#ocTEL MOOC (week 1 Laurillard Downes webinar) Surprise, surprise, language may be the problem.

Among the recommended resources to "watch, read and research" to prepare week 1 of the #ocTEL course, there was a discussion between Diana Laurillard and Stephen Downes on the extent to which learning design should be supported computationally – (look at the webinar recording [here]). The discussion started by a presentation by Diana Laurillard of the Learning Designer, a "software to engage university teachers in the design of technology-enhanced learning (TEL) which is informed by pedagogic research and appropriate theories of teaching and learning." Then followed a presentation by Stephen Downes looking at learning design as a language, and hence with the power and the limits of a language. As we know,language is a tool to communicate, to represent, to share, to argue and to reason. But to some extent it is a poor and complex way of representing and communicating, and at the same time a marvellous and powerful instrument. That is our everyday reality... nevertheless,  language is necessary for practitioners and researchers. Stephen suggests that the latter tends to conform to the preference of science for "pure abstraction and formalism" (Bourbaki would have said "naïve formalism", indeed beyond toy examples only computers handle pure formalism), whereas reality is always more complex than whatever formalism can capture. Then comes the difficult question: "Is there a functionally useful language which can describe learning and teaching?" I guess that if the response is "no", then the ambition of Learning Designer (and the project of the like) shrinks dramatically or even worse becomes irrelevant; if the response is "yes", it may be because of a "hidden positivism" and the dream for a language about learning being interpretation independent (a "stupid" language). This is a rough summary, I agree, but I think fair to the content of the discussion and enough for the comments I would like to share.

When we engage in a discussion, there is always the tacit assumption that it exists and/or it is possible to build a common language even if locally in time and space for the sake of the communication. Many events during the conversation are meant to call for or facilitate this construction (esp. all the events revealing misunderstanding). Indeed, articulating and interpreting are the key processes. It may be the case that this common linguistic space vanishes with the end of the conversation; this is not a problem as long as it has played its role. But there are situations in which it is better if we have not to build again this space, for example for teacher training courses. This means that it exists a de facto functional language useful to describe learning and teaching, it is the language of training, or the language of the professional literature, or the language of the #ocTEL MOOC. This does not mean that it is completely fixed, static, unified and unique. On the contrary this language evolves under the requirements of practice and with the improvement of our understanding of teaching and learning. It is a language rich enough to welcome a variety of approaches and theories, from constructivism to connectivism. Actually, it is not because there would be a common language that we would have a unique model of learning and teaching. Such a language must be flexible and open enough to express different models (just as the mathematical formalism allows to express Euclidean or non-Euclidean geometry, as it were). Indeed, we must keep in mind that this common language is a social construct.

Looking at these issues from a scientific perspective, there are some objectives which come into play which change the ambition. Since I think that this conversation is not the kind philosophers had at the birth of psychology as a science, I accept the idea that it is good and possible to identify invariants in learning and teaching, and that it is possible to model some of the phenomena which arise with both. To describe them and to come collectively to an agreement on the validity of the related claims, it is indeed necessary first to have a precise language (and hence definitions) and some insurance that interpretation will be under (a reasonable) control. Indeed, this implies abstraction, that is: not taking all the complexity of teaching-learning on board. This is not a problem as long as researchers are not dogmatic and humble enough to be clear about this limit. It is here that we have the problem of communication between research and practice, which in fact is a problem only when underestimated or forgotten. No body is right by principle, we must have discussions, argumentations, efforts to share a language as a condition to understand the models and there limits, possibly indeed their failure. The computational support of learning design is just a specific case for this issue. It means that the science of teaching-learning as made enough progress to make such computational models possible. Indeed, such a model, even Learning Designer, is conjectural: it has to be discussed, its limits must be explore. It is important that users be aware that buying the software, they buy the underlying approach and model of teaching-learning. Hence, they have not to look at it as the orthodox way of thinking, but a possible way that they must confront to their own understanding, perspective and practice.

From these confrontations among practitioners, among researchers, and between practitioners and researchers will come the progress of our knowledge about teaching and learning theoretically and in practice. So, language is not a problem, it is a tool which gets its strength and efficiency from its adaptivity and dynamic nature (even in science which vocabulary and meaning evolve continuously).

#ocTEL MOOC (week 1 A12) Snapshot on our approach and practice

The second part of the activity of this week focus on our pedagogical approach and our practice. I must say that I have no teaching duty since 1988, when I got a Senior Scientist position at the CNRS. However, I still continued to teach PhD courses and to a certain extent this is not that different from teaching undergraduate. So, let see how I can achieve this A12 task of week 1) From a learner perspective ("My Approach"), we are invited to locate ourself in the following space:

First, I would very much like to balance directivity which would allow me to know where I am going as a learner and whether I am not too far out of the track, and autonomy which would  allow me to experience knowledge and build my own understanding. I imagine that this opinion is very common.

