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Lessons Learnt and the Value of Sharing

Kate reflects on the importance of taking little steps to introduce powerful new methods, and how sharing and discussing with colleagues amplifies her ability to learn and improve as a teacher.

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How exciting it is to look back on the impact the ACoM program has had, not only my own practices and beliefs when it comes to mathematics, but that of those around me too. Since my last blog entry so much has happened, and it’s hard not to share it all!

In our Mid-Program Questionnaire, I was delighted to see a massive shift in student responses since the start of the year. Overall, my class have moved towards enjoying maths lessons almost all the time, enjoying challenges and feeling more confident in their own abilities. To me, these survey results were the evidence I needed to prove the observations I had made about increased student engagement and attitudes, and, a fantastic way to convince others to begin this journey themselves.

Lisa and I have continued to develop all that we have learnt in our classrooms and have now been able to start spreading this across the school.

I collaborate closely with the other Year 6 Teacher at our school, a new graduate. Before my journey progressed too far and I forgot where my class had come from, my line manager suggested sharing the approach with him and helping to get his journey started. We thought the best way to do this was for me to model a lesson in his classroom with his students. I decided to use a problem my class had recently tackled ‘At the pet shop, it was found out that for every seven female goldfish born, only 5 male goldfish are born. If there are 156 goldfish born in one year, how many will be females and how many will be males?’

Alcoa Maths Enrichment Program Learning goals by Kate Archibald
Lesson Plan (Above)

Before commencing the solving time, I briefly spoke with the students about the problem, participation expectations, respectful debate and efficiency (most likely an information overload!). Once the solving time had commenced, students seemed disengaged and were struggling to provide some kind of solution and reasoning as to how they got their answer. Upon reflection, I realised I’d gone ‘too hard, too soon’, hitting them with too many elements of this problem solving process all at once and in a classroom where this was a new approach to mathematics. Whilst the students regularly participated in group work, their ability to confidently and collaboratively debate ideas using mathematical language was not yet developed.

Teaching this lesson in another classroom reminded me of all the little steps I took to get my class working at the stage they are now. This inspired me to share a blog with those of you who may be reading our entries and wanting to try it for yourself, but not knowing where to start!

Here are my top 3 tips 
Teach students the expected behaviours:
We did multiple repetitive lessons over the first few weeks to reinforce these in a timely manner. It’s important for the students to get used to the expectations of working in groups of 4, sharing their ideas with the class, accepting the random group generator, and participating in group situations. Spend time deconstructing what these expectations are and what they ‘look like, feel like and sound like’ to students. There is a photo in my first blog entry that shows the poster products of our classroom discussions.

It’s important to start simple!
The lessons you’ve been reading about from us all surely haven’t been our first ones. When I first began teaching this way, the questions I provided to students were much less challenging. This allowed me to focus on the skills they needed in these situations rather than the content in problems that foster ‘productive struggle’.

One of the main sources I got my problems from in the beginning were Blake’s Problem Solving PDF Downloadables available for free from  An example of one of the first problems I did was “Susan and Marilyn both go the gym each week. Susan goes every three days but Marilyn goes every fourth day. If they both attend on Monday when will they next be at a class together?”.

IMG 8710 2-web1


As you can see from the team’s samples above, the mathematical ideas and processes weren’t great… BUT, we were really able to work through the expectations and students were able to celebrate their achievements. We tackled more and more problems like this and became confident in following the ‘5 Practices’ approach. This resulted in the students being ready to move to the vertical whiteboards, and to tackle more challenging problems and the idea of ‘efficiency’.

Focus on the positives:
As you start, be sure to praise students for what they are doing, don’t focus on what they aren’t yet doing. Highlight to them the examples of the respectful discussions you heard around the classroom and acknowledge that even verbalising and contributing their processes and ideas with others is a win, no matter the quality of their sharing. Another great idea that I’ve seen in Lisa’s room is asking the students to share ‘sentence stems’ they heard each other using. ‘Sentence stems’ are partial sentences that students use make a statement or to branch into a discussion. Some examples are “I’m not sure what you mean about…” or “I disagree/agree because…”(for more info on sentence stems and respectful debate, read Lisa’s Blog here!).

I believe that focusing on these 3 things has really maximised the way my students are now able to engage in this process. The time and effort invested at the start was so worth it! To look back on how my class were first approaching problems and compare it to recent experiences has been just another confirmation of the work we’ve been doing. To be able to throw them a ‘reasoning’ task and watch them be quick to start, resilient to share, seek efficiency, give convincing reasoning and respectfully debate with each other (although just like any class, they still need some reminders!) makes me so proud! They think carefully and genuinely want to further themselves mathematically.

IMG 0850 web
Photo of class working on reasoning

On top of following these tips, my one piece of extra advice is to not be afraid to talk to others about your lessons and planning! It has been invaluable this year to have people watching my lesson and debriefing afterwards. In the same way, I’ve thoroughly enjoyed observing Lisa’s lessons, absorbing her ideas, and helping others along their journey. Since I modelled the lesson in the other Year 6 teacher’s classroom, we’ve both been able to watch and learn from each other. We’ve shared our lessons, resources and ideas, as a result both us, and our students have benefited. Shyam has also helped me to provide feedback and coach others using this approach. Opening yourself and your lessons up to others can be a daunting thing, but for professional growth, it is so important. As many quotes that we see floating around say, teachers need other teachers, it is not a job we can do alone!

If you’re keen to begin this journey, connect with others around you. Begin by reading these blogs and dabbling with your understanding of what we’ve shared. Look for a ‘simple’ problem you feel your class will feel confident to tackle, teach the expected behaviours and focus on the positives. As you and your class become more proficient, gradually change your goals for each lesson. If you want to debrief or float any ideas by me, please feel free to send me an email, I’d love to be part of your journey too!


Find out more about the Alcoa Maths Enrichment Program or read the next article.


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