*(I highly recommend you follow her on Twitter for her insights into learning or read her blog: momentssnippetsspirals.wordpress.com She will challenge your pedagogical thinking in a great way leading you out-of-the-box and then back in because everyone is thinking outside of it only to lead you back out again. She is the teacher that you wish you could be a fly on the wall of her classroom for a few weeks at least.)*

I think about her quote quite often actually in class lately as a barometer of when I should step in to assist children when they are doing mathematical enquiries and when I should keep a step back and give them the opportunity to go where they want to go and to also solve problems they might be in a state of confusion over.

We are having an amazing time lately continuing to enquire into our central idea:

The children have identified curiosities they want to explore and have either buddied up or chosen to investigate alone. Some of their investigations stem from wonderings we have posted on our central idea wonder wall throughout our unit and some have stemmed from this poster provocation I created:

From examining and discussing with tables we were able to create some interesting investigation questions (or lines of inquiry):

The children have had a few days to investigate one or two questions and are ever so proud whenever they make a discovery of connections or relationships.

For much of this, I stand back and contemplate Cristina's quote.

If a student needs some inspiration of where to go next, I step in to discuss where they are at where their wonderings are leading them to help them find a new direction. But essentially, they are coming up with amazing discoveries without a teacher's assistance.

Today one of the many interesting chats that was generated amongst groups was whether a two-sided shape existed (eventually a semi-circle was suggested) and whether a line is actually a shape and therefore a 2 sided shape or not. These wonderings didn't directed connect with our central idea , but they were wonderings that sparked interest in those that were in ear-shot of them and so some students debated their own theories and tried to support those theories with examples.

Other groups were proudly declaring that they had disproven their theories. Yes,- disproved. Proudly.

That is a pretty amazing mindshift we have managed to create amongst us. that maths isn't about being correct and there is just as merit is disproving as well as proving our own maths theories we formulate.

Whilst one group has been investigating if there is a pattern with the total interior angles of polygons- triangle, quadrilateral, pentagon, hexagon etc they themselves felt it would be great to buddy up with another group who are investigating the same but with exterior angles. Both groups were amazed at what the other had discovered and are now in the process and gaining even deeper understandings of how angles have relationships and connect.

I like to think that when we can get to a point with our students when they are challenging their own and each other's thinking without a teacher guiding them, then some mathematical magic is happening. This is what enquiry-based learning is all about. You can't get this sort of deep and self-directed learning from textbooks, teacher-directed instruction or worksheets. When we can create a learning environment where the children are driving their own enquiries from their own chosen wonderings, then self-pride as mathematicians and the wonders of mathematical thinking are planted and grow.

And for us, as Cristina says so profoundly:

"Making myself progressively unnecessary. Therefore, a teacher."

I love this being my recent mantra in the classroom......

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