Although important, the social dimension was not the main thing, apart from the joy of collectively arguing. Actually it depends on the content at stake. In mathematics and natural sciences learning collaboratively is quite productive thanks to the fact that the disciplines clearly gives the rules to solve conflict. In literature and several other topics, this is more difficult and the benefit of social interaction is less clear; indeed it brings the context to shape arguments and learn how to manage contradictions. It is a case where "reflective communication with the instructor" is really beneficial.

Hence, I would not fill one graph, but one for each discipline.

From a teacher perspective ("My course"), my first concern once I know what I want to teach is to find a way to pass to students the understanding that there is somewhere a problem and that the knowledge I claim to bring to them is the optimal one (possibly the not the only one) to solve this problem. For this, I start by a situation which allow students to express views, opinion, conceptions about a situation which later on will appear to be problematic in the sense I need in order to teach. If this is successful, for example (A11) having shaped a variety of evidence based opinions on behaviourism, I would stimulate the formulation of the problem(s) which will be the best to justify the knowledge I target, for example (A11) the problem of nature of the meaning built at an outcome come of the learning situation and the problem of its assessment. We understand that these situations blend individual, social and with-the-teacher situations.

Actually, this view is substantiated by the Theory of Didactical Situation, which provides the tools to assess continuously the relations between the activity, the situation and knowledge (to be learned, as it were).

#ocTEL MOOC (week 1 A11 ) Champions and critics of teaching machines

The task: Watch this 6 minute video on Teaching Machines, presented by B.F. Skinner (exact date is unverified but believed to be in the 1950s). To put it in historical context, you may find it useful to skim this short history of instructional design, which is itself a historical artefact from the early years of the World Wide Web.

Pick one or two of the following thinkers or approaches and read a bit about them, starting with the resources linked. What would they like about the Teaching Machines approach? What would they oppose, and what alternatives would they propose? Explore the notes made by two or three of your fellow participants. What patterns do you detect? (Socratic Method, Communities of Practice (Etienne Wenger), Paulo Freire, Ivan Illich, Social Constructivism, Actor Network Theory, Emergent Learning Model).

I have some ideas about Teaching machines and Behaviourism, but it is the first time that I hear Skinner himself and his view about his machine. The first thing to be noticed is the rather modern discourse about this "device which creates vastly improved conditions for effective study": one machine per child, immediate feedback (like cognitive tutors), learners relieved from uncertainty or anxiety. Eventually the "work" of students is "pleasurable" with "intense concentration". Personalisation is the main benefit from Teaching machine, Skinner emphasizes that it generates interest and enthusiasm, the student moving at his own pace despite the heterogeneity of the classroom. However, the design of the Teaching machine is based on Behaviourism, a learning theory for which we know now the key weaknesses. The argument of Skinner was that the learner would cover the curriculum passing through "a large number of very small steps" carefully ordered maximizing the chance for most students to be right (actually, Skinner mentions that learners are right almost 95% of the time).

Considered with what now know or through the lenses of more recent learning theories we can see several important differences and missing points, if not wrong principles of Behaviourism. Essentially: the reductionist view of knowledge (seen as the sum of its components), the cognitively passive involvement of active learners (and indeed, we can see how active they are in this short video), the social dimension totally absent.

#ocTEL: my first MOOC experience (week 0 Webinar)

This first ocTEL webinar is introduced by Davib Jennings, the project manager. Then Diana Laurillard proposes a synthesis of the "Big questions in TEL" that we have proposed. Unfortunately, I was not able to participate in the webinar this time, but read the slides and learn and comment from them.

The ocTEL participants' big questions split in two groups: pedagogic and strategic with just one question recorded in the latter.

The pedagogic questions selected are mainly organisational (dealing with time zones, large lecture-only courses, balance between guidance and freedom, balance between teachers and learners needs). Some questions address directly learning issues (ensuring the desired outcomes, assessing learning outcomes). Hence, if ocTEL is meant to help its users to find responses to their questions, one expect that it gives some elements and principles to analyse the characteristics of a TEL environment from the perspective of learning management, and some elements to assess learning qualitatively (nature of the outcomes). My own big question about learning outcomes is considered, having it in mind might be a relevant guide to drive my participation.

The strategic question: "how do we persuade 'reluctant' members of staff to engage with TEL" is of a different nature than the former indeed, but it is closer to the so-called  "Candidate big questions" which are of a "cultural", "management" and "economic" nature.

As a matter of fact, economy seems to be the keyword describing at best the core content of this presentation, with one equation which I discover :

1:25  staff:student

The main challenge seems to be able to solve this "ratio problem". Eventually, I am somewhat surprised. I perfectly understand that the economy of education is a real problem (especially nowadays), but having it on the fore front invites to look at TEL in rather specific way; it makes me wonder what will be the orientation of the course. In any case, I am still interested to learn. Let's see!

