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Tuesday, December 22, 2009

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96 BT Technology Journal • Vol 22 No 4 • October 2004
Models of growth — towards fundamental
change in learning environments
D Cavallo
This paper proposes that a major reason for the lack of change in education is not due to lack of ideas about learning on a micro or
individual level, but rather is due to a lack of models for growth and change at a macro or systemic level. We critique existing models of
growth and provide examples of broad social change in other fields. We look at their properties and use those as a guide to thinking
about change in learning environments. We propose that there exists a grammar of school reform. We provide examples of attempts to
facilitate fundamental change at a large scale, and attempt to synthesise their properties, leading to thinking about new models for
growth.
1. Grammar of school reform
David Tyack and Larry Cuban postulated that there exists a
grammar of school, which makes deviation from our
embedded popular conception of school feel as nonsensical as
an ungrammatical utterance [1]. They describe how reform
efforts, whether good or bad, progressive or conservative,
eventually are rejected or denatured and assimilated. Reform
efforts are not attempted in the abstract, they are situated in a
variety of social, cultural and historical contexts. They do not
succeed or fail solely on the basis of the merit of the ideas
about learning, but rather, they are viewed as successful
based upon their effect on the system and culture as a whole.
Thus, they also have sociological and institutional components
— failure to attend to matters of systemic learning will
facilitate the failure of the adoption of the reforms.
Reviewing reform efforts of US schools over the previous
century, one can note that there also appears to be a grammar
of school reform. Two models predominate: either there is a
predetermined, usually massive, fully formulated design
imposed from above, with the intention of every location
carrying out this reform according to its prescribed steps, or
take a particular change, test it in a small, controlled setting,
and then attempt to spread it through the entire system.
It is not enough to have a new model of education that looks
beautiful on the drawing board or that has given superior
results in pilot implementations. The true challenge is to
devise ways of implementing new forms of educational
practice on a large scale. This means finding a workable model
for how a new paradigm of practice can take hold and grow.
Yet, what should one do? At what models should one look?
Two terms comprise the predominant models for growth —
replicate and take to scale. Both models are explicitly topdown
and hierarchical, and implicitly view education as a
series of depersonalised, decontextualised steps carried out by
willing, receptive, non-transforming agents. Yet, as Tyack and
Cuban demonstrate [1], these models have proved insufficient
for creating substantive change on a large scale. Oddly,
despite the lack of success, not only is there a scarcity of
models, but also there appears to be relatively little attention
paid to thinking about systemic change and creating
alternative models. Moreover, the terms replication and
scaling are themselves problematic and misleading for
development in learning environments. It is easy to think of
replicating the hardware of the reform (i.e. the technology, the
textbooks, the materials, the curriculum); however, these may
be necessary but have proved insufficient to produce
sustainable reform. The level of description for replication is
inadequate. The form can easily be copied but the substance
remains elusive, and thus the reform is compromised.
Canonical approaches such as pilot programmes suffer from
becoming isolated experiences that do not influence the whole
system and eventually die out or become assimilated. Train
the trainer schemes work for rote applications and simple
closed systems, but fail when needed to address open,
the challenge is to devise
ways of implementing new
educational practice on a
large scale
Models of growth — towards fundamental change in learning environments
BT Technology Journal • Vol 22 No 4 • October 2004 97
complex situations such as learning environments. The push
towards scientific, research-based approaches aimed at
improving education as mandated in the No Child Left Behind
act [2] will suffer due to the implicit model of growth as a
matter of grafting a series of discrete treatments into a
complex system and assuming they will be applied faithfully
and uniformly and will fit into the existing local cultures.
Naturally, the greatest positive impact over the largest
population in the shortest time is the goal. However, major
change cannot be implement everywhere immediately. Still, it
is curious that when attempting large-scale effect, the time
dimension is typically de-emphasised and the scale dimension
maximised, usually to the detriment of the quality of impact.
Rather than only considering maximising the number of sites
(dimension 1) in the shortest amount of time (dimension 2),
one must aim to maximise higher quality (dimension 3) over
sites over time, even if this means slower growth in the initial
period [3]. This approach implies the early steps should lay the
groundwork for greater subsequent growth and that the path
is not necessarily linear.
This paper presents an optimistic view of the potential for
fundamental change in learning environments on a large scale
and offers hope for addressing the great educational needs
created by the digital age by drawing upon two of its
important innovations — digital technology, and the approach
to organisation and organisational change that has come in
the wake of the technology. We1 describe examples to evoke
new models for change based on our experience in Brazil of
introducing different approaches to learning with the intention
of facilitating large-scale impact. While our approach to
learning and learning environments draws upon a variety of
thinkers such as Dewey [4], Piaget [5], Vygotsky and Freire [6],
as well as many contemporaries, the ideas about models of
growth are not limited to such an approach. We believe the
lessons potentially apply towards paradigmatic change with
other approaches to learning as well as change in other fields.
Simply stated, we believe that global transformation in
learning environments will more felicitously occur through the
greater aggregation of local powerful personal experiences.

2. A new framework for thinking about
change and growth
This paper describes a form of intervention that intends to
take steps towards a fundamental change in learning
environments on a broad scale. Naturally, this can only be
determined longitudinally, so this report is premature in some
respects; still, we believe it can contribute to thinking about
how to more productively create change in an essential area.
2.1 Kuhn and paradigms
In Second Thoughts on Paradigms [7] Thomas Kuhn states that
paradigms consist fundamentally of three elements:
• exemplars,
• models,
• symbolic expressions.
We find Kuhn’s construct useful for thinking about what needs
to be developed in order to create different mindsets and
practice about learning. Exemplars stand for the canonical
examples of the new paradigm. Models provide a way of
thinking about what one should expect to happen, what
behaviours are paradigmatic. Symbolic expressions (or, for our
purposes, the language of description) serve an explicatory
purpose. Rather than failing by attempting new blueprints, we
attempt to create an emergent design that does not plan
every step in detail, but searches for models of robust growth
and uses Kuhn’s description of the components of paradigms
to provide principles.

2.2 Change as learning — micro-level change and
macro-level change
Seymour Papert has suggested [8] using a developmental
framework for thinking about systemic change in education.
Just as one cannot merely tell a child his thinking is incorrect
and then expect everything to fall into place, so too we cannot
expect simply to tell a school, a school system, a country, that
its schools are wrong and how to fix them. He has also
suggested using a lens of micro and macro levels to think
about change. We find it useful to think of systemic change as
a problem in learning as well, and many of the principles for
learning environments for individual learners (the micro level)
apply for thinking about learning and development of the
system (the macro level).
As we see it, real change is inherently a kind of learning. For
people to change the way they think about and practice
education, rather than merely being told what to do
differently, we believe that practitioners must have
experiences that enable appropriation of new modes of
teaching and learning that enable them to reconsider and
restructure their thinking and practice. The limitations
inherent in existing systems based upon information transfer
models are as impoverished in effecting systemic development
as they are in child development.

2.3 Ecological, viral and genetic models
We look to ecological and evolutionary models of change for
ideas about how new educational patterns will emerge and
how we can actively contribute to them. We believe emergent
design to be a useful tool for educational change [9]. It
the terms replication and
scaling are themselves
problematic and misleading
1 The author adopts the plural ‘we’ as the work has been a
collaborative effort, and the ideas developed in this paper have been
a group effort among the Future of Learning group at the MIT Media
Lab and its collaborators.
we cannot simply tell a
school system that it is
wrong, and then expect
everything to fall into place
Models of growth — towards fundamental change in learning environments
98 BT Technology Journal • Vol 22 No 4 • October 2004
supposes an evolutionary model, where we are not passive
observers: we design and introduce new variants along certain
principles and see how well they grow. We study the fitness
functions, the social niches, and the local ecologies of culture
and thought. We study change itself as a process of learning.
Our role as the exogenous element in conducting the learning
projects is to show the existence of a new way of instantiating
dynamic learning environments. We bring in powerful ideas
about learning and through our practice illustrate how to put
them to work. The possibility for spread and growth is not
through the exact replication of the actions since the context
will be different and the culture is dynamic. Rather, the goal is
for the appropriation of the principles and the development of
models of thinking so that the agents can adapt and apply
with the ability to continually develop through reflection on
the feedback and changing environmental conditions.
When we run learning projects, we build upon and take
practical action towards existing local concerns. We do not
arrive with a fully pre-packaged project design. The design of
learning projects evolves and changes in dialogue with
personal, collective and local interests, conceptions, and
needs. It does not assume that all host environments are the
same and that one can merely impose a new model. This
design dialogue is what generates involvement, commitment,
and staying power — people are learning what they need to
know to take action about issues that are important to them.
Learners are motivated to master the knowledge they need to
solve problems that mean something to them.
Emerging viral models of communication provide another
exemplar for how non-hierarchical structures can facilitate
growth and operation on a large-scale with intelligence at the
leaves [10]. Indeed, people are developing these models
simply because of inherent limitations in hierarchical models
with centralised control. Open software development [11],
small-world networks [12, 13], and peer-to-peer sharing [14],
are all salient examples of effective distributed nonhierarchical
models.

