New Mathematics Curriculum

Dr Craig Hansen

Addressing Royal Society Te Aparangi report 

Use recommendations to

- improve achievement

- create more equitable learning opportunities

Supporting NZ teachers

Recognise the dedication of NZ teachers and aim to support them further 

Providing Clear Guidance for Teaching

Clarify what and how to teach at each level, to achieve better outcomes for all students

Positive Relationship

experiences, encouraged, see patterns and logic

Poor Relationship

Never had the time or chance to understand 

The teacher spoke too fast, and many in the class were unable to do the task

Parents tried to teach and at times confused students

Need to Foster a Positive Relationship with Maths

Students need to know what they need help with  and what they need to learn next

Students' confidence in teaching maths

Understand Know Do

Why the change? Lifting progress in achievement

The learning that matters!

Progress outcome - Understand Know Do (UKD)

UNDERSTAND - stays the same

Know and Do changes - per curiulum area

UKD

What a great maths lesson should look like, from planning to gaining understanding, to using tasks that students can connect to and be challenged by. Creating Light bulb moments!

Make connections to, and for understanding

Real learning for the real world

Not just maths - connections to the real world

Cultural roots are used to make connections

Students having the chance to say I don't get it

Hurdle - students knowing what they are being asked to do

Making links to storybooks

The student is in the middle of symbols, reasoning, and is in a cycle, engaging with learning

The Purpose Statement is the philosophy/vision/ideology statement that drives the UKD

Structure is the out working of the purpose

Retrieval -

Know describes the meaningful and important mathematical and statistical concepts and procedures through which students develop an understanding of the

big ideas.

Do describes the processes that are fundamental to all mathematical and statistical activities and that underpin students’ learning of the big ideas, concepts, and

procedures.

Understanding describes the deep and enduring mathematical and statistical big ideas students develop over phases 1–5.

Definitions

 Conceptual Understanding 

 Procedural Fluency 

Choosing product - Practise Practise Practise Practise

Connections between the Purpose Statement and the Structure of Mathematics and Statistics

In the mathematics and statistics learning area, students learn about

and appreciate the power of symbolic representation, reasoning, and

abstraction.

Students engage with mathematics and statistics through the exploration of problems, patterns, and trends and appreciate the everyday value of this learning in many areas of their lives.

Throughout their learning, students engage with diverse perspectives as they apply their mathematical and statistical understandings. Learning in mathematics and statistics builds literacy by developing students’ skills in oral and written communication, reasoning, and comprehension. The learning area opens pathways into a wide range of industries that rely on mathematical and statistical knowledge and

reasoning.

Each phase has:

› A progress outcome describing what students understand, know, and can do by the end of the phase

› An introduction to the teaching sequence highlighting how to teach during this particular phase

› A year-by-year teaching sequence highlighting what to teach in the phase, along with teaching considerations for particular aspects of content.

Progress Outcomes - Learning objectives - students' experiences of their learning is at the beginning of each phase

Science of Learning

Phase 2 - 

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Teaching at our year level

Challenges

• Gaps from previous years

• Needing to go to phase 1 to find the thread to plug the gaps

• Teaching 2-year levels

Benefits

• Exposure to appropriate learning for their year

• Tuakana Teina opportunities

• Ability to move, increases the ceiling - extend through rich tasks.

• Thinking deeply and working with other to solve meaningful problems

PHASE 2 - Teaching Sequence

Four Components - 

Explicit Teaching

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I do, we do, you do - Interactive - Carefully Sequences

    Warm Up

    Examples to break down - walking around and pulling together opportunities to teach/reteach

    Connect Maths with links across learning

    Plan Ways to consolidate learning

Positive Relationship with Maths and Stats

    Encourage curiosity - 

    Highlight thinking

    

Rich Tasks

    Plan to explore situations that are realteable

    Meaningful problem- solving and investigation experiences, designed to invoke curiosity and engagement

    

Communication in Maths and Stats 

Celebrating Success and those who ask for help

Unpacking the Sequence

Teaching Sequence Statement (Not the Learning Outcomes)

Teaching Considerations - (Tasks) is the floor low enough, and how can I raise the ceiling to challenge others?) - Pitching within the Year level.

Strand is Number Subtrand is Number structure or Operations. There is a thread for each year level.

Rational Numbers = percentages, decimals, fractions

Over the next 2 years, there should be less discrepancy as the curriculum becomes more consistent 

Identify areas of need and then help students catch up fast.

Be the car on the race track, when pulling into the pit stop, filling in the thread they need for that learning! Not all the gaps, as then in the garage for too long and miss out on current content.

This curriculum is asking teachers to expose students to where they need to be, providing them the opportunity to be at their level. 

He waka he eke noa

In our Phase Groups 

How does the phase move through the stages? 

