4 March 2018 ............... Length about 1800 words (15,000 bytes). (Document started on 25 Jan 2018.)
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How to refer to it.
Papert, S.A. (1980/1993) Mindstorms: Children, computers and powerful ideas
(2nd edition) (Basic Books: New York); and especially the Preface
"The gears of my childhood" (which is also
online on Papert's website).
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
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.
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.
The idea that such early childhood experiences have a crucial
Papert says (wrote ) that: "I fell in love with the gears."
Not something taught, 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.
Piagetian ideas mentioned
(Papert was (roughly speaking) one of Piaget's postdocs).
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).
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.
That learning one's first language is effortless; but later languages are
That 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.
That Piaget studied "learning without a curriculum". That that 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).
That 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?
That 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.
But normal 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]
Papert talks about "math-speaking adults" (in the Introduction, p.9 and
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
The great Anna Sfard has
a book on this ....
(See also my
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
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.
That we can learn through our bodies, and that this doesn't apply only
to sports, or knowledge about bodies and feelings but ALSO to learning
purely mathematical things (not least, velocity, kinematics,....).
Fear of maths, fear of learning, Dweckian mindsets
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
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
Plan for the meeting on this topic by the CCSE reading group
Go round the table and each person picks one topic (e.g. from the list
above) which they would most like to discuss, and hear discussed.
Matt and Lovisa. Is having a very personal idea, as a beginning PhD
student in any way like Papert's gearwheels, even though age 2 and 22 are
very different intellectually?
Matt Barr with his conviction / experience, that video games had a deep
connection with turning points in his own eduction. Lovisa with her
conviction / experience that creating drawings, particularly drawings
depicting analogies, had a deep connection with her own academic learning.
What makes a childhood play activity good, or not, for promoting later