As we have said elsewhere, Roy, Simone and I have spent many weeks, months, even years, discussing the language we use in our work on Footprints of Emergence. This week we posted our latest version of the critical factors we consider when drawing footprints of emergence. The content of this list (attached) is not different to the previous one, but it does include images. We thought these images might make the factors easier to use. What do you think?
Which of these images resonate with you? Which don't? And why?
Do you have any comments about the factors themselves and the way they have been organised into clusters?
We'd love to have your thoughts.
I should have put my post here! I did a footprint (template 2) the interactive and loved using the interactive tool. I also used the "mapping sheet for visual learners" to help me to create the map.
Yes, I am sure that you 3 have spent countless hours discussing the language and so congrats on getting it out there. I found myself pondering what the words meant to me and also found myself wondering if I was interpreting the words in the way that you 3 might have meant for them to be used/considered. I think what happened for me is in doing this footprint on my own (without your expert coaching : ) I was left to my own devices to figure out and work with the language. I think this is fine. I had no real trouble doing this.
Truthfully, the process helped me to consider my experience and I found myself wondering if the instructor's intentions of the course that I mapped would be reflected in my own experience and map. So, alignments "was her intention and my experience of the course similar or hugely different"? I wonder. I think I should send her your link and get her to do a map and then we can have a cool discussion about her online course for 500!
As for the images - they can be a useful trigger but wiht all images, they are the designers' representation of what they mean so for me they too shape a construct in one's mind. It's hard to find images that fully and accurately represent intention. I found myself using the text against my own thoughts to help me with the factors.
Clustering - again is a complex process and no doubt you have spent hours re-orgnizing the clusters....let me think about it and get back to you on this.
Hi Barb - many thanks for this considered post. It's really good to know that you have tried drawing a footprint and that you managed it on your own.
One or two people we know have managed to draw their footprint without any discussion with us, by reading what is on the wiki and watching the video - but we know it is not easy and time consuming. Heli Nurmi wrote a series of six blog posts about drawing a footprint (http://helistudies.edublogs.org/). She is now steeped in EdcMOOC so you need to scroll back through the posts to find those about footprints. It would be interestingif you could get your course instructor to draw a footprint and then compare them - but she would need to be prepared to give up a bit of time!
The comment you make about images shaping constructs in the mind is interesting. We thought the images would be helpful, but i now wonder how much they will influence the way people interpret the factors. Interesting thought!
Jenny, interesting question - how much do the images influence the way people interpret the factors?
As I said elsewhere here, hopefully the images help to keep the thinking more open (than texts, which tend to tie meaning down), but thinking about your post, I guess images could be too strong, and too directive too.
What would a usefully open image be like? And have we got any in our mapping sheet?
My first impressions are that the images for Unpredictable Outcomes, Open Affordances, Presence/Writing, Informal Writing, and Autonomy - in that order - are the most open, Networking is the most clunky [please help out if you have a better one], and Liminality is the most closed. But maybe that's just me.
Barb, good to hear that the 'interactive' tool worked.
Language, language ... and odd business. On the one hand we dont mind making the footprint creator do some work in thinking about the language and the terms, and to make them specific enough, (and reference the work of the many people who have designed and researched and thought about this before us) - but on the other hand we would like the creation of a footprint to be as intuitive as possible.
That means that the simpler the language the better, particularly if the accompanying graphic still opens up the possibliities for mearning and context. All suggestions on both these issues will be gratefully received and acknowledged!
An 'I'll show you mine if you show me yours' sharing of footprints is exactly what we have in mind, to open up a 'collaborative reflection' conversation. That's, really, where we think this should all be heading.
So ... interesting questions and processes for engaging on 'alignment' and alignments (there are so many things to align with), and hopefully an iterative process for open/ended conversations - which ends (or doesn't end) when you have completed what you want to do.
Yes, I suspect that the "footprint creator" must do the work! : ) Yes, also to the opportunities to "show" the footprints for a "learning design" conversation.
Here's the thing....last night I rode the bus home with a colleague from the teaching and learning centre and I had a print out of the templates - we "worked" it on the bus home. In describing to him my experience of this seminar and ultimately your work with Jenny and Simone on the tool, I realized that this tool might be a way for ongoing "feedback" for instructors if the tool was embedded in the course as a mechanism for students to "record their experience" on certain factors and for the instructor to see the recorded experience and then do something to support the student.
I immediately started to think about the fact that we do too much in terms of pen and paper evaluation forms on teaching and NOTHING on the experience of the learner! (I am in higher ed and a mid-sized, research-intensive setting) so you can imagine the process that unfolds at the end of the term regarding course/instructor evaluation. I believe that a tool like this can be used to have the "conversation" or take the pulse if you will of the experiences (learner by learner) and then there will be a pattern for the instructor to also see and the instructor has also got their own map going of their experience of teaching.....
I also want to see this tool in a "computational" environment where it is possible to visualise in 3D thus making it possible to see the spatial qualities which might lead to ideas about what is happening between students. For me the 2D interactive map is great but I would love to see what would happen if we could rotate and translate these maps in a computational space! what are your thoughts on this?
Now I am heading into the research potential....will save it and see what you have to say to these whacky, imaginary comments of mine : )
How does a student experience a class? The footprint seems like good way to record a student response--better than surveys. Learning that is expressive needs a place to live in the students' experience. And be recorded somehow.
Just reading a bit on Rudolf Arnheim at:
"This discovery of the gestalt school fitted the notion that the work of art, too, is not simply an imitation or selective duplication of reality but a translation of observed characteristics into the forms of a given medium (Film as Art, 3).
