Tuesday, 25 June 2019


During his address at AMA HOD day @elsubash laid down the wero for us to join the twittersphere and take part in NZ's rebooted MathsChat.

And guess what happened ...

MathsChatNZ  trended #1 in New Zealand on the night!

The next MathsChat is coming up 8.30pm Tuesday July 2nd

Wondering what goes on in a Twitter chat ?
Its a straightforward model - questions are posed to the group and then people answer them starting with Ax (x being the question number) and adding  #MathsChatNZ at the end.

Here is a snapshot of the 2019 reboot on June 4th. To see the whole chat jump onto Twitter and search MAthsChatNZ.

Theme - Being a connected maths teacher

Q1: How many Maths PL days have you had in the last 12 months and what has been the best PL for you in the last 1 and a half years?

  • One day - Stats day. My best learning is from student voice, this drives my new learning. I am a very online learner.
  • Sadly 4 replied none
  • 5 days AMA Sept Saturday 2018, AMA Stats Day 2018, AMA Calculus Day 2018, Ormiston Maths Day 2019, AMA HoD Day 2019.

Q2: What PL sources set you up with the best enduring connections to other passionate Maths and Stats teachers?

  • A2: Twitter has been one of the best sources in terms of connecting with teachers outside of NZ particularly with Desmos and Geogebra. #MathsChatNZ #edchatnz
  • A2: Our NZ Maths Facebook group has also been great to connect with kiwi maths
  • A2: NZ Maths Teachers' Facebook site is gold.

  • Twitter for the brilliant UK PD and ideas. (And the NZ stuff already discussed!) Main people I follow are @mathsjem , @DrBennison and @DrFrostMaths . All fabulous.
  • @nzamt writing camps (@LisKiwi!) and CMA regional association events #mathschatnz
  • I must say @MathforLove Dan Finkel has been very kind, and I have learned heaps through twitter about the gamification of the math classroom. Also NZCER...
Q3: Is it a Fact? Algebra can not be learnt properly if taught in the context of other subjects.
  • I think there is a lot of scope for teaching Algebra through other pathways. Actually came across this old resource this week, and a little time on the laser cutter had a class set of pieces to try it out. http://mathematicscentre.com/taskcentre/071algeb.htm
  • Wouldn't say 'fact' but there is real benefit to teaching algebra explicitly

Q4: Have you had resistance from other staff or students when you tried to introduce technology in the maths classroom?
  • 7 people commented on this question  login to twitter to read at #mathsChatNZ
Q5: How often do your students play mathematical games? Which mathematical games do they play?

  • another person highlighted Hospice Shops as a great source of games - I can vouch for this - my classroom had a games cupboard. and several teachers got students to make their own
 Year10 Aorere College students

Q6: How do students talk in your classroom?
  • A6 #MathsChatNZ The games encourage literacy. The 'student help desk' encourages questions and answers. Ss are NOT quiet. We are casual, friendly and we learn lots. Fast. We discuss the math is a messy manner.
  • A6: My classrooms are noisy, and (mostly) productive. If you're on-task, I usually don't care how much noise you're making. A bit of banter back and forward keeps me sane too. I try to have a culture of helping each other, with varied success
Q7: How can I better assess junior students for different levels, without increasing workload and to improve student feedback? #MathsChatNZ
  • A7: using rubrics in student-speak that describe depth of conceptual understanding, or better yet, comparative marking for students’ answers to conceptual questions. Went to great PD on comparative marking for assessing conceptual understanding last year #mathschatnz
Q8 What advice do you have for teachers wanting to be more connected? #MathsChatNZ

How do I get involved?

Organisers set the Theme - Next months is Developing statistical writing  

  1. Questions are crowd sourced,  fill in this form if you have an idea to share 
  2. At 8.30pm on the first Tuesday of the Month fire up twitter 
  3. Search for #MathsChatNZ and follow along
Ben's tip:
To answer a question Write “A” then the number to answer that question. Eg “A1” to answer Q1. And bang that #MathsChatNZ on your tweets so everyone can read them! 
Ss = students, ts = teachers

Next MathsChatNZ is on July 2nd: Theme Developing statistical writing

Friday, 10 May 2019

Helen's day with Professor Jo Boaler

This post is from Helen Teal the Kaiārahi for Northland Maths Association. Helen was one of the 520 teachers who spent a day with Jo Boaler and Cathy Williams from Youcubed.com during the April break.

