In 2008 I commenced a coursework Masters in mathematics at the University of Queensland. I have downgraded this to a Graduate Diploma and should officially graduate in a few weeks.
My original goal for commencing postgraduate study was to improve my knowledge in programming languages and make the current research more accessible. Unfortunately the local universities teach very little (relevant) theoretical computing science, so I enrolled in mathematics with a focus on discrete mathematics, logic and abstract algebra. After the first year I discovered that there is no real future in programming language research here in Brisbane. I had achieved my goal in the context of the courses available and so switched my study to statistics as data analytics is both interesting and hopefully more viable locally.
To complete the Masters I need to do the equivalent of four courses in research. As I am enrolled in a coursework masters, I pay 2-3 times the standard undergraduate fees. The last course cost $2010. Therefore there is approximately $8000 in fees remaining.
I would enjoy the remaining Masters research component if could find the right supervisor and topic. However employment as a researcher now generally requires a PhD, not a Masters and while a PhD is longer, it also has no fees. So if the circumstances were right to do the Masters research it makes more sense to consider a PhD anyway.
The value proposition for completing the Masters is too low. I have fulfilled the requirements for a Graduate Diploma and so will finish with that.
And we have sold ourselves into a fast food model of education and it's impoverishing our spirits and our energies as much as fast food is depleting our physical bodies.
-- Ken Robinson
The role of the proof for mathematics is similar to that for orthography or even calligraphy for poetry. A person, who had not mastered the art of the proofs in high school, is as a rule unable to distinguish correct reasoning from that which is misleading. Such people can be easily manipulated by the irresponsible politicians.
-- V.I. Arnold
Teaching for understanding didn't offset the destructive effects of telling them how to get the answer. Any step-by-step instruction in how to solve such problems put learners at a disadvantage; the absence of such instruction was required for them to understand.From: Education's Rotten Apples
-- Alfie Kohn
My mathematics lecturers often try and introduce a new topic with a motivating example. I think this is a great idea. I am a slow learner and find that an initial concrete example is the best way to approach a new abstract concept. I realise that this can sometimes pose challenges further on, i.e. in generalising from the concrete to the abstract, but this way seems to work the best for me.
Unfortunately, there are many times that the motivating example is not that motivating. I view teaching as often building a bridge from the student's current position to where you want to take them. To achieve that, requires providing an initial high-level context in terms that the student can relate to.
As an example, earlier this year I studied introductory linear algebra that included eigenvectors. Kudos to the lecturer for trying to motivate with a modern example (search engine page rank). Even though I am a professional programmer, this example didn't really work for me and I finished the subject with only a vague idea about them.
Recently I read this article which introduced them with simple physical examples. The second paragraph of the current wikipedia page nicely related it back to matrices and vectors and it all fell into place.
Some mathematical ideas are represented as a sequence of steps, e.g. calculating Maximum Likelihood Estimators in statistics. Once a good motivating example is done to provide context, things can proceed between two extremes.
I currently study at one uni and work at another (not in an academic capacity though). Unfortunately Why I am Not a Professor OR The Decline and Fall of the British University seems to aptly describe things.
To the claim that academia is living a lie, I would add that many in industry and government are doing just the same, except with different situational parameters.
I enjoy learning, especially in the context of improving whatever it is I am doing. I do not enjoy the university lecturing system, even when the content is relevant and the lecturer is good. In contrast to interactive learning in the context of relevant activities, it is very inefficient.
In the industrial model of student mass production, the teacher is the broadcaster. A broadcast is by definition the transmission of information from transmitter to receiver in a one-way, linear fashion. The teacher is the transmitter and student is a receptor in the learning process. The formula goes like this: "I'm a professor and I have knowledge. You're a student you're an empty vassal and you don't. Get ready, here it comes. Your goal is to take this data into your short-term memory and through practice and repetition build deeper cognitive structures so you can recall it to me when I test you."Provocative but unfortunately sometimes true. In The Impending Demise Of The University Don Tapscott goes on to write about the generational and technological forces that are impacting the traditional university model of learning.