3. Cultural examples
How can one overcome the design dialectic between
instantiating significant change — which implies small, local
scale since one cannot implement major change immediately
on a large scale — and having the change grow to significant
scale without diluting the change? To answer this question we
first look to some examples of macro-scale learning from other
fields in order to shed light on the potential for fundamental
change in learning environments.

3.1 Better eating in America
Consider the change in cuisine in the USA over the past forty
years2. This was a large-scale change that altered the social
landscape, which was based upon myriad micro-actions that
emerged without any preconceived plan. One can say there is
a more widespread collective intelligence about food. Until the
1960s, despite having the benefit of immigration from many
countries, the choices for eating did not reflect the richness of
the possibilities. Chinese and Italian restaurants, while
ubiquitous, did not exemplify the beauty and flavours of the
real cuisines. While in 1975 a North American had to live in a
major city to have a cosmopolitan choice of foods, this was no
longer the case in 2000, by which time a myriad of new food
options have become widely available in the North American
milieu. How did this happen? Here are some ideas:
• people gradually became aware of more options,
• televised cooking shows demonstrated new possibilities
and made them believable and accessible,
• people gradually had more opportunities to try new kinds
of food as new restaurants and more speciality stores
opened,
• more learning and demonstration materials became
available through magazines, books, and eventually the
Web,
• cooking courses,
• people could experiment and try things out,
• people had powerful personal experiences in creating and
enjoying new cuisines,
• a new feedback loop was established — more choices
available, more choices made, even more choices
available.

3.2 Paradigmatic change in manufacturing3
In most other fields, including traditionally staid ones such as
the military or large manufacturing plants, models of
organisation and process have begun to move away from Ford/
Taylor/Sloan models of hierarchical centralised control of
standardised operations [15]. These models were not
implemented in a top-down fashion throughout
manufacturing, nor were they invented in the research lab and
rolled out to society at large. Rather, advocates implemented
them in order to fit local microculture. Progress was viral and
evolutionary.
The spread of ‘lean production’ techniques is illustrative of the
growth and development of a macro change. In post-war
Japan, Toyota studied the state of the art in auto
real change is inherently a
kind of learning
2 Within cuisine, with Walter Bender I am deeply appreciative of gains
made in microbrewing. Our programme director, Jacqueline
Karaaslanian points out that fashion also fits this macro learning
model.
3 I am extremely grateful and deeply indebted to John Seely Brown,
Kent Bowen, and Dan Roos for most of this information and analysis
I received through personal communication. I have benefited greatly
from their research, observations, and comments. The insights are
theirs while the mistakes perhaps introduced are mine.
rather than merely copying
the ‘best practices’, they
studied the underlying
principles
Models of growth — towards fundamental change in learning environments
BT Technology Journal • Vol 22 No 4 • October 2004 99
manufacturing [16, 17]. However, rather than merely copying
the ‘best practices’ of the time, or their phenotypic
manifestations, they studied the underlying principles. They
investigated how they could improve the processes and fit
them into local culture. Even more important than putting into
place any particular set of activities, they built a process for
continuous learning throughout the organisation. They
instantiated the process of looking at what works, focusing on
underlying principles, and adapting the ideas, even if it means
a radical transformation. The work is not finished with the first
plan. Rather, the process of continuous improvement is what
is important, and people, rather than serving as unthinking
agents implementing preplanned activities, become active
thinking agents working and reflectively critiquing the ongoing
processes in order to improve them. Japanese auto
manufacturing grew from the rubble of World War II into the
envy of the industrial world.
Yet, despite the overwhelming evidence, many manufacturing
experts in the USA and Europe tried to deny the success of the
new paradigm. Initially, rather than re-assessing their own
assumptions and critically analysing the ideas and processes,
they attempted to find excuses for why the evidence must be
misleading in order to justify their own mindset. They alleged
that the Japanese took advantage of the workers and forced
them to work harder (not true — not harder, but better). They
alleged that Japanese culture fostered the individual creativity
and problem-solving ability demanded at every level of the
workforce (not true — this approach was not ubiquitous across
all institutions in Japan, and in particular did not permeate
Japanese schools, which were extremely rigid, hierarchical,
and resistant to change). The point is critical as, even though
the existing manufacturing system prided itself on results,
objectivity, logic, and squeezing every bit of productivity out
of the system, rather than accept and attempt to appropriate
the ideas, because the results were produced by a different
paradigmatic mindset, they tried to rationalise the data away.
Eventually, tired of losing market share, mavericks within
General Motors (GM) proposed to try the new Toyota
management within GM. They took a plant GM had recently
closed due to its problematic operation. It was the worstoperating
GM plant, with labour strife, high turnover,
absenteeism, and substance abuse among the work force, and
low quality and production rates for their cars. They took the
same work force, and in a pilot project called NUUMI under
Toyota management applying Toyota manufacturing
techniques, they turned the plant around so that it became by
far the highest performing automobile plant in the USA [17]. A
key metric is that it became the highest performing US plant
relatively quickly, but that was more a condemnation of the
state of US manufacturing than a statement of overall quality,
as the NUUMI plant lagged Japanese-based plants. What
must be noted is that what was recently assumed to be the
best possible, that is US auto production, was rapidly
outpaced, not through incremental improvement but by
fundamental re-thinking of process.
It is critical to realise that Toyota did not just try to transplant
its practices back to the USA. Even though they documented
the process, they knew it was insufficient to send manuals or
run rapid training workshops. Developing understanding
among people who could organically grow the overall process
was key, as merely attempting to implant the practices would
not produce the desired results. They knew that the results
were more than just a sum of the practices and that it was the
mindset built upon the practices that needed to be developed
in place, not merely transferred. Neither Toyota nor GM
adopted the initiative as something that could be realised in
the short term. Both companies dedicated substantial time
and resources, including their best people, in order learn the
principles in their full context and to develop trust and respect.
As systems and processes improved, the ‘intelligence’ of the
people involved improved. Detractors previously would claim
that manufacturing workers did not have the ‘capabilities’ to
carry out the debugging, problem-solving, decision-making,
creative process design, statistical quality control, and so on.
Clearly, this was not a fault of human capability, but rather a
systemic flaw producing waste by not enabling people to
develop their full potential. We hear similar critiques regarding
the lack of capability among teachers and others who work in
learning environments. Our belief and experience is that in
learning just as in manufacturing this perceived lack of
capability is due to systemic and not personal flaws.
After such a success at GM, what happened next? Despite the
entreaties from some of the NUUMI team, GM did not agree
to try the same paradigm in a greenfield approach. The
advocates thought that instead of turning around an existing
facility with its legacy, culture, and incumbent problems,
beginning from scratch, a greenfield, would enable them to go
even further. However, despite the recognised success at
NUUMI, management declined. Unlike in education, the
metrics of manufacturing are easily quantifiable. There are
profitability, production rate, quality rate, pace of new model
development, and so on. Yet, better quantifiable results do
not guarantee convincing management of benefits or
adoption of a different paradigm. GM does recognise they
have much to learn from NUUMI and have used NUUMI to
fashion their entire global manufacturing system and even
placed a research centre next to the NUUMI facility. However,
adopting the phrase of John Seely Brown, they have copied
the ‘syntax, not its semantics’. This distinction is crucial for
thinking about learning on either a micro or macro scale.
more important than any
particular set of activities,
they built a process for
continuous learning
rather than re-assessing
their own assumptions, they
attempted to justify their
own mindset
Models of growth — towards fundamental change in learning environments
100 BT Technology Journal • Vol 22 No 4 • October 2004
Did this mean the end of the new paradigm in manufacturing?
Not at all, as other mavericks in other places adopted the
ideas and fitted them to their own situations. Thus, the growth
was inter-institutional and bottom-up as opposed to intrainstitutional
and top-down. This fits how Richard Lester
describes firms having their own cultures, and new ideas from
other places, even best practices, cannot simply be grafted
incrementally on to existing companies [18]. Rather, the
ideas, no matter their merit, must be re-formed to fit the host
culture.
What is clear from the manufacturing example is that
fundamental change and macro-level learning is possible,
even in places such as manufacturing where it was commonly
believed that the personnel involved where not educated
sufficiently to perform sophisticated thinking and analysis.
What was needed was time, investment, continuity,
commitment, and access to people with expertise and
experience, and that the learning process was not merely a
research-based accumulation of best practices grafted on to
existing cultures.

