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.

You can also follow us on Facebook

Tuesday, 4 September 2018

Tongan Language Week

Malo e lelei.  It's Tongan Language Week all week. Uike Kātoanga’i ‘o e Lea Faka-Tonga.

Did you know?
With a population of over 106,000 people, Tonga is an archipelago of 169 islands (of which 36 are inhabited). The 175th largest country in the world in terms of area, Tonga consists of 748 square kilometres of land scattered over roughly 700,000 square kilometres of ocean.

Do you know about Coconet TV, a national treasure and fantastic classroom resource.

What could we do in maths classrooms?

Taha.   Learn the Tongan number system

0= noa     1= taha     2= ua    3= tolu     4= fā, 
5= nima    6= ono    7= fitu    8= valu     9= hiva

10 is hongofulu (hoh-ngoh-foo-loo)
 100 is teau (teh-ah-oo)

every other number is made up of the words for 0-9 with 3 exceptions
  • sixteen is one six taha ono
  • twenty becomes two zero – ua noa
  • 54 is nima valu
 22 uo ua,  55 nime nima and 99 hive hiva

Ua.  Explore linear relationships with the Figure it out activity - Tongan Travel (level4)  or
Tolu. Create Pasifika patterns 

Fa. check out the coco cooking section of Coconet TV for ideas for a shared lunch and a lot of maths.

From NZ Curiculum online
"Tongan Language Week / Uike Kātoanga’i ‘o e lea faka-Tonga supports the curriculum principles of cultural diversity and inclusion, and provides an opportunity for students to:
  • demonstrate the vision of connection to a global community
  • explore the values of diversity, community, and respect
  • achieve learning outcomes described in the learning languages area
  • make use of key competencies, especially using language, symbols, and texts, and relating to others."

Friday, 29 June 2018

What's on

The longest night is behind us and its time to look forward to the days getting longer and the calendar of events for Term 3

Kalman Awards - apply now! 
The Margaret and John Kalman CharitableTrust is again generously supporting the achievements of secondary Mathematics and Statistics teachers in the Auckland region. John Kalman was a professor of Mathematics at the University of Auckland from 1964 to 1993, and a leading promoter of Mathematics in New Zealand.

The inaugural winners  were Subash Chandar K, Ormiston College and Mala Nataraj, Selwyn College. They each received a prize of $5000 from the Margaret and John Kalman Trust. In addition they spent a day at the Department with 30 of their students.
Students made Enigma machines with Pringles tubes and conjectured and generalised about “stacks of cans”. Tanya Evans spoke about employment and careers for those with a Mathematics degree and students were intrigued to view and learn about a Gomboc. One student made a ‘vlog’ about her experience that featured interviews with members of the Department and showcasing her Enigma machine and the Gomboc. They also visited the Unleashed Space in the Department of Engineering. This space includes Maker Space which houses the latest 3-D printers, laser cutters and much more. The day concluded with a Maths Trail around Albert Park

Applications will be accepted from individual teachers and groups of teachers from Secondary schools in the Auckland Council region.
Details may be found here .
Applications must be received by 5pm July 30th

Kohia Exam Papers: order now for delivery July 20
Practice exam papers will be available for each of the mathematics and statistics externals for Level 1, Level 2, and Level 3 Statistics and Calculus.
orders can be placed now for delivery from July 20th

Australian Maths Competition: August 9
Entries close Friday July 6th. Use this link if you have yet to register or have extra students you would like to register for the competition.

 Derek Glover, has taken over from the late Alan Parris as the new national director for the Australian Maths competition. Email Derek if you have any questions about the competition.

Maths Week August 13-17

Maths week is turning 21 in 2018. Lets celebrate by topping the2017 numbers where 297,258 students and 4,882 teachers took part.

Registrations are open

Image result for image for balloons 21Image result for image for balloons 21Image result for image for balloons 21

This years topics include:
The Golden Ratio, A.I., The Largest Prime Number, LOP codes, Noughts and Crosses, The Maths Chase, Indices Cycle Race, Maths Millionaire interactive, Daily Dollar Questions, Maths Games.

