Flow channels: gradualness of learning
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Maria Droujkova
Oct 22, 2010, 9:56:15 AM10/22/10
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I have added the following blurb to the Flow Channels brainstorming page. For those new to the topic, this is a discussion about BALANCE in mathematics education. Instead of having wars about which opposite is better, find a way to balance both of them.
~*~*~*~*~*
The flow channel model assumes the Western "more is better" value. The Featuritis curve above is an example of a different approach. In learning, we want to expand the Happy User Peak and turn it into a Happy User Plateau. I am not sure how to draw this as a flow channel. The following is my reply to a LinkedIn discussion at the Math, Math Education, Math Culture community (members only). People who brought up these ideas were Victoria Kofman and Michael Friedberg.
Students need to learn to deal with BOTH gradual and non-gradual situations. Everybody has a natural "window of comfort" about how gradual learning has to be. If you go more gradually than that, you are bored. If you skip more than that, you will be anxious. Both lead to (different) failures to learn.
Cheers,
Maria Droujkova
Make math your own, to make your own math.
~*~*~*~*~*
More is better? Gradual/abrupt
The flow channel model assumes the Western "more is better" value. The Featuritis curve above is an example of a different approach. In learning, we want to expand the Happy User Peak and turn it into a Happy User Plateau. I am not sure how to draw this as a flow channel. The following is my reply to a LinkedIn discussion at the Math, Math Education, Math Culture community (members only). People who brought up these ideas were Victoria Kofman and Michael Friedberg.
Students need to learn to deal with BOTH gradual and non-gradual situations. Everybody has a natural "window of comfort" about how gradual learning has to be. If you go more gradually than that, you are bored. If you skip more than that, you will be anxious. Both lead to (different) failures to learn.
Cheers,
Maria Droujkova
Make math your own, to make your own math.
Angela Giuliani
Oct 22, 2010, 11:56:30 AM10/22/10
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Interesting Maria,
I have noticed that with Noah – in more than just math – easier (bored) is worse and leads to many more incorrect/partial results.
Angie
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Maria Droujkova
Oct 22, 2010, 12:18:52 PM10/22/10
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Angie,
Thank you for the example! I know exactly what you are talking about - I've seen that!
More gradual, step-by-step tasks have their value and may present a challenge. They are conventionally called "easy" but are they? For example, TEACHING is like this. Highly intuitive people often find it hard to teach math. Documentation ("showing your work"), editing, searching for errors are more examples of "gradual" tasks.
Everybody agrees that making large conceptual leaps is hard. We need to acknowledge that being more sequential, gradual, analytical than is normal for you is also hard, and valuable.
Maybe I should remove the word "boredom" in the diagram, because it's not just that.
MariaD
Thank you for the example! I know exactly what you are talking about - I've seen that!
More gradual, step-by-step tasks have their value and may present a challenge. They are conventionally called "easy" but are they? For example, TEACHING is like this. Highly intuitive people often find it hard to teach math. Documentation ("showing your work"), editing, searching for errors are more examples of "gradual" tasks.
Everybody agrees that making large conceptual leaps is hard. We need to acknowledge that being more sequential, gradual, analytical than is normal for you is also hard, and valuable.
Maybe I should remove the word "boredom" in the diagram, because it's not just that.
MariaD
Alan Kay
Oct 22, 2010, 1:23:15 PM10/22/10
to natur...@googlegroups.com
Have you folks run across the eminent psychologist Mihalyi Csíkszentmihályi, and his 30 year long studies of "Flow: The Psychology of Optimal Experience"?
He has been a long time colleague and advisor to Viewpoints, and many of these ideas were used in the earlier designs of the GUI.
Cheers,
Alan
From: Angela Giuliani <angelag...@earthlink.net>
To: natur...@googlegroups.com
Sent: Fri, October 22, 2010 8:56:30 AM
Subject: RE: [NaturalMath] Flow channels: gradualness of learning
He has been a long time colleague and advisor to Viewpoints, and many of these ideas were used in the earlier designs of the GUI.