Operations

Thread = Add and subtract two- and three-digit numbers

Phase 1

During the first year:

• explore addition facts to 10 and corresponding facts in subtractions, doubles and halves, family of facts

During the second year:

• recall facts up to 10

• explore add/sub facts to 20 + double and halves, family of facts

During the third year:

• recall facts to 20

Phase 2

during Year 4:

• add/sub 2/3 digit numbers

during Year 5:

• add/sub whole numbers upr to 10 000

during Year 6:

• add/ subtract any whole numbers

Phase 3

during Year 7: (disappears/ but is practised with)

• use estimation to solve calculations 

How to you get students to engage - Enablers

Extenders - Used to challenge students 

Data Reflections

 Data Reflections - Cluster Schools

Checking out the goals for the Cluster first is a great way to orientate our focus and update those of us who are new or in my case returning to the cluster.

This book came out in 2019 and reflects what we, as great teachers, are trying to do: teaching to improve student achievement and progress. We're not just aiming for students to make the usual year's progress; we're talking about making two years' progress in a year.

Russell Bishop has recently released Leading to the North-East. The Government has used this research to help develop the Common Practise Model being implemented across Aotearoa.

As Leaders how do we make sure teachers have time to do what needs to be done to maintain the integrity of teaching and making sure it is explicit.

Looking at the Network data if students stay in a Network school for 3 years they achieve above the norm. This can be seen with the e6 data points over these 3 years.  Unfortunately, students made less progress last year in the cluster than they had in previous years. 

In Writing are we still:

• Using explicit instructions?
• Are we teaching how to write using different genres, structures, and descriptions?

This is the summary of the Writing. We also discussed having genuine experiences for students to help build their writing understanding. By immersing them in the bush they will understand how to use their sense to describe.

In Reading we noticed: We need to get on to our intervention not just talk about it. 

Our Y6 students are tracking slightly below the norm but on the same trajectory. The Years 7-8 data appear to look better however there is only a very small cohort. How intentionally are we teaching, How do we ensure the Pillars of Practice are being upheld after RPI.

In Maths we discuss the changes for PAT leading into this year's round of data collection. The norms have changed.

LCS - Learning happens all the time!

 Learning happens all the time how can we take advantage of that for Students?

We have just had the Ako Hiko Learn Create Share Staff Meeting with a focus on LEARN.

Phil took us back to the Kaupapa of Ako Hiko and Manaiakalani:

Connected | Rangitamiro, Empowered | Rangitū and our focus for the day

UBIQUITOUS | RANGIWHĀ & VISIBLE | ARIARI 

We watched this clip.

During the second viewing, we had to identify blocks the team made so the returner could succeed. 

With this in mind that the runner is the student and as teachers we are to stop or limit the barriers that hinder learning.

In order to make learning ubiquitous it needs to be rewindable, not just available online, but workable. So not just a list of questions where the book is at school. Maybe include a video on the same topic, and a copy of the book with audio so a student can listen if they prefer.

We had the opportunity to look at Class onAir and how teachers their make lessons rewindable for other teachers and students through their class site. A wonderful opportunity as you can search lessons for age or topic.

And I thought this was something to think on!

Words - Can you make them make sense in Maths?

What do we know from reading that we can apply to maths?

• We can find the key ideas or information (What we already know after reading the question)
• We can find out what we need to know!

In this particular lesson, students are being shown how to use a tree diagram to organise the choices or options available from the question.

Click on the image to go to Class onAir.

Finding Angles

 I have enjoyed setting out to find new ways to inspire students in Maths. After seeing tape and student writing on tables, I want to have a go in my class. Using Masking tape I taped a range of angles across the student tables (grateful I teach math first thing in the morning). They were all very intrigued to find out what we would be learning about that week.

Check out my Class on Air Lesson to find out more. 

A quick summary, students investigated complementary angles, how angles around a point add up to 360 and could make their own assessments and justify their thinking.

Enrich Math - Capacity

 Popcorn Capacity

What a great way to start a maths lesson. The students talked about capacity and predicted, guessing which container would hold more. They got to make the containers to verify their thinking. The best part according to the students was when I brought out the POPCORN! Check out this episode of Class onAir to see what happened.

What I like about using these tasks is I can engage a range of students with maths and then teach them the relevant skills they need to move to the next step, such as using formulas to work out the capacity on a container.

Talk Moves -

After using rich maths activities and starting the talk, now we need to learn to dig deeper and get students to say what they see. As 

Having looked at a couple of my Class OnAir Videos, I realise that the more talk the students do the more they learn. So to me this is very important part of the lesson.

This is an important idea to grasp, as we want students to learn and remember new concepts so we need to give them opportunities to discuss, experience and teach others.

To Help Students with discussions here are some easy phrases to encourage more talk include:

• "What else?"
• "Tell me more..."
• "And.."

I look forward to working out more phrases to encourage discussion and to encourage to student to think deeper.

