This blog aims to record and reflect on ways I demonstrate knowledge and application of Our Code, Our Standards as outlined by the New Zealand Education Council. This blog was created in 2018 and the intention is for it to continue to be used in years to follow.
My Math Learning Journey Planning a Math Programme
27 Māehe 2025
We started the day in break out rooms to share about our mahi kāika and how we have been going. An idea that I hadn't thought of, was the kids creating the learning outcomes. Mary had some great ideas. Another of hers is to allow students to work on their workbooks in Math No Problem. She also uses Canva to model and explain concepts. I might need to look in to this.
We are able to get a free upgrade on Canva - check how I can upgrade. Also look at Demoz for an online whiteboard. A favourite of Tiff's is Polypad. Mathagon is the website and Polypad is within that. There is something similar to Prototec on Mathagon.It's always going to be free.
Dorothy Burt - Planning a Maths Programme.
The learn part of Learn Create Share is strong when in the planning part of math and being deliberate about effective practice.
Directives from the Ministry, research, local curriculum feed into effective practice. Make learning and teaching visible. Hāpara is visibility of student learning for the teacher. Google Sites are about the learners having visibility of the learning programme. Too much time is wasted, so within our design, ensure learning is accessible for learners.
Engagement - Personalised Learning -
Four step method to access learning:
There should be no need for QR codes and passwords on paper for students to get to their learning. We have access to facilitators who can help with organising our site etc.
Three click rules. How long does it take for your learners to get to their learning? Think about the navigation and capture the tricky parts of learning content.
Use this when designing and updating the Google Site.
Go and have a look at Ngā Whetu o Manaiakalani for ideas and inspiration.
Make sure learners are taking screenshots of their online mahi. They could have a slide similar to the one I use for Prototec.
Every student must have access to content at their year level. Remember to incoude and use enablers and extenders. This will be helpful for some kāiako in my hub for their learners who are needing extension.
Although this is for junior levels, it is still relevant and a helpful guide for all teachers.
When planning a comprehnsive math programme, we need to integrate across strands. Number is ongoing and is integrated. Develop plans and lessons using teaching sequences. Consider how we can revisit and consolidate learning. When doing our long term plan, find ways to integrate math across different curriculum areas. What connections can we see and always ask, what math can we bring in?
This can help to map and ensure coverage.
Oh my gosh, this for Canva. It's what I wanted to use in class recently.
On reflection after using this tool, I wonder how my whole class would go with this. Maybe teaching in small groups first.
It has been acknowledged that these expectations are quite difficult to meet. Share planning with teacher aides to help utilise Teach the kids who need us the most and use teacher aides to consolidate etc.
Grouping Your Learners
The expectation is to teach to the year level. Flexible grouping is the key word for groupings.
I have often struggled with mixed ability grouping, but bhave been delving into this since using Math No problem. Who would have thought that being told to teach to the year level would prompt me into this? At first I was thinking, oh my goodness, but now it is working pretty well and has given ākonga some voice and awareness in their learning.
Next Steps: I need to get my planning onto my learning site through a task board. I've been struggling with how I will do this because of not yet having specific groups. I'll start with one for the majority and then an enablers slide.
Math Talks: Estimation
Ground rules are behaviours and expectations. Talk Moves are specific strategies to deepen student thinking and engagement.
A symbol for estimation - I didn't know this was a thing.
Next step: Introduce an estimation task for next week.
Viewing these images, ākonga can have discussions and explain their thinking about their estimations. This would be a great for practicing Ground Rules for Talk. I think my students would love these, especially if I use images of things they are excited about such as dinosaurs, Minecraft etc.
This activity was fun and I think it's a great way to introduce estimation. I'll add this to my Math learning for next week. Estimate before calculating. The supermarket is a perfect real life context.
Some learners have confusing around rounding and estimation. Rounding is a skill within estimation.
We need to ensure that ākonga understand when estimation is appropriate vs when calculation is needed.
Rich Math Tasks
I've been looking forward to this as I had a conversation about rich tasks and ended up getting confused.
Rich tasks are math problems that can be solved in different ways. They have a creative aspect to them.
Thinking can be extended through collaboration and sharing. A variety of problem types is beneficial and ensure that problems are balanced. Students will need scaffolding and support, so be mindful of cognitive load.
