framework perspective - TPCK, 3E, and SAMR

When thinking about the effective use of educational technology, you need perspective: theoretical perspective.

We need methods of evaluating learning activities that make use of technology, ways of making decisions about how to use technology in our own teaching practice, and guidance in how to help teachers use technology effectively.

Luckily bright folks have been thinking about these things, and have come up with theoretical frameworks to help us. Three of the most widely used frameworks for understanding the effective use of educational technology are TPCK, Triple E, and SAMR.

The TPCK framework takes a teacher knowledge perspective. You can learn more about TPCK here.

The TPCK model is useful when answering questions like: what does a teacher need consider when designing tasks and selecting technology in a particular subject area? A teacher draws on understanding of content, pedagogy, and technology - and most importantly an understanding of the interplay between these.

The Triple E (3E) framework takes a student learning perspective. You can learn more about 3E here.

The 3E model is useful in answering the question: how is the technology affecting student learning in this particular task? A 3E analysis may reveal that it is primarily promoting engagement but technology, when used effectivel,y could potentially enhance student learning, or even help facilitate its extension beyond the classroom.

The SAMR framework takes a task-design perspective. You can learn more about SAMR here.

How do we use SAMR? You may want to know concretely: How is the technology actually employed in the task, and how does this affect learning outcomes? Some technology acts primarily as a substitution for another, but it may also be augmenting, modifying, or even redefining what can be done in a particular task. 

Linking the frameworks
As these three frameworks approach the effective use of educational technology from different perspectives, they can be seen as complementary: each provides a different lens. The frameworks can also be viewed as being concerned with overlapping stages in the lesson/task design process: from teacher knowledge, to task design, to student learning outcomes - each framework offers insight into all these stages, but each has a particular focus. Teacher knowledge, described by TPCK, provides the foundation for the decisions made in task design, SAMR describes how the technology is used in the task design, and Triple E provides a concise description of how the knowledge and design choices affect student learning.

References

Kolb, E. (2013) Engage, enhance and extend learning: Find out what these terms really mean when you integrate technologies into your lessons. Learning & Leading with Technology, 40(7), 21-27. Retrieved from http://www.learningandleading-digital.com/learning_leading/201305?pg=22#pg22

Mishra, P., & Koehler, M. J. (2006). Technological Pedagogical Content Knowledge: A Framework for Teacher Knowledge. Teachers College Record, 108(6), 1017–1054. http://doi.org/10.1111/j.1467-9620.2006.00684.x

Puentedura, R. (2009). The SAMR Model. Retrieved from http://hippasus.com/rrpweblog/archives/2015/10/SAMR_ABriefIntro.pdf

computational thinking

The 2017 NMC/CoSN Horizon Report (K–12 Edition) identified teaching computational thinking as a persistent and difficult problem.

Although correctly highlighting its importance and the challenge that educators face in teaching it, the report, like some of its sources, perpetuates some common fallacies about the nature of computational thinking and its relationship with modern computer technology.

The report strikingly asserts that "The roots of computational thinking can be traced to algorithmic thinking of the 1950s and 1960s..." making the fundamental mistake in assuming that understanding computational thinking is a response to the sudden arrival of digital computers.

The truth is the reverse: the advent of digital computers in the 1940s and their wide adoption in the decades that followed was the result of humanity's centuries-long study of computational thinking, and in some senses, modern computers represent the crystallisation of a very elaborate understanding of what computational thinking is.

In other words - mathematicians, linguists, philosophers, engineers and scientists had been working on gaining better understandings of computational thinking for a very long time. The results of this research included several mathematical models of computation (Turing machines, and the Lambda calculus are examples), understandings of the logic and workings of formal systems (Boolean algebra, for example), the limitations of computation (Godel's famous theorems), an understanding of formal languages (Chomsky hierarchy), and also key results in how to express problems and ideas computationally. One of the fruits of this long research programme, that dates back at least to Leibniz, is the digital computer.