AMA Casio-Mathex August 22 & 23
August 22nd  (Years 9 &10)  
August 23rd (Years 7 & 8) 

The AMA Casio Mathex competition is one of the largest maths events in the country. Almost 2000 students attend the  each year.  
Make sure you don't miss out by getting your registrations in early. Schools may enter up to two teams from each year level. Entry is free to AMA and PMA member schools.
The event is again being held at the recently renamed  Barfoot & Thompson stadium, Kohimaramara Rd Rd. (at Selwyn

2017 Casio Mathex Final in action

AMA Saturday morning  September 1.
Where: Faculty if Education & Social Work, THe University of Auckland, Epsom Ave
When: 8.30 am - noon, September 1
$5 Koha

Friday, 25 May 2018

Tall poppies

There is a tendency for us all to look off shore for expertise, however many countries look to NZ as a world leader in education. In this post I have gathered together links to sites of NZ teachers and schools that are leading the way in open sharing of their resources for math & stats teaching and learning.  I am aways in awe of how teachers manage to complete these sites on top of everything else that is part of a teachers life.

If you have a site or know of other sites let me know and i will update this post

STEM Online A resource for NZ students by NZ teachers
Hosted under the University of Auckland learning management system CANVAS which requires a double sign up. The effort is worth making, to access the rich resource that STEM Online offers us. Resources for tables equations and graphs (AS 91028) are live and more is in the pipeline for other standards.

Nayland College is world famous in NZ for their  maths & stats site Started by Max Riley, now retired, Nayland College pioneered the open sharing of resources for teaching and learning maths.

The new Google sites makes it easy to build and share a site.
Priscilla Allan, Pakuranga College, uses Google sites to put students in charge of their learning. Have a look through her  2018 junior classes site.

Jamie Sneddon, St Kentigern College, has put together a comprehensive site for Level 2 Networks
This is a huge leap forward from the Padlets I created for Networks and Co-ordinate Geometry  a couple of years ago.
A Padlet is still however a useful tool for sharing information or collecting student feedback.

Jamie also has sites  for AS 91587 Systems of Equations  and  AS 91574 Linear Programming  and AS91264 Inference  All sites are being gathered together for easy access on Sned Maths

Tamaki College maths department site which then links to each teachers site. Miss Munoz's Year 9 class use a blog to reflect on their learning.

Best Maths is full of content for Year 7 to Year 13 . 
Ro Bairstow of Kings College is behind BestMaths

Ormiston Senior College: are leading the way in the use of spheros, personalised learning and youtube
Liz Sneddon and Subash Chandar K  are both recipients of the Earnest Duncan award for the work they have done for students and teachers across NZ.
Liz has produced a series of statistics workbooks for all  and shared via a google site
Subash is the author of the you tube channel infinityplusone. When I last looked there were over 2500 subscribers.

Jake Wills of MathsNZ fame not to be confused with NZMaths made all our lives easier with NZGrapher . In the 28 days leading up to April 18 over 900 000 dot plots alone had been created.

If you are teaching stats, which is all of us, a must read is Anna Fergusson's blog teaching stats is awesome.  I recently discovered the online VIT module of iNZight there. Perfect for a visual representation of sampling variation. Anna has also has a companion site Learning stats is awesome  with some very cool tools.

You will find all sorts at  Jim Hogan's (Team solutions) site.  Jim's site includes an archive from years gone by.

I am dabbling with google sites. I started with junior Algebra & 91028
I am liking the collections feature of Google+ to curate things.

I have found SOLO useful for helping  teachers new to NCEA understand relational and extended abstract thinking. Lots of resources available from HookED

Last week I came across these resources for pedagogy curated by The University of Auckland. This site covers many things digital for the classroom.

and recently launched is The Education Hub . At The Education Hub they are helping us to bridge the gap between research and classroom practice. Currently there are short articles and guides that could be used as a focus for department meetings around self assessment, high expectation teaching and the importance of learning skills.