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Deep Dive – Science

My school had a mock science deep dive with an OFSTED inspector (I know, you are preaching to the choir if you disagree with this practice).

Nevertheless, I thought some use should come out of it and I would share what they asked of us and the children. A lot of this is what you have heard before, but hopefully something is new and of use to you.

They wanted to know about:

  • Logic behind our yearly overview – why certain topics were taught in that particular order (i.e. we teach Plants in Spring because plants are growing in the school environment)
  • Medium term plans – did they link to the National Curriculum (we follow the NC) and the logic behind the flow and sequence of objectives. Did they all lend themselves to the next step of learning?
  • Why did we use a particular scheme of work? (Kent Scheme)
  • Progression of knowledge and progression of scientific skills – what was the prior knowledge from the year before (if topic also appeared in that year group) and what were the prior scientific skills? Was the current class teacher aware of these?
  • They wanted our subject leaders to be able to pick out on the medium term plan which learning objective or lesson each class was on right now
  • How are misconceptions addressed? Are teachers thinking of them prior to teaching in order to prevent/tackle them? Teachers should then be targeting lower and middle attainers when dealing with said misconceptions
  • During lesson observations, they asked leaders to pick out all higher attainers, disadvantaged and SEND chn – then checked to see if class teachers were targeting these children with questioning – also wanted to see their books and chatted to those children
  • Wanted to see if teachers were specific with their questioning and if questioning was targeted and in a sequential/chronological order
  • They were big on digging deeper with questioning – trying to find out children’s reasoning (i.e. awareness of disciplinary knowledge)
  • When speaking to children, they checked prior knowledge – what could the child tell them from previous years of learning on same topic? Then asked children to tell them something new they had learnt from current year group/topic
  • Was interested in differentiation and wanted to see difference between higher, middle and lower ability (or whatever PC term EduTwitter currently values for those three groupings)
  • They got KS1 children to read out the learning question or objective to make sure they could access it and then checked the meaning of words with the children – e.g. properties in an LO – what does properties mean, Tommy?
  • Our reception class learnt about sound and sounds of particular animals – inspector suggested phonics should be linked with this
  • Asked teachers what they wanted the children to get out of the lesson and that it matched the lesson objective and outcome of the task

Interview with children

All children were asked not to mention teachers’ names and to say what learning in science was like for them. They were also asked to open their books to the last piece of work they did and talk about it – children had to explain their learning from that lesson and questioned them to try and catch them out around misconceptions of that topic/lesson.

Here is a list of questions they asked the children, ordered by class and topic:

Year 1 – Changing Materials

  • What is the difference between hot and cold?
  • What is melting?
  • How do you know when something is melting?
  • Pointed to thermometer and asked them what it was and what unit of measurement was used on a thermometer
  • Mentioned degrees and Celsius – asked them what they meant

Year 2 – Plants

  • Today, you learnt about evergreen, what was the other words you learnt about? (deciduous)
  • Child explained that they knew ‘it’ was evergreen – what is ‘it’?

Year 2 – Habitats (Plants topic had just so started so questioned on previous topic)

  • Explain what a food chain is
  • What does a food chain start with?
  • Tried to catch children out by saying lettuce was a herbivore
  • Asked what a nut and berry were
  • What is a herbivore? Carnivore? Omnivore?
  • Point out an omnivore in your book.

Year 3 – Rocks, Fossils and Soil

  • What do you know about fossils?
  • Is it only animals that can be fossils?
  • Does an animal have to be eaten to be a fossil?
  • If a plant can be a fossil, do plants have bones?
  • What is sedimentary, igneous and metamorphic?

Year 5 – Earth and Space

  • What did you learn today about the moon?
  • What does orbit mean?
  • Why can we only see half of the moon?
  • Are their particular names for the moon/s?

Year 5 – Changes of Materials

  • States of matter – what is reversible and irreversible change?
  • Can you give me an example of a reversible change and an irreversible change and explain how they are reversible and irreversible?

Assessment

They were also particularly impressed with how we assess in science. We do two different assessments.

An assessment of substantive knowledge – children define keywords and give examples.

An assessment of disciplinary knowledge – children answer questions using their scientific knowledge to come to a conclusion.

Below I have shared a picture of both types of assessment.

Assessment on substantive knowledge – keywords:

summative

Assessment on disciplinary knowledge – questions to show scientific understanding:

disciplinary

You can read more about these two types of knowledge here – https://mrmorgsthoughts.wordpress.com/2020/01/03/how-can-we-assess-knowledge/

Twitter – @MorgsEd

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BrewEdMaths – Speaker Summary

Below are the notes that I wrote as I listened to the speakers at @BrewEdMaths 2020. If you want further clarification on a point, it would be best to contact the speakers directly, as they will be able to elaborate much better than I will. The notes are written in a bullet point format, as that was how I took them on the day. Some talks were more visual than others, so there may be fewer notes – that does not mean the talks weren’t as good! Thank you again to all the speakers who took part and everyone who came. We are in discussion about making it an annual event!