"Jo & Cathy kept us engaged for the entire day as they shared ways of developing a growth mindset with students and setting up positive norms in the maths classroom. They inspired us to think about how we could teach maths in such a way that gives students mathematical freedom. 

Using low floor and high ceiling tasks was recommended as it makes mathematical learning accessible to all while providing scope for extension and the opportunity for students to seek connections and develop a deeper understanding of mathematical concepts. 

They suggested planning lessons around big ideas rather than methods. Ideas like
  • Number Sense,
  • Learning to Generalise, 
  • Maths as pattern seeking, 
  • Algebra as a problem solving tool and that you can teach the content/methods as the need arises.
Jo talked about moving away from rote learning, speed tests and practicing very similar questions repeatedly (such as with textbooks) as this can turn kids off maths, lead to less effective brain processing and sometimes to maths anxiety. 

She reminded us to value mistakes and that struggling with a problem and learning from mistakes is where the most learning and brain connections happen. This seems to be the way of the future in maths education and is more in line with how we do maths in the real world. 

One really interesting point Jo made was that we need to look at changing the way we are assessing if we really want students to value mistake making and allow deep thinking and these brain connections to occur. 
Using the traditional tests where students get marked down for getting a question wrong will be counterproductive to developing these messages.
Rubrics and Overall Teacher Judgements can be used for years 1-10 but how might this play out in years 11-13 with NCEA assessments. 

Certainly this approach will help develop understanding and students’ ability to think in an extended abstract way but it is all a bit unknown for those of us who were taught maths in a fixed way and who have been teaching it like that up until now.

Many primary and intermediate schools in Northland are already using Jo Boaler's ideas and methods in their classrooms.

A key takeaway for me was that people can change and that you can only do something if you believe you can."

Helen Teal, Kaiārahi, Networks of Expertise, Northland Maths Association

To explore the teaching resources advocated, read up to date research  or enrol in one of the online courses goto the  Youcubed website 

A huge thanks to Te Whai Toi Tangata, Institute of Professional Learning for organising this event. 
Six Key Takeaways from A Day with Professor Jo Boaler is a summary of their reflections from the day.

Wednesday, 24 April 2019

Unpacking Standards

Over Term 1 in Auckland we have been unpacking the external Level 1 standards.
Both new and experienced teachers have found unpacking standards useful. New teachers found it useful for developing a deeper understanding of the New Zealand curriculum and for experienced teachers it has provided a checkpoint to ensure teaching and learning is still relevant for their learners, connected to the curriculum and meeting the requirements of the standards used to assess the learning.

Unpacking standards provides a checkpoint to make sure we are not teaching what we are teaching because "this is the way we always do things around here ,TITWWADTAH, but are focusing on the wider skills of solving problems, and understandings so that students can apply their learning and adapt when faced with different problems and challenges.

Upgrade your Teaching ASCD Webinar Mctighe & Wills 2019
Unpacking template for  External Assessment

I have found the template  we used, adapted from Wiggins and McTighe, one of the most useful tools for really thinking about the what and why of what we want our students to learn. It helps to focus our thinking on what it is we really want our students to take from their learning.

I also find the template fits well with the SOLO framework - Skills & knowledge provide the pre structural to multi structural thinking; essential questions & understandings fill the relational thinking box and extended abstract thinking comes from the application in a wider context, the big picture or transferable goals.

It could also fit with John Hattie's thinking around surface level & deep learning

Upgrade your teaching: Mctighe & Wills
Completing the template
In my experience it is much better to work with others when filling out this template. A jigsaw approach or think pair share work well when you have several teachers involved.

