Maths- Rob Proffit-White

Manaiakalani Refresh with Angela

Ako ~ Hanga ~ Tohatoha

Ako ~ Learn - What is quality teaching and learning ? (RAT) - Recognise Amplify Turbocharge

New Zealand Teaching Standards 2026

Effective Teaching Practice = Accelerated Learning

R.A.T.E - Recognise Amplify Turbocharge = Effective Practice

Knowing the success criteria is essential for student understanding as well as effective feedback. It answers the question: "What does success look like?" 

When students co-construct these, it directly activates their agency into the mahi.

Teachers need to know what is being learned and what constitutes success. There needs to be aclear difference between a Learning Outcome and an Activity

Digital technology is not just a tool!

Great Teaching + Digital Affordances = Acceleration

Visible Teaching Practices
Learning Objectives vs Activity - what is the difference?
Rewindable Learning

Hanga ~ Create 

Creative skills helps student become better problem solvers, communicators and collaborators. 

MaryAnn F. Kohl (2008) describes what creativity looks like in young children when she states, "Creativity focuses on the process of forming original ideas through exploration and discovery.

In children, creativity develops from their experiences with the process, rather than concern for the finished product. Creativity is not to be confused with talent, skill, or intelligence. Creativity is not about doing something better than others, it is about thinking, exploring, discovering, and imagining".

Children need to be creators, not just consumers. 

Tohatoha ~ Share

We don’t need to be psychologists to understand WHY we share.

We share to make connections with people.

Sharing requires an audience. And not just any old audience - an authentic audience

Most of us have probably experienced that occasion when we were sharing and the other person or people were clearly not interested! As teachers, one of the strangest things we have done over time is ask learners to write for an audience - when the only audience was a teacher with a red pen. Not an authentic audience.

Definition of Authentic Audience: People who choose to listen to you

There are two kinds of audience:

Compulsory - forced to listen to you

Eg when a child reads their work to the class (class has no choice), assembly (classes are forced to be there)

An authentic audience - one who chooses to listen to you

Eg has the remote in their hand, the power to click away quickly, one who pays to be there

Connected learners share.

Formative and Summative Assessment

More Rob Profitt-White

Creating Rich Routines

In pairs, give out dice - 2 dice to some, 4 to others, 6 to others. 

1. Pairs create either ones, tens, or hundreds depending on how many dice they have. 
2. What's one more, what's one less?
3. Add them together, subtract one from the other.
4. Show them both on a number line.

Lucky Dice Game

100s board. Dice. Select a number. 

Roll a dice. Question to pose - will skip counting in that number you rolled land you on that number you select? If it does land on their number, they get a point. If it doesn't, I get the point.

Notes to my future forgetful self

- a notebook where kids can write things to job their memories - non examples etc.

Resource books are procedurally based!

Elements of a good maths programme - Knowing (blue) Revisiting (yellow) Doing (green)

Knowing (blue) - procedural. Worksheets. Oxford books.

Doing (green) - DMIC 

Revisiting (yellow) -moveNprove, revisitNretrain, discussNdefend, recallNreason

moveNprove is related to the unit - linked to the anchor task.

revisitNretain - scrap paper question. Short, purposeful, fluency quiz

discussNdefend - other strands

recallNreason - academic games to monitor fluency

Where are we at at HPS

2026 - Perfect the yellow!  Have our negotiables - what must we do? How? When? 

Rob Proffitt-White PLD

MORE changes in the curriculum refresh! 

UKD is now woven through (code word = removed)

What's the purpose of these recent changes? Turn the curriculum to a list of skills that can be tested at the end of the year!

All curriculum are designed for the lowest common denominator teacher. Don't interpret the curriculum too literally at the moment.  

Knowledge

The facts, concepts, principles, and theories to teach

Practices

The skills, strategies, and applications to teach

The Knowledge is what the tamariki need to understand. The Practice is what we as teachers need to know, our explicit teaching.

Knowledge are the 'Big Ideas'.

Knowledge are the goals, Practises are the success criteria.

Practises are the text book activities.

