Gary Stager, TEDxASB, Seymour Papert, Inventor of Everything (Good in Education), YouTube Video published March 24, 2014:

1) “Learning happens as a consequence of experience, that it’s based on mental structures built within-side your head and Papert suggests that constructionism tells us that the best way to insure that that construction inside our head takes place is through the active construction of some artifact that is sharable outside of the computer or outside of our heads…the making of something tangible is the best way to insure that we learn something by concretizing experiences.”

• As an educator constant recurring questions of meaning bounce around in my mind. Does what I'm experiencing as a teacher, in the current teaching process, have meaning? Is my learner, within the current learning process, creating meaning? How do I know? If not, why not? It's by one's expelling of an object from the subject that I have the assurance that meaning exists - that there is purpose in our exchange as teacher and learner. As Stager put it "the making of something tangible is the best way to insure that we learn something by concretizing experiences.”

While I fully agree with Stager, it is also possible to concretize experience without creating something tangible - it can also be something metaphorical: Martha, in a video clip of Seymour Papert's work at MIT on the LOGO programming language for children, was using LOGO and happened upon a problem, “Oh no, when it was doing it in his mind, the little turtle, the little triangle thing, was on an angle so it drew the picture on an angle. So now I’ll go back and have it draw it in its mind again while its in the right position.” Martha uses the "mind" as an expression of her making meaning of the program. She has expelled the notion of a "mind" (the object) in reference to programming (the subject) in such a way as to concretize the experience. As Papert said, in reference to this act, “Martha is getting mathematical knowledge in a meaningful context for use now.”

2) “How can we create Mathland?” 

• One way is to allow creation as opposed to absorption - to create more than consume - to dishonor rote and allow students to recreate math around them.

3) It’s important “to mess about in mathematics” and to “Mess about with powerful ideas”

• See above.

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Seymour Papert in a YouTube Video, Uploaded on Jun 18, 2009, Edited from Artificial Intelligence Projects: A Student Perspective, Created at CSAIL by Heather Knight, August 2006 and Edited by Thomas Greene, December 2006

Martha, “Oh no, when it was doing it in his mind, the little turtle, the little triangle thing, was on and angle so it drew the picture on an angle. So now I’ll go back and have it draw it in its mind again while its in the right position.”

“Martha is getting mathematical knowledge in a meaningful context for use now.”

"When I was at school they told me to learn long division because I would need it when I grew up, and I think I knew it was a lie, and the effect was to make me to despise the teachers a little more.

“Does the computer program the child or does the child program the computer?"

“When ideas go to school they lose their power.”

"Constructionism v. Instructionism"

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Selected quotes from:

Mindstorms: Computers, Children, and Powerful Ideas, By Seymour Papert

Chapter One - Computers and Computer Cultures

“In most contemporary educational situations where children come into contact with computers the computer is used to put children through their paces, to provide exercises of an appropriate level of difficulty, to provide feedback, and to dispense information. The computer programming the child." p. 19

• A thought well worth hanging on to - how much is the technology creating the child? Students should have power over self-creation with technology providing avenues for that.

“…when a child learns to program, the process of learning is transformed. It becomes more active and self-directed. In particular, the knowledge is acquired for a recognizable personal purpose. The child does something with it. The new knowledge is a source of power and is experienced as such from the moment it begins to form in the child's mind.” p. 21

• Recognizable personal purpose - Meaning Making.

“…many children are held back in their learning because they have a model of learning in which you have either "got it" or "got it wrong." But when you learn to program a computer you almost never get it right the first time. Learning to be a master programmer is learning to become highly skilled at isolating and correcting "bugs," the parts that keep the program from working. The question to ask about the program is not whether it is right or wrong but if it is fixable.”  p. 23

• Another way of saying messing about in "Mathland." Where children can safely play and (re)discover math all about them without fear of judgement.

