Why, though a period when so much human activity has been
revolutionized, have we not seen comparable change in the way we
help our children learn?
One could indeed make kitchen math part of the School by making School part of the kitchen.
Are there any snakes in the house?
Yes there are, there are zero snakes in the house!
So. negative numbers are numbers too, and their reality grows in the course of playing with turtle.
You can't retire from a good project simply because it has succeeded.
Constructionism: It does not call in question the value of instruction as such
The kind of knowledge that children most need is the knowledge that will help them get more knowledge.
If the children really want to learn something, and have the opportunity to learn it in its use, they do so even if the teaching is poor.
Constructionism looks more closely than other educational -isms at the idea of mental construction. It attaches a special importance to role of constructions in the world as a support for those in the head, thereby becoming less of a purely mentalistic doctrine. It also takes the idea of constructing in the head more seriously by recognizing more than one kind of construction and by asking questions about the methods and materials used.
How can one become expert in constructing knowledge?
What skills are required?
Are these skills different for different kinds of knowledge?
School math, like the ideology, though not necessarily the practice, of modern science, is based on the idea of generality - the single, universally correct method that will work for all problems and for all people.
Use what you've got, improvise, make do.
The natural context for learning would be through particiaption in other activities other than math itself.
The reason is that the educators who advocate imposing abstract ways of thinking on students almost practice what they preach - as I tried to do in adopting a concrete style of writing - but with very different effects.
But however concrete their data, any statistical question about ``the effect" of ``the computer" is irretrievably abstract. This is because all such studies depend on use of what is known as the ``scientific method," in form of experiments designed to study the effect of one factor which is varied while taking great pains to
keep everything else same. ... But nothing could be more absurd than an experiment in which computers are placed in a classroom where nothing else has changed. The entire point of all the examples I have given is that the computers serve best when they allow everything to change.
The concept of highly rigorous and formal scientific method that most of us have been taught in school is really an ideology proclaimed in books, taught in schools and argued by philosophers but widely ignored in actual practice of science.
They count the same, but it's more eggs.
My overarching message to anyone who wishes to influence, or simple understand, the development of educational computing is that it is not about one damn product after another (to paraphrase a saying
about how school teaches history). Its essence is the growth of a culture, and it can be influenced constructively only through understanding and fostering trends in this culture.
I would be rather precisely wrong than vaguely right.
- Patrick Suppes
It had been obvious to me for a long time that one of the major difficulties in school subjects such as mathematics and science is that School insists on the student being precisely right. Surely it is necessary in some situations to be precisely right. But these situations cannot be the right ones for developing the kind of thinking that I most treasure myself and many creative people I know.
What computers had offered me was exactly what they should offer children! They should serve children as instruments to work with and to think with, as means to carry out projects, the source of concepts to think new ideas. The last thing in the world I wanted or needed was a drill and practice program telling me to do this sum of spell that word! Why should we impose such a thing on children?
The opportunity for fantasy opens the to a feeling of intimacy
with the work and provides a peep at how emotional side of
children's relationship with science and technology could be very
different from what is traditional in School. Fantasy has always
been encouraged in good creative writing and art
classes. Excluding it from science is a foolish neglect of an
opportunity to develop bonding between children and science.
Errors can become sources of information.
Although the ultimate goal was the same, the means were more than
just qualitatively different; they were episte,mologically
different in that they used a different way of thinking.
Traditional epistemology is an epistemology of precision:
Knowledge is valued for being precise and considered inferior if
it lacks precision. Cybernetics creates an epistemology of
The real problem was that I was still thinking in terms of how to
``get the children to do something." This is the educator's
instinctive way of thinking: How can you get children to like
math, to write wonderfully, to enjoy programming, to use
higher-order thinking skills? It took a long time for me to
understand in my gut, even after I was going around saying it,
that Logo gaphics was successful because of the powet it /gave/ to
children, not because of the performance it /got from/ them.
Children love constructing things, so let's choose a construction
set and add to it whatever is needed for these to make cybernetic
What will they [children] learn from it [Logo]? And won't it favor
boys over girls?
The first question concerns what piece of the school curriculum is
being learned but I attach the most importance to such issues as
children's relationship with technology, then idea of learning,
their sense of self. As for the gender issue, I am thinking more
about, how in the long run comoutational activities will affect
gender than how the gener will affect the activities.
Their work provies good examples of material that overlaps with
School science and math, and of an alternative style applied to
these subjects - instead of formal style that uses rules, a
concrete style that uses objects.
It is worth noting that the students appreciated the
self-organizing nature of the traffic jam only because they had
written the programs themselves. Had they been using a packaged
simulation, they would have had no way of knowing the elegant
simplicity of the programs underlying the jam.
Emergent stuctures often behave very differently than the elements
that compose them.
The cathedral model of education applies the same principle to
building knowledge structures. The curriculum designer in cast in
the role of a ``knowledge architect'' who will specify a plan, a
tight progra, for the placement of ``knowledge brick's'' in
What is typical of emergently programmed systems is that
deviations from what was expected do not cause the wholw to
collapse but provoke adaptive responses.