 

Dr Helen – @helenjwc – ‘Pass It On’

  • Helen’s talk was mostly about the use of dialogic talk in EYFS and how we should make the maths to do with the children, including building their decision-making, curiosity and predictions.
  • She got a few groups to do an activity known as ‘Pass It On’, while the rest of us observed and had to comment on what we saw happening.
  • In the game, each person playing had a handful of items. They would roll a die and then give/take the number of items on the die to/from another person.
  • The whole activity was focused around talk and how the individuals had to engage with each other – e.g. when one person rolled a 4, but they only had 1 item left, they had to engage in conversation with another person in their group about borrowing from them.
  • Helen explained that maths games should focus on the maths and not on the rules.
  • Think about having a single rule and children then negotiate around it through the maths they are learning
  • She went on to explain that a review body for ELGs had secondary school teachers on it and that she didn’t think this was fair as she wouldn’t put herself forward for a GCSE board as an EYFS specialist.
  • She suggested we read up on ‘Re-proposal’ from Italian preschools – which is about turning children’s thinking back on them
  • The aim of her game was to increase dialogue between pupils – “Vocabulary isn’t the issue, dialogue is the issue. We need more dialogue in maths”.
  • Message her if you would like to see research about the ELGs pilot
  • “Mathematics could be like rollerblading, but usually it’s like being told to stop rollerblading and come in and tidy your room”. (Winter, 1992).

 

Matt Swain – @mattswain36 – ‘25’

• Matt talked about the idea of ‘corridor kids’ – children who towards the end of primary school can spend most of their school day in booster interventions, often in poorer environments like school corridors, away from their peers. He noticed from speaking to these children that they seemed disenfranchised and they felt separated from their class.
• 25% of children (mean taken from the past 4 years) didn’t make the EXS standard at KS2 leaving without life maths – see that as being 25% worse off than their peers.
• ‘Mastery’ – this means all children can understand the same concept, but not necessarily at the same time.
• Pareto principle – 80% of effects come from 20% of causes
• The only currency we have in school is time
• Teach, do, practice, assess, behave. Schools don’t encourage enough of the ‘behave’ part. What Matt means by that is children using what they have learnt as a behaviour – applying it themselves.
• Marking is a dirty word – but it does have value when done in a lesson. Marking after the fact is a waste of time.
• Matt suggests there 5 things to focus on:

1.) Hardwiring facts – there is still place for learning facts – e.g. 7×8 came up 3 times in the SATs last year

2.) Worked examples – the 25% need these. Problem pairs – show the class’ worked example alongside an example for the class to solve

3.) Error tracking – when looking at whiteboards get each row/group/table to go down one row/group/table at a time. Everyone must put them up at the same time, so they don’t copy each other. Give them space for their answer to be put down very clearly on worksheets – e.g. a clearly separate box. During work, don’t talk to kids as you go around, instead just note down misconceptions and then deal with it all afterwards so you can get to every child during the activity.

4.) Exit ticket – single multiple choice Q with 4 possible answers on the thing you really wanted them to learn. Return them to original learning. Make the 3 wrong answers misconceptions you have seen during the activity/ones you know children traditionally have.

5.) Same day keep up – any child who needs an extra 20 mins stays with you after lessons, like during assembly that day – giving the 25% that time they need. This can prevent them from being separated from the rest of their class during lessons in the afternoons. This way every day the 25% get to feel success.

 

David O’Connell – @doctalkteach – ‘Lesson study and the 5 domains’

• Focus: challenge for all
• Follow @ban_har – the ‘yoda of maths’ – wrote Singapore Maths textbooks
• Lesson study has replaced performance management at David’s school
• You need a knowledgeable other in order to undertake lesson study – this can be a person, a book to refer to etc – something to refer and compare to
• Study, plan, observe, reflect, revision, reteach – 3 day cycle
• His school uses Singapore maths
• 5 part lesson – the anchor task, journalling, reading and reflection, guided practice, independent practice
• A focus on dialogue – talking together, helping each other – teacher enriches by going around and supporting
• There are research questions that guide the lesson study – how do we ensure all children understand the lesson whilst also challenging the advanced learners? What do generalisations look like and how are these addressed so misconceptions are not embedded? How are rules formed?
• Time – allow ample processing time for exploration, look at a problem informally and at low stakes, and eavesdrop on pupil conversations
• “The hardest thing to do as teacher is to shut up and eavesdrop”
• 5 domains of challenge is the differentiation