Gather prior knowledge about the content and ask questions to clarify and consolidate prior knowledge. Read the question and turn and talk about the task. How can we rephrase the question? Bring in estimation.
It takes time to understand and use these practices.
Pre-planning could be done at hub/syndicate level.
Use the learning intentions and success criteria at the end of the session to reflect on the task and level of understanding.
From your anticipating and monitoringof their discussions, choose an idea that is useful to explain further (addressing misconceptions), based on the most important strategies or number knowledge learners need to know If you’re not sure which ideas are the most important, choose from the teaching sequences!
We created a bank of rich tasks. Insert
Monitoring, Selecting, Sequencing, Connecting
Have equipment ready and available prior to starting the lesson. (Have a look at the Think Through Template).
Recap the Ground Rules For Talk to make sure I am not just dealing with behaviour etc.
We are aware of who our not so confident kids are, so giving roles can allow them to engage and contribute their ideas. We are wanting to create opportunities to succeed. Also, having the mindset that we are smarter together. Rich tasks are easier to implement when we have done the ground work before the lesson.
Something new to me...
This is a digital modelling book. At the moment, I don't feel confident in my planning to explore this yet.
Selecting
Teacher selects particular learners to share their thinking with the rest of the class.
The selection is guided by the maths goal of the lesson
Sequencing
Make purposeful choices about the order in which students’ thinking is shared back
Sequencing anticipated responses is key to the lesson
There is not one right way to sequence - it depends on the goals for the lesson
Connecting
Teacher helps students draw connections between their solutions as well as the key mathematical ideas in the lesson
Student presentations build on each other
When looking for rich tasks, we are wanting tasks that generate conversation and discussion.
Allow time for learners to do the rich tasks.
Independent Learning
We need to keep track of student progress. The teacher workbook has progressions, although they don't align to the curriculum yet.
Make sure we aren't just doing 'busy work'.
If we give students an online task and don't actually follow-up and give kids time to share, we are wasting their time and they are not effective.
Using a mahi tracker sheet helps to gather evidence of student learning. I used one for Literacy last year which was great, but I didn't sustain it. The positive thing about that was that students asked where it was.
I need to remember to teach to the curriculum and not just following the books of Math No Problem. I do think I viewed the books in that way for a while there.
I feel a lot clearer about what rich tasks are, which is great because it was something that I wanted to delve into.
I feel like I have been a bit slack with my mahi kāika, among other things, so my goal is to create the time and space to get the mahi done before our next session.
My class of Year 6 students completed a learner profile for me to gather information about attitudes, confidence and engagement in Mathematics.
CONFIDENCE
I was pleased to see that the majority of ākonga feel confident in math. There is a small group that don't, so they will be my target students with a focus on developing their confidence. I will also do some work in class around mindsets and learning conversations.
CHALLENGE
This made me laugh. The question was about the level of difficulty of math problems and there are quite a few of my students who prefer easy problems.
I am really interested in seeing how students answer this question at the end of the year as at the time of the survey, we hadn't done a huge amount of Math. I would be wanting more scores of 4 and none in 1 and 2.
This was another interesting graph and showed me that just over half of my students say they prefer working on their own. We have been doing quite a bit of collaboration and having learning conversations in groups since this survey was done, and the majority seem to enjoy that. The end of year survey will be interesting to see if any of these preferences shift.
I used this graph as part of my introduction to Ground Rules for Talk in math and was anticipating discussion suggesting that students should do more math at home, but nobody voiced that opinion. Since this survey, we have been doing Mahi Kāika/Home Learning and basic facts has been part of it.
I intend to do the survey in Term Four and compare the findings. There are definite shifts that I would like to see, so I have quite a bit of mahi ahead.
Numicon, a multi-sensory approach to teaching mathematics, was developed from a classroom-based research project by Ruth Atkinson, Romey Tacon, and Dr. Tony Wing, aiming to improve children's understanding of arithmetic through visual, structured imagery.
Purpose:
The researchers, Atkinson, Tacon, and Wing, sought to understand why some children struggled with arithmetic despite excelling in other areas.
Key Principles:
Concrete-Pictorial-Abstract:The Numicon approach is based on this proven method, where children first explore math concepts with concrete objects (Numicon Shapes), then move to pictorial representations, and finally, abstract symbols.
