Sunday, 31 December 2017

On The @TES Blog: Six Books That Chart My Reading Evolution

On The @TES Blog: Six Books That Chart My Reading Evolution
Another personal blog post about reading (sorry). This one was hugely enjoyable to write due to the fact that books are not just bound and covered collections of paper with words printed on them - they are intertwined with life's real events and characters. I could not have picked six books without thinking particularly of my dad and my wife as well as times and places in my life.

I hope you enjoy reading about the six books that chart my evolution as a reader; I'd love to hear about the books that you'd consider to be elementary in your growth as a lover of books.

https://www.tes.com/news/school-news/breaking-views/six-books-chart-my-teacher-a-reader-evolution

Friday, 29 December 2017

My #52Books2017 (And Why I Won't Be Doing #52Books2018)

My #52Books2017 (And Why I Won't Be Doing #52Books2018)
In 2016 I accepted my first reading challenge (from @saysmiss), set myself the target of reading 50 books and proceeded to beat that target. In 2017 I decided to try for 52 - 1 a week - and set about encouraging others to do the same. So far I've read 63, with a couple of others on the go that might get finished before the year ends.

A great motivation for me has been to have a better knowledge of children's literature, as well as to be genuine in my enthusiasm for reading when teaching it to children (read more in my blog post 'Being a Reading Teacher'). However, what began in 2016 in 2017 has become an indispensable habit. Reading to my target in 2017 has been a product not of hard work but of a matter of course. I am a reader.

Having said this, my original motivation still shines through in my reading list this year - I largely read children's books. I see this as a duty but I also love them intensely.

My #52Books2017 (And Why I Won't Be Doing #52Books2018)
I'm often asked for book recommendations and I happily oblige but when it comes down to making top ten lists I'm hopeless! But look at the average of ratings I've given - 4.2. Read almost anything from this list because I've more than likely enjoyed it.

In 2018 I won't be setting a challenge - after two years of challenging myself I have created a reader in myself and no longer need a challenge to continue my habit. This might mean I read fewer books, longer books, more varied books - who knows? I may just read a similar selection of books and that's OK too. But if you are looking to train yourself to become a reader, setting yourself a challenge is a good way of doing this - some on Twitter are doing #52Books2018 and on Goodreads you can set any number of books as you want.

I regret that I have not tracked the excellent picturebooks that I've read this year - this was because I felt that they shouldn't count towards my 52 (a downside of doing such a challenge). However, there are some reviews of picturebooks here in my book reviews thread: https://thatboycanteach.blogspot.co.uk/search/label/Book%20review

Now for the books I've read, loosely categorised. I have provided links to ones I've reviewed:

My #52Books2017 (And Why I Won't Be Doing #52Books2018)
Young Adult

Island – David Almond
The Rest of Us Just Live Here – Patrick Ness
Northern Lights (His Dark Materials, #1) – Philip Pullman
More Than This – Patrick Ness

Middle Grade

Cogheart (The Cogheart Adventures, #1) – Peter Bunzl
Holes (Holes, #1) – Louis Sachar
Kensuke's Kingdom – Michael Morpurgo
The Girl of Ink and Stars – Kiran Millwood Hargrave
Eragon (Inheritance, #1) – Christopher Paolini
Mold and the Poison Plot – Lorraine Gregory
The Wonderling – Mira Bartok
The Light Jar – Lisa Thompson
Sky Song – Abi Elphinstone
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Stormwalker – Mike Revell
Skeleton Tree – Kim Ventrella
The End of the Sky (A Slice of the Moon #2) – Sandi Toksvig
The Kites Are Flying! - Michael Morpurgo
The Island at the End of Everything – Kiran Millwood Hargrave
All The Things That Could Go Wrong – Stewart Foster
Moonlocket (The Cogheart Adventures, #2) – Peter Bunzl
Time Travelling with a Hamster – Ross Welford
The Last Wild – Piers Torday
The Bubble Boy – Stewart Foster
It Ain't So Awful, Falafel – Firoozeh Dumas
Hitler's Canary – Sandi Toksvig
Who Let the Gods Out? (Who Let the Gods Out?, #1) – Maz Evans
The Night Spinner (Dreamsnatcher #3) – Abi Elphinstone
The Shadow Keeper (The Dreamsnatcher, #2) – Abi Elphinstone
Watership Down – Richard Adams
The Goldfish Boy – Lisa Thompson