Although this was brought to my attention again through Math PD it is true in all areas of learning.

Enrich Maths - Decimals

 Talofa

This week's session for Class on Air was in Maths, one of my favourite subjects. The fact we can give students real-world problems and then dive into the patterns and understanding behind in through maths is inspiring and a lot of fun. Click on either image to find out more.

Productive Struggle

 Reflection on Co-teaching in Maths

What will you take away from the co-teaching?

        How do we know it is half e.g. 9+9=18 - numbers are the same

        Think about the answers/anticipate student responses, to be mindful of misconceptions and what will         help direct and redirect students.

        Continue to pitch at level 4/5 and put in place just in time workshops.

What will you do differently next time?

Thinking from the beginning of the year:

• high expectations teaching
• acceleration vs remediation = planning, how can we make this less not more.
• key role of formative assessment - this leads to productive struggle!

Unproductive Struggle - weight lifting - too heavy or not heavy enough 

Spotter - assess the struggle, and have their back if it is too much of a struggle for them

             

Productive Struggle is better than unproductive and looped with feedback gives us results.

Discuss and model with students - How to work in a group, helping students to get results with their learning. 

Click on the image to see more.

Something to remember is - 

Better than formative assessment is monitoring feedback and scaffolding - Dylan William

What I want to know is how to get the discussion going to help students develop understanding rather than just telling the answer or what to think!

Grow our Math Brain

 To help grow our brains, we need to be asking questions and use productive struggle.

What do you notice? What do you wonder? 

These two questions are a great place to start and as students answer, ask what else soliciting other answers from other students. 

3 Act Task such as a Video, create a provocation, giving students the chance to notice to wonder even question.

Progress Tools Ministry have created to help the Learning Progression. or the PaCT - Progress and Consistency Tool.

There are 8 Aspects of the Maths Framework:

1. Additive Thinking
2. Multiplicative Thinking
3. Patterns and Relationships
4. Using symbols and expressions to think mathematically
5. Geometric Thinking
6. Measurement Sense
7. Statistical Investigations
8. Interpreting Statistical and Chance Situations

The Framework clarifies expectations in Mathematics to help stop negative talk. I can't do it Yet! Using complex problems we are encouraging students to take risks.

The Reader and Writer who is struggling, we look at the student not just what they produce to help them accelerate. So we need to know how a mathematician operates.

Maths Mahi and Expectations

Increasing Acceleration in Maths

High expectations are essential in all learning areas, as students need to be involved in the tasks to find success. Games and hands-on investigations can help to achieve this. Students are often unable to see the purpose or relevance to their daily lives to work in textbooks. 

The focus is not on remediation, informing students they are behind. The focus is on acceleration. Skills that are needed are taught using a just in time strategy, then utilised straight away, giving students a sense of power. The tasks are constantly relevant and inspire students to engage. The pace of learning is maintained and students feel they are part of the core class not lagging behind.

As a group, we all had 10 seconds to look at this image and then describe what we saw.

   

Initially, teachers were reluctant to share their ideas. Sound familiar? All ideas were accepted with no judgement, just the question 'What else?'

Ways we can ignite curiosity with Maths:

• 
  Photos, images, posters
• Saying, Riddles
• Meme
• Video
• Guest Speaker
• Article
• Facebook Post

These two images created a lot of discussion in my class the first was an introduction to decimals and what was wrong with the sign. The second was used to introduce fractions before heading into decimals.

Acceleration Framework

1. Generate Thinking
2. Clearly Articulate learning and expectations
3. Scaffold, practise skills
4. Introduce vocabulary, and review Prior knowledge
5. Dip into new concepts
6. Conduct Formative Assessment

To help with Vocab use a Tip Chart (Term Information Picture) best when student-driven.

We need to change the disposition of teachers and students towards maths before attainment will change.

Numicon - Uses and Usefulness

We started using Numicon in our Junior School to help bolster numeracy in our school.

I could see how it was useful for adding, making tens, and adding with ten. I was told it is so much more but, as I only had access to the coloured number shapes, so it was hard to believe.

Today 

The Numicon number shapes are weighted. If you put the shapes for 2 and 2 together on the scales, it weighs the same as the 1 and 3 which is the same as the shape 4. The new Cuisenaire rods are also weighted in this way.

 

Numicon is great to help students to move from the concrete use of materials to the idea of imaging for the more abstract concepts.

As for all new learners in a topic, the mathematical language is often lacking. With Numicon students can show their understanding through manipulation of the shapes. Group discussion helps students to learn the language through talking. 

 

Students and teachers often learn while they are fiddling. A teacher can be explaining the method to the group while they are moving the shapes. While reinforcing the concept to a slower learner, the group can continue to work on other examples to show their understanding.

The more they touch the more they enjoy, the more they enjoy the more they engage.

 

Breaking Barriers - Teaching Handbook

Assessment Booklet