DOs are completely gone. They're what the KNOWs were. The teaching considerations have been removed. 

Changes nothing about how we teach -  75% is still the same.

Important - Read the 'Purpose Statement' on Page2

Still use the considerations.

A large % of the new new refresh is the same as the 2006 curriculum.

The new, NEW refresh is more specific and prescribed. 

Geometry Tasks

Set the anchor/diagnostic (DMIC/Rich) task. 15minute diagnostic.

Prior to the session - highlight/list key vocab you would expect tamariki to be using at that year level. Know the language! 

Teacher recording sheets - note the language/categorisation children have used and see what they know/don't know. 

Afterwards - organise the intervention groups. What could you do to explicitly teach/ or support them to retain the language?

• Articulate, don't gesture.
• Role-model using the vocabulary
• Link it to literacy
• Redo the task at the end of the week. 
• Use equipment, eg. Beebots

Take the task from the Concrete - Pictorial - Abstract

Going forward - 

• Language of Mathematics - can we translate for ESOL?
• Share out the most recent changes of the Math refresh with staff

Wonderings - 

• The anchor/diagnostic task is only a15minute diagnostic. How does this work with DMIC (40min task)?

Rob Proffitt-White PLD - day session

The govt provided resources only really address the 'Know' of Know/Understand/Do. Teachers must facilitate the learning. Work books are for the lowest common denominator teacher! Too much bookwork = learned helplessness!   

4 components of a comprehensive math programme

• Explicit teaching (feedback and feed forward)
• Positive relationships with maths
• Rich tasks
• Communication in maths

The difference between procedural fluency - the process/how you do it, accuracy, appropriateness, efficiency, and flexibility. Conceptual understanding - relating it to other others, representation, pictorial, abstract.

Would children know that 3 x 4 = 4 + 4 + 4? Or is it rote learned? Or only shown on an array (like in most standardised testing/DMIC tasks)? 190,000 Australian children were asked this question, only 31% knew what repeated addition equation it was.

discussNdefend 

"Two truths and a lie"

These can identify - which kids need more guided practice from Oxford resource? These can also be the rice task.

What do i notice? What do I wonder? 

moveNprove

Ask the question and give thinking time. You can use hand signals, don't have to physically move to a corner. Use the Talk Moves (these came from 1992 ESOL teaching!) Call on the 'pause' group to repeat what someone in a corner said. No more than 10 minutes! This can become the rich task for the week.

revisitNretain

Reactivate and practice something that has been taught previously. Practise and deepen the knows.

• Daily questions - 3 days worth of questions, 4 questions each day. Keep the same concept for the week. Don't have the 3 days all shown on you slides for kids to see! Do on a white board, I was just encouraging kōrero. The last question could be related to another strand. "I've seen a few wrong answers today, let's see what made them wrong." Pull your weekly focus/objective from the curriculum. These could be planned each term by 1 teacher per term. revisitNretain
• Number talks - SPQ (scrap paper question)  Rob's site  Creates good discussion. Dot talks + picture talks for subitising. Interestingly enough - studies show subitising does not go past 6!  Good practise would see children using estimation to check the accuracy of their 'answer' before they work it out. Eg. 5 x 18 =. "Well, I know it's got to be around 120". They know if they end up with a number way off, it's not going to be accurate. To teach efficiency - 1 + 5 + 9 = 15. Ask, "What number wold you start with?" Kangaroo example, less jumping. Use tally marks to show the kids, how can kangaroo makes less jumps? He's tired! Teaches kids you can move numbers around. Kids are able to analyse their movements. 
• Calendar Maths/Maths wall  - this is not necessarily something you do in math time, could be a settling after break activity. 

Main takeaways

• Teacher should be sitting down in teams and planning together! 
• SPQ Once a week, a class could bring their SPQ to the team hui and share the thinking of the class. Creates good discussion.
• SPQ - collect in answers and bring back 5 options the next day to discuss 
• Number sense is in the eye of the beholder!
• Use whiteboards for deeper thinking

Structured Literacy Zoom

 We want to optimise the intrinsic load.

