As every keen aficionado of fashionable pedagogic theory is aware, learning intentions are a key feature of the model lesson. Woe betide the student teacher, probationer or teacher under inspection who fails to place sufficient emphasis on the learning intentions at the start of each lesson and assiduously check they have been covered at the end.
Sadly, it remains a possibility that pupils will fail to discern even the most obvious facts, concepts or skills, but will retain in perpetuity the trivia, the incorrect answer, the casual aside, the irrelevant factor, or unintended outcome. Cognitive culs-de-sac lurk at every turn, blindsiding even the most sophisticated teacher.
Context is not necessarily helpful. Revising number systems with an S4 foundation class, I began the lesson with a brief reference to Aboriginal counting systems. Six months later, as the class filed into the hall for the final examination, I spotted one of the more worthy members of the class. I greeted him, expressed my delight, if not amazement, that he was there at all and then, in the spirit of maintaining an academic ethos, I asked if he was prepared for the exam. He mentally reviewed four years of mathematical education and finally replied: "I remember about the Aborigines." I regret to report that the SQA failed to include Aboriginal counting systems in that year's paper.
The irrelevant factor may be the killer blow. Marking one girl's decimal calculations, a colleague was disappointed to see how many were incorrect. The girl herself could not understand it. As she observed to her teacher: "But when you multiply, the point moves towards the window." At one time it very probably had done, and under the right conditions, it might well do so again.
As a brand new probationer teacher back in the antediluvian era when remedial classes were in vogue, and usually to be found on the timetables of brand new probationer teachers, my S1 remedial mathematics class enjoyed the pleasure of my company last period on a Friday afternoon, a state of affairs which afforded much satisfaction to all concerned.
A little light conversation oiled the wheels of our journey to mathematical excellence. During one such discourse, I enquired of one boy what he had been working on in his technical class during the previous period. He beamed, held his hand at knee height and announced: "I made a pile of shavings this high."
And the check on learning intentions at the end of a lesson may be counterproductive. In response to a biology teacher's request for the names of the five food groups, the last, loud, confident answer was "Poultry". The bell rang, and every brain in the class switched off with this word indelibly etched thereon. I rest my case.
Carole Ford is former head of Kilmarnock Academy and former president of School Leaders Scotland.