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Post date: Apr 3, 2016 8:27:35 PM
Just over two years ago, I was approached by The Educational Company of Ireland, or Edco, as it is often more commonly known, and invited to be involved in co-authoring a new maths programme. Two years later, and numerous hours of work, I'm delighted at last to see the fruits of my labour, with the publication of Operation Maths.
Operation Maths is a pioneering new maths programme for junior infants to sixth class.
Written by a team of six experienced teachers, 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.
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.
Concrete activities and experiences are emphasised and outlined throughout the Pupil's Book and Discovery Book. 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 Discovery Book.
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 in their books.
Equally important, Operation Maths is also the most teacher-friendly primary maths scheme currently available, as will be shown below.
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.
In this post, I'm going to introduce you to some of the features of the senior end books that make it stand out from the crowd.
In a follow up post, one of my co-authors from the junior end will highlight some of the unique features of the junior end books.
Most teacher-friendly primary maths scheme:
Designed by a team of practically minded teachers, our aim was to make it as simple as possible for any teacher to use Operation Maths.
Each section in the Teacher's Resource Book (or TRB which is free to adopting schools) includes:
For long term planning, 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, we have included versions of the plans that would suit a 3rd & 4th class combination and another for a 5th & 6th class combination.
Also included in the TRB:
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.
The other free resources available with this programme include:
A free assessment booklet, which contains a one-page assessment for each chapter, a maths
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.
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.
attitudes questionnaire, a chart to record progress and three revision assessments which cover all of the chapters completed to that point. These are specifically designed to resemble the structure of the standardised tests so that the children will be less intimidated when they encounter these towards the end of the school year A free mini white board (MWB) for every child. This tool maximises participation while also providing instant feedback and enabling teacher assessment. Activities based on the use of the MWBs are included regularly throughout the books, as well as there being a whole host of digital resources (see below), which have been custom made to utilise the MWBs.
Free place value manipulatives: for 3rd -5th classes these are place value discs to hundreds, thousands and ten thousands respectively (see bottom right of image above), and for 6th, these are base-ten block representations designed to be used as a means to explore decimals to thousandths.
A whole suite of custom-made digital resources which are all completely integrated with the print and digital version of the pupil book; simply click on the icon/hyper-link when viewing the digital version of the pupils book on your IWB or device and you will be brought directly to the relevant digital activity or video. These can be used in conjunction with the free MWBs to offer unlimited opportunities for assessment for learning and whole-class participation.
Specially designed to help children to focus on the maths, the digital resources include:
Seven fully flexible e-Manipulatives based on real classroom objects, that are designed for teacher-led learning and to encourage whole-class participation
Ready to go activities
Create activities
Write – Hide – Show videos
e-Manipulative videos
Real-world Math Around Us videos
Scratch programming activities with step-by-step instructions for teachers
Follow-on weblinks to online games
Along with the inclusion of place value grids (3rd-6th), 100 dots arrays for multiplication (3rd & 4th) and visual structures for fractions (5th & 6th) on the inside covers of the books this all ensures that both the teacher and the pupils have everything they need to explore the concepts when they need them and no time is wasted sourcing materials.
Operation Maths: 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!
Specifically, as mentioned earlier, Operation Maths is based on a CPA approach. Of this approach, exploring pictorial representations of materials, numbers, shapes etc., is a vital, but sometimes neglected, step on a child's journey towards understanding. In my own experience, I would often have to source templates, grids, tables, hundred squares, blank number lines etc., that the children would draw on, fill in, annotate etc., as a way to facilitate their learning in a pupil-friendly and yet time-efficient way. This in turn, often necessitated a lot of photocopying on my part, since in my school, as with most others, the children don't write on the books in third to sixth class. This in turn was often quite time-consuming, expensive and, ultimately, soul-destroying as these lovely pages of work invariably ended up squashed or worse at the bottom of a school bag.
Again, to make it easier for teachers and pupils, these types of activities have been collated into a Discovery Book, which acts as a write-in companion for the Pupils Book as well as an ongoing record of the child's learning on their journey towards mathematical understanding. Priced very keenly at €6.95 and in colour, it also provides a very cost-efficient and environmentally-friendly alternative to reams of disconnected photocopies.
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.
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 Operation Maths, addition and subtraction are taught together as part of the same chapter(s), as are multiplication and division.
