Monthly Archives: January 2017

Enabling Computational Fluency


‘Fluency requires the children to be accurate, efficient and flexible.’ (Russell, 2000)

One of the main aims of Operation Maths, from junior infants to sixth class,  is to enable the children to be computationally fluent. And, the main way to achieve this, is to enable them to become flexible thinkers.

In the presentation below from the IPPN Education Expo 2017, the concept of computational fluency is explored, while also outlining how Operation Maths supports this approach in its programme.

Operation Maths: also the most child-friendly primary maths programme!

Not only is Operation Maths the most teacher-friendly programme currently available, but it is also the most child-friendly. Read on to find out why.

Enabling children to understand maths, not just do maths

In case you haven’t picked up on it already, Operation Maths is all about understanding, understanding, understanding!

As mentioned before, Operation Maths is based on a concrete, pictorial, abstract (or CPA) approach.

Concrete activities and experiences are emphasised and outlined throughout the pupil books. The Teachers Resource Book (TRB) also provides further suggestion for the ways in which a teacher can use concrete activities with their class.
These experiences are then further developed via the pictorial activities; this may be through interaction with the digital resources and/or via the write-in activities in the books. Of the CPA approach, exploring pictorial representations of materials, numbers, shapes etc., is a vital (but sometimes neglected, particularly at the senior end) step on a child’s journey towards understanding.
All of this should greatly enhance the children’s ability to visualise and understand maths and be more prepared when they meet the more traditional, abstract activities.

Active participation

The high number of concrete based activities within Operation Maths ensures that the children have regular, if not daily, opportunities to be engaged in active learning. The inclusion of free mini-whiteboards  (MWBs) as part of the programme also encourages the active involvement of all the class in any activities as all children must visibly participate. Moreover, the custom-made suite of write-hide-show videos and Maths around us videos (see below for samples) further increase the opportunities to use the MWBs. I challenge you to show the estimation video to your class and not have them all excited and active!

Mastery curriculum

Research suggests that changing chapters/topics every week, especially in senior end and especially the case of number topics, is not conducive to developing a strong understanding for the various topics and that preferable to this is a mastery curriculum approach, where the children are afforded a longer time to engage with, and ultimately master, the concepts. Therefore, in Operation Maths, these topics have a dedicated two weeks block, allowing the children to fully engage with the concepts before moving to a different topic, thereby increasing the likelihood for the children to master the content. So, if you look at the contents page of the Operation Maths books, you will notice that there are fewer chapters than usual but that many of these are “double” chapters, designed to be taught over ten school days, as opposed to five.

A better understanding of the operations

Similarly, research suggests that teaching opposite or inverse operations together, allows the children to better grasp the connections between the two, therefore promoting deeper conceptual understanding. So, in the senior end, addition and subtraction are taught together as part of the same chapter(s), as are multiplication and division. A similar approach is taken to the operations in first and second class once the children have been formally introduced to subtraction.

A seamless transition…

I was primarily involved in authoring all of the number and algebra chapters in the 3rd to 6th class books, while my co-authors Michael Browne and Siobhán Kelleher authored the chapters for measures, data, shape and space for the same classes. This means that, for the children, their experience of the content is very cohesive as it flows seamlessly from one class to the next.
Similarly the 5th and 6th class books were written in light of the NCCA Bridging documents and Project Maths at junior cycle in second level. In particular, extra attention was paid to the correct and accurate use of mathematical terminology which also helps ensure that the child’s transition from primary maths to second level maths is also as seamless as possible.

Other ways in which Operation Maths promotes the development of deeper connections and understanding include:

  • Linkage: the topics are all taught in a very connected way, with cross references being made where appropriate. In particular, measures are not just confined to their own chapters: they are taught in an integrated way across all suitable chapters and particularly across number 
  • Integration: The use of maths across other subjects is also emphasised regularly and particularly as part of the suggested activities in the TRBs. In the senior end there are also themed revision pages in the Pupil’s Book, where maths is explored through History, Geography, Sports etc.
  • The books have a clean, uncluttered design making them easier for children to focus on the concepts and not be distracted by unnecessary images
  • In the senior end, the Pupil’s Book also has clear and detailed teaching panels (easily identifiable by their yellow background) right throughout each chapter, to aid both the teachers and the children, and can be particularly useful if the children are working independently or in small groups.
  • To help make connections with the environment there are dedicated Maths Around Us videos in the digital resources, Maths Around Us activities in the Pupil’s Book and Maths Trails in the TRB photocopiables and in selected Discovery Books

Operation Maths: the most teacher-friendly primary maths programme

Resource BooksDesigned by a team of practically minded teachers, our aim was to make it as simple as possible for any teacher to use Operation Maths, while also reducing their planning and preparation work. This is why the content of the Operation Maths Teacher Resource Books (TRBs) is the most comprehensive currently available.

For the senior end:

Each topic dedicated section in the Teacher’s Resource Book (or TRB which is free to adopting schools) includes:

  • An overview of the topic that doubles as a short term plan and includes learning outcomes, vocabulary, resources, differentiation, assessment, linkage, integration etc., etc. Simply photocopy this and use it both as a plan and as a way to record progress through each topic. All of these plans are also available to download as MS Word documents from
  • A brief synopsis of potential difficulties that a class or individuals may have with the topic.
  • A day-by-day breakdown (see opposite) of suggestions to teach the topic that is so comprehensive, the like of which has not been seen before. This includes daily suggestions for oral and mental starters, concrete activities, questions, games as well as guidance for the suitable pages to use from the books.
  • Suggestions for further activities that will further enhance the children’s ability to understand the topic
  • Detailed instructions for how to use the digital resources specific to that topic.


