For the Transferring Meaning section, different working groups focused on each strand of mathematics - Number, Data Handling, Shape and Space, Pattern and Function and Measurement - and rearranged them into organising titles that encompassed the important aspects of each strand. For example, in Pattern and Function the strand titles were - Identifying Patterns, Representing Patterns and Rules and Relationships. The aim of this was to make the progression of learning indicators in this section more explicit for teachers to use as signposts for their learners' next steps. We designed each indicator to be written in two ways - an 'entry in to phase' version and an 'exiting phase' version. This helps with differentiating content for individual learners as they work towards a conceptual understanding.
The resulting document is rather lengthy and in some ways this is unfortunate. As a group we discussed our concern that some teachers may use the scope and sequence as a 'to-do' list, hastily aiming to tick off as many of the learning indicators as possible. Well-intentioned, but not conducive to the development of conceptual understanding. The relentless pursuit of doing and knowing doesn't allow time for true reflection or any form of genuine application in order for the content to take on meaning for the learner (i.e. understanding). So, while we had a useful document for teachers to use as a road map for their students' learning, it wasn't as effective as it could be.
I was fortunate to connect with some deep educational thinkers during a visit to Thailand a couple of years ago and was introduced to the idea of a maths POI by Mignon Weckert. The maths POI provides a conceptual framework for mapping the maths scope and sequence across the grade levels. Because it focuses the learning around big ideas, it helps teachers to assess for understanding in mathematics and ensures that facts, procedures and algorithms are underpinned by concepts.
The implementation of this has been an interesting exercise. We are coming to the end of our first year and some parts have worked well while others need tweaking. A couple of common questions are:
(1) Is the PYP is meant to be trans-disciplinary then why are we planning all of our maths as standalone units? We are fully committed to the trans-disciplinary nature of the PYP. However, we are also aware that not all units allow for a seamless weaving of mathematics alongside the other disciplines. On review, the eagerness our teachers to embed all of their maths into the POI was leaving us with some areas that weren't being addressed, or were only being addressed as an after-thought (i.e. "oh my gosh, there's only 2 weeks left of the year and we haven't looked at mean, mode and median yet! Quick, do this, kids!". By mapping everything out into conceptual units, we can ensure that a cogent arrangement of the scope and sequence is achieved without any gaps in the learning. Once this was finalised, teachers then looked for the links to their units of inquiry. This helped to decide the order that each unit would be taught in as teachers were able to see if the unit itself provided a lens to inquire into the mathematical ideas, or if they needed to be introduced prior to the UOI so that maths could be used as a tool for inquiry. So although they're planned as standalone units, the teaching of them is still as trans-disciplinary as it was previously.
(2) If the PYP is designed around phases of learning then why do you assign units to certain grades? This is aspect that we've found the most difficult to manage. Students are not robots that progress in a perfectly linear fashion each year they attend school so of course some are ready for different aspects of a maths concept than others are. The message to our faculty has been that, additional to the other benefits of this framework, the Maths POI provides us with a system for organising the units. The way we've approached the application of this (i.e. the teaching side of things) is that teachers in a grade could be accessing unit of inquiry planners directly above or below the one that is allocated to them. This isn't the perfect system yet. We need to figure out a way of tracking which students have had access to different UOIs than might have otherwise be expected. Its not fair on, for example, a grade four teacher if they plan to work with their allocated measurement unit only to find out that half of the students have already investigated these ideas during the previous year. It's feasible that class teachers could be running three separate (yet related) maths units concurrently to cater for the readiness needs of the students in the class. This is a tricky balancing act on by itself, let alone without a clear system of knowing who's where. So, in summary, the units are arranged by grade but the actual teaching still adopts a 'phase' approach with students working at several different stages.
The Maths POI is a useful way of framing teachers' thinking about their teaching of mathematics. It provides a way to unpack content in a way that aligns closely with the principles of the PYP. The real impact, however, is in the teaching and assessing that accompanies this approach. If teachers plan conceptually but teach traditionally then it serves no purpose.