Cheers,
Alan
From: Angela Giuliani <angelag...@earthlink.net>
To: natur...@googlegroups.com
Sent: Fri, October 22, 2010 8:56:30 AM
Subject: RE: [NaturalMath] Flow channels: gradualness of learning
Maria Droujkova
Oct 22, 2010, 1:38:07 PM10/22/10
to natur...@googlegroups.com
Alan,
His work is the basis of this discussion. I have not talked with him, but I've read his work.
I know his work is on your reading list: http://www.amazon.com/Alan-Kays-Reading-List/lm/R5KOU7F2T6RX7
Are the connections of his Flow to your designs explained somewhere?
His work is the basis of this discussion. I have not talked with him, but I've read his work.
I know his work is on your reading list: http://www.amazon.com/Alan-Kays-Reading-List/lm/R5KOU7F2T6RX7
Are the connections of his Flow to your designs explained somewhere?
Alan Kay
Oct 22, 2010, 1:59:50 PM10/22/10
to natur...@googlegroups.com
The connections are probably explained in several of my (videoed) talks that various people have put on the web.
25 years ago I used to do a 90 talk on user interface design that incorporated all the ideas that we drew our designs from.
I probably said something in the chapter I did for Brenda Laurel's Human Computer Interface Design Book.
The diagram I made was to have "Challenge" be the vertical axis, and Skill Level be the horizontal. The simple way to look at this is that when these are roughly equal, "Flow" happens along the 45 degree arrow drawn from the origin. But this arrow is pretty narrow, so if you have more skill than challenge you get easily bored, and more challenge than skill you get easily anxious.
And right around the origin is pretty uninteresting in general.
The way we used this was to ask "How can we widen the flow arrow to be more tolerant of disparities between Challenge and Skill Level?
For more challenge than skill, one way to stave off anxiety is to make the environment safer -- so safety lines for climbers, nets for acrobats, and in a computer user interface, put in a very comprehensive UNDO, which allows the user to make mistakes but to always recover. This encourages exploration.
And for more skill than challenge, one tries to raise the level of attention and interest. Tim Gallwey had 20 or more ways to help his tennis students see what seemed to be the same old yellow ball, as a new kind of thing each time (what is the shadow like on it, how fast is it spinning, etc.?).
In cooking prep, it's all about the satisfaction of tuning in on your muscles and how it feels to slice and chop and peel. Similarly, one of the things you can do in a computer interface is to supply small reactions to everything the user does, so there are things that are like tactile feedbacks (e.g. dragging, etc.) We even made a mouse at Apple that gave enough force feedback so you could feel the "mass" of the stuff you were dragging around.
This is all "Xerox PARC 101" but very little of this has made its way into the rest of computing (or education).
In any case Mike's work is really worth delving into.
Cheers,
Alan
25 years ago I used to do a 90 talk on user interface design that incorporated all the ideas that we drew our designs from.
I probably said something in the chapter I did for Brenda Laurel's Human Computer Interface Design Book.
The diagram I made was to have "Challenge" be the vertical axis, and Skill Level be the horizontal. The simple way to look at this is that when these are roughly equal, "Flow" happens along the 45 degree arrow drawn from the origin. But this arrow is pretty narrow, so if you have more skill than challenge you get easily bored, and more challenge than skill you get easily anxious.
And right around the origin is pretty uninteresting in general.
The way we used this was to ask "How can we widen the flow arrow to be more tolerant of disparities between Challenge and Skill Level?
For more challenge than skill, one way to stave off anxiety is to make the environment safer -- so safety lines for climbers, nets for acrobats, and in a computer user interface, put in a very comprehensive UNDO, which allows the user to make mistakes but to always recover. This encourages exploration.
And for more skill than challenge, one tries to raise the level of attention and interest. Tim Gallwey had 20 or more ways to help his tennis students see what seemed to be the same old yellow ball, as a new kind of thing each time (what is the shadow like on it, how fast is it spinning, etc.?).