The definition of a lecture has become the process in which the notes of the teacher go to the notes of the student without going through the brains of either.
I have conducted an extensive research program in atomic physics over many years that has involved many graduate students, on whose professional development I have spent a lot of time and thought. And over the years I became aware of a consistent pattern: New graduate students would come to work in my laboratory after 17 years of extraordinary success in classes, but when they were given research projects to work on, they were clueless about how to proceed. Or worse — often it seemed that they didn’t even really understand what physics was.He goes on to talk about measuring student learning, research on learning, the role of technology and various approaches tried. Towards the end of his multi-part series he offers the following summary.
But then an amazing thing happened: After just a few years of working in my research lab, interacting with me and the other students, they were transformed. I’d suddenly realize they were now expert physicists, genuine colleagues. If this had happened only once or twice it would have just seemed an oddity, but I realized it was a consistent pattern. So I decided to figure it out.
Our society faces both a demand for improved science education and exciting opportunities for meeting those demands. Taking a more scholarly approach to education—that is, utilizing research on how the brain learns, carrying out careful research on what students are learning, and adjusting our instructional practices accordingly—has great promise.
Research clearly shows the failures of traditional methods and the superiority of some new approaches for most students. However, it remains a challenge to insert into every college and university classroom these pedagogical approaches and a mindset that teaching should be pursued with the same rigorous standards of scholarship as scientific research.
A humorous, but poignant view on how our education system devalues creativity in the interests of industrialism to the detriment of people in general.
I disagree with the implication that mathematics is not creative. Paul Lockhart in A Mathematician’s Lament writes about the education system destroying the curiosity and creativity in maths.
I agree wholeheartedly that the education system values certain qualities in people over others and that can deeply (negatively) impact the self worth of young children on the wrong side of that.
Lockharts Lament is a very interesting and worthwhile read. It is about mathematics, art, society and education. Especially education. A few interesting quotes and ones that made me laugh:
"The only people who understand what is going on are the ones most often blamed and least often heard: the students. They say, “math class is stupid and boring,” and they are right."
"High School Geometry: Instrument of the Devil"
"We’re killing people’s interest in circles for god’s sake!"
"The first thing to understand is that mathematics is an art."
About 15 years ago, I was finishing my undergraduate degree in Computing Science. I remember feeling like it was largely a gross waste of time, but I had come this far, so I should finish to get the piece of paper. Furthermore, upon finishing my degree I vowed not to do any more programming! Somewhat ironic since I now run a software company.
Fast forward to the present day and I have just started the first subject of a Masters. This subject is an undergrad course on Discrete Mathematics, which I am really enjoying. So, why the difference between these two university experiences?
I am postulating it is because I see the relevance of the topic to my own context. I am able to apply what I am learning in some meaningful way. There is a reason for learning this stuff!
Note the university has helped very little here. They no longer have a program containing significant theoretical computer science. So I am investigating courses offered in the school of Mathematics and selecting them best I can.
Back to my undergraduate degree. I chose Computing Science because I had an aptitude for computers. I had already learnt simple imperative programming and relational databases at high school and in my own time. So listening to a lecturer read the database textbook was pretty boring and why was I doing a compulsory accounting subject when I had enrolled in computing, not business?
As far as I can remember, the University did little to give me a reason as to why I was studying the subjects I was, or to draw me in and engage me on the topics at hand (apart from a crypto subject in final year, run by the Dean at the time). I went straight from high school to uni and had never worked on a significant software project, so I certainly didn't have the context to find relevance myself.
Now I look around at the first year students, many straight out of high school, doing the maths subject with me. I wonder how many of them will probably grow to dislike this subject, as they struggle with the formality of the content for the first time. How many will study for the exam and then promptly forget most of what they learned. What a waste of time, effort and money!
If my conjecture about context and relevance is correct, would it be better to study programming as an apprenticeship - where there are periods of practical work in industry, separated by periods of classroom time? Or should Universities simply do a much better job?
