I'm off to the MathML conference on Friday. For the uninitiated, MathML is "mathematical markup language", the set of tags that will let us put math text on the web without being forced to go through a major song & dance with GIFs, tables or other contrivances. It's been a while coming and isn't really quite here yet: the standard exists, and some authoring tools, but the major browsers have only just recently been jigged to display it - sorta.

I attended the previous MathML conference two years ago and came back somewhat disillusioned: all the existing implementations seemed unusable by non-techies without advanced degrees in the appropriate acronyms. The program for this one looks more promising. There's more to MathML than just displaying math text, too; we want to mainpulate that text and feed it into calculations, for example, and the program promises more of that as well.

Should be an interesting weekend.

The title of a rant from e-learning Magazine about the use of interactivity for interactivity's sake.

"It's not that interactivity is a bad idea. It's just too simplistic to be a useful guide for instructional design. It can even be dangerous."

The author has a point: merely including interactivity in an instructional design need not make learning more effective. Interactive eye-candy or "edutainment" often does little to promote learning and in fact may actually hinder it by distracting from essentials. But even more serious forms of interactivity often fail to enhance learning, despite the best intentions of designers, and it's often not at all clear why.

"Interactivity is often present in learning designs that improve learning, but it's not the interactivity, per se, that causes the learning improvements. Instead it's something inherent in the interactivity." The author then rules out (with references) increased attentiveness, feedback and rewards as possibilities and concludes that "... interactivity prompts learners to retrieve information from memory, and it's this retrieval practice that prompts the learning improvements."

I think reducing the effects of interactivity down to mere enhanced memory retrieval is at best a gross oversimplification and more likely totally wrong. It completely ignores learning by interactive exploration, for example, or building an understanding of issues through interactive discussion. The plain fact of the matter is, we just don't understand yet how interactivity really works, and are "winging it" when we include interactivity in instructional design.

To be successful, interactivity must be designed into the learning, not merely tacked on. At this point in time, however, interactivity design is not a science but a very imprecise art. Clearly, it must depend heavily on learning theory, cognitive science, HCI and related fields; equally clearly, it must depend even more on the subject matter. To design interactive mathematics, for example, I have to understand thoroughly the nuances of that mathematics (and how to teach it) before I construct an interaction to help learners acquire some of that understanding. Beyond that, however, I currently proceed by instinct corrected by trial and error; I've found very few useful design principles to guide me.

There's a huge amount of research and design experimentation that needs to be done before we develop a coherent and applicable theory of interactivity. We should be aiming to understand interactivity, not dismiss it.

Yes, I know summer started last week; I'm behind on a lot of things, and spring cleaning is just one of them. Actually, it's more than cleaning: I've been unpacking the last of my boxes from my move last fall, the stuff I've been too busy to get to until now. I don't have as much space as before, so I'm culling stuff: what doesn't get kept gets tossed or goes into boxes for Sally Ann. The place looks much better now without all that clutter around.

I really like this apartment. The building is older but well maintained, and has some nice design features - large floor-to-ceiling windows, for example. It's quiet but not dead; there's a distant background of people noises - a piano somewhere, kids playing - which I can hear if I pay attention but which rarely intrude if I don't. Quite pleasant, really - I'd hate to live in soundproofed isolation.

I'm a few minutes walk from a major shopping centre, yet from my windows I can see only trees. Right now, it's late evening, and I'm sitting on my balcony in a comfortable papasan chair looking at the moon through the branches of a huge pine tree and listening to distant train whistles. Blissfully peaceful!

Tomorrow will be another day of unpacking boxes and lugging stuff around from apartment to storage locker. I've promised myself I'd get everything done before the end of the month. I may actually manage to keep that promise.

I'm a sucker for eye candy, particularly when it moves or is interactive. I also have a strong preference for naturalistic images. These pieces (click the pictures) combine both, and are more organic art than eye candy. From play/create. Just because I like them, and because I've watched them mesmerized for more than a while today while waiting for my @#$%& ISP to fix things so I can upload again! Somewhat soothing ...

Present, by David Claerbout.

"Once it is implanted onto the user's hard drive, the flower manifests the rhythms of a natural lifecycle in an environment where time normally lacks organic reference. ... whenever the icon is clicked, the flower shows itself in a light appropriate to the local time. Not only is the flower's duration unknown in advance, but since one cannot speed forward nor go backward, one is forced to view the flower in the real-time progression of its natural cycle. "

Choose a gabera, amaryllis or rose. Dia Center for the Arts.

I went to see Of Heaven and Earth this evening, billed as "the first real Action-Musical - a show that utliizes an appealing story to display a kaleidoscope of human movement against a background of music and unique sound efffects". The music was actually the least interesting part of the spectacle, ranging from schmalz to frenzy; the performance itself was a lively combination of ballet, classical Chinese dance, modern dance, and Cirque du Soleil-style acrobatics, all loosely held together by the story, a romantic love tale about a weaving goddess and an earthly cowherd. I found the dancing and the atmosphere created by the dramatic lighting and sound most interesting; my companion, an accomplished juggler himself, liked the acrobatics, but was disappointed that he wasn't permitted to practise his other hobby, photography.

