Une vie pour l'apprentissage des mathématiques et la pensée informatique

Mathématicien et pionnier des technologies éducatives, Seymour Papert a contribué de façon décisive à l’orientation des recherches sur les environnements informatiques pour l’apprentissage humain (EIAH). Son œuvre est à l’origine d’un courant de recherche international sur l’apprentissage des mathématiques avec lequel la recherche en didactique des mathématiques entretient des relations – que l’on pourrait qualifier de dialectiques – depuis le début des années 80. Victime d’un accident en 2006 à Hanoï, où il était l’invité d’une conférence de la 17° étude ICMI2 sur l'utilisation des technologies numériques dans l'enseignement et l'apprentissage des mathématiques, Seymour Papert a dû brutalement interrompre son activité académique. Il est décédé le 31 juillet 2016.

La revue Recherches en Didactique des mathématiques a souhaité lui rendre hommage, c’est le sens du texte que j'ai proposé pour le numéro 37/2-3 qui vient de paraître. Après avoir évoqué des jalons importants de la vie scientifique de Seymour Papert, ce texte revient sur deux concepts clés, micromonde et constructionisme, qui constituent les piliers fondateurs de son œuvre.

Papert lors de l'ouverture officielle du London Knowledge Lab (début à 14min 15s)

L’héritage de Papert est bien vivant, et l’exploration des voies qu’il a ouvertes est prometteuse. Un Lutin m'a suggéré avec malice de conclure par une citation ; clin d’œil et manière  d’invitation :

"What make our century’s science thinking different from any other century are the ideas associated with computation, computers and information science, and the idea that we should  give children this powerful thing they care about more than anything else, that they ought not to know what goes on inside it - it blows the mind." (Papert 2004)

Teaching, an emergent property of learning environments

Teaching, an emergent property of learning environments - IST 2000

I first presented this view of teaching in the context of the design of learning environment in 1999 on the occasion of a EU-US conference in Stuttgart (see the notes here and there). This new version was prepared for a talk at IST 2000 held in Nice; it includes outlines of the project Baghera which was emerging:

The project Baghera, a leading project of the Leibniz Laboratory, has the objective of shaping and experimenting radically new perspectives on the design of eLearning environments. First, by eLearning environment we mean not only the technology but the whole complex constituted by the machinery, its users and its environment. Second, it is the project basic belief that the complexity of human learning can be faced only if the design of eLearning environments takes the collaboration between artificial and human agents as a foundational principle. This requires a strong pluridisciplinary approach at every stage of the design and of the implementation.

A platform like the one we look for, is structured by several different types of interaction and cooperation: between teachers and artificial agents, between human teachers with the mediation of the technology, but also between learners mediated by the technology. Indeed we must add the interactions between learners and teachers either in an asynchronous mode or in telepresence, and between learners and the learning environment. Learning does not occur because of one specific type of interaction, but because of the availability of all of them. One type of interaction, or one type of agent, being selected depending of the needs of the learner at the time when the interaction is looked for, as well as of the specific characteristics of the knowledge at stake.

Then, the learning environment, constituted by content specific resources and conception specific resources (taking into account the variety of learners possible conceptualisations) gets its teaching power not from the property of one of its components, but the emergent property of the interactions of all the agents involved—either artificial or human, learners or teachers. In this approach the crucial issue is not that of the genericity of the technological environment (which is always obtain to the detriment of its cognitive and epistemological specificity), but of its adaptability and openess to change.

May be this is just rediscovering that education has never been the result of the action of one isolated tutor, or single intitution, but of the Society at large...