The Gestalters thought that these principles–figure/ground, completeness, good continuation, and the like–were fundamental to all human perception, across times and cultures. Art and Visual Perception makes a powerful case for this view. Today this position is so unfashionable that Arnheim’s calm confidence in it is quite stunning. For many scholars today, all that matters is what divides and differentiates us. But for eighty-plus years Arnheim emphasized ways in which we share a common experience of the world and of art"
Thanks for sending this to me. I absolutely love this and incidently will pass it on to faculty I work wtih in the School of Interactive Arts and Technology here at SFU.
I really appreciate your bridging to the "gestalt" as described in Art and Visual Perception. I have read the blog post and will go back over it again as there are lots of ideas to mull over.
I really believe that "experiencing" is full bodied in the sense that there is somatic, emotive, cognitive, spatial and other dimensions in learning and they all come together as a full package. The footprint seems to alert us to a more wholistic view of what might be happening in a given context and it makes sense that we must pay greater attention to the whole than the parts.
Barb (and Scott), looking at you own footprints (shared elsewhere in these forums) confirms that this is not the same kind of 'data' that we usually get from our students in feedback and evalutation forms, to wit ...
1. The learner is, really, the primary researcher, and in working through the process of creating the footprint, they are researching reflexively: i.e they research both the course and their experience of it (which is why it can feel quite different from filling in a questionnaire). You, as a faculty member (or researcher) are really a secondary researcher, researching their research, no?
2. The footprint is a 'gestalt' of the learner's experience at a particular time, there is a limit to the extent to which an individual factor 'mapping' can make sense on its own (as Scott points out in his reply to you in much more detail, below) - the factors interact with each other.
3. However much I can make sense of your footprint (particularly now that we are asking footprinters to use and share the 'my comments' column - borrowed from Jutta's group), the footprint+comments doesnt yield many answers, but it does yield lots of questions that I would like to discuss with you.
4. #3 changes everything, and establishes a space for collaborative sense-making ...
4.1 Epistemologically, it yields opportunities for exploring sense-making, but provides little in the way of conclusions at the footprint stage, although it does provide, intuitively(?), a gestalt of that point in the event.
This inverts the usual process too - it starts at the gestalt (synthesis) and then proceed to analysis - and in all likelihood, returns back to a quite different - possibley collaborative - gestalt.
4.2 Methodologically, it pre-empts premature evalution (excuse the pun), particularly if everyone focuses on the work of description.
And it sets aside the evaluative and normative process and judgements until later.
4.3 Ontologically, is changes the status of the people in the conversation - the learner and designer (can) become collaborators in making sense of what happened / is happening - particularly as the learner (or learners) have rich, complex 'data' - better data than the designer or facilitator has - at their disposal.
My footprint does represent my experience of this course however, since I did this footprint after the course was completed, the data offers a summative report - back on my experience.
I agree that for the learner and the designer to "co-design" the learning experience, this tool is best positioned in a different way than how I used it (for this activity) and thus would generate different, timely, dynamic data. In my mind then this tool is an "actor" and with it's own "agency" - and is a bridge between the learner and teacher - as they work together (hopefully) towards "collaborative sense-making" as you point out.
am I getting it? : )
Barb, you got it! For sure. The footprints as an actors (or a tribe of actors) with their own agency, and role in collaborative sense-making - we couldn't have put it better.
I am not certain that to comment is useful, since what I have to say is outside what I perceive to be the focus of this seminar, and there is a debt of respect that suggests to me that I should refrain from comment. All the same...
I wasn't able to attend the seminar yesterday. I wanted to because footprints seem to me to be a challenge in the sense that to me they seem to be an interpretive way of presenting data, insofar as they draw a picture that drags the mind. Words and numbers force the mind to engage. Pictures seduce. So I wanted to know more.
I missed it. So the thoughts I post here are from outside. Considered, but external. I work on the edge of research, I do it, but spend my life defending its relevance because that is where I work. I would have trouble getting people outside full time research to use this. Though of course this may not matter.
Personally I find footprints potentially useful. I can see a lot of ways of using them, within the research context. But I am always concerned by what research does to explain itself to the people that fund it (whoever). Footprints are a step in the right direction, in that they help to visualise the situation, but in the wrong direction in the sense that that serious engagement with them requires a whole new literacy.
So, I see it as a great research tool but forget ease of use. Just a quick look at this makes me think I would hesitate to use it even if I could dedicate a couple of months to it:) It is very very rich, but there are more than 20 elements to assimilate in this particular version, and then the way the data is visually represented. As you say you have spent serious time on it. That's fine, and it is a good tool, as long as it is clear that it is for use inside the field (with all that implies) and that later there will be a job of communication to the world outside. And that is the challenge.
These are impressions. As I say I may have missed something said in the session that clarifies this. But my perspective is that this, as it is, is unlikely to be comprehensible outside the "tower". That term may really rankle, and it may be seen a different discussion, I would argue that it isnt. Science happens in society. Our lives as researchers are funded by others. We have a duty to be able to explain what we do.
Hi Nick - many thanks for your 'thoughts from outside' which are very helpful.