 Explicit teaching does not need to be 'drill and kill'. It is interactive!

Kids need exposure to learning at their year level.

Sentence structure to writing is what phonics is to reading.

Adverbial phrase - running quickly. 

Mathematics & Statistics PLD with Core Education - Session 2

 "Plan for all students to experience all of the learning in the sequence for their year level" NZC pg24
What are my thoughts on this?

"Ma te huruhuru te manu ka rere ai" "Adorned with feathers, the bird is able to fly". 
He waka eke noa!

Phase 1 - thriving in an environment of literacy and numeracy. 

 Always ask - Is the answer reasonable and logical? - we can talk about this when we do our Kōtahi Pikitia; Kōtahi mano tau!

Accelerated learning - does not mean pushing them ahead of their level. Students are able to learn. concepts and procedures more rapidly than expected. Strategies that deepen understanding. We don't want the tamariki to fly fast, we want to deepend their understanding.

Create good entry point tasks!

Mathematics & Statistics PLD with Core Education - Session 1

The Refresh - why?

The Royal Society Te Āparangi put out a report with recommendations to improve teaching, provide clear guidance, and improve outcomes. 
Don't believe the media buzz! PIZA results - our average is still above national average, but our tail has spread too wide.   

2022 revised curriculum
2023 common practise model - for literacy and numeracy. It was a seperate document.
2024 experts combined these documents

Key competencies are no longer separated out.

Tahūrangi - online platform 

Conceptual understanding 
The comprehension of concepts, relations, and relations - connecting, representing, identifying, communicating, interpreting.

Procedural Fluency
Choosing procedures appropriately and carrying them out flexibly, accurately, and efficiently.  Eg. knowing how to use a ruler, or when a ruler is the right tool to use. 

There are 4 components of Mathematics & Statistics

1. Explicit teaching - structured and carefully sequenced
2. Postive Relationships
3. Rich Tasks - supplement your explicit teaching
4. Communication

Maths resources that were rolled out by the govt came before the refresh was finalised. They are 'best' fit, not 'perfect' fit.

Plan for students to have experienced all the statements in the sequence for their year level. Teach to the needs of the child! 

Structured Literacy Zoom

 c or k rule - List 9 The Code 

At the beginning of a word, the vowel that follows indicates which letter to use.

k takes i and e, c takes the other 3.

c takes a o u, k takes the other 2.

Review/Revise - daily - something recent, tricky, paced. Everyone says everything. It is not a test. Everyone writes. Fresh page, pens down. Every time you review, you are forgetting a little bit less.

What suffix means past tense? ed

What are the 3 sounds of ed? /d/t/ed/ played/locked/hunted. Revisit 'base' word.

What 2 letters do we use to represent the /k/ sound in a one syllable word after a short vowel? /ck/ snack bucket

Say there. Sit over there. How do we spell there? 

Homophones

Teaching - introduce. use a repetitive introduction. Today i am going to teach you the sound /o/. This is the phoneme /au/. 

Model x 3 The word is launch. We will watch the rocket launch. Segment l/au/n/ch/

Practice

Apply - dictation. Opportunity for kids to apply new learning. I do, we do, you do. No opportunity to call out if they have forgotten. 

A blended review might occur towards the end of the week.

Koia te Matauraki

Stephen McConnachie from ThinkeLearning - creating a site for aspirational reo progressions in auraki. https://ktmexample3.wpcomstaging.com/

Year 4 - 6 - Level 2
Year 1 - 3 - Level 1

Dianne Robinson - Ngāi Tahu 

https://koiatematauraka.org/

https://sites.google.com/southhornby.school.nz/uru-mnuka-cultural/te-reo-m%C4%81ori

Mathematics - Rob Profitt-White - PLD

 Starter

A picture is worth 1000 numbers - put up a picture of something - burger, animal, whatever! Children have 5mins to come up with as many numbers they can connect to that picture. Eg. 10km away from my house, 100 calories. 

Eg. 6 weeks old,  2 ears, 4 feet, 1,000,000 hairs etc.