We are living with an edicational systsem that is fundamentally as
irrational as the command economy and ultimately for the same
reason. It does not have capacity for local adaptation that is
necessary for a complex system even to function effieciently in a
changing environment, and is doubly necessary for such a system to
be able to evolve.
Defininf educational success by test scores is not very different
from couting nails made rather than nails used.
But calling hierarchy into question is the crux of the problem if
Each of these cases suggests ways in which a little school created
in a militant spirit can mobilize technology as an assertion of
I could continue in this spirit, but this may be enough to make
the point that little schools could give themselves a deeper and
more conscious specific identity. Everything I have said in this
book converges to suggest that this would produce rich
intellectual environments in which not only children and teachers
but also new ideas about learning would develop together.
I see little schools as the most powerful, perhaps an essential,
route to generating variety for the evolution of education.
The prevailing wisdom in the education establishment might agree
with the need for variety but look to other sources to provide
it. For example, many - let us call them the Rigorous
Researchers - would say that the proper place for both variation
and selection is in the laboratory. On their model, researchers
should develop large numbers of different ideas, test them
rigorously, select the best, and disseminate them to schools.
In my view this is simply Gosplan in disguise.
The importance of the concept of the little school is that it
provides a powerful, perhaps by far the most powerful, strategy to
allow the operation of the principle of variation and selection.
This objection depends on an assumption that is at the core of the
technicalist model of education: Certain procedures are the best,
and the people involved can be ordered to carry them out. But even
if there were such a thing as "the best method" for learning, it
would still only be the best, or even mildly good, if people
believed in it. The bueracrat thinks that you can make people
beleive in something by issuing orders.
The design of learning environment has to take account of the
cultural environment as well, anad its implementation must make
serious effort at involvement of the communities in which it is to
It is no longer necessary to bring a thousand children together in
one building and under one administration in order to develop a
sense of community.
I do not see that School can be defended in its social role. It
does not serve the functions it claims, and will do so less and
Talking about megachange feels to them like fiddling when Rome
burns. Education today is faced with immediate, urgent
problems. Tell us how to use your computer to solve some of the
many immediate practical problems we have, they say.
Impediments to change in education such as, cost, politics, the
immense power of the vested interests of school bureaucrats, or lack
of scientific research on new forms of learning.
Large number of teachers manage to create within the walls of their
own classrooms oases of learning profoundly at odds with the
education philosophy espoused by their administrators...
But despite the many manifestations of a widespread desire for
something different, the education establishment, including most of
its research community, remains largely committed to the educational
philosophy of the late nineteenth and early twentieth centuries, and
so far none of those who challenge these have hallowed traditions
has been able to loosen the hold of the educational establishement
on how children are taught.
Do children like games more than homework because, the later is
harder than the former?
Most [games] are hard, with complex information - as well as
techniques - to be mastered, in the information often much more
difficult and time consuming to master than the technique.
These toys, by empowering children to test out ideas about working
within prefixed rules and structures in a way few other toys are
capable of doing, have proved capable of teaching students about the
possibilities and drawbacks of a newly presented system in ways many
adults should envy.
In trying to teach children what adults want them to know, does
School utitlize the way human beings most naturally learn in
If it has so long been so desperately needed, why have previous
calls for it not caught fire?
Is reading the principal access route to knowledge?
Ask a symapathetic adult who would reward her curiosity with praise.
Literacy is being able to read and write. Illiteracy can be
remedied by teaching children the mechanical skill of decoding black
marks on white paper.
/Letteracy/ and /Letterate/
Reading from Word to Reading from World
... the Knowledge Machine offers children a transition between
preschool learning and true literacy in way that is more personal,
more negotiational, more gradual, and so less precarious thant the
abrupt transition we now ask chidlrento malke as they move from
learning through direct experience to using the orinted word as a
source of important information.
.... School's way is the only way beacause they have never seen or
imagined convincing alternatives in the ability to impart certain
kinds of knowledge.
* Babies learn to talk without curriculum or formal lessson
* People develop hobbies at skills without teachers
* social behavior is picked up other than through classroom
Parable of the Automobile:
... certain problems that had been abstract and hard to grasp
became concrete and transparent, and certain projects that had
seemed interesting but too complex to undertake became
Paulo Freire: "Banking model" information is deposited in
child's mind like money in a savings account.
/Tools/ for creating new experiments in effective fashion.
* Dewey: children would learn better if learning were truly a
part of living experience
* Freire: chidlren would learn better if they were truly in
charge of their own learning processes
* Piaget: intelligence emerges from an evolutionary process in
which many factors must have time to find their equilibrium.
* Vygotsky: Conversation plays a crucial role in learning.
Why did the discovery method fail?
