cK¢, an introductory talk on the occasion of the PMENA annual conference

Next fall, on the invitation of PMENA (the Psychology of Mathematics Education North American Chapter), I will have the occasion to present an introductory talk to the cK¢ model. The text of the talk entitled "cK¢, a model to reason on learners' conceptions" is now available on the arXiv.org. Here is a summary:

"Understanding learners' understanding is a key requirement for an efficient design of teaching situations and learning environments, be they digital or not. This keynote outlines the modeling framework cK¢ (conception, knowing, concept) created with the objective to respond to this requirement, with the additional ambition to build a bridge between research in mathematics education and research in educational technology. After an introduction of the rationale of cK¢, some illustrations are presented. Then follow comments on cK¢ and learning. The conclusion evokes key research issues raised by the use of this modeling framework."

 The PMENA 2013 conference is held in Chicago from the 14th to the17th of November.

cK¢, une introduction à l'occasion de la conférence PMENA 2013

J'aurai l'occasion cet automne de présenter les principes et objectifs du modèle cK¢ dans le cadre de la conférence annuelle de la section américaine du groupe international Psychology of Mathematics Education. Voici le résumé de mon exposé dont le texte est disponible sur HAL sous le titre "cK¢, a model to reason on learners' conceptions"

"Understanding learners' understanding is a key requirement for an efficient design of teaching situations and learning environments, be they digital or not. This keynote outlines the modeling framework cK¢ (conception, knowing, concept) created with the objective to respond to this requirement, with the additional ambition to build a bridge between research in mathematics education and research in educational technology. After an introduction of the rationale of cK¢, some illustrations are presented. Then follow comments on cK¢ and learning. The conclusion evokes key research issues raised by the use of this modeling framework."

 La conférence PMENA a lieu du 14 au 17 novembre à Chicago.

Experiential learning, the new entry of the TEL Dictionary

What does exactly mean "experiential learning"? Is it learning serendipitously from an eventful life or is it learning from empirically from experiences one managed for you or that you managed yourself? How far is this concept from "inquiry learning" or "exploratory learning"?

The documented definitions of Experiential learning prepared by Vyara Dimitrova and Paul Kirschner for the TEL Dictionary clarify these issues and are excellent basis for further discussion.

One more question: would "experiential learning" from an educational perspective be a concept enhancing our tool box to understand the theoretical tensions between informal and formal learning?

#ocTEL MOOC (week 4 A42) Why would the student do or say this rather than that?

The second activity of this week on "Producing Engaging and Effective Learning Materials" is about the evaluation of resources in our area. So, it means, in my case, evaluating a resource for the learning of mathematics. However, I will start from a more general perspective. Whatever is the targeted learning, the first thing to check is the validity of the content the resource claims providing the learners with respect to the referent discipline. Then only, I will assess it from a learning perspective. Indeed, there are many issues to consider from accessibility to usability, motivation and autonomy. But, three questions have a hight priority in driving my evaluation:

Why would the student do or say this rather than that?
What must happen if she does it or doesn’t do it?
What meaning would the answer have if she had given it?

I borrow these formulations from the Theory of Didactical Situations (Brousseau 1997 p.65), but the questions are very pragmatic. The theory works here as a driver of our thinking; it is a tool to anticipate what could be the learning outcome, its likeliness, the possible limits and hence the needed intervention of a teacher. Depending on the responses, one may have to stage the use of the resource in one way or another.

Interaction and feedback are the main objects of the evaluation. The issue is not that students will do that or this, but why they do it,  because the constructed piece of knowledge must appear as the best adapted to the situation. Knowledge is something you reconstruct for yourself and appropriate because of its use value. The next issue is to verify, if the resource is interactive in some way, that it can feedback students so that they have a chance to realize that something went wrong and then react to that. If the resource is not interactive, then the issue is whether it is possible to figure out any thing about the activity (possibly, just reading) of students and find the appropriate support to bring. Eventually, the stake of this inquiry is the meaning possibly constructed by the student.

All this means that there is enough documentation about the resource, otherwise one has to guess or invent... just having a resource without information about its design, the intention of the designer and indications about its use, it is hardly possible to make a proper evaluation. This may be the reason why I couldn't do it for the proposed resource. But, anyway, I will make the exercise when achieving the third task of the week.

Some thoughts about Learning aware environments

Reference: Nicolas Balacheff, Learning aware environments, eAgenda 2006 European Forum, Castelldefels, Spain, 24 October 2006
 

Could we “introduce learning in every human activity”? From a non-English speaking perspective this question may sound strangely. Isn’t it the case that learning is present everywhere and at every moment in our life?  This is a matter of survival. Learning is a competence shared by all living organisms. Learning is life-long; it starts with our first breath and continues until the very last one. 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.).

At this point it is interesting to come back to the origin of “learning” and “teaching” in the English language. Both words have a German origin, tracing back respectively to “læran” and “tæcan” in Old English. While the latter meant “to show” or “to persuade”, the former was preferred to mean “to teach” or “to guide”. Then, could we suggest that the English word learning has a teaching connotation, and that as a result the meaning of  the question is: “can we introduce læran in every human activity?”, what introduces the idea of environments with “teaching” capabilities.
 

Designing environments likely to stimulate and support learning outside formal education and training —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 technologies 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. They are 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 technological 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).

#ocTEL MOOC (week 4 A41) Can TEL be taught or only learned?

The theme of the week is "Producing Engaging and Effective Learning Materials", with as a first task comparing learning resources, with three examples. As one can easily realise, since the content is completely different in each case, the comparison will be at the level of the style, organisation, choice of media and ways of involving learners. But let's see what is proposed...