In cooking prep, it's all about the satisfaction of tuning in on your muscles and how it feels to slice and chop and peel. Similarly, one of the things you can do in a computer interface is to supply small reactions to everything the user does, so there are things that are like tactile feedbacks (e.g. dragging, etc.) We even made a mouse at Apple that gave enough force feedback so you could feel the "mass" of the stuff you were dragging around.
This is all "Xerox PARC 101" but very little of this has made its way into the rest of computing (or education).
In any case Mike's work is really worth delving into.
Cheers,
Alan
From: Maria Droujkova <drou...@gmail.com>
To: natur...@googlegroups.com
Sent: Fri, October 22, 2010 10:38:07 AM
Subject: Re: [NaturalMath] Flow channels: gradualness of learning
Alan Kay
Oct 22, 2010, 1:57:48 PM10/22/10
to natur...@googlegroups.com
The connections are probably explained in several of my (videoed) talks that various people have put on the web.
25 years ago I used to do a 90 talk on user interface design that incorporated all the ideas that we drew our designs from.
I probably said something in the chapter I did for Brenda Laurel's Human Computer Interface Design Book.
The diagram I made was to have "Challenge" be the vertical axis, and Skill Level be the horizontal. The simple way to look at this is that when these are roughly equal, "Flow" happens along the 45 degree arrow drawn from the origin. But this arrow is pretty narrow, so if you have more skill than challenge you get easily bored, and more challenge than skill you get easily anxious.
And right around the origin is pretty uninteresting in general.
The way we used this was to ask "How can we widen the flow arrow to be more tolerant of disparities between Challenge and Skill Level?
For more challenge than skill, one way to stave off anxiety is to make the environment safer -- so safety lines for climbers, nets for acrobats, and in a computer user interface, put in a very comprehensive UNDO, which allows the user to make mistakes but to always recover. This encourages exploration.
And for more skill than challenge, one tries to raise the level of attention and interest. Tim Gallwey had 20 or more ways to help his tennis students see what seemed to be the same old yellow ball, as a new kind of thing each time (what is the shadow like on it, how fast is it spinning, etc.?).
In cooking prep, it's all about the satisfaction of tuning in on your muscles and how it feels to slice and chop and peel. Similarly, one of the things you can do in a computer interface is to supply small reactions to everything the user does, so there are things that are like tactile feedbacks (e.g. dragging, etc.) We even made a mouse at Apple that gave enough force feedback so you could feel the "mass" of the stuff you were dragging around.
This is all "Xerox PARC 101" but very little of this has made its way into the rest of computing (or education).
In any case Mike's work is really worth delving into.
Cheers,
Alan
25 years ago I used to do a 90 talk on user interface design that incorporated all the ideas that we drew our designs from.
I probably said something in the chapter I did for Brenda Laurel's Human Computer Interface Design Book.
The diagram I made was to have "Challenge" be the vertical axis, and Skill Level be the horizontal. The simple way to look at this is that when these are roughly equal, "Flow" happens along the 45 degree arrow drawn from the origin. But this arrow is pretty narrow, so if you have more skill than challenge you get easily bored, and more challenge than skill you get easily anxious.
And right around the origin is pretty uninteresting in general.
The way we used this was to ask "How can we widen the flow arrow to be more tolerant of disparities between Challenge and Skill Level?
For more challenge than skill, one way to stave off anxiety is to make the environment safer -- so safety lines for climbers, nets for acrobats, and in a computer user interface, put in a very comprehensive UNDO, which allows the user to make mistakes but to always recover. This encourages exploration.
And for more skill than challenge, one tries to raise the level of attention and interest. Tim Gallwey had 20 or more ways to help his tennis students see what seemed to be the same old yellow ball, as a new kind of thing each time (what is the shadow like on it, how fast is it spinning, etc.?).