1.) Cognitive – the actual maths

2.) Metacognitive – pupils being able to recognise mistakes, recognising and selecting the most effective methods

3.) Social Collaboration – contributing to the learning of others

4.) Affective – showing perseverance, restraint and enjoyment within the lessons

5.) Mindsets – having a productive set of beliefs

  • Metacognition is built through children writing journals, of which there are 4 types:
  1. Descriptive – students explain different ways to attempt a question
  2. Evaluative – students make a judgment of efficiency of select methods
  3. Investigative – students may be asked to explore if a certain method will always work
  4. Creative – students created their own problem for a friend to solve
  • Ask chn to break down their method into 5 steps. Often children will just say, “I don’t have a method, I just know it”.
    • Take focus off marking and change it to dialogue in class
    • “Learning floats on a sea of talk”- Britton (1970)
    • David recommends you read Gaunt and Stott’s book – Transform teaching and learning through talk
    • Dialogic teaching – it should be collective, reciprocal, supportive, cumulative, purposeful (Alexander, 2010)
    • Try to get children to ask more questions. The proportion of questions is often heavily swayed in favour of the teacher. Kids do ask questions a lot in maths, but are they questions that will further their learning?

 

Andrew Jeffrey – @AJMagicMessage – ‘Magic, Maths and the Rosetta Stone’

(The notes on this talk aren’t as detailed as I spent most of the time laughing!)
• John Holt said, “Maths is not about what you know, but how you behave when you don’t know” – Andrew believes maths to involve a lot of magic
• We should visualise our mathematics
• Numicon pieces weigh the same – one 8 piece weighs the same as a 3 piece and a 5 piece (mindblown!)
• It is all about the language we present and how we code it (saying 21 = 3x rather than 3 x 7 = 21)
• Algebraic reasoning can be done very young, especially when using the language as shown above
• “You can’t do arithmetic unless you learn algebra first” – Caleb Gattegno
• Comparing the Rosetta stone with algebra – the Rosetta stone had hieroglyphics that they couldn’t translate, but they used two of the languages on it (ancient Greek and Demotic) to translate it – we can do that with algebra using Numicon – If a 2 piece and two envelopes (with Numicon inside them) weighs the same as one envelope and an 8 piece then 2 + 2e = 8 + 1e, which can be changed to 2 + 1e = 8 and so on
• “It’s important to get stuck at maths, even if you’re quite good at it!”
• Andrew made his case for being against the National Lottery and how slim your chances are of winning, although his friend Grant won about 10 prizes in the raffle!

• He has a new book out called ‘Greater depth in Primary Mathematics’ – you can buy it from his website here – https://www.amazon.co.uk/Greater-Depth-Primary-Mathematics-Strategies/dp/170169123X

Peter mattock – @MrMattock – ‘Let It Make Sense!’

It is very hard to recreate this talk as it used a lot of visuals, but these are the points I did take from it that are worth sharing. Peter made a great case for Cuisenaire rods and Algebra tiles and how versatile they are in explaining abstract concepts such as -1 x -1 = 1 and 2/5 ÷ 3/4.

  • Mathematics makes sense – it is consistent within itself. Focus on this. It must always make sense.
  • Peter recommends that we read up about ‘Arbitrary and Necessary knowledge’ (Hewitt, 1999)
  • Arbitrary – all students need to be informed of the arbitrary by someone else e.g. the x axis is horizontal
  • Necessary – some students can become aware of what is necessary without being informed
  • Arbitrary – cannot be worked out, might be so
  • Necessary – can be worked out, must be so (mattock’s emphasis)
  • Patterns in maths are there to be explained
  • 3 x 1 and -3 x 1 as reflection of each other or rotating 180 around the point of 0
  • -1 x -1 = 1 and 2/5 ÷ 3/4 use visuals to teach these problems not mnemonics like KFC (keep it, flip it, change it)
  • Just telling a child 2/5 ÷ 3/4 = 2/5 × 4/3 is not good enough
  • What was clear from his talk was that the more increasingly abstract the concept/teaching becomes, the more important visual representation is (and it’s always important) – especially for fractions and algebra which we all know to be difficult topics for all ages
  • Peter has a book out called Visible Maths which you can buy here – https://peter-mattock.visiblemaths.co.uk/search/label/Visible%20Maths%20Book

Jo Morgan – @mathsjem – ‘Bursting Our Method Bubbles’

