Thursday, 26 January 2017

Mathematics Dreaming - From Rational to Real : On Curiosity and Wonderment

Mathematics Dreaming - From Rational to Real : On Curiosity and Wonderment

On Curiosity and Wonderment

Australian of the Year awards: Biomolecular scientist Alan Mackay-Sim receives 2017 honour.

So here we are again, the beginning of another school year in Australia.  A brand-new set of students, each with their own strengths, attitudes, and degrees of self-confidence towards learning mathematics.

As a high school Mathematics teacher, have renewed my Mathematics teaching goals this year, and they are not about grades, achievement standards, or personal accountability.  Those are expected elements of my role as a teacher.  My personal goals for teaching mathematics are directed at engaging my learners:

Goal 1:  to love mathematics
Goal 2:  to challenge themselves
Goal 3:  to embrace curiosity and wonderment when exploring maths

Why these goals?  I want maths to come alive for my students as it does for me.  And I want to help my students to unlock their potential for learning in the same way that our Australian of the Year, Alan Mackay-Sim did.

Australian of the Year 2017 used his curiosity and wonderment about the biology of the nose and sense of smell to assist with the first successful restoration of mobility in a quadriplegic man in 2014.  Imagine that….an expert on noses helps a man to walk again.  Now that is a powerful endorsement for teaching students to engage with curiosity and wonderment.

Curiosity and Wonderment is nothing new.  It is embedded in Art Costa’s ‘Habits of Mind’ which have been around for a long time.  As maths teachers, however, I think it is time to re-embrace the ‘Habits of Mind’ as intentional ‘learning outcomes’ within our lessons.

During my years of teaching, I have found that Curiosity and Wonderment needs to be to explicitly ‘re-taught’ to most of my students.  By reconnecting students with their innate senses of curiosity and wonderment they will be able to draw on these to play, explore and find solutions such as the ‘Stem Cell Breakthrough’ achieved by our Australian of the Year, 2017, Alan Mackay-Sim.

How do we teach curiosity and wonderment?   It is nothing new. The first step is to include as a learning outcome for the lesson something such as the following:

  • ·      In this lesson, students will learn to develop their curiosity by asking questions….to challenge what they believe that they know…

  • ·      In this lesson, students will develop their wonderment and awe by ‘changing the conditions’ for a problem and then having fun figuring it out.

Maths teachers have always had techniques to implement ‘Curiosity and Wonderment’ in the classroom.  Unfortunately, we kind of kill it by giving it a more maths sounding name:  the dreaded 


Simple Solution:  Change the lexicon. 

Curiosity and Wonderment are the ‘creative and natural’ words for something we strive to do all the time in Mathematics……
…..Conjecture and Proof.

So next time you plan to ‘introduce an investigation’ into your lesson, I challenge you to throw caution to the wind, and just tell the students that in today’s lesson we are going to ‘play'.  The play needs of course to have a relevant purpose – one connected to the topic of a lesson.  And, the ‘language of curiosity and wonderment’ must be modelled by the teacher…..

                        …..I wonder what would happen if we increased the weight of……
                        ….What if we tried to make it …..
                        ….I wonder if we can find a pattern that will help us to predict….
                        ….I am curious to know if it would work with hexagons as well as pentagons…

Maybe, by just tweaking the language that we use when inspiring our students to engage with mathematics, we can encourage more of them to join us in our wonderful world of Mathematics.

Friday, 6 January 2017

Two of My Favourites - 2016 in Review

Favourite Number One:  Clearing up Misconceptions

This is an excerpt from a post I wrote earlier this year.  The tool I used is called 'My Favourite No".  I found that with less confident students, using "My Favourite No" on a regular basis both cleared up misconceptions and helped students to feel that they are not 'alone' in the classroom.

 'My Favourite No'

I first learned about this strategy when I took a professional learning course called 'How to Learn Math for Teachers’, presented by Jo Boaler of Stanford University.

Leah Alcala, the presenter of 'My Favourite No'  uses a simple warm up routine to help students learn by analysing and discussing mistakes.

What I love about 'My Favourite No'

  1. It is a simple, safe technique that engages the students!  Everyone does the same problem, anonymously.
  2. When to solution cards are quickly checked, students will see that they are not alone in making mistakes.
  3. When critiquing solutions, we always look for the positives first.  What did this student do really well?
by helping students to understand that they can learn from their mistakes, as well as the mistakes of others, we can promote a growth mindset in a safe classroom environment.

My challenge to you:

Try 'My Favourite No' in your next lessons!  And send your feedback in the comments section.

Favourite Number Two: The Power of Student Centred Learning

2016 was a stellar year for active Mathematics learning in my classroom.  My goal was to work smarter, not harder than my students - and the result was astounding!  I found, by moving more toward active, student-centred learning that my students
  • developed more initiative
  • asked more questions
  • used more reasoning and justified that reasoning with their peers
  • looked to each other, not to me as their learning partners
  • became better problem solvers
  • were more engaged, 
  • embraced challenges
  • gained in self-confidence

My Favourite tools for moving towards student-centred learning were:

For  teacher inspiration, ideas, research:
Twitter feed - this could always re-inspire me after a rough day at work
Continuous Everywhere, Differentiable Nowhere   a positive, pleasure to read
dy/dan  - for great links to great teachers and ideas
TEDEd - Lessons Worth Sharing - Especially the Logic videos
YouCubed -  to keep maths accessible to all students and their parents
NCTM - Journals   Mathematics Teacher and Math Teaching in the Middle School 

For Interactive Learning Tools and resources:
Desmos - Card Sort,  graphing
Scootle - Education Services Australia - for great topic specific interactives
Twig - Maths and Science Videos and worksheets - visual, real world connections

For Student Motivation and Challenge:
NRich - try a challenge at the start of each lesson to get the students going
Desmos  - Marbleslides - My students thank you!
Stile Education  - A great, free platform to introduce Flipped Learning

My New Year Resolution: 

In 2017 I plan to continue to use these resources and tools to continue to find motivation and inspiration for the role I love - teaching students to learn and LOVE mathematics.