Connectivism

I have just finished reading the seminal work of Siemens (2005) on his notion of connectivism, and so I thought I would record some initial thoughts.

A lesson from physics
Firstly, connectivism is painted as a challenge to the traditional learning theories of behaviourism, cognitivism and constructivism. The motivation behind this is the observation that the three dominant theories were formulated before the modern computer age. Thus connectivism seeks to supersede the older theories.

However, it occurred to me that a parallel might be drawn here with scientific theories in physics. In particular, Einstein’s work on general and special relativity improved upon Newtonian physics, but did not completely supplant it. Although it is possible to apply Einsteinian mechanics to a macroscopic dynamics problem, it would be needlessly complicated to do so, whereas modelling the problem using Newtonian dynamics would be far more sensible and still accurate enough for the purposes of a problem of that size.

Perhaps the same is true of connectivism. Maybe on a larger scale of interconnected individuals and organisations, connectivism models more accurately the learning process; however, on an individual level, within the context of a classroom, perhaps learning should be modelled on behaviourist, cognitivist, or constructivist principles.

Mathematics
Another point which occurred to me is the applicability of Siemens’ ideas to mathematics. Siemens talks of rapidly changing fields, where knowledge becomes redundant so quickly that constant learning needs to take place. This doesn’t apply to what I, as a teacher of mathematics, do on a daily basis. I teach concepts and methods which are hundreds (if not thousands) of years old, which are established facts for all time. Pythagoras’ Theorem is eternal: no amount of innovation will change it. Does that mean that the connectivist metaphor has no application to mathematics? Are the knowledge networks fixed, suggesting a cognitivist view would be more appropriate?

Similarly, Siemens plays a high value on the ability of networked computers to automate a lot of what we do, meaning that learning shifts from individuals having to memorise skills and processes to networks increasing their connectedness. Does this also apply to mathematics? Is Siemens suggesting that all calculations should be outsourced to calculators and computer algebra packages, so that learning focuses on more complicated calculations?

If so, this seems to misunderstand how mathematics works. One needs to know how to do the easier calculations in order to be able to do the harder ones. Sure, computers can do calculations in a fraction of a second that learners struggle over for hours, but if learners don’t learn the basics, they won’t be able to program computers to perform more difficult calculations.

What is more, this would miss the point of learning mathematics as learning abstraction. Mathematics is not always about applying calculations to do things; sometimes it is innovating approaches to problems that have no real-world application (yet). If all computation is outsourced to a network, where is the deep individual understanding that is necessary in order to abstract?

Innovation and the role of the teacher
Lastly, I had a thought which seeks to explain why innovation is so important within a connectivist metaphor. If teaching and learning is to some extent outsourced to a network, then this goes some way to explain why there needs to be so much focus on innovation.

As Siemens says, “[t]he pipe is more important than the content within the pipe.” This suggests that the role of the teacher is not to push the material through the pipes, but to find new and/or different ways to extend the network of pipes, and this is at the heart of what innovation is.

However, this leaves the question: if teachers are primarily innovators, who does the actual “teaching” in the traditional sense of the term? Are teachers expected to do both? Or is their job to be outsourced to the network of resources as well?

The problems with innovation

I have a bit of a chequered history with innovation in my own practice, which has ranged from feeling inspired to feeling completely downtrodden.

I think the low point was when I was in my probation year as a teacher in a secondary school. My Head of Department came into my classroom to have a quiet word with me, which she only did when I had done something wrong. She told me that there had been a complaint made against me by a parent that my lessons were too innovative, and there was not enough focus on doing examples from a textbook. I remember feeling distinctly discouraged and unsupported, which was one of the reasons I left teaching in secondary.

Nowadays I work across three different institutions, all of which are supportive of innovation, at least in theory and in policy documents. However, in each of these institutions there seems to be a disconnect between the policy which encourages innovation and says all the right things, and the actual day-to-day practice of practitioners on the ground.

There is a widespread view that innovation is a management buzz-word, and although practitioners are enthusiastic and supportive in principle, they need support to be able to put it into practice. Furthermore, many of the examples of innovative practice are seen to be inapplicable to mathematics, which only further entrenches a conservative view that mathematics teaching is “different” and old-school methods are inescapable.

Having said that, there are many innovations that both myself and other practitioners would love to implement. I have come away from CPD sessions feeling inspired, or had flashes of inspiration that I am going to try out a new activity for a lesson. However, there are often barriers to actually implementing innovative practices, the three most pertinent of which are:

• Time: when will I find time to do the work necessary to implement this innovative idea of mine, while also keeping on top of my day-to-day duties?
• Support from colleagues: often the negative attitudes of colleagues can make me think “I don’t want to stick my neck out here, because if my idea fails, everyone will say ‘I told you so'”.
• Institutional IT issues: I can think at least two examples where colleagues have tried to implement innovative teaching practices, only to be hindered by the lack of IT equipment which works with the institution’s ageing and inadequate IT infrastructure.