  • People are defensive about their methods – we need to burst our method bubbles – just because it is the one we learnt as a child, doesn’t make it the best one or better than others
    • There are loads of interesting methods and people just don’t know about them
    • Are you aware of how an individual concept is taught in India? Scotland? North of England? The classroom next door? It is worth researching this to broaden your knowledge.
    • Speaking to a colleague might get you to change the methods that you teach
    • 84 – 27 written method can be done as decomposition as 70 + 14
    • Or equal addition like this 84 – 27 can be done as 94 – 37 (which was the dominant method before decomposition)
    • She recommends reading ‘Relative merits of the methods of teaching subtraction’
    • 9 different methods of subtracting in her book! And she recently learnt a 10th! How many subtraction methods can you think of?
    • Parents thinking methods are wrong because it’s not the method they learnt – being defensive about methods, we mustn’t let them influence the children we teach to think the same way
    • Jo has a new book out (A Compendium of Mathematical Methods), which you can find here – https://www.amazon.co.uk/dp/1912906600Kieran @Kieran_M_Ed and Lloyd @lwilliamsjones – Purposeful Storytelling
  • The world we see is a representation applied to what we already know
    • Language is a structure that is capable of creating infinite representations
    • Late language model – evolutionary leaps for language came around the same time as retrieval ability came for homoerectus/homosapiens – an ape’s memory is purely episodic, ours is not.
    • Willingham talks about the 4 Cs – narrative comes from these 4 Cs
    • Character – how it influences meaning
    • The meaning derived from the story depends in part to the character children relate to/identify with
    • Consider a teacher’s role as a ‘real actor’
    • The embodiment principle – we learn more when there is gesturing, movement, eye contact etc
    • They recommend we read Greg Ashman’s blog
    • Pupils should relate to characters
    • Remembering is similar to person perception (perception of characters)
    • Causality – output depends on current and past input
    • In understanding, readers try to explain why characters act like they do
    • Predicting doesn’t meant we are going to necessarily understand, but that we will be more likely to remember it
    • Conflict – central character faces obstacles and they prevent the goal from being met (purposefully getting a question wrong by missing out a step or incorrectly performing a step could perhaps be an example of this)
    • Stories with obstacles were found to be more memorable than those without
    • Powerful narratives and their effect on memory and recall, not understanding
    • Conflict provides a point of view through which you can remember the story
    • Narratives are sticky in the memory

 

Bernie Westacott – @BernieWestacott – ‘’Genesis: The Birth of Number in Young Children (and rats and chickens)

  • Clever Hans the horse from 1904 – he could tap out using his hoof any addition like 3 + 5. It could also do 2/5 + 1/2 and the divisors of 28 (it had been trained to react to its trainer’s eye movements)
    • Poupette the dog could tap a paw to add digits and lick a hand to show it was finished
    • Rats could press a lever a certain amount of times to release food – press too early and it would reset or the light would go out
    • If it needed to press the lever 4 times, it would press between 3 and 7 times
    • The bigger the number required, the bigger the range of their error 12: 16-27 – but they still demonstrated a sense of keeping track of the number of presses
    • A chimp could compare two numerical amounts – possibly using an approximate comparison
    • A chimp had pile of 4 and pile of 3 together and a pile of 5 and a pile of 1 together – after thinking for a while, it went for the piles of 3 and 4 – this suggests that the chimp carried out some form of arithmetic
    • Distance effect (the distance between the numbers in two quantities) and magnitude effect (how large each quantity is) affects our ability to compare two quantities using our Approximate Number System (ANS)  -ANS is a gross quantity system that does not result in an exact number
    • To read more about the chimp experiment, search for Woodruff and Penmark
    • Babies looking at slides of 2 dots/items – when they looked away, a new slide was shown (also 2) – the time they looked at each slide got less until a slide of 3 was shown. They spent longer looking at this 3 slide, indicating that they were aware that this was different to 2. This was odne with 6 -7 months old children and later replicated with babies a few days after birth
  • Clements and Sarama 2019 – check out their website ‘Learning Trajectories’ – including the subitizing song
  • Subitizing is direct perceptual apprehension and identification of the numerosity of a small group of items without the need to count them
  • Perceptual Subtizing – without counting, to know exactly how many there are when dealing with small quantities. Children can subitize 1, 2, 3 and even 4 objects. Well know patterns, such as 5 dots on a die, are easier to subitize than if the 5 dots were spread out randomly
  • Conceptual Subitizing – 8 in a 10-frame is subitized in two groups – a full row of 5 and a group of 3 below that – which are then combined; or as 10 with 2 missing
  • Manipulating numbers spatially through use of dice, dominoes and ten-frames plays a significant role in building number sense and understanding of arithmetic
  • This can be used to develop addition strategies beyond counting in 1’s. For example,  using two frames to model 9 and 5 which becomes 10 + 4 (moving 1  over from the 5 to the 9)
  • Some children have a poor start from age 0-3 because parents don’t include a focus on number in their interactions with their children – thus, they may not develop Spontaneous Focus on Number (SFON) tendencies. This may also be the case with children in other environments, such as day care centres
  • Research shows that intervening with children as young as 3 to increase their SFON can result in signficant improvement in their SFON and cardinality recognition. The more they notice number all around them, the more practice they get with number, which results in further mathematical development

