A five-year-old’s first engagement with Cuisenaire: Joyful Learning

Written by Chris McGrane Thursday, 31 January 2019

I’ve used Cuisenaire occasionally in my career. Much of the time it was as an aide in the teaching of fractions to younger secondary pupils. However, this fabulous resource has so much more potential. It can be used to introduce the very basics of arithmetic such as additive relationships, or extended into harder topics such as simultaneous equations, Pythagoras and equation of a straight line.

Allow me to share a reflection of “a learning episode”.

This evening my five-year-old son, who is as inquisitive as children of that age tend to be, spotted a small bag of Cuisenaire rods on my desk. He was immediately drawn to them. “What are those daddy? Can I see them?” The verb “to see”, for a five-year-old is not just an interaction of the eyes and brain. It is a tactile action, it involves touching the object and interacting with it in some way.

He poured all of the blocks over the table, gazing in my direction to ensure that this was OK. Immediately, he began to play with them. He built little patterns and began to group the rods. There is something about these little rods that is inherently enticing.

An initial arrangement

Mark McCourt had told me that young children will begin to behave mathematically with these blocks, given enough opportunity to play with them. I was stunned, when, after just a few minutes, my son said “Maybe after this I could do it by sizes”. The level of categorising went beyond the first level I’d expected him to consider; colour. Instead it was a mathematical idea. I let him play with them for a while. I was minding my own business, leaving him to it and not prompting him in any way.

All of a sudden, a loud announcement, coloured with the excitement and joy of a profound revelation: “Its colour is its size!” In that moment, these little rods had gone from being toy blocks to being something else. It’s impossible to make inferences about the connections he was making. However, what was to follow demonstrates, to me, that he was thinking hard.

Some organisation

“Orange is the biggest one!”

I’d resisted the urge to prompt or direct him until now, but I couldn’t help myself, I wanted to play too. Displaying a little bit of shock for his benefit I asked him “Is it really bigger than the blue?”

He was, correctly, adamant that it was. Having his conjecture challenged, he did what any mathematician would do – he sought out a proof! Carefully lining up the blue and orange he showed me that there was a gap. “Look – you can put a white one there”.

He’d just modelled a number bond to ten. While he can already “do” addition he hadn’t yet recognised that the calculations he does at school were synonymous with his demonstration with these little rods. I think that will come in time – after all, the pace of progress in his use of the rods is startlingly fast.

He continued to play freely with the rods. He made some domino trails. This is the beauty of this manipulative – there is fun to be had with it! A short while later I saw him looking at the purple and dark green. “This is four more taller than purple”. I was perplexed with this idea of four, as the green is only two blocks more than the purple. I chose not to judge, but instead try to understand his interpretation of the situation. I asked him to show me why.

He motioned with his finger four equal steps from the end of the green to the end of the purple. I suggest that there were two possible thought patterns here: the first is that there was some unit of measurement, known only to him, which was his point of reference. Alternatively, he hadn’t quite grasped the relative size of the white block to the others.

Maybe in asking why, I challenged him in a way that made him reconsider things. He presented me, absolutely delighted with himself, the following set up:

Comparative thinking

The mathematics is simply pouring out of this free play. These are exactly the sort of comparative models I watched Mark McCourt share with teachers yesterday!

The free play continued with “now I want to count them all”. This was going really well. He had counted past 50 when, all of a sudden, his twin sister appeared. He continued to count but her presence (she was asking me about the rods) put him off a little. He said he thought he’d counted properly, but wanted me to double check. His sister volunteered – she was keen to get involved too. Midway through counting I heard her brother say to her “you’ve missed out all of the fifties and sixties”. He had been listening intently. They decided to count them again together, this timing getting the correct total. I didn’t check the total for them. They have the knowledge between them to be sure of succeeding.

They began to discuss the orange rod. He told her how it was the biggest one. She replied, clearly insulted that he thought she hadn’t realised this “I know! Look – it’s two yellows”. She lined up the rods to show him her thinking. I hoped they’d follow this line of inquiry further, so offered a suggestion “how many white ones to get the orange?”. The guesses were wildly inaccurate. One thousand is the phrase they like to use for “lots of something”, so this was the figure they last mentioned. They each made their own models, slowly and deliberately placed the whites against the orange. This was a real test for their fine motor skills.

“The big one is the same as ten.” I noticed that neither of them said “ten whites”. Could it be that they had stumbled upon the standard numerical values of the rods? I was about to offer another prompt when my son asked me for a pencil, so he could measure it. They have done a little bit of measuring in school recently. Did the number ten resonate with him in some way as to remind him of this?

The first attempt at measuring
A further attempt

Before long the pencil was cast aside and a box was to be measured. This looks like a potentially intuitive introduction to the idea of perimeter. Yet more rich mathematical activity.

