The interesting thing is that strategies that fail in the long term are precisely the ones that we used to teach these new concepts in the short term. we relate numbers to counting, often using real “counters”. We relate multiplication to repeated addition. There is nothing wrong with this. Mathematics builds new ideas on old ones. it is hard to see hoe else one can teach it but eventually the training wheels have to come off the bike: students have to internalize the new idea. the art of mathematics involves switching effortlessly from one of those viewpoints to the other, do however, be aware of it when teaching. if one of the students is having a trouble with a procept (process cum concept), that cause may be a past failure to proceptualise one of the processes involved. thus the job of a teacher is to back track through the series of ideas that leads up to the new one – not so much so on looking for the first place where the student fails to answer a question but rather looking for the first place where they can answer it only by using some simpler idea as a crutch.

The 4 critical questions to follow when planning activities for children:

– WHAT do you want the child to learn? (i.e., the objectives)

– HOW do you know if they have learned? (i.e., how to assess or to see if a child has learned)

– WHAT IF the child is unable to do so? (e.g., a struggling learner)

– WHAT IF the child is able to do more? (e.g., an advance learner)

Likewise, whether I am delivering a lesson or talking with my students, I have to remember that what seems perfectly obvious and transparent to me may be mysterious and opaque to those who have not encountered the ideas before. There is room for input from the teacher myself, and there is a delicate balance between helping the students by putting my own stamp on the material, and confusing them by introducing too many extraneous ideas or strategies.

I see the need in building spaces where each person is visible to me and everyone else – and most importantly to themselves. I believe students should sense their own unique power and potential where in my classroom, each is known and understood, recognised and valued; asking questions out of the world, to interrogate common sense, to challenge the orthodox ‘why?’; so much so that the classroom is unsettled in such a way that students have a sense of curiosity and wonder and astonishment.

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