Younger Children’s

Coming to England: An Autobiography - Floella Benjamin
Dragons at Crumbling Castle – Terry Pratchett
The Worst Witch – Jill Murphy
The Great Cat Conspiracy – Katie Davies
The Children of Noisy Village – Astrid Lindgren
The Reluctant Dragon – Kenneth Grahame
The No. 1 Car Spotter and the Car Thieves (No.1 Car Spotter, #3) - Atinuke
The Firework-Maker's Daughter – Philip Pullman

Education

What Does This Look Like In The Classroom?: Bridging The Gap Between Research And Practice – Carl Hendrick & Robin Macpherson
100 Ideas for Primary Teachers: Mindfulness in the Classroom (100 Ideas for Teachers) – Tammie Prince
Making Every Primary Lesson Count: Six Principles to Support Great Teaching and Learning – Jo Payne & Mel Scott
Hopeful Schools – Mary Myatt

Non-Fiction

Land Rover: The Story of the Car that Conquered the World – Ben Fogle
Quiet: The Power of Introverts in a World That Can't Stop Talking – Susan Cain
The Empathy Instinct: How to Create a More Civil Society – Peter Bazalgette
True Friendship – Vaughan Roberts
The Joy of Service – Julian Hardyman
Reasons to Stay Alive – Matt Haig
The Big Ego Trip – Glynn Harrison
Soldier Spy: The True Story of an Mi5 Office Risking His Life to Save Yours – Tom Marcus

Adult Fiction

Utopia – Thomas More
Go Set a Watchman – Harper Lee
Chocky – John Wyndham
Who Was Betty? – Laura Jukes
A Clockwork Orange – Anthony Burgess
Transreality – Chris Lackey
The Handmaid's Tale – Margaret Atwood
Towards the End of the Morning – Michael Frayn
The War of the Worlds – H.G. Wells
The Picture of Dorian Gray – Oscar Wilde
Rivers of London (Peter Grant, #1) – Ben Aaronovitch
The Colour Of Magic (Discworld, #1) – Terry Pratchett

So with no challenge and a huge 'to read' pile (I received quite a few books at Christmas) I look forward to next year - what will I read? What will you read?

Tuesday, 26 December 2017

Book Review: 'Urban Jungle' by Vicky Woodgate

Publishers Big Picture Press do not disappoint: they produce very big books full of wonderful pictures and this one by Vicky Woodgate is no exception. 'Urban Jungle' is an oversized non-fiction book which explores the fauna of the world's major cities.

Did you know that Spinybacked orbweavers can be found in Lima, Peru? Or that Milk sharks patrol the waters around Mumbai? Or that Vancouver is home to Bobcats, Coyotes, seals, bears, skunks, turtles and Rufous hummingbirds? With each turn of a page the reader encounters the surprising inhabitants of some of the world's busiest cities and surrounding urban areas. 

Each page begins with clear geographical summary of each city, a map of where in the country or continent it can be found and a plethora of stylistic animal illustrations. A particularly nice touch is the 'Animal Stories' box that can be found on each page where a particular animal is highlighted, sometimes with a funny story that made the news and often with tales of historical significance or surprising facts about the creatures.   

The book is split into sections based on continent and each part opens with a double page map - the book doesn't skimp the geography side of things. Urban Jungle definitely isn't just a book about animals; it's a brand new beast combining an Atlas with a natural history book, although it perhaps couldn't be used as either - it must be treated as something different.

With publishers pushing he boundaries of what non-fiction books look like this is an exciting time to be a child who loves to gather facts. With maps and animals being popular obsessions for primary aged children this book is sure to be a hit both at home and in the classroom and will hold up to repeat reads such is the wealth of information contained.

