Metaphors for emergent learning

Re: Metaphors for emergent learning

by Maria Droujkova -
Number of replies: 3

Roy writes, "How do you approach the movement of math ed participants across different degrees of freedom?.."

First of all, I have smaller units of analysis: individual activities, which may take literally a few mintues, not whole courses. Or maybe individual game mechanics and mini-games: one boss encounter rather than the whole World of Warcraft.

Each person needs a balance between activities that are at different points on each spectrum: give-observe-take, freedom-structure-restraint, exercises-problems-inquiry... Different people have different personal preferences for each of these mixtures, and these preferences change from day to day, or from minute to minute. For example, take problem-solving: a student may need some chaos (no problems! hakuna matata!), some inquiry (open problem-posing), and some grindy meditative exercises. A very anxious person who's been repeatedly burned may prefer a lot of easy exercises and will shy from inquiry, especially if observed or tested. Toddlers often, but not always, need a lot of inquiry and chaos. It's not like people strive, fight, and work toward more and more freedom, in all circumstances.

The main problem I meet with math is that so many people have PTSD, more or less. It's almost a tautalogy that self-regulation requires freedom. For example, it's very difficult to me to explain to parents why kids need the freedom to shift their attention - "to become distracted" - during math activities. How do you know if the activity is right for you if someone directly manages your attention?

I try to address most of these balancing issues with experience design. Maker tasks are especially good for helping people to self-balance, because people have healthier metaphors about making things: following other people's recipes, or remixing them, or experimenting more openly. 

"How do you (and the participants) work with the homologies between maths and gaming?" - a game is a type of experience, so game design is a type of experience design. It can be just a tool for time and task management (a gamification of some other activity), or it can be an intrinsic way to engage content. I am very interested in intrinsically mathematical game mechanics - in games like Set or Nim. It's very hard to design a game intrinsic to a given math concept. 

About the "Synaesthesia" piece: I do think the whole idea of "abstraction" needs a good shake-up. In particular, I work with very young kids on relatively advanced math ideas, such as algebra with three year olds. This Fall I started a series of math circles called Inspired by Calculus for kids ages four to ten. Conventional thinking tells us numbers are concrete, algebra is an abstraction of numbers, and calculus is an abstraction of algebra. But it isn's so if you take the embodied, grounded approach. Kids who can't reliably count to twenty already love infinity, and function machines, and fractals, and covariation grids, and zooming through powers, and...

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In reply to Maria Droujkova

Re: Metaphors for emergent learning

by Roy Williams -

Maria, thanks for the detailed reply and the examples. 

The embodied exercises, and an infinity of elephants (etc) makes it all so concrete, embodying the abstract. I can really see it working.  

In a sense all abstraction is, by definition, emergent, or derivate from the embodied and the concrete, but without these kinds of exercises, and without a range of degrees of freedom, abstraction is often too big a jump, and appears to have no 'grounding' and therefore no utility.  

What strikes me too is that the footprints thinking needs to emphasise the value of offering a range of degrees of freedom, as a range of entry points - exercises, inquiry, (edge of) chaos, which ideally should be available simultaneously, all of the time.  

This could be difficult to deliver, but its a key element of really open learning design, because if there is no suitable entry point, or point of engagement, no amount of emergent learning design will mean anything to that student. And as you correctly point out, "different people have different personal preferences for each of these mixtures, and these preferences change from day to day, or from minute to minute" - that's a challenge, and its an important one. 

My experience of mathematics is much more limited - but this is in principle so similar to the work I did in LOGO (with kids)  many years back, which provided the opportunities for kids to use complex variable programming to draw beautiful shapes - they were concentrating on the shapes, and iterative variations in shapes, and had no idea they were learning about variables and functions. 

In reply to Roy Williams

Re: Metaphors for emergent learning

by Maria Droujkova -

Want to make a list of tribes (communities, networks) that have a strong value alignment with emergent learning design and thus may grok footprints?

LOGO, now Scratch and Mindstorms and so on - that whole constructionist tribe is definitely on the list.

Unschoolers, for sure.

Who else?

Child made of building blocks

In reply to Maria Droujkova

Re: Metaphors for emergent learning

by Roy Williams -

Sure ... please share what you have / come across. 

We are starting to use the hashtag #emfeet to try to aggregate some of this stuff - early days, but it should allow everyone to contribute and to take stuff and run with it - in other work or other aggregations.  

Add other hashtags too ...