Measuring round the box

All of the above happened in less than 30 minutes. With no direct instruction from me a whole wealth of possible starting points for further exploration have been encountered. Cuisenaire is an incredibly powerful and versatile manipulative. The extent of how it can be used to support learning and teaching is vast. You can learn more about this by coming along to one of our Concrete, Pictorial, Abstract and Language CPD days.

Meaningful Times Tables Practice

Thursday, 16 November 2017

At La Salle Education, we believe that pupils benefit enormously from having a deep understanding of multiplication and division facts, which can later be efficiently recalled for use in more complex problems.

A secure knowledge of times tables facts makes pupils able to engage in interesting mathematical problems without having to worry about working out basic facts first – these facts are part of the underlying mathematical grammar that pupils call upon to engage with mathematics throughout their learning and application of the subject.

But mathematics is not simply a list of facts to be remembered. At La Salle, we are interested in the interconnectedness of mathematical ideas. Most times tables practice is focused on simple rote learning and memorisation of the facts. This misses opportunities to build deeper understanding of multiplication and division and results in a superficial ability to simply regurgitate numbers. Our times tables app draws on variation theory to give multiple representations of multiplication facts, which builds more meaningful connections in pupils’ minds and gives a greater chance of the facts becoming embedded in the long-term memory.

Through a variety of representations and metaphors, the Complete Mathematics Times Tables app gives pupils a better chance to ‘meaning make’ than traditional times tables apps.

Representations and metaphors

The Complete Mathematics Times Tables app deliberately intertwines a variety of ways of looking at and thinking about multiplication and division (and their connections to addition). The app includes standard recall prompts

but also makes connections to multiplication grids

and introduces pupils to arrays

The app also includes a pinboard manipulative, which not only connects the tables facts to multiplication grids, but also draws on the metaphor of multiplication and division as a view of area

Why no timer?

Becoming mathematically literate is not a competitive sport, it is a fundamental basic right for all. Although we want all pupils to be able to quickly recall times tables facts and be able to work efficiently with a wide range of problems that draw on these facts, we believe that – at the point of learning and embedding – it is far more important to carefully consider the problems and metaphors and to build a deeper understanding through meaningful practice.

Suggested uses

The Complete Mathematics Times Tables app is ideal for use in the mathematics classroom, at home, on the bus or… well… anywhere! Pupils can use the app on any device with a web browser.

With daily use, pupils will achieve a very secure knowledge of times tables facts. More than this though: unlike traditional times tables apps, which focus purely on the list of facts, using the Complete Mathematics Times Tables app daily, pupils will acquire a deep understanding of why the facts are true.

The times tables app could be used during tutor time, with pupils setting the quiz at 50 questions and recording each day how they are improving and which multiplication facts they need to continue to work on. Just 10 minutes per day for all pupils will help to drive up pupils’ mathematical literacy across the school.

So, why not try the app today with your pupils and start a journey towards truly meaningful understanding of times tables rather than just fast regurgitation of meaningless numbers.

Visit the Complete Mathematics Times Tables app page now.

EEF - Improving Mathematics in Key Stages Two and Three

Friday, 03 November 2017

Today, the Education Endowment Foundation has released its much anticipated report, "Improving Mathematics in Key Stages Two and Three"

La Salle Education welcomes the report and all of its recommendations, which we believe describes long established good practice in mathematics teaching. The report fully supports our mastery approach and backs up the model we use in the Complete Mathematics platform and CPD programmes.

Recommendation 1: Use Assessment to Build on Pupils' Existing Knowlege and Understanding

Complete Mathematics: contains extensive assessment and monitoring features, which are uniquely tied to what has been taught and future planning, giving teachers immediate insight into gaps in learning and quick and easy ways to adapt planning to account for such gaps. Our granular assessments also allow teachers to give targeted and contextualised feedback. Complete Mathematics also contains guidance on common misconceptions that can arise, meaning teachers are able to plan lessons that address such misconceptions

Recommendation 2: Use Manipulatives and Representations

Complete Mathematics: All Members have regular access to CPD on concrete, pictorial and abstract approaches to teaching mathematics, which includes extensive training on the use of manipualtives across the age and ability range. The Complete Mathematics platform also contains a suite of digital manipulatives for teachers and pupils to use when exploring mathematical concepts. Guidance is provided on the importance of seeing manipulatives as a scaffold, which is gradually removed to leaves all pupils with the ability to use quick and efficient abstract and symbolic methods.

Recommendation 3: Teach Pupils Strategies for Solving Problems

Complete Mathematics: contains extensive guidance on problem solving for all concepts in maths. Members also have regular access to our CPD events, including the popular Mastery in Mathematics day, which include deep exploration of strategies and dispositions for solving problems, reasoning and analysing. Our work on variation theory also includes guidance on understanding and being able to select from a variety of approaches. The Complete Mathematics platform includes thousands or problem solving tasks.