Book Review: 'The Elephant in the Room' by James Thorp and AngusMackinnon

This surprising and striking book appears to stand alone in today's picturebook market - there certainly aren't many books like it, illustrated in an psychedelic style reminiscent of The Beatle's Yellow Submarine film but with an even trippier colour pallete. This is a book which aesthetically stands out a mile and its eye catching design will draw children in, keen to know what this strange-looking book is all about.

Featuring a rhyming text (and a rather nice, but perhaps not always child-friendly Art Deco typeface) the story gets as bizarre as the illustrations themselves. But this bizarre story will be all too familiar to adults who, with a wry smile, will read this aloud to children and recognise the narrative: something gets broken and the culprit makes up all sorts of excuses in order to escape punishment. This story concludes however with a stronger moral message for adults as Father Giant realises that maybe he had been too busy and the accident had happened because he hadn't been with the children. It is certainly food for thought for the grown up who might be reading this to younger children.

However, subtext aside, children hearing the story and taking it face-value will laugh uproariously at its silliness and witty wordplay - lots of lovely alliteration and rhymes (rowdy cloudiness, yucky yakkiness) and made up words (squinching) will delight young minds ready to soak up new and imaginative language. They will identify with the protagonists and the feeling of guilt that comes with accidental misdemeanours and might even begin to question the folly of not telling the truth in such situations.

The Elephant in the Room, a title which bears multiple significance, is like one of those brilliant children's films which is clearly intended to entertain adults just as much as the kids. As C.S. Lewis said “A children's story that can only be enjoyed by children is not a good children's story in the slightest.”. James Thorp and Angus Mackinnon have produced a good children's story. Highly recommended.

Book Review: 'Sky Song' by Abi Elphinstone

Once you've understood the particular brand of magic (which is not believed in even by many of the inhabitants of Abi Elphinstone's new fantasy world) you'll be taken on an adventure of discovery, unity and salvation. An evil queen is taking the voices of the icy land's adult subjects (literally in the story, but this metaphor would be exciting to explore with young readers) in order to gain immortality and Eska, although initially imprisoned, must do something about it.

Sky Song capers around the fringes of what has been termed Theological Fantasy with its undertone of the importance of belief, yet Elphinstone has no religious agenda to push. It plays with concepts from Greek and Roman mythology, traditional fairy tales and some more recent literary triumphs and blends them cohesively for a younger audience, than say, His Dark Materials was intended for. 

Whilst Erkenwald definitely feels like a realm that could be further explored, Eska and her eagle companion Balapan certainly give it a good initial once-over, encountering on the way, in the manner of all good expeditions, a number of problems which they must overcome, often with the help of Flint, his puppy pebble and his sister, Blu. The animal companions and the magic ways that some of the group's problems are solved definitely aim this book squarely at 8 to 10 year olds.

But this story, like all the best books, does more than just describe an adventure. It speaks of growing up and discovering one's own capabilities, facing adversity and the importance of companionship and collaboration. Sky Song is an important lesson in why tribalism, whilst comfortable, will not save the day - a political message that might give children a starting point to thinking about what their role on the world stage might be. Flint's character provides hope that people can change their ideological views in order to become more mindful of others. The character of his sister Blu, based on Elphinstone's own relative who has Down's Syndrome, is also a possible discussion starter for readers to explore and change their thoughts about those with genetic disorders and resulting learning difficulties.

Children who were a few years ago obsessed with Frozen, or those who have recently discovered and loved the more accessible parts of Narnia, or those looking to move on from reading short myths and fairy tales will find their perfect next book in Sky Song. Fans of Abi Elphinstone's Molly Pecksniff character will find another well-rounded female lead character to follow and be inspired by. With Sky Song, Abi Elphinstone invites her young readers into a new and exciting world which will not only thrill and entertain but might set children on the path to discover more of the brilliant fantasy fiction available for advancing readers.

