Tracy Johnston Zager's book,

Tracy takes a range of things that real mathematicians do as her starting point. Chapter 7 for instance is titled,

My favourite part of the chapter is one of the dips into real (and yes, vibrant) classrooms, this time with Deborah Nichols' first and second grades (p152). The question had come up, 'Are shapes math?'

The first step was to find out what the students wondered about shape.

And here are their questions. What an amazing set:

I want to ask some of these students what they meant by some of these! That first one, 'How big can circles go?' - is that about the practical constraints on us creating circles? Or is it about how circles start to look straight when they're really big? Like us walking on our planet. Or is she asking about circles in space? Or something else? Is the question 'How round can a circle be?' related?

Also, 'Are shapes fragile?' Did the questioner mean can shapes be distorted easily? Like the way a triangle or a tetrahedron model made of edges is quite robust, but a square or cube can be deformed easily?

Anyhow, what the teacher did was to arrange a sequence of experiences, with shapes that allowed for there to be a real dialogue between these questions, the shapes themselves and what the teacher needed to be learnt. Without allowing the inquiry to go off in directions that wouldn't really answer the questions, the students' questions - and the answers that came - stayed to the fore. Bit by bit the students built up the knowledge and vocabulary they needed to answer the more mathematical sides of their questions. And they thoroughly covered the learning that's set down for those grades.

As Tracy writes:

*Becoming the Math Teacher You Wish You'd Had: Ideas and Strategies from Vibrant Classrooms*is a - perhaps I should say*the*- book that I'd recommend to all math/maths teachers, and that includes all of us primary/elementary teachers. And for those of us working in inquriy-led IB PYP classrooms, the fit is perfect.Tracy takes a range of things that real mathematicians do as her starting point. Chapter 7 for instance is titled,

*Mathematicians ask questions*. She starts with a quote from Jo Boaler's book*What's Math Got to Do with It?*:Peter Hilton, an algebraic topologist, has said: “Computation involves going from a question to an answer. Mathematics involves going from an answer to a question.” Such work requires creativity, original thinking, and ingenuity. All the mathematical methods and relationships that are now known and taught to schoolchildren started as questions, yet students do not see the questions. Instead, they are taught content that often appears as a long list of answers to questions that nobody has ever asked.She gives examples of resources for encouraging questioning, like 101questions and Notice and Wonder.

My favourite part of the chapter is one of the dips into real (and yes, vibrant) classrooms, this time with Deborah Nichols' first and second grades (p152). The question had come up, 'Are shapes math?'

The first step was to find out what the students wondered about shape.

And here are their questions. What an amazing set:

I want to ask some of these students what they meant by some of these! That first one, 'How big can circles go?' - is that about the practical constraints on us creating circles? Or is it about how circles start to look straight when they're really big? Like us walking on our planet. Or is she asking about circles in space? Or something else? Is the question 'How round can a circle be?' related?

Also, 'Are shapes fragile?' Did the questioner mean can shapes be distorted easily? Like the way a triangle or a tetrahedron model made of edges is quite robust, but a square or cube can be deformed easily?

Anyhow, what the teacher did was to arrange a sequence of experiences, with shapes that allowed for there to be a real dialogue between these questions, the shapes themselves and what the teacher needed to be learnt. Without allowing the inquiry to go off in directions that wouldn't really answer the questions, the students' questions - and the answers that came - stayed to the fore. Bit by bit the students built up the knowledge and vocabulary they needed to answer the more mathematical sides of their questions. And they thoroughly covered the learning that's set down for those grades.

As Tracy writes:

Perhaps knowing that students' inquisitiveness leads to the same ideas that mathematicians study and standard-writers emphasize can help us feel less pressure to tell and cover and explain. If we allow students to ask, we will likely end up in the same place but with much more engaged, empowered students.