Multi-Sensory Learning:Numicon encourages learning through seeing, feeling, and manipulating the shapes, making math more accessible for diverse learners.
Pattern Recognition:The shapes are designed to help children identify and understand patterns, which is crucial for developing a strong sense of number and mathematical relationships.
Fluency and Reasoning:Numicon aims to develop both fluency in basic math skills and the ability to reason mathematically, using concrete objects and language to explain and justify thinking.
Self-assessment task - Looking at the different shapes. We self-assessed to gauge where we are as far as our Numicon knowledge goes. This was a quick and easy way for the presenters to notice where the group are. This could be used in class. Numicon is about what you see and notice.
What is Math?
We had a discussion about the number 5 and what it makes different people think of.
Numbers are an abstract concept. We attach meaning. There are many different perceptions and understandings of what 5 is. What doea that mean for our learners?
Te Matāiaho - The New Zealand Curriuclum
What is Numicon?
It is more than just manipulatives, it emphasises three key aspects of doing math. Communicating mathematically, exploring relationships, and generalising.
Communicating Mathematics
We are always looking and listening to see what our ākonga are thinking and what prior knowledge they have.
We need to offer illustrations that help ākong to see and feel how numbers for together.
Use language like, if, then, what about or or?
Getting Started - Base Boards
These have 100 spaces. As children get older, you could use the printed version instead of the baseboard.
How many 2s did you use How many 5s? How many 10s? Hoew many shapes altogether? Could you use it again?
Look at shapes, introduce the names and then the numbers.
Good activity: Putting the shapes into a row, add the one shape to a range of them, what happens when we add and then take away?
Exploring Generalisation.
Two odd numbers makes an even.
Using Feely Bags
What can feel? What do you notice? What do you see?
Can you find the largest? Smallest? Describe it. One less one more?
Teen Numbers
Commutative Property
Equivalence
Equivalence doesn't mean the same thing as equal. We use the word same instead of equivalent - unfortunately, equivalence doesn't mean, the same.
CPA Concrete, Pictorial and Abstract
We go between concrete and pictorial and when we are showing fluency, we can show understanding and can work in the abstract. Capable learners can move through to the abstract stage quite quickly.
It doesn't matter how we got there, as long as we can explain how we did so.
Attach the value to the numeral.
Subitising features quite a lot in the new curriculum. There are 55 sight facts (number bonds). Subitizing is the ability to instantly recognise the number of objects in a small group without needing to count them individually. Some people can subitise straight away and others can't. Some initially can't, but can get there with practice.
Dyscalculia is a specific learning disability that makes it difficult to understand and work woth numbers and math concepts, affecting a person's ability to learn and apply mathematical skills.
Make the pattern, see the pattern and know the pattern, so we are not reliant on counting when working with larger numbers.
Addition and Subtraction
Use number sandwiches helps children make connections with how many ways you can make different numbers.
Getting Started
Be mindful of the attitudes and mindset of children in the senior school. Use assessment data to make decisions. Some gaps will need to be filled. You can start at the expected level and adjust, depending on your students.
Big ideas section is used to plug gaps and are currently being used as an intervention in high schools.
Planning
Units of work are planned for about a week, not going over two weeks. unit plans are done with the expectation that teachers will read them.
There is a clear scope and sequence. Firm foundations are different to other units.
As the first activity, teach the language and what the words actually mean. Learning opportunities are the learning intentions.
Addition and subtraction go together - doing and undoing.
Review -Revisit - Recall
Doing something once is not mastery. The assessment sheet can be downloaded from Numicon.co.nz
Read and understand the content.
Consider the week's sequence of lessons
Know the learners
Use the assessment opportunities
Flexible groupings.
Keep moving and don't stay too long on one thing.
Numicon - Mastery approach to teaching.
Each coloured band is one week of teaching and learning.
This is great for my learners at the moment as we have struggled a bit with using the Math No Problem workbooks, and understanding what the question is actually asking and being able to select an operation to solve the problem. I think it is also great for my ākonga who are currently struggling with the Year 6 content.
Oh my gosh...the interactive whiteboard.
My Wonderings:
-Data entry. It looks like a lot. Is it able to be on Hero and give us the same information at a glance? Looks like it.
-How can I use Numicon to support my learners and align with Math No Problem?