3.3 Characteristics of fertile environments for growth
We begin to see patterns for felicitous conditions for macro
scale growth. These include:
• volition — people must want to do things,
• appropriation and experimentation — people need to try
out their own conceptions of the ideas in their own
settings based upon their own priorities,
• concrete exemplars — there is a need to experience real
examples of the ideas,
• community and communication — peer-to-peer
interchange of ideas, explanations from practitioners at a
variety of levels of expertise and experience,
• feedback — when one experiments one must not only see
the results, but also get feedback from others,
• debugging — one must get the chance to ‘make
mistakes’ and then use those to design and implement
further work,
• materials — one needs things to work with that facilitate
the new paradigm, and not merely work with the tools of
prior instantiations,
• language — new paradigms re-appropriate old terms for
new connotations, and even invent new terms to describe
things in new ways,
• bottom-up and emergent — large-scale growth comes
from the basis of many little contributions,
• time and continuity — major changes do not happen over
night, as there needs to be enough continuous time to
experience and develop the ideas in their full complexity,
• hope and expectation — people must come to believe
that improvement is desirable and possible.

4. Emergent design and contexts for change
One cannot look at change in any major social realm such as
education out of its cultural and historical context. Ideas about
learning and education have historical roots, and ideas from
the general culture have impact. That is, not only should one
design to leverage cultural elements to enhance the change
process, but also the full burden for change does not lie within
the particular change effort alone. We divide the elements into
three broad categories (reminiscent of Kuhn) — materials that
enable leaning, cultural factors, and exemplars. Naturally,
these categories build upon and inform each other. How
groups choose to intervene and interact is emergent, both
because certain elements are influenced by the broader
culture and one cannot predict exactly what and in which ways
ideas will take hold, be appropriated, and given meaning.
Materials that enable learning and doing are moving with
increased rapidity into the world. These materials enable
people to undertake their own projects and, through doing,
learn a variety of things. Media plays a critical role in helping
to form how we think about things due to the affordances of
how knowledge can be represented in that medium.
Computational media enables representation, sharing, and
rapid modification of dynamic and complex ideas in ways that
other media cannot. Evelyn Fox Keller has written eloquently
about how the growth of biological knowledge was facilitated
through the capability to model and visualise enabled by the
computer [19].
The spread of computers, and their continuing rise in speed,
memory, and connectivity combined with their relative
dropping of price, has fundamentally changed the ways people
learn and work. The range of options for learning and doing
has dramatically increased, and thus people can learn and do
more, with guidance and examples from more places, than
ever before. The types of devices have also increased. Robotic
devices such as programmable Lego bricks, other
microcontrollers, cell-phones that are always on a network,
more data enabled, digital still and video cameras, MP3
players, with more to come, bring more powerful devices into
people’s lives for appropriation for tasks of their choosing.
Significantly, some localities are experimenting with giving
each student a laptop computer. This action has the potential
to fundamentally alter the environment in a large way [20].
Having powerful learning examples one can experience and
participate in helps to break the mindset that learning must
happen by being taught in schools. The attraction of such
participation trumps the pessimistic view that technology is
too difficult to learn and most will not do it. People are
developing technological fluency in order to benefit from
participation in the digital world. Combined with this more
positive experience is a growing dissatisfaction with
standardised, institutionalised schooling. Many people are
beginning to reject the dominance of standardised tests and
the resulting pressure on children and disfiguring education
[21, 22]. Moreover, many are beginning to recognise that
perhaps the greatest casualty of standardised,
institutionalised schooling is children’s creativity and joy in
learning. Observing the harm to their children’s spirit, many
parents are increasingly turning to alternatives, including
home-schooling in a variety of manifestations [23]. These
Models of growth — towards fundamental change in learning environments
BT Technology Journal • Vol 22 No 4 • October 2004 101
various small steps all help to combine into something much
larger culturally.

4.1 Exemplar projects
Rather than focusing exclusively on micro-level questions (e.g.
How might we better develop mathematical thinking?) with
the implicit assumption that a cascading of growth to scale will
necessarily follow, we pursue the possibility of taking microlevel
approaches that improve practice and simultaneously
aim to maximise the possibility for macro-level change. If one
had the opportunity to take the challenge of everyone learning
and try to dramatically improve opportunities, thinking and
practice, what should one do? We provide some brief
examples.

4.1.1 Pilot schools
Pilot schools enable the trying out of a particular set of ideas
without the limitations of fitting into an existing institution or
overcoming management resistance. They have focused on
particular themes (e.g. math and science or performing arts or
health), approaches to learning (e.g. progressive or basic skills
or high-density computer use). Their primary benefit is to
create examples of how things can be different. The major
constraint inherent in pilot approaches is their difficulty in
having an impact on the rest of the system due to their
isolation (as we saw with the NUUMI pilot of General Motors).

4.1.2 Computer labs as islands of innovation and
change
An early hope towards creating fundamental change was to
use the computer lab as its own pilot to instantiate the
potential of the computer as a powerful learning device;
because the computer lab was new its use was not delimited
by historical traditions (except the powerful ones owing to the
fact that the labs were located in schools and thus inherited
the constraints of the grammar of school). Costa Rica’s early
adoption of widespread computer labs at the primary-school
level is perhaps the best example of what can be achieved. It
has led to the development of technological fluency among a
large proportion of the population, which in turn has led to
Intel locating a semiconductor fabrication plant in the country.
It has also connected many people to modern technology, new
possibilities for learning, and set a precedent for national
educational innovation. The major constraint here, though, is
the same as in other pilot efforts. That is, while the design
goal was that the computer lab would influence the school as a
whole and help reform the teaching and learning not just in
the lab but overall, the lab was isolated and could not broadly
influence the schools.

4.1.3 Influencing the system by operating outside
the system
Since the ideas of ‘School’ or ‘Education’ are truly
paradigmatic in the Kuhnian sense, they carry with them a
web of meaning, connections, processes, and models. Kuhn
also described the incommensurability when the same terms
are used by different paradigms [7]. Thus, any project that is
situated in a school setting must overcome these inherent
meanings, culture, and process.
Some projects then determine to work outside the system,
setting up new learning environments that are explicitly not
school. One such project was Project Lighthouse in Thailand,
which we began in 1997 and continues to exist [24]. The four
major thrusts within Project Lighthouse were:
• creating village technology learning centres,
• new programmes within the national non-formal
education system,
• workplace-based programmes,
• a new ‘e-school’ in Bangkok.
A benefit of this approach is that . After all, no one knew what
a village technology learning centre was, so there could not be
existing rules. The success of this project was that certain
prejudices based upon the standardised school experience
were shown to be products of the system and not inherent in
the culture. These included conceptions such as that rural
families did not care about learning, that it was out of Thai
culture for students to take the initiative and work in an open,
learner-centred environment, that rural teachers were too
poorly educated themselves to be effective, that once people
learned technology they would abandon the project, that
Thais could not innovate with technology, that it would take
many years of prerequisite training before rural youth could
effectively use the technology for learning and solving local
problems. The downside to this approach was the same as the
others: the overall system could not adjust on a broad scale to
take advantage of what was demonstrated. The government
did pass a new national education act, influenced in part by
Project Lighthouse, that set aside a fund for experimental
projects, and the current Prime Minister, an early benefactor
of the programme, has instituted a number of laws to enable
everyone to purchase computers, develop technological
fluency, and build educational opportunities.