#ocTEL: my first MOOC experience (week 0 A02 A03)

Satisfied: I have found the way to limit the mail I receive from the mailing list to a summary. Still, there is quite a lot to read:

April 5: "83 messages totaling 9277 lines in this issue."
April 6: "38 messages totaling 7531 lines in this issue."

To be frank it is a bit discouraging. The invitation to "Read other people’s accounts from the previous activities and comment on what you observe about individual preferences and other differences" in 30 mins is a somewhat optimistic. I think that I will postpone exploring who is there and wait until the real course has started; I may be in a better position to understand how to organise my exploration in relation with the issues raised and the real content of the MOOC.

To start, I have joined the "Small group for art, design and architecture" for two reasons: the first is that it is a domain which I don't know so I will have the opportunity to follow and possibly contribute as a learner, second I am interested in contemporary art (on which I write but not in English).  

PS: to have an account to register a mailing list, an other one to upload a picture, is a bit too much. I think that such a platform should offer single sign-on.

This first week, interestingly numbered "0", the ocTEL MOOC has five activities which add up to about 4 hours of work. It is designed in a way which first invite you to think why you are here, and second to stimulate socialization.

My first impression, before starting effective working, is that there really  a lot of informations to go through. So, I understand the importance of the advice: "keeping calm in the face of abundance" (I may already join Patrick plea: "please stop emailing me, my inbox is full & I can't turn it off on your website" -- may be an idea: create a dedicated mailbox when joining a MOOC...). Any way, I have to dive into real activities, for the time being it is A-0.1.

 My big question:

How to reliably make sense and assess learners' learning outcomes which result from their use of  a TEL environment?

This question may seem close to a question like "do they learn?",  actually my point here is "what do they learn?" (I may add "precisely"). Being able to respond to this question will allow us to better respond to many other questions which come from teachers, parents, decision makers and advisers, as well as designers and indeed learners themselves (what do I know now and better, that I didn't know before?)

Quelques éléments de vocabulaire, à propos de preuve et de démonstration

Première publication : La lettre de la preuve, [original ici]

Avertissement original et d'actualité : contribution informelle et provisoire...
Ce qui suit est issu de Étude des processus de preuve chez des élèves de Collège -- Balacheff 1988 ; à propos du vocabulaire dans l'enseignement voir plutôt Balacheff 1982 avec quelques éléments sur la transposition.

Les verbes expliquer, prouver, démontrer, sont souvent considérés comme synonymes dans la pratique de l'enseignement des mathématiques en France. On peut s'en assurer aisément par une consultation rapide des manuels scolaires. S'en tenir à ces habitudes constitue à notre sens un obstacle aux recherches sur le domaine qui nous intéresse dans la mesure où elles conduisent à amalgamer différents niveaux d'activité des élèves qu'il est en fait nécessaire de distinguer, comme nous essaierons de le montrer, pour comprendre la complexité du problème de l'apprentissage de la démonstration. Nous proposons dans ce qui suit de préciser ce vocabulaire.

A la suite de Piaget (1970) nous dirons qu'expliquer, "sur le terrain des sciences déductives", c'est d'abord dégager les "raisons" pour "répondre à la question du pourquoi". Mais du point de vue même de la pratique des mathématiques, donner des raisons d'un théorème, l'expliquer et le démontrer relèvent de deux exigences distinctes. C'est le sens de la remarque suivante :

"tout mathématicien sait d'ailleurs qu'une démonstration n'est pas véritablement «comprise» tant qu'on s'est borné à vérifier pas à pas la correction des déductions qui y figurent, sans essayer de concevoir clairement les idées qui ont conduit à bâtir cette chaîne de déductions de préférence à tout autre". (Bourbaki 1948, p.37 note1)

Expliquer renvoie aux significations, c'est-à-dire à la compréhension de la validité d'une assertion, non au sens de la logique, mais au sens de ses relations avec le corps des connaissances mathématiques. Cette "organisation inférentielle de significations" (Halbwachs 1981) peut échapper à une démonstration par ailleurs irréprochable du point de vue de la logique. En témoigne, par exemple, l'aveu célèbre de Cantor quand il interpelle Dedekind à propos de la démonstration qu'il vient d'écrire : "je le vois mais je ne le crois pas" (cité par Cavailles 1962, p.211).