“the computer as an "object-to-think-with.”” p. 23

• This in Papert's mind is not always a computer - it can be any artifact that is made by the child. I think knitting is a great way to teach coding to younger children.

“I have invented ways to take educational advantage of the opportunities to master the art of deliberately thinking like a computer, according, for example, to the stereotype of a computer program that proceeds in a step-by-step, literal, mechanical fashion. There are situations where this style of thinking is appropriate and useful. Some children's difficulties in learning formal subjects such as grammar or mathematics derive from their inability to see the point of such a style.” p. 27

• Teaching computational thinking offline is a valuable way for children to transfer knowledge from one discipline to another and way for children to be more meta-cognitively aware.

“Even the simplest Turtle work can open new opportunities for sharpening one's thinking about thinking: Programming the Turtle starts by making one reflect on how one does oneself what one would like the Turtle to do. Thus teaching the Turtle to act or to "think" can lead one to reflect on one's own actions and thinking. And as children move on, they program the computer to make more complex decisions and find themselves engaged in reflecting on more complex aspects of their own thinking.” p. 28

• Again, a walk down the meta-cognitive path - showing the power of object oriented education.

“[As in the QWERTY keyboard] We are in the process of digging ourselves into an anachronism by preserving practices that have no rational basis beyond their historical roots in an earlier period of technological and theoretical development.” p. 33

• Frustrating and true. My fear is that I will find myself in a learning environment where I will have to spend more energy helping people rethink education then serving as a model.

Chapter Two Mathophobia: The Fear of Learning

“Once Johnny and his teacher have a shared perception of Johnny as a person who is "good at" art and "poor at" math, this perception has a strong tendency to dig itself in. This much is widely accepted in contemporary educational psychology. But there are deeper aspects to how school constructs aptitudes. Consider the case of a child I observed through his eighth and ninth years. Jim was a highly verbal and mathophobic child from a professional family. His love for words and for talking showed itself very early, long before he went to school. The mathophobia developed at school. My theory is that it came as a direct result of his verbal precocity. I learned from his parents that Jim had developed an early habit of describing in words, often aloud, whatever he was doing as he did it. This habit caused him minor difficulties with parents and preschool teachers. The real trouble came when he hit the arithmetic class. By this time he had learned to keep "talking aloud" under control, but I believe that he still maintained his inner running commentary on his activities. In his math class he was stymied: He simply did not know how to talk about doing sums. He lacked a vocabulary (as most of us do) and a sense of purpose. Out of this frustration of his verbal habits grew a hatred of math, and out of the hatred grew what the tests later confirmed as poor aptitude.” p. 45


• However we can discover what makes meaning in a child's work is what needs to be nurtured and mirrored back to the child to prevent this type of instance.

“The analogy of the dance class without music or dance floor is a serious one. Our education culture gives mathematics learners scarce resources for making sense of what they are learning. As a result our children are forced to follow the very worst model for learning mathematics. This is the model of rote learning, where material is treated as meaningless; it is a dissociated model.” p. 47

• Meaning-Making again. A useful and memorable analogy.

“But now it was apparent that her difficulty with grammar was not due to an inability to work with logical categories. It was something else. She had simply seen no purpose in the enterprise…she found herself classifying words into categories, not because she had been told she had to but because she needed to. In order to "teach" her computer to make strings of words that would look like English, she had to "teach" it to choose words of an appropriate class.” p. 49

• Purpose - creating meaning so as to bring light to an activity (verbs and nouns) that confounded her previously. 

“…every educated person vaguely remembers that y = xz is the equation of a parabola. And although most parents have very little idea of why anyone should know this, they become indignant when their children do not.” p. 52

• Reverse Purpose - to know because it's known, but not used. Teaching how to know is far superior than knowing. We have information at our fingertips - but can we create with that information once we have it?

“A dignified mathematics for children cannot be something we permit ourselves to inflict on children, like unpleasant medicine, although we see no reason to take it ourselves.” p. 54

• A "dose" of meaning-making (again).