4.2 Mass attempts in large systems — Curitiba
In order to get beyond the limitation of pilot attempts while
still accepting that immediate mass attempts cannot produce
significant change, we focused on attempts within an entire
city system. Curitiba is a city in Brazil famous for its bold and
innovative attempts at urban planning, transportation, and
sustainable environmental development [25]. In the current
municipal administration they are extending this pioneering
spirit to public education, modernising not only the
organisational physical infrastructure of the schools and
improving traditional education, but also investing in bridging
the digital divide and giving access to computation. However,
again they are not merely computerising existing learning
environments, but using the technology to dramatically
improve the city, the environment, and the schools.
The Future of Learning group at the MIT Media Lab
collaborated with the Curitiba municipal education secretary
Paulo Schmidt and his team to use the new computer
presence to carry with it a new epistemological approach as
well. In order to take root within the system as a whole, we
adopted a three-pronged approach. We began with small
workshops for around twenty teachers at a time, and a team
within the secretariat dedicated to supporting the use of
Models of growth — towards fundamental change in learning environments
102 BT Technology Journal • Vol 22 No 4 • October 2004
technology to improve learning. The goals of the workshops
were to not only introduce the new technologies to be used,
but to use these workshops as models of the types of learning
environments we hoped these teachers would begin to create
for their students. Thus, the activities we put into practice
served as the basis for reflection on learning and school that
we would discuss in the course of the workshop. Also
attending the workshop was a new staff group within the
secretariat devoted to supporting learning with technology.
This group would continue to hold workshops for more
teachers on a regular basis.
However, as there are more than 100 000 students in the
municipal public school system, there was no way that small
workshops would ever reach all of the teachers. We thus ran a
larger workshop, the ‘Instituto de Inverno4’, attended by more
than 120 teachers from Curitiba, as well as activists from other
projects throughout Brazil.
A primary goal was to give a sense of critical mass towards
change. With twenty at a time, with two or three from a
school, participants did not have a sense of change. However,
with more than one hundred, even though this was a small
percentage overall, the teachers began to believe that there
was critical mass sufficient to make something compelling
happen, and, critically, that the administration was committed
to change.
Another major goal of the institute was to challenge the
implicit mindset about the grammar of school by creating an
environment for participants to experience powerful personal
experiences. We could not do this by giving arguments in the
abstract about learning, even though thinking about learning
was critical for our purposes. Nor could we do this just by
teaching a new computer environment, even though a critical
element of what we bring is creative, expressive, and
constructive use of computational technology to open new
possibilities for learning and new possibilities for
accomplishing the logistics of progressive learning on a large
scale. Rather, we try to create an environment for powerful
learning experiences to help create agents of change. We want
these participants not to blindly follow a new set of
instructions, but to further develop the capability to think
about learning and learning environments. By developing this
capacity and then having the freedom to apply these principles
through reflective practice while also participating in a forum
for collaborative discussion, they have the chance to continue
to develop and progress autonomously as more effective
actors.
We organised the institute into five major parts:
• morning talks to the whole group, focusing on learning
and the underlying ideas, by a wide variety of people with
varying areas of expertise,
• project work by teams of participants,
• small mini-workshops on using the various tools
available,
• small group discussion on topics of importance to the
participants,
• daily wrap-up discussions with the whole group,
reflecting on the institute.
As always, the institute itself tries to practice what it preaches
regarding learning environments. It is project-oriented,
learner-centred, interest-based, and situationally driven (see
Figs 1 and 2).
There is one critical difference, however, and that is time.
When we work with children, there is ample time. We are not
limited by only having a 2-week workshop period. Children can
work on projects for a whole year or more, and thus have the
time to go sufficiently deep to do serious work, uncover
important ideas, and gain the satisfaction of accomplishing
difficult tasks. In workshops we cannot do this and this has two
fundamental limitations — the first is that there is no
opportunity for the learning just described; the second is that
there can be the tendency to merely replicate the workshop
experience in the schools, thus negating the ideas of the
experience. Not surprisingly, but true to how learning works,
even though we tell participants that when there is time this is
not what we do, they tend to do as we do and not as we say.
The experience led the teachers to use the final afternoon to
discuss how to continue the spirit of the institute and improve
the schools on a broad basis. One group proposed starting
some new pilot schools where all the teachers were dedicated
to the change. One teacher from this group had previously
described how social pressure from her peers made her reform
of her own classroom exceedingly difficult. Her students loved
her class so much that they told their friends and parents who
naturally put pressure on the school principal and the other
teachers to change. Unfortunately, rather than change they
put pressure on the popular teacher to toe the line and not be
different. She did not desist but at the beginning of the
institute she was pessimistic about the possibilities for
change. Now energised, she and colleagues proposed new
schools where all would be committed to change. This
suggestion was popular until another teacher warned that the
majority of children would not be able to attend the pilots and
would thus be disadvantaged. She also said the new schools
would be isolated from the overall system and would be in
danger of eventually dying out. This argument proved most
popular among the teachers until we suggested that both
ideas could be accommodated. There could be a group of pilot
schools that would serve as exemplars to the whole system.
one is not encumbered by
pre-existing mindsets about
what one must and must not
do
4 This translates as Winter Institute and follows the joke of Secretary
Schmidt as the previous year we had invited him and his team and
teachers to our ‘Summer Institute’ held in July in Mexico City,
sponsored by Telmex and the Inttelmex Foundation. He responded
they would be happy to come but inquired as to why we were holding
a Summer Institute in July in the middle of winter. Accepting the
perspective of the southern hemisphere, we held our Winter Institute
in July, 2002 in facilities in a park in Curitiba.
Models of growth — towards fundamental change in learning environments
BT Technology Journal • Vol 22 No 4 • October 2004 103
The rest of the system would also strive to improve and adapt
as there would be interchange among the projects.
The city would also create a new non-governmental
organisation in order to continue past changes in city
administration, as continuity is a major problem. The
foundation’s mission would be to support the schools by
providing learning experiences for teachers, students, and
parents, and by co-ordinating projects among the schools.
Significantly, I received an e-mail from one of our participating
teachers ten days after the event. She said she told her
colleagues how wonderful the institute was and how excited
she and the other participants were about how they could
change the system. She felt frustrated that despite her
advocacy, her colleagues who did not attend were not moved.
I reminded her that before she participated in the institute,
she too would not have been compelled to change just by
hearing about it. She had to experience it. This illustrates the
limits to growth. Just hearing about a new paradigm is
insufficient to motivate a change. How to spread the
experiential component is the critical issue.