 

Follow @BrewEdMaths for all things maths and the BrewEdMaths team – @MorgsEd, @MissSDoherty, @mattswain36, @lwilliamsjones, @MrAlmond_Ed, @Kieran_M_Ed, @RebeccaTurvill

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Education from a Hegelian perspective

G.W.F Hegel is not the most well-known philosopher, however, he massively influenced the musings of Karl Marx and Friedrich Engels and their writings on Communism and Socialism. Although Marx ultimately rejected the Hegelian view of the world as idealistic, it actually influenced Marxist philosophy quite drastically. Although I too feel it to be rather idealistic, I think it has some merit in explaining the current state of education.

Hegel’s principle of view of history posited that it was a series of events that displayed a process of development and that in order to understand one part, you must first understand the whole. I believe this notion parallels quite aptly with the state of modern education. In order to understand how teachers teach effectively now, we must first understand what methods teachers used before us and why they were deemed to be ineffective, or how our methods have grown from them. Furthermore, you cannot understand an individual concept within teaching, whether it be Constructivism or spacing, without first understanding education as a whole. Constructivism and spacing both co-exist and spawn from other theories that contradict them (e.g. Behaviourism and Blocking). In order to understand the merit of spacing, I must also understand the pitfalls of block teaching.

Each concept exists under the umbrella of education within which it manifests itself.  It can therefore be assumed that education is always developing, because each concept draws and improves upon concepts that have preceded it. In that sense, education is dynamic and imperfect, but has the capability and potential of achieving perfection, or so Hegel would have argued (this is why Marx deemed Hegel to be a bit of an idealist).

Unlike other philosophers, Hegel rejected the notion that philosophers should comment on or predict the future. His ideas focused on the zeitgeist of the period. This too mirrors the current state of educational theory and dialogue. We often analyse and comment on the contemporary condition of education, and often look backwards to do so, but we rarely comment on the future. This links back to Hegel’s view about the dynamic system that is always progressing by utilising the views that preceded it. In this sense, it is impossible to comment on the future because we have not yet had enough experience of the concepts that dominate the present zeitgeist. Perhaps a current example would be the idea of retrieval practice. We are unsure of what will follow it, or how it will be improved upon, because its prominence is very current and is yet to be held up to intense critique. At the moment of writing this, retrieval practice has swept across education as the saviour of ‘remembering more’ and ‘changes to long-term memory’. But overreliance on this concept without first truly critiquing it will inevitably lead to retrieval practice that is, at least in some part, rather ineffective. For example, the emphasised focus on low-stake quizzes tends to focus only on substantive knowledge and largely ignoring disciplinary knowledge. You can see more on that in these two blogs – https://mrmorgsthoughts.wordpress.com/2020/01/03/how-can-we-assess-knowledge/ and http://www.thatboycanteach.co.uk/2019/12/beware-reverse-engineered-curriculum-or.html

The Hegelian perspective is characterised by the idea that ideas can develop and progress by looking backwards. From this, Hegel’s view of the ‘dialectic’ was born. This entails that we must carefully examine an idea by linking it to other ideas (previous or current), either because it can contradict or complement it. So Hegel’s view of history was not just that of a simple list of events, but that history is the view of how all these events link together. Education again parallels this. All educational theory links together, whether you choose to adhere or align most to Piaget, Vygotsky or Skinner (those are the only big names I can remember from my PGCE). Where I think the ‘dialectic’ relates to education most is in its origins. The term originated in ancient Greece, whereby a ‘dialogue’ was established upon opposing views and this led to the formulation of truths. Hegel believed that by having these opposing views or contradictions, only then could we progress (I think a lot of EduTwitter trolls could learn a thing or two from that statement).

The ‘dialectic’ entails three steps. Thesis, Antithesis and Synthesis – always in that order. Thesis is the original idea that starts off the dialogue; antithesis is the contradicting idea that builds on this dialogue by presenting an opposing point of view; and synthesis is the reconciliation of these first two steps into a new, established truth. Of course, the synthesis part can be ongoing and challenged itself, and that is why we continue to have multiple new theories that are born out of singular, past ones. The process is very cyclical because of this. This led Hegel to conclude that changes can be gradual, but that they can have a very sudden impact (see retrieval practice mentioned above). Ergo, the state of education changes slowly for the most part, but with very sudden transformations.