For me I start with the big picture goal - what are the transferable goals and then there are no rules as to the best way to complete. I have always gone with the flow of the group thinking.

 Useful resources for completing the template for learning connected to the external assessments
  • The mathematics and statistics teaching and learning guides aka the curriculum  is the place to begin when planning teaching and learning.
  • The standard itself is important as this is what students are assessed against. Standards specify what a candidate needs to know, do, and understand for the assessment.
  • The assessment specifications - these are updated each year and summarise the key elements offer further clarification of what is required in the standard.
  • Assessment reports; published towards the middle of the next year and are a summary of what the markers saw, across all of the scripts. They are a very useful summary of what did and didn’t go well and common issues.
  • Previous exam papers, exemplar scripts and assessment schedules are useful to highlight exam literacy. Students need specific exam literacy so looking at previous exam papers, exemplar scripts and assessment schedules is useful as they show the sorts of questions that are asked and the way they are worded and the criteria for Achieved, Merit and Excellence.
  • For statistics standards Census at school is a key resource
Internal achievement standards
The unpacking template can also be adapted for looking in depth at the learning that will be assessed internally. My version and samples are here.

The resource list changes slightly when thinking about internal assessment, the teaching and learning guides and the standards are the first port of call. Then 
  • The clarifications - latest interpretations of the standards.
  • Moderators newsletters and the reinstated National Moderators report
  • Conditions of assessment - considerable flexibility is allowed so it is worthwhile spending time considering the best way to collect evidence against the standard. 
  • Exemplars, of student work. I think the best exemplars you can find are those drawn from your students and have been externally moderated. The ones on the NZQA site are there to illustrate grade boundaries. 
To make finding information easier the curriculum, the standard the clarifications and conditions of assessment have been summarised onto one A3 page for each internal & updated for 2019.

Find all the blank and sample unpacking templates here  

Jay Mctighe says his greatest lesson learned, is to plan backwards with clarity about the desired outcome or problem you need to solve in mind before you take action.

Friday, 22 March 2019

Something old something new

Recently NZQA added a National Moderators report to the maths & stats home page . It highlights general issues and trends that have been identified during external moderation of the internal Mathematics and Statistics standards in 2018. THe report includes information about 
  • Volume of Evidence Produced
  • Excellence at Level 3
  • Group Work
  • Integrated Assessment of Standards
  • Sample to Population Inference
A  National Moderators report was last published in 2011 after which it was replaced by moderators newsletters and clarifications. Its worth having a quick read  

Moderators newsletters and current clarifications can be found from the  Maths & Stats home page

A3 summaries for internal standards containing links to the curriculum, conditions of assessment, clarifications and the standard for quick reference, click the NCEA A3 Standard Summaries in the link on the sidebar of this page. These documents contain  the current clarifications.
You can also read what I took from a workshop hosted by Northland Maths Association on Feb 23rd where a National Moderator was a guest speaker here and from the archives of the National Newsletter clarification of a range of ... and a selection of ... at Level 1 & 2.

Sunday, 10 March 2019

A Range of ....

As students begin completing assessment tasks I have had a number of queries about what is meant by a range of... and a selection of... in EN4 of the the maths & stats standards.

I dug into the archives and found the following in a National Newsletter from 2016  (P. 2)  It is my understanding nothing has changed.
  •  At Level 1, “a selection of....” means 3 or more methods that are relevant and contribute towards solving the problem. 
  • At Level 2 & 3, “a range of...” means 2 or more methods that are relevant and contribute towards solving the problem. 
  • For statistics standards all bullet points must be present in the report for achieved. 
What constitutes a method in L1 and L2 trig standards?, is another common query
For 91032: 
Related image
  • Using Sin, Cos or Tan to find a side is a method
  • Using Sin, Cos or Tan to find an angle is another
  • Taking measurements at a precision appropriate to the task is a method. The students must choose what to measure and use their measurement in solving the problem. 
  • Using Pythagoras to find a hypotenuse is a method
  • Using Pythagoras to  find a short side counts as a separate method. 
  • Utilising similar shapes 
For 91259: 
  • Using the Sine Rule to find a side or angle is one method 
  • Using Cosine Rule to find side or angle is another method 
remaining methods include finding ..
  • Length of an arc of a circle 
  • Area of a sector of a circle
  • Area of a triangle
The use of a Triangle Solver app would be appropriate, however the students must clearly communicate their thinking to show the trigonometric relationship.

