This post was originally published last year, and I thought it timely to republish considering many teachers in Australia are busy spending the school holidays programming and planning for Term 2.Often when I work with teachers I am asked for advice regarding the design of a scope and sequence for mathematics. The programming and planning of mathematics seems to cause much concern, and often the reason is that there is no ‘magic fix’ or one-size-fits-all solution.
Traditionally, schools have planned their mathematics teaching using a topic-by-topic or strand-by-strand approach. Sometimes there is a formula for teaching the Number and Algebra strand for a certain number of days per week, with the other days dedicated to the remaining syllabus strands. Often, the strands are split into single, stand-alone topics. Unfortunately, there are issues with this approach. Teaching individual topics in mathematics hinders students in gaining a deep understanding of mathematics and the connections that exist between and among the strands. Teaching in this way can promote a traditional, rote learning approach where the opportunities for mathematical thinking are limited. Our curriculum places the Proficiencies (Working Mathematically in New South Wales) at the forefront of teaching and learning mathematics – teaching topics in isolation does not promote the Proficiencies.
So what’s the solution? Consider planning and programming using a ‘big idea’ approach. What’s a big idea? Big ideas are hard to define and different people have differing ideas on what the big ideas in mathematics actually are. However, all the definitions in literature have one thing in common – they all refer to big ideas as the key to making connections between mathematical content and mathematical actions, and they all link mathematical concepts. Take, for example, the big idea of equivalence. This relates to number and numeration, measurement, number theory and fractions, and algebraic expressions and equations. Connections can be made across the strands and these links should be made explicit to students.
Charles (2005) presents a total of 21 big ideas across the mathematics curriculum, however he states that these are not fixed – they can be adapted. He also states that a big ideas approach has implications for curriculum and assessment and professional development – teachers need to develop their pedagogical content knowledge to ensure they have a deep understanding of the connections within the curriculum if they are to teach mathematics successfully.
Of course, there are challenges to teaching using a big ideas approach. Teachers often feel under pressure to address all curriculum outcomes, and often this is the reason that the topic-by-topic approach is adopted. Using a big ideas approach can feel messy – it is not linear and in some ways feels as though it is conflicting with the organisation of our curriculum. However, we must remember that although our curriculum is separated into strands and sub-strands, this is simply an organisational tool and does not mean that mathematics should be taught in this same way.
My advice would be to take our curriculum, pull it apart and try seeing it differently – what areas of the curriculum have obvious links? How can you link aspects of measurement to the number strand? Where does measurement and geometry link? And how can you use the statistic and probability strand to teach number concepts? Making connections will make your teaching easier in the long run, and more importantly, will result in deeper learning and deeper engagement with mathematics.
Randall, C. (2005). Big ideas and understandings as the foundation for elementary and middle school mathematics. NCSM Journal, 7(3), 9-24.
This sounds absolutely spot on. It would be great if people had a way to share their big idea planning. I know I would find this a great starting point from which to develop something for my context.
Thank you for this article. Although I am a secondary maths teacher and head of department, this is the approach I’ve been working on getting the maths faculty to take when teaching middle school maths – especially with the introduction of the Australian Curriculum and those wonderful proficiencies. This came about originally because I read Jo Boaler’s book – The Elephant in the Classroom – where she wrote about having students engage with the maths curriculum by giving them big ideas and problems to solve that might require explicit teaching along the way, but that covered a range of mathematical concepts. I encountered a huge amount of opposition from the maths faculty and, indeed, from the site leadership team who didn’t understand what I was attempting to do. Still working on it.
This is a fantastic post, Catherine! I really enjoyed reading it, and it’s made me feel a lot better about some frustrations I’ve had with programming lately.
I’m struggling with our school’s traditional scope and sequence because it seems really disjointed and it feels like we’re teaching skills/concepts that don’t flow nicely into others/build upon one another. It’s frustrating, because as you say, there are some really beautiful cross-strand links that allow for knowledge integration.
I’ve been having a play with different content combos this week, and it feels like there must be almost a perfect way to sequence and align the content under umbrellas of big ideas, and there’s also opportunities for some of those big ideas to be connected authentically to learning in other KLAs. It’d be great to explicitly teach a bunch of connected concepts and finish with an authentic rich task that uses them all.
I can see a giant jigsaw sitting there, waiting to be solved. I just don’t have the time or maths confidence to put all the pieces together! 😦
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Ronda, I agree totally with your frustration. It would be great to hear from someone who has “had a go!”
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Hi Jan, Ann and Ronda,
Not sure if you will see this but
This link is quite a useful related article I think
Click to access Chapter%202%20Siemon.pdf
It talks about big ideas in number like Place Value, Multiplicative Thinking, Partitioning, Proportional Reasoning etc
I think your approach is fabulous and I am certainly trying to do a similar thing in programming, findings connections between different strands and concepts. Where can we find others who have done this before and what are the big ideas/concepts that they have found? Would love to hear/read about how this is being done.
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Thanks for that link to that big ideas article,Pru! I’m sitting down today with a colour-coded syllabus all cut up into pieces to see which bits fit together nicely. That article’s going to give me a nice framework for my puzzling 🙂