FREE
Fluency in Five 
 

This free resource aims to balance the discussion about fluency and spaced retrieval versus conceptual understanding. Both are critical. However, fluency can only be achieved after the battle for conceptual understanding has been won, and then only requires a consistent 5-minute morning routine, as outlined above.

This ensures the main maths lesson every day can focus on significantly richer tasks, with explicit teaching that focuses on concrete materials and visual models, meaningful real-life links and engaging stories that trigger long-term memories. These elements grow students' deep conceptual understanding, reasoning and problem-solving skills, which are critical foundations for later fluency and richer skills for life as well.

It must be noted that early number facts are not 'basic,' as otherwise these would not be so problematic in the first place. Without materials and Singapore's concrete-pictorial-abstract approach (CPA), even small number facts are very abstract for young learners and - therefore - complex for this developmental stage.

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Genuine fluency is based on flexibility with mental strategies, not speed and instant recall alone. The ultimate proof is that if you put a student who cannot use near doubles in front of a developmentally inappropriate drill sheet, they will mostly resort to count all or count on (embedding less efficient strategies in the long-term), and will not learn near doubles without hands-on, sequential units focused on slow practice with materials and mastery first. Students may learn ‘instant recall’ of 6 + 7 if you drill for long enough, but ask 60 + 70 and they won’t know, because they have not been given a chance to generalise, reason or apply with materials or problem-based reasoning – they have been drilled in one fact at a time, and that is all. Maths is a brilliant shop (you buy one, you can get 100 for free), but if the teacher never shows you the discount codes with materials and real-life links, you come to see it as a very expensive shop – one where a textbook/worksheet/technology dominated main lesson approach makes you buy and memorise each item one-at-a-time.

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Fluency is only one piece of the puzzle - and our results show it is achieved easily in a 5-minute morning routine, but only once genuine number sense and flexible mental strategies are developed using materials first, so that deep conceptual understanding is established. Please see our 2024 student gains and comparison to like schools at our most intensive PL school (Chirnside Park PS) on our Research-basis page.

That is why we have dedicated ten years in classrooms to developing sequential units focused on understanding, reasoning and problem-solving - Early Years Pack and incoming Years 3-6 Pack.

A critical issue in this discussion has been what is 'evidence based.' Our approach is based on the research of Emeritus Professor Doug Clarke, Professor Anne Roche and Professor Matthew Sexton (Engaging Maths); Professor Dianne Siemon (Big Ideas in Teaching Mathematics: Foundations to Middle Years); Professor Peter Sullivan (Challenging Mathematical Tasks); the coaching careers of internationally-renowned experts in primary numeracy Michael Ymer and Rob Vingerhoets; among others, who all champion the use of real-life links, materials, flexible mental strategies and number sense over textbooks, worksheets and PowerPoints.

For us, an approach cannot be evidence-based without evidence of results. Those advocating for PowerPoints claim to be evidence-based, yet have not presented Australian NAPLAN results comparable to those our approach has achieved at our most intensive member schools, including Thomastown East PS, Kinglake PS, Dandenong North PS or Chirnside Park PS over the past eight years. Please see our evidence of 15 whole-school case studies of results using a hands-on, sequential, engaging, materials-based approach to maths.

More important even than results is how students and teachers feel about maths, because if they hate it, the battle has already been lost. Students at Top Ten schools love maths, and so do teachers (but don't take our word for it - please read the feedback that hundreds of Australian schools have provided to us after using our unit plans for a year or more).

Learning numeracy for real-life is the ultimate goal, and that is something that cannot be achieved through a PowerPoint, textbook or the fluency routines set out on this page alone. It can only be achieved through a hands-on, engaging, sequential, explicit teaching approach that uses materials, emphasises understanding and reasoning, and regularly 'throws students in the deep end' with challenging problems.

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As a result, we are giving away an entire approach to fluency, with 77 sequential skills (plus 11 extension-level skills when achieved at fluency pacing) for free, because fluency is of no value unless students first develop deep conceptual understanding and trust in their own mental strategies. That is what our hands-on units are about – real numeracy (not just mathematics).

We hope this resource is used with care – it will be powerful in the right hands; that is, in schools that value reasoning, problem-solving, understanding and student engagement as their first priorities in growing numerate adults who still love maths throughout their lives.