Hegel determined that the ‘dialectic’ was governed by certain laws. The most relatable one of these laws to education being that of ‘the law of the unity of opposites’. This states that all things in the world exist in opposition to something else (e.g. hot and cold, short and long) – so too does educational theory (e.g. Constructivism vs Behaviourism) and every teacher’s opinion on Twitter!

 

I hope this made sense to someone. It mostly feels like nonsensical ramblings when I read it back. This is simply my interpretation of how the Hegelian perspective applies to the modern state of education and in part to EduTwitter. Still, I’m glad the sociology part of my undergrad degree finally came in use for something.

NB: For a better understanding of my ramblings, read through Rupert Woodfin and Oscar Zarate’s Marxism: A Graphic Guide. This blog was written after reading that book.

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How can we assess knowledge?

Before we can discuss how to assess knowledge, we must first define what knowledge is. With regards to teaching, I believe in a rather simplistic dichotomy of knowledge: substantive and disciplinary.

Substantive knowledge is the knowledge produced by any specific academic subject. It is therefore sometimes referred to as ‘content’ knowledge. It is the knowledge you learn from a topic or unit. In science, this might be what respiration is. In geography, it might be about the economic development of a region. In art, it might be the style of Impressionism. You get the idea. Substantive knowledge is the knowledge children gather as established fact. The concepts, the words, the dates and so on.

In contrast, disciplinary knowledge is the understanding of how that knowledge was formed, how it continues to be formed and a general understanding of how that subject manifests itself and operates. In science, this may be understanding how a scientific investigation is conducted. In geography, this could be an understanding of how geographical fieldwork is undertaken. In history, it could be how we gather information from historical sources. Disciplinary knowledge is understandably harder to teach and arguably less common in classroom assessments than it is in external assessments (e.g. GCSEs). I am proposing we address this imbalance.

We need to think about the validity and reliability of the assessments we use with regards to these two types of knowledge. If our assessment only tests substantive knowledge, then has the pupil learnt about how the discipline itself operates? Likewise, if the assessment only tests the disciplinary knowledge, can we truly know if the pupils have learnt the content of the topic and successfully added to their schema of pre-existing knowledge? Therefore, arguably, our assessments must provide opportunity to assess both types of knowledge together or assess them individually. I suggest the latter.

Previously, at my school, we (regrettably) used KWL grids to assess children’s progress through a topic. A KWL grid assesses what a child knows ( K ), what a child wants to know ( W ) and what they have learnt ( L ). I always found the W section to be particularly frustrating, as children will always write the most absurd questions here that you never get any time to address in depth, or you simply don’t know the answer to because your limited subject knowledge exists outside the realm of their wild imagination and its far-fetched questions. So then, what is the point in allowing children to ask these questions?

We believed these assessments showed progression in children’s learning simply because the third column had more writing than the first column, but this was no real indicator of children being successful in their learning long-term. Moreover, there are many problems with an assessment of this type. First, they seem to only test substantive knowledge, as they only ask children to recall what they know. Secondly, the opportunity for recall is rather lacking. Just asking children to write down everything they remember without any retrieval cues is unsurprisingly rather ineffective. For us, we needed to ensure our assessments were more effective in the foundation subjects.

An example of a blank KWL grid:

Untitled.png

I will use my most recent history topic of the Great Fire of London to model the two separate assessments we came up with.

Testing substantive knowledge – vocabulary wordbank. Children are provided words from the topic and then asked to write down what they know about them. These act as retrieval cues, rather than simply asking children to write down everything they know about a topic with no prompts. If they can’t think of anything, they simply leave it blank so the teacher is aware of what needs to be revisited. Children can write in as much or as little detail as they can. The teacher can then assess their understanding by looking at the level of detail in their answer and how well they have linked it to other words and concepts learnt.Untitled.png

Testing disciplinary knowledge – answering questions linked to the discipline itself. This would always be conducted subsequent to the assessment on substantive knowledge, because children would need to draw on that substantive knowledge to help them. This assessment would focus on unpicking the elements of the subject discipline we wanted them to grasp (e.g. for history, that could be how historical knowledge has accumulated over time, the reliability of sources or the correlation between cause and effect). Below is an example of this type of assessment. I have added the disciplinary knowledge each question sought to assess in red next to each question. Children would be given more space to write their answers for this assessment, as it would provide more scope for more detailed answers.

