Snowflakes and Icebergs

= a. isomorphic form in writing, b. deep learning

The snowflake

There is an isomorphic, even fractal (especially, perhaps, when the isomorphism is more than merely structural, i.e., when it’s semantically loaded), relationship between the structure of the sentence, paragraph and essay, viz.

a. essay: intro (with TS), body (with aspects of the T in the t-s’s), and conclusion (returning to the TS)

b. paragraph: t-s (intro), evidence (body) and argumentation (conclusion)

c. sentence: S + P

Or you might say that it is a structure-preserving mapping relation.

[T(S) = thesis(-statement)
t-s = topic-sentence
S= subject
P = predicate

An isomorphic (ἴσος isos “equal” + μορφή morphe “shape”) structure is structurally identical, i.e., if two objects are isomorphic, then any property which is preserved by an isomorphism and which is true of one of the objects is also true of the other.
A fractal (L fractus, “broken” or “fractured”) is “a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,” a property called self-similarity (B. B. Mandelbrot, The Fractal Geometry of Nature [W.H. Freeman and Company, 1982]). A mathematical fractal is based on an equation that undergoes iteration (recursive feedback).]

The iceberg

a. Deep and shallow learning are not attributes of individuals: one person may use both approaches at different times, although he or she may have a preference for one or the other.

b. They correlate fairly closely with motivation: “deep” with intrinsic motivation and “surface” with extrinsic, but they are not necessarily the same thing; either approach can be adopted by a person with either motivation.

(There is a third form, known as the “achieving” or strategic approach, which can be summarised as a very well-organised form of surface approach, and in which the motivation is to get good marks. Learning is construed as a game, so that acquisition of technique improves performance.)

The features of deep and surface approaches can be summarised thus:

Deep

Surface

Focus is on “what is signified”

Focus is on the “signs” (or on the learning as a signifier of something else)

Relates previous knowledge to new knowledge

Focus on unrelated parts of the task

Relates knowledge from different courses

Information for assessment is simply memorised

Relates theoretical ideas to everyday experience

Facts and concepts are associated unreflectively

Relates and distinguishes evidence and argument

Principles are not distinguished from examples

Organises and structures content into coherent whole

Task is treated as an external imposition

Emphasis is internal, from within the student

Emphasis is external, from demands of assessment

(based on Ramsden 1988)

(See F. Marton and Säljö, “On Qualitative Differences in Learning—1: Outcome and Process,” Brit. J. Educ. Psych. 46 (1976): 4-11; “On Qualitative Differences in Learning—2: Outcome as a function of the learner’s conception of the task” Brit. J. Educ. Psych. 46 (1976): 115-27.)

The Surface learner is trying to “suss out” what the teacher wants and to provide it, and is likely to be motivated primarily by fear of failure. One study has suggested that efforts by teachers to convey that what they want is deep learning only succeeds in getting surface learners to engage in ever more complex contextualising exercises, trying to reproduce the features of the deep approach from a surface basis (P. Ramsden, D. Beswick and J. Bowden, “Effects of Learning Skills Intervention on First Year Students’ Learning,” Human Learning 5 [1986]: 151-64).

[James Atherton, http://www.learningandteaching.info/learning/deepsurf.htm%5D

Or you can look at it slightly differently: deep learning is something you deliver sotto voce—or sotto agua, to use the iceberg metaphor—along with the surface learning (which should be strategically, rather than extrinsically, motivated): modelling, reflecting, critically reading, in a way that is charitable, positional and “de-authorising,” i.e. contextual and co-constructed.

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