Friday, 9 February 2018

teachers learning from teachers

Today  Ormiston Senior College opened their doors to mathematics teachers to share how they are personalising learning utilising technology. Teachers came from Albany in the north to Onewhero is the south.

I was definitely the kid with a new toy as I learned to drive a sphero.
With a bit of trial and error however the sphero was off.

I think the best day of school just got better.

Many thanks to Ormiston Senior College, Subash and his department for hosting us - A great morning - lots of learning - and lots of ideas shared.

Next stop
Auckland Maths Association AGM & Quiz Night
Get a team (of 4) together  or join a team on the night

Wednesday February 28th 
Mt Eden Bowling Club, Epsom Ave, Epsom.
Happy Hour 6-7pm
AGM followed by quiz night, 

Thursday, 8 February 2018

Real stats?

With the census looming on March 6th 2018 we have an authentic context for our stats teaching and for meeting the intent  of The New Zealand Curriculum.

advertising the 2013 census

TKI notes Students can:
  • demonstrate the curriculum vision of being connected, actively involved, lifelong learners
  • explore the future focused issues of sustainability, citizenship, and globalisation
  • consider the NZC values of diversity, respect, community, and participation
  • make use of key competencies, especially using language, symbols, and texts, relating to others, thinking, and participating and contributing

In Maths & stats students may meet acheivement objectives by
  • designing and conducting their own census investigations using the statistical enquiry cycle
  • evaluating their findings
  • analysing the findings of the 2018 census and those of previous years
  • evaluating the effectiveness of different data displays.
TKI has links to a number of ideas that could be incorporated into lessons including using past data to answer questions like :

Usng an Excel spreadsheet Stats NZ combine historical data from 1876 with the latest national population projections to give an indication of the age you're likely to live to.

I particularly liked the discussion that goes with these questions
Eg. The Trends
  • New Zealanders are living progressively longer
  • women live longer than men
  • death rates continue to decline at all ages
  • life expectancy increases further for each additional year we live.
and then the  discussion about the certainty of these statements along with definitions and assumptions

From Stuff NZ: A century of change in New Zealand


Official NZ Census site
TKI - NZ Curriculum online
Census at School - the goto site for all stats teaching
NZ population statistics;

Tuesday, 17 October 2017

End of Year Exam - Fight or flight

Term 4 is the time when we pull everything together and students prepare for end of year exams. Exams can cause anxiety. Maths anxiety simply compounds this.

Its time to stop the clock on maths anxiety - read the latest research on Youcubed

Is Maths Anxiety Real? adapted from 

Does just hearing the word 'maths' make your heart race and your palms sweaty? 
Does  maths anxiety  exists. 
Many scientists believe maths anxiety is a very real condition. It can be defined as emotion including stress and tension that interfere with a student's ability to solve maths problem

Causes of Maths Anxiety

Test anxiety is the impending feeling that you will or are failing an exam, and often leads to poor results
Maths classes often exacerbate this condition because students sit a lot of tests during the year.  
Causes for anxiety include:
  • Prior  maths experiences - Anxiety is often cumulative, and pupils may look back at a frustrating experience learning maths or even from parents
  • Timed tests - Maths tests tend to put a lot of material into little time, and this perceived pressure can lead to further emotional and physical stress.
  • Risk of public embarrassment - Who doesn't cringe at the thought of being publicly embarrassed?

This  PDF has strategies that you could use in class to help guide students in revision and exam taking
Revision can be more effective when done in short bursts of a longer period of time and help reduce aanxiety.

The following 3 activities can be found on this blendspace (you may have to sign in to TES to see)
  1. Linear graph Treasure Hunt
  2. Quadratic graph Treasure hunt 
  3. Evaluate algebraic expressions : Always sometimes Never activities
  1. Algebra matching   Algebra Choice   Expanding and Factorising
  2. Solving Equations : starts at Level 1 and goes to Level 5 (not NZC levels)
  3. Algebra in action, lots of short word problems at different levels

From Don Steward's blog, Median,  to help clarify common algebraic misconceptions
  1. Spot the error
  2. Find the incorrect simplification
  3. Matching symbols and words 

Monday, 7 August 2017

Making Connections

If  algebra is about seeing patterns and making connections, how can we connect number, geometry & algebra?

One approach... think about the number 180;
  • 180 degrees on a straight line
  • 180 degrees is the sum of the interior angles in a triangle
  • 180 degrees in a semicircle
  • 180 is an even number and a multiple of 10
  • 180 in standard form looks like this 1.8 x 10 ^2

Is 180 a happy or an unhappy number?

  1. What pairs of numbers add up to 180?
  2. How many different pairs can you find?
  3. What patterns can you see?
  4. How do you know if you have found all the pairs?

A spreadsheet is one way for students to experiment :

Use the View> Show Formula option to introduce students to the algebraic logic behind spreadsheet formulae

How could we draw this?
How else could we draw this?

