Partnering with whānau

Whānau often ask what they can do to support their child's learning at home. We always recommend reading and talking about what has been read. We encourage whānau to find ways to enable their child to participate in our holiday blogging programmes to support literacy. However, with the change to the way in which Maths teaching and learning is happening in our learning spaces, there was the opportunity at last night's parent-teacher interviews to empower whānau to strengthen the connections between school maths and real-world maths.

The Developing Mathematical Inquiry in a Learning Community (DMIC) approach to teaching and learning in Maths requires learners to think, talk and collaborate to solve relevant, real-life Maths problems as a group. So, to support learning conversations about Maths at home, I created a Maths @ Home pack for each learner and enjoyed many conversations with whānau about how they might use this to support their child's learning at home.

Talking about Maths has never been so much fun!

Teaching As Inquiry: mid-year reflection 2018

What steps have I taken to change my practice in the first half of 2018?  My practice has inevitably changed with the transition from levelled-group teaching to the Developing Mathematical Inquiry in a Learning Community (DMIC) problem-solving approach to Maths with in-class mentoring provided by Dr Bobbie Hunter’s team at the University of Waikato.

An important focus during the first half of the year has been setting up the norms and expectations for learners when working together in a small group to solve a Maths problem. It is easy to forget that this change in approach to learning Maths is also new for the learners and vastly different from how they have historically learnt Maths at school. Unpacking and exploring the key competencies of managing self and relating to others has been crucial throughout this period so that students feel empowered to embrace this new way of Maths learning. It is beautiful to hear something as simple as a learner politely asking a presenter to speak up so everyone can hear significant Maths thinking.

Consequently, Learn Create Share has taken on a different emphasis during these early days of DMiC problem-solving:

• Learn: learning to work with others to be able to solve a Maths problem
• Create: creating Maths learning collaboratively with others in a small group while being thoughtful of others, respectful of their ideas and empathetic to their feelings
• Share: sharing Maths thinking orally as a cohesive group for the benefit of others

Naturally, opportunities for students to learn together in small collaborative groups have been provided across all learning areas to build positive relationships and encourage a sense of community responsibility.  Not only does this support the DMiC approach to learning Maths but is helping Room 11 make headway in its "waka".

As for my target learners, there are positive and observable shifts in their attitude towards Maths. I no longer hear talk of “I don’t like Maths”, “I suck at Maths”, “I’m dumb at Maths”. Maths is now viewed as a time when you work with others to talk about a problem and how it can be solved. Within the small social groupings, everyone brings different perspectives and knowledge about how to solve a problem. It is still very much a work-in-progress but collaboration is replacing suspicion and competitiveness now that people realise that there really is no top Maths group! It is noticeable that everyone is more confident to share their Maths thinking in front of others and, equally as important, most are much more confident to ask questions if they don’t fully understand what someone else is talking about.

As far as possible, Maths problems have been created to integrate number and strand, while balancing curriculum demands with student prior knowledge. Interestingly, a problem was posed recently to explore number flexibility and explicitly begin the transition from additive to multiplicative thinking (as many learners rely on skip-counting to solve multiplication problems).

This context with blocks of wood was chosen as real blocks of wood have been available for building bases in the playground recently. These objects have been the source of great enjoyment and frustration as groups of students build and knock down each other’s bases. Much talk at our first exploration of this problem centred around the fairness of the problem: Why can’t they put all the blocks together and make one big base? Why do they have different amounts? It would be fair if all the blocks were added together and then shared equally so there won’t be any arguments.

Rich oral language and the key competencies were clearly on display while the Maths in this problem was explored further on a second occasion. There are the beginnings of understanding that numbers can be broken up and recombined in different ways - and that some numbers are more flexible than others. Some connections have been made that using your times tables is more efficient for solving some problems than skip-counting - based on the arrays that were drawn to show how the flexible number 24 can be broken up in a range of different ways.

Measuring the fun in Maths

As part of our learning about how things move, I created a practical learning activity which integrated Inquiry, Reading, Writing and Maths. The purpose was to learn about some big Maths ideas (Shape and Measurement) and related vocabulary whilst making a model parachute based on the design of Leonardo da Vinci.

A number of challenges needed to be addressed to remove potential literacy barriers that could prevent some learners from engaging with the activity. After introducing the topic through a video, the initial focus for the whole class was exploring key vocabulary from the instructions. This was similar to launching a DMiC Maths problem to check everyone's understanding about the story of a problem. Learners then worked with buddies or in small groups to support each other as they tackled their challenge by reading the instructions, asking each other questions, checking understandings and taking risks to share their ideas and thinking.


Learners were required to accurately measure and cut out four equilateral triangles before combining these to create a square pyramid. Further precise measurement was needed to cut the correct length string (dental floss) for the parachute.

Nearly everyone created a parachute and many enjoyed experimenting (with varying degrees of success) how they could reduce and speed up the rate of fall by adding/ removing weight. Most learners could identify that they had used four plane shapes (equilateral triangles) to create a three-dimensional model of a square pyramid. Most developed an understanding that we measure angles using a standard unit of measurement (called degrees) with a protractor.



Overall, learners engaged positively with this integrated learning activity and worked well together. It seemed to offer the right amount of challenge whilst requiring cooperation and collaboration to achieve success. Additional support was provided for those who required it. Consensus was that it was a lot of fun and didn't really seem like Maths.

A Catalyst for Inquiry

The MIT-2018 cohort took time out today to share progress with our inquiries and collaborate at our second meeting at KPMG's headquarters in Auckland.