Friday, 22 December 2017

Teaching Mathematical Problem Solving: What The Research Says


Recently the EEF published their guidance report for KS2 and KS 3 maths. It gives 8 recommendations for improving the teaching of mathematics:


In this blog post for Bradford Research School I focus in on problem solving but touch on the use of manipulatives, developing a network of mathematical knowledge and other areas of the guidance. In the article I outline a maths lesson which follows much of the advice given in the guidance (the cube trees at the centre of the lesson):

https://bradford.researchschool.org.uk/2017/12/20/teaching-mathematical-problem-solving-what-the-research-says/

Monday, 18 December 2017

On The @TES Blog: Idealistic Leaders vs. Realistic Teachers




"Teachers must…", "Teachers need to…", "Teachers should…"

These are potentially my most used phrases when writing articles on education. Occasionally other groups will be on the receiving end of my strongly worded ‘advice’, but usually it’s teachers because teaching is what I know.

Recently, I have been pulled up on my use of these phrases – turns out teachers don’t like being told what to do. Now there’s a surprise.

My sharing comes from a desire to help others, never from a position of wanting to overburden and bludgeon teachers who are already striving to do their best. But I can see how it comes across sometimes and it got me thinking...

Click here to read more over on the TES blog

Friday, 15 December 2017

Why You Might Be Getting Feedback Wrong! (Part 2)


At the launch of Bradford Research School I held a workshop entitled Why You Might Be Getting Feedback Wrong! The workshop is now available in blog form over on the Bradford Research School blog. It comes in two parts:

Part 1 addresses 5 myths:

  • Myth 1: marking is evidence-based
  • Myth 2: feedback = marking
  • Myth 3: marking is time consuming
  • Myth 4: Ofsted require a particular kind of marking
  • Myth 5: children need to know what level/grade their work is

Part 1: https://bradford.researchschool.org.uk/2017/12/08/why-you-might-be-getting-feedback-wrong-part-1/

Part 2 addresses 4 more myths:

  • Myth 6: marking needs to be done in great detail
  • Myth 7: marking will have an impact on progress
  • Myth 8: all errors are equal
  • Myth 9: triple/dialogic marking is best

Part 2: https://bradford.researchschool.org.uk/2017/12/15/why-you-might-be-getting-feedback-wrong-part-2/

I have also uploaded the PowerPoint I used in the workshop for anyone to use in their own training or discussions with SLT: https://www.tes.com/teaching-resource/why-you-might-be-getting-feedback-wrong-powerpoint-for-staff-training-11795794

Thursday, 14 December 2017

Scaffolding Structures for Reading Comprehension Skills

This is a very different blog post to the sort I normally write; it represents some very hypothetical thinking and the purpose of writing it is to open it up to discussion. My hypothesis is that the reading skills outlined in the English Reading Test Framework for KS2 (and KS1) might be best taught in a particular order. I also hypothesise that when teaching particular skills (represented as being higher up the model pictured) teachers can guide children through how to use other skills (lower down the model) to arrive at a better ability to practice and use the skills that are higher up the model. First of all, here's the model I've put together to which I refer:


Skills (taken from English Reading Test Framework for KS2) are listed in the order that they might best be taught. This suggested order is based on the idea that some reading skills might be required prior to developing others. The most basic skills are towards the bottom.

The inclusion of 2d (inference) may depend on the text type. For example, in many non-fiction texts there is no requirement to infer information, only to retrieve it. In these cases the 2d (inference) step/building block can be skipped.

The only reading skill from the test framework which isn’t included here is 2h (make comparisons within the text). It is possible that texts can be compared at many different levels, for example, the vocabulary used can be compared (2a), summaries of plot can be compared (2c) or structure of the text can be compared (2f). The skill of making comparisons (2h) could be seen as a ‘floating’ skill – one which could be applied in different ways alongside other reading skills.

All of the following symbols and colours refer to the Reading Roles, a system I designed to make the different skills memorable for children and teachers. Read more about the Reading Roles here: http://thatboycanteach.blogspot.co.uk/2016/12/reading-roles-cognitive-domains-made.html


In order for children to begin to make inferences they need to at least be able to retrieve information in the text, and before this they need to be able to understand what the words mean.