The first suggestion is to use one resource from Khan Academy’s YouTube videos. So, I chosen the "Introduction to Vectors and Scalars":

Actually, a surprise! This introduction aims at clarifying the distinction between "vector" and "scalar". If I have understood well: a scalar is a quantity (for example, a distance of 5m between two points) and a vector is a scalar associated to a displacement (for example, moving 5m to the right). It could be a bit more complex, introducing change of time, suggests the teacher. Then, he introduces a distinction between velocity (vector quantity, the move has a direction) and speed (scalar quantity, the direction is not specified). I am unsure of what will be the conceptions of vector and scalar that learners could develop after this lesson (e.g. what about scalars operating on vectors). So, the benefit from this staging of vectors can be discussed, but I recognise the power of the enchantment of the blackboard: the speed of the discourse regulated by that of the hand, the hesitations and small mistakes which give the flavour of informal discourse, the always positive style: it might sound like very complicated ideas, but we will see in the course of the video that they are actually very simple ideas... (quasi verbatim). There is a kind of illusion of being close to the tutor, feeling that he is speaking to you. Well done! But still unsure about what could be the learning outcome...

So, now let's move to the second example, taking one example from one resource from ElearningExamples e-learning games. Among the great many possibilities, I chosen the "Learning center for young astronomers". This center gives access to several resources either texts or video, possibilities to navigate among resources. Some questions give opportunity for engaging in kind of interactions. The resource includes suggestions for use in the classroom. This is a classical environment for getting information along a not too boring journey in an encyclopaedia. It is not motivating by itself, but if learners have some motivation they may enjoy. I had a look on other resources of this set of examples, they are essentially game-like. The most difficult was to understand how learning is addressed. Games? yes, but learning... not obvious.

Eventually, I visited the iEthiCS simulation as suggested. The thing to emphasize is the clarity and the simplicity of the environment, and still an engaging style. Indeed, it is for adults and moreover medical students usually with a quite hight motivation towards case-based learning. After watching he video of the case, the student can make choices and get video commentaries (there is a text-based version). This is rather lively and efficient. The feeling of a contact with the tutor, although with little interaction (just decision choices), is realistic and convincing. This is a good video-based teaching.

So, now back to the task: "comparing resources". To be frank, global comparisons is likely to be meaningless. But it is possible to make some on aspects shared by these resources. For example comparing the use of video by Khan Academy and iEthics, or the way learner's navigation is framed by the Center for young astronomers and iEthics. All seems adapted to a certain conception of learners and of their autonomy, and they look quite well with their own style (that one may indeed always discuss). But an other question is whether they would succeed in "passing" the content they intend to give learners an access to. A question that #ocTEL does not ask, but the question which in the end is the most important. Khan academy treats knowledge as information so everything will depend on the listener, the Center for young astronomer does that too but in a more active way. Only iEthiCs treats knowledge as a tool for problem solving and not as information only, this is this which drives the design of the environment and it is, in my opinion, the key challenge of the design of TEL environments.

Eventually, the task includes a question about the extent to which these resources "differ from that of the resources we’re using in ocTEL?" There are two remarkable differences: these resources are rather focussed, while ocTEL is totally and vastly open (real risk to get lost), these resources target delivering some knowledge in some form, while ocTEL organizes exchanges of ideas and opinions about something which may be or not supported by some knowledge about TEL.I have not the feeling of following a course, but of being on a market place with a lot of possibilities. But it is hardly possible to identify what I am learning, and if there is something to learn beyond getting all these information.

Actually, we are touching there the main difficulty, challenge and weakness of TEL. So, my question: can TEL be taught or only learned?

#ocTEL MOOC (week 3 Webinar) Did the 3E framework inspire the design of the ocTEL MOOC? I wonder...

This week 3 webinar on "Activity design for online learning" was presented by Keith Smyth based on the 3E framework that he used in support to the improvement of the adoption of TEL at Edinburgh Napier University. Surprisingly the link with the three activities proposed by #ocTEL for this week 3 is not obvious and may be empty but at a very general level -- that is the level of the word "activity". It is not to mean that the webinar was not interesting, but one may expect more coherence between the activities in a MOOC.

The 3E framework is "based on a tried and tested Enhance-Extend-Empower continuum for using technology to effectively support learning, teaching and assessment across disciplines and levels of study", explain the authors. Here is a view of the continuum:

Enhance	Extend	Empower
Adopting technology in simple and effective ways to actively support students and increase their activity and self-responsibility	Further use of technology that facilitates key aspects of students’ individual and collaborative learning and assessment through increasing their choice and control	Developed use of technology that promotes learner autonomy and requires higher order individual and collaborative learning that reflect how knowledge is created and used in professional environments

In a way, I see that as a meta-model to frame the type of use of the technology one may want to adopt. This continuum seems especially relevant for adult education with the last stage coming closer to professional situations. Then within each of these levels we are left with nothing very tangible and operational to develop the design. We were left with 3 to 4 minutes to fill in the table with one example... a real challenge.

There is a lesson to be learned anyway, which is that whatever is the design a the level of actual student activity, there must be also attention paid to the higher level of design which is that of the course management as a series of activities and their evolution. In this respect the webinar was interesting and relevant. But, thinking about and learning "learning theories" was probably not the most relevant to prepare to it, something closer to curriculum development and/or course management would have been welcome.

Eventually... did the 3E framework inspire the design of #ocTEL? I wonder...