Monthly Archives: March 2016

E-Dynamic.Space: A 21 ST century tool to stage-manage and build experience in the field of the history of mathematics and its teaching

This study aims to answer the question of how can the history of mathematics resort to a digital tool – E-Dynamic.Space – designed by teacher-students and intended to serve as a workbench not only to create supportive knowledge from historical material, which has proved to support the understanding of mathematics but, also to orchestrate both, their actual learning of the tangent line problem and their future mathematics teaching experience. It, therefore, explores aspects for the design of the teaching activities, and it analyses the ‘whys’ and ‘hows’ of including the historical dimension into the teaching experience. It is part of a bigger research project that looks at how can teacher-students favour from a historical informed pedagogy of mathematics that uses a personalised learning environment as a means to learn.

Source: E-Dynamic.Space: A 21 ST Century tool to stage-manage and build experience in the field of the history of mathematics and its teaching

I wrote this paper for a conference I assisted in 2014: Congress on Educational Research in Mathematics Education, CERME9. It is part of the Proceedings of the conference.

Bildung and rhizomatic learning. Is the question resilience?

While reading the post on rhizomatic learning that David Cormier wrote, I suddenly started to make connections between Bildung and his idea of knowing as he describes it:

(…) It is a long process of becoming (think of it in the sense of ‘becoming an expert’) where you actually change the way you perceive the world based on new understandings. You change and grow as new learning becomes part of the things you know

Where did I find the connection? In the word becoming. Although Wilhelm von Humboldt spoke about Bildung two centuries ago as the process of self-formation or as I prefer, self-cultivation which had a huge influence in the concept of Higher Education, the idea has not lost currency. Bildung is closely related to the idea of shaping, giving form to, in education it is developing the self and the way she/he thinks and understand phenomena.

Bildung is seen as a reciprocal process of formation between the individual as a self and the world she/he meets actively rather than passively (Fossland, et al. 2015). It suggests self-education as a path to transformation, to strive and change in the process of meeting the world. In words of Humboldt, it is about uniting individual and culture in a rich mutual and complex interplay.

Bildung has been contextualised within the academic environment in a relatively new idea set by Fossland (2015), -Academic Bildung- it is called. The word academic before Bildung is to contextualise the process of education or -to become- in the academic context. So the world the person is meeting with is the world of knowledge in this formal understanding of academic knowledge, that what we meet when we go to university.

When Cormier talks about rhizomatic learning and the nomad as the subject of that learning who is becoming a different self, transforming in that process of becoming, there is a similarity with the idea of Bildung as an idea of transformation.
He says:

Nomads have the ability to learn rhizomatically, to ‘self-reproduce’, to grow and change ideas as they explore new contexts. They are not looking for ‘the accepted way’, they are not looking to receive instructions, but rather to create

The question to ask might be if there is any desired shape that transformation would look like? When we say that the idea is to become active and critical citizens, what does that mean? What is what they need to critique? Shall we educate students, or in words of Cormier, shall we create the context to enable students -nomads- to challenge given structures that are replicating the telos of our current society? How can one (and I talk for myself) do this if one is also, in some sense, imprisoned within those structures? How can we foster agency in students so they can be agile in their process of adjusting to change? And even more challenging, in a society where change happens at such a rapid pace; like when fluids travel the shapes they will inhabit, it all happens to fast to be able to track the process (fluids of a low density of course 🙂 ). The change of shape in liquids is very fast, it is slippery, as Bauman describes it in his book, Liquid Modernity:

Fluids travel easily. They ‘flow’, ‘spill’, ‘run out’, ‘splash’, ‘pour over’,’leak’, ‘flood’, ‘spray’, ‘drip’, ‘drip’, ‘seep’, ‘seep’, ‘ooze’; unlike solids, they are not easily stopped -they pass around some obstacles dissolve some others and bore or soak their way through others still. (…)the extraordinary mobility of fluids(…)

It seems to me that in times of liquidity resilience is what students need, not only in their daily lives but more so in academic context where despite the affordances and changes that digital tools offer for the learning experience, it is complex to grasp how they work for us and what activities they can mediate. How to deal with the short lives they have? How fast do tools change and how important it is to understand thoroughly the functioning of the tool, or it maybe being able to understand the use and not be so attached to the tool so when it ceases to exist we can look for another one more easily?
How can we teachers, create that contexts for learning where change is embraced, and the core idea is to learn the know -how (how they operate, what can they do, etc) of digital tools, how tools can mediate particular activities and in knowing that the brand of the tool loses importance, the mediation of the process is what comes to the fore and how tools can facilitate that process.We should focus on family of tools and not on a single tool, as Ricardo Torres @torresk suggested in his research, understand the properties of tools and not the brand, in short the idea would be to expose students to different tools and activities they can mediate, the knowledge that will allow them to operate in the digital environment and take advantage of what the plethora of tools have to offer

I would think that all these things are relevant in order to become and to flourish in a society that is digitally mediated. Of course, this is only one of many aspects nomads will encounter in the journey of becoming who they want to be.

paper, thesis and book titles – think ‘key words’ and ‘the point’

We all know that it is now more important than ever to have searchable paper, (digital) thesis and book titles. So, as well as the key word list, titles need to use the kinds of words that will sho…

Source: paper, thesis and book titles – think ‘key words’ and ‘the point’