You are right - 'forget ease of use'. We have wondered whether we should cut down on the factors and in one workshop we ran we highlighted factors in each cluster and said to participants that if they found 25 too many, then just use the highlighted ones - but they all used them all anyhow. We also always say that it is a palette of factors, therefore select the factors that are appropriate and leave the rest - but usually people use them all. In one workshop we ran, a participant said that the factors were interesting because they raise questions and consider aspects of learning that are not usually found in evalution questions - and certainly we have tried to represent the complexity of learning. So - yes - the process is time-consuming and no- it is not easy, particularly to begin with and until the meaning of the factors and process has been somewhat internalised.
It is true that the factors have only been used to date in academic situations and within Higher Education - but not only in research situations. Our colleague Jutta Pauschenwein from Austria has used the footprints extensively with her colleagues and her students. She is interested in creating open learning environments and uses the footprints to explore how open they are. She blogs about her use of the footprints - http://zmldidaktik.wordpress.com/. You need to scroll through to find the posts and some are in German. So the footprints have not only been used for research purposes, although we and Jutta have pubished papers on them. I think some people can see the potential of using them for evaluation purposes - as Lisa Lane explained in her blog post following the workshop - http://lisahistory.net/wordpress/2013/11/course-footprints/ . Roy, Simone and I have never received any funding for this research. In fact, in all the research I have done, only one project has been funded.
But I think the most interesting question you raise is around this tension of how to represent the complexity of the learning process whilst at the same time making the process of drawing the footprints more accessible. I agree that it is something we need to work on if we want the footprints to reach a wider audience, but it's difficult to know quite where to start. We do know thought that if we could find some way of automating the drawing of footprints that would be a start. We also know that we have further work to do on the language we use.
Lots to think about and any suggestions would be welcome :-)
Nick, wonderful, thank you so much. Critique, paricularly from 'outside' our own 'echo chambers' is refreshing. By definition, we have little or no 'outside' perspective available to us, personally, any more as we have been working on this for far too long.
- It started, and progressed, I guess, as a research tool, from the inside. It shows, you are quite right. (As researchers, that does not matter, as members of a community of users 'of learning' it does - a difficult paradox).
- This was not funded, it was done in the time we could find, or steal, between the demands of our day jobs This was good because it gave us freedom from delivering the goods to funders (we have published a lot, so I suppose we had to deliver to the journals, but IRRODL and NLC (amongst others) have been very supportive. More recently we have bumped up against the 'big data' / instructivist /xMOOC / 'physics envy' lobby, and have had a few refusals, including a refusal from our first funding application! mmmmmm ....
- A whole new literacy - exactly. I often think about doing a meta-mindmap of the factors and clusters - literally, placing the palette in the centre of the mind-map, and drawing in the miriad links to the researchers whose shoulders we are standing on - but that would probably make it even more complicated, and more of a challenge for a whole new 'meta-literacy'. Aaaaaaggh!
- Question: how far can one go in developing new tools, without losing most of your audience in the process? Food for thought. This is very new, taken as a whole, but it is also very old, and builds, for example, on some central ideas and experience that we got from Montessori pre-schools, many years ago, and that she developed more than 100 years ago now. That doesn't answer the 'user friendly question though, I know.
- Question: Is this an 'app', and should it be an app that can be downloaded and used in the first 5 minutes, or is it a new tool that requires two webinars and two weeks of discussion to use?
- Based quite largely on the experience of running these webinars and forums in SCoPE (the first time we have attempted it fully online), I am tempted to 'package' it as a two-week engagement event - I think we might have been over-ambitious in trying to do it in 60 or 120 minute workshops before, but hey, that's also a learning experience for us. For me, this 14 day format (for participants, and for us) looks about right, though I must say that we have had some seriously useful and positive responses from quite a few people (in education, admittedly, but some of them were students without too much research experience).
- We would seriously like to make it more interactive, which might (?) make it more user friendly.
- But ... should we / can we ... still demand of our users that they do some work on a new literacy first?
- I am reminded of the 20 years I spent trying to convince my brother (otherwise quite intelligent, he was a fellow of an Oxford college) of the sense of post-modernism - he finally got the point when someone said "for example, you have to be able to see the dog as text ...". I sometimes wonder if it will take another 20 years to convince people of the 'sense' of complexity theory (which we try to avoid, and just talk of 'emergence' instead - dont know if that works).
Any thoughts/ suggestions? We would love to find some 'get out of the tower' cards / ideas. Cutting the list down from 24 or 25 is one idea we have considered, but rejected - so far.
Thank you again - these are crucial issues, and not 'external' to the debate at all - though of course your 'external' vantage point gives you an advantage!
This is my first reply to this Scope seminar, so I need to say where I am coming from. I like Nick's metaphor about the edge of research, which describes me as well. I do research mostly for the sake of development. In the last ten years or so, my goal has been supporting networks of small communities in mathematics education, in three directions: other developers (Math Future project and its subgroups like Math Game Developers), authors (Delta Stream Media), and parents/homeschool coops/math circles (Moebius Noodles and Natural Math projects).
I find this list of metaphors hugely useful. I have made several Degrees of Freedom lists (what you call Emergence lists) for my communities, for example:
- Problem-solving - Inquiry - Self-organized learning, a rubric for parents who map activities during Math Circles
- A bunch of math game design lists, such as the spectrum from gamification to intrinsic math, and another one from Takers to Makers
- Intellectual consumerism at the lowest rungs on Bloom's ladder in math, and the producer communities (producer-consumer spectrum, the same as Takers and Makers)
- Learners' influence in computer environments (p.386) - which turned out to be too complex for casual use
In my experience, people love well-organized lists with pictures! Just look at the popularity of sites like Cracked or Buzzfeed. However, nested lists like you have in that document (lists within lists) or other complex, nonlinear data structures need a whole lot of visual support, and require a lot of storytelling. When the time is short, complex data structures are only for specialists.