Recommendation 4: Enable Pupils to Develop a Rich Network of Mathematical Knowledge

Complete Mathematics: contains the whole of mathematics, with every single idea and concept from early years through to the end of A Level. The map through mathematics is presented to all pupils in their platform, giving them the ability to explore all maths and the detailed connections that exist. Our team spent many years creating the detailed map of mathematical ideas and the interconnectedness between them. All members have access to this map and can therefore plan schemes based on careful progression and connectedness. The platform contains extensive guidance for both teachers and pupils on every concept, including the underpinning knowledge and skills required.

Recommendation 5: Develop Pupils' Independence and Motivation

Complete Mathematics: members have access to regular CPD throughout the school year, including much about promoting thinking skills and developing metacognition. The platform contains an independent, adaptive learning system for pupils, which allows them to take ownership of their learning - pupils can pursue areas of mathematics independently, based on assessment and quiz data. We see large numbers of pupils taking quizzes on the Complete Mathematics platform and then choosing to do further study and solve further problems until they have better understood the ideas.

Recommendation 6: Use Tasks and Resources to Challenge and Support Pupils' Mathematics

Complete Mathematics: members have access to the UKs most extensive mathematics teaching and learning platform and the UKs largest network of maths teachers. The platform contains hundreds of thousands of questions, problems, activities and tasks. We believe, as the EEF does, that these resources are just tools, which must be use appropriately in order to be effective. This is why every single resource is also supported by pedagogical advice. The community of teachers also share their thoughts on the resources and how to use them for impact. All resources are tied to quizzes, which can quickly identify pupils' strengths and weaknesses and help teachers plan to overcome misconceptions. Complete Mathematics members have access to regular CPD exploring conceptual and procedural knowledge and how to use stories to build understanding.

Recommendation 7: Use Structured Interventions to Provide Additional Support

Complete Mathematics: platform contains extensive assessments with linked analytics, allowing teachers to target support and plan for early intervention. This means interventions can be explicit - teachers have the information they need to know at the granular level what mathematics is holding the pupil back and are then provided with comprehensive support in terms of pedagogical advice and resourcing to be able to address the specific issues. Furthermore, the platform allows for 'self-intervention' through its pupil interface, where pupils can explore mathematical ideas further based on the platform analytics of their understanding

Recommendation 8: Support Pupils to Make a Successful Transition Between Primary and Secondary School

Complete Mathematics: platform contains the pupil "Learning Diary", which records every interaction a pupil has with the system - all the work they do, all the questions the answer, all assessments and quizzes and associated analytics. This profile of the pupil grows with them. As the move from class to class, year to year, and primary to secondary, all of their data and information travels with them. This means that teachers meeting new Year 7 pupils can begin with a deep understanding of their mathematical backgrounds. Furthermore, the Complete Mathematics platform contains comprehensive diagnostic capabilities, meaning teachers can quickly identify strengths and weaknesses of new cohorts. Because Complete Mathematics is entirely integrated, these diagnostics can then be easily used to inform planning and the building of schemes for individuals, classes or entire year groups. The diagnostic information can also be used to identify the most appropriate pupil groupings.

The EEF report is a very welcome addition to the mathematics education canon. We wholeheartedly endorse the report and its recommendations and are proud to have already been doing all of the suggested approaches contained in the report.

The full report can be found on the EEF website.

Complete Mathematics Research Schools

Tuesday, 06 September 2016

Dear Colleague

At La Salle, we are determined to ensure our work truly reflects the needs of real classroom teachers. To achieve this, we work closely with schools across England. We are now recruiting additional Research Schools. Please read on for information on what being a Complete Mathematics Research School entails and how to apply.

Complete Mathematics is already the most extensive support platform for maths teaching and learning, but we are committed to keep growing, improving and making the system more and more useful, so that every maths teacher can benefit.

To help us make the right decisions, we have a number of Complete Mathematics Research Schools across the country, who we work closely with.  We are now seeking to recruit 30 new secondary school partners this Autumn and then primary schools and FE colleges in the Spring term.

To apply, you must be a Head of Maths or the mathematics coordinator in a school or college in England. 



  • Completely free access for all staff and students to Complete Mathematics
  • Free on-site training for you and your team
  • Free tickets to all of our #MathsConf conferences for all of your maths team
  • Reduced fees on our national programmes of CPD
  • A Complete Mathematics Research School badge to use on your website and communications

Combined, this package of resource and support is worth tens of thousands of pounds!



There is, of course, a catch.

We are sincerely looking for Heads of Maths or Maths Coordinators who want to work together with us.  You are the experts, you know what is going on in the classroom.  We can only make the right product for you with your help.  So, we are asking for your input and advice.



