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Papert's gearwheels

The Reference

• The gears argument is in the Preface (pp.xviii - xxi), and added to on p.11 (in the Introduction).
• The explicit comparison/contrast between pre-school learning of maths and of our first (not second) language is at p.6 (Introduction).
• "Talking maths" is introduced/mentioned on pp. 6, 9, 10, 13 of the Introduction.
• Fear of maths, and fear of learning in general are introduced on p.4 of the Introduction; and developed in ch.2.

Papert introduces many important ideas in very few pages

1. Papert's engagement with gears was a VERY early childhood experience (age 1-2 years), but which he says continued to have an important effect for many years, including making maths (STEM) "easy" for him.
   And this early experience had a prolonged and positive effect, as a bridge that made certain kinds of further learning later on, much easier. (A kind of cognitive acceleration that makes future learning faster -- cf. Adey&Shayer.)
   There are several different types of pre-experience with significant consequences for enhanced later learning. (This needs a new page.)
   • Masses of content in the area e.g. novels for EngLit; construction toys for science and engineering.
   • Papert's gear wheels: highly personal private schemas.
   • Adey & Shayer cognitive acceleration. Reaching the Piagetian stage of Formal Operations.
   • Pre-training in learning how to learn. And in how to learn the particular discipline in question.
2. Such early childhood experiences have a crucial affective component. Papert says (wrote ) that: "I fell in love with the gears."
   Not something taught, yet with a big effect ....
   What is the role of affect in learning? A huge part of our intellectual culture is to seek reasoning that is independent of affect.
3. But ordinary educational research could never detect the effect by normal methods — only possibly by long term effects.
   On the other hand, I think finding a sig. effect at all in Quintin's et al. ITiCSE survey should perhaps be regarded as a huge result given the extreme length of time between cause and effect?
   Cutts et many others (2018) "Early Developmental Activities and Computing Proficiency" [from ITiCSE proc. of 2017] doi:10.1145/3174781.3174789   https://dl.acm.org/citation.cfm?id=3174789
4. Some Piagetian concepts (Papert was, roughly speaking, a postdoc of Piaget's).
   
   • The model of children as builders of their own intellectual structures. (What "constructivism" can / should mean.)
   • "Genetic" as in "genetic epistemology", meaning how knowledge is generated; and the corollary that we cannot understand knowledge structures in isolation because they depend not just on truth conditions or evidence, but on how they were created (often in early childhood).
   • (The mode of) Learning without a curriculum.
   • Body knowledge.
   • Bricolage (A French handyman who tinkers.) pp.xv, 173; See also
     R.W. Lawler (1985) Computer experience and cognitive development : a child's learning in a computer culture (Chichester : E. Horwood ; New York, N.Y. : Halsted Press) See also videos
   • Assimilation p.xix (i.e. Piagetian Assimilation).
     N.B. in ch.5 p.120ff. Papert talks for longer about this, and about three approaches learners show to resolving conflicts between their prior knowledge and new material.
5. Papert talks about "math-speaking adults" (in the Introduction, p.9 and elsewhere) and the importance of this for children learning maths. Though he was trained by Piaget, this is a deeply Vygotskian idea.
   Paul Black's argument: how can you expect (in a school classroom for a science subject) a learner to make any sense of science, if they have never heard an argument whose outcome depended on reasons (as opposed to violence, or shouting, or voting on one's feelings or guesses).

   The great Anna Sfard has a book on this .... (See also my entrance lobby.)
   The fanatical way of putting this view is that knowledge, or at least knowing, simply consists of, just IS, acquiring a new type of conversation. Not just new words, but ways of speaking, the values built into that type of conversation. So learning English literature is learning to talk with other literateurs; to learn physics is to learn how to talk with physicists; .... But to learn compSci is not to learn the language with which to talk to computers, but the language or conversation style which lets you talk to other programmers. On the other hand, Papert argues that with computers, children can "speak maths"; so that the benefit of computers in education can be supporting this learning when they don't have surrounding people who are competent at this, or more importantly, find it natural and interesting to do so.

6. Learning one's first language is effortless; but later languages are effortful.
   
7. The same is actually true of maths: the "conservations" that Piaget argued all normal children acquire are actually highly abstract mathematical ideas; but effortlessly learned, in contrast to school maths.
8. Piaget studied "learning without a curriculum". And this (Papert says) is the way to characterise such early learning in contrast to school learning. And, implicitly, Papert is reminding us that there is not one universal way of learning; but that learning in school and not in school may be very, very different kinds of process.
   More exactly: it is learning without letting the learners know there is a curriculum in the teacher's minds. And so without their having a goal of learning, and certainly not learning something specific because it's a duty. Cf. the way some countries run kindergartens up to age 7, as opposed to the nasty UK habit of starting school from age 5, and testing the learners, and (the bit that is actually bad) comparing them, their teachers and their parents publicly on that basis.

   But perhaps this cuts both ways. Learning without curriculum often wins on motivational quality and quantity, and affect. But increasingly I'm starting to think of learning in HE, and especially by the Honours years, as extraordinarily efficient. The quantity final year students learn, with amazingly little scaffolding, is astounding, once they have fully absorbed how to learn in HE, and still more, how to learn in and about their particular discipline. Studies of learning without curriculum love to boast about affect, but do not report figures on quantity. On the other hand, it may be that such Honours material is tacitly limited both by the pre-training on learning to learn that discipline, and also limited to a particular subset of the subject that is well and very explicitly understood so it can be taught. You don't get to hear of students cramming a doctor's bedside manner in a 10 credit module; how to be an innovative researcher; etc. These may be more like topics that are only learned in a kind of apprenticeship, over much longer periods; knowledge that is still partly or wholly tacit (implicit).

9. Papert's gears were highly personal: you couldn't possibly try to induce them in all /any other children. So whatever you do as an early intervention, it should NOT be a fixed curriculum, a single kind of thing. Papert promoted computer use early on exactly because it is a general purpose machine which could be exploited by educationalists to support self-personalised materials for each child.
   Would Papert resist the introduction of CompSci as such to primary schools as the very worst thing that could be done?
10. We can learn through our bodies, and this doesn't apply only to sports, or knowledge about bodies and feelings but ALSO to learning purely mathematical things (not least, velocity, kinematics,....).
11. Fear of maths, fear of learning, Dweckian mindsets (see here). An earlier (and better) version of Dweck's mindset concept is Papert's discussion of fear of learning (ch.2).
    1) What is true is that many people believe they can't learn maths when it is pretty sure that they could.
    2) However what is unsatisfactory (for me) about all versions of this is the failure to discuss it in the context of how something we all (and most especially children) must do is to decide the things which we can't/shouldn't learn no matter how full we are of self-confidence, self-efficacy, and growth mindset; e.g. that you can't fly by jumping off a cliff and flapping your arms, that you shouldn't stick your finger or tongue into an electric socket to see what happens. These examples of "fixed mindset" are essential to survival – and so are far more important than any case Dweck looked at for when a growth mindset pays off.
12. Computational thinking. A lot of the book "Mindstorms" is in fact about this: a particular view of what this is, is a large part of Papert's argument in this book. He thinks that before computers no-one had (and still today, those without some education in programming) are without vocabulary or concepts for debugging, for systematic procedures and what is involved in them. E.g. ch.1, p22-23; and p.174ff.
13. ...

The gearwheels

Some videos (animations):

• This "animation" is in many ways the best instructionally
• Good use of colours to divide or group cogs into sets.

Plan for the meeting on this topic by the CCSE reading group

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