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]]>We could certainly view this from a domain-theoretic perspective, by imposing a dcpo on , namely (your flat domain of Booleans). Then, lifting this order on the codomain to an order on functions , my equation (1) can be interpreted as requiring . I agree it’s a natural way to look at it from a theoretical perspective, and opens the door to some interesting generalisations.

Re etymology of fibre, I don’t know. I guess it’s topological?

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]]>And I’d like to see the slides!

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]]>I checked out your post on multiplication (http://followinglearning.blogspot.com/2018/05/multiplication-with-cuisenaire.html). One mathematical observation I’d make is that in an equation such as 2r = p, laid out in the way you have it, it’s always multiplication of a rod by a *numeral*. This is natural because 2r is shorthand for r+r. But the multiplication itself is not expressible in the syntax we gave with the rods, only in the *language used to talk about the rods* – the meta-language of teaching. It’s possible in Cuisenare to express , as a 2D array of rods – without recourse to numerals. This is not the case with topological bar models: we can write x in a bar, but we have no way of representing . One interesting avenue to pursue is whether there’s any useful way to write in Cuisenaire as part of a sentence that holds obvious meaning, e.g. is there an obvious syntax for ?

Multiplication (and division) would be well worth pursuing further. (As would a formal study of the meta-language of teaching!) I also think that – as you imply – psychology could tell us a lot and would be a valuable addition to the maths / education collaboration!

I wonder whether Charlotte (https://twitter.com/CNeale78) has observed the same unit issue you highlight in her practice.

Thanks again for your kind comments on our work!

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]]>I’m intrigued by how the rods help young students to grasp concepts for themselves. It doesn’t seem to be a simple thing. In a recent blog post

http://followinglearning.blogspot.com/2018/05/multiplication-with-cuisenaire

I wondered about a more psychological effect of the presence and absence of competing units.

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