Term 4 Maths PD: Observing Jo Knox

Maths Professional Development at Pt England is being supported this year by Jo Knox of Maths Development. During the year so far we have enjoyed rich discussions about the process of making Overall Teacher Judgments and the sources of information and assessment tools available to support us in robust decision-making.

This week our team was given the opportunity to observe Jo’s practical expertise as she modelled a fractions lesson for students at Stage E5 and another for students at Stage E6. The purpose was to challenge ourselves to find ways in which we can apply her knowledge and wisdom to remove potential barriers and accelerate the achievement of the Year 5 and 6 learners in our shared learning spaces.

Each of Jo’s lessons began with diagnostic snapshots to check current knowledge and conceptual understandings, before smoothly flowing towards new learning through manipulation of materials, imaging and number properties. It was interesting to note that Jo only explicitly shared the learning intention of her lessons during the conclusion of the session when she stated the mathematical concept in general terms.

The consistency of Jo’s language and questioning when interacting with the learners through the flow of her lessons made the biggest impression on me during the modelled sessions.  The use of the talk moves and wait time made her expectations very clear to the learners that everyone was required to think and then talk about the Maths problems before them. The focus was very quickly on Maths vocabulary, manipulating materials and explanations in a positive and respectful group setting.

Additionally, Jo explicitly modelled "imaging" during these lessons as learning moved from the concrete to abstract:

“Close your eyes.  I’m going to hide a number under the table.”

[Pause while Jo writes a number on a piece of paper]

“Okay.  And open.  What number have I made?  2.8  Bingo! What will I need to make it?

I’m hoping you can picture this in your head.”

Finally, it was fascinating to observe the ease with which learners were able to make connections to their prior knowledge about our place value system and addition strategies to begin adding decimal fractions when using different materials, namely decipipes.

I really did feel that they were able to visualize the decipipes and the motion of sliding tenths onto a threading stick to create a whole number.

As I reflect on my Maths programme following this observation, there are definitely opportunities for me to adjust aspects of my Maths teaching and learning to incorporate Jo’s key points with the goal of better supporting the identified needs of my Maths learners.

Teaching As Inquiry 2017: what have I noticed?

Today we each shared our latest Teaching as Inquiry wonderings and reflections within collaborative groups. It was empowering to listen to Pt England's CoL teachers provide an insight into their hypotheses, hunches and thinking as part of Collaborative Inquiry Meeting #5.

Such sharing has gifted me the knowledge that I face many of the same teaching and learning challenges and opportunities in Maths as other teachers at Pt England - and that all opportunities to collaborate further to unpack and explore would benefit all of our learners. 

It particularly resonated when Rob Wiseman commented that students do not always demonstrate that they have fully understood a new concept or strategy when completing follow-up tasks independently. When learning strategies to solve number problems within levelled ability groupings, I have also noticed that students are mostly able to explain clearly how they have used an efficient strategy to solve a particular problem. They are able to do this using materials and appropriate language based on our learning intention and seem ready to move off and complete follow-up tasks independently. However, their full grasp of the strategy is not always evident in their completed follow-up tasks.

How can I do my best to provide students opportunities to create their own meaning in order to enhance their mathematical understandings? 

1. Create rewindable opportunities for learning.
Dorothy Burt recently shared her wisdom that creativity empowers learning with Pt England staff. A next step for my inquiry and my target learners is to plan for them to be creative, to make their own meaning using a SISOMO approach to explaining their problem-solving strategy and mathematical thinking. My hunch is that the benefits will be twofold. Those learners creating a screencast or video will affirm their own mathematical thinking. Their peers will have access to authentic rewindable resources to support learning any time, any place, anywhere.

I have created a first Maths tutorial, explaining subtraction by breaking up a number, as a starting point for such creativity to empower learning:



2. Teaching and learning using rich, worthwhile Maths tasks.
At our most recent Maths PD session with Jo Knox, she gave us practical advice about integrating Number and Strand in a fun and collaborative way using the NZ Maths unit, Giant Mystery. As well as planning opportunities for creativity, it is time for a rethink about the types of learning tasks used for teaching and learning within my Maths groups. By providing groups of learners with rich, open-ended tasks in a collaborative setting, will they be able to make their own meaning and retain those conceptual understandings? To begin to answer this question, I will need to reflect upon how I organise my Maths groupings and the flow of a typical Maths session.