 

Explication

A la suite des linguistes, nous situons l'explication au niveau du sujet locuteur. C'est d'abord pour lui qu'elle établit et garantit la validité d'une proposition, elle prend racines dans ses connaissances et ce qui constitue sa rationalité, c'est-à-dire ses propres règles de décision du vrai. Mais elle est aussi ce discours qui vise à rendre intelligible à un autrui la vérité de la proposition déjà acquise pour le locuteur. Elle ne se réduit pas nécessairement à une chaîne déductive. Miéville la décrit ainsi au terme d'une étude sur "Explication et discours didactique de la mathématique" :

"elle vise à établir chez l'interlocuteur un système d'objets qui ont entre eux une certaine homogénéité. Ces objets se rencontrent, s'agencent, et dans leur affinité, déterminent l'organisation d'une explication qui s'oriente vers la découverte d'un savoir nouveau…" (Miéville 1981, p.150).

Preuve

Lorsqu'une explication est reconnue et acceptée, il convient pour la désigner de disposer d'un terme qui permette de marquer son détachement du sujet locuteur. En mathématique, il est clair que le terme «démonstration», du fait de son acception très spécifique, ne convient pas. Nous retiendrons celui de preuve.

Le passage de l'explication à la preuve fait référence à un processus social par lequel un discours assurant la validité d'une proposition change de statut en étant acceptée par une communauté. Ce statut n'est pas définitif, il peut évoluer dans le temps avec l'évolution des savoirs sur lesquels il s'appuie. Par ailleurs une preuve peut être acceptée par une communauté mais être refusée par une autre. On en a un exemple récent en mathématiques avec le «théorème des quatre couleurs» dont la preuve par Appel et Haken, qui n'est pas une démonstration au sens classique, est acceptée par certains mathématiciens, tel Swart (1980), et est refusée par d'autres, tel Tymoczko (1979) :

"the reliability of the four-colour theorem is not of the same degree as that guaranteed by traditional proofs [en français : démonstration ], for this reliability rests on the assessment of a complex set of empirical factors" (Tymoczko cité par Hanna 1983, p.85).

Mais l'acceptation de l'«explication» de Appel et Haken ne repose pas sur de simples critères de vérification logique : "the very reason those of us who have worked on reducibility testing are happy about Haken, Appel and Koch's reducibility results is that they have to a large extent been independently checked by the use of different programs on different computers" (Swart 1980, p.698).

Démonstration

Le type de preuve dominant en mathématiques a une forme particulière, il s'agit d'une suite d'énoncés organisée suivant des règles déterminées : un énoncé est connu comme étant vrai, ou bien est déduit à partir de ceux qui le précèdent à l'aide d'une règle de déduction prise dans un ensemble de règles bien défini. Nous appelons, suivant ici l'usage, "démonstrations" ces preuves. Ce qui caractérise les démonstrations comme genre de discours est leur forme strictement codifiée. En fait, cette rigueur formelle doit être nuancée au regard de la pratique. Par exemple, certaines étapes de la démonstration peuvent ne pas être explicitées mais laissées aux bons soins du lecteur. Si, en principe, être une démonstration relève, pour un discours, de critères logiques, dans les faits les processus sociaux au sein de la communauté mathématique jouent un rôle important :

"a proof becomes a proof after the social act of «accepting it as a proof». This is true of mathematics as it is of physics, linguistics, and biology " (Manin cité par Hanna 1983, p.71).

Nous prenons, en parlant de communauté mathématique, un point de vue naïf ou, disons, du sens commun. Nous n'ignorons pas qu'au regard même de la démonstration cette communauté n'est pas monolithique. Des doctrines s'opposent (méthode axiomatique, intuitionisme, formalisme, etc.), on en trouvera une discussion intéressante dans Hanna (1983). Mais, comme le reconnaît cet auteur ce qui divise les mathématiciens ce n'est pas la démonstration en tant que telle, mais le choix des axiomes logiques et mathématiques (ibid. p.64-65).

 

Raisonnement et processus de validation

Le mot «raisonnement» a, de façon usuelle, principalement deux acceptions que résume bien

"si le raisonnement, entendu comme acte de l'esprit, se rapproche de plus en plus de l'intuition à mesure que se concentre la pensée, inversement, quand celle-ci se détend dans son expression, verbale ou symbolique, il apparaît comme une certaine manière d'organiser le discours, pour devenir, à la limite, une suite d'opérations formelles exactement réglées, c'est-à-dire un calcul ". (Blanché 1973, p.39) :

Dans l'étude qui nous intéresse cette double acception présente une difficulté car elle introduit lorsque l'on parle du raisonnement d'un individu une ambiguité évidente en ne distinguant pas assez clairement s'il s'agit de l'activité intellectuelle ou de l'explication produite.

Nous réserverons ici le mot raisonnement pour désigner l'activité intellectuelle, en général non complètement explicite, de manipulation d'informations, données ou acquises, pour produire de nouvelles informations. Nous désignerons par processus de validation cette activité lorsque sa finalité est de s'assurer de la validité d'une proposition et éventuellement de produire une explication (resp. une preuve ou une démonstration)