I will be adapting these Footprint Metaphors for my math ed communities, for sure. The adaptations will include:
- visual mapping of structures, such as branching trees or concept maps
- three concrete examples with every term
- rephrasing some of the terms into lay language
- inserting and naming middle points on the spectra where only two extremes are named
- math pictures! - like fractals to depict complexity and emergence
Thank you very much for your work!!!
Maria, very interesting - degrees of freedom and the way you map different aspects of maths and gaming (and the overlap between the two). Please let us know how you get on with adapting the footprint metaphors in your math ed communities.
How do you approach the movement of math ed participants across different degrees of freedom, and abstraction, and how do you (and the participants) work with the homologies between maths and gaming? Gaming is embodied (or vitrually embodied) algorithms, no? Or is there also a homology between algorithms and programming in gaming?
And the fractal of hands is quite disconcerting. We might use it as an icon sometime - with you permission.
And ... time, paticularly when it is short - does that engage participants in new ways? I am particularly interested in the link (and transition) between embodied, intuitive engagement (/learning) virtually embodied learning, and abstract learning. We have a follow up paper dealing with some of these issues, with some links to emergent learning coming out in Leonardo journal next year - see the abstract here ...
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...
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.
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.
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 ...
And ... Maria
I sometimes wonder (or dream) of just giving participants the title and the image, and asking them to respond: Risk (with the image of the boy 'jumping the skyline) or Tranformation (with the image of the butterfly and larva) [not 'liminality' that's too specialist].
This would cause more or less confusion, and make it more or less accessible?
Just getting people together with a prompt works great - with friends! I've tried it many times, with such mixed results that it's not something I would do again in a random group, not anymore. At least in math, many people are way too anxious for anything of that nature. And others simply prefer less openness. However, with a bit of scaffolding it may work. For example, you can tell people to write down three phrases that first come to mind when they look at the butterfly and larva, and think about learning. But you need to prepare some other scaffold for when they have the phrases. For example, they can tape their phrases to a whiteboard and create bridges to someone else's phrases.
Chapter 4 The Development of Reasoning by analogy by Usha Goswami
From "The Development of Thinking and Reasoning" edited by Pierre Barrouillet and Caroline Gauffroy Psychology Press.
“Reasoning by analogy can be considered a core component of human cognition. Analogy is important for learning and classification, for thinking and explaining, and for reasoning and problem solving. The history of science demonstrates the role of analogy in key scientific discoveries. Indeed, many argue that reasoning by analogy is central to creative thinking (Holyoak & Thalgard, 1995). The contribution of analogical reasoning to cognition has been defined in various ways, including Holyoak and Thalgard’s concept of “mental leaps”. ...argue that even the simplest analogy involves a mental leap, as it requires seeing one thing as if it were another. The reasoner must make a ‘mental leap, between domains that may not previously have been connected. These mental leaps are often evident in famous analogies in the history of science.”
On to Keith Holyoak and Paul Thalgard 1995: “Mental Leaps: analogy in creative thought” MIT Press 1996
“When we are young, before most of the familiar patterns of everyday life have been learned...Knowledge of the world awaits construction. For the child the pool of known situations is still small, and novelty is the norm; so much has to be understood with so little. But already the fundamental thought processes that guide the creation of understanding are hard at work. Perhaps it would be more accurate to say they are hard at play, since for a child (as for a scientist), understanding the world often becomes a game driven by natural curiosity.
Consider the following discussion between mother and her four-year-old son, Neil, who is considering the deep issue of what a bird might use as a chair. Neil suggested, reasonably enough it would seem, that a tree could be a bird’s chair. A bird might sit on a tree branch. His mother said that was so and added that a bird could sit on its nest as well, which is also a house. The conversation went on to other topics. But several minutes later, the child had second thoughts about what a tree is to a bird: “The tree is not the bird’s chair—it’s the bird’s backyard!”
In this conversation Neil makes a mental leap, exploring connections between two very different domains. He is trying to understand the relatively unfamiliar world of creatures of the air in terms of everyday human households. This small example conveys what we mean by reasoning by analogy, or analogical thinking. The child’s everyday world is the source analog: a known domain that the child already understands in terms of familiar patterns, such as people sitting on chairs and houses that open onto backyards. The bird’s world is the target analog—a relatively unfamiliar domain that the child is trying to understand. Analogical thinking is not “logical” in the sense of a logical deduction—there is no reason why birds and people should necessarily organize their habitats in comparable ways. Yet the analogy is certainly not haphazard. In a loose sense, there is indeed some sort of logic—call it analogic—that constrains the way the child uses analogy to try and understand the target domain by seeing it in terms of the source domain.” P.2
Scott, what are you thinking about the connections between these two quotes on analogies and the above discussion? I don't think I see any direct bridges. Please help me make that "mental leap" as the second story has it!
When I first noticed these quotes there was a very strong feeling in my mind that they were connected. Now that you ask I’m not sure about the relationship here. This often happens in thinking about how things relate to each other, the link, at first strong, turns out to be too weak to hold.
Been thinking a lot about how problems are solved and the tools needed to accomplish this. In the young boy I see the development of understanding that is impermanent and will develop as he develops. And this brings up the idea that decisions, assumptions, strategies, whatever are not end states but stops on a path. We start with the evidence as best we can from what we have, and build on that to finer and finer understandings.