How could this be written using symbols?
120 + 60
or 120 + 60 = 180

Target 180
Two numbers add to 180. If I know one number what could the other number be?
Use a table like this as a starter/energiser  for a lesson

How else could this idea be represented ?

A picture maybe?

Using symbols and text?
120 + ? = target   or 120 + x = target 

In this case the target is 180 so we could write :
120 + x = 180

What would this equation look like if the target number changed?
What does this tell us about the values that x can take?

Other ideas might involve rectangles , perimeters,  area 

What other ways can we connect algebra, geometry & number?

Monday, 10 July 2017

20 years on

As we embed the changes to 91027 and prepare for a changed format in  91028 I wondered how things used to be...

From the 1996 School Certificate chief markers report.

In the first paragraph it was noted  that there was a "continued requirement for candidates to interpret information,  to explain, describe and justify their mathematics clearly and concisely"

I discovered investigation tasks in exams are not new -
In 1996 candidates had to  carry out an investigation to discover what length and width of a box would give the greatest base area.
To find a solution they could chose their method and were offered a table or grid as a guide.

School Certificate 1996

These investigative type questions first appeared in 1995 and these was one in each paper up to the introduction of NCEA.

I have scanned the questions and put them in the shared 91028 folder  

You will see there is a folder called GIVE ONE GET ONE that all teachers can add a question to - this is the quickest way we will build a useful resource. Please be careful to not delete any of the files in this folder

It seems we are singing the same song as our 1996 colleagues when it comes to algebra. The report noted basic algebra techniques were poor - these included
  • expanding
  • factorising
  • changing the subject and 
  • solving equations
It was recommended that students should be exposed to problems that are challenging enough to not be solved by guess and check and while rote learning of processes allowed students to pass the exam they did not prepare them for higher levels of mathematical understanding

All was not doom and gloom, the chief marker reported there were many "excellent examination papers and a large number of candidates were well taught and had a rich range of mathematical experiences throughout the year"

Monday, 19 June 2017


Each winter the stars of Matariki and Puanga signal the end of one year in Aotearoa, and the beginning of the next. Traditionally Mäori have recognised the rise of Matariki as a time to celebrate and prepare for the new year.

Matariki  takes place on the  25th June however  the Matariki celebrations have begun.
To see what's on check out the Matariki Festival 2017 website.

Matariki gives us an opportunity to enrich students’ mathematical experiences in a meaningful context.

Click here for a an integrated unit from NZMaths 
The unit begins with an investigation into some of the mathematics of astronomy associated with the rising of Matariki and learn where to look for the stars at the beginning of Matariki. As students work through the unit they learn about the significance of whakapapa, our family tree, and the mathematics of our descendants as they go back generations.  They discover the algebra behind a famous tukutuku design and finish off using percentages to help them build kites.

More resources

  • Make rewana bread using the recipe on this page
  • Click here for instructions to make a Manu taratahi

Thursday, 6 April 2017

Jump Start

  1. What do you do for students who arrive with significant academic gaps?
  2. How you will identify them?
  3. How you will you know you have made a difference?

This post highlights a recent discovery that will help  address question 1, that is a book written by Suzy Pepper Rollins,   Learning in the Fast lane, 8 ways to put ALL students on the road to achieve academic success.

Suzy argues that we spend too much time focussing on  filling the gaps rather than  moving forward. In otherwords we spend far too much time remediating rather than accelerating students.
 "instruction that aims to catch up lagging students or fix all their past problems ends up providing classroom experiences that are not compelling, rigorous, or engaging. Such instruction may inadvertently widen rather than close achievement gaps."

How do students feel?
sourced from

A colleague  likened this to someone falling off a boat while out on the harbour sailing. If someone who can't swim falls overboard , you don't jump in and teach them to dog paddle while the boat sails away, you haul them aboard and teach them to dog paddle as you keep sailing.

Acceleration comes with the usual logistical challenges - which students, who will teach them and when will we do this. Acceleration in this context is meant to be an enriching experience for students and  designed to encourage thinking, build vocabulary and scaffold missing pieces as they learn alongside their peers.

Learning in the Fast Lane is an essential guide that identifies eight high-impact, easy to use, research-based instructional approaches that will help you
  1. Generate thinking, purpose, relevance and curiosity
  2. Clearly articulate learning goals and expectations
  3. Scaffold and practice pre-requisite skills
  4. Introduce and practice key vocabulary
  5. Apply the new concept to a task
  6. Regularly assess and provide feedback (ie: formative assessment)


    read the first chapter of Learning in the Fast Lane  online here .

    listen to a podcast with Suzy Pepper Rollins  here

     watch a webinar  here

    Check out the effect of some of the evidenced based strategies that form the pedagogical basis for the Learning in the Fast Lane model here. An effect size of 0.4 or more is considered significant.

    Get Learning in the Fast Lane from Kohia Teachers Centre Bookshop