In cooking prep, it's all about the satisfaction of tuning in on your muscles and how it feels to slice and chop and peel. Similarly, one of the things you can do in a computer interface is to supply small reactions to everything the user does, so there are things that are like tactile feedbacks (e.g. dragging, etc.) We even made a mouse at Apple that gave enough force feedback so you could feel the "mass" of the stuff you were dragging around.
This is all "Xerox PARC 101" but very little of this has made its way into the rest of computing (or education).
In any case Mike's work is really worth delving into.
Cheers,
Alan
Sent: Fri, October 22, 2010 10:38:07 AM
Subject: Re: [NaturalMath] Flow channels: gradualness of learning
Bradford Hansen-Smith
Oct 22, 2010, 7:55:18 PM10/22/10
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| Alan, you said; |
"The diagram I made was to have "Challenge" be the vertical axis, and Skill Level be the horizontal. The simple way to look at this is that when these are roughly equal, "Flow" happens along the 45 degree arrow drawn from the origin. But this arrow is pretty narrow, so if you have more skill than challenge you get easily bored, and more challenge than skill you get easily anxious. |
And right around the origin is pretty uninteresting in general." |
I tend to see thing dimensionally so I will offer a slightly different interpretation where the 45 degree arrow is the third axis of physical reality representing the active journey through the intersection of both ascending development (challenge) and personal interaction (acquiring skills). They are all ninety degrees apart and come together at origin, the center point of concentric spheres flowing out in balanced movement on all three axis. The spherical balance of symmetrical flow is usually distorted when the sense of curiosity about our journey is diminished. Boredom is loss of interest in activity at any given point on our journey. It is not necessarily about the disparity between challenge or skill, rather about finding personal balance and curiosity as we journey through this 3-axial landscape. We have educationally depressed curiosity in many young people and we must understand what we have done to be able to educationally support individual curiosity. Potential is lost when there is no curiosity about the journey we are on. Brad Bradford Hansen-Smith Wholemovement 4606 N. Elston #3 Chicago Il 60630 www.wholemovement.com wholemovement.blogspot.com/ --- On Fri, 10/22/10, Alan Kay <alan...@yahoo.com> wrote: |
Maria Droujkova
Nov 5, 2010, 4:47:17 PM11/5/10
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I added Alan's explanation, the diagram and Alan's 1987
video with older (1968) Doug Engelbart pieces, and Alan's GUI talk to
the Flow Channel page: http://naturalmath.wikispaces.com/Flow+Channels
I think Bradford is saying that the synthesis of the two opposites can be considered a third, independent dimension. Because I am focusing on the balance of the two, it's hard to see what entity their synthesis is (other than the generic "flow") or why it's independent. I will have to think about it.
I think Bradford is saying that the synthesis of the two opposites can be considered a third, independent dimension. Because I am focusing on the balance of the two, it's hard to see what entity their synthesis is (other than the generic "flow") or why it's independent. I will have to think about it.
Bradford Hansen-Smith
Nov 5, 2010, 11:47:37 PM11/5/10
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| Maria, Three dimensions is not a synthesis of two dimensions. I am not referring to synthesis, rather to three individualized aspects to any function. Most fundamentally there is one, and other, and interaction; our 3-axial landscape. I might interpret that as body, mind and spirit. Those are three individual qualities of human consciousness that work in association, even before there is awareness of what we call opposites. Our tendency is to polarize differences into opposites and that is what gets us into conflict. Then we look to balance what has gotten out of balance and have forgotten the structural nature of three in association. There are only differences except when we get into the generalizations of language. You have discribed in your math sessions with children beautiful interactions of physical, mental and spirit engagement in many activities. Synthesis is what comes together from the organization of those associations; and that is what I would call learning. |
Brad Bradford Hansen-Smith Wholemovement 4606 N. Elston #3 Chicago Il 60630 www.wholemovement.com wholemovement.blogspot.com/ |
| --- On Fri, 11/5/10, Maria Droujkova <drou...@gmail.com> wrote: |
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