Monday, 14 December 2015

The Power of the PYP Key Concepts


Haven't used the PYP Key Concepts yet with maths learning? Then, perhaps this might entice you to start playing around with them.....

In my eight years of experimenting  with how to align the PYP framework with maths learning (and rubbing sore knees from all the tripping and stumbling along the way), what I continue to discover as I observe the learning of our kids, is how lucky we PYP teachers are to have the Key Concepts.

Looking at other educational maths frameworks, what they lack are tools that can allow children to foster their own enquiries in a directed way that meets learning outcomes. 

The PYP Key Concepts are an amazingly effective tool we and our students can employ to transform traditional maths learning to enquiry-based learning.  They can form the framework for structured, guided or open enquiries in maths and also naturally help children to develop deeper wonderings about the concepts and skills explored.  They can radically change mathematical thinking from skills-based learning to student-owned, deep conceptual explorations.

As enquiry-based teachers, we know that a pivotal part to the enquiry learning process is for kids to ask questions and wonder.  In maths, children can often struggle to know what to wonder about in the first place, especially if we are introducing them to new maths concepts.  Using the Key Concepts gives children the (sometimes) needed framework for them to develop deep wonderings and the more they use them in maths units the deeper and more powerful their questions become.

Using them to generate questions they can enquire into arouses a lot of curiosity in children and they can also greatly broaden the conceptual thinking behind a maths concept.  Shallow questions suddenly start transforming into deep questions with their use. Quite often the questions raised fascinate me too so I also embark on an enquiry journey with the children and they love sensing that. (I was never much of a maths student through my own schooling, but making up for it now :P)

Mental Addition Strategies with Year 6

For example, recently my Year 6 children did a unit on mental addition strategies. 

We would think by the time they arrive in Year 6, addition wouldn't be that interesting to them anymore. But, look at some of the questions they wanted to explore using the Key Concepts:

° PERSPECTIVE:  What strategies do adults prefer to use and why when
                          adding mentally?
- They asked their parents and other teachers and made some interesting discoveries. 

° REFLECTION:  How do we know which is the best mental strategy to use with different numbers?

- This took their enquiries to much deeper levels of thinking as they learnt when to use the compensation or other strategies.

° CAUSATION:  Why are some mental strategies better to use than others?

- Here they needed to analyse the properties and place values of different numbers to determine what makes some strategies better to use than others.

° CONNECTION: How are these strategies used with mental subtraction?

- Children here tested their own theories as to whether or not we can apply the same mental addition strategies when subtracting.  They made some fascinating discoveries as to why or why not and excitedly shared these with their peers.
Year 6 students excited about addition?  I wonder if that would have happened without the use of the Key Concepts.

With these sort of student-generated questions, my role as the teacher is to then simply ask:  What can we do to find out?

We brainstorm a list of possible ideas, we test those ideas out, share our findings together. Reflect on whether our ideas in finding out were successful or not. If not, why not?  What else could we do to deepen our understandings? Continue.....continue.....continue......

It's now not only student-created, but also completely student-owned and student-driven learning.

Compare this approach to a traditional teacher-directed unit into mental strategies and that will hopefully help us to see how powerful the Key Concepts can be to learning.  

Next year my new students are likely to create very different Key Concept questions to find out about and that is great too.  

This approach not only helps deepen student learning, but it also helps them develop stronger inquiry skills that they can transfer to other learning domains.

When the united ended and they had time to share their reflections, genuine pride in what they had achieved was felt by every student. I don't think that could have happened had I directed them what to learn and how.

Students Create Their Own Maths Unit:
Below are questions children generated that they wanted to learn in our unit on data handling.  Being student-owned, the children are instantly they are on board for learning because they haven't had a teacher direct to them what they should learn: 

Link to how we created this maths unit )

Or sometimes even using a Key Concept in a stand alone maths activity can be a powerful learning tool:

Link: Sample PYP Central Ideas with Lines of Inquiry 

Simply given children a maths topic (instead of a central idea) and the Key Concepts as a wondering framework can arouse a lot of deep, conceptual questions and when we use these as the basis for our maths unit, we have suddenly created an enquiry-based approach to maths that the children want to discover. 

The Key Concepts are an enquiry-based maths classroom's most powerful tool!


  1. New to this stuff - not thought about applying concepts to maths before. How young an age can we do this? (I teach grade 3). Just starting a unit on multiplication and it seems like a good place to try!

  2. As a pre-service teacher I am loving your blog. THIS is how I want to teach! please keep sharing


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