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 Further Activities in the TRB and in the 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
The Pupil's Book also has clear and detailed teaching panels (easily identifiabel 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 (mentioned earlier), Maths Around Us activities in the Pupil's Book and Maths Trails in the TRB photocopiables and in selected Discovery Books
Other ways in which Operation Maths stands out from the crowd:
Problem solving:
Oral and Mental Maths:
Again, similar to its approach to problem-solving, Operation Maths promotes the structured development of mental computation skills in a spiral way throughout the classes, by introducing and teaching explicitly a range of mental comprehension strategies from 3rd to 6th class, including, among others:
Doubles and near doubles
Using compatible/friendly numbers
Partitioning
Sequencing (addition and subtraction in stages)
Compensation
Constant different subtraction
Basic number facts (the more PC terminology for the traditional tables) are taught using a thinking strategies approach, where the children are encouraged to use what they know to solve what they don't know. The focus is also not limited to the basic facts/tables, i.e. if you understand that five times any number is equal to half the ten times, not only should you be able to mentally calculate the answers to all the usual five times tables, but you should also be able to work out 5 x 16, 5 x 28, 5 x 42 etc.
This is further supported via the incorporation of a wide range of estimation strategies for number, including less common strategies such as examining the reasonableness of an answer, using front-end estimation, as well as the more familiar rounding approach.
In a very innovative way, Operation Maths emphasises the use of accurate mathematical language and terminology from the start, enabling the child to better describe their concepts and explain their understanding to others. This also ties in with the NCCA bridging documents, thereby ensuring the children experience an easier transition to second level maths.
This active promotion of the acquisition of oral and mental maths skills is further enhanced via:the use of the MWBs
the Starters' Bank and daily starter suggestions in the TRB
Regular Talk Time activities in the books
Regular Team Work activities which encourage talk and discussion alongside collaborative learning via pair and group work tasks.
Assessment for learning:
In a way, never done before, Operations Maths specifically introduces and teaches a variety of Problem-solving strategies in a developmental way through 3rd to 6th class: bar model drawings, empty number lines and T-charts among others. These are repeatedly incorporated where appropriate to enable children to appreciate the variety of situations in which they can be used.
These strategies are also an integral part of the RUCSAC problem solving approach, used throughout the books and available to reference also as a convenient fold out-flap on the Discovery book
"Work it out" sections (blue panels) are problem-solving sections which incorporate a variety of word problems, puzzles etc., and are dotted throughout the chapters (almost daily) and not just confined to the end of the chapters. Sometimes, these might be used as daily challenges for the early-finishers and, at other times, they may form the basis for a whole class collaborative task.
A "Let's investigate" feature at the end of each book provides ideas and examples of open-ended investigations, that can be dipped into at any stage during the year.
Thematic revision spreads: there are five of these spaced out through every book, which have problem-solving at their heart. They also are linked to everyday themes such as going to the cinema, going on holidays etc., or integrate with SESE topics eg the Egyptians, mountains, the Renaissance etc
And, as mentioned previously, there are plenty of extra problem-solving challenges also in the early finishers photocopiables.
The objectives/learning outcomes for each lesson (not just chapter) are clearly outlined at the start of each section using the sentence stem "I am learning to……." (see opposite)
Prior learning and understanding is elicited via:
the suggested questions in the TRB (e.g. in conjunction with the MWBs)
assessing the children's responses to the digital videos (e.g. Maths Around Us and/or Write-Hide-Show videos) on their MWBs (see earlier photo)
more structured brainstorms/question activities to be completed in the Discovery Book.
I presume it's obvious at this stage how enthusiastic I am about this programme.
And, it's not just because I was so involved ..... I genuinely believe that this scheme is great and has the potential to revolutionise the way maths is both taught and learnt.
But don't take my word for it!
Take a closer look at the programme for yourself:
Come along to one of the launch nights throughout April, at a venue (hopefully!) near you.
Or contact your local rep and ask them to drop samples into the school. They are also very willing to come out to your school and demo the books and the digital resources at a time that is convenient to you.
Or feel free to contact me with any queries via my email (claire.primarycpd@gmail.com), Facebook or Twitter pages.
At the end of each chapter, the children also complete a Learning Log in the Discovery Book, where they assess their own learning (self-assessment). Not only does this require them to record their own perceptions of their achievement against the initial learning outcomes but the child must also provide evidence by completing some simple tasks. Also included here are more open-ended maths-journal-type statements to be completed
And, this is all in addition to the aforementioned free assessment booklet
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