4.3 Emergent participatory design — São Paulo
The São Paulo municipal school system has more than 1.1
million students in approximately 1000 schools. Effecting
change in such a large system is non-trivial. Fernando Almeida
became the education secretary in 2001. He told us that he
would not support pilot projects within the schools as ‘quality
for a few is a privilege’. He challenged us to come up with a
plan that could have an impact on all the schools in as short a
time as possible.
Building upon the Freirean tradition [6] to which the secretary
was committed, we proposed a project we called ‘A Cidade
que a Gente Quer’5, where students would build
computational models in a variety of media modelling how
they would choose to improve life in their city [26]. The basic
premise is that students will perform a critical inquiry into the
life, culture, and functioning of their city and create new
models of how they would like some aspects to be. They can
either address something they perceive as problematic (e.g.
waste recycling, transportation, energy generation and
consumption, employment, crime), or propose a model for a
grand new idea to provide some elements desired but not
previously possible or conceived (e.g. interactive public
entertainment and art spaces for the community, dynamic
customisable clean transportation, instant playgrounds,
responsive environments).
The project is based upon constructivist ideas that merge
Freirean tradition and constructionism [26]. Constructionism
builds upon constructivist ideas by asserting that learners
construct their own knowledge especially felicitously through
the thoughtful and reflective design and construction of
personally meaningful artefacts [27]. The strength of Freire’s
tradition is to work on what he termed generative themes, as
determined by the community of learners. The unifying
concept of the focusing on the city provides a generative
theme whereby any participant will have their own ideas and
beliefs and can use these to guide their conception and
implementation. Moreover, the participants can identify with
the situation as they can place themselves inside their
projects, using this as a means to guide their design.
We also wanted the project to better re-link the schools and
their communities. The community provides the basis for
Fig 1 Teacher soldering own electronic sensor at Curitiba
Winter Institute.
Fig 2 Teachers from Winter Institute with their robotic
multimedia system for young children learning hygiene. 5 This translates as ‘The City That We Want.’
Models of growth — towards fundamental change in learning environments
104 BT Technology Journal • Vol 22 No 4 • October 2004
study and content. The school becomes a contributor to the
improvement of its host community. Moreover, we designed
the project so that students could place their projects on the
Web and to discuss the merits of the ideas and analysis
through a forum. A major goal in addition to the learning in
mathematics, science, and other disciplines, was for the
students to develop the belief that they could have impact on
their environment and that they could be agents for positive
change. Just as the desire to make a design implementation
actually function forces the learner to deal with the underlying
scientific principles, the desire to convince other participants
of one’s own analysis and solution requires the learner to
support his or her argument with data and reasoning.
We designed this project not just as an end in itself, but also
with a goal of how it could best help lead to macro change, so
that the project itself could serve as an object to think with
[28, 29]. We proposed the project as a concrete example of
how to work in a more open, active learning environment and
what content could be different. We would utilise this
experience as a case for the teachers and administrators to
reflect upon ideas for teaching and learning. The project is
case-based active learning at the macro level.
We intentionally did not tell the schools exactly how to
implement the project. We tried to navigate the dialectic
between proposing an intervention from outside the system in
order to help break its dynamic equilibrium and knowing that
people will tend to resist changes forced upon them from the
outside in which they have no vested interest.
We engaged in the design of the project with the secretary of
education, his staff, and the technology group of the
secretariat. It was important not only that each of these
groups had a sense of ownership of the project, but also in
order to improve the design through the incorporation of their
local knowledge. Once we had obtained approval, we held an
open session for administrators, pedagogues, and teachers of
all the schools to present the ideas, show the project, show
what similar things we had done elsewhere, introduce the
technologies, show examples of projects children and teachers
had previously constructed, and to take their questions and
have a discussion, leading to the local and global decisions
(see Figs 3 and 4).

4.3.1 Design for growth
We introduced two essential elements fitting to our model of
growth that are curiously atypical of most efforts — schools
had to volunteer into the project in order to participate, and
the schools themselves would decide how and with whom they
would implement the project in their schools. It is rather
obvious that in any large organisation, when compliance is
compulsory results suffer: people either ignore the new
programme, comply minimally, waiting until the fervour
passes, or even undermine the new initiative.
We wanted to focus on the dimension quality first, not fixating
on number of sites at the expense of quality. The underlying
hypothesis is that fewer places of higher quality activity create
more felicitous conditions for sustainable growth with quality
over the long term than a larger number of initial sites with
subsequently lower quality. The design tension is over creating
a sufficiently large, critical mass of sites such that they will not
die out, combined with a mechanism for communication and
contagion so that they can affect (or infect) other places.
By asking the schools to determine how they want to
implement the programme locally, we set the conditions for
growth on a number of levels. Firstly, they come to be the
owners and implementors of the project, not merely order
followers. This typically ensures a more dedicated
Fig 3 São Paulo youth with their ‘intelligent bus’ built from
scrap materials.
Fig 4 São Paulo youth with their ‘citizenship robot’.
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BT Technology Journal • Vol 22 No 4 • October 2004 105
participation, but also lays the seeds for growth, as they now
are charged with thinking about the issues underlying the
project. This also enables the project to take advantage of
their local knowledge as well as their imagination and ideas.
From the outside, we could not know who might be the best
teachers to participate. By following an emergent
participatory design, we were better prepared to overcome
the limitations of centralised, hierarchical, bureaucratic
approaches.
Another benefit of this approach emerged quickly — virtually
all the schools adopted different approaches. This diversity of
ideas and examples gave a more fertile ground for the next
round of participants to appropriate models, improve on
ideas, and extend the possibilities. This helped solidify the
idea that learning should not be one size fits all and can be
customised to local ideals, interests, and concerns, and that
deviation from a standard model can be a strength.

4.3.2 Lessons from this experience
Key to the ideas about models of growth was that the
experiences did not remain only in the locality in which they
occurred. Because we designed for collaboration across the
system, the diversity of experiences, both the successes as
well as the means of dealing with events that did not go as
anticipated or were difficult, were concrete cases for reflection
and discussion. Just as at the micro level, having to construct
a mechanism to accomplish something provides a variety of
fine-grained situations for learning and discovering principles,
this approach is designed for construction at the macro level
by the participants. Rather than dictating exactly what to do
with all the residual problems, we allow for the initial potential
lack of total certainty about action as this can serve as the
learning basis so that people can continue to make better
decisions on their own, as well as feel pride, accomplishment
and ownership over the project. They are thus developing
capacity, which not only aids sustainability but also creates
openings for innovations from every level of the system, not
just the curriculum designers and administrators.
We had hoped to have a high-bandwidth telecommunications
infrastructure installed in time for our project, but
unfortunately its deployment was delayed. This deeply limited
one critical aspect of the project: we had wanted different
groups of students in different schools and socio-cultural areas
of the city to communicate, deliberate, and collaborate over
their projects. In an emergent design approach this is both an
important learning aspect and an important part of the model
for growth, as the connectivity expands the circle of
interaction for ideas on projects, mechanisms, and solutions.
Lack of connectivity limited the types and amount of
interaction between the teachers and supporters of the
project.
We also had to work with three different secretaries in the
three years of the project; the disruption and lack of continuity
occurring with each administration change also severely
limited the possibilities for change. Such intra-institutional
problems highlight the difficulties of change as well as the
need for broader models of growth that do not depend upon
any one institution. With this in mind we had already planned
and began a similar effort with a Brazilian foundation that
operated schools around the country. Our purpose was to
enable continuity by planting yet another seed, even if
elsewhere, even if local again, and then to re-connect back. It
is both the recognisable ‘signature’ of the new local
experiment and the mechanism of re-connecting back that are
the keys to sustainability. It also is the recognition that
individuals more than institutions are the generators of
growth, enhancement, and sustainability.

4.4 Combining in-person and on-line — Bradesco
foundation schools
The Bradesco Bank is the largest private bank in Brazil. As a
contribution to the society, Bradesco runs a system of forty
schools attended by over one hundred and five thousand
students. In keeping with their basic charter, the Bradesco
schools are to be found in every state in Brazil, a large country
with profound regional differences in culture and social life.
These are private schools, but tuition is free. Students are
either children of bank employees or are chosen according to
highest economic need. In short, the Bradesco schools serve
students who would otherwise be in the public schools.
Bradesco engaged our group because they felt they were not
getting the full benefit of the considerable investments they
had made in technology. The Bradesco schools were well
equipped with computers and Internet connections; they had
students programming in Logo and doing robotics. Typical of
many schools, Bradesco wanted to get better results with
computers.