At the beginning of this is my looking into diagnostic training for mechanics and how mental leaps can as often lead to miss-diagnosis as to correct diagnosis. I see a connection between emergence and diagnosis but struggle with there being more than one correct answer as in there being wrong’ish or right’ish but not perfect solutions.
The more I try to explain this the deeper in trouble I get:-)
Scott, the discussion of "right-ish" or "right-er" solutions sounds promising to me. In mathematics and sciences, even with open problems, you better have criteria for judging right from wrong. Which brings me to what I want to discuss: analogies vs. metaphors. I think the boy and the bird quote is more about metaphors than analogies. And here's one more quote:
“I cordially dislike allegory in all its manifestations, and always have done so since I grew old and wary enough to detect its presence. I much prefer history – true or feigned– with its varied applicability to the thought and experience of readers. I think that many confuse applicability with allegory, but the one resides in the freedom of the reader, and the other in the purposed domination of the author.” -J.R.R. Tolkien,
Even in emergent designs, we do need scaffolds and structures, common WHYs, and other ways to bring participants to a particular contextual neighborhood. But I think it's better not to exercise purposed domination all the time; and when we do, it has to be consensual ;-)
My hope: footprints and other mappings as tools of freedom and consent. These tools address one of the biggest pro-coercion arguments in education: that learners don't know pedagogy and design, don't know what's good for them. Learners who are aware that activities come in different types can make more informed choices about learning.
The JRR Tolkien piece on the 'degrees of freedom'/ agency in applications (high) and allegories (tends to zero) is very instructive. And from the footprints that we and many others have created so far, and taken into a range of conversations, its clear that learners have a keen, instinctual feel for pedagogy (or heutagogy - if you must), and a keen, instinctual aversion to the abstractions of pedagogical discourse.
In the Nested Narratives project (which overlaps with footprints to some extent - see the link to the BJELT paper, here, for details) we got students to engage in complex layers of reflective practice (using prompted narratives), which they loved, but only because they learnt reflective practice by doing, not by instruction. All we told them was that we wanted them to tell us stories about something they had learnt which was important to them - no mention of pedagogy, and we deliberately did not mention 'reflection', as they had told us they would tell us stories only on condition that it would involve no reflection, and no critical thinking - both of which they found deadly boring.
So ... why are we constructing a footprints tool that is immersed in abstract pedagogical discourse? - a good question. (Best answer I have, and its a poor one, is that we started off this developmental process as researchers, exploring the wonders of pedagogical, psychological, neurological, ecological, sociological, etc discourses - particularly me - I love the stuff!).
However ... tools of 'mapping and consent' (involving real choice) must ensure that there are some clear entry points into 'doing' footprints that are unencumbered by the requirement to first learn pedagogical abstraction - alongside entry points for the specialists who want to engage through (and with) pedagogical abstraction too, no?
Barb - if you are folllowing this thread, this might resonate with the concerns you raised about course designers who demand that participants 'learn (the technical, software skills) by doing' alongside learning the content and conceptual tools of the course itself. Food for thought.
The discussion of mapping in absract or lay language reminds me of "The hundred languages of children" from Reggio Emilia. There is no reason to ostracize a minority language, such as tech terms from a research field, as long as it's not mandatory for everyone. But we need some universal translators or Babel fish. Diagrams may be more universal than words.
Love the anatomy of Babel fish - and yes, we do need universal translators, and yes, no need to ostracise the strange language of academics.
Jutta (in Austria) will be running her next workshop using some of the images in the new mapping sheet - although I dont know in detail how she want to use them - it'll be interesting to see, and interesting to find out if the images 'travel' or not.
Right’ish and wrong’ish suggest to me a spectrum of possibility that might be free of the need for being exact. Not an estimate but a range of working possibilities.
Not knowing much about math doesn’t help me here, though I do sense within the logic of math is the permission to approach problems from different, but equally valid solution strategies. Not that any old thing is right only that “right” has some signature characteristics of being got to that a procedure was followed. Not necessarily the “proper” procedure—more like a defendable series of decisions that lead to the answer. For instance the “birds backyard” statement is arrived at by a repeatable process that might yield clues to its reason for being an answer that is legitimate? As might emergent artifacts leave evidence of how they came to be?
My definition of allegory would be a completed object of thought that has a point to make. An allegory is a completeness beginning with a rhetorical problem that is “solved” by a culturally biased correct answer. I think of it as a resolution pre-made to prove the point of itself that exists in a closed logic. Even though math seems to me to be closed into a world of rules and proper procedures it somehow allows itself to not pre-judge outcomes. I don’t know why that is beyond guessing that an open universe is more enticing to the intellect over a closed universe where everything has an unchanging final condition.
Do you think an analogy is more restrictive than a metaphor? That an analogy is an object of dominance, or at least an expected outcome that is correct at the level of approval by others over a metaphor being a raw outcome of the thinker’s mind? A decision unique to the thinker?
This is getting kind of ‘out there’ but thinking about it has brought up the realization (right, wrong or something else) that studying humans as individual processing units is not the path to understanding or explaining uniqueness. A social beings we have antenna finely tuned to a field of fertile suggestions evidenced somehow in our choice of what we mark as discovery or significance. We are referential, knowing and doing among the presence of others while also being consensual in having to convince ourselves to believe. As well as permitting or inviting others to teach us to the depth of our being.
Does any of this work? The idea of “the learner” is so complicated.