There is no set format for our research schools, with teachers contributing in different ways, but being a research school might involve some or all of the following:

  • Having visits from one of our team
  • Running a workshop at a MathsConf
  • Running a TeachMeet (we will pay for refreshments and provide PR and a slot)
  • Making introductions to your feeder primary schools
  • Featuring in a case study or blog
  • Running a CPD event in your region (we will do all the PR and sign up delegates)


In addition, we ask all of our Research Schools to really throw themselves into Complete Mathematics.  So, we do require you to get your entire maths team on board in using the system fully (we will give you all the training and support you need).



If this opportunity is something you are interested in and can commit to becoming a Research School, then we would love to see hear from you.

To apply, please fill in the Research Schools Application Form.  We will be in touch as soon as possible.

I do hope you can join the programme and help us to keep Complete Mathematics growing and relevant to classroom practitioners.

Kind Regards 

Mark McCourt

Maths teacher shortage?  A La Salle Mentor can help.

Thursday, 20 August 2015

We all know that the very best position for a school to be in is to have each and every maths lesson delivered by a specialist mathematics teacher.  We share that aim and aspiration, but the reality is that many schools across the country are dealing with the impact of a national recruitment crisis.  There simply is not enough maths teachers to fill the roles.

Head teachers are then faced with tough decisions about how to staff the provision of maths.  In many cases, long term supply, the use of HLTAs or other non-qualified staff, or internal day to day cover by colleagues is the only option.  These staff strive to provide the best possible learning experience for their students and heads of maths work hard to support them.  But what if there was another solution?  What if those colleagues standing in for a maths teacher were also able to deliver effective maths lessons, while at the same easing the crushing burden on the head of maths?

La Salle Education specialises in improving mathematics education in schools and colleges in England.

Using our extensive platform, Complete Mathematics, teachers are able to access teaching, learning and assessment resources and support covering the entire age and ability range.  Many teachers use the system to deliver their maths curriculum.

La Salle is also able to offer schools a unique solution to a maths specialist shortage.  Using the Complete Mathematics platform and working alongside your HLTA, cover manager or supply teacher, a La Salle mathematics expert will plan and monitor every lesson, giving extensive support to the temporary staff member to ensure that they are delivering impactful lessons that get the most out of your students.  In addition, your Complete Mathematics Mentor will set regular, meaningful homework for every child and monitor their progress, providing frequent reporting to the head of maths.

The process is simple and flexible so that head teachers are able to continue their search for a specialist teacher, safe in the knowledge that the temporary solution is as effective as possible.  A La Salle Mentor will visit your school, meet with the head of maths to learn about schemes of work and the current attainment of the students.  Where possible, the Complete Mathematics Mentor will also meet face-to-face with the member of staff who will be delivering the lessons.  Then, through the Complete Mathematics platform, the Mentor will plan every lesson for each class involved.  Students will also have access to an online environment where they can see their maths lessons and collect and submit their homework.  During the period of mentorship, the Mentor will discuss progress regularly with the HLTA, cover manager or supply teacher, engaging them with co-planning and exploring effective approaches.

We understand that head teachers need flexibility, so contracting a La Salle Mentor is made easy with a simple month-to-month commitment.  We don’t tie you in and will even do all that we can to help you find a full-time specialist teacher to fill your post as quickly as possible.

Only La Salle has the ability to offer such a comprehensive service to schools.  Complete Mathematics covers every single lesson from Year 1 to Year 11, so no matter what the ability range of the classes involved, we have it covered.

Of course, nothing beats having a specialist teacher, but in the meantime why shouldn’t your students receive the most effective lessons possible?  For more information about the programme, please visit the Solving Maths Teacher Shortages page.

GUEST BLOG: Why I am still an optimist

Written by Peter Hall, Beacon Academy, Crowborough Thursday, 30 April 2015

After 20 years teaching there are days when things seem not to be going well.  My year 11 ought to be at their best, working hard to squeeze the most out of every last precious minute, but instead I find too many of them happy to chat and achieve very little.  In the department we seem to be struggling to be aiming for anything more than a narrow focus on exam success, as a school the government’s cuts for sixth form funding are starting to bite and as a country education seems to be redefined almost daily as politician’s battle for the voters’ attention.

And then I spend an hour with my year 7 group, a small group of students who find maths a huge struggle, whose number sense isn’t complete, who mostly need to count on their fingers and who usually can’t remember very much from one day to the next.  But they are so charming and so polite (most of the time) and keen to learn and although terrified of tests they do arrive for each lesson with a positive outlook and a cheerful nature.  And we tackle probability and they make good contributions and ask good questions and a good hour is had by all.  And our good hour isn’t because I’ve made good use of different learning styles, and I’ve not had to address thinking skills and they are happy to learn and discuss without  any hint of “when are we going to need this”.  An hour spent explaining and practicing and encouraging seems to have worked again. 