By closing off a much larger basis of knowledge that should
serve as a foundation for formal mathematics taught in school
and perhas a minimal intuitive basis directly connected with
The central problem of mathematics education is to find ways
to draw on the child's vast experience of oral
mathematics. Computers can do this.
Giving chidlren opportunity learn and use mathematics in a
nonformalized way of knowing encourages rather than inhibits
the eventual adoption of formalized way, just as the XO,
rather than discouraging reading, would eventually stimulate
children to read.
The design process is not used to learn more formal geometry.
Traditionally teh art and writing classes are for fantasy but
science deals with facts; union of technology with biology.
It allows them to enter science through a region where
scientific thinking is most like there own thinking.
Reading biographies and iterrogating friends has convinced me
that all successful learners find ways to take charge of their
early lives sufficiently to develop a sense of intellectual
Piaget's first article: a paradox?
Schools have inherent tendency to infantilize the children by
placing them in a position of have to do so as they are told,
to occupy themselves with work dictated by someone else and
that, morever, has no intrinsic value - school work is done only
because the designer of the curriculum decided that doingthis
work would shape the doer into a desirable form[for the
NatGeo: Kidnet??Robert Tinker
Researchers, following the so-called scientific method of
using controlled experiments, solemnly expose the children to
a "treatment" of some sort and then look at measurable
results. But this flies in the face of all common knowledge
of how human beings develop.
The method of controlled experimentation that evaluates an
idea by implementing it, taking care to keep everything else
the same, and measuring the result, may be an appropriate way
to evaluate the effects of a small modification. However, it
can tell us nothing about ideas that might lead to deep
change... It will be steered less by the outcome of tests and
measurements than by its participant' intuitive understanding.
The prevalent literal-minded, "what you see is what you get"
approach measuring the effectiveness of computers in learning
by teh achievements in present-day classroons makes it certain
that tomorrow will always be prisoner of yesterday.
Example of Jet attached to horse wagon.
... most people are more interested in what they learn than in how
the learning happens.
But math is not about feeling the relationship of your body to
Turtle lets you do this!
Intellectual work is adult child's play.
Example that if observation of schools in some country where
only one writing instrument could be provided for every fifty
students suggested that writing does not significantly help
The change requires a much longer and more social computer
experience than is possible with two machines at the back of
/Balkanized Curriculum and impersonal rote learning/
What had started as a subversive instrument of change was
neutralized by the system and converted into an instrument of
Schools will not come to use computers "properly" because
researchers tell it how to do so.'
It is characteristic of a conservative systems that
acoomodation will come only when the opportunities of
assimilation have been exhausted.
* Immediate Feedback
* Individualized instruction
* Neutrality *
CAI will often modestly raise test scores, especially at the low end
of the scale. But it does without questioning the structure or the
educational goals of the traditional School.
Today, because it is the 15th Monday of your 5th grade year,
you have to do this sum irrespective of who you are or what
you really want to do; do what you are told and do it the
way you are told to do it.
Piaget was the theorist of learning without curriculum;
School spawned the projectof developing a Piagetian curriculum.
The central issue of change in education is the tension
between technicalizing and not technicalizing, and here the teacher
occupies the fulcrum position.
Shaw: He who can, does; he who cannot, teaches.
The system defeats its own purpose in attempt to enforce them.
School has evolved a heirarchical system of control that
sets narrow limits within which the actors - administators
as well as teachers - are allowed to exercise a degree of
Hierarchy vs. Heterarchy
The major obstacle in the way of teachers becoming learners
is inhibition about learning.
The problem with `developed' countries as opposed to `developing' ones
is that the developed countries are already there, there is no further
In education, the highest mark of success is not having imitators but
inspiring others to do something else.
As long as there is afixed curriculum, a teacher has no need to become
involved in the question what is and what is not mathematics.
Society cannot afford to keep back its potentially best teachers
simply because some. or even most, are unwilling.
The how-to-do-it literature in the constructivist subculture is almost
as strongly biased to the teacher side as it is in the instructionist
/Mathematikos/ disposed to learn
/mathema/ a lesson
/manthanein/ to learn
\ldots mathetics is to learning what heuristics is to problem solving.
What is that feeling when you look at a familiar object, with a sense
that you are looking at the object for the first time?
It is /jamais vu/.
Attempts by teachers and textbook authors to connect school fractions
with real life via representations as pies simply reuslyed in a new
* What is the difference in learning at school and all other learning?
Generally in life, knowledge is acquired to be used. But school
learning more often fits Freire's apt metaphor: Knowledge is treated
like money, to be put away in a bank for the future.
* What does /Computer Literacy/ mean?
* The Technology of the Blackboard and The Technology of The Computer
* Lines You can use:
The computer to program the student...
The student to program the computer...
Computer as an expensive set of flash cards.
If the students scores improve, our approach must be right.
Self-directed activities versus carefully guided ones
If the scores improve does it mean that the strategy is effective/
approach is right?
Heterarchical versus Hierarchical
Totalitarian Education or Trivialized Education