Mathematics is very creative, in that you are allowed and encouraged to make things up from scratch. There are no restrictions about your creations matching the physical world (as in natural sciences), or being useful (as in engineering and technology). What you make up is not even required to have an aesthetic value; it just has to follow its own logic, which you are also welcome to make up. You can search the web for "algebras" or "geometries" (plural) to see pretty exotic stuff! But there are certain values and traditions within math as a human endeavor, such as consistency, precision, elegance, and so on.
You write, "Even though math seems to me to be closed into a world of rules and proper procedures it somehow allows itself to not pre-judge outcomes. I don’t know why that is." The seeming contradiction is resolved by viewing math as an open, creative world. It can be an allegory or analogy for something, but at its heart it's metaphoric. This brings me back to metaphors vs. analogies.
Both are two-parter structures with sources and targets. But analogies have pre-determined, pre-judged, pre-solved target. In contrast, metaphor is a tool for generating your own targets. I like the social links in your last paragraph (not seeing humans as individual processing units), because other people's suggestions, references, cultures, etc. mediate targets of our metaphors. But analogies not just mediate - they prescribe. Which is perfectly fine in many cases, for example, when bringing up a novel context. Say, to start playing with a non-commutative algebra, I might use the analogy with unrequited love. If I play with a toddler, I would use a sillier analogy, like the chair sitting on you not being the same as you sitting on the chair.
In terms of footprints, metaphor is a near-boundary tool, while analogy is a near-center tool.
Elegant analysis, thanks.
So, mathematics is an infitite set of transformational metaphor processes /structures /tools, sometimes linked to other (less abstract, bu possibly equally complex) practices?
My first insight into metaphor was from my philosophy lecturer, who said they are 'deliberate category mistakes' - precisely a near-boundary / edge of chaos tools, and his favourite metaphor (and one of mine too) is a fruity one, see here ...
Neat example. As a funny aside (the example's not about it), in affluent societies, food is easier to come by than sex, so food usually serves as the metaphor source, and the relationship as a fantacized target. It can be the other way around in different circumstances.
Yes to math as an infinite set of human-made processes, structures, tools, and practices, with everyone invited to make their own. However, if you don't adhere to past practices, others may not care about the math you make. As usual, it's harder for some populations (kids, women...) to change practices. Ironically, it's very important for kids' learning and development to create their own math in their early years - the time the world typically gives kids the least opportunity to do so. And in many countries, it's still harder for a woman to publish a math article than it is for a man.
The idea of things being consistent to some sort of logic or structure makes sense. Without structure we have a nonsense of no relationships or interactions. From what reading “The Work of the Imagination” by Paul L. Harris, even children in a state of pretending have rules and are sensitive to falsehoods that are inconsistent with the “story” they are enacting.
Left to their own without the attraction of structure how do we discover meaning? Where would it be in the scattering of ideas that don’t somehow connect? Structure seems different from orderliness. To be in order is just an arrangement or collection of things. They don’t touch or need to interact for something emerge because without connection they are lifeless. Structured things call to each other, intermingle and create newness.
Have to think of an example of what I’m saying.
Here is an example of how I understood what you are saying about emergent structure with consistent rules vs. pre-determined order with pre-determined rules.
Emergent structure. A kid makes up a function machine. A number goes in, the machine does something to it, and a number comes out. I give the kid who built the machine numbers I want to try, untill I can guess what the machine does.
- 5 in, 10 out. Does the machine add five? Oh.
- 2 in, 4 out. Does it double the numbers? No?!
- 1 in, 2 out. 0 in, 0 out. 10 in, 20 out. I say it doubles! No? I give up.
- Oh, it adds three, then doubles, then subtracts six? How neat! It works like doubling, but it's much harder to guess. What other function machines work like doubling?
Pre-determined order. Write down times two tables.
Here are a few more function machine examples from our Moebius Noodles book, including iterations of the doubling machine. Because when kids can easily double, they do it again and again and again: an emergent but predictable behavior!
Scott, your question about emergence and diagnosis ...
Might it be that although the process of intervention - in mechanics - might be very specific, with little room for the luxuries of 'emergent thinking', the process of arriving at a diagnosis (and even tentative prognosis) might be of a different nature, and might involve tacit, fuzzy, decisions about not what specific interventions to employ, but what metaphors or homologies to employ in thinking about the diagnosis.
This reminds me (I hope this is pertinent) of a piece of research into mis-apprehensions in problem solving in science, in which the root of the mis-apprehensions was in the misapplication to either a calorific or a Brownian conceptualisation of heat, which led to 'bugs' in thinking through the problem, and that in turn led to an inability to think through a strategy to achieve the solution. It was only when the two frameworks were made explicit, and discussed openly, that both students and the teacher realised that the two frameworks / metaphors / models were appropriate to different kinds of context.
Wonder if I'm substituting emergence for interruption in diagnosis. Many diagnostic strategies seem to rely on assumptions of causality that need to be questioned or 'interrupted' or displaced from their comfortable placing.
I like the idea of there being alternate successful paths or proceedures to reach a viable solution and agree that making them explicite and discussed openly is critical. Moving from one decided thing to anouther until a final decision is come to isn't diagnosis as far as I'm concerned. I've seen unsuccessful diagnosis done from a manual without thought because it was considered the right proceedure.
How would we force ourselves to openly observe the evidence without constantly coming to conclusions about it?
By learning to live on (and love) the edge of chaos.
No, that's too easy. Avoiding jumping to conclusions is a prerequisite for learning, and for many unusual diagnoses, no?
