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.

Photo Credit

Thursday, October 27, 2016

Multiple ways of knowing - an inquiry into conflict resolution

I couldn't resist sharing the progression of this inquiry as it unfolds among our grade three students here at BHA. The UOI that our three Grade Three classes are currently exploring falls under the TDTheme of 'Sharing the planet' and the central idea is: Effective communication can resolve conflict. The focus on this post will be on the important role that our single subject teachers have played in this inquiry so far.

The students were prompted to consider the last time, or worst time, they were involved in a conflict with friends or siblings. They were asked to think of this as a story with a beginning, middle and end.

Beginning - what happened to give rise to a conflict situation?

Middle - what happened during the communication process to try and solve the conflict situation?

End - how was the conflict resolved and how did it move into peace?

In small groups they then chose one story to represent in a drawing. The students were given long sheets of paper and asked to think about the kinds of colours, shapes, lines, forms and patterns that would best describe what was happening in the three different parts of the conflict story. The drawings below show the conflict stories and their 3 parts; conflict, communication, resolution/peace. The next step is for the students to add emphasis and further structure to the drawings using collage shapes. They will then transition over to our music teacher and consider similar concepts such as dynamics and rhythm that represent the ideas of conflict and peace. To synthesise everything, the students will cut-out and re-arrange their designs as they compose an original score to reflect their stories.

This process clearly offers a tremendous insight into the students' understanding of the process of conflict resolution. Conflict starts out as a range of different opinions and ideas all jostling for the front position. Sometimes it's messier than what it started out like before it gets better. There's usually a breakout moment that occurs prior to the solution. When you get to a stage of finding common ground it is like the pieces fit together. Peace and love may not always be the outcome - sometime we try to cover up a conflict with a resolution. These are all big ideas that are worthy of inquiry into peace and conflict at any age.

So it teaches us two very important lessons about inquiry. (1) Students of any age are able to think conceptually and (2) Teachers must be open to providing multiple pathways for their students to express their understandings.

It is highly unlikely that the students at our school would have been able to articulate these ideas in written form alone. Yes, the teachers helped to tease out the verbal responses from the students (with translation required for some), but that's their role - to listen, not to tell. The point is that those responses were constructed by the students themselves and they may not have seen the light of day if this opportunity had not be available to them. This is succinctly summarised by any Reggio-inspired educator when they talk about the hundred languages of children.

The other beautiful thing about this connection to the UOI is that it was completely unplanned in terms of collaboration between the homeroom teachers and specialists. The idea started as a conversation between our Music and Visual Art teachers and they thought they'd give it a shot. There was no pressure to ensure that they fit in with what was happening in class* so there was a lot of freedom to test out different approaches. When the connections began to appear as significant and highly relevant for the learning that was also happening in the classroom, a lot of discussion between all teachers followed. Although making a strong connection with the unit of inquiry may not have been the first priority for music and art, creating an authentic learning experience certainly was. This idea grew legs because of the teachers' commitment to genuine learning and the lens of the unit of inquiry provided this without being forced.

* To clarify this, at this stage in our school's journey we ask that subject specialists meaningfully collaborate on at least one UOI with each grade throughout the year. They can certainly contribute to more than that, but one is the minimum requirement.

Monday, August 29, 2016

What Hamilton can teach us about intelligence and leadership

As a fan of musical theater I have been swept up in the fanfare surrounding Hamilton, the musical based on the life of American founding father Alexander Hamilton told through medium of hip-hop and rap. While my friends and colleagues wouldn’t describe me as a rap diehard, I do have an appreciation for the form and the lyrical tapestry that Lin Manuel Miranda weaves to tell the tale of Hamilton is something to behold.

Manuel Miranda appears to correlate the ability of a character to rap with their perceived historical place in the spectrum of intelligence. Those that are characterised as prodigiously intelligent (Hamilton, George Washington, Aaron Burr, Marque de Lafayette, Thomas Jefferson) rap regularly, often with intricate rhyming patterns. Those that are less intelligent rap less sophisticated verses, or sometimes not at all. One of those characters is that of Hamilton’s eventual wife - Elizabeth Schyler. Eliza comes from a well-to-do family and also has two other sisters (Angelica and Peggie) that are constant targets of affection from suitors looking to elevate their status by marrying into such a family. Eliza does not rap throughout the entire musical whereas her revered sister, Angelica, has many moments where she raps her story. She is said to be able to ‘match wits’ with Hamilton and certainly earns the moniker of being the most intelligent of all the Schyler sisters.