When Ada Lovelace wrote programs for Babbage's Analytic and Difference Engines, she was

applying, and developing, our growing understanding of computational thinking.

A helpful reminder that computational thinking predates our notion of computers, is to remember that computers used to be humans. The book and film Hidden Figures provides a nice window into that time, not so long ago, where people were employed to do the sort of problem solving and calculations that today are solved using software and hardware.

People solve problems and do calculations - but how do we do it? This is the basic question that fuelled the interest in studying computation itself, beginning hundreds of years ago. To the surprise of some, it was found that there was no magic spark within the human brain that allowed us to add numbers together: a formal system (a system with no deeper meaning, only symbolic manipulation) could express all of the operations of arithmetic. In fact, machines could be developed to carry out calculations.

Understanding computational thinking is not something that needs to happen in response to computer technology - computer technology is the result of our already deep understanding of computational thinking.

Why do so many people treat computational thinking as a new problem, one that is forced upon us by the advent of new technology?

We all like new problems.
New problems give us a chance to come up with new and exciting solutions. We don't like to be reminded by historians and other scholars that there is really nothing new under the sun. Coming up with a new solution to a new problem makes us a creative genius; recognising something as an existing problem conveys far less excitement and prestige.

We like to think of technology as something new.
Although the consumer aspects of computer technology are new, the underling ideas that modern consumer technology is based, particularly at the computational level, are not new. We think of computers as having emerged, as if out of nothing, sometime in the 1950s - an iceberg analogy might be useful: the applications that we have seen more and more of in the last 70 years are the tip of a large structure that previously went unpercieved, except by a minority. Our job is not to invent a new way of understanding the tip, but rather to look beneath the surface and appreciate what we were not previously aware of.

We don't like the answer to "what is computational thinking?"
We'd like it if there was something new here, but computational thinking is about using mathematics, logic, language, and problem solving (using, for example abstraction, modelling, and methods of representation).


Bringing computational thinking into the mainstream is an ongoing challenge. Computational thinking involves topics that have always been among the most challenging to teach: mathematics, language, logic, problem solving. From these subjects, we can use what we already know about computational thinking to structure their curriculum in a way that emphasises the most relevant parts of computational thinking.

Framing these topics in in the context of computational thinking does represent a shift in emphasis. For example, Calculus has traditionally been treated as the pinnacle of highschool mathematics - it makes sense, given the applicability of Calculus such a wide range of real-world problems, and the importance of the mathematics that an understanding of Calculus allows students to develop. However, a high school mathematics curriculum more interested in computational thinking might nudge Calculus out of its revered place in favour of mathematics that is more focused on discrete functions and other topics more aligned with computational thinking.  As Arthur Benjamin puts it in his TED talk "Teach Statistics Before Calculus":

Look, the world has changed from analog to digital. And it's time for our mathematics curriculum to change from analog to digital, from the more classical, continuous mathematics, to the more modern, discrete mathematics -- the mathematics of uncertainty, of randomness, of data -- that being probability and statistics.

emergence

One of the clearest examples of emergent phenomena is provided by the mathematical concept of cellular automata - a cell has one of a number of states (the simplest might just have states on and off), and is aware only of the states of its immediate neighbors. Different types of automata have the cells change their states based on simple rules - the most famous example is Conway's Game of Life, which has a rule that if a cell is turned off but has three neighboring cells that are on, it should turn on. Although the rules for automata are small, simple, and local, surprising large-scale patterns can emerge - patterns that are neither intended nor predictable based on the local rules themselves.

patterns that emerge
in Ulam's two-step automata

Often when we think of emergent technology, we imagine new technology: technology being born, emerging into the world as an entity onto itself. The notion of emergence provided by cellular automata and other models of emergence tell us something different - the elements at the local level (think of this as individual technologies and their intended uses) do not prepare or inform us about what patterns will play out at larger scales.

