Thursday, 17 May 2018

Why maths talk ?

Communication and collaboration are touted as essential skills for the modern workplace.
Being able to think creatively and articulate your thoughts is a highly valued skill in an increasingly competitive world.

Encouraging talk in maths classes not only helps prepare students for the modern workplace, it also builds competency in reading and writing (Britton, 1970).

 Maths Solutions suggest that getting students to talk in maths classes also supports:
  • robust learning by boosting memory
  • deeper reasoning
  • language development
  • development of social skills 
and that it also
  • reveals understanding and misunderstandings

If I want my students to talk more in class then i must think about 
  1. How do I facilitate classroom discussion ?
  2. What would my classroom a safe place for students to talk and take risks
  3. How do I encourage students to communicate  
To encourage students to communicate 
  • Build the relationships with and between students in the class (whakawhanaungatanaga)
  • Encourage voicing of  "other ways" 
  • Make student thinking public via scribing ( board, padlets, shared doc)
  • Restate students’ strategies
  • Use their contexts rather than mine
To make the classroom a safe space for students to share their voice 
  • Build the relationships with and between students in the class (whakawhanaungatanaga)
  • Develop a risk taking mistake making culture
  • Make sure all students have enough time to think and process (wait / thinking time)
  • Value all responses without judgement
To facilitate discussion
  • Ask questions that have multiple answers. Students could discuss the answer in teams, then in pairs and finally I could get them to  individually write a response for their team mate to read. the response could be  a single sentence.  eg two numbers sum to 180 what could they be?
  • Use prompts like those on Which one doesn't belong , 101qs what is the first question that comes to mind?  or  a statistical graph from census at school data viewer so every students can participate. and have them start their discussions using prompts I notice ... or I wonder ..., I agree/disagree with ... because...; I think ... doesn't belong because...
  • Use discourse rich tasks eg investigating number patterns

 100 Questions to promote discourse  is one of the most useful documents I have found. Questions are grouped in categories eg questions that help students work together, rely more on themselves, reason, evaluate their progress

Want to read more? This white paper offers strategies for Orchestrating Mathematical discourse

or if you prefer to watch

Monday, 23 April 2018

How do we get students excited and curious about mathematics?

When students are curious they are more likely to be engaged. But why? What, is curiosity and how does it work? A study published in the journal Neuron suggests that the brain's chemistry changes when we become curious, helping us better learn and retain information

In their study Grubner and Ranganath(2014) explored how curiosity influences memory. They found that states of high curiosity enhance both the learning of interesting information, and also the more boring stuff.  Applying this to the classroom maybe we could interpret this as  "students will learn more about topics they are curious about"
The authors of the study also discussed how much of what a person experiences in a day is forgotten.  This made me wonder, how much of what happens during an average school day do our students remember? 

How do we get students excited and curious about mathematics?

Do we uncover the magic?
Eddie Woo, Mathematics teacher and youtube star says "It is magic until you understand it and then it is mathematics" 

Multiplying by drawing lines - an ancient mayan method appears to be magic until you find out Why it works

Do we create an element of surprise?
These curated tasks for  primary and secondary aim to do that. they were Featured in an article from nrich's recent news titled from WOW to Why.

Do we use  hooks?
A hook could be a real-world example, an interesting problem, or a novel way of looking at a familiar situation. Middle-school math teacher Michael Giardi was featured in ASCD's weekly news. He uses hooks and prompts at the beginning of class to engage students. In this blog post, he describes how this approach promotes productive struggle and gets students thinking like mathematicians.

Do we build on the successes of others?. 
This recent ERO publication: Teaching approaches and strategies that work - keeping children engaged and achieving in  mathematics highlights approaches used by schools that focused on improving outcomes for students in mathematics in years 5-8.

Gruber, M. J., Gelman, B, & Ranganath, C. (2014) States of curiosity modulate hippocampus-dependent learning via the dopaminergic circuit. Neuron, 84(2), 486-496. .

Monday, 5 March 2018

making connections 2

My first making connections post was about making the connections between strands of the maths &  stats curriculum. This post is about making connections between people.

He aha te mea nui o te ao. He tāngata, he tāngata, he tāngata
What is the most important thing in the world? It is people, it is people, it is people.

Thinking about this whakatauki and our our first two Team days of 2018 I decided that this year that I would be more explicit about the place of whakawhanaungatanga in my practice.

Whanaungatanga: (noun) relationship, kinship, sense of family connection - a relationship through shared experiences and working together which provides people with a sense of belonging. It develops as a result of kinship rights and obligations, which also serve to strengthen each member of the kin group. It also extends to others to whom one develops a close familial, friendship or reciprocal relationship.

As we worked together in our teams of three, learning to 4 strand plait we reflected on the fact that relationships come in many forms. In our work we have the learning relationships that are built between teacher & student, the socio-emotional relationships that students build between each other. There are also the relationships we build with colleagues, families and whānau. 

Building strong relationships is often taken for granted as a skill all teachers possess; yet this might be an area in which teachers need support and professional guidance. (Aspden, McLaughlin & McLachlan, 2015)

We talked about  “Knowing your learner" being like an iceberg. Learners only show you what they want you to see. It is important to go below the surface to find out what is really going on. 

The Iceberg

Knowing your learner has many layers:

The behaviours they display – Our perception from observations

What makes them tick – the things that engage and inspire them

Their relationships – How they interact with other people

How they feel – Their perception of the world around them in different situations

We also acknowledged that in our work as facilitators we must ensure we are being honest, trusting and respectful as this forms the basis of successful strong relationships. (Bryk & Schneider, 2002)

Screen Shot 2017-06-09 at 8.10.28 PM.png

We all acknowledge that relationships are at the heart of our work. Our learners do better when they know they are respected and cared for. We work better with our colleagues when we feel valued and our ideas and beliefs are respected.

The big question is how do we ensure that we form, nurture and maintain these relationships?

Bryk, A., & Schneider, B. (2002). Trust in schools: A core resource for improvement. Russell Sage Foundation.

McLaughlin, Aspden, and McLachlan. (2015). How do teachers build strong relationships? A study of teaching practices to support child learning and social–emotional competence, Early Childhood Folio Vol 19 NO 1: 2015

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?