This newsletter and the Secondary Student Achievement Professional Learning and Development initiative is funded by the
Ministry of Education. The providers are The University of Auckland and Te Tapuae o Rehua consortium.
National Newsletter: Mathematics and Statistics
Information and resources for middle leaders in secondary schools | Term 3 2013
Whakatauki
Nā tō rourou, nā taku rourou ka ora ai te iwi.
With your food basket and my food basket the people will thrive.
Welcome to term 3 - the winter/spring transition. We hope that you have
had the opportunity to recharge the batteries and relax over the break.
Please make sure that this newsletter is circulated to your department staff.
Munro Doran joins the facilitation team this term until the end of 2013.
Munro has taken leave from Otago Boys’ High School and will be working in
the Southland/Otago regions. A warm welcome, Munro.
Feedback from term 2 national workshops
In term 2, the Mathematics and Statistics facilitators around the country
delivered the second of the two planned national workshops (‘Getting
Connected’). It is great to see “communities of learning” developing from
these workshops and middle leaders increasing their knowledge in areas
that have not traditionally been seen as part of Mathematics and Statistics,
or as appropriate professional development in our subject.
Feedback from workshop 1 indicated that many teachers are engaging with
Teaching as Inquiry and have made a considered change in their practice.
Research shows this makes a difference to priority students. Middle leaders
at the same time are developing their capability to drive change.
‘Knowing your students’ as part of inquiry can be an illuminating experience
for a teacher, with comments emerging such as: “I had no idea that Sasha
did not speak English at home.” Subject specific literacy is another idea that
is now seen as part of teaching and learning in Mathematics and Statistics.
Feedback from these workshops was generally very positive. Thank you for
attending and for your contributions. Well done on exploring and making
change. The inquiries must continue.
The main foci of the workshops were:
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The importance of learning progressions from NZC Level 1 to Level 8 and
understanding the foundations on which senior work is based. The
strands were number and algebra, measurement and geometry.
Utilising the resource websites which support the teaching and learning
based on NZC (2007).
The design of sensible pathways for student achievement.
Revisiting NCEA Level 3 – tasks/resources/pedagogy.
External examination preparation and subject specific literacy.
Writing and editing assessment tasks.
Aspects of the SOLO taxonomy and the ALiM initiative.
Building iNZight skills and access.
The provision of an opportunity for middle leaders to talk, share, ask
questions and learn together.
Secondary Student Achievement Professional Learning and Development - National Newsletter
Contact details
Northland
Sandra Cathcart
National Co-ordinator
The University of Auckland
Based in Whangarei
Phone: 027 555 4660
s.cathcart@auckland.ac.nz
Auckland
Marion Steel
The University of Auckland
Based in Auckland
Phone: 027 498 8109
m.steel@auckland.ac.nz
Central North Island
Jim Hogan
The University of Auckland
Based in Taupo
Phone: 027 461 0702
j.hogan@auckland.ac.nz
Lower North Island
Derek Smith
National Co-ordinator
Te Tapuae o Rehua
Based in Wellington
Phone: 021 913 150
derek.smith@otago.ac.nz
Marc Paterson
Te Tapuae o Rehua
Based in Palmerston North
Phone: 021 627 287
marc.paterson@otago.ac.nz
Nelson, Christchurch, West
Coast
Karen Barks
Te Tapuae o Rehua
Based in Nelson
Phone: 027 405 6725
karen.barks@canterbury.ac.nz
Otago, Southland
Munro Doran
Te Tapuae o Rehua
Based in Dunedin
Phone: 03 479 4203
Email: munro.doran@otago.ac.nz
NZQA Facebook subject pages
NZQA has launched a series of Facebook pages for each senior secondary
school subject. Pages can be located by typing the subject name and
NZQA into the Facebook search tool. These pages alert people to new or
updated information for internally assessed standards on the NZQA
subject pages. Click Like and then alerts are posted to your own Facebook
home page or arrive in your email inbox. It is not necessary to revisit the
page once it has been ‘Liked’. These Facebook pages are not intended to
be a subject forum. This is a trial in 2013 and NZQA welcomes teacher
feedback on this new initiative to see if it is helpful. Visit: NZQA on
facebook
Resources and weblinks
Traditional tales with a
mathematical twist
Literacy Online and annotated student work
This annotated exemplar on the level 2 achievement standard AS91265
‘Conduct an experiment to investigate a situation using statistical
methods’ helps teachers to support the literacy and language learning of
students in mathematics and statistics. Visit:
Literacy-Online-Annotated-exemplar-Mathematics-and-Statistics
Clarification of achievement standards
AS 3.5 Complex numbers
The sample examination has been recently updated. The student
exemplars have not. See: 91577-sam-2013.doc
AS 3.14 Distributions
The sample examination has been recently updated. The student
exemplars have not. See: 91586-sam-2013.doc
Traditional tales provide a setting
for mathematical investigation
that can include pure fantasy.
