Mathematical Mindsets

A while ago I reviewed some material from the Mathematical Mindsets book by Jo Boaler

I was given an article by my wife and she was very excited about it so I read it.  It felt familiar but it has only just dawned on me that it was a chapter from the book.  What that particular chapter has to say does fly in the face of some of our current practices around sorting kids into groups of like ability for reading.  Teaching is a complex business and I guess the only answer to that problem is that different strategies for different purposes.  I will say this though it does sit closely with my believe that all students should be offered the opportunity to work with kids of all different abilities.  The process of withdrawing children for support or intervention does not really sit well with me and I don’t really believe it is the best practice for a range of reasons.

Anyway I thought I would share some other resources about this book and the topic:

A free course:


In the business of empathy

Positive Education

The Gap State High School is an active member of the Queensland chapter of PESA (Positive Education Schools Association) and recently hosted Mr Simon Murray who up until 5 days ago was the Headmaster of St Peter’s Boys College in Adelaide.  This school has a big focus on wellbeing and positive education.  I thought I would take this opportunity to share some resources that were shared in this session.


Mindset Kit and other resources

This has been a bit of a theme across the last few posts but thought I would share some more.  It is something that we might look into with respect to PD in the future and a whole school approach.

One free course you can complete is at:

Other courses and resources you may wish to explore:

The Power of Yet

Growth Mindset: The Power of Yet

Growth mindset – a phrase that can easily be coined the education fad of 2015-2016. Although I do like to avoid most fads (bleached hair, suntanning oil, and silly bands were all lost on me), why not take the best from the proverbial education pendulum and allow it to positively impact our classrooms? Recently my 1st grade classroom has morphed into a K/1 combination classroom resulting in HUGE gaps (academically, socially, & emotionally) between my students. Today I’m sharing one of our most powerful community-building lessons we’ve shared since becoming a combined classroom!


Intentional Read Alouds

Intentionally chosen read alouds and texts in a classroom have tremendous power. From writing mentor texts, to texts that lend themselves to particular reading strategies, our students need models.

Giraffes Can’t Dance (affiliate link) is one of my favorite read-alouds. It’s a smooth read, include rhymes, and is a perfect platform for launching a conversation about differences in the classroom. The book centers around a Giraffe who can’t dance like all the other jungle animals and is made fun of because of his lack of dancing skills. Gerald is the perfect character for teaching students about growth mindset!

The rest of this lesson can be found here:

Other resources:

Growth Mindset

How often have we said the following to a child who is struggling with a particular subject, thinking we were being helpful: ‘Don’t worry, I was never very good at Maths [or English, French, Science etc.] either. Sometimes our brains just aren’t wired that way.’

There is a growing school of thought that intelligence and ability are, in fact, not fixed. Brains and talent are just the starting point for us all and, with effort and dedication, intelligence can be grown as the brain continues to develop over the course of our lives. This idea is known as the ‘Growth Mindset’.

According to Stanford University Professor, Dr Carol Dweck, if we teach to the Growth Mindset theory, we develop in our students the belief that their basic abilities, such as intelligences or talents, can be developed through dedication and hard work. This is very empowering for a young person.

In this talk, she describes two ways to think about a problem that’s slightly too hard for you to solve. Are you not smart enough to solve it … or have you just not solved it yet?

Staff Wellbeing

We have reached the end of another term and I thought I would share a couple of resources I have found online and some tips from a recent QELi conference I have attended.

It is important to plan for wellbeing…a strange concept to plan to feel well but if you don’t take the time this job can take over your life.

At the QELi conference it was suggested to plan weekly for these elements:





In short plan for your fitness, time with those that matter, something that makes you feel good and something intellectual to feed your mind (read a thought provoking book).

The stats:

Here are some eye-watering statistics:

  1. over half of teachers (52%) say that they have seriously considered leaving their current job in the last 12 months and nearly half (47%) have seriously considered leaving the profession;
  2. two fifths of teachers (41%) say their job satisfaction has decreased in the last 12 months;
  3. teachers’ biggest concern regarding their job is workload (79%), followed by pay and pensions (66%), changes or reforms in the curriculum (59%) and school inspections (51%). The vast majority of teachers (86%) say that their workload has increased in the last 12 months;
  4. the majority of teachers disagree that teaching is competitive with other occupations in terms of either the financial rewards on offer (80%) or salaries (67%) and only 21% of teachers feel optimistic about their career opportunities;
  5. the top three things teachers love most about their jobs are seeing children learn and progress (91%), interacting with pupils (90%) and making a positive difference (83%). (Source)
  6. research by the Association of Teachers and Lecturers (ATL) found that 55% of teachers said work pressure is having a detrimental effect on their mental wellbeing. Note, the research was conducted in April 2014 by polling agency ComRes, surveying 2002 adults, of whom 1548 are parents and 933 have children under 25.


The published article stems from the following questions:

  1. Accountability: to whom are teachers accountable? Children, parents, school management, Ofsted, the secretary of state, the public, the media? Or are their own consciences the hardest taskmasters of all?
  2. Are the biggest pressures internal or external? What can management do to alleviate those pressures and help teachers cope with the workload?
  3. Professional development: should schools spend on this as an investment in people, rather than take a negative view and see it as a cost?
  4. How has the decline in status affected teachers? Do they feel the need to justify their working patterns?
  5. What does support look like? Preventative measures.

Intent vs. Impact

Speaking to a group of principals, one of the participants, thanked me for my time, and gave a very elegant “call-to-action” to the group.  It was not simply discussing what I talked about, but what they needed to do to move forward.

