# Mathematician’s Lament Part Deux

In an early post, A Mathematicians Lament, I made a call for other mathematics teaches to provide their thoughts on Paul Lockhart’s Paper, *A Mathematicians Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form*. I did this as I was trying to unpack some of the provocative arguments that Lockhart notes in his paper. In many cases I found that I was agreeing with these statements and in some cases I found I was saying, “yes but …” I find that when I read a paper like this I need to not only digest it by myself but also hear the diversity of opinions others have. This post is the story of what happened after my initial post, the power of social media and an invitation to others to join in on the continuing conversation.

After making my original post, David Wees (@davidwees) and I entered in a dialogue via Twitter to organize an on-line meeting. We agreed that this could be organized using Elluminate and the Math Future Wiki after David talked with Maria (@MariaDroujk) about making this part of the Mathematical Future: Open online events organized trough the wiki. Information on how to join the event can be found on the “Mathematician’s Lament”: The conversation continues section of the wiki.

So let me point out a couple of important points about social media as it has unfolded:

- I wished to engage in a dialogue with others about a piece of writing and have been able to do so through my Blog and Twitter
- I have found a co-facilitator (actually I think David has done more with this than I have) who I have not met face to face
- We (notice that this has moved from I to we) have managed to find a third person willing to help out and host info on a wiki
- We have been able to use Elluminate which is provided free to British Columbia Teachers to connect people across the world with this session
- We have been able to advertise the event on-line through Twitter, Blogs and hopefully your contacts as well.

Now back to the A Mathematicians Lament. As I read the book I was left with some thoughts and questions which include:

- I believe this paper to accessible to all regardless of your mathematical ability but can all teachers see how to put this into practice?
- Yes, I can see the beauty and art of mathematics but does this mean that we all can? The parallels with music struck a chord with me (pun intended) but I can not play any musical instrument.
- The statements made about proofs resound with me. It reminds me of the theorem we had in my university geometry class, OAT – Obvious Angle Theorem. Naturally this was not accepted on any assignments.
- How do the ideas presented impact generalist teachers who teach all subjects?
- The Mathematics Curriculum chapter was one that I was really interested in. How do you have a school/district/provincial/territorial/national curriculum which follows these principles when we all define curriculum differently?
- Loved the Exultation section and the discussion around even, odd and square numbers.

I could add more points to the list above but I am curious as to others thoughts. I am therefore making an open invitation for others to add their thoughts in the comments below. We can then use these comments as discussion pieces around the Elluminate session on the June 9th. I hope you can join us.

Richard,

I’ve also posted this event to the BCAMT listserve, and I would recommend that other math educators should do the same for their own local email lists. We cannot let another generation of people grow up believing that they are incapable of doing mathematics.

David

There’s a point that the music analogy breaks down. I often think reading/writing is a better analogy. We cannot each write like Shakespeare – of course – but not even like Grisham. But we can learn to appreciate good writing, and the better we write the more options are available to us.

I feel like the necessary discussion that Lockhart avoids, mostly, is now what? We have constraints of tests, time and standards. What can we do and how do we do it?

I think this is a good point to discuss at the June 9th Elluminate session. Thanks for bringing it up.

As someone with a “formal” music background ([University of Toronto] Royal Conservatory of Music – which sounds more impressive than what it really is) and computer science degree with a minor in mathematics, I’m able to relate with the words in Lockhart’s paper.

Right from the get-go, with the musician’s nightmare; aspects of my “History & Harmony” theory lessons/classes came back to haunt me. Even worse, with my RCM training, there too is a “formal exam” which is both performance based (as in I have to play a few pieces in front of an adjudicator) and final exams where I had to “write” stuff down about harmony/history/theory/etc. Transpose this into that key, “fill in” the cord progressions, etc. That aspect of my “music training” I did not enjoy. It wasn’t until I was able to stop this did I start to appreciate the music that I heard, the music that I could play, the music that I could make.

Similarly with math. I see myself in a lot of what was written – the rules learned/memorized that made up “math”. That I was an “ok” student – nothing came to me super easy, but at least if I worked at it, I could fill in the right answer, even though I didn’t know or understand why I was doing it.

Which brings me to my computer science degree. It all started when I was about 9 or 10, when my dad brought back an IBM PC-XT Compatible computer from Hong Kong. He showed me a few things about it – how to turn it on, what disk to use to boot it up, etc. but where I started to learn about programming is the curiosity I had to figure out how this hunk of junk worked. I looked at some of the BASIC programming books that he had, and simply copied the code out. I didn’t gain “understanding” of the code I was writing by simply reading the text in the book and following it to a “T”, but when I tried different things with the code – by breaking it, by changing things here and there.

This breaking of things lead me to try out different things – figure out how to do this, or that. How a loop worked, what had to happen for it NOT to work, how hexadecimal numbers worked, etc. It was all through exploring and playing. Of course, that eventually turned into “formal training” which led me to my degree, but the appreciation of computers started back in my “just playing around” days. Same with my musical background. All the theory I learned really has very little to do with my ability to appreciate music. It basically helps me communicate to other musicians (“let’s try a D-dim here at bar 14 at beat 2”).

As a teacher, I have been fortunate enough to be given the opportunity to facilitate a games development course. It is completely student driven in the sense of actual “programming theory”, I have pretty well much let the students discover it along the way. When a problem comes up, either the student finds the solution in how to solve it, or we come up together with a possible way to get the job done. Obviously play based – they are, in fact creating computer games – as they struggle to find solutions to the programming problems in their game. Failures? Lots of them. In programming, they’re called bugs.

Failures in the class? Heck no! All my students in this course are engaged with the process of creating their masterpieces. They just happen to be learning about digital media & artwork, game design, public speaking, team work & communication, and oh yeah – computer programming too.

After having read only the original article of the Lament, I find myself searching out for more depth. (All the bookstores in Vancouver seem to have mysteriously ‘sold out’ of the book)

I was struck by analogy to both music and painting, which compelled me to read more in depth than I might have originally. I came away a little flattened, especially by the final descriptions of the math courses (obviously American, but they hold true here, as well). I have always seen the beauty and art in mathematics and nothing gives me more pleasure than a problem that requires more than a quick recognition of the ‘pattern’ to solve. However, I am also a firm believer that mathematics is a language (which can be co-opted for science, technology, inventions, architecture, art (tessellations, etc), and music). It is important to me for students to learn this language to help them see this beauty.

I see elementary math as two fold: teaching students the language of mathematics; giving them the aesthetic skills to see the beauty and art of mathematics. One cannot be done without the other. In literacy, we read to students wonderful stories before they can even begin to decipher the scratches of the written word, but we don’t stop there. We give them to tools to express themselves with those weird scratches, not to have them become the next Shakespeare (or Grisham, although I wouldn’t normally put them in the sentence, artistically). Each student has many stories to tell, and this is true for their numeracy as well as their literacy.

Just my two bits…..