By the way, why “Baghera”? Because at the core of the system we intend to develop a society of non-human agents whose interactions will aim at the education of a human learner. But unlike the famous story, this time some human agents will take part in the adventure…

Learning aware environments

Retrieved from Nicolas Balacheff (2006) e-Agenda European Forum, Casteldefeld

Once upon a time (Eden research workshop, Casteldefeld 2006), I was asked the question: “Can we introduce learning in every human activity”? From a non-English speaking perspective this question may sound strange. Isn’t it the case that learning is present every where and at every moment in our life?  This is a matter of survival. Learning is a competence shared by all living organism. Learning is life long. It starts with our first breath and continues with it until the very last second. However there is something specific to human beings, which is that not only do they learn to survive in their biosphere, but also they have to learn to survive in a noosphere that humanity is continuously building, renewing, transforming. The noosphere is made tangible by human artefacts, but essentially by language. Learning in the noosphere is so complex that specific strategies have been developed to support it, namely teaching (or education, instruction, training, coaching, etc.).

Designing environments likely to stimulate and support learning outside formal education and training experience—or situations mimicking these—was in most cases out of reach until the emergence of the digital technology which bridges the biosphere, where our bodies and activities are developing, and the noosphere where minds and intellectual constructs are developing. While language and the related symbolic technology (writing and reading) were the privileged tools to support learning, digital technologies go beyond by producing highly interactive simulations and virtual worlds. But more significant is the development of augmented reality, the systematic embedding of sensors and system on ship in all artefacts which open the possibility of a “merge” of both spheres. Here is the challenge of ambient computing.

Just as the rest of our environment, modern digital technology cannot support learning if they have not been designed on purpose by incorporating teaching (coaching, instructing, scaffolding, or else) features. This is the challenge of designing, implementing and understanding learning aware environments. That is environments which have the capacity to recognize and capture relevant events from observing the human activity, the ability to understand the learning needs and then to provide the adequate feedback in whatever form. This is a scientific and technology challenge for ambient computing and research on cognitive systems. This is also a political challenge because the full development of learning aware environment will not be possible without addressing ethical (protecting the individuals and the communities) and economical problems (accepting that knowing is a universal right).

Teaching, an emergent property of learning environments (2)

Retrieved from Nicolas Balacheff (1999) notes for the EU/US conference, Stuttgart

One of the main characteristics of complex knowledge is on one hand that to master it requires to master several different pieces of knowledge organised in the form of a system, and on the other hand that its use depends on methods which are not mere algorithms. Such knowledge cannot be constructed spontaneously even when the learner is provided an adequate problem-situation, an in some cases such situations are still unknown (e.g. linear algebra). As a result complex knowledge requires specific learning environments and content specific teaching strategies.
The complexity of such knowledge also comes from the fact that the corresponding conceptions, i.e. cognitive constructs, can be very different the one from the other and rather complex to understand and to model. The current research on students' understanding of the concept of "function" in mathematics or of the concept of "energy" in physics witnesses it. The development of technological tools to use these knowledge (formal computation, simulation, etc.) increases the difficulty by modifying within a kind of systemic loop the nature of the users conceptions.
One cannot expect one universal agent to be able to handle the complexity supporting the learning process in the case of complex knowledge. On the contrary, there is a need for specialised agents, either artificial or human, able to cooperate and to coordinate their actions in order to provide the best support to the learner.

The development in Grenoble of the project TéléCabri, within the "Computational Environment and Human Learning Group" (EIAH) of the Leibniz Laboratory, allows us to get an insight of this complexity at different levels:

• At the epistemological and educational level, e.g. all the problems of learning in an environment which associates the best technology, like the microworld Cabri-geometry, and the classical means (books, notebook, etc.), as well as the teaching problems raised by the cooperation of teachers through the technology but also with the technology, with a full distribution of learners, teachers and resources within space and time.
• At the technological level, e.g. the problems of ensuring that the platform which associates different types of machines, visiocommunication, TCP/IP and H320 protocols, access from the TéléCabri site as well as from students or teachers places. At this level the institution has to realise that education may quickly need not only buildings, teachers and administration staff but also engineers.

A platform like that of TéléCabri is structured by several different axis of interaction and cooperation: between teachers and artificial agents, between human teachers with the mediation of the technology, but also between learners mediated by the technology. Indeed we must add the interactions between learners and teachers either in an asynchronous mode or in telepresence, and between learners and the learning environment. Learning does not occur because of one specific type of interaction, but because of the availability of all of them depending of the needs at the time when the interaction is looked for.

