Philosophy of Teaching and Learning Mathematics
James A. FitzSimmons
Wilmington College

At the core of my teaching style and philosophy is a concern for my students.  I care deeply about each and every student and strive to help all students reach their potentials both as students of mathematics and as people.

I have found in my experiences with my own professors at Xavier University and the Ohio State University and with my students at the Ohio State University and Wilmington College, teaching and learning mathematics involve more than just the mathematics itself.  Teaching and learning mathematics also involve enthusiasm, relationships, and commitment on the parts of both the professor and the student.  My teaching methods are based on all of these.

Enthusiasm fuels my mathematics classroom and motivates my students.  I thoroughly enjoy and am excited by mathematics and the teaching of mathematics.  The atmosphere is contagious; I feel my students can sense my enthusiasm and become more interested in mathematics themselves.  I have found that nothing is more motivational to students than genuine interest in what they are learning.

My mathematics classroom features a variety of methods of instruction that depends on: 1) the subject matter of the lesson and 2) my experience with how individual students and classes best learn mathematics.  Some days feature student-centered group or whole-class discussions, others involve small-group investigations, and still others see individuals working one-on-one with another student or with me.  This classroom interaction helps build relationships among students and between students and me.  These various classroom practices help address the varied learning styles found in the mathematics classroom.

Despite the differences of format, one thing remains the same: my role as facilitator.  I believe that students learn mathematics best by doing mathematics and then working to communicate about mathematics.  Therefore, my classroom involves discussion among students and with me.  As a facilitator, I frequently use the Socratic method in class to elicit mathematical thought and foster engagement with mathematical concepts.

I have found that using multiple representations of mathematical ideas (e.g., algebraic, graphical, and numerical) in my classroom is beneficial for two reasons.  First of all, different students learn in different ways, and one representation may be easier for a student to understand than another.  Secondly, knowing multiple representations and methods of solution makes for better problem solving; if students know several ways of attacking a problem, then there is a better chance of them being able to solve it.

As an aid to my use of multiple representations, I make use of technology in my classroom, especially graphing calculators and the Maple computer algebra system.  Through my own use of technology and my teaching with technology, I have come to realize that there are more and less effective ways of using it.  Students need to understand that technology is a tool, much like a compass or a protractor, and that technology must be used only as a tool.  Central to my use of technology in the classroom is the idea that students must understand what they are doing mathematically even when they use technology as an aid.

Similar to the idea that students learn mathematics in different ways, is that students also express mathematical understanding differently.  Consequently, I use multiple forms of assessment in my classroom to give students the opportunity to explain their understanding of mathematics in a variety of ways.  These forms include such things as writing assignments, interviews, group quizzes, portfolios, and asking students to write and solve their own problems, as well as the usual tests and homework.

One commitment I make to my students is to always be available to students outside of class.  To this end, I give my students ample time to meet with me in my office, furnish them with my home phone number, and encourage them to communicate with and meet with me as often as they can.

Another part of my commitment is to strive to teach mathematics as well as possible.  I assess both how I have grown and how I continue to grow as I teach.  From the time I began teaching to the present, I can see many things that have evolved in my teaching to make it more responsive to and effective for my students.  Some of this is from time spent preparing lessons and self-evaluation of those lessons.  With each and every lesson that I teach, I am constantly evaluating student understanding (from their questions, assessments, etc.) and their responses to the methods that I am using.  Through this, I am able to constantly work to improve my teaching.

The other part of my teaching evolution is through feedback from my students.  This is fostered especially by the relationships that I have with my students.  I make it clear to all students from the beginning that they should talk to me if they ever have suggestions about how to improve my classroom.  In addition to this, I hold class meetings at least once per semester to discuss student concerns and class goals.  Lastly, at the end of every semester, I stress to my students that student evaluations are important vehicles for helping me to become a better professor.  I ask them to make suggestions for things that I should change to improve my teaching as well as things that I should continue doing because they found them to be beneficial.

Using my evolutionary teaching style, I strive to improve each and every time that I enter the classroom.  Through my teaching style and methods described here, it is my hope that my students leave the classroom excited by and knowledgeable in mathematics and confident that I care about them and their mathematics learning.

 

Copyright 2014 [James A. FitzSimmons].  All rights reserved.