And then I remember those in the year 11 class who are constantly asking good questions and have made good progress – those who were a struggling and nervous grade C in their December mock some are now a much more confident grade B with hopes (on a good day) of achieving a grade A in the summer.  And then I’m grabbed by a conversation on Twitter and the teaching matters again.  And then I’m planning some lessons with Complete Mathematics and are overjoyed to see resources that others have shared so that I’m not planning from scratch again.  And the funding and the politicians?  I remain hopeful that wiser heads than mine will triumph and sensible thinking will prevail and the outlook isn’t so bleak after all.


Monday, 27 April 2015

Over the last couple of years, the team at La Salle Education has been thinking about assessment without levels.

National Curriculum Levels served a purpose in their original guise – a way of suggesting that mathematics is an interconnected subject, where the learning of a concept rests firmly on the foundations of earlier concepts, which must be secure before moving on.  Levels, in a very broad sense, drew a picture of what this progression might look like and suggested a pathway through mathematics as a child learned more and more.

There is nothing at all wrong with this idea.  In mathematics in particular, not only is it a correct assertion, but it is a very useful one too.  Ensuring that a student has secured underlying concepts before trying to build on top of them is the best way of giving them the chance to really learn mathematics and be successful.

Levels, in their original format, also did a good job at showing interconnections across strands of mathematics – showing that, say, some statistics should not be encountered before the underlying number work.

The abolition of National Curriculum Levels was due to a multitude of reasons, many of them ideological and many of them ignorant of the differences in subject areas.  But there were also several good reasons for their scrapping.  National Curriculum Levels, as with any metric in a high-stakes system, was an idea almost doomed to abuse at its inception.  In no time at all, because of a desperate need to ‘measure progress’, the levels were subdivided and misinterpreted.  Suddenly, the once broad and general pathway through mathematics became an ill-informed and utterly ridiculous statement of mathematics learning that simply ignored the way in which mathematics learning happens. The notion that a child can be a Level 4b in mathematics is nonsensical.  What on earth does it mean?

This is a far cry from what Level 4 was supposed to mean – a broad statement of an approximate place on a journey of learning mathematics.

Then, with such predictability, we started to see the granularity become more and more extreme.  The idea that a single test could tell you the level of a child or, worse still, that a single lesson with perhaps just one activity could brand a child with an extremely specific level.  Even a 20 minute lesson observation was starting to demand an assessment of each child’s level.

One other issue with National Curriculum Levels is that they had become a fundamentally dishonest measures.  With a fairly obscure language, it became easy for parents to misinterpret the true meaning of the metrics.  A parent told that their child has achieved Level 3, when last year their child was just Level 2, might well be pleased and feel that all is well.  But what if that child is 14 years old?  Levels all too easily disguise low attainment because they can be used to exclusively highlight progress.

At La Salle, a group of around 30 people have been constructing an assessment system with two overarching aims.  Firstly, the metric should be honest and show not only progress but attainment also.  It should give a clear indication of a trajectory so that everyone (teacher, student and parent) can play a part in intervention as soon as it is required.  Secondly, the system should reinstate the correct intentions of the Levels system – that is to say, the system should give clear guidance of a pathway through mathematics, where concepts underpin each other and the journey through an interconnected mathematics curriculum is one that gives the best possible chance of success.

We have experimented with the ideas over a couple of years.  The team is made up of a wide variety of people, from those of us who created things like the NCETM self-evaluation tool or were part of creating national programmes of study, or members of the team who are currently working in schools of various types and circumstances, to colleagues who write assessment materials for awarding bodies.  We have debated long and hard, tried various ideas and consulted with lots of teachers (and continue to do so).

The emerging result is MathsAge.

The early version of this system is already incorporated into Complete Mathematics and, as with every aspect of our work, we will continue to research and refine.  You can imagine, as more and more students interact with the system and more and more teachers give feedback, the metric can be honed and continually made more rigorous.

So what did we do?  Initially, our work centered around curriculum design and then learning design rather than assessment.  All too often, assessment is allowed to drive curriculum and learning design – this is something we have no interest in.  Curriculum and learning come first.  This meant spending years creating a journey through school age mathematics from counting to calculus.  There were many iterations of this curriculum.  The result – a progressive journey through mathematics based on the fundamental principle of securing concepts before building on top of them – is, of course, not the only pathway.  There are many areas of school age mathematics that are axiomatic, which means that there are many entry points to starting particular strands of the journey.  Nevertheless, we wanted to put in place a journey that does work – not a unique journey – but one that will work if followed.