It is rather clear that the solution to the problems one meets on such a platform cannot be solved by one super-ITS being implemented on a learner super-machine. It is also clear that the availability of human teachers is crucial either because of the limits of the technology or because of the needs of students for a human presence. Then, the learning environment should be constituted by lot of resources, content specific as well as conception specific (taking into account the variety of learners possible conceptualisations); the teaching power of the whole system will not the property of one of its components but the emergent property of the interactions of all the agents involved either artificial or human, learners or teachers. May be it is just rediscovering that education has never been the result of the action of one isolated tutor but of the Society at large...

Cuban wrote in 1987: "[Teachers] will either resist or be indifferent to changes that they see irrelevant to their practice, that increase their burdens without adding benefit to their student learning, or that weaken their control of the classroom" (p.71). After more than a decade focussing on the learner, we could rephrase this quotation to emphasise the need for more investigations on what could be the conditions for the educational efficiency of learning environments from the point of view of general education or training as well.

Up to now, most of the basic or applied research, have been carried out in classical environments (schools or training centres). This has strong limits since it is not true that teachers and learners can involve in a radical way the new technology.The TéléCabri project is an attempt to do so, targeting students being not being able to join the classical schools (they are cured at home or in an hospital). By the way, this platform developed in the Grenoble Academic Hospital is an excellent example of a EU-USA collaboration (it is the product of a joint effort from the EIAH group, Hewlett-Packard and PictureTel).

A step further would be to set up an Educational Technology Centre (like those suggested by the "President's information technology advisory committee" to President Clinton—august 1998), this would be a very expensive and complex initiative which would surely benefit from an international synergy, putting together the best of education and technology from EU and USA.

Teaching, an emergent property of learning environments (1)

Retrieved from Nicolas Balacheff (1999) notes for the EU/US conference, Stuttgart

The trend of research in educational technology, during the last decade, has been to focus on learners and learning. The evolution of the ideas could be sketched in the following way : the initial paradigm was to design Intelligent Tutoring Systems (ITS) as autonomous machines with strong instructional functionalities and some sort of modelling of learners' needs and cognitive characteristics, a second paradigm has been the development of learning environments (eg microworlds) opening to the learner a real space for the exploration and the construction of knowledge. The former has not led to clear success, the later has evidenced serious difficulties (well documented by the Logo literature) and the need to complement the environment by teachers input and guidance. The lesson then, is that if teaching reduced to instruction is not the more successful avenue, the absence of teaching features in a learning environment does not guaranty either the quality of the learning output.

What are the lessons ? Clearly the need to search for a new paradigm which could ensure a better equilibrium between learning and teaching, between human and machines. The common interest of Europe and the US, either in general education or professional training (lifelong learning), to overcome educational difficulties especially in science, mathematics and language learning, together with their common recognition of the potentialities of educational technology, should lead to a fruitful synergy in this area.

The reasons why the learner, either a child or an adult, needs "teaching inputs" are very often hidden as a result of the strength of the emphasis on the constructivist principles of design of learning environments. These needs are especially important with modern environments which are largely distributed and provide a potential access to a huge range of knowledge and information. These reasons could be sketched by the following questions which acknowledge that the learner has in general a low level of control on the events which are on the edge of the learning process in which he or she is involved—unlike the expert problem-solver:

"How to look for something you don't know? "
"How to know that you have found what you looked for? "
"How to know that you have learned?"

A last question raises a crucial question related to the fact that in many cases learning is related to a willing to get the adequate qualification with respect to a given competence or activity. Indeed, the issue of certification must be considered together with the design of a learning environment, since…

"How will others know that you know?"

These issues, which call for the involvement of teaching (agents) in the learning environment, are even more essential in the case of complex knowledge (as opposed to basic skills).