Arnold Rosenbloom

Thoughts on Math and CS Education

Are students well prepared for mathematics at University? Every faculty member wants their students to be ready to get an A in their course. This is not a realistic expectation, so in some sense, we never think that students are well enough prepared. I would like our students to be better problem solvers. I would also like our students to understand the why of mathematics as well as the how. To understand that there is a 'why' and it can be understood. To make this concrete, think about why you add fractions the way you do. Why are all integers ending in 0,2,4,6 and 8 divisible by 2? There is a 'why' and it can be understood. I do feel that students are not as well prepared for their first year since Grade 13 was removed from Ontario High-schools. This is for a number of obvious reasons, students are one year younger so less mature, students have seen one year less of math content. You might just as well have asked whether the University, or more appropriately, whether I, have properly adjusted to the missing grade.

What do I do to prepare our students for the real world? I set the bar high and I do whatever I can to help them get over the bar. I don't believe that we should simply use the high bar to exclude those that can't, initially, get over it. I don't believe that it is in our students' interest to lower the bar either. They need the ability implied by high achievement in my courses. It is in their interest that we maintain the strong reputation of the courses, the program and the University.

Should students be forced to take mathematics? I believe that you can not force a person to become a great mathematician. Student must be convicted of an A in my courses. They need means, motive (or motivation) and opportunity. My job is to provide 50% of the motivation as much opportunity as I can. Students bring the other 50% of the motivation as well as the means to learn, their brains. If a student really does not want to learn, they won't. On the other hand, motivation, both provided by the student and the University counts for quite a lot. I don't believe force is good motivation. Interesting problems, interesting and relevant material are good motivation. Giving them the ability to succeed is good motivation. Providing them with a broad range of courses, chance to explore ideas and engage with the material and work with each other and with faculty are opportunities.

Does the corporate world still look to Canada for talented individuals? Our graduating students seem not to have difficulty finding employment, even in these trying economic times. The dot com bust has severely limited our numbers, but this appears to be changing. Our students have, and continue to, find employment at IBM, Microsoft, Google, RedHat, etc. This also seems to be holding true for other Universities such as Waterloo. The point here is that these companies continue to find value in the product we produce. On a related note, in the last few years I have seen a good collection of my students start their own companies. Some are patenting ideas and working on rounds of funding. We have confident students with great ideas, motivation and business sense.

Should the University produce more Mathematicians and Computer Scientists? Do we need more? Are enough of our students going to graduate school? Well, of course I believe that everyone should understand and appreciate Mathematics and Computer Science. If not, then why would I teach it. Does industry need more of our students? I believe they do, we certainly have not saturated the market. We also send a steady stream of students to graduate school. Only the top few that are so inclined should, and do go to graduate school. I think this is appropriate.

One point I did not make, though I wish I did, is that I believe that students outside of Computer Science should take at least an introductory course in Computer Science. Everyone should understand the power of the tool that will most likely be in their offices at work. Simply understanding the possibilities that are opened up by a computer is an asset in practically any field. Even better is an employee that can actually utilize this tool in their own area. Just think of the number of computational tools at your service, the number that you are carrying around, even at this moment. At UTM we will be offering CSC288 (Tools of the Trade) to serve this purpose.

Why is enrollment low in Computer Science? Mostly a result of the dot-com bust. The other reason, Computer Science is difficult. It requires a lot of time, effort, persistence and focus to solve computational problems, to write software. Computer Science requires deep mathematical thought, reasoning, ability to problem solve, ability to prove, an esthetic sense of what a simple, clear, concise solution looks like and a good collection of communication skills. On top of all of this, our job is to understand not just the computational tools that are used to solve a problem, we also have to understand the problems that need to be solved, often in areas outside our own. For example, some Computer Scientists end up working with Biologists (Bioinformatics), others work in the Financial Sector (Financial Modeling), others work with Artists (Computer Graphics). Most of our students will end up using the computer to solve problems outside of the areas we train them for. We don't teach our students about banking, securities and accounting, but do expect them to be able to learn enough about those areas to write banking, securities and accounting applications when they are on the job. The final piece of the difficulty, the field is, by its nature, in flux. My Web Programming course is not the same Web Programming course we created in 2002. Programming languages are changing, operating systems are changing, the tools are changing. I would like my students to learn the latest in the areas I teach them, but more than that, I need to teach them how to keep pace with a field which is changing by the second.

Why should someone be in Computer Science? I recently told my first year students that the software is the magic. I asked them

"If I offered you Harry Potters magic wand, and told you that you could use it to do practically anything you imagined, but it would take a large effort to master it. Would you be interested in taking the wand and learning to use it. Would you feel it is worth the effort?"