Activities are accessible to
students with a wide range of
abilities. An entertaining
mathematical read, written by
Vince Wright.
The Curious Incident of the
Dog in the Night-time
For clarification of achievement standards for all NCEA levels visit:
mathematics and statistics clarifications
Practice assessments for externals on NZAMT
If you are a school member of NZAMT for 2013 then you will have access
to the assessment tasks for externals from the secure site. You can also
find the retired examination papers in a link called "Examination
documents for expired standards". They are on the NZQA Mathematics and
Statistics subject resources page:
Visit: qualifications/ncea/subjects/mathematics/levels/
Credit splitting for UE subjects
Students entering University in 2015 will need 14 credits from each of
three approved subjects. From 2013 there are now three UE approved
subjects defined by NZQA: Calculus, Mathematics, and Statistics. If a
student gains 14 credits from Mathematics standards AS91573 to
AS91579 and AS91587 they will have a UE subject in Calculus. A student
who gains 14 credits from Statistics standards AS91580 to AS91588 will
have a UE subject in Statistics. 14 credits from a combination of
Mathematics and Statistics standards is a UE subject in Mathematics.
Note that in 2013, for entering University in 2014 the UE requirement is
still for only 2 approved subjects, but Mathematics can be one of these
subjects. For example, a student getting 22 credits of new standards in
Statistics (8 spare credits) and 6 credits of new standards in Calculus
will meet the University Entrance requirements using Statistics and
Mathematics as two approved subjects. They will still require 14 credits
from one or two additional domains or approved subjects.
Maths Week 2013
Held from Monday 12 August until Sunday 18 August, Maths Week
continues again this year but with a number of changes.
Information: http://www.mathsweek.org.nz/
Registration: http://www.mathsweek.org.nz/registration.html
Secondary Student Achievement Professional Learning and Development - National Newsletter
A story narrated by 15-year old
Christopher Boone, who describes
himself as a mathematician with
some behavioral difficulties. A
great detective read with
mathematical twists and turns,
humour and autistic insights.
Pasifika Education Plan
Aiming to achieve optimum
learning to guide and support
Pasifika learners, their families
and educational providers.
http://www.minedu.govt.nz/NZE
ducation/EducationPolicies/Pasifik
aEducation/PasifikaEducationPlan
2013.aspx
iNZight - Mac update news
A new graphics driver for Mac
allows animations to play at good
speed. Replace your existing copy
of iNZight from here.
https://www.stat.auckland.ac.nz/
~wild/iNZight/dlw.html
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NZAMT13 conference
Venue: Wellington Girls College. Date: 1-4 October 2013.
Visit: http://nzamt13.org.nz/index.php
Select the workshops you want to attend on the website during term 3.