Our focus was digging deeper into our inquiries through Catalyst, a collaborative inquiry game created by Core Education. This board game has been developed around the OECD's Seven Principles of Learning. Each person was allocated a different questioning role within the game which proved an effective way for the group to drill down and ask those tricky questions of each other to challenge ideas and current thinking.

I found that the game created a supportive structure and environment in which to articulate and clarify my thinking about my inquiry.  The scanning and focusing stages of the game were particularly potent for me as they highlighted and reaffirmed the importance of learner well-being and engagement as we strive to optimise achievement. This may sound like common sense but it has strong connections to the goal of our school-wide professional Maths learning, Developing Mathematical Inquiry in a Learning Community.  Through the careful selection of Maths problems with contexts that relate to the immediate world of our learners and our community, I believe we are strengthening the balance and connections between well-being, engagement and achievement.


Catalyst image retrieved from: https://core-ed.org/shop/catalyst/

DMiC: Reflecting on a mentoring session

At a recent DMiC professional development session, images were explored as a medium for  creating culturally-responsive problems for Maths.  This siapo image was highlighted as an example of a problem which is accessible to all.  As Pt England had celebrated Fiafia 2018, its bi-annual cultural festival, at the end of Term 1, this image was selected as an authentic opportunity to begin our Maths problem-solving in Term 2, which coincided with a visit from our DMiC mentor.
























Planning prior to sharing this problem with learners considered what learners might notice in the image and how this might connect to conceptual understandings about patterns:

Working in groups of four, students shared and discussed their ideas and thinking about the image while only one of these learners was allocated the role of recorder. 





























It was wonderful to listen to the rich discussions taking place within the different groups.  I noticed a range of both everyday words and precise Maths vocabulary being used to describe the shapes and patterns within the image.

Having reorganised the groupings for Term 2, I also observed positive progress in attitude and engagement as students took more time to listen to each other and took turns to share their thinking within these social groupings. There is still much to work on within our DMiC Maths journey but in these early days there were plenty of reasons to celebrate the small successes, notably amazing individual learners who stepped up, took the lead in their group by showing empathy to enable the group to approach problem-solving in a positive way.

MIT-2018: Challenging My Thinking

An Achievement Challenge identified by the Manaiakalani Community of Learning is the need to lift achievement in Maths for all students in Years 1-13. This is the challenge I have selected for my Manaiakalani Innovative Teacher inquiry during 2018. My initial thoughts were that I would approach this challenge by creating a toolbox of rewindable, visible video resources to support student understandings about number strategies and Maths concepts in a Manaiakalani context. However, as we begin to explore Dr Bobbie Hunter's DMIC approach to teaching and learning in Maths at Pt England, I have been challenged in my thinking to change, alter and expand how I might approach accelerating achievement in Maths for my Year 4 and 5 learners. After a "Crazy 8s" design thinking activity, the following graphic shares how much my thinking has shifted:

Teaching As Inquiry 2018: Where do I start?

I am inquiring into accelerating Maths achievement as part of MIT-2018 and through Teaching As Inquiry 2018.  My inquiry focus is using video DLOs to create rewindable, visible teaching and learning opportunities.

My initial hunches are that Bobbie Hunter’s DMIC approach will support this goal through:

• Social groupings to build self-esteem about Maths and Key Competencies
• Culturally-responsive contexts
• Selection of rich problem-based tasks that are worth spending time on
• Vocabulary acquisition:
• Technical Maths terms
• Positive face-to-face language of friendly argumentation

What can I try? One idea that I have just introduced in the classroom is a word journal to record Maths terms to support/expand/explore language of Maths.

Some ideas to investigate at the beginning of the inquiry cycle:

• Integration of strand and number within the DMIC problem-solving approach for greater curriculum coverage.
• Acceleration workshops for target students, ie needs-based prior to socially-grouped problem-solving 2-3 times per week @ 8.30am or at lunchtime.
• Students sharing their thinking about Maths and their attitude to Maths with surveys to determine how this changes over time.
• Record student explanations of Maths terms to (hopefully) show increased oral ability and confidence to share their understandings.
• Record students sharing their thinking about big Maths ideas (strategy/solving problems) which can be used as rewindable, visible DLOs for others.

Challenging the status quo

To kick off our whole school PD for 2018, Dr Bobbie Hunter shared her research and expertise on Developing Mathematical Inquiry in a Learning Community (DMIC).

The latest data quoted by Bobbie reveal that only 26% of Māori students and 11% of Pasifika are achieving curriculum standards at Year 8.  Consequently, when students are not achieving at this level, it is difficult for them to engage with or achieve at Maths in college.  She put forward various reasons why this comes to pass: deficit theorising on the part of both teachers and students; a mismatch of Pasifika values and teacher values; barriers created through levelled ability groupings; and the lack of value given to Maths by students because they don't see how school maths relates to the real word and life after school.

According to Bobbie, we can address these alarming statistics by adopting into our practice the DMIC approach to teaching and learning in Maths: high expectations within an inclusive, culturally-responsive learning environment;  co-constructing Maths inquiry learning in social groupings; connecting rich mathematical thinking and reasoning with worthwhile tasks through explicit and expertly-framed mathematical practices.

To embark on a way forward, Bobbie began by unpacking the values central to Pasifika culture:

How do these match our own values?  In what respect do these differ from our own values?  What do we understand by the notion of service in a Pasifika context?  How does current Maths teaching and learning in our classes connect with DMIC?

As we launch into a new academic year, challenging the status quo in Maths presents itself as a goal for Teaching As Inquiry and a path to accelerating achievement.  I’m so looking forward to our future PD sessions with Dr Bobbie Hunter and dipping my toes into her DMIC sandbox to support this teaching and learning journey.