4.4.1 Activities with Bradesco
Our engagement at Bradesco took place over an eighteenmonth
period. We aimed for a combination of types of
interactions; in-person, from prepared materials, and through
synchronous and asynchronous on-line experiences. We ran
small workshops as a primary activity. Teachers from every
school except one attended these workshops, as well as some
teachers from neighbouring schools of the public system.
When some administrators and technical help first heard a
general description of the work, that it would be ‘projectoriented,
learner-centred, constructionist’, they replied ‘We
already do that’. By the middle of the first week, however, the
same group of people told us, ‘This is quite different. When
we do projects we decide beforehand what the projects will be.
We don’t let them just choose’. We have had this experience
in several locations. The terms had been disempowered and
schoolified, losing their essence. Only through the
participatory experience did the differences emerge.
Over the course of our engagement with the Bradesco
schools, we have conducted a range of activities.
• We ran small intense workshops focused on re-thinking
the learning process and environment, using the project
theme as a coalescing force, and introducing the
we intentionally did not tell
the schools exactly how to
implement the project
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106 BT Technology Journal • Vol 22 No 4 • October 2004
technologies as a means of displacement from normal
experience, habits and mindset.
• We held big meetings to give talks about learning, to
introduce the basic ideas and orientation of the emergent
paradigm, and the kind of learning projects that we do,
and the technology we use. The talks were broadcast
throughout the school network and archived on the
foundation’s Web site.
• We held small group discussion meetings, which were
forums for reflecting on practical questions about
implementing various projects ideas, as well as big
theoretical questions about learning itself.
• We initiated regular monthly videoconferences dedicated
to thinking about learning.
• We set up an electronic forum, so students and teachers
could get on-line when they were stuck and get help. It
turned out there was no time in the teachers’ schedules
to go on-line, and electronic chat was not part of the
culture. So we shifted course and started setting up online
meetings at particular times on pre-announced
topics. We are now developing new Web-based
environments designed more in the spirit of
constructionist, collaborative learning and less along the
lines of information presentation.
• We made a lot of short how-to videos relating to different
facets of computational technology, programming, and
sensors. This is a resource for the teachers and students
who would otherwise lack the initial domain knowledge to
begin to tackle more complex learning projects.
• We made videos using the technology but focusing on
powerful ideas for learning.
• We gathered multimedia documentation on all the
various learning projects that were under way in different
schools.
We overcame some of the previous limits to growth as, when
we arrived at new schools, thanks to the videoconferences,
most people already knew what the projects were like and
what technological tools were involved. Thus, instead of
having to introduce everything at each site with the incumbent
delays and confusion due to lack of familiarity, the barriers to
entry at each site are diminished and things start much faster
and with more depth.
Initially, there was the tendency to copy the first projects, but
over time, because each learning project becomes individual,
the set of exemplars expanded and diversified as more and
more of the participants’ local voices and viewpoints were
expressed in the projects. There started to be various genres
of learning projects, with strong individual variation within
them (see Figs 5—10).

4.4.2 Digital documentation process
Another way of making learning visible was to have students
document their projects using digital materials [26]. This
included digital cameras, video, voice, and text. We have
always tried to have children document their projects. The
idea was to have them reflect upon their ideas, and to take a
stance about what they were thinking and why. The different
media, the representation, and the narrative all serve to
enhance the learning experience.
As the students documented their projects in digital media, we
made the material available at a fine-grained level for others
to browse and search through the Web. This helped overcome
a previous limit to growth of our projects. The main limits were
technical (teachers did not have enough technical experience
and expertise, as well as often lacking a ‘hacking’ spirit) and
pedagogical (they did not have the experience of teaching and
learning in a non-traditional environment). The images,
Fig 5 Bradesco Foundation school in Manaus project to clean
the rivers.
Fig 6 Bradesco Foundation school in Bodoquena project
studying water quality to create a fish farm.
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BT Technology Journal • Vol 22 No 4 • October 2004 107
videos, and accounts of the participants combined with
commentary and connections layered on top of it, helped to
overcome these limitations.

4.4.3 Lessons from the experience
Through taking part in our workshops, the Bradesco people —
students, teachers, and administrators — shifted their
understanding of what they are working to accomplish from
the technology to thinking about teaching and learning. At the
final reflection meeting during the first one-week workshop in
Manaus, one student gave the bittersweet comment that ‘I
won’t be able to enter my classroom on Monday and look at it
in the same way’. We were happy that he had such a moving
experience with us, but still saddened that he would enter the
old-style classroom. However, in Manaus, the school director
told the students it was now their obligation to take this
special experience that they had received and offer it to the
other students of the school. The students and the excellent
computer room teacher then continued to run workshops for
groups of students, and the richness and diversity of projects
increased considerably.
As witnessed in other programmes, where the school director
was most involved, the projects progressed better. The
Foundation’s technology team accompanied us in every
workshop, and they were a strong source for growth, support
and development. They, the school directors, the activist
teachers, the continuing students, the parents who witnessed
the changes in their children, chose to become the engine for
sustainability and further development.
On the other hand, there was a limited use of the on-line
environment that hindered development. Primarily, it was not
in the school culture to spend time on-line. Teachers’ time is
more than fully accounted for already. They have virtually no
extra time for seeking answers to their questions, for
edification, for curiosity, for improvement. This obviously is a
Fig 8 Measuring temperature and relative humidity.
Fig 7 Bradesco Foundation school in Bodoquena studying
cooling of classrooms and dormitories.
Fig 9 Studying air flow and heat transfer.
Fig 10 8-year old girls’ investigative report on school
bathrooms.
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108 BT Technology Journal • Vol 22 No 4 • October 2004
limitation for improvement within a system and a reflection of
an outdated view of their function as purveyors of fixed
information and not as developing professionals and learners.
Still, what was clear, relative to thinking of models of growth,
was that through enabling powerful personal experiences in
learning environments based upon constructionist uses of
computational technology utilising generative themes
connecting to culture and personal interests, combined with a
multimedia support and collaborative environment made
possible through broadband telecommunications access, we
were able to overcome previous limits to growth. Previously,
approaches based upon powerful personal experiences had an
inherent limitation in the number of sites in which one could
create environments with sufficient contact to catalyse the
powerful experience. There was a vicious circle, where the
limit on contact constrained the development of people, which
constrained the number of sites for fundamental change,
which limited the potential for scale. While still far from ideal,
by using videoconference and image and voice combined with
text and computational media, other sites ramped up projects
much more quickly, and ideas, experiences, and shared
reflections had a chance to spread through a larger network
more effectively.

4.5 Evolution of projects
Having a telecommunications infrastructure combined with an
overall sense of purpose enabled us to use the ‘Cidade’ project
generative theme to not only develop a local learning culture
but also to enable a broader learning culture in a heterarchical
manner. We will use the evolution of a project across sites in
order to highlight key facets towards technologically enabled
models of growth. Significantly, this was not the only project
that was appropriated and re-appropriated across the sites,
but in the interest of space is the only one we mention here.
In the Curitiba workshop a group of teachers chose to do a
project around food and hunger. Concerned about the amount
of hunger in Brazil and the world, the teachers wanted to
sensitise their students to the issue. They decided to make a
scale that would weigh the amount of food wasted within their
school, and use that to extrapolate how much food might be
wasted on average across their city and country, and then to
calculate how many hungry children could be fed with this
leftover food.
A first observation was that although virtually everyone has at
some time weighed themselves on a scale, very few thought
about the mechanism for weighing. This highlights a recurring
theme of searching for understanding of mechanism, of
artefacts and systems. Rather than telling the group the
answer, we engaged in an exploration of how it might possibly
work. In this large gathering many of us served as facilitators.
As the group of teachers had not had the benefit of prior
engineering or technical experience, they asked a number of
us at different times how we might approach building a scale.
Not by plan, each of us engaged in a discussion with them
where different ideas for mechanisms developed. Rather than
finding this confusing or ‘wrong’, this diversity of opinion was
an asset in that in many interesting and rich problems, there is
not necessarily one right way to solve it. If we gave them the
answers and the steps, this chance for analysis and learning
would be lost. On the other hand, we do not say nothing
either. We help based upon a number of factors, but more
with the goal of fostering the learning process as opposed to
having people quickly converge on a ‘right’ answer.
When we showed this project during the first Bradesco
videoconference, the project idea resonated with a group from
the second workshop site located in the northeast of the
country where traditionally hunger has been a major problem.
This group could neither merely copy it, as they did not have
the same materials, nor could they see exactly how it worked.
The stories and images with which to work were evocative and
not prescriptive. Whereas the first group used a bend sensor
to determine weight by translating calibrated movement into
weight, the second group did not have a bend sensor and had
to use a rotation sensor. Rather than being able to translate
vertical movement into weight, they had to translate rotation.
However, in the best constructionist sense, a new subproblem
emerged: how to enable small quantities of weight to
move accurately while still maintaining sufficient tension so
that an empty scale would not simply unroll. Searching for
other mechanisms to keep tension while allowing movement,
the group settled upon a spring. Searching for delicate
springs, the group found one in a ballpoint pen. Thus, while
ostensibly the projects were ‘the same’, the experiences were
quite different. We did not want everyone to repeat the same
experience, as it would not have the same meaning, import,
freshness, sense of discovery, or emotional connectedness.
The Cidade project as a whole, as well as particular projects
within it, were easily adapted by facilitators from the Omar
Dengo Foundation and applied in schools in Costa Rica. Costa
Rica has a basis in constructivism, constructionism, computer
programming, and Freirean ideas. Through their experience,
merely by hearing a description of the idea and viewing
examples of projects, the facilitators from the foundation were
able to quickly implement the project and achieve exemplary
results6. Working in an intellectually fertile environment, with
experienced and committed people, they were able to quickly
adapt new resonant ideas.
We have described this process as the roots, fruits, and shoots
of projects [9]. There is a local rootedness, in this case,
concern about alleviating hunger. The fruits are in the learning
at a variety of levels, within the disciplines (e.g. knowledge of
physics of the mechanisms, the mathematics underlying the
calculations), in learning management of one’s own learning
projects, and in the meta-knowledge behind solving problems,
searching for mechanisms, working by analogy from
examples, using powerful ideas, etc. New shoots develop as
the learners build new mechanisms and try the new and old
mechanisms in new project areas. As this process reifies, new
the goal is to build an
understanding of the
underlying design choices