A favourite of mine: in my (brief) days as a medical student, I worked in a rural hospital, including a Leprosy unit - in which 'feeling no pain' is the key evidence for the disease (nerve degeneration leads to loss of sensation), which is why it is missed so often by doctors who don't normally see cases of Leprosy, and 'can't imagine' why NOT feeling pain would ever be a key symptom for disease.
So ... the rarer it is, the more difficult it is to diagnose.
Roy, jumping to conclusions is definately a bad habit in diagnosis. In your example 'feeling no pain' is also improprly placed in the brain as a category wellness and unnecessary of further investigation. I imagine it as a kind of switching phrase to relieve obligation to act.
My cardiologist's booking clerk likes 'no news is good news.' The problem is, she's busy and can't follow up to see why I never received the news that was bad news.
Excellent! Just the right kind of 'light-touch' scaffolding. Thank you so much for pointing the train of thought in this direction.
Let me see if I can take it further ...
Bringing their own associations and experience in, to add richness to the images is a very sound workshop technique. It might take longer, but it would be so much more grounded in their own sense-making, rather than asking them to 'detour' through the obscurity of pedagogical theory (which very few people have a taste for - even academics, lets be honest ...) and trying to use such abstract terms for their own sense-making.
In other words it might answer your and Nick's challenge to make the 'ivory tower thinking' more accessible - not by editing and reconfiguring it, but by destroying it, and getting the learners to build their own versions of the mapping sheet instead, just from the images. Wonderful idea!
If we go back to your design principle of always making a range of degrees of freedom available (and perhaps add a range of modes too), we could offer mapping sheets based on:
- Scoring (we started with a scale of 1-30 (and up to 40 for factors that fell off the edge of chaos). We later decided to move on, beyond 'scores', to emphasise the push and pull of the factors (as dynamic vectors, rather than discrete scores), but why not keep them available for people who want to use them?
- Mapping sheets:
- Our current 3.0 version, with graphics and text
- A new version, 4.0, with just graphics - but with collaborative exercises to generate associations and texts and more images (maybe a range of images for Risk, for example, from low to high risk, or comfortable to uncomfortable risk?) We could do this with graphics selected from the web, or created in collages, etc.
- A version 4.1, with graphics and factor titles only (perhaps a bit simplified, if possible)
That could be crazy and unmanageable, but it might allow precisely the range of degrees of freedom, and the range of light to heavy scaffolding which could provide an inviting entry point for just about everyone. It might increase the workshop team though, to support all these options. Mmmmm.
This might wreak havoc with comparisons between footprints, but perhaps not - if the factor points are kept in the same places, and if there is a reasonalbe commonality of meaning across various people's and various groups' self-generated factors, the footprint 'gestalt', comparisons between footprints, and collaborative conversations about them would still work.
And of course one of the underlying principles, namely that the footprints are visualisation tools for the learners (and designers and teachers) to explore their OWN experience of the learning, would be fully aligned with the practice of asking them to flesh out, and enrich their OWN sense-making of the factors.
Yes, people need to bring - or to make - their own content. As you explain, the main challenge in such designs is to integrate everybody's experiences into a coherent whole. We want to avoid the feeling of Babel - everybody speaking a different language!
How can some common analysis of big WHYs happen? How can I look at your footprint and you look at mine in ways that we can see similar big SO WHATs? Your footprint looks like a butterfly and mine has a big protuberance in the southwest - so what does it mean for the compatibility of our dreams and beliefs?
Most citizen science has citizens collect data, which is then analyzed back at the ivory tower. How can citizen scientists analyze data, too? Say, how can parents in my math clubs compare notes on how they help their five-year-olds with scavenger hunts for nonlinear functions? One parent helps by providing examples, another by asking questions, another by dispersing hugs. Different footprints; how can people analyze results together?
How can citizen scientists analyse data (or should we say create data) too? mmmm...Your examples of comparing notes (on asking questions, providing examples, and dispersing hugs) is a great start. Let me try and think it through a bit further ...
So ... if we can provide the tools (graphics, free association exercises - what words, what texts, what images, what sounds, what smells do you associate with this graphic, when you think about what happened when you were learning? -
... or vice versa: we could ask: What graphic would you associate with "risk", and the way it affected you and your learning? - and if we could provide an app for them to replace the label 'risk' with a thumbnail of their own graphic for risk, which they could double click to expand (and reduce) it, so that they could show it to others in a discussion, and tell the story of how and why they chose it, and what 'risk' means to them)
plus: ... we could provide different degrees of freedom for low, medium or high "risk': i.e. i) select from a given, small, set of images, or ii) find their own images, or iii) make their own images - in collages, in new graphics, etc.
and if ... participants (learners, designers, teachers) created footprints on that basis -
Then we could invite them to join in a conversation in which they could all compare notes: gestalts and icons and stories about how they arrived at their particular footprints.
They could do this on paper. It would be more fun and more interesting it they had ipads, or laptops, or mobile phones (?) or interactive tabletops, sure, but what a conversation it could turn out to be!
And ... we could add an app that allowed participants to i) superimpose, aggregate, etc, their footprints with other footprints or ii) play-back a series of footprints created at different stages of a learning event, to show the underlying narrative dynamics?
and so on ...
Like Nick, I missed the webinar, though the ensuing discussions here have captured my attention thoroughly.
As we work with people to help them learn - and as we work with ourselves to learn - we realise that each person has their own algorithmic pattern of learning. When I heard the word "footprint", I immediately thought "past learning" - already learned. It invoked a visual of tracking what had been learned. Useful if simplified into a constructive, easy to build personalised model (think app here) with simple learning layers defined and easy methodogy for understanding and assembly (think IKEA).