NZAMT13 is running two competitions in conjunction with the Conference
http://nzamt13.org.nz/competitions.php
Supporting teaching resources on nzmath
The table presented in the link below provides information relating to both
the New Zealand Curriculum achievement objectives and the Mathematics
standards, illustrating links to where the student was working at, prior
learning and next steps:
http://www.nzmaths.co.nz/nzc-and-standards
The Secondary mathematics link is
http://www.nzmaths.co.nz/secondary-mathematics-and-statistics
Youth Guarantee update
How well does your school compare in terms of the Government’s Youth
Guarantee goal of having 85% of school leavers achieving NCEA Level 2 by
2017? Sensible pathways leading to meaningful employment and career
choices are vital. For more information click this link:
youthguarantee.net.nz
NZ Education Gazette: Secondary Focus
Each issue of the Education Gazette features a series called Secondary
Focus looking at resources, teaching and learning or professional
development relevant to the secondary sector. You can view all the
Secondary Focus pages at: tki Secondary-focus-updates
Educational Leaders website
The Educational Leaders section of TKI has important resources, readings
and case studies relevant not only for senior leaders but for middle leaders
too. In particular, check out the ‘Leadership development’ link on the menu
and then the ‘Professional information’ tab:
View: Leadership-development - Professional-information
Level 3 internal formula sheet
There will not be a level 3 internal formula sheet posted on NZQA’s
Mathematics and Statistics web page. It is up to schools to provide the
appropriate information for each internal standard to assist students in
providing evidence for the task presented.
Consider also the ‘Conditions of Assessment’ documents for the internal
standards and especially this statement:
“Internal assessment provides considerable flexibility in the
collection of evidence. Care must be taken to allow students
opportunities to present their best evidence against the standard
that is free from unnecessary constraints. Collection of evidence for
these standards could include, but is not restricted to, an extended
task, an investigation, or a more formal activity.”
Conics
You may like this video link for the teaching of conic sections, and there are
others on the site that could be useful to look at. An interesting question is,
“If students did this kind of activity would there be evidence of methods?”
Can you see relational thinking? What about extended abstract? Enjoy! Click
here:
youtube - conic
You get over 53,000,000 hits by Googling “utube mathematics”!
Secondary Student Achievement Professional Learning and Development - National Newsletter
Web links
nzmaths Learning Community
Forums
These forums are still active and
we encourage you to continue
posting questions so that the
mathematics community can
continue to be well informed.
Registration for new participants
via: http://nzmaths.co.nz/user
All seven forums can be accessed
via: http://nzmaths.co.nz/plc
Secondary Literacy online
These pages will help all
secondary teachers gain an
understanding of the literacy
demands within subject areas:
http://literacyonline.tki.org.nz/Lit
eracy-Online/Secondary-Literacy
ESOL online
Online resources for ESOL
specialists, primary, and
secondary teachers:
http://esolonline.tki.org.nz/
Teachers as learners
Teachers as learners: Improving
outcomes for Māori and Pasifika
students through inquiry:
http://nzcurriculum.tki.org.nz/Cu
rriculum-stories/Casestudies/Teachers-as-learnersInquiry
Leading from the Middle
The qualities, practices and
activities middle and senior
leaders need to lead in ways that
enhance learner outcomes.
http://www.educationalleaders.g
ovt.nz/Leadershipdevelopment/Professionalinformation/Leading-from-themiddle
Wellbeing@school
http://www.wellbeingatschool.or
g.nz/about-inclusive-practicestools
ERO report link
Report on Teaching as Inquiry Responding to Learners
http://www.ero.govt.nz/National
-Reports/Teaching-as-InquiryResponding-to-Learners-July2012
My Friend Google
Use Chrome as your browser and
explore the add-ons in “Play”.
Google “Math add on for Word”
and add 3d equations solver and
grapher to your computers.
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nzmaths: e-ako maths
A new algebra pathway has been added to e-ako maths, with 16 e-ako
teaching about symbols, equations and expressions, and three assessment
e-ako. Read more at: e-ako maths
Geogebra
As more and more schools shift to cloud computing, there is a need for free
Mathematics and Statistics programmes available online. Geogebra now has
an online version http://www.geogebra.org/webstart/geogebra.html. It can
be used for teaching algebra and geometry in junior classes and NCEA.