6 Personal observation and communication with the Omar Dengo
Foundation. They are currently preparing a report on their
experiences, and are attempting to expand the effort.
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BT Technology Journal • Vol 22 No 4 • October 2004 109
roots develop and a virtuous learning cycle can emerge. This is
what enables meaningful, bottom-up models of growth.
5. A tool for documentation and
re-appropriation
Ideas of constructionism, the uses of digital documentation,
and the goal of making ideas appropriable, leads us to the
design of support materials and collaborative environments to
support more widespread adoption of new learning
environments. We view the underlying mindset of Web
publishing as fitting primarily at two extremes of a continuum
— typically, there is either high granularity (publication of
complete, finished projects), or low granularity (step-by-step
instructions of what to do to complete a project). High
granularity provides full concept examples of what to do, so if
one is fluent with the ability to do it, then it is rewarding. If one
is not fluent, however, then there is no handle with which to
get started, or, once there is complexity in the development,
one is lost. At the other extreme, step-by-step instructions are
useful if one just wants to complete a particular project, but
are not so useful if the situation differs or if the goal is to build
an understanding of the underlying design choices. This is
because at either extreme, the design choices and principles
were made by the project designer and are thus opaque to the
viewer. We are designing for learning through appropriation,
and thus will present projects at various levels of granularity,
along with commentary, animation, and opportunities for
collaboration.
6. Developing new models of macro-level
learning
With the critical mass of deployment of and fluency with
computational technology new ways of learning and knowing
became more possible at a broad scale. The inertia of
institutions, their proclivity towards acting as immune systems
isolating, rejecting, or co-opting and assimilating change, can
make one pessimistic towards the possibility of change. While
any one particular institution may resist change, change can
occur through the work of individuals through the culture.
Manufacturing is one example of this. In learning, the spread
of the influence of Freire is another. Freire created his most
powerful exemplar of his ideas in the northeast of Brazil. His
compelling description of the ideas in The Pedagogy of the
Oppressed provided the language and models [6]. His
influence did not reach global proportions through any
institution, through replication of his project. Rather
individuals appropriated and adapted his ideas to their local
interpretation and situation. As they tried the ideas, their
thinking developed. Others then were influenced. This
recursive virtuous cycle, where each stage benefits and builds
upon itself, is typical of a new model. However, simply
challenging the mindset is not enough unless one provides the
basis for new models. There must be something to replace
what is being challenged.
We are not claiming to know exactly how learning
environments of the future should function, nor are we
claiming we know exactly which model of growth will optimally
facilitate the development of better learning environments.
We are proposing a more nuanced study of models that enable
learning on macro and micro scales, developing new models
and mechanisms that can optimise impact over time.

6.1 Paths of change
Rather than focusing only on change within an existing
institution, we adopt a broader view of change with human
agents as carriers hosted by a variety of institutions with the
change developing through improving practice and developing
ideas through the reflective trial and error of creating
exemplars. We note that dramatic changes can occur more
easily in situations like manufacturing or in scientific fields, as
the resistance is less, the metrics of and mechanisms for
feedback are better, and the barriers to entry are lower (there
are far more resources and thus it is far easier to start a
company with different ideas and demonstrate effectiveness
than to start and maintain a new school or learning
environment with different ideas). Still, the critical element is
change through powerful personal experiences, with the
ensuing possibility to create and join new efforts attempting
to further the growth and development of the ideas and
practice. Connectivity and new computational media afford
new possibilities to extend the time and space for
collaboration such that these powerful personal experiences
can be shared.
Kuhn noted how scientific progress was not just a monotonic
accumulation of scientific facts and knowledge, but rather that
world views predominate. The mechanism for change of world
view was through the existence of a critical mass of data that
contradicted or did not fit the prevailing paradigm. This
enabled the acceptance of new models. We can note that on
the micro scale this path holds as well. Children do not develop
through the simple monotonic accumulation of new facts, but
through development when the world pushes back and
previous ideas can no longer account for the new phenomena
and ideas.
Thus, we believe that a key element to enable fundamental
change is to create experiences that challenge ideas about
learning and simultaneously provide the basis for the reflective
development of alternative models. A focus then is not on
maximising scale too quickly, but rather on planting the seeds
for subsequent impact even if it appears slower in the short
term. Maximising the short term typically is at the expense of
real impact over time. Returning to the characteristics of
macro-level learning enumerated above, we find that these
remain key elements for developing new models of growth.
These include the need to experiment, voluntary participation,
appropriation, concrete exemplars, communities of practice,
communication of ideas, feedback, debugging, new materials,
development of new language, a bottom-up, emergent
nature, time and continuity of purpose, and built upon a
passion for a significant improvement.
technologies can be
generators when they are
designed for appropriation
and adoption
Models of growth — towards fundamental change in learning environments
110 BT Technology Journal • Vol 22 No 4 • October 2004

6.2 Generators — things that make more things
Another element for re-framing is to not look only at structure
(i.e. the thing for replication) but to examine the dynamics
(i.e. the process of change). One must cede the possibility for
certainty of outcome, and look instead at creating
environmental conditions for growth. Instead of creating a
particular thing that one would propose to replicate to scale,
we can look at creating a mechanism that can grow and adapt.
Such generators can be people, technologies, powerful ideas,
and exemplary activities that others may appropriate.
We look to develop people as generators through experiential
means. Through compelling experience people can gain the
volition to become the early adopters of the new practice.
John Seely Brown uses the term ‘stolen knowledge’ to refer to
how practice can be appropriated by people since so much of
practice is implicit and thus instruction is an insufficient means
for acquisition [30]. Not only does this framework fit a model
of growth through a community of practice, but also we
particularly appreciate the subversive appeal of the idea of
‘stolen’ as it has been our experience that belief in being part
of a movement to create change in itself helps to fortify the
commitment to change. Taken in this light, we view people as
generators of change not in the ‘multiplier’ role as a cog in a
machine cranking out identical parts, but as adaptive creators,
developing more people and new ideas to continue to fit,
adapt and alter the environment. We aim for exponents of
exponential growth, and not multipliers for geometric growth.
Technologies can be generators when they are designed for
appropriation and adoption. This fits a model of enabling
authorship and creation within the user community, and not
merely as information delivery devices. Their function as
generators is dependent upon the possibility for development
of fluency of use and expression. When people are
comfortable to explore and create, and there are communities
of practice and communication mechanisms for sharing ideas
and creations, then growth can be facilitated. The
development of the personal computer is an example of this,
as is the free software movement.
Powerful ideas are also generators. As people come in real
contact with such ideas, they appropriate and use them. Our
use of generative themes within our projects is based upon
this idea. Not only can virtually everyone have an idea for
development from good generative themes, but they too are
carriers of powerful ideas within the activities.