This curriculum design then led to the most extensive piece of work: learning design.  We have been working on this for a while, with a very large team, and will continue to work on it for years to come (forever in fact), with every single teacher in Complete Mathematics also able to add to the design and debate.

Combined, these two areas of our work produced a framework - not unlike a neural network when we draw it out on paper!  This gives us a way of identifying key signposts along the journey and dividing the journey in a practical and sensible way.

The obvious response is to work with what works for schools.  So we took the full journey and divided it into 11 very broad steps, going from counting to early calculus.  The idea being that any student who successfully passes through the 11 steps will be able to achieve a Grade 9 at GCSE.

These steps contain broad statements of attainment, showing the areas that must be secure before moving on.  It does not mean that the mathematical topic will never be encountered again, but simply that there are stages in strands / topics / concepts that need to be addressed at certain points along the journey.

Why did we choose age rather than stage?  It would be easy, of course, to use the 11 steps to say ‘this is what stage you have reached on the journey’, but we wanted the metric to be really honest, particularly for parents.  So each stage is related to an age and that is what we communicate back.

It is nonsense to say a child is, for instance, a low age 12 because areas in the broad step will mature in different ways.  So we make no judgment about this sort of granular level.  Instead, and this is where the assessment design phase really kicked in, we are more interested in the ‘strength’ of the measure.  Any interaction might result in a judgment being made, but how robust is that judgment and how reliably can a teacher alter their planning?  That is our focus.  So the MathsAge comes with a ‘strength’ measure.  This will become more and more accurate as the child provides more and more evidence.

Unlike most systems available for maths education, Complete Mathematics is not a static system, which means that all of this work will continue to evolve based on real users’ interactions and real teachers’ observations and feedback.  This means that the trajectory measure will become ever more accurate.  In the meantime, the trajectory (the system is predicting what final GCSE grade a child of any age will achieve at the end of school) is underpinned by the statistics collected at national level over the last couple of decades, which give fairly accurate probability distributions of where a child will progress to given their current attainment.  We have used these probabilities as the starting point, which can then be tested over time as real children progress through the age groups.


MathsAge is therefore a way of allowing everyone involved – teachers, pupils and parents – to have a clear picture of where the pupil is right now and where the pupil is heading.

Because the Complete Mathematics curriculum was the starting point, knowing a pupil’s MathsAge also allows us to know precisely which concepts are holding them back. This will give schools the ability to change their planning or to provide meaningful intervention, rather than generic booster sessions.

Complete Mathematics – Summer Term 2015

Sunday, 12 April 2015

What a year it has been so far.  With thousands of teachers getting involved in Complete Mathematics through our ‘Research Schools’ project, the National Mathematics Teacher Conferences and our regional CPD roadshows, ITE and TeachFirst students learning their craft with the support of collaborating teachers, and those schools that have adopted the system in school to help raise standards in maths, we have been amazed at the way the community has engaged with La Salle.


Summer term is now kicking off and we are determined that Complete Mathematics will continue to grow and reflect the views of our community of thousands of teachers.  Over the last few months, teachers have been telling us what will really help them in the summer term.  We have a standing joke in the La Salle office: Complete Mathematics, it will never be complete!  You see, Complete Mathematics is not like other systems – it has always been our intention for the project to grow and grow and grow, reflecting the real needs of those actually teaching in classrooms day-to-day.


So we are proud to announce that during this next half term, we will add the following new features to Complete Mathematics:


1.     Core Maths

With the school leaving age now increasing and all students expected to continue with the study of mathematics up to the age of 18, many schools and colleges will be faced with the enormous challenge of creating a new programme of study for those students not following an A Level course.  For many, this will mean putting together a pathway and resources for the new Core Maths course.  Thousands of teachers will be faced with the same problem of creating a robust structure and scheme of work.  That’s why La Salle will add Core Maths into Complete Mathematics at the end of May.  This will give schools access to a fully resourced scheme (and assessments for tracking!), which can be deployed to their students.  Of course, being in Complete Mathematics, the course will not just be a scheme of work and some content – as with all other areas, Core Maths will be fully supported with pedagogical notes, misconceptions, exemplar questions and a host of other support materials.  Given that many schools and colleges will be faced with the challenge of delivering Core Maths without additional specialist staffing, we hope that these support materials will enable all teachers to deliver the highest quality lessons for those post-16 students taking up the course.

2.     New GCSE Mathematics Courses

We have already put together a comprehensive scheme for the new key stage 4 national curriculum (you can use it right now in Complete Mathematics), but will now be going further to create specific schemes for AQA, Edexcel and OCR GCSE mathematics.  Rather than having to build a scheme, you will be able to simply select the level (higher or foundation) and the awarding body for an immediate, fully resourced and supported scheme of work and online learning and assessment materials.

