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.

MIT 2018 @ KPMG: Sharing progress in our thinking

It was wonderful to reconnect with our fellow Manaiakalani Innovative Teachers today at our first session at KPMG's head office to further challenge our thinking in relation to our inquiries: As we have faced the reality of the cohort of learners (and teachers) we are spending 2018 with, how has the thinking you developed ... gelled when ‘the rubber hit the road’?

My thinking, ponderings and wonderings returned to my identified problem: the need to lift the achievement in Maths for all students in Years 1-13 within the Manaiakalani Community of Learning.  What does this mean for my inquiry? Am I on the right track?  What is the most effective way of getting our waka to move through the water faster?

While getting to know my learners and gathering data for my target students, it has become evident that the language of Maths needs building up in order that learners can express and explain their mathematical ideas and thinking appropriately and clearly.  For example, when asked to find a quarter of a set, two of my target students asked "What is a quarter?"  In answer to the same question, another explained that the answer is 4 because a quarter is written 1/4.  These examples have thus caused me to return to the problem and progress my thinking by choosing to focus on four areas, the first of which is the language of Maths:























This focus on the language of Maths will also build support for our school-wide Teaching As Inquiry.

Now that my thinking has progressed and clarified, my next step in the inquiry process is to prototype a digital framework to support my learners acquiring the language of Maths.

Teaching As Inquiry: Student Voice

To kick off my MIT-2018 inquiry and the Teaching As Inquiry cycle for 2018, I have explored learner attitude to Maths to gain student voice through oral language. The result is Room 11's movie contribution to Pt England School's daily news network, PENN, for Term 1 in which learners share what they like about Maths, with a few examples of when they use Maths outside school.


While listening to these Year 4 and 5 learners share their ideas and thinking about why they like Maths, I was struck by the common words and themes of "cool" and "fun". While their genuinely positive attitude was evident and heart-warming, many learners found it difficult to expand upon their one word or short phrase answers to articulate their thinking further. Through questioning, scaffolding and some paired or small group discussion, some learners were able to add to their ideas to share the "because" part of their thinking.

What does this mean for my inquiries for 2018?

• Using the structure of the Talk Moves for oral language to create a safe and positive environment in which learners focus on ideas, thinking and friendly argumentation.
• Ongoing oral language activities to allow all learners to feel more confident sharing their thinking with others.
• Activities to build student capacity to use the language of Maths.
• Oral language and Maths problems that strengthen student understandings of the connections between Maths at school, home and in the real world.

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.

Concluding Teaching As Inquiry 2017

During 2017 I have been inquiring into how I can make use of small group teaching and learning to accelerate shift in Mathematics. To meet this focus, teaching and learning of Maths in Room 9 this year has been predominantly achieved through 33 students being organised into four levelled groups (which have been reorganised during the year based on ongoing assessment).

My initial target group was selected from amongst those learners who were Well Below National Standard based on assessment data from the end of Year 4.  Mid-year data determined that nine students were working towards the National Standard expected at the end of Year 5 while 24 students were working Well Below the National Standard expected at the end of Year 5.  Based on this data and following discussions with colleagues, my target group was changed to focus on those nine students who were working towards National Standard. However, one learner left Pt England early in Term 4; there is no comparative data for one learner who arrived at Pt England during Term 1.

• During the year there has been a strong focus on number knowledge and basic facts through daily online Maths activities (Xtra Maths and Maths Whizz) and teacher-created resources to support number knowledge acquisition, both digital and physical resources.  The rationale is a bit like the chicken and egg scenario: what came first?  How can learners move from  skip-counting or repeated addition to using times table knowledge to solve multiplication problems if they don’t know their times tables?  It is tricky for learners to make that shift from Stage 4 to E5 (which they are expected to achieve after being at school for three years) until multiplicative thinking is used.  Students are expected to be working at Stage E6 of the Numeracy Project by the end of Year 5.  Some learners don’t see the need to learn their times tables and, consequently develop their multiplicative thinking, as they see themselves as managing quite happily with skip-counting.
• From my observations and data, these target students know a greater range of times tables with confidence and are beginning to use this knowledge to solve problems.
• Outside my target group, some students find it difficult to work and learn independently to complete follow-up tasks.
• Literacy is a barrier to learning Maths for some: some learners need support to complete independent follow-up tasks.  Literacy is also a barrier to completing PAT standardised Maths testing: students can pick out the numerals/numbers but don’t necessarily understand the problem to know how they should manipulate the numbers.
• The Key Competencies of Managing Self and Relating to Others play a major part in teaching and learning. It is challenging for a group to function cohesively if learners are still learning to manage themselves to listen, respond appropriately and take turns when sharing ideas and materials.

There are some small positives to be taken from my inquiry:

• Two of my target group of seven are at the National Standard expected at the end of Year 5.
• The difference in PAT scale score from the beginning of 2017 to year-end 2017 is consistent with the progress made in Maths based on GLOSS data.

• Some small shifts of accelerated achievement across the three domains are evident from GLOSS assessment data.

• A teaching-learning balance between number knowledge and strategy was achieved during the year.
• All of the target group have improved their times table number knowledge significantly and are beginning to make connections between times tables and problem-solving.