Create 3 right and 1 wrong problem. Eg. Balancing the = sign.

Move and Prove - 2 tens and 15 ones can be presented as - a) 215, b) 25, c) 35, d) 2015. Kids physically move to corners of the room.  A good way to assign competence to children who know. Tuākana who can 'teach' less confident peers. Once you've had the initial kōrero, allow another 30 seconds to hold ground or change their thinking. BUT - if a child move, they need to explain why. A moveNprove can become your rich task for the week.

Make sure you show good coverage/representations of examples and non-examples. Eg. Triangle example - 39% (National norm) of Year 3 NZ children get PAT question wrong because they haven't been exposed to scalene triangles. They are used to only seeing equilateral triangles. The power of the visual is over riding their thinking. Introducing these concepts in Year 2 is much easier than Year 6! 

It takes 4-7 years to become proficient in DMIC!

Know - Understand - Do - comes from Canada!

Workbooks from PRIME, OXFORD, iDeal etc - Publishers can't afford for schools to 'run out of work'. When creating them, they took a typical amount of work a teacher could achieve in 5 hours, then added on 50%. Do't be  a slave to the publishing company! The guide is good, it promotes teacher pedagogy. The workbooks do not! It's all about $$$ 

Mathletics - sneaky! They take free tasks from Nrich, NZMaths etc, change then up, and sell them back to schools!

There are 4 main types of task.

Surface

Exercise - Practice of known facts or procedure. Surface skills. Equiations. eg 18 + 31 =

Application - Simple routine word story problems. Little skill. Jo has 15 balloonns, and her friend has 17. How many all together? 

Rich

Open - Multiple solutions. Opps for exploration. Jo and Olivia have a bunch of balloons. 32 in total. 

Unfamiliar - Investigations or complex tasks. 

Secrets behind the Refreshed Mathematics Curriculum

Know

Concepts (big ideas) - what the tamariki need to know. Kids would benefit from teachers reading this blue bit.

Content (skills) - this is where Twinkl and HERO go to. Multiple goals, fancy dials etc.

The Holy Trinity of Maths

Patterns and Variation

Logic and Reasoning

Visualisation - teach the regular, the non-regular and non-examples. CPA = concrete, pictorial, abstract.   

There are 3 parts to a maths problem - WHAT (the answer), HOW, and WHY?

Rich Routines that activate the KNOWS and DOS

moveNprove - notice, recognise, respond. Great for the start of the week to identify global misconceptions.

discussNdefend - see - think - share. Slow reveal graph. What do you notice? What do you wonder? Show some non-unit items, eg, length of string, pencil, dice. Kids have to estimate how long the string is. Show the answer in the reveal. Show more pics (of same items) to estimate.  https://stevewyborney.com/

recallNreason - explore - play - create. Great for once a week to enhance relationships, fun, academically rich games

reviseNretain - remember - apply - solve. SPQ - Scrape Paper Question - once a week. Eg. 201 - 198

When children make errors - Teachers needs to categorise who needs procedural, conceptual, or language support. Teachers usually only focus on procedure.

GLOSS - Gliding loosely over surface skills! Not helpful. Not teaching to the north east!

RevisitNretain 

Reactivate and practise something that has been taught previously. Deepen the know.

Whakamahana/Warm up/Hot spot/ Coneptual starters - all the questions should focus on the same skill.This does not have 2 be every day, could be 2 or 3 times a week.  

Rob's view - writing in a text book is detrimental to kids development in maths! Too much structure creates zombies. 

A typical child should have had 75 - 90 hours of math instruction by the time they get to Year 4. 

Algorithms are necessary, but children need to have an understanding of place value, otherwise they are parroting (barking at the page!) 27 - 19 (algorithm). When renaming, children need to know that 17 is made up of 1 ten and 7 ones.

Patterning

10 - 7 = 

11 - 8 = 

111 - 108 =

1111 - 1108 =

Just like in DMIC - when and child is doing well/on the right track - stop the class, draw everyones attention - public praise, assign competence. Send them back. Copying is great!

We have 4 days over the year with Rob. 