3.     A Level Maths

Complete Mathematics already contains a fully exemplified scheme of work for KS1, KS2, KS3 and KS4.  Later in the term, we’ll also be adding schemes for A Level maths.  Another great addition to the system, which will allow you to continue to use Complete Mathematics with your older students.

4.     Scheme of Work publisher

Already, hundreds of teachers have built schemes of work in Complete Mathematics, using our quick and easy SoW Builder. We’ve been so impressed by the quality of curriculum design and thought that has gone into these that we are soon introducing a SoW Publisher – this means you will be able to send your scheme to other people in your school, colleagues you have added as ‘friends’ or the entire Complete Mathematics community!

5.     Super-Customisable Lesson Planner

You have been telling us that you want even more flexibility in your lesson planner, so that is what we are working on now.  Thanks to suggestions from teachers across the country, the Super-Customisable Lesson Planner will give you all the freedom you need to chop and change, add in additional concepts, repeat topics, or simply ‘go off on one’ mid-lesson!

6.     Even more La Salle content for KS1

The primary specialist members of our team have been busying themselves with creating ever more content and support materials for KS1.  These materials are already appearing online and will continue to grow in the coming weeks.  All ‘new curriculum’ compliant of course!

7.     Community Content

Perhaps the most rewarding aspect of Complete Mathematics to date has been to see the hundreds of resources and lesson notes being added by teachers across the country – particularly those ones marked ‘public’.  It never ceases to cheer us up when we see how keen teachers are to support each other.  Complete Mathematics is a very different environment to other maths education sites – everything that makes it onto the system goes through a curating and QA process, which means, unlike some sites, you can be assured that the materials you use are of the highest quality.  During the summer term, we’ll be looking out for the most interesting and effective materials added by teachers – there will be a prize for the best!

8.     MTN

If you haven’t yet heard about the Mathematics Teacher Network, summer term is the time to get involved.  Oxford University Press, AQA and La Salle Education have joined forces to bring high quality CPD to maths teachers across the country entirely for free.  See our MTN page for details.

9.     Mathsconf4

During this half term, we will be preparing for the National Mathematics Teacher Conference.  This will be the fourth conference and will take place on Saturday 20 June in Manchester.  The venue is stunning and vast – but it needs to be, the conference is open to 1000 teachers!  Our conferences have fast become the largest gatherings for maths teachers from primary and secondary schools.  If you haven’t joined an event yet, be sure to come along.  You will have the chance to collaborate and learn from teachers from across England.


What next?


So, a very busy half term on the way, but Complete Mathematics will never stop growing.  In the second half of the summer term we have even more exciting new developments to tell you about.  But, more importantly, we also want to hear from you – your feedback and suggestions are what lead to our developments.  Please do get in touch if there is something we can do for you and your school.  Help the wish list grow and influence the Complete Mathematics of tomorrow!


Have a great half term.  Enjoy the sunshine and warming weather.  And keep doing the most amazing job on earth: being a teacher.

Virtual mathematics environment for all SSAT schools

Thursday, 26 June 2014

A new collaboration will engage SSAT schools with Complete Mathematics, a virtual teaching and learning environment created by La Salle Education. SSAT schools will contribute to the further research and development of Complete Mathematics to ensure that the tool offers teachers of mathematics effective support. SSAT member schools that take on the use of Complete Mathematics will also have access to high-quality, subject-specific professional development delivered by La Salle Education as part of its National Mathematics Support Programme.



“With the changes in the National Curriculum and the higher expectation of pupils’ achievements in mathematics, it is vital that our member schools have access to up-to-date resources that genuinely enhance teaching and learning,” explained Anne-Marie Duguid, Head of Teaching and Learning at SSAT. “Complete Mathematics holds pedagogy at its heart and places the teacher at the core of its activity, using technology to support rather than replace their role, which we believe will help deliver excellence for our member schools.”


Mark McCourt, Chief Executive of La Salle Education said: “SSAT is focussed on improving the quality of teaching and learning and Complete Mathematics can be a valuable partner in achieving this. A core element of Complete Mathematics is continual assessment, giving teachers detailed information on each pupil’s progress, enabling them to develop personalised learning using the activities and tools within Complete Mathematics.”      



Media contact: Nicola Hern, Seventh Corner This email address is being protected from spambots. You need JavaScript enabled to view it. m: 07980 098652


Notes to Editors


La Salle Education and Complete Mathematics

La Salle Education is run by mathematics educators with the aim of supporting all mathematics teachers with high-quality resources and continuing professional development. In April 2014, La Salle Education launched Complete Mathematics, an online environment that caters for every aspect of mathematics education for the 5-16 age range. With the teacher at its core, Complete Mathematics enables all aspects of teaching, learning and assessment.  As an online tool, Complete Mathematics is updated regularly to support developments in the curriculum and teaching and learning approaches.