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text

2f and 2g are very interlinked as they are both about meaning – one with a focus on word and phrase choice, and one with a focus on content choice. It is possible that 2g and 2f should precede 2d in the teaching sequence but if making inferences is one way in which we take information from a text, then arguably we need that information to make meaning; we can then go on to identify and explain how that meaning is enhanced through word choice and how the content included contributes to the meaning. The fact that these skills are not included in the KS1 test framework might suggest that this is correct, and that these are more advanced skills than making inferences.

2g – Author’s purpose

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases

2f – Language structure and choice

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases
(2f)        identify/explain how information/narrative content is related and contributes to meaning as a whole

Once children understand word meanings, can find and infer information, explain how language has been used to communicate meaning and, as a result, can understand the meaning of a whole piece of text, then they can begin to summarise the text, or make predictions based on their understanding. It might not be necessary to summarise a text before making a prediction, and the ability to summarise a text should not rely on the ability to make predictions based on it. These two skills are both included in the KS1 test framework, but children at this stage summarise and make predictions based only on word meaning, information retrieval and inference (missing out 2f and 2g) – summaries and predictions at this stage might be at a simpler level. It is probably true that in KS2 similar summaries and predictions could be made, without paying heed to 2g and 2f.

2c - Summarising

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases
(2f)        identify/explain how information/narrative content is related and contributes to meaning as a whole
(2c)       summarise main ideas from more than one paragraph

2e – Predicting

(2a)       give/explain the meaning of words in context
(2b)       retrieve and record information/identify key details from fiction and non-fiction
(2d)       make inferences from the text/explain and justify inferences with evidence from the text
(2g)       identify/explain how meaning is enhanced through choice of words and phrases
(2f)        identify/explain how information/narrative content is related and contributes to meaning as a whole
(2e)       predict what might happen from details stated and implied

The model suggests that an understanding of word meaning is core to all reading – this model assumes that children already have the skills of decoding, sight recognition and phonological awareness. The model only includes reading skills outlined by the test framework and does not include factors such as the necessity of activating prior background and literacy knowledge when reading.

The model also suggests that there is a hierarchy of reading skills and that children might benefit from having some reading skills taught before others.

It also suggests that when requiring a child to work on a skill which is ‘higher up’ the model that they work through a sequence of skills usage in order to initially scaffold their ability to exercise the ‘higher’ skill. For example, if requiring a child to summarise a passage, they might first answer questions about the vocabulary used, the information contained within (given both literally and inferentially) and what the authors purpose was with regards to structure and language choices.

This model focuses on the following strands of Scarborough’s reading rope: vocabulary, verbal reasoning and language structures:


I hope I have made my thinking clear in this blog post and I would really appreciate any thoughts about what I have proposed. If you can back any of your comments either with research or with case studies from experience then even better!

Tuesday, 12 December 2017

My Year As A Teaching Leaders Fellow

I use my blog as a kind of scrapbook, a central place to keep a record of things I've written that have ended up elsewhere in other publications and on other websites. This time I wanted to preserve these photographs from my graduation from the Teaching Leaders programme that I took part in during the '16/'17 academic year.

I was pleased to graduate with commendation and to also have won the Ann Brougham values award for the primary North cohort. I was peer nominated (thank you, whoever you are!) for the award which was created in memory of the first Lead Coach on Teaching Leaders, and is presented to a Fellow who has remained true to their values, supported their peers on the programme and displayed an unrelenting commitment to the Ambition School Leadership mission. The award goes to the Fellow that has demonstrated ASL's core organisational values of mastery, grit, empowerment, teamwork and integrity to an outstanding level throughout the programme. For the prize I was able to choose a book; my choice was Patrick Lencioni's 'The Five Dysfunctions of a Team', and there is significance in that choice.