From the conditions of assessment 
1. “Students are expected to have access to appropriate technology”. For statistics standards this would include statistical software. For mathematics standards it might include the use of Geogebra or Desmos.
2. “Care needs to be taken to allow students opportunities to present their best evidence against the standard(s) that is free from unnecessary constraint”.

Feedback from teachers whose students are creating their own reference sheets report increased engagement. Are you giving your students the opportunity to create their own reference sheet for internal assessments? These sheets must be the students’ own work and not compromise the authenticity of the assessment.

3. “Students are expected to have access to appropriate technology. For statistics standards this would include statistical software.” All graphs for statistics standards could be generated by technology.

Wednesday, 27 February 2019

Reflections from Northland Maths Assoc day

Over the weekend I attended the Northland Maths Association day where a National Assessment Moderator from NZQA was a guest speaker. This post includes my understanding of some of the conversations on the day and may not necessarily be the views of the moderator or NZQA.  If you have queries please check.

The role of NZQA and the external moderation process is outlined in the NCEA annual report published in May each year. See page 88 at this link

"Each year NZQA moderates approximately 100,000 individual pieces of student work that are submitted by schools as part of their external moderation process. The standards moderated are from the range of standards for internally-assessed standards that schools can select to use in their teaching programmes"

From this work our moderators build a national picture where we as teachers see only our school picture.
"The focus of the moderation process is to ensure that student evidence for specific standards meets the criteria of the standard on a national basis"

What moderators do & not do? 

"The moderator will consider if the students’ evidence meets the requirements of the standard. The assessment tasks or activities are only moderated if the moderator has cause to consider that the assessment tasks or activities were the cause of the inappropriate awarding of the grade" (NCEA 2018, p 88)

They moderate assessor judgments in the student work you submit against the standard not your mark schedule.

They do not moderate your task unless they disagree with your judgements and the task is the reason for the grade disagreement.

If you have sent in a piece of student work that you feel is a grade boundary - err on the side of the student and put a note with the work that explains your thinking.

Sometimes you find yourself submitting work from the year prior. NZQA suggest you date the work being submitted and make it clear that the work is from a previous year.

Unsure about your feedback?

You have an opportunity to query your moderation report rather than go through the appeal process. The purpose is to ensure you are clear about comments in your moderation reports. NZQA will respond to these queries as quickly as possible. Do this through your Principal's Nominee.

Resubmission & Reassessment

There is a lot of misinformation or what I call "bush law" sitting around resubmissions and reassessments. NZQA have published a series of Myth sheets which highlight some of the main issues surrounding Myth 4; Resubmissions & Myth 5; Reassessments

A question that was asked of us "if we are completing our internals as assignments/open book assessments should we need to be doing this?". What do you think?

We were also reminded that we cannot direct students when doing a resubmission. "we should not be prompting them for a message they did not deliver"

About Exemplars

The exemplars on the NZQA website are designed to help teachers identify the grade boundary. They are not intended to be "models" for students.

Read the annotations carefully.

The best exemplars you can use for students are from your own benchmarking folder. (folder of examples from your own students, in particular the student work that has been externally moderated). You should get students permission before using their work as exemplars for other students.

Collecting evidence from one task

As always in a workshop we deviated from the plan as questions came up. One such question related to collecting evidence against more than one standard from a single task.

Two standards highlighted were Physics (1.1) and Bivariate data (91036).
On reading the detail of each standard I noticed in Physics the students may conduct their investigation "with direction" and in 91036 students must identify and communicate how they will manage their variation.
In Physics students have a requirement for only 4 pieces of data and in 91036 they must collect enough to see a relationship and so it goes on.

