How do I see my role as a math teacher? What would I like to accomplish as a math teacher? How to convince my students about purposes and reasons for studying mathematics? I have been confronted with these questions many times and the answer never comes easy. The expectations I have set for myself as a math teacher are as follows:

To enable students to become familiar and technically proficient with knowledge and specific skills defined by the curriculum (mathematical operations, reasoning, problem solving, applications, etc.); help them to understand the purpose of learning these particular skills.

To show mathematics on a wider cultural and historical background; to show it as an important part of human culture, as quintessence of human ability to think.

To instill in students the notion that a successful study of mathematics requires systematic, diligent work, precision of thinking, and asking questions; to convince them that these qualities will be useful for them in further studies and in life.

Try to enrich students’ study by providing interesting examples, such as the history of fundamental discoveries in mathematics, and to convince them that for those who are willing to put effort in its study, mathematics can be a source of intellectual satisfaction; encourage them to see value in this kind of satisfaction.

Make students feel good about themselves for trying to overcome obstacles and for willing to learn and understand not only useful facts, but also abstract concepts.

This list isn’t long, but, in my opinion, it is extremely demanding. How can I realize these purposes in practice? I would like to share some of my reflections about teaching and learning mathematics on a school level, and this way try to answer this question.

There is no doubt that necessity, purpose, and benefits of studying mathematics are not so obvious for many students and parents. I often ask myself a question, why in the era of great advances of science and technology, necessity of mathematical education generates so many controversies and misconceptions. There are many myths concerning a study of mathematics. I think that these myths are in a big part responsible for widely spread "math phobia". Children are exposed to those myths from very early ages; as a result, many of the children are afraid of mathematics and learn to hate the subject. What are those myths?

One of them is a popular belief that mathematics is so difficult that only a few chosen ones are able to understand it. It would be dishonest convincing students that everyone can do math on the same level; unfortunately, for most of us professional level of mathematics is out of reach. However, I truly believe that everyone is able to learn mathematics on a school level. (Of course, there are always exceptions, e.g. children with certain disabilities; but we are talking about a general population of children.) Two conditions are indispensable for achieving this goal: a willing, motivated student, and a good, well-educated teacher. The importance of a good teacher cannot be stressed enough. But even the best teacher cannot achieve much when students do not want to learn or put any effort into understanding. The problem is how to motivate students and get their attention. This is not easy since many students hear at home that their mom and dad have never learned math and somehow survived, and they are "comforted" that they will not need math either. My role as a teacher will be to counter this attitude by making classes interesting and creating the atmosphere in which mathematic is not scary or out of reach.

Another myth that is responsible for students’ problems with learning math is an unfortunate belief that mathematics is a set of formulae which one has to memorize and apply. A student’s role is just to figure out which formula is to be applied to a given problem. This approach is, of course, doomed to fail. If students will not see that formulae are natural products of some thinking processes, they most certainly will not understand them. If they do not understand them, they cannot properly use them. It is not possible to "memorize" mathematics. Of course, the demand to prove everything is not realistic in school, also not always needed, but some things should be proven while others may be justified in an intuitive manner. Proving some facts would not only satisfy mathematical rigor, but also would give students a little glimpse at what "real" mathematics is about.

One more myth our students are exposed to is the opinion that mathematics is so important in our life that we practically cannot function without it. This opinion, which is in a direct contradiction with one that states that we do not need mathematics at all, may sound more convincing, but it is not true either. After all, a vast majority of people function rather well without knowing much math. I think we should be honest about this with our students. Instead of indoctrinating them with this kind of myths, I would stress, that mathematics is extremely important in many careers, and that they may like to pursue some of these careers in the future

What was said above was concerned mainly with fulfilling postulates 1 and 3 on the list of goals I hope to realize as a math teacher. To satisfy the remaining goals, I would like to show to my students some interesting facts from the history of mathematics; show how this purest product of human abilities to think has grown and developed over centuries. I would like them to be amazed when they discover how some very simple (and for a long period of time perceived as without any applications at all) ideas gave an impulse for inventions that are now indispensable in our life (e.g. binary system as a basic idea for the computer).

I would also stress that every student should learn math because, as a distinguished mathematician Underwood Dudley put it, "math is good for your mind"; that this is the most important benefit of studying mathematics. Math teaches us to think precisely, to reason logically, and gives us tools to work with in many fields of human activities, from understanding charts in newspapers to exploring the universe. And for many people it is a source of a deep intellectual satisfaction. To feel this satisfaction one doesn’t have to be a famous mathematician; sometimes it is enough to figure out what is going on with these two trains going from A to B…The source of joy is to figure it out by yourself.

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   The Reflections on ITEC 501 Experience

   This is the abstract of the paper

     The increasing necessity for integration of modern technology into teaching process in today’s schools has become a non-reversible reality. This, in turn, calls for educating present and future teachers in this domain to equip them with skills and knowledge that they would be able to apply in a classroom. This paper is a reflection on the ITEC 501 class, which is designed to accomplish those goals, and on challenges faced by the students in this class.

   To read the whole paper click here.

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