An interesting evening, made even more enjoyable by air-conditioning: we've had record temperatures today and it's been near impossible to concentrate on any real work.

I'm exhausted, and it's all Mark Bernstein's fault. A bit back, he disagreed with my contention that scientific arguments are inherently linear, and cited the Misner, Thorne and Wheeler text Gravitation as "probably the best paper hypertext ever published". I haven't looked at MTW for years, well before I even knew what hypertext was, so I certainly don't remember it as such. But my copy is hidden in one of a large stack of boxes of books still unpacked from my move last November, and Mark's claim finally goaded me to get them out of the boxes and onto my bookshelves.

This far, I've unpacked about 15 of the mover's "2-cubes" lining my hallway. Unpacking books can be heavy work, and time consuming if you want to arrange them in any sort of useful order. I've had to cull them: since I work mostly at home nowadays, my technical books are here as well competing for shelf space. Destined for the local library are all of my SF paperbacks except for a Heinlein anthology and the marvellous Alexei Panshin book Rite of Passage, all my mystery paperbacks except the Peter Wimsey series, and several boxes more.

I don't think I'll miss them. I'm at a stage in my life where I need to simplify things down to essentials, and getting rid of books and other possessions that have little relevance to where my life is now is part of that. Sorting through possessions for what's quality and what's dross is a useful mental exercise as well as a practical one.

Haven't found MTW yet, though - it must be in one of the 20 or so other boxes still lining my living room wall.

Slates, slide rules and software: an interesting historical collection of technologies used to teach mathematics in the US, and a nice reminder that technology need not be electronic. I still have my slide rule from Physics 101 (in Chem 101, we used logarithms, another technology). My first calculator was a birthday present; I swapped it for a small television.

In addition to the classics like the Piltdown man, the midwife toad and Linnaeus's butterflies, the Museum of Hoaxes exhibits other less well-known but interesting hoaxes, for example

"1874: The Case of the Miraculous Bullet. How a bullet passed through a soldier and struck and impregnated a virgin"

and

"1726: Mary Toft and the Rabbit Babies. Woman gives birth to rabbits".

See also the April Fools Day Gallery.

One of the most irritating educational slogans of recent memory appears to be fading into disuse, and not before time: the one that exhorted university professors to be "not a sage on the stage, but a guide on the side".

The slogan was meant to express the constructivist viewpoint of education: students don't learn by absorbing content from their professors, but by actively building their own interpretations through engaging with that content. True enough: we math profs have always known that you can't learn math passively; you have to "get your hands dirty" with calculations and problems to really understand the subject. Most of us have tried very hard to induce this atitude in our students, with admittedly varying degrees of success.

What's irritating is the image the slogan sets up: the pontificating professor dispensing information from a stance of authority and expecting students to absorb it unconsidered and regurgitate it appropriately on exams. This is a straw man, an unreal stereotype easy to discredit in favour of the more enlightened constructivist professor - or indeed, in favour of any other professor; choose your theory.

I know more than one dedicated university teacher made uneasy by the slogan's implied insult. For the record: very few of us have ever considered ourselves to be a "sage on the stage"; we've worked very hard to involve our students actively in their learning. We may indeed lecture, but we show, we don't tell - there's a difference - and we expect students' active involvement in their learning to include an active, involved attention to those lectures.

We may also teach through discussion, activities, or a host of other subject-specific methods, honed through years of experience. Few of us would claim that we've achieved perfection or that those methods will work unchanged in new contexts such as online education. Many of us look to the academic education community for appropriate new techniques. That community does itself a disservice and alienates those it's trying to help by misrepresenting what they already do.

From a post to the mathcdd list:

I think this is is a harbinger of things to come: in the future, mathematics learning will be done more from onscreen materials (web or CD ROM), with books devolving into supplements or workbooks. Books will not disappear, but their role in the learning process will change.

I've been thinking about the role of paper-based vs onscreen materials in the context of the "ideal" calculus course I'm designing (as a theoretical exercise; I don't yet have the resources to implement it). My conclusion is that each medium should do what it's best for: onscreen activities for animation and interaction with mathematical content; paper for extended reading and doing problems. Each medium does what the other can't do or do as well: computers support interaction and visualization better but not extended reading or problem solving. Onscreen reading is still problematic, and producing symbols and diagrams onscreen is much more tedious than with pencil and paper. This may change: I've seen prototypical handwriting recognition systems that handle math symbols, and if stylus-and-tablet computers ever become a workable reality, they may well do away with pencil and paper. But not any time soon.

Help this cow reach musical fame! Choose metal, hip-hop or disco, then mix your own music video.

From Milko. Swedish residents can enter the contest for best video.