The philosophy behind our courses
Learning to do mathematics is not unlike learning how to dance, or play the piano, or golf, or play hockey or basketball. To be good at any of these activities, one must spend hours in repetitious practice of laws of exponents or pirouettes or scales, or a golf swing or skating backwards or dribbling. You can participate recreationally without this level of commitment to the activity but universities aren’t about a “recreational” involvement with learning. This is the basis for our philosophy of learning mathematics.
Mathematics is a subject which builds upon itself, not unlike a house. If you are building a house, the first thing you put in is a foundation, then you put up some walls, and finally you put on the roof. In a similar fashion, when you are learning mathematics, first you learn some addition facts, and then you use that knowledge to learn how to multiply, and then you use your knowledge of multiplication to learn about division. All of mathematics is like that, so if someone misses something early on in his/her schooling because s/he is sick or moves or whatever, then it makes it very difficult for him/her to learn any mathematics which comes after that that uses the knowledge s/he doesn't have. This is the primary reason why many people do poorly in mathematics.
To avoid this happening in our program, we use the mastery concept of learning. This means you do not go on to study higher levels of mathematics until you have demonstrated a good, solid knowldedge of every bit of mathematics required to do the next level. This entails continuous assessment and high pass standards, often as high as 80%. [This is not the case for the Math 1051 course that is offered at the MLC as part of the accelerated M103F/M1051 course.]
Our learning materials place emphasis on building essential mathematics skills and fostering independent study habits. The learning and exercise sequence will ensure that new terms, concepts and proceses are well understood before they are used in solving more complex problems. Explanations are given which relate new concepts and skills to what is already known and fundamental skills are used to solve relevant practical problems.
Our M10XF and M1090 courses are NOT self-paced. The textbooks used are written in a 'self-study' style so that students can learn much of the content on their own. But the classroom experience is essential for the student to put the mathematics in context so that s/he knows how to use the mathematics effectively and meaningfully. Class sizes are kept small to allow students enough individual attention but students are expected to work on their own for at least 8-10 hours each week.
"A familiarity with mathematics is nice. Understanding mathematical concepts is fine. But to participate in post-secondary courses involving mathematics, there is an expectation that the student can do mathematics. This does not come with mere familiarity and/or understanding; this comes with hours of practice, much of which is repetitive."
"Many people who have never had the occasion to learn what mathematics is, confuse it with arithmetic and consider it a dry and arid science. In actual fact it is the science which demands the utmost imagination. One of the foremost mathematicians of our century says very justly that it is impossible to be a mathematician without also being a poet in spirit. It goes without saying that to understand the truth of this statement one must repudiate the old prejudice by which poets are suppose to fabricate what does not exist, and that imagination is the same as "making things up". It seems to me that the poet must see what others do not see, must see more deeply than other people. And the mathematician must do the same."
- From Sonya Kovaleskaya