6.3 Exemplars — powerful new learning experiences
Integrating different learning environments into existing
institutions is non-trivial. We have gone outside the system to
create new entities (as in the village technology centres of
Thailand) and we have used workshop experiences in schools
to create an ambience for different practice7. The workshops
were intended to:
• provide powerful personal experiences of a different
approach to learning,
• break pessimistic mindsets about people’s ability to
learn,
• surface, reflect upon and discuss participants’ own prior
explicit and implicit assumptions about learning to the
surface, and compare them to the new experience,
• encourage participants to think about the learning
process itself,
• engage in thinking about the design and practice of
learning environments in the local context,
• identify local people whose thinking and acting appear
promising so that they can take on greater roles for
change,
• debug our own thinking about the mechanisms of
learning and our own pattern of practice in designing
learning environments.
It is only natural, then, that the learning experiences the
participants have in the workshops became valuable as case
studies of learning itself, as objects-to-think-with, as concrete
experiential data that could be shared and discussed and
pondered and brought to bear on ideas about the basic
mechanisms of learning and teaching. Learning things in new
ways themselves, seeing other people learn things in new
ways, seeing everybody operate as learners far beyond
previous expectations, thinking about the basic mechanisms
of learning — this was the long-term takeaway for the
participants. They added a new stock of powerful ideas and
techniques to their repertoire as learners — and as students,
teachers, and administrators. They began to act and think in
new ways.
This is not the work of a day, or a week; this is not a work of
rhetorical persuasion, or philosophical conversion, or
administrative fiat. This is a process where the chance to
experience directly a powerful new practice of learning leads to
a fundamental rethinking of what might be possible, and how
to achieve it.
We found with Bradesco that if we can first establish the
methodology, the ‘how’ of creating learning environments,
then we can work to continually add content, the ‘what’ of
learning environments. Significantly, this is not the same
content as traditionally is taught in schools. The old content is
technologically dependent upon paper, pencil, and textbooks.
Ideas believed to be out of the reach of many children were
not necessarily due to the inherent complexity of the content,
but of the limitations of the materials. A key to models of
growth of new learning environments is to develop new
content that enables new learning.
The central focus of the workshops was to reflect on the
learning process itself. This is a distinctive feature of our
learning paradigm — epistemology all the way through. In
order for a deep change to take hold and to avoid merely
repeating the same experience, we want everyone to become
a learning theorist. Sid Strauss points out how this is true in
learning environments implicitly as the models of learning
7 The term workshop itself is problematic as people have come to
understand workshops, particularly those using technology, as
isolated environments introducing the syntax of a software tool or
some technique of action, and not as part of an on-going process for
re-thinking and change. We sometimes use the term atelier but have
not yet settled on a term that invokes the proper full image.
Models of growth — towards fundamental change in learning environments
BT Technology Journal • Vol 22 No 4 • October 2004 111
people hold guide their practice [31]. Yet, these models are
not part of an on-going process of reflection and
improvement. It is popular to speak about the importance of
learning to learn, but how often do we get the chance to truly
reflect upon our learning and to learn better ways of learning?

6.4 Lessons from the Bradesco experience — a model
of growth
What we witnessed in the Bradesco Foundation schools was an
example of how digital technology and telecommunications
potentially enables going to scale. The work carried on at a
site could have influence over multiple sites throughout the
network. We were no longer bound so tightly by the
limitations of spreading people to places. We no longer had to
rely on exact definition of curriculum and could then
accommodate a more personalised approach to learning
based upon place and interest. The ability to communicate
and collaborate synchronously and asynchronously combined
with the use of digitised, searchable materials, enabled more
people and places to engage more deeply with the new ideas.
We were able to continue the development of a community of
learners so that one did not only learn with the people in one’s
classroom, but with others throughout the network. We also
were not limited to place as we could learn in the community
and better re-connect the school and its host culture.
By working within the school but outside the normal structure
and operation of the school (by having teachers and students
learn together, by having long-term inter-disciplinary projects
on a generative theme, by eliminating age segregation), we
had some of the benefits of a greenfield approach. We were
free to innovate and create real examples of what we would
like to see in learning environments, while still remaining
connected to the people and culture. Significantly, this
enabled a change in thinking from ‘we already do that’ and
‘improving the computer lab’ to ‘re-thinking all the teaching
and learning of the school’. The work provided a concrete
basis to question existing practice, try new practice, and
examine learning.
6.5 Emergent design for macro-level change
We think macro-level change in education will emerge as the
outcome of a large number of micro-level changes that
coalesce and set up a tipping point. When we examine how
paradigms of practice have changed in other fields and other
areas of society, we see the following patterns:
• new paradigms do not start out operating full-scale at the
macro-level,
• contradictions gather and eventually there is too much
that the existing paradigm cannot account for — people
see a need for change,
• new models are posited,
• new technologies often prompt the change as they open
the possibility for new ways of seeing the world.
We think that a new paradigm of educational practice can take
hold and grow through an emergent design strategy for
change. This follows from certain properties inherent in the
situation — meaningful changes must proceed from local
concerns, and no one knows the right answers in advance. In
education as in other areas, we should expect the best designs
will emerge from a process of modelling and testing and
debugging and adapting to local conditions on the ground.
Ours is a strategy of creating diversity, of deliberate variation.
Every project we do turns out differently, and yields
unexpected results — this is an inevitable result of genuinely
engaging with the local learning culture and local concerns.
This is a great advantage for the progress of our research into
learning, and it is the essence of what we are trying to do —
encourage local variants to arise and adapt while creating
mechanisms so that the variants have a chance to spread and
adapt.
John Dewey has so eloquently described the role of learning
for human development and the role of human development in
the formation of just and equitable societies [4]. For Dewey a
just society could only be built not based upon the dictates of
clergy, royalty, or an elite, but depended upon the informed
collective decisions of all, where every voice should be heard.
This philosophy provides a basis for thinking of models of
growth for learning environments. As Tyack and Cuban have
described [1], it has proved insufficient to dictate new
curricula and expect every actor in the system to merely follow
the instructions. Efforts that depend upon existing personal
expertise and rich networks of contacts have intrinsic
limitations for scale. The only possible path, as well as the
most just and equitable approach, is to foster development of
all participants.

Acknowledgements
The author would like to acknowledge the support of Rodrigo
Mesquita of Radium Systems and Agencia Estado for support
to enable this work. I also wish to acknowledge the support of
and collaboration with the Bradesco Foundation and their
schools, the municipality of Curitiba, the municipality of São
Paulo, and the support from the MIT Media Lab Digital
Nations research consortium. The ideas expressed in this
paper naturally result from the collaboration and contribution
of many. I especially wish to thank Seymour Papert, Walter
Bender, John Seely Brown, Edith Ackermann, Etienne Wenger,
and the students and collaborators of the Future of Learning
Group for the development of these ideas. Chris Cleary was
invaluable as a discussant for the paper as well as in his help
putting together early drafts. It has truly been a group effort.
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David Cavallo co-directs the Lab’s Future
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Media Lab, he led the design and
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American and Caribbean region. Cavallo received his MS and PhD from
the Program in Media Arts and Sciences at MIT, and a BS in computer
science from Rutgers University.

Tuesday, August 19, 2008

To show the derivative of sinx based on simple geometry

We always face the struggle as year 10 Maths teachers in trying engage pupils in deep learning of the derivative of sinx. If we try to show the derivative of sinx by first principles, we'll need to invoke L'hospital's rule for sinx/x which can be shown via the squeeze theorem of sector area between 2 triangles. Unfortunately, pupils may not have the prior knowledge for this to make meaningful connections. I've thus attempted to show the derivative of sinx from another perspective based on simple geometry via the following videos.

After going through the process of creating the videos to show and explain the derivative of sinx, I realized how powerful a learning process this can be if students were to go through similar process in collaboratively explicating the gaps of reasoning in the Maths Java applets. In a way, by representing the thinking behind the creation of these Java applets, students will be thinking more deeply to make meaning of new concepts to be learnt based on

  1. the understanding that derivative of a continuous function at any point x is the gradient of the tangent line at that point x which is given by the gradient of the secant line very near the point x
  2. their prior knowledge of simple geometry
The process of students creating these mathematical reasoning videos (should have some drafts) can also be leveraged on to provide ongoing and immediate feedback to help bridge their understanding and refine teachers' instruction.















Here's another similar learning design idea.