Prior to becoming a PYP teacher, when I reflect upon my teaching I think I was a so-so maths primary teacher. I understood the skills and concepts children in my class should be learning and tried to make maths learning fun mixed with the all-important skill rote learning routines I had also grown up with whilst in school which still seemed to be the expectations of the day.
Joining my first PYP school 7 years ago, I started experimenting with how we could use the PYP framework with maths learning.
I began playing around with central ideas for my students to explore and lines of inquiry that matched PYP key concepts. That became a big game changer for me in how I'd help guide my students towards their maths learning and importantly, allow them to take ownership of their learning.
When we create a successful maths planner using a strong central idea married with supporting lines of inquiry (matched with key concepts) some of the benefits are:
° students have a clear understanding of what the unit is about
° it gives them freedom to explore areas of maths thinking that interests them
° it transforms the learning to become inquiry-based learning in a natural way
° it creates a shift from skills-oriented to more meaningful concept-oriented learning
° it provides them with opportunities to take ownership of their learning
° by generating their own questions to explore they are doing what real mathematicians do and their engagement increases
° they gain a sense of pride in what they have decided to enquire into
The tricky part, which I still stumble over occasionally, is getting that great central idea. It takes time and a lot of thought to create a central idea that allows children to:
° foster a curiosity towards the concepts
° instill a need to explore skills & strategies
° to be broad enough to allow students to take ownership and inquire into avenues that they find interesting in that particular maths strand.
° should be able to cater to all the different inquiries when they reflect during their summative (see below)
Looking at the PYP Maths Scope & Sequence, the conceptual understandings can be a good place to start creating a central idea. Tweaking them to add some grit for students to inquire into rather than just being told the fact needs to happen.
(I wish the IB would create some 'think tanks' and share possible central ideas with possible lines of inquiry out to PYP schools as a starting block for teachers.)
Present or Don't Present a Central Idea?
There are two camps it seems amongst PYP teachers: those that present a central idea towards the beginning of a unit and have it displayed for constant reference and discussion and those that don't reveal the central idea till the end of a unit or have children determine what the central idea could be as a summative.
Personally, I'm in the former camp and so I feel it is important to discuss a maths central idea early on in a unit. By presenting the maths central idea, kids are encouraged to generate their own questions in small groups of things they feel they need to know and what they need to do to gain a deep understanding of it. This provokes curiosity towards the maths topic and also allows them to take ownership of their learning because they will be given opportunities to explore their own questions during the unit.
Quite often we are in the midst of a maths unit and when I see all the different avenues the children are taking their learning, I can find faults in the central idea we are discussing. The central idea can sometimes feel limiting to where they have actually gone with it so at the end of the unit, we discuss how the central idea could be improved. This serves as a in interesting reflection activity for the children and it helps me create better central ideas for next year. My students enjoy when I share with them: "This was a central idea students last year created. Let's explore it and see what changes we think we should make to it over the next few weeks." They appreciate the idea that there new central idea they create will then be used in the following year for the next students to explore and possibly debate over its effectiveness.
Lines of Inquiry
Using the PYP key concepts to form lines of inquiry, I feel, is an easier process. You can look at the maths concepts and skills you want the children in the unit to explore and so use this to create the lines of inquiry.
An example maths unit:
Central Idea: When angles co-exist, connections and relationships form.
° FORM: What different types of angles, triangles and quadrilaterals are like
° FUNCTION: How we can estimate and measure the size of angles
° CONNECTION: Patterns and relationships that exist between angles
° CONNECTION: How we use angles in our daily lives
Because the maths unit becomes student-led due to them generating their own questions to explore from the central idea, sometimes areas outside the planned lines of inquiry are examined. I think this is great.
The children needn't be constrained within the lines of inquiry I had planned for the unit. Usually I don't share the lines of inquiry with the children anyway. I use them as a personal skeleton guide of where I feel the learning should go based on the scope & sequence. If particular students or the class as a whole,aren't taking their learning to broad enough avenues, then I can refer to these to help guide the class.
Everytime I create a maths unit, I always create a line of inquiry using 'connection'.
Eg, CONNECTION: How we use angles in our daily lives
CONNECTION: How we use mental maths strategies in our daily lives
CONNECTION: How we use 3D shapes in our daily lives
This serves as a reminder to me that I need to guide the children to understanding why we are learning about this maths topic. Children need to know the relevance of what they are learning and by finding a connection that what they are learning does or will relate to their own life experiences, they will become far more engaged. An easy, but powerful way for the children to inquire into this is they will often ask their parents how they use this particular maths in their lives. We collate all the parents answers and discuss together.
Since the unit becomes student-led, the summative assessment needs to accommodate all the diverse learning that took place. It would be ridiculous and grossly unfair to have my class all inquire into different avenues of a maths concept only to then hit them with a traditional maths test which wouldn't serve any real purpose. So, what I have found to be a powerful assessment (and reflection) tool is to simply give the children the central idea and they write /draw what they understand about it.
Here are some blogspots explaining how the summative assessment works and the advantages I have found in using them:
° No more maths tests!!!
° Measuring Time Summative Assessment
° Probability Summative Assessment
Blogpost with some example central ideas & lines of inquiry I've experimented with:
Example Central Ideas & LInes of Inquiry