In conclusion, I guess you could say that although I am enthusiastic about innovation, it is important to me that I don’t feel that I am “on my own”. The encouragement of colleagues and management is vital to wanting to invest my time and energy into risky innovative projects. Surely I am not the only one who feels like this?

iSpot

As part of this week’s activities, we were asked to try to come up with a definition of innovation and how it applies to one of the OLnet tools. I chose iSpot, as I have often been interested by nature.

I am still in the process of refining my definition of innovation, but I am thinking of something along the lines of “experimenting; trying new or different approaches, either using new or established technologies or practices”.

Measured against this definition, the iSpot project would seem to me to be an innovative one. Users can upload their photos of plants or animals that they have encountered in nature, in order for other users to identify and classify species. Users tag the geographical location where the photo was taken, so a map can be populated with all the observations in a particular area, and thus provide data for the spread of populations of certain species.

Thus the iSpot project in some sense kills two birds with one stone. It provides users with the means to learn about their local ecosystems, while it provides researchers with valuable data that would otherwise be costly to collect. In this sense I would classify it as an innovative project.

As with all of these types of project, however, it relies on users to actively participate in the project for it to be worthwhile. Most of the observations of mammals seemed to be from 3 years ago or longer, which makes me wonder if the project is on the decline.

This raises an issue for me that I have often feared in analysing innovation: with technologies and the way in which users interact with those technologies constantly changing and developing, is it a good use of time, effort and money to develop innovative learning projects if their lifespan is limited to 3 or 4 years? If practitioners’ time is precious (and in my experience, it increasingly is), are cost-benefit analyses required before implementing innovative projects? Should high-risk projects which require a constant large active user base be evaluated on this basis? Will this dampen innovation?

Lots of questions to think about! I’d love to hear your thoughts, so please leave me a comment!

Minds On Fire

I have just finished reading Seely Brown and Adler (2008) Minds on fire: open education, the long tail and learning 2.0 and was interested to learn about the Hands On Universe project, which “invites students to request observations from professional observatories and provides them with image-processing software to visualize and analyze their data, encouraging interaction between the students and scientists” (Seely Brown and Adler, 2007, p.24).

This project seems to be still going strong in 2016, as the website indicates that there was an annual conference which took place in 2015. I was also able to use Google Scholar to find scholarly articles from 2009-2012 which talk about the project. It seems that the project has been extended from its home at Berkeley, California to Harvard and across Europe.

In reading this article, the perennial question occurred to me: “How does this apply to maths?”

I remember when I was an undergraduate, pursuing an individual project in a mathematical topic of my choice, one of the assessment criteria was how well my research contributed something new to the field. I had chosen a particularly pure mathematical topic, and so I was reading about difficult abstract concepts that had been known for 100 years or more. Just understanding these concepts was difficult enough, never mind trying to contribute something new of my own! To do so would have required 4 years of postgraduate study in itself!

Is it any wonder, then, that mathematics is rife with “pointless” word problems that are artificially constructed in order to test students’ understanding? Is it possible for high school students or undergraduates to engage in “legitimate peripheral participation” of pure mathematical research, if it requires graduate study just to learn what the questions are in current research? Does this explain why so many students are turned off from maths? Does the inability to see the immediate applicability of their studies make students think that there is nothing left to discover, and so their mathematical studies are pointless? I can’t count the number of times someone has said to me, “How can you do research in mathematics? Isn’t everything already discovered?” This fundamental misunderstanding in what maths is resulting from the gulf between “learning mathematics” and “doing mathematics” may well be the reason!

Does anyone from a different subject discipline feel similarly? Or is maths the only one who suffers from the difficulty of finding legitimate peripheral activity in mathematical research that learners can actually access?

Reflecting on Reflection

And so another year of study begins! Having completed “H800 Technology-enhanced learning: practices and debates” last year, I am embarking on my second module towards the MA in Online and Distance Education (MAODE) with the Open University (OU). This year’s module is entitled “H817 Openness and innovation in elearning”.

Last year in H800, blogging was an optional part of the module, and I didn’t really engage with it all that much. For me, reflection is a participative activity, and so I prefer to discuss my thoughts with others. I have had few positive experiences with keeping a reflective journal for my own eyes only. However, I am willing to give it another try this year, and I would appreciate any comments you can leave to encourage me along.

How do you use your blog? How would you like to use your blog? Do you need an audience, or do you prefer to keep your reflections private? What barriers do you find to posting? Let the discussion begin!