Structured Literacy March 2025 - Day 3

Review 6-8 graphemes/morphomes/ word lists in each session.

Blended reviews - where you revise a few different patterns.
"In August we can take the dog over the brigde."

Fluency has 3 main parts 

Vocabulary

Tier 1 - high frequency - every day words, found in everyday language. Eg. run, jump, chair...

Tier 2 - Academic - wide ranging and high utitily. Eg engage, emerge, fortune. THESE ARE WHERE WE FOCUS OUR TEACHING.

Tier 3 - Technical, low frequency. Subject specific, maths, science. Eg. isosceles, photosynthesis.  

Changing our writing

Traditional

More = better

Assign eriting tasks after modelling (guide on the side)

Allow students to write the way they speak

Give the child a fancy pen or border to write within!

Structured Literacy

Explicitly teach writing in careful logical way

A few well-crafter sentence will lift over-all quality

Explicitly teach syntax, allow for mastery

Spend regular time explicitily teaching

Self Regulated Strategy Development

Use SRSD

P = pre-read to get the gist, pull apart, pick ideas.

O = TIDE - Topic, ID info and details, or CSPACE - CS Characters & Setting, PA Problem & Action, CE Climax & End.

W = Sentence expansion and combining.

E = CUPS - Capitals, usage, punctuation, spelling.

R = ARMS - Add, Remove, Move, Substitute.

Review

I have got a smudge on my badge.

Blended - We can't budge the trolley out of the ditch. 

Blended - The friendly judge spoke softly to the man about his driving.

Read the sentences one at a time, get kids to spell out words, "tick it or fix it."

Whole Class teaching

'Core and more' philosophy.

Tier 1 - everyone (hoping for 80% to be in this group - able to grasp new learning)

Tier 2 - intervention group - 15%

Tier 3 - 5% 

 

Tier 2 and 3 are targeted groups. These groups are taking target groups while tier 1 are doing independent work. 

Oral Reading Fluency Assessment

Once you have done the assessment and data has been entered. 

If accuracy is below the benchmark - Phonics Assessments need to be done to identify where the gaps are.

If fluency is below the benchmark  - Choral reading/partner reading is needed. Repeated readings.

Ministry requirements for taking part in this PLD

Nonsense words - Yr 4 only

Oral reading fluency

MAZE

Spelling assessment

Take aways

Using the same names for all terminology. There needs to be consistency.   

Do we all use Casey the Caterpillar?!

Pick a stick for warm calling children to share their ideas.

What assessments do we have to do? How will that add to what we are already doing! 

Structured Literacy March 2025 - Day 2

 Using Talk Moves 

Use a visual in books. Tamariki can tick off or mark in some way when they have used it. It moves them from social conversation to professional and academic dialogue. 

The Not So Simple View of Writing

If it's not automatic, it's dominating the child's memory. If students can not write, it a misery task. "How do I form this letter? How do I write this word? Now I still need ideas!

Text generation also shown as Composition' in some visuals.

Transcription (Tuhi-ā–ringa)

What we can write, we can read. This does not go the other way! If we can spell it, we can read it. 

The Code - List 40 - modelled session. 

Review - Anything recent, tricky, hasn't been used in a while/retrieval from long term memory. Not just what you taught last week.

Seen review

Short vowels on the board (say them) e a  o i a

As in burn - ur,  as in farm - ar, as in sauce - au

Homonyms - 1. Here, 2. Hear. "I can hear you." Which number? "I am going here." Which number?

Unseen review 

Which 2 letters make the /er/ sound in bird? Write bird. Now write first. 

See example below. 

Write homophones. Eg. write/right. Here/hear

Then move onto morphology, contractions

New learning - The CVC doubling rule (1 syllable word)

Base word ends in CVC + vowel suffix = double the final consonant  

There are 2 steps to Review

Step 1 - decode - read some sounds

Step 2 - encode - spell some sounds

Explicit Teaching

Model and write pattern - see above.

Practice
There are 2 steps to practising the new learning 

Step 1 - decode new words

Step 2 - encode new words

Apply/Application

Dictation