Geogebra (version 4) now supports statistical calculations and graphing
from imported spreadsheets. The statistical software is not as capable nor
as user-friendly as iNZight, but will do comparative boxplots and statistics.
A PowerPoint on the mathstatsfacilitators website for using geogebra in
statistics explains how to organise spreadsheets to import data into
Geogebra. The Geogebra programme can be downloaded
from http://www.geogebra.org/cms/download
RSS feeds: TKI, NZQA and NZAMT
Register for these updates via RSS feeds or add to your favourites:
TKI
www.tki.org
NZQA
www.nzqa.govt.nz
nzmaths www.nzmaths.co.nz
NZAMT www.nzamt.org
Census@school
http://new.censusatschool.org.nz/
The new PLD landscape
The Facilitator role is not the same as the Mathematics advisor role from
pre-2012. The Facilitators now work as part of the Ministry of Educationfunded Secondary Student Achievement PLD Contract. The major part of
this role is to work indepth in selected schools identified by the Ministry as
needing support to improve student achievement.
This is achieved via:
•
Working together to improve outcomes for priority learners: Māori
students, Pasifika students and students with special education
needs
•
Using ‘Teaching as Inquiry’ at all levels of the school
•
Working collaboratively with schools to build capability and
sustainable improvements.
The second part of this work is providing a national programme of
workshops and also developing these newsletters. Additional responsibilities
which the Facilitators will undertake as time allows are: monitoring and
contributing to the forums on nzmaths; supporting local cluster meetings;
facilitating regional workshops; answering questions from mathematics
teachers; and helping share resources among teachers.
Realignment has preoccupied teacher professional development for the past
3 years. It will continue to be a learning process as feedback from the
moderators and the development and dissemination of new resources
continue to inform teaching and learning in the senior school. Teachers
should not feel inadequate if they do not get assessment right first time
round. It is vital that the specifications of each achievement standard, the
conditions of assessment, clarifications of the standards and support
material from the senior secondary subject guides assist to inform the
learning involved, and how assessment via SOLO taxonomy guides teachers
to give the best outcomes for our students.
There is also now a growing emphasis on the need for middle leaders to
review their year 9 and 10 programmes to assist students in their
preparation for high stakes assessment via NCEA.
NZQA Best Practice workshops
Registrations for Wellington (22 August), Auckland (12 September) and
Palmerston North (24 October) are needed to make sure minimum numbers
are met. Register now!
Secondary Student Achievement Professional Learning and Development - National Newsletter
How to Solve a Problem
1. Read the question
2. Draw a picture
3. Devise a strategy
4. Do the calculations
5. Answer the problem
Students need to learn how to
solve a problem. They are often
good at the skills, have the
knowledge but are unable to see
a big picture. This process takes
time and uses previous
assessment tasks as material to
learn problem solving.
Read the question
This is the literacy issue. Tasks
or problems are almost always
given in words so reading with
understanding is vital - the skills
required of finding important
information in the task.
Draw a picture
If you cannot draw a picture of
what the task is then you do not
understand the task well
enough! Pictures are visual
language. A sketch, not a work
of art!
Devise a strategy
What steps do you need to
follow to work through this
problem? Make a list. This is a
strategy and already the student
could be heading towards Merit,
making the connections between
concepts and ideas. Note any
assumptions. A better solution
may emerge as well. Students
can move directly to the
calculations and record their
strategy simultaneously.
Do the calculations
Take each step of the listed
strategy and rewrite with the
necessary calculation. “What is it
that I am doing? ... Here it is.”
This provides a reason for what
the calculation does and
illustrates the connections. To
justify is to be Merit!
Answer the problem
Make sure well-structured
sentences answer the problem
to the task presented. Once that
is done elaboration,
improvements and qualification
of its meaning could head a
student towards Excellence.
Target is being multiplicative
Keep a focus in junior classes on
turning students into becoming
multiplicative thinkers. Get
students thinking multiples,
factors, patterns, nth terms,
basic facts at every opportunity.
- from Jim Hogan
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