What led to Numeracy Ninjas?
Numeracy Ninjas is the culmination of many years of professional development related to understanding what barriers to their learning students have when they study GCSE Maths.
Through rigorous diagnostic testing, we found that the majority of KS3 students had gaps in their mental calculation strategies and their timestables. These became barriers to learning GCSE maths topics as students attempted to use inefficient mental strategies, or working-memory-consuming calculations to do the basics involved in higher-level topics. For example, when learning how to add fractions, the learning barrier for some students was being able to find a common multiple of the denominators. From the students’ perspective, it was a lesson improving their timestables knowledge, rather than about adding fractions.
To be able to focus on GCSE Maths concepts, students need not only to be able to do the basics, but to do them automatically at speed and with accuracy- fluently. Our diagnostic testing showed even middle-and-high attaining students had some concerning gaps in their fluency of basic strategies.
But what about understanding? We are not for one minute advocating solely rote learning. Conceptual understanding is essential and we are strong supporters of teaching using visual models, such as bar models and algebra tiles; and rich learning activities such as those available from NRich. However, for speed and accuracy to develop, fluency, students need regular practise. Numeracy Ninjas is a project created to make it easy for teachers to give students these fluency-building practise opportunities in their lessons.
Fluency in which topics?
The need for fluency in mental calculation strategies is obvious. The mental strategies in the Numeracy Ninjas resources were taken from a brilliant National Strategies publication: Teaching children to calculate mentally. There’s no doubt we’ll have missed some strategies and it is our hope that schools running Numeracy Ninjas will help us in identifying these so we can improve the product over time. However, we believe the 26 strategies used in the product are a good base.
Next, we mapped the GCSE Maths curriculum asking ourselves the question, ‘which topics are the required prior learning in order to be able to access each GCSE Maths topic?’ This helped us identify the key topics that must be mastered with fluency at KS3 in order to remove potential barriers to learning at KS4. Timestables were most important, along with many other number topics. In the Timestables and Key Skills sections of the Numeracy Ninjas resources we have based the chosen topics on our curriculum mapping project conclusions.
The topics in each section are as follows:
|Mental Strategies||Timestables||Key Skills|
|Number bonds to 5||1 timestable including corresponding divisions||Multiply whole numbers|
|Number bonds to 10||2 timestable including corresponding divisions||Divide whole numbers|
|Number bonds to 20||3 timestable including corresponding divisions||Add whole numbers|
|Number bonds to 100||4 timestable including corresponding divisions||Subtract whole numbers|
|Doubling a single digit number||5 timestable including corresponding divisions||Order of operations- easy|
|Doubling a two digit number||6 timestable including corresponding divisions||Order of operations- harder|
|Halving a single digit number||7 timestable including corresponding divisions||Multiply decimal numbers|
|Halving a two digit number||8 timestable including corresponding divisions||Divide decimal numbers|
|Adding 10 to a number||9 timestable including corresponding divisions||Place value|
|Subtracting 10 from a number||10 timestable including corresponding divisions||Convert between fractions, decimals and percentages|
|Adding multiples of 10 to a number||Multiply by 10, 100 and 100|
|Subtracting multiples of 10 from a number||Divide by 10, 100 and 1000|
|How many to a multiple of 10?||Add decimal numbers|
|Add near doubles and compensate||Subtract decimal numbers|
|Partitioning single digit numbers||Multiply negative numbers|
|Partitioning two digit numbers||Divide negative numbers|
|Add using number bonds to bridge a multiple of 10 and compensate||Simplify fractions|
|Subtract using number bonds to bridge a multiple of 10 and compensate||Round to decimal places|
|Count from the smallest number to the largest in a subtraction||Substitution|
|Reorder an addition||Simple directed number|
|Understand multiplication as repeated addition||Add a negative number|
|Understand division as the inverse of multiplication||Subtract a negative number|
|Equivalent calculations to make an addition easier||Read a number from a number line|
|12 hour clock||Round to significant figures|
|24 hour clock||Factors|
|How many minutes to/ past a time?||Multiples|
|Square numbers and square roots|
|Cube numbers and cube roots|
|Fraction of an amount|
|Percentage of an amount|
How often should students practise these topics to maximise retention over time?
There is research that answers this question and we were heavily indebted to the work of Robert Bjork and Doug Rohrer. For an introduction the main ideas, read: Forgetting is necessary for learning, desirable difficulties and the need to dissociate learning and performance.
Doug Rohrer has done a lot of work into researching the benefits of spacing practise in a maths context and also into the optimal spacing interval. See Doug’s publications and in particular, his paper, Cepeda, N. J., Vul, E., Rohrer, D., Wixted, J. T., & Pashler, H. (2008). Spacing effects in learning: A temporal ridgeline of optimal retention. Psychological Science, 11, 1095-1102.
From the discussed research we decided that topics in the Mental Strategies and Key Skills sections of the Numeracy Ninjas resources would be revisited on approximately a 3 week basis. You will see topics that appear in week 1 also appearing in weeks 4, 7, 10 etc. In the early weeks you should expect students to forget their learning over the 3 week interval; it requires a number of recall events before the learning will be retained over time. This is normal and don’t give up early on if progress gains are not immediate! Students need to be told this message too! “Rapid and sustained progress” is oxymoronic; sustained progress takes time to develop.
Numeracy Ninjas is the result of all this professional development we’ve done over the last few years. We’ve tried to turn these findings into a product that will ensure students develop sustained fluency in the right topics to make GCSE Maths concepts fully accessible to them.
We’ve built the principles of gamification into the product, see the work of Prof James Paul Gee, to make it engaging to students. We are indebted to the work of Matt Wright for all his graphic design. We do plan to develop online gamification of the product in the future.
Numeracy Ninjas is based around the main product, the free Ninja Skill Books. The ideas is that students complete 10 mental strategies questions, 10 timestables questions and 10 key skills questions in a 5 minute activity, regularly at the start of Key Stage 3 lessons. They mark their answers and efficient strategies for key questions are discussed by the teacher. They relate their attained Ninja Score to a colour Ninja Belt so they can ‘level up’ over time, aspiring to the coveted Black Belt!
Where is the differentiation? Through experience we have found that the Ninja Skill Book activities are suitable for nearly all students. We don’t like the idea of placing a glass ceiling on what the lower-attaining students can achieve and we’ve found that nearly all students can access the resources, achieve a belt and improve. It is of course up to your professional discretion as to whether you feel the resources are appropriate for your particular students.
Once per half term, the highest achieving and the most improved students in each class are awarded Grand Master status. There are free certificates you can download from the Promotional Materials section of the website and optional further prizes available for purchase from the Online Shop.
An additional suite of free resources for students who have extra maths intervention time, or for students who wish to practice individual skills is available, see our Ninja Skill Focus Worksheets.
There are lots of things we’d like to do to develop Numeracy Ninjas in the future. Your feedback is going to be very important in guiding us. If you decide to run Numeracy Ninjas in your school make sure you let us know how it goes and what we can do to improve if further via the Contact Us page. Make sure you sign up for our email updates so we can keep you in the loop as the project grows over time.