One of her quotes that resonated with me was, “Intention is not good enough; we need to look at our impact.”1  It jolted me.  There are very few people in the world that don’t want to do important things, yet what is the impact of our intentions?  Everyone wants to be a great teacher, but do all educators do things that keep them up to date and moving forward in their work? This would obviously apply to any profession.

I have always believed that you could have been a great teacher ten years ago, changed nothing, and now be irrelevant.

This is one of my favourite quotes from a college dropout who felt a post-secondary education was no longer relevant to what he needed to be successful in our world today:

“Wanting” is not good enough on it’s own; the impact of our actions are how progress is always measured.

George Couros Principal of Change


How Open-Ended Math Tasks will transform your math block

Learn how you can use open-ended math tasks to teach your students valuable mathematical problem-solving skills while deepening student engagement, understanding, and retention – Absolutely FREE!

What You Will Learn On This 1-Hour Free Webinar:
Even if you’ve heard of open-ended math tasks, it’s likely that you have yet to try them in your classroom. And trust me, you’re missing out! This slight tweak to math tasks completely changed my math block, and for good reason.

After I started using them, every student in my room became more capable and independent math thinkers. And perhaps more importantly, they became confident problem-solvers because they knew what strategies to apply when. If you’re skeptical, so was I. It took me four days of training before I even wanted to try them in my classroom. But once I did, I never went back.
In this training, we’ll talk in detail about what open-ended math tasks are, and why they’re so powerful. I’ll also show you everything you’ll need to know to implement open-ended math tasks into your math block right away.


Patience, persistence, and a willingness to grow

Another good article by George Couros:


A good friend always talks to me about the willingness to just put in the work when no one is watching. I think about this all of the time, and what it means for educators, and what it means for our students.  The most meaningful things in your life will come with effort. We know this but do we aspire to it?

The image above is not only showing what people don’t see, but it is also shows what some people are not willing to see.  Many look for the easy route, but is this what we want to teach our students?

Another friend of mine talked about some of her frustration recently and reached out to me for some advice. What I told her was that, “You feel bad because you care and you want to do awesome things.  Understand that not everything works the way we plan, own it, and then move forward.” Sometimes it is good to cry, be upset, feel like you failed.  It is not about embracing failure; it is understanding that it exists, and then moving on, and moving forward.  One of my favourite movie quotes is from Jerry Maguire, and it is simply two words;

“Breakdown? Breakthrough.”

Patience, persistence, and a willingness to grow.

What if these were traits that all of our students walked out of school with?  The future would be pretty bright.

Some other resources:

Assessment for a Growth Mindset

Failed Test ca. 2001

Students understand mathematics in many complex ways.  Students ask questions, see ideas, draw representations, connect methods, justify, and reason in all sorts of different ways.  But recent years have seen all of these different nuanced complexities of student understanding reduced to single numbers and letters that are used to judge students’ worth.  Teachers are encouraged to test and grade students, to a ridiculous and damaging degree; and students start to define themselves – and mathematics – in terms of letters and numbers.  Such crude representations of understanding not only fail to adequately describe children’s knowledge, in many cases they misrepresent it.

This chapter deals with the growth in standardised testing and that often in mathematics classes this practice is mimicked through the delivery of low-quality standardised tests.  This is despite the knowledge that these tests only assess a narrow focus within mathematics.

The testing regime of the last decade has had a large negative impact on students, but it does no end with testing; the communication of grades to students is similarly negative.  When students are given a percentage or grade, they do little else besides compare it to others around them, with half or more deciding that they are not as good as others.  Commonly students describe themselves by saying “I am an A student” or “I’m a D student”.

So this is where FEEDBACK comes into it…the reason it is in the top 10 of strategies to improve learning.

The students receiving comments (not grades) learned twice as fast as the control group, the achievement gap between male and female students disappeared, and student attitudes improved.

This is the response to a mathematics homework study where half the group were given grades and half the group were given diagnostic comments and no grades.

Race to Nowhere

An American documentary that addresses the stress upon today’s students:


Assessment for Learning

Paul Black and Dylan Wiliam provide some valuable insights into the use of assessment for learning.

Teachers who use A4L spend less time telling students their achievement and more time empowering student to take control of their learning pathways.

The 3 vital questions:

  1. Where students are now
  2. Where students need to be
  3. Ways to close the gap

Developing Student Self-Awareness and Responsibility

The most powerful learners are those who are reflective, who engage in metacognition – thinking about what they know – and who take control of their own learning.  A major failure of traditional mathematics classes is that students rarely have much idea of what they are learning or where they are in the broader learning landscape.  They focus on methods to remember but often do not even know what area of mathematics they are working on.

There are many strategies for encouraging students to become more aware of the mathematics they are learning and their place in the learning process.  Here are 9 favourites of the author of Mathematical Mindsets:

  1. Self-Assessment
  2. Peer Assessment
  3. Reflective Time
  4. Traffic Lighting (understand (green), partially understand (yellow) and need help (red) – some Teachers hand out coloured paper cups)
  5. Jigsaw Groups (work together to become experts on a particular area and then split and join new groups to share information)
  6. Exit Tickets
  7. Online Forms
  8. Doodling
  9. Students write questions and tests

Advice on Grading

Many teachers, unfortunately, are forced into grading, as it is a requirement of their school district or the administrators of their school.  The following lists compiles advice on ways to grade fairly and to continue communicating positive growth messages even when faced with a grading requirements:

  1. Always allow students to resubmit any work or test for a higher grade;
  2. Share grades with school administrators but not with the students;
  3. Use multidimensional grading
  4. Do not use a 100-point scale
  5. Do not include early assignments from mathematics class in the end-of-class grade
  6. Do not include homework, if given, as any part of grading

Not all practical but worth thinking about and discussing at another time.  Some of our feedback work should be designed to provide students with opportunities to improve on drafts and early tests.