act concepts physically, places to discuss, places to sit in quiet, etc. Also, sufficient time should be given to learning math – one cannot expect that a concept that seems simple to the teacher will seem simple to the student.  And finally, an understanding of what students are interested in can certainly help frame an otherwise dry mathematical concept.  A combination of patience, trial and error in approach, and an understanding of how to make math interesting and accessible help students acquire mathematical concepts.

The job of a teacher is not necessarily to pass their knowledge on to static students, but to create a dynamic environment where students can use inquiry to discover new understandings.  Teachers must be models of this process of discovery.  Teachers must also be likeable, have relationships with their students, and be sensitive to their needs.  Teachers must be cognizant of the fact that students are human beings, not simply learners of math.  When this framework is used, a classroom of comfort, compassion, and trust is formed and students feel comfortable try new things, make mistakes, and learn.  

Children are human.  Teach them with this in mind so they can continue living with confidence both inside and outside their classroom.

Mathematics Classroom


In an ideal world, my classroom may look something like this.  There would be several available spaces depending on the type of task students are working on.  Tables for group type projects, individual desks for individual work, a more comfortable area with a rug and other seating for brainstorming and discussion, and of course, a teacher area.

This article: What Happens in the Arcade Shouldn't Stay in the Arcade: Lessons for Classroom Design is a very interesting read in so far as how a teacher may go about setting up a classroom.