Numeracy Ninjas was born from the realisation that there are two big issues in UK maths education that need to be addressed. The project aims to empower maths teachers to rise to these challenges, giving them the resources to do so.
1. The levels-based assessment culture has resulted in gaps in students’ basic numeracy skills going unnoticed and unchallenged
We diagnostically tested the numeracy skills and fluency of our entire Year 7 cohort in 2014-15. We did this at the start and end of the academic year and found significant gaps in students’ basic mental calculation strategies. Level 4 students had gaps with level 2 skills. Even the higher-attaining students had noteworthy omissions from their numeracy capacity and fluency. Read more.
This table shows the results of our diagnostic assessment. The percentage values are the mean accuracy of the students in each Key Stage 2 sub-level group on each skill tested.
We realised it is not only the lowest-attaining student that have concerning gaps in many basic numeracy strategies. The diagnostic testing at the end of the year showed no significant improvement- students had typically risen two or more Key Stage 3 sub-levels, but their mental calculation strategies fluency was unchanged. This was also true for their timestables. Would the inefficient calculation strategies they were using to make progress in Key Stage 3 become barriers to learning when they moved to Key Stage 4? We realised unless we explicitly teach students the mental strategies, these gaps would not close before they begin their GCSE Maths studies. Numeracy Ninjas is that intervention. And, it’s not just the lowest-attainers that need it…
As the profession moves towards an ‘assessing without levels’ culture we must not replace our assessment strategy with one that has the same flaws. Levels hid gaps in students’ basic mental calculation strategies and timestables. We need assessment systems that identify these so we can intervene. It is our hope Numeracy Ninjas can play a role in welcoming this new dawn.
2. To be fully prepared for GCSE Maths study, we need to recognise that complete mastery of some topics is more important than others
This image is the 1MA0 Edexcel GCSE Maths curriculum. Each node is a topic on the course. Each link represents where one topic is the prerequisite learning required to learn the other topic. For example, you need to know your timestables in order to find HCF and LCM.
The nodes are colour-coded by the assessment strands: number and calculating- red, shape space and measure- purple, algebra- turquoise, data handling and probability- light green.
The nodes are scaled in size by the number of out-going links they have. I.e. the largest nodes are the required prior learning for a greater number of topics. The importance of mastery of number is clear to see. What’s the largest node? This analysis suggests ~50-60% of all topics on the GCSE rely on fluency with timestables (and corresponding divisions).
In addition to fillings gaps in mental calculation strategies and timestables, Numeracy Ninjas also features questions on ‘Key Skills’; these are the top ~20 largest nodes from this diagram. If students master all these before they begin Key Stage 4, they will find they have an excellent foundation of knowledge that will make learning GCSE Maths concepts easier. Of course this won’t be an exhaustive list and it will vary from student to student, but the importance of mastery of number topic shown clearly in this curriculum map agrees strongly my first-hand experiences as a maths educator.
This table shows the results of our year 7 cohort when tested on the Key Skills at the start of the academic year. Students were allowed to use written calculation methods for the Key Skill topics if they wanted to (but not the mental strategies or timestables assessments).
We’re not claiming silver bullets here, or that our approach is fully comprehensive. There will be things we’ve missed and assumptions we’ve overlooked. We are simply trying to gain a better understanding of what will help our students do better in their learning of maths. Rather than just ideas alone, we’ve tried use research findings and meaningful assessment data to create the best product we could think of to allow maths teachers take on the discussed challenges. We believe these issues are so important we’ve made it free.
We hope this gives you a good understanding of the motivations for the project and what we are trying to achieve. If you’d like to come on this journey with us feel free to give Numeracy Ninjas a trial in your own school and let us know its impact.