Untitled.png

With the recent emphasis on retrieval practice in education forums, it would be easy to ignore disciplinary knowledge and focus solely on substantive knowledge. But, both types of knowledge are equally as important as one another. They are inextricably linked and inform one another. Together, they allow children to formulate a schema of knowledge that allows them to understand and interpret the world around them.

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education

Using ‘spacing’ to redesign our geography curriculum

With the introduction of the new OFSTED inspection framework in Sept 2019, my school quickly realised we were not up-to-scratch with certain subjects in our curriculum. When the new curriculum was introduced in 2014, we should have been changing and redesigning our curriculum then, but for whatever reason, we didn’t.

I was tasked with examining the current state of our geography curriculum and asked to try and improve it. It’s probably worth mentioning here that I am no geography expert and that I’m not even a geography subject lead (our actual lead is part-time so I was drafted in to help). I spent an entire day out of class to think about our three Is (intent, implementation and impact) as laid out in the OFSTED framework and how to redesign our curriculum to suit what we wanted.

Our old geography curriculum looked like this:

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We deemed it to be insufficient. There had been no careful thought or planning into it other than to make sure there was haphazard and sporadic curriculum coverage. Our enacted curriculum (the one we were teaching) matched the formal curriculum (the one the government made) rather poorly and only in a rather reductionist and functionalist way. We hadn’t considered that the formal curriculum did not dictate when to teach, how much to teach or even which year group to teach each topic in. Therefore, instead of looking at rainforests in-depth and frequently, they were taught for just the length of a single half-term in just one year group (as seen above). There was no opportunity to draw upon that knowledge later on in their geography learning. This was true for many topics that deserved better, more regular coverage and this was the driving force behind redesigning our curriculum for the better.

Intent – What did we want children to learn and how would we make it rich, in-depth and meaningful? How would our curriculum demonstrate this richness and depth? We concurred that our intent should be that we want the children to understand the world in its vast variety of contexts (rich and poor, hot and cold, northern and southern etc). Our school context is a poor one, in which the vast majority of children do not receive much ‘life experience’. We therefore wanted a curriculum that could provide a wealth of cultural capital, by looking at as much of the world as possible. For example, in meeting the curriculum objective about understanding geographical similarities and differences of a small area of the United Kingdom, and of a small area in a contrasting non-European country, we decided to use Edinburgh as our focus from the UK, rather than London, as our children live there and are already familiar with it. We also wanted children to remember more and would place a greater focus on long-term learning than before. Our previous complacency of using a ready-made scheme had prevented this. We simply assumed that there was great coverage of the curriculum, a lot of drawing on prior knowledge and revisiting of content, when simply, there wasn’t. It was up to us to make sure this was planned out effectively.

Implementation – How were we going to ensure this long-term learning and variety of contexts was covered? The answer to that question was utilising the concept of ‘spacing’ in our curriculum design. For those unfamiliar with this term, ‘spacing’ entails teaching content in depth and then revisiting it at multiple points. Normally, teachers will do this across the teaching of a single unit. At the start of each lesson, they may use a low-stake, retrieval-based quiz that asks children about learning from previous lessons on the same topic. While this is effective, we wanted to negate the previous problem of only teaching something like rainforests for just one term, in just one year group. We therefore applied the concept of spacing to our entire curriculum.

In the younger years, children would start to create their schema of knowledge by looking at things that were familiar to them from the curriculum – e.g. where they are from, where they live and local habitats. We would then revisit these throughout the rest of their time at our school. In reception, children would start to look at the things mentioned above. This would then be consolidated in years 1 and 2, when it was revisited alongside the teaching of seasons, countries and continents and weather patterns.

Coupled with the idea of using spacing, our curriculum also operated on a ‘zooming-out’ model. Children would start by learning about where they live. Children would ‘zoom-out’ to learn about the local area, then another region in the UK, then the UK as a whole, then northern Europe, then North America and so on. The idea behind this was that each new topic provided children with a chance to draw on previously learnt knowledge. When looking at a region of the UK and the UK as a whole, how did they compare? When looking at Northern Europe and North America, were they similar by both being in the northern hemisphere? What was different about them? The other reason for doing this was that it allowed more scope for curriculum coverage. Instead of just learning about rainforests for one topic, children could look at them in every unit. Are there any rainforests in northern Europe? Why not? Is it because northern Europe does not fall on the equator? OK then, what must the climate be like in northern Europe then as it must differ to that of a rainforest?

I also found it useful to look at individual topics and lay out how each one could meet the different curriculum strands, but also to write the rationale behind teaching it in that specific year group at that specific time. This helped to make the spacing effect more readily apparent and maintained that each topic built on the already existing schema of knowledge the children have.