So what does a person do when they're a part of the hip hop scene but don’t rap? They provide a backdrop for the artists to rhyme verses. Us lay-people typically know this as beat boxing and it can take many different forms. Those who beat box provide a tailored backing track for others to rap to. So there you have it, intelligent people rap and those lower down the cognitive ladder beat box.

This analogy serves as a useful backdrop for learning, leadership and education. As it did back in the 1700s, society still has a tendency to define intelligence through a narrow lens. Unfortunately it appears as though our definition hasn’t evolved over the past 300-odd years. Typically those that are competent scientists and mathematicians find themselves somewhere near the top of the pile, then come those that are gifted with writing, reading and speaking. The humanities usually follow and everything is rounded out by followers of the arts and physical pursuits. Despite recent commentary from modern educational thinkers, this model still pervades many societies and cultures.

By following this, Eliza is not seen as being intelligent. Hamilton is clearly adept with words and numbers (and can rap very well), so he has her covered. But one thing that we know about intelligence is that it manifests itself in different ways. What the beat boxers of this world show us is that they possess a great deal of emotional intelligence. No-one in this world can claim to be the top dog at everything and those that beat box show us that they possess the self-awareness to not only recognise talents in others, but also to notice when opportunities arise for them to support these talents. I believe that good leaders are like this. They know when to rap and when to beat box. They are able to adapt their leadership style to either engage and facilitate inquiry among their colleagues or just as easily support, pacify, console and coach, depending on what the situation requires. After all, leadership is context-driven. I often wonder what our current world would be like if some of the leaders of the past were more like Eliza and less like Hamilton.

Intelligence isn’t a one-size-fits-all model to behold and it most certainly isn’t hierarchical (at least not in the way that we most commonly define it now). We need to challenge ourselves to expand our view of intelligence so that both the Eliza’s and Hamilton’s of our time are able to find their place in the world in a meaningful way.

Photo Credit: Gamma Man via Compfight cc

Monday, May 23, 2016

Assessment validity

Over the past few weeks I have been part of several interesting discussions on the topic of cultural validity in assessment. There is so much to talk about here but I will offer just a short few thoughts now and aim to follow up with greater insight as I construct my own understanding over next few weeks.

The experience that prompted me to write this post occurred yesterday at my school. I was helping out with the assessment of some prospective students that have applied to join our school. I was asked to conduct a reading diagnostic with a student who happened to come from China. The goal of this task is to ascertain a broad range of the student's literacy and language development. This information is useful to handover to classroom teachers so that the can develop a profile of their new students as efficiently as possible. This particular diagnostic hails from North America and, as such, contains several references to North American culture and life in general. I was asked whether this particular student demonstrated comprehension of the reading material at a D level. My response was that she could read this text with fluency and was able to answer the related comprehension. This was true, she could read it with comprehension, however I explained to her the context of the details. In the story a skunk causes an array of animals to run away. I know that this is because skunks use their odour as a defensive weapon against potential threats. The reason that I know this is that I've grown up with several cultural influences via the media and in print that have allowed me to establish this in my own mind. For a 6 year old girl from rural China this is not relevant or significant for her life. I don't believe that its fair to judge a child's ability to comprehend something on content that is completely foreign to them.

Benign as the intention may be, the data gained is not useful. Had I not explained the relevance of the skunk to the story, the student would not have got the question correct and could possibly have been labelled something that she is not. I wonder how often this happens - particularly in international schools. If we take diagnostic reading programs, for example. Although teachers may have an educated, research-based opinion on what an appropriate process is to learn how to read, if the measure that is being used to assess achievement within the process is faulty then the process itself is invalid.

To quote Guillermo Solano-Flores (pg. 3):

"Tests are cultural artifacts. They are part of a complex set of  culturally established instructional and accountability practices; they are created with the intent to meet certain social needs or to comply with the mandates and legislation established in a society; they are written in the language used by those who develop them; their content is a reflection of the skills, competencies, forms of knowledge, and communication styles valued by a society - or the influential groups of that society; and they assume among test-takes full familiarity with the contexts used to frame problems, the ways in which questions are worded, and the expected ways to answer those questions."

Assessing the Cultural Validity of Assessment Practices: An introduction. In: Cultural Validity in Assessment: Addressing Linguistic and Cultural Diversity. 2011. Routledge, NY, USA.

Photo Credit: Damian Gadal via Compfight cc