Patrick Lencioni's 'The Advantage' really helped me to wrestle with gaining a clarity of vision way back in November of last year at the beginning of my Teaching Leaders journey; I blogged about it in a post somewhat bizarrely entitled 'Dogs & Sledges: Harnessing Action To Clarity Of Vision':

Patrick Lencioni recommends that once that first question 'Why do we exist?' has been answered leaders can then go on to ask themselves 'How do we behave?', 'What do we do?', 'How will we succeed?', 'What is most important, right now?' and 'Who must do what?'. In schools, we often have deeply entrenched answers to these questions and we carry on in those ways regardless of whether we know our 'why' or not.

In that blog post I also referenced many of the speakers from the Teaching Leaders residential: 
I was challenged by some inspirational leaders to ensure that I was clear in my vision. Steve Radcliffe, coach to powerful and influential figures the world over encouraged me first to think of the future before engaging others in that vision of the future. Andy Buck told me to focus on one thing in order to gain clarity. Baroness Sue Campbell reiterated the need to be clear on where we are going, asking me to consider if everyone gets my vision and wants to follow me. She also caused me to consider whether my targets were good enough and whether or not I knew what great looked like. James Toop discussed creating culture - my key piece of learning from that session: 'Be clear on what my vision is', I wrote in my Moleskine - I knew that without a clear vision I would struggle to create a culture within my own team. Sir David Carter issued a performance challenge, the first point of which was to 'de-clutter'...
Since then I have written three blog posts for the Ambition School Leadership blog, each reflecting on an aspect of my leadership journey:

My Ambition Isn't Just About Me: 
http://thatboycanteach.blogspot.co.uk/2016/11/my-ambition-isnt-just-about-me.html
The education system has its challenges but I see potential in a system whose workforce are positive and optimistic about how they can influence those within their sphere. Imagine the impact that could be had if every leader in every school saw the potential in being solution-orientated, finding innovative ways to make the system work for the schools we work in. It is my ambition to ensure that this is always done, for the benefit of the learners, at the schools I work in.
Leadership Lessons: Letting Go And Letting Them: 
http://thatboycanteach.blogspot.co.uk/2017/03/how-watership-down-and-unique.html

I realised that, as a leader, I often attempted to do it all, even when there were others in my team who were better for the job. Furthermore, the experiential brought it home to me that I actually felt threatened by those who were better at something than I was. I found that I harboured feelings of resentment towards those I was supposed to be leading and my negative feelings were not conducive to good leadership and teamwork. 
Looking Back On My Moleskin Moments:
http://thatboycanteach.blogspot.co.uk/2017/11/on-ambition-school-leadership-blog.html
Although so much of what I learned last year on Teaching Leaders is now internalised and has become a natural part of how I function as a leader, it’s good to know that whenever I need a reminder my moleskine is there, immortalising the wisdom of a year so well spent honing my leadership skills.

Saturday, 9 December 2017

Why You Might Be Getting Feedback Wrong! (Part 1)

At the launch of Bradford Research School I held a workshop entitled Why You Might Be Getting Feedback Wrong! It's a slightly clickbaity title, and I wouldn't have been surprised if no-one came to it, after all, who wants to be told they're doing something wrong?

Anyway, people did come and I've begun to write up what I presented in the workshop. The information I was presenting all came from the EEF's review of the evidence on marking 'A Marked Improvement' - my workshop was an attempt to summarise their findings into a 20 minute bite-size chunk.

Read part 1 here: https://bradford.researchschool.org.uk/2017/12/08/why-you-might-be-getting-feedback-wrong-part-1/

Saturday, 2 December 2017

Mathematical Misconceptions And Teaching Tricks: What The Research Says

Imagine a factory. Think of the vast machines clanking away. Think of the whirring, the turning, the raw materials becoming a finished product. Beneath those metallic exteriors cogs, cams, belts and levers are working together to effect that change. But all but the most initiated don't really understand how the machines do what they do, they just know that if they put the right parts in at one end, the machine will produce the desired item.

And this is how many children feel about maths. They know that putting some numbers into a calculation will give the desired answer, but they don't really have a clue what goes on inside the 'machine' of that procedure. This is all well and good until that child has to apply this learning - having no understanding of the mechanics of mathematics makes it very difficult to use procedures in context.