A similar caution about identifying what is important about technology with what is new is provided by David Edgerton's book The Shock of the Old (see a review in the Guardian, here), which reminds us that the impact of new technology is dwarfed by older technology, and that "invention is not the same as utilization". In looking at the phenomena of emergence, utilization - how technology interacts with people, systems, and life, is what matters.

Attempts to predict large scale patterns that will emerge from technology show how hard it is to anticipate emergent phenomena.

In 2010, then Google CEO Eric Schmidt authored an article for the magazine Foreign Affairs entitled The Digital Disruption: Connectivity and the Diffusion of Power (available here), which attempted to peer ahead into how connection technologies (Google, Facebook, Twitter) would impact geopolitics. It is instructive to read this article in light of how these connection technologies have since been used to undermine democracy - from the scandals of Brexit, the 2016 American election, and the use of data obtained from Cambridge Analytica to fuel the false news supplied by troll farms. Schmidt's insistence that governments should get out of the way of corporations so that connection technologies can be allowed to promote transparency, freedom and democracy, seems worse than self-serving.

Futurists, techno optimists and pessimists cannot be blamed for being wrong - emergent technology is more than the hardware and software that corporations are selling, and technology use is not directed by our intentions, good or otherwise.

hello world

Why blog?

After about 10 years of working in the software industry, I am easing back into working primarily in education (I am a secondary mathematics and computer science teacher). I'm working as an occasional teacher, teaching online, and doing other education-related work.

In some ways I've never left education - I have taken on a few curriculum writing contracts, have led some workshops, but mostly I have stayed involved with teaching by hanging on the periphery of online education communities.

When I left teaching, I still found myself thinking about math - math done for fun and education, so I started a blog mathrecreation to share the math I did for fun, and a twitter handle @mathrecreation to follow mathematics practitioners and educators. My social media presence has been somewhat anti-social: as someone on the periphery of education doing other work, I didn't insert myself into education-related discussions. My posting also was not focused on education in the strong sense - mostly on sharing what interested me, which occasionally included things that might be of interest to educators. Although on the outside, and somewhat anti-social, I have still made some great connections with other educators and enthusiasts, and this has helped me keep the education-side of my life alive.

Part of my re-entry into education is taking courses about education - I hope to use this blog and a new twitter handle (@danmackinnon7) for posts that are related to coursework and other aspects of my education journey, and keep my "math recreation" posting on mathrecreation.

How blog?

While beginning to look at resources for one of my courses, EDU5287 at UOttawa, I was reflecting on how I currently create digital learning resources, and how I engage with online communities of educators and enthusiasts.

I have started publishing the code that I write on Githhub. This is for convenience - I use Git as part of development and like having access to code anywhere, but it also has connected me to others that share similar interests - a social side effect that I was not looking for, but is nice. Most of the code I write is related to my recreational mathematics interests, or related to learning new (to me) technologies. My Github repositories are at github.com/dmackinnon1, and my Github pages are at dmackinnon1.github.io. Although Github is not primarily associated with education, I am interested in looking into how it can be used as a platform for publishing online learning resources.

Whether it is about a piece of math-related code I have written or some other topic, I use the Blogger platform to post. My blog is hosted at www.mathrecreation.com.

A long while ago, I used Google Reader to keep track of articles about math and math-education. Unfortunately that service ended, and I switched to keeping interesting links on a Tumblr blog, mathrec-links.tumblr.com.

Many of my recreational mathematics interests are in the area of geometry, and sometimes generative geometric art. I share math-inspired images that I create using code or software packages on another Tumblr blog, mathrecpics.tumblr.com.

The Blogger and Tumblr blogs automatically publish tweets to the Twitter handle @mathrecreation. Most of my tweets there are automatically published - I don't generally tweet about opinions or personal things.

I'm not quite sure how I will use this new blog and twitter handle... we'll see how it evolves. :)