SSAT, a membership organization with more than 2,000 schools as members in England, offers schools a range of products and services designed to improve the quality of teaching and learning and to raise achievement in schools.



National Mathematics Support Programme

The National Mathematics Support Programme (NMSP) is a series of seminars and conferences taking place across England to offer teachers high-quality continuing professional development (CPD). Created by La Salle Education, NMSP events are free to attend and are open to primary and secondary mathematics teachers and headteachers.


National Mathematics Teacher Conference

Saturday, 24 May 2014

The National Mathematics Teacher Conference takes place on Saturday 14th June.  It is the UKs largest single day event for mathematics teachers and is entirely free to attend.

The event is organised by La Salle Education as a means of ensuring that all teachers of mathematics, across primary and secondary schools, have access to high quality professional development as we move towards a new school year that sees the introduction of a new national curriculum and the removal of the longstanding system of curriculum levels.

The event is kindly sponsored by AQA.

The day consists of a variety of talks, workshops, networking, resource sharing and a panel debate.

With over 220 delegates attending, the vast majority being current practitioners, La Salle Education and AQA are proud to host what should prove to be an exciting, interesting and enjoyable day.



9:30 - 10:00

Arrival and Networking / Morning Refreshmets

Maths Magic with Dr Maths

10:00 - 10:20

Welcome and Introduction

Mark McCourt, Chief Executive, La Salle Education

10:20 - 10:30 Welcome from the Event Sponsor, AQA
10:30 - 11:00 Keynote Speaker, Dr Vanessa Pittard, Assistant Director, Curriculum and Standards, Department for Education
11:00 - 12:00

Morning Workshop

A: The New GCSE - Andrew Taylor

B: Images, Language, Symbols, Concrete - Mark McCourt

C: The New Mathematics Curriculum in Primary Schools

D: Why do we Teach Maths? - Richard Perring

12:00 - 12:30 The Idea Exchange
12:30 - 13:00

Lunch and Networking

Magic with Dr Maths

13:00 - 14:00

Afternoon Workshop 1

E: Assessing without Levels - David Thomas and Alan Gothard

F: Leading an Outstanding Maths Department - James Gatrell

G: Effective Use of Diagnostic Questions - Craig Barton

H: Developing a Framework for Fluency - David Cook and Rachel Rayner

I: Taking Maths Beyond the Classroom - Steve Humble

14:00 - 15:00

Afternoon Workshop 2

J: Blindingly Obvious... - Bruno Reddy

K: Making Sense of the New Curriculum - Tony Gardiner

L: Outstanding Maths Lessons Using Web - Douglas Butler

M: An Outline of PBL - Julia Smith

N: The Next Questions in Maths - Luke Graham

15:00 - 15:30


The panel will take questions from the audience and debate current issues.

The Panel includes:

Lynn Churchman

Tony Gardiner

Andrew Smith

Craig Barton

15:30 - 15:40 Closing Remarks
15:40 - 16:00 Networking and Farewells


National Mathematics Support Programme

Tuesday, 29 April 2014

La Salle Education is proud to announce the launch of the National Mathematics Support Programme (NMSP).

With the upcoming changes to the new national curriculum and the removal of national curriculum levels, the NMSP is a nationwide series of support seminars aimed at helping primary and secondary schools to prepare for the new school year.

NMSP events are taking place in 9 locations across England, with the vast majority of schools being within 60 miles of an event.

Events are entirely free to attend.

Places at events are limited - please use our online booking to sign up.


Regional Seminars to Support the New Mathematics Curriculum in Primary and Secondary Schools

The National Mathematics Support Programme is a series of seminars taking place across England to help ensure that all teachers of mathematics have access to the information they need in order to prepare for the introduction of the new national curriculum and the removal of the system of NC Levels.

At a time of unprecedented change, it is important that all schools have access to high quality CPD and information.  At this seminar we will address three key issues facing mathematics teachers:

  • The New National Curriculum - What is different and what practical steps can schools take to successfully prepare for and implement the changes.
  • Assessment without Levels - What frameworks can be used to assess pupils' progress and how do teachers accurately measure understanding and mastery.
  • Outstanding Lessons - What practical steps can we take in our classrooms to ensure pupils make outstanding progress and have a thorough understanding of mathematics from which to build upon.


NMSP events are FREE to attend and open to mathematics co-ordinators and Headteachers in primary schools, heads of mathematics and senior leaders in secondary schools.  Local Authority advisors may also attend. 


Primary Events





25th June

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26th June

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2nd July

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Derby / Nottingham

9th July

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Secondary Events





25th June

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26th June

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27th June

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2nd July

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Derby / Nottingham

9th July

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