Having looked closely at the data as we conclude the year, I feel disappointed that more steps were not climbed towards the top of the hill. I have been reminded that learning is not a consistent upward trend towards the top of the hill: students learn and consolidate understandings at their own pace and in their own way; life events and attitude to learning impact achievement. I am beginning to wonder if Maths succumbs to a summer drop-off as can happen in reading.  I believe there is much more to explore and inquire into in order to accelerate and sustain achievement in Maths and I am looking forward to inquiring into this further as part of the Manaiakalani Innovative Teacher initiative during 2018.

Visible Teaching and Learning enables accelerated shift

At Pt England's Manaiakalani Staff Meeting this afternoon, we were urged by Dorothy Burt to celebrate the accelerated shift of one learner.

As we approach the end of the year, it is timely to reflect on  the visibility of our teaching and learning and the part this played in achieving that accelerated shift.

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: Term 3 Reflection

Reflecting on inquiry and practice often creates internal tension: What am I doing that is making a difference? What is important? Am I doing enough for my learners? What went well today?  How can I improve that tomorrow? What can I do to promote learner agency? How can I tighten routines in the learning space?

After the self-talk and deliberations, it was refreshing to listen to colleagues as they presented their latest Teaching As Inquiry reflections. How similar many of the challenges we face: development of oral language to express mathematical concepts, supporting reading to enable comprehension of written maths problems, enabling learners to make that shift from additive thinking and skip-counting to multiplicative thinking.

Overall, what a powerful and positive way to take time to stop, smell the roses and count our blessings - the baby steps we are taking.

Exploring our CoL's collaborative inquiries

At yesterday's staff meeting, we were given the opportunity to explore how the leaders of learning within our Manaiakalani Community of Learning (CoL) are inquiring into the achievement challenges facing our learners.

I identified Achievement Challenge 6 (Lift the achievement in maths for all students in Years 1-13) as an area of interest as it relates to my teaching as inquiry.  It was inspiring to read about the research, hypotheses and reflections of Paula @ Glen Taylor to gain an insight into her collaborative inquiry.

Link to Paula's blog
Link to my comment

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.

"Do your best!" says Ned

At a special assembly yesterday we were entertained by the NED show, a programme championing character education:

As well as being a positive mantra containing valuable messages for all our learners, I believe these messages are pertinent for me as a teacher too.  Am I doing my best?  Do I encourage learners to try their best?

We are halfway through our school year and it is time to reflect on the cycle of teaching and learning in Room 9, with particular reference to my Maths target learners.  My seven target learners have made mixed progress during the first half of the year.  Do I continue to focus on these learners?  Based on what I know now (after six months of building relationships, knowledge of my learners and knowledge of their learning), do I need to adjust my group of target learners to try my best to make a difference for others?

Looking at my Maths class overall, there are 33 learners: 9 are working towards the National Standard expected at the end of Year 5; and 24 are working well below the National Standard expected at the end of Year 5.  I have reorganised my Maths groups to accommodate individual learner needs based on achievement during Terms 1 and 2.  Coincidentally, within these new groupings, the social dynamics have changed and there is early evidence that learners are becoming confident to communicate with and learn alongside a range of other learners.

So, where does this leave my target learners?  Who are my priorities if I am trying to accelerate the achievement of 33 learners so that they are closer to working at National Standard at the end of Year 5?  After much pondering and wondering, I have identified those nine students who are currently working towards National Standard at the end of Year 5 as my target learners for the remainder of the year.  My reasoning: by attacking and filling identified learning gaps, building number knowledge and explicitly teaching strategies to solve multiplication and proportion/ratio problems, can these target learners move closer to working at National Standard by the end of Year 5?  As these nine learners form one Maths group, my next step is to identify their learning gaps, particularly in Geometry & Measurement and Statistics, to support them as a group to become well-rounded and confident Year 5 mathematicians.

In order for me to do my best with focus and persistence, I think it’s time to go and buy a NED yo-yo!

Teaching As Inquiry 2017: Term 1 Reflection

A term into my inquiry for 2017, my thinking and reflections about this inquiry are presented here as planning for teaching and learning in Maths during Term 2 commences.

Teaching As Inquiry 2017: An introduction

In order for young people to become confident, connected, actively-involved lifelong learners, every child needs a positive attitude and growth mindset towards Maths and their own ability to solve everyday Maths problems by manipulating numbers.

During 2017, I am inquiring into how I can make use of small group teaching and learning during Maths to accelerate student achievement in Maths.  A target group of learners who were below or well below National Standard in Mathematics at the end of 2016 have been selected for this purpose.  Within this context, how will I organise learning experiences and follow-up activities to support the acquisition of number knowledge and use of different strategies by these learners so that they are able to begin solving problems demonstrating part-whole and multiplicative thinking?

Linking my things: a ThingLink for Spark-MIT 2016

To help join the dots within my Spark-MIT inquiry 2016, I have created a ThingLink to share my inquiry so far in one Digital Learning Object (DLO). Using ThingLink for the first time to create this DLO reminds me of the learners in Room 10 when they are faced with new learning - they challenge themselves and ultimately persevere to make sense and meaning!

Spark-MIT: Sharing at a staff meeting

On Tuesday there was an opportunity to share my hui and uLearn presentation at a Ruapotaka staff meeting to update my colleagues about my Spark-MIT inquiry: what have I discovered while involving and engaging whānau in their children's learning while trying to cause accelerated gains in their children's reading?

Manaiakalani 1:1 Digital Immersion 2015: Teaching as Inquiry