Monthly Archives: April 2017

The p-prim path to enlightenment…?

The Duke of Wellington was once asked how he defeated Napoleon. He replied: “Napoleon’s plans were made of wire. Mine were made of little bits of string.”

In other words, Napoleon crafted his plans so thay they had a steely, sinewy strength that carried them to completion. Wellington conceded that his plans were more ramshackle, hand-to-mouth affairs. The difference was that if one of of Napoleon’s schemes broke or miscarried, it proved impossible to repair. When Wellington’s plans went awry, he would merely knot two loose bits of string together and carry on regardless.

I believe Andrea diSessa (1988) would argue that much of our knowledge, certainly emergent knowledge, is in the form of “little bits of string” rather than being organised efficiently into grand, coherent schemas.

For example, every human being has a set of conceptions about how the material world works that can be called intuitive physics. If a ball is thrown up in the air, most people can make an accurate prediction about what happens next. But what is the best description of the way in which intuitive physics is organised?

diSessa identifies two possibilities:

The first is an example of what I call “theory theories” and holds that it is productive to think of spontaneously acquired knowledge about the physical world as a theory of roughly the same quality, though differing in content from Newtonian or other theories of the mechanical world [ . . .]

My own view is that . . . intuitive physics is a fragmented collection of ideas, loosely connected and reinforcing, having none of the commitment or systematicity that one attributes to theories.

[p.50]

diSessa calls these fragmented ideas phenomenological primitives, or p-prims for short.

David Hammer (1996) expands on diSessa’s ideas by considering how students explain the Earth’s seasons.

Many students wrongly assume that the Earth is closer to the Sun during summer. Hammer argues that they are relying, not on a misconception about how the elliptical nature of the Earth’s orbit affects the seasons, but rather on a p-prim that closer = stronger.

The p-prims perspective does not attribute a knowledge structure concerning closeness of the earth and sun; it attributes a knowledge structure concerning proximity and intensity, Moreover, the p-prim closer means stronger is not incorrect.

[p.103]

diSessa and Hammer both argue that a misconceptions perspective assumes the existence of a stable cognitive structure where, in fact, there is none. Students may not have thought about the issue previously, and are in the process of framing thoughts and concepts in response to a question or problem. In short, p-prims may well be a better description of evanescent, emergent knowledge.

Hammer points out that the difference between the two perspectives has practical relevance to instruction. Closer means stronger is a p-prim that is correct in a wide range of contexts and is not one we should wish to eliminate.

The art of teaching therefore becomes one of refining rather than replacing students’ ideas. We need to work with students’ existing ideas and knowledge — piecemeal, inarticulate and applied-in-the-wrong-context as they may be.

Let’s get busy with those little bits of conceptual string. After all, what else have we got to work with?

 

REFERENCES

diSessa, A. (1988). “Knowledge in Pieces”. In Forman, G. and Pufall, P., eds, Constructivism in the Computer Age, New Jersey: Lawrence Erlbaum Publishers

Hammer, D. (1996). “Misconceptions or p-prims” J. Learn Sci 5 97

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Filed under Education, Philosophy, Physics, Science

Room 808

Image credit: https://www.flickr.com/photos/costi-londra/3989596804

MiniEd: the Ministry of Education, Airstrip One, Oceania

It was a warm but overcast day in late August and the clocks were striking thirteen.

Mr Winston Smith, Principal of the Victory G+MINDSET Academy (formerly the Bogstannard Comprehensive School), woke to find himself lying on something that felt like a camp bed, except that it was higher off the ground and it seemed that he was fixed down in some way so that he could not move. Light that seemed stronger than usual was falling on his face.

He gasped as he realised that the infamous MiniEd interrogator, “Grammar School” O’Greening, was standing at his side, looking down at him intently. At the other side of him stood a man in a white coat, tapping an iPad.

“Tell me, Winston,” said O’Greening gently, but with a chilling undercurrent of steel in her voice, “how many buckets am I holding up?”

Winston swallowed fearfully as he realised that he had been deposited by mysterious forces into the deepest bowels of the dreaded MiniEd. 

“Erm…two?” he quavered. The two buckets had “EBacc”and “More bloody EBacc” scrawled on them in crayon.

There were a couple of muffled metallic clangs as O’Greening did a rapid double take. “Nick!” she hissed furiously through clenched teeth. The other man ran to join her. He groaned as he strained to lift a third bucket. “Why do I always have to do the Maths and English bucket? It’s sodding well double-weighted, you know…” he muttered resentfully.

O’Greening ignored him. “How many buckets, Winston?”

“Three! I see three buckets!”

The man let the third bucket drop with an explosive gasp and rubbed his tired arms. “Thank God for that! We had that Sir Ken Robinson in here last week. Kept claiming that he could see a fourth bucket called ‘Unleashing Children’s Inner Demiurgic Muse’. I thought my arms were going to fall off…”

“Comrade Gibb!” snapped O’Greening. The man lapsed into sullen but acquiescent silence. “Now, Winston,” she said sweetly, “from whom have we taken our maths mastery pedagogy? From whom have always taken our maths mastery materials?”

Winston locked his dry lips nervously. “Eastasia…we get our maths mastery materials from Eastasia…” O’Greening nodded encouragingly​. “… but up until a couple of years ago, of course, we were encouraged — well, ordered, actually — to get them from Eurasia instead…”

Gibb had stuck his fingers in his ears and was humming “La la la! Not listening! La la la!”

O’Greening glowered at Winston. “Lies! Delusion! Comrade Gibb: take him to . . . Room 808!”

“Erm, this is Room 808, ma’am.”

“Oh. Then fetch me . . . the school’s RAISEonline report!”

Gibb placed the iPad so that it filled the trembling Winston’s entire field of vision.

“Currently, I have a ‘good pass’ set to ‘4’,” she said conversationally. Actually, thought Winston, it didn’t look too bad. The screen was mostly green with only the odd patch of blue. 

Image from https://johntomsett.com/page/21/?archives-list=1

“Now observe what happens as I now define a ‘strong pass’ as a ‘5’!” O’Greening twisted the dial from 4 to 5.

Winston screamed as the entire screen turned blue. “Arrgh! Don’t do it to us! Do it to another school! DO IT TO ANOTHER SCHOOL!”

O’Greening and Gibb patted him on the shoulder. “Oh, we will. We most certainly will.”

They left Winston Smith alone in Room 808. Tears ran down his face, but he smiled quietly to himself as he stared at the screen. Students, happiness, staff, well-being, people — none of that mattered any more. He had finally won the battle against himself. He loved Big Data.

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Filed under Education, Humour, Satire