Monday, June 27, 2011

"Visions of Students Today" - Whose Education is it anyway?

If a picture is worth a thousand words much is a video worth? These ones are priceless – for educators of post-compulsory students. To call the two videos featured in this post “thought provoking” is an understatement.
Both videos are created by Michael Wesch – with a lot of help from students at Kansas State University. The first, “A vision of students today”,is widely known and has been circulating around the internet since October of 2007 while the sequel, “Visions of Students Today”, was released in June, 2011. Both give a sense of what it is like to be a university level student today. I won’t elaborate specifically on the content of the videos – except to suggest that they should be compulsory viewing for all teachers, lecturers and professors.
Expressing concern about the “irrelevance” of education is nothing new. It was already an established theme back when I was a student – not long after the ark found dry land. However, even if we put aside the issue of the appropriateness or otherwise of the curriculum itself and just contemplate the educational experience itself, educators should be asking some serious questions. We know what modern life is like for our students. Why have our schools and universities not kept up? Why do we not use the technology and the equally important associated attitudes available to us? To some extent there will always be a lag period between technological innovation and educational practice – technology evolves faster than institutions do. But, as these videos show, when we use new approaches, or rather when we allow our students to use the technology that is already available to them, significant learning can occur.
So we have the situation where often the curriculum itself can be of little relevance or significance and the process by which students interact with their “education” is disconnected from their daily life with its heavy emphasis on modern technology. Is this really good enough? It begs the question – whose education is it anyway, the student’s or “the system’s”?

Anyone interested in more background in the creation of “Visions of Students Today” can follow this link to the associated blog pages.
Associated background story

Visions of Students today link

A vision of students today link
Michae Wesch photo:

Wednesday, June 22, 2011

Mathematical Maverick – Dan Meyer – “Be less helpful”

If mathematics has a poster boy it is – or at least should be – Dan Meyer. Meyer is something of a rarity in the field of public discussion of mathematics; he is not an academic, he is not an educational administrator, he is a teacher - someone who works in real classrooms with real students with real mathematics. It is this “real world” context that makes him worth listening to – and which provides the grounding for his instruction.
Meyer is an advocate of authentic learning in mathematics. If you think of “drill and practice” worksheets or textbooks, or even the Khan Academy online learning site, then Meyer is at the opposite end of the spectrum. However, Myer is not “warm and fuzzy” or laissez faire when teaching mathematics – he expects his students to learn and master the material; it is just that he considers it far more important that students understand the concepts involved before reducing mathematics to pencil and paper exercises devoid of any connection to the real world experiences of students.
In his recent TEDxNYED talk Meyer claims that the traditional text book approach to teaching mathematics destroys mathematical reasoning and patient problem solving, replacing it with an attitude that mathematics is all about plugging in some given information into a formula, which incidentally is also given by the text book, and churning out an answer with little or no meaning. It need not be so and in his talk Meyer demonstrates how to use effectively teach the same material.
He gives some general advice as well. One piece of wisdom he shares is to “Ask the shortest question you can”. Another is “Be less helpful”. These adages may appear to be counter to conventional wisdom – and perhaps they are. They make more sense in the context of his talk – which can be viewed here.
If you teach mathematics – or know anyone currently being taught mathematics, this is a “must see” video.

Meyer also maintains an informative mathematics based blog that can be accessed here.

Friday, June 17, 2011

Mathematician's Lament - Paul Lockhart

Following on consistently in my habit of being the last kid on the block to discover something I recently fell upon “Mathematician’s Lament” by Paul Lockhart.

The history of the book is interesting in itself – it actually started life as a 25 page type written document that was presented to math guru Keith Devlin at a conference. Devlin was intrigued and impressed by the brief piece – so much so that he tracked down the author and sought permission to feature the article in his regular math opinion piece at Mathematical Association of America online site (a great site which will reward frequent visiting or follow this link  to Devlin’s column with a link to the PDF of the original piece). Publication in that forum lead to the publication of the book form – complete with some intriguing examples of what Lockhart considers “real maths”. There are some stylistic features of note – not the least of which is Lockhart’s homage to Galileo’s 1632 tome “Dialogue Concerning the Two Chief World Systems” which features two characters involved in discussion. At seemingly random times around the book Lockhart uses the same conversational format and even two of the character names, Simplcio and Salviati, to advance his arguments. This actually simplifies the discussion - no prose or description, just the two characters “talking” about issues related to current mathematics instruction.

However, the section I would like to share is where Lockhart describes math education via a dreaming musician early in the book.

“A musician wakes from a terrible nightmare. In his dream he finds himself in a society where music education has been made mandatory. “We are helping our students become more comptetitive in an increasing sound-filled world.” Educators, school systems, and the state are put in charge of this vital project. Studies are commissioned, committees are formed, and decisions are made – all without the advice or participation of a single working musician or composer.

Since musicians are known to set down their ideas in the form of sheet music, these curious black dots and lines must constitute the “language of music.” It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory. Playing and listening to music, let alone composing an original piece, are considered very advanced topics and are generally put off until college, and more often graduate school.

As for the primary and secondary schools, their mission is to train students to use this language - to jiggle symbols around according to a fixed set of rules....

… In their wisdom, educators soon realize that even very young children can be given this kind of musical instruction. In fact it is considered quite shameful if one’s third-grader hasn’t completely memorized his circle of fifths. …

In the higher grades the pressure is really on. After all, the students must be prepared for the standardized tests and college admissions exams. Students must take courses in scales and modes, meter, harmony, and counterpoint. “It’s a lot for them to learn, but later in college when they finally get to hear this stuff, they’ll really appreciate all the work they did in high school.” Of course, not many students actually concentrate in music, so only a few will ever get to hear the sounds that the black dots represent. “

And so it goes ...

Now, I have to say that I have now read the book twice – and I don’t agree with everything that Lockhart says. I’m still debating whether I think Lockhart got some things wrong – as well as an awful lot right – or if I’m simply not brave enough to agree with him; for to agree with Lockhart means that maths instruction MUST not only change but change dramatically.

For me a key aspect of the musician’s dream is the notion of providing “skills” now that a student will need later - even if they have little or no relevance to the students now. Lets think about this - we are actually saying to our students - we know this is irrelevant to you now - but we are going to teach it to you anyway. How did this become accepted practice? What learning theory does this reflect? Why do the conventions of the educational system outweigh the needs of our students?

“Mathematician’s Lament” is not a flawless work - but it does provoke some important questions; it is well worth reading and thinking about - and I’d suggest not just for math’s teachers but any teacher who considers themselves a “subject teacher” rather than a teacher of students.

Addendum:  The link provided above was not active as of 8/12/2011.   The document can still be accessed however by following this link.