Clocks and Cognition; Looking at Representation and Symbolism in Learning

December 8, 2010

There was a recent conversation on Twitter regarding the value of children learning to read an analog clock – one person classed it as an irrelevant skill, right along there with using slide rules.  It was the sort of side discussion that almost looks like a trivial bit of chit-chat, when it really is something quite important.   The crux of the conversation was: “we have a newer, more efficient tool (digital clock) so the old tool (analog clock) is irrelevant”.

But there’s something missing from that picture – we are not digital beings, we live and move and think in an physical world – we are physical people who happen to use digital tools.   Analog tools are exactly “what it says on the tin”: they are analogs, physical analogies, representations rooted in the world in which we live.    We connect to analog – it models physical realities or even complex abstractions.  Finding the meaning of abstractions represented digitally is a different game altogether – they might be a shortcut of expression, but they are not physically analogous representations; they add an extra layer of symbolism for the brain to process.

For this reason it probably takes most  people a few seconds to figure out the joke:
Q.  Why do computer scientists get Halloween and Christmas confused?
A.  Because Dec 25 = Oct 31.
(If you don’t spend a fair amount of time in the Math or CS playground, it may takes an extra step or two of mental translation to get this one.  Hint: Dec = base 10, Oct = base 8)

Time, in and of itself, is an analog tool: taking the day and breaking it into equal chunks for purposes of planning and communication.

The nature of non-digital gives us something we can naturally connect to.

The analog clock is a beautifully simple illustration of this.  It is an analog reference to an analog concept – a physical representation of the turning of the earth, if you like; mapping an abstraction (time and its passage) into a tangible, touchable model. Roitblat and Meyer describe it this way:

“The time representations in an analog clock directly reflect the similarities between times rather than symbolically describing them.  For example, on a digital clock, the representations of 9:58 and 9:59 share quite a few features relative to those represented by 9:59 and 10:00, but those times differ by exactly one minute.  In an analog clock, on the other hand the similarity between 9:58 and 9:59 is exactly the same as the similarity between 9:59 and 10:00.  An analog clock is a nonsymbolic (in the sense described here) representation that preserves the correspondence between the event to be represented and the characteristics of the representation.”

Beyond that, the analog clock is something learners can touch and feel and play with – see the mechanics and how the gear ratios drive the motion, grasp spatial and numeric relations based on something real and tangible that users experience everyday.  It is a tool that is understood experientially, not merely a classroom lesson, so it can provide a meaningful schema for complex and abstract concepts beyond telling time.   Supplanting analog totally with digital (replacing physical representation with symbolic) might lead to faster reading of clocks, but not necessarily a faster grasp of the relation between different times (which is a significant part of the value of clocks).  It also, incidentally, removes a tool that gives grounding to abstract concepts such as ratios, through meaningful everyday experience.

math-manipulatives If I were obliged to provide an analogy for analog clocks in the realm of mathematics tools,  it would be closer to manipulatives in a math class than to a slide rule.   (I would hope that I need not argue the case for students benefitting from understanding the meaning of mathematical operations, as opposed to merely memorizing the appropriate algorithms).

Symbolism has it’s place, and its merits, but generally these are after the learner has a real understanding of the concepts.  And understanding of complex or abstract topics often comes from use of representation.  It is not “either-or”, it is “both-and”.
As learning professionals, at the end of the day, our evaluation of tools and methods must directly correspond to how humans actually think and interact with the world.  Unfortunately, wholesale, or careless, dismissal of tools and methods that are out of vogue is not an uncommon situation; and this leads to a more difficult question.

The deeper issue ties back how we evaluate evolving tools.  If we’re going to assess the relative merits of tools, and their relevance, we have to take into account not merely their objective use, but how they actually used; as an example an interesting post by @hypergogue considers the “affordances”, or qualities, of digital and paper documents in the sphere of knowledge work.  Paper documents, messy and tangible and shuffle-able, allow a for different kind of off-loading process for our brains than digital ones.  Neither digital nor paper documents are inherently useful or relevant (nor inherently un-useful or irrelevant) – relevance for learning is tied to use, cognition and meaning.  It is our task (among other things) to weigh tools well and use them wisely on their own merits and within this framework.  To do this requires a shockingly old fashioned tool-set: knowledge, logic, objective evaluation (the same tools needed for the dying art of discourse).  To acquire and apply that tool set requires something even rarer in this modern age than discourse; what it requires is Time.

The question is: Are we willing to find that Time?


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