Also included in the senior end TRBs:

  • Long term planning is in the introductory section of each TRB and not only is there a plan/grid with month-by-month suggestions of when to teach each topic for every class but, specifically for those teaching in multi-classes, there are versions of the plans that would suit a 3rd & 4th class combination and another for a 5th & 6th class combination.
  • A starters bank containing a whole suite of oral and mental maths activities.
  • A games bank with suggestions for simple, fun games, most of which are based on readily available resources such as dice, playing cards etc.
  • Reinforcement photocopiables (a minimum of one per chapter) for the lower attainers (LAs) which provide opportunities for extra practice for those requiring it.
  • Early finishers photocopiables (one per chapter) for the higher attainers (HAs) providing them with rich tasks to challenge them to think deeper and broader about the concept.
  • Dear Family Letters: these slips, which can be sent home in a homework journal or copy, explain to the family about the topic and suggest how they might support the child at home.
  • Target boards: designed for display on the class IWB, these are accompanied by questions specific to each class level and chapter.
  • A range of other photocopiables and cut-outs which can be used to further enhance the children’s understanding of the topic at hand.

For the junior end:

For the junior end , the TRB each section covers a specific month and each month has an overarching theme eg Capacity,  which then connects the other activities even if then are from another strand unit. Each month section is then subdivided into fortnights to aid planning and then subdivided further into weeks eg January week 3.

Each of the monthly sections includes:

  • Two fortnightly overviews of the topic(s) that doubles as a short term plan and includes learning outcomes, skills, vocabulary, resources, concrete materials,  differentiation, assessment, linkage, integration and home-school links. Simply photocopy this and use it both as a plan and as a way to record progress through each topic. All of these plans are also available to download as MS Word documents from
  • A weekly breakdown (see below) of suggestions to teach the topic that includes suggestions for warm-ups (starters), activities, questions, games as well as guidance for the suitable pages to use from the books.
  • Suggestions for stations in the 1st & 2nd class books that will further enhance the children’s ability to understand the topic
  • Suggestions for Aistear links in the infants books (see doc above).
  • Detailed instructions for how to use the digital resources specific to that topic.

Also included in the junior end TRBs:

  • Long term planning is covered with the yearly scheme in the introductory section of each TRB and outlines the strand units within each month and cross references this to the relevant pages within the pupils books.
  • A reproduction of the curriculum objectives for the specific class level and details when each is covered during the year
  • Early finishers photocopiables for the higher attainers (HAs) providing them with rich tasks to challenge them to think deeper and broader about the concept.
  • A range of other photocopiables, games and cut-outs which can be used to further enhance the children’s understanding of the topic at hand.

Understanding maths, not just doing maths…the Operation Maths way!

Operation Maths is a pioneering new maths programme for junior infants to sixth class.

Written by a team of six experienced teachers, Operation Maths is built on a concrete, pictorial, abstract approach, or CPA approach, (based on Jerome Bruner’s conception of the enactive, iconic and symbolic modes of representation) which research has consistently shown to be the most effective instructional approach to enable students to acquire a thorough understanding of the concepts required.

This blog post, and future posts, will explain some of the various features of the Operation Maths programme as well as outlining further ways in which this programme can be used to its full potential  to enable your students to truly understand maths, not just do it!

Background & Research

As authors, we researched, and were inspired by, the maths books and schemes used in those countries which are the highest-ranking internationally in relation to attainment in primary maths, for example Singapore, Hong Kong, Japan and Finland.

We also looked at best practice in New Zealand, Australia, Great Britain and the United States, as well as the recommendations of our own home-grown publications including the PDST handbooks, NCCA publications (e.g. Bridging Guidelines, Assessment Guidelines etc.) and programmes such as Aistear and Mata sa Rang.

Finally, this was blended with the requirements of our primary school curriculum, in order to create a scheme that is truly innovative in its approaches and strategies and the most forward-thinking maths programme currently available for the Irish market.


Programme Components

For pupils in infants to second class:

  • At School BookOperation Maths Junior End
  • At Home Book
  • FREE Pupil Assessment Booklet
  • FREE Mini-white board
  • FREE Frames (five, ten or twenty frame)



For pupils in third class to sixth class:

  • Pupils boSenior Endok
  • Discovery book
  • FREE Pupil Assessment Booklet
  • FREE Mini-white board
  • FREE place value manipulative



For teachers of adopting schools:

  • Resource BooksFREE Teacher copies of all the relevant pupil resources
  • FREE Teachers Resource Book (TRB) which contains all necessary plans, teaching strategies, photocopiables, games, starters etc.
  • FREE access to all of the Operation Maths digital resources on, including ebooks, editable plans, and a whole suite of custom made videos  and eManipulatives which greatly enhance the teaching and learning experience for both teachers and pupils.

Furthermore, Operation Maths is the most teacher-friendly  and child-friendly programme currently available.

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