Surely a computer is only one medium, so multimedia implies using non-computer stuff too… ;-)

I’m not sure I have a grasp on what exactly it means for a good problem to reveal it’s constraints quickly and clearly, but I do know that if I took my students to a theater with an escalator, calculating how long it tool to go up the down escalator wouldn’t be on their radar unless I explicitly asked the question. Multimedia allows us to bring a lot of noise, propose a question without having to ask it and makes the learner decide what is needed to solve it. Not sure how to do that on a static page. That’s why curricula like CPM were ahead of their time. There was no way to withhold information in a book.

I feel it’s less to do with the strengths of Dan’s videos and images and more to do with the weaknesses of textbook problems. Any written question or diagram in textbooks I’m familiar with give the values you need and rarely one single piece of surplus information.

When using an artefact or video or photo I think we should seek to provide too much information so that students have to tease out the pertinent information themselves.

Your question hints at another pro-con argument (discussion if you will) about tech vs. non-tech. That’s a smoke screen. The better question is what can I do to motivate the powerful idea (i.e. slope formula) that will engage kids and get them intrinsically focused on what I would like my kids to get out of my lesson. This can be done hi-tech, lo-tech, or no-tech. I love to use technology (which includes most multi-media) to motivate because it has this incredible power to engage and motivate quality learning. But like any other learning object it can fall flat on its face if not done well.

I’m sorry I will miss today’s Math 2.0 session. I’ll be on my way to do time on the beach at the Jersey shore this week, but I’ll pick up the archive as soon as find some Wifi.

@Josh, @Dan (#1, 2) – My reply was identical to Josh’s – use the physical object itself. Of course physical media isn’t embeddable, linkable, remixable or reproducible in the ways digital media is. My answer to the concern of scarcity/reproducibility is, “Don’t aggregate learners in huge groups that can’t share an object sensibly.” Even “World of Warcraft” – a good model of scalability, and a digital world – caps most coherent content experiences at 5 to 25 people at a time.

There is one thing you can’t reveal constraints without, and media isn’t it. It’s geeky love. It leads to immense amount of attention to the features of the subject, and to noticing and categorizing properties by importance. This includes intrinsic (to the subject of love) ways to reveal constraints.

For example, paper folding provides great problem-posing opportunities to those who love it. Reference: http://www.youtube.com/watch?v=bzF_YldL-jU

Multimedia lends a (more tangible) richer experience of the problem than word-only questions.

More importantly, most students IMHO don’t care about planes in space (maybe rockets in space) – where’s the buy in?

These are not math undergrads who’ve declared their love for math is so strong they want to pursue it for 4 years. If you’re teaching a class of gifted / advanced / eager students who love to debate and dissect abstractions then fine, but for the regular high school kid – make it relevant.

I agree that multimedia lends itself to a certain class of problems. And that you’ve done some really good exposition of that, especially in contrast to the way textbooks spoonfeed process.

I guess my biggest qualm is that the “real world” is 3D, and multimedia is essentially a 2D representation of that world. I completely understand that it matches the math we teach in school, so that works. But there are some things (like the paper folding example above) can’t be done unless you get some paper out and fold it yourself. Now, whether that translates to the math we teach kids… that’s a whole ‘nother question.

That said, I’d be happy to see ANYTHING interesting done in most math classrooms. This conversation is quibbling about what the edge of the envelope looks like in changing the way kids learn math. It’s fun to talk about with the folks who are immersed in the attempt to change, but honestly, I am NOT complaining about anything you are trying to accomplish.

Planes in space or ticket rolls – I don’t see the buy in. And I did spend 4+ years in university math, and I do enjoy the beauty of the completeness of real numbers, and many other abstract things. I just don’t think this type of specific problems are interesting.
Honestly, by fighting so hard to make math interesting (content wise) for the students, we’re only at most making it slightly more tolerable. I think it’s the process that’s the key, and the ticket roll image is a great layout of constraints and a base for questions – so it opens up for some real problem solving. A well-crafted mathematical problem (planes in space, for those who care about such things) does the same, without the multimedia. But maybe the multimedia puts a different twist on things and variety is nice?

I just don’t think we should overestimate the importance of students posing their own problems, buying in, as it were. If they do, great. If they don’t, OK. Mostly, in math, they do it to please us. I teach psychology as well as math and it’s worlds apart. In psych, they’re dying to know things. In math, at best they’re enjoying the challenge of problem solving. I don’t see that changing, multimedia or not.

@Julia – A tiny minority of people are hotly interested in any particular context at any given time, including math. So, “math as its own context” – aka intrinsically interesting problems – will probably interest 3-5% of people, just like any other context. Others won’t do it if they have a choice.

Good news is that we can, first, use metaphors – math in other contexts – and second, help people choose their own contexts, because math is everywhere.

I just blogged about it a couple of days ago, with examples and diagrams: http://www.naturalmath.com/blog/its-own-context/

@Maria – Yes, I completely agree. Just like to add that far more than the 3-5% do enjoy problem solving – it’s simply intrinsically fun to see oneself grow, especially together with other people. That’s why I’m calling for more effective problem solving guidance, instead of searching for interesting content.

>What percent of people choose non-applied problem-solving as their regular (at least weekly) activity, selected among all the other contexts freely? This is my definition of “like.” By this definition, my estimate is 3-5%.

Maria, don’t the people doing Sudoku and KenKen – and other puzzles – count? And people playing chess? I’d expect the total to be higher than 5%. (Although perhaps not more than 10%. And of course I’ve been known to be wildly, inaccurately optimistic.)

Maria, can I read your essay about problems vs. puzzles?

Sorry I’m late to replying. My thought for this one was, have students in groups of 4-ish, and have one roll of tickets per group (or one for every two groups if they’re hard to come by). That should strike a good balance between accessibility for the students vs cost.

Don’t get me wrong, I agree that good use of media is a great tool to make data and reality accessible in the classroom. But the roll of tickets example is relatively easy to swap in direct access to reality. I tend to think that if you can bring in the real thing without too much fuss, that’s going to trump the indirect representation most of the time in terms of engagement and usefulness.

Obviously this doesn’t work with everything. I’m not bringing in a half-dozen hoses and giant water jugs. Plus, it may be harder to set those specific constraints that make the problem interesting (ie. pressing the pause button at the right time). And with an actual roll, you have to convince them that they’re not allowed to just, you know, unroll it or something.

Also, reality is easier for students to work with as they don’t have the intermediate step of dealing with scaled photographs. (Which is either a pro or a con, depending on what you want them to practice / demonstrate.)

“If the only tool you have is a hammer, then everything looks like a nail”. Just as a carpenter knows when to use a hammer or a nail gun, as teachers we need to evolving our repertoire of tools so that we can bring out what tool is appropriate to maximise learning. I think it is our job as educators to look at the way our students learn (visual, auditory, kinasthestic..) and teach to that, with passion!