The message I took from this is, if you are going to collect evidence for multiple standards from a single task it is important that all stakeholders sit down and develop a clear picture of what is required. The students need to be given the opportunity to meet the requirements of each standard at all levels.
Always use the NZQA subject page to find these documents. The links on the subject page take you to the most up to date versions of documents. (A google search sometimes takes us to out of date documents)

Students can achieve at different levels for each standard.

Tasks must give the students the opportunity for achieving at the excellence level in all standards the task is collecting evidence against. In my experience this is the most difficult part.

We came to the conclusion that it was very difficult to do this well and meet our obligations to the standards and process.

The conversation turned to the inference standards and in particular 91035.

Why is understanding of this standard is still problematic? From our general discussion we came to the conclusion that maybe not enough time is being given to stats in the junior programmes.

91035 - Multivariate data.

Common misunderstandings raised in the discussion
  • Data sets do not have enough variables for students to make their own decisions around the variables they investigate. A multivariate data set should have a minimum of 2 categorical variables
  • The students are taking a sample from the data set given. Students are not required to take a sample, they should be provided with the sample data
  • Awarding a "holistic" grade if only one step of the statistical inquiry cycle is missing. All steps of the statistical inquiry cycle (bullet points in explanatory notes of the standard) must be evident in a students report.
  • Assuming a generic discussion of sampling variation is enough for an E grade. Discussion of sample variation is not a requirement for 91035
  • Awarding 91035 from 91264. It is difficult to integrate these standards using one task. There are some differences in the statistical enquiry cycle (See explanatory notes of each standard) and the type of question that needs to be posed.
  • Analysis of the sample is descriptive of each group. Analysis should be comparative
  • The question (& inference) is about the sample. The question and inference must be about the population and contain a world like "tends to".
  • Quantity does not equal quality
  • Generic statements like "back in the population". Students should be using the context of the investigation.

The question posed is about the population which should be included in the question ----->

When checking your students question before they do their analysis it is important to check that  they have identified the population accurately

Contextual knowledge 

It is important for us to have the conversations around the context in class so students know what the population is. Understanding the context and the population will help them better write an appropriate investigative question . It will also give them the opportunity to better integrate their personal contextual knowledge. 

To achieve at Excellence student’s personal contextual knowledge (PCK) should be integrated throughout their report. It is particularly important that this is evident when students are posing a comparative question, discussing features of the distributions and when communicating findings such as their informal inference and supporting evidence in a conclusion.

Students should not be seeing unfamiliar contexts in their assessment task

What are the  expectations around contextual knowledge?

TKI Link

  • At level 6 students should be working with contexts that are familiar to them.
  • At level 7 students should be provided with relevant contextual knowledge about the situation under investigation.
  • At level 8 students should be sourcing relevant contextual knowledge about the situation under investigation from places such as the internet, the school or local library, newspapers and magazines.
By familiar we mean students have personal contextual knowledge of the context - you may have to have in class discussions to develop this.

By relevant we mean relevant to the question and variables rather than simply context.

What is the step up across the inference standards

1. Contextual knowledge (see above)
2. The complexity of the analysis: which broadly is...
  • Level 5; visual comparison to see if one group tends to be bigger than another
  • Level 6; visual comparison with a rule to see if one group tends to be bigger than another
  • Level 7;  visual analysis with an informal confidence interval used to see if the median of one group is likely to be bigger than the median of the other
  • Level 8; quantifies the difference between the medians of two groups using Bootstrapping

This document written by Michelle Dalrymple on Census at school is essential reading for inference progressions. You should also read through Pip Arnolds document on What makes a good investigative question.

As usual we needed more time. I am looking forward to Episode Two.

Thank you Northland Maths association and NZQA these sessions are really valuable for the sector.

Read about hosting an NZQA "on-request" workshop in your region or on-line  here


As one door closes another opens. 

2019 has me taking on a part time role with the Networks of Expertise as the Kaiārahi for the Auckland Maths Association after Team Solutions closed its doors for the final time in December last year.

I will continue to post regularly on topics of interest for NZ secondary maths and stats teachers.

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