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Our new, working progress curriculum therefore ended up looking a bit more like this:

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Impact – It is still a working progress, but it is far better than what we were previously working from. It is too soon to witness any real impact as of yet, but presumably our children will leave with a much more rich, in-depth understanding of the world than they would have done in the past few years. We left it late and were slow to react, but it’s nice to know we are heading in the right direction.

 

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education

Why reading David Walliams’ books is OK…

NB: July 2020 Update

I’ve never read the books myself. I’ve seen a few tweets recently discussing the books’ use of tropes and stereotypes. I am in no way defending their use. This blog was commenting purely on their popularity among children, rather than their content. Acknowledging how popular these books are, it is very important that we discuss with children in our classes about why this content is wrong.

This blog was prompted by a few tweets I have seen in the past few days about supermarket shelves being dominated by the books of authors like David Walliams. Some teachers are seemingly disappointed by the popularity of these books, because they do not deem them to be challenging enough or of a high-enough quality. This blog is not an attack on those people who tweeted their own point of view. It is merely me explaining why I think reading those books is ok.

It is perhaps the lack of challenge which explains their popularity; the ‘easy read’ aspect may travel some distance in explaining the enjoyment children get from reading them. Their basic language and frequent humour allow the books to be read across different ages. In fact, the 2019 ‘What Kids Are Reading’ Report (which surveyed over 1 million children from Year 1 through to Year 12 from nearly 5000 different schools) shows that Walliams’ books are among the most read titles for children in years 4, 5, 6, 7 and 8. Therefore, it is completely understandable that supermarket shelves are stocked with Walliams’ books, as they are operating on a popularity model of supply and demand. Yes, Walliams’ books seem to dominate, but this is obviously because children actually enjoy reading them. Not only can they read them with their peers in class, but they can discuss them with children or siblings who are a couple years younger or older than them. This surely only leads to more engagement with reading, as children have more opportunity to recommend other books from the same author or discuss parts they liked with each other. This is an opportunity for reluctant readers to engage with others about reading. An opportunity that should be capitalised upon, not condemned.

For the reluctant readers out there (of which I was certainly one as a child), books like the ones Walliams’ writes might be the only ‘buy-in’ to reading that they can find and truly engage with. They might not enjoy reading the lengthier fiction books that use long words they don’t understand (I only liked the Beano comics and Match magazine as a child). By discouraging children from reading these books, we run the risk of discouraging reluctant readers from reading altogether. Once we have children engaged with reading, then we can start to encourage them to read texts with more challenging vocabulary or more complex plots and character arcs/development. When reading independently in class or at home, they should be allowed to read what they want, otherwise reading becomes a chore.

We shouldn’t be saying to children, “Oh no, don’t read that. It’s too easy for you. Read this instead”.

We should be saying, “Why don’t you try this book when you’re finished with that one?”

When I was a child, Roald Dahl’s books were all the rage. To some extent, they still are now. Not once have I ever seen anybody criticise his writing. His plots and characters were never too complex (although wonderfully creative) and the vocabulary used was never particularly challenging (although often completely made up). His books featured a lot of peculiarity and humour. His books were read in many different year groups. See where I’m going with this? I’ve likewise never heard any criticism of Jeff Kinney’s Diary of a Wimpy Kid series, which seems to be just as popular and challenging as Walliams’ books. 2 of the top 20 books that high-achieving Year 9s read are from the Diary of a Wimpy Kid series. Should we tell them to stop reading them because they are too easy for a 14-year-old? Of course not. Francesca Simon’s Horrid Henry books don’t seem to be receiving any criticism either. The WKAR report states that 6 of the top 10 books struggling readers in Year 5 read are Horrid Henry books. Another 3 are Roald Dahl. So why the focus on David Walliams? There seems to be a bit of an unfair bias here (speaking of bias, be aware of my confirmation bias because of the stats I am using).

Another point I think a lot of people are forgetting is that we underestimate how quickly children can get through a book. The WKAR report states that children of a year 3 age tend to read around 37 books in one school year on average. What does it matter if one or even five of those happen to be Walliams’ books? Reading for pleasure is as equally important as reading to improve vocabulary, to widen our knowledge base or to improve comprehension ability. We cannot teach children how to access reading if we can’t get them enthused about reading itself. Children like to read multiple books from the same author, so let’s allow them to do so. The most important factor in fostering a love of reading is choice.

What is important is that we explain to children that popularity does not correspond with quality. The number 1 song in the pop charts is the most popular, but that doesn’t mean it has the most meaningful lyrics or the most beautifully played instruments. A film reaching