I teach mathematics in Mount Vernon since the spring of 2009. I truly like training, both for the joy of sharing mathematics with trainees and for the chance to return to older themes and enhance my very own comprehension. I am assured in my ability to tutor a range of basic courses. I consider I have been reasonably efficient as an instructor, as proven by my good student evaluations as well as numerous freewilled compliments I got from trainees.

The goals of my teaching

According to my opinion, the major facets of mathematics education and learning are mastering practical analytical skill sets and conceptual understanding. Neither of the two can be the only target in a good mathematics course. My aim being an instructor is to strike the right symmetry between the 2.

I am sure good conceptual understanding is really essential for success in an undergraduate maths program. A lot of attractive suggestions in mathematics are simple at their base or are built upon previous approaches in straightforward methods. One of the aims of my training is to expose this simplicity for my students, in order to both boost their conceptual understanding and reduce the harassment aspect of mathematics. A sustaining issue is the fact that the elegance of maths is typically at odds with its severity. For a mathematician, the supreme realising of a mathematical result is usually supplied by a mathematical proof. Students typically do not think like mathematicians, and therefore are not necessarily equipped to deal with this kind of points. My duty is to distil these concepts down to their essence and clarify them in as easy way as I can.

Pretty often, a well-drawn picture or a quick translation of mathematical expression into nonprofessional's expressions is one of the most beneficial method to report a mathematical principle.

Learning through example

In a typical first maths program, there are a number of abilities that trainees are actually expected to be taught.

It is my point of view that students normally find out mathematics better through example. Thus after introducing any unknown ideas, the bulk of my lesson time is normally spent dealing with numerous models. I carefully pick my cases to have complete range to make sure that the trainees can identify the aspects that prevail to each from those aspects that are specific to a certain sample. During developing new mathematical techniques, I often present the content like if we, as a crew, are uncovering it mutually. Typically, I present a new kind of trouble to resolve, explain any kind of concerns that protect preceding techniques from being applied, advise a new strategy to the trouble, and then carry it out to its logical conclusion. I feel this strategy not simply involves the trainees yet inspires them by making them a part of the mathematical system rather than merely spectators that are being told how they can perform things.

The aspects of mathematics

As a whole, the problem-solving and conceptual facets of mathematics go with each other. A solid conceptual understanding forces the techniques for solving problems to seem more typical, and hence easier to absorb. Without this understanding, trainees can tend to see these methods as strange formulas which they must learn by heart. The even more experienced of these trainees may still have the ability to solve these troubles, but the process ends up being worthless and is not likely to become retained after the course ends.

A strong experience in problem-solving likewise builds a conceptual understanding. Working through and seeing a range of different examples boosts the psychological picture that a person has about an abstract concept. Hence, my aim is to emphasise both sides of maths as clearly and briefly as possible, to ensure that I make the most of the trainee's potential for success.