What this raised in my mind was a dynamic process (emergent and evolutionary learning) with a sense of present and future yet mindful of the footprint which could define strength or gap areas.
My work involves lots of visualisations - some happening live, some with fixed models, and almost all with high level engagement and interactivity. Gamification of processes could make the model building element easier for people.
What are we actually trying to achieve? Do we want to reveal each person's learning algorithm? Are we trying to capture what people have learned from us so that we can build on that? From my experience, qualifying the query process so that individuals can contribute to the HOW something gets built has been quite key to how they adopt it into practice.
Since I literally teach people how to build concepts - the frameworks, methodologies and organising systems are crucial. Metaphors are brilliant if they can be used constructively and systematically to tell the story.
As a physicist, mathematician and creative director (yes, crazy combo), my challenge is to help people find their own paths, starting places and define where they really want to go, and how to make the choices and cope with the transitions to get there...and visualise that in simple ways. This is why this discussion has captured my attention.
What about learning mindsets and their role in metaphors for learning? Complex is much easier than simplification so...how can we distill this complexity into an essence that captures each mindset and generates a simple basic working model that people could build on? Spreads the learning even further.
Anyway, thank you one and all for enriching my own thinking. Much appreciated!
Here's something to inspire your thinking: http://blog.clerestorylearning.com/patterns-learning-thinking-creating
Colby, great to meet you here. Welcome.
See my reply in the conversation with Maria, above:
"Bringing their own associations and experience in, to add richness to the images is a very sound workshop technique. It might take longer, but it would be so much more grounded in their own sense-making, rather than asking them to 'detour' through the obscurity of pedagogical theory (which very few people have a taste for - even academics, lets be honest ...) and trying to use such abstract terms for their own sense-making.
In other words it might answer your and Nick's challenge to make the 'ivory tower thinking' more accessible - not by editing and reconfiguring it, but by destroying it, and getting the learners to build their own versions of the mapping sheet instead, just from the images. Wonderful idea!"
As you say: "...so that individuals can contribute to the HOW something gets built has been quite key to how they adopt it into practice".
We are trying to find ways /partners / funding to make the footprints more interactive, and more of a creative, building, exercise than a tool-using exercise.
And a spin-off of this reseach and development is a paper on another related theme, 'creative synaesthesia', exploring some of Ramachandran's research on neurology, with links to emergence and embodied learning. The paper is coming out in the Leonardo journal, but only mid-2014. Read more here ..., and if you want a copy of the paper ahead of publication, send an email to one of us (see our emails on the wiki here ....)
Just sharing some thinking here...
What about a polling system to help build the footprints?
Each person would answer a short series of questions to generate a framework. Then they would answer a second series of questions to generate the layers. Once that basic model is established, they would continue to answer a few more sets of polling questions over time to define sectors and fill in content.
This would be highly engaging, reflective of a personal journey, interactive, emergent and could evolve over time. Would also be useful in comparatives or gap-finding when grouped into communities of learning.
We have used this to generate models and content development when working with people from around the world and limited to online practices. Has anyone else worked with this?
Colby, sounds fascinating. Can you talk us through an example?
Mapping emergent learning (or, more specifically, mapping the balance between emergent and prescriptive learning) is, to start with, an individual reflective exercise - would each person generate their own framework, layers and sectors? And what would 'content' of learning process look like??
I have worked with mind-maps (and more specifically CMaps) to get people to generate mapppings of concepts and fields, and - most importantly - to map out the (layers of ) relationships between them, and I guess we started with a mind-map kind of format for visualising emergent/prescriptive learning.
But then it developed into something a bit different - one person said, when we showed him a footprint of a course that he was familiar with: yes, that looks like that kind of course. We took that as confirmation that the shape, the gestalt, the footprints as a whole (the way the 'blob' is pulled this way and that) - can make sense at that, immediate, and hopefully intuitive - level (as well as at more detailed levels of granularity). I'm wondering how all these different kinds of mappings and frameworks, and generative processes align - or resonate.
Roy, Maria, Jenny, Colby
Not sure where this goes but it does suggest metaphores. Found in my files I'm not sure where it came from:
Connectivism: 21st Century’s New Learning Theory
Transformed into a large collaborative learning environment, the Internet is comprised of information reservoirs namely, (a) online classrooms, (b) social networks, and (c) virtual reality or simulated communities, to expeditiously create, reproduce, share, and deliver information into the hands of educators and students. Most importantly, the Internet has become a focal point for a potentially dynamic modern learning theory called connectivism. Like any learning theory, connectivism has its share of supporters and critics. Unlike any other learning theory, connectivism attributes learning through cyber nodes specifically rooted in social networks. The purpose of this article is to introduce or reacquaint readers with three of the largest reservoirs of information attributed to the principles of connectivism. In addition, it aims to examine these information reservoirs through modern empirical studies in order to determine if their findings carry sparks of likeness or alignment with the principles of connectivism.
And because you never find just one interesting thing on the net:
Pawel Althamer: Nomo from Mars, 2011
Pawel Althamer (b.1967) originally trained as a sculptor, but today he combines his object-making with pioneering work in social, collaborative and participatory art. For the ongoing project Common Task, begun in 2008, he enlists his Warsaw neighbours, whom he outfits in golden space suits, to travel with him to distant lands. Through the fantasy of space travel, he reframes mundane reality as a zone of mystery and possibility, expanding the act of art-making to encompass the activities of the entire group.