In my blog post for Third Space Learning entitled 'Maths Tricks or Bad Habits? 5 Bad Habits in Maths We're Still Teaching Our Pupils' I make several suggestions for how to use visual representations to teach good conceptual understanding of some tricky aspects of the maths curriculum, such as the ones below:



The recent EEF guidance document on improving maths in KS2 and KS3 backs up the importance of modelling good conceptual understanding in maths lessons, rather than relying on tricks that work but don't help children to have an understanding of the 'why' and the 'how':
Recommendation 4: Enable pupils to develop a rich network of mathematical knowledge 
"Pupils are able to apply procedures most effectively when they understand how the procedures work and in what circumstances they are useful. Fluent recall of a procedure is important, but teachers should ensure that appropriate time is spent on developing understanding. One reason for encouraging understanding is to enable pupils to reconstruct steps in a procedure that they may have forgotten. The recommendations in this guidance on visual representations, misconceptions, and setting problems in real-world contexts are useful here."
In order to teach maths well, and in order for children to succeed in maths, teachers need to make sure children understand what is going on when they carry out a mathematical procedure. A great way of developing this understanding is using manipulatives and representations:
Recommendation 2: Use manipulatives and representations 
"Manipulatives and representations can be powerful tools for supporting pupils to engage with mathematical ideas. However, manipulatives and representations are just tools: how they are used is important. They need to be used purposefully and appropriately in order to have an impact. Teachers should ensure that there is a clear rationale for using a particular manipulative or representation to teach a specific mathematical concept. The aim is to use manipulatives and representations to reveal mathematical structures and enable pupils to understand and use mathematics independently.
Teachers should: Enable pupils to understand the links between the manipulatives and the mathematical ideas they represent. This requires teachers to encourage pupils to link the materials (and the actions performed on or with them) to the mathematics of the situation, to appreciate the limitations of concrete materials, and to develop related mathematical images, representations and symbols."
As I wrote in the guide to Bar Modelling that I produced for Third Space Learning (click to download for free):

If we don't do this, we run the risk of allowing children to proceed in their mathematical education with misconceptions:
Recommendation 1: Use assessment to build on pupils’ existing knowledge and understanding 
"A misconception is an understanding that leads to a ‘systematic pattern of errors’. Often misconceptions are formed when knowledge has been applied outside of the context in which it is useful. For example, the ‘multiplication makes bigger, division makes smaller’ conception applies to positive, whole numbers greater than 1. However, when subsequent mathematical concepts appear (for example, numbers less than or equal to 1), this conception, extended beyond its useful context, becomes a misconception. 
It is important that misconceptions are uncovered and addressed rather than side-stepped or ignored. Pupils will often defend their misconceptions, especially if they are based on sound, albeit limited, ideas. In this situation, teachers could think about how a misconception might have arisen and explore with pupils the ‘partial truth’ that it is built on and the circumstances where it no longer applies. Counterexamples can be effective in challenging pupils’ belief in a misconception. However, pupils may need time and teacher support to develop richer and more robust conceptions."
When we do teach children using appropriate models and images so that they understand the mathematical concepts behind the procedures (or the 'tricks'), we provide children with something that they can actually look at and explain. Explaining something that is concrete is easier than explaining an abstract concept.

In the bar modelling guide (click to download for free) I pointed out that:


By developing children's skills to represent and explain their understanding using a model, we develop their independence and motivation:
Recommendation 5: Develop pupils’ independence and motivation
"Teachers can provide regular opportunities for pupils to develop independent metacognition through:
  • encouraging self-explanation—pupils explaining to themselves how they planned, monitored, and evaluated their completion of a task; and
  • encouraging pupils to explain their metacognitive thinking to the teacher and other pupils."
Next time you plan a maths lesson question how you will ensure that children have a good conceptual understanding of the content you teach. Often, concrete or pictorial representations will be the best way to show children the inner-workings of the concepts you cover. Following Psychologist Jerome Bruner's research-based CPA (Concrete - Pictorial - Abstract) approach means that children (and adults) are more likely to understand what is going on inside the maths machine as calculations and processes take place.

Further Reading and Resources: