I’ve been doing a little light reading and exploring the new PYP: From principles into practice digital resource in the PYP resource center. This led me to nose around the Programme standards and practices documentation to see if anything had dramatically changed. I was surprised at how much it had changed in wording, not just swapping section letters for numbers but how some of the ideas have shifted to articulate the “enhancement” of the programme.  Here’s something that stood out to me:

(2014)Standard C3: Teaching and learning

Teaching and learning reflects IB philosophy.

1. Teaching and learning aligns with the requirements of the programme(s). PYP requirements

a. The school ensures that students experience coherence in their learning supported by the five essential elements of the programme regardless of which teacher has responsibility for them at any point in time.

 

(2018) Learning (04)  Standard: Coherent curriculum (0401)

Learning in IB World Schools is based on a coherent curriculum.

Practices: The school plans and implements a coherent curriculum that organizes learning and teaching within and across the years of its IB programme(s). (0401-01)

This led me to question and scan through the standards and practices documentation to examine how “stand alones” are being viewed in the enhancements. Since I wonder how they fit in with this idea of “coherency”, (which was not defined in the glossary of terms, oddly enough) they could be problematic as they might conflict with transdisciplinary learning.

And why do I think this?-because I’ve been struggling with trying to “cover” the math standalone along with the transdisciplinary maths. At schools in which TD (Transdisciplinary) Maths and SA (Stand Alone) Maths are taught simultaneously during a unit of inquiry,  I’m sure many of you PYP educators share my pain and are trying to “fit” it all in while not sacrificing the main UOI.

Oh, I can hear you–

Judy, but TD Maths is supposed to be embedded naturally into our UOIs. We shouldn’t know where one subject begins and where ends in transdisciplinary learning. 

But math is not a noun, it’s really a verb. And unless you write units of inquiry that create the context to do mathematics organically, it hardly lends itself to transdisciplinary learning. Perhaps it is for this reason why our school has created a whole Math Programme of Inquiry (POI) around the strands of Number and Pattern & Function. Christopher Frost wrote a brilliant blog post that articulated his school’s challenge with the PYP planning puzzle: mathematics so I can appreciate why our school has attempted to create a Math POI. However, because we only developed it within those strands, in my opinion, this has further complicated the challenge of integrating math into our units of inquiry.

For example, our last Math UOI  in 1st Grade was:

Patterns and sequences occur in everyday situations.
–Patterns can be found in numbers.
-Types of number patterns
-Patterns can be created and extended.

This was our conceptual rubric for this Unit of Inquiry:

The lines of inquiry came from the learning outcomes (which we refer to as “learning territories” at our school) from the IB’s Math Scope and Sequence, under “constructing meaning” in Phase 2 in the Pattern & Function strand.  But then this stand-alone wasn’t enough, and we had to then create a TD math focus to go with our How We Express Ourselves unit:

Language can communicate a message and build relationships.
-Different forms of media;
-The way we choose to communicate;
-How we interpret and respond.

So there we were, as a team, staring at this central idea and wondering what would be a natural match, conceptually, with this unit. We could definitely DO data handling as a component of this unit, creating graphs and charts that reflect the 2nd and 3rd lines of inquiry. However, since we were stuck on the CONCEPT (rather than the skills), we ended up focusing on the word LANGUAGE and eventually wrote another conceptual rubric based upon the conceptual understanding (from the Math Scope and Sequence): Numbers are a Naming System (Phase 1, Number), using the learning phases from the Junior Assessment of Mathematics from New Zealand–a standardized assessment that we use across all grade levels.

Although we felt that we “covered” the learning outcomes or “territories”, we definitely felt dissatisfied with how we approached planning and learning these of concepts. Recently, I read the Hechinger Report, OPINION: How one city got math right, something stuck out at me and made me reflect deeply on our process and purpose of math in the PYP.

The top countries in education have shown that going deeper and having more rigor in middle school are the keys to later success in advanced math. Compared to high-performing countries, American math curricula are a “mile wide and and inch deep.” Students who want to go far in mathematics need a deeper, more rigorous treatment of mathematics…..

Going for depth of understanding in the foundational years, and accelerating only when students have solid backgrounds and have identified their goals, has paid off. This is progress we can’t risk undoing by returning to the failed practices of tracking and early acceleration.

Here are the questions that surfaced after reading that article and reflecting on our context:

1. Is having TD math and SA math taught during the same unit of inquiry really “best practice”? Are we creating a “mile wide and an inch deep”?
2. Is focusing on conceptual understandings vs. skills really the best approach to transdisciplanary learning in math?
3. Do broad conceptual understandings help or hinder the assessment of a math UOI?

Now I’d like to add one more question after reading the Standards and Practices……

4. How can we create coherency, not only by “covering” all the learning expectations for our grade, but create authentic math connections for transdisciplinary learning?

 

Where we are in place and time with Math in How the World Works.

Our new unit began this week. Originally our upcoming Number SA Central Idea was going to be:

Making connections between our experiences with number can help us to develop number sense.

As we were beginning to develop lines of inquiry for our “learning territories”, we decided that this central idea seemed hard to approach and written for the teacher, rather than the learner. (In my opinion, if students find Central Ideas to be goobly-gook, then how on Earth can they make meaningful connections?) We went back to the IB’s Math Scope and Sequence to provide clarity and direction to developing skills.

Will mathematics inform this unit? Do aspects of the transdisciplinary theme initially stand out as being mathematics related? Will mathematical knowledge, concepts and skills be needed to understand the central idea? Will mathematical knowledge, concepts and skills be needed to develop the lines of inquiry within the unit?

When we looked at those questions, our team nodded their heads in agreement–Yes, of course this is a TD Math unit–it’s a scientific thinking unit, for heaven’s sake–the best kind to connect with!

Thus we rewrote the Central Idea and created our lines of inquiry based upon what they might be “doing” with number, recognizing that other math strands might be employed in our How The World Works unit (Central idea: Understanding sound and light can transform experience), thus combining the “Stand Alone” with our “TD Math“. Here is the unit we created:

We collect information and make connections between our experience and numbers.
–use number words and numerals to represent real-life quantities.
-subtitize in real-life situations.
–understand that information about themselves and their surrounding can be collected and recorded
-understand the concept of chance in daily events.

To be honest, I’m not sure if this is the best approach either and I spent a good amount of time cross-referencing pacing calendars and scope and sequences from other national curricula. However, this not only would help us to “kill 2 birds” with one planner, but it also helps us lean towards creating math units that develop the context of discovering vs. “being told” when and how to do math. This is true inquiry, in my mind, whether it is through a SA or a TD Math lens of learning. But when you are trying to squeeze in teaching two maths (TD and SA) during a unit then there is the challenge of approaching problem solving as a rote skill instead of having enough time for students to make decisions based on their math understanding. Documenting and analyzing those student decisions require time in order to evaluate appropriately what our next steps might be and in order to guide them towards a deeper understanding and more flexible thinking. So stay tuned.

If any other schools have been fiddling around with integrating math into units, I’d love to hear some of your stories–indeed anyone reading this blog would!! So please share your approaches in the comments below.  It benefits all of us trying to put “Principles into Practice”.