The Front and Back of Mathematics- a very simple view.

The following is an email that I have sent to all K-4 staff at school. I’ve been moved by an experience I saw during one of my visits into a Stage 1 classroom and felt compelled to put some words to it.

Good afternoon all,

This week’s mini-PLM comes in the form of a quote from Reuben Hersh, an American mathematician and academic. He maintains that Mathematics has a front and a back. He notes,

“the finished product of mathematicians belongs in the well-ordered and more-or-less highly polished front of mathematics while the back is the area where mathematicians are busy engaging in but often practically fruitful activities of mathematicians​.​”​ ​​

While it may be difficult to think of our littlest students or even most vulnerable students as mathematicians in the vein of Rueben Hersh, his point was at the fore of my mind after hearing a S1 girl grapple with her understanding of faces on 3D shapes, in particular a sphere. It was clunky, with moments of dialogue between students and teachers. There was silence, coupled with sentences that began small snippets of conjecture. All  equally enabled by the students, teachers, the class environment, and curiosity.

It would have been far cleaner and easier to grab control of a such a conversation and steer it directly, but my point is, this was true mathematicians work. In this experience, each learner (teacher, too) had access to the front and back of mathematics. And it didn’t come through a pre-loaded worksheet where the content and process was delivered by teacher to the ’empty student’.

My final thought is this: do we value and make space for both the formal, precise and abstract front , AND the messy, intuitive and often clunky back side of Mathematics?

Enjoy your week.

Hersh, R. Experiencing Mathematics: What Do We Do, when We Do Mathematics?​American Mathematical Society​ (2014).​ ​p.35​​.