An inquiry teacher is someone who is more curious about how the students develop their thinking, rather than the actual answer itself. Many PYP teachers recognise what this should look like in Units of Inquiry, but how does this translate to Maths? Many teachers would argue that, in Maths, of course the actual answer is of vital importance and those teachers might place the emphasis on their students reaching one answer, using one method and achieving computational mastery. However, structured and purposeful inquiry is supposed to be the main approach to teaching and learning mathematics in the PYP. So how do we build a bridge between these two approaches?
Lana Fleiszig (@lanafleiszig), the Numeracy Co-ordinator at an IB Primary Years Program school in Melbourne, has been a mentor for us at ISHCMC over the past few years and has helped us to change our mathematic practices in order to become more inquiry based. Through her guidance, each Grade team has written units of Math inquiry for all the number strands. These units have a central idea, lines of inquiry, key concepts and are shared with the students. Within these units we embed all the number standards from AERO and create a sequence of understanding, which are based on Math Strategies identified in GLoSS (The Global Strategy Stage interviews from NZ).
Here is an example of a unit in Grade 2 for addition and subtraction:
Our central idea is “There are many mathematical strategies that help us to solve addition and subtraction problems”.
Our Lines of inquiry are:
- Understanding and applying mental strategies (Function)
- Different ways of knowing (Reflection)
- The place value of numbers help us to understand addition and subtraction (Form)
At the start of each number unit of inquiry, we use provocations to spark curiosity and to promote an inquiry mindset in Math. These provocations might involve a story book, games, a photo, a video, a statement, art or manipulatives arranged in a certain way. the provocations should generate data for the teacher to identify the students’ level of understanding. We often have a week of provocations at the start of a unit so that teachers know what strategies the students are already comfortable using and what concepts they understand so that we know, as teachers, what the next step should be to develop their mathematical thinking.
Here are some examples from our provocations from week one, the problems were related to the real world, they built on student knowledge of place value, it involved discourse and the students had a variety of ways to record their thinking (from using manipulatives such as base ten blocks, numicon, sketching, whiteboards and written strategies).
Through my professional development with Lana, my Grade 2 team now places greater emphasis on: the mathematics process, using a variety of strategies, connecting mathematical concepts, using manipulatives to make maths understandable, real-life problem solving, finding out what students already know and building on these understandings and using mathematical discourse.
By using an inquiry lens, students can link concepts together and as a result we find that our students gain deeper understandings. We frequently use visible thinking routines, such as claim-support-question, see-think-wonder or tug-of-war to enable the students explore and dig deeper into ideas.
Lana taught us the value of opening up math tasks to create open-ended questions, these questions are a great way to differentiate mathematics instruction and to enhance learning. The research center of NRICH (Cambridge University) which I first discovered when I did my masters degree at the Cambridge faculty, were possibly the first group to coin the term’Low threshold, high ceiling’ tasks. These activities are problems which everyone in the group can access and then work on at their own level, which includes possibilities for challenging math. By using open ended math activities it promotes a positive classroom culture because the whole class does maths together.
George Pólya, a Hungarian mathematician, said that it is far more beneficial to solve a problem in many different ways, rather than solving one problem. When students work on open ended math problems, they can reflect on their practice and identify the most efficient strategies.
There are many elements to fostering inquiry mindsets in Maths with your students, as well as with your colleagues and, in your own practice. My colleague, Tiffany Eaton, just shared this powerful graphic from Jo Boaler (@joboaler) on Twitter and I think it is a great visual to remind us of some of the ways to foster inquiry mindsets in Maths: