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Philosophy of Teaching and Learning Mathematics

The teacher is the most important factor in classroom learning. The teacher organizes. The

teacher manages. The teacher motivates. The teacher leads. The teacher creates an environment

in which learning occurs. Learning is a function of the quality of the teaching.

The teachers influence reaches far beyond the subject matter that is discussed from day today. As an active learner the teacher inspires students to attain knowledge. Through his or her

interactions with students the teacher influences moral development. The teachers behaviors

affect the students work ethics. The teachers quest for personal excellence inspires students to

strive for higher aspirations. The person, called the teacher, has a far-reaching influence on the

lives of students.

Mathematics plays an integral role in the lives of every member of our society. Numeracy is

essential to each functioning member of our society. The need for mathematical knowledge is

increasing as our culture becomes more saturated with technology and information. Everyone in

our educational system must have an opportunity to learn mathematics and to achieve a level ofknowledge commensurate with his or her personal potential, needs, and aspirations.

Mathematical knowledge opens doors of opportunity. Thus, mathematics education must be

accessible to all.

It is my belief that all can learn mathematics. Unfortunately, many in our education system

have been erroneously convinced that they cannot learn mathematics. Not all students have the

same motivation or aptitude for learning mathematics. Not all learn at the same rate. Not all

learn in the same way. Not all process information at the same rate. Not all comprehend

abstractions with the same level of understanding. But all can learn, given the conditions that

meet the individual learner's needs. Many students have gaps in their knowledge base. The

mathematics teacher must recognize these individual differences, seek to accommodate thesedifferences, and teach so all can have the opportunity to learn.

Learning is a multifaceted process. Learning occurs from visual and audio stimuli. Learning

occurs from reading. Learning occurs when writing or communicating orally. Learning occurs

from experience. Students learn not only from the teacher but from each other. Traditionally,

mathematics teachers have not utilized all the components of learning. We must acknowledge,

and respond to, the fact that learning occurs in many varied, yet equally important, ways.

Good teaching is crucial to the successful development and growth of children and adults.

Good teaching is essential to the success, achievement, and progress of a nation. Much depends

on teachers. It behooves them to give their best each day.

http://arapaho.nsuok.edu/~wyattw/webfiles/philosophy.html

http://arapaho.nsuok.edu/~wyattw/webfiles/philosophy.htmlhttp://arapaho.nsuok.edu/~wyattw/webfiles/philosophy.htmlhttp://arapaho.nsuok.edu/~wyattw/webfiles/philosophy.html

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Philosophy of Teaching and Learning MathematicsJames A. FitzSimmonsWilmingtonCollege

At the core of my teaching style and philosophy is a concern for my students. I care deeplyabout 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; Ifeel 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

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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 myclassroom 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 assessboth 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 studentconcerns 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.

http://plato.wilmington.edu/faculty/jfitzs/tchg_phi.htm