Thursday, April 6, 2017

Maths POI

Over the past two years I've been leading a group of teachers through an inquiry into the way we structure our mathematics scope and sequence here at Branksome Hall Asia. During the first year of this process we identified aspects of our current scope and sequence document for mathematics that we felt needed further clarification or enhancement. We wanted to maintain the conceptual focus that is essential for the PYP so decided to keep the same descriptors for the Constructing Meaning and Applying Understanding sections that are highlighted in the IB Scope and Sequence document. We'll examine these as part of our next review.

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. 

Friday, January 6, 2017

Learning for the future

Over the past few months I've been reading a lot about where people consider the future of education to be heading. I find it interesting to delve into the various perspectives about what education might look like in the future and would like to share some of these.

The first is a summary of some key points from a webinar discussion between two key players in the world of education and learning, Ken Robinson and Peter Senge. Their discussion was entitled 'Learning for the Future' and offered the following snippets:
- Schools are still the answer. What we have to re-think is what a 'school' is.
- It's not that (some) students don't want to learn, its that they don't want to learn the way that we're teaching.
- Schools as communities of learners: We learn from each other - learning is a social act. It is deeply personal and inherently collective (I love this quote). Learning for the future involves learning what it means to think together, to act together.
- Schools are organised the way they are because of the technologies available at the time.
- Just as in an agricultural model of farming, too much emphasis on the yield, output and results will eventually destroy the soil and land beneath the surface. The same metaphor applies to learning. Too much focus on output, results and the yield will eventually destroy the 'story of learning' that exists as part of the culture.

I'm also currently reading through Future Wise: Educating our Children for Changing World by David Perkins. He offers the following six broad trends that are pushing the boundaries of what's taught and the way it's taught:

(1) Beyond basic skills - 21st Century skills and dispositions: There appears to be a global trend converging towards the cultivation of critical and creative thinking, collaborative skills and dispositions, leadership, entrepreneurship and the related skills and dispositions that speak strongly  to living and thriving in our era.

(2) Beyond the traditional disciplines - renewed, hybrid, and less familiar disciplines: Themes such as bioethics, ecology, recent ideas from psychology and sociology, and other areas that address opportunities and challenges of our times.

(3) Beyond discrete disciplines - interdisciplinary topics and problems: Many curricula introduce students to daunting, contemporary problems of an emphatically interdisciplinary character, such as the causes and possible cures of poverty or the trade-offs of different energy sources.

(4) Beyond regional perspectives - global perspectives, problems, and studies: Attention not just to local or national but also to global matters, for instance, world history or the global interactive economic system or the possible meanings of global citizenship.

(5) Beyond mastering content - learning to think about the world with the content: Educators are encouraging learners not just to master content academically but also to notice where content connects to life situations, yields insights, and prompts productive action.

(6) Beyond prescribed content - much more choice of what to learn: In some settings, educators are supporting and coaching learners in choices about what to study well beyond the typical use of electives.

I find it an interesting exercise to reflect on how many, and to what extent, my school is enacting these 'six beyonds'. For some schools, these have been a part of the conversation for many years, yet progress is limited. Others have been shaping the path for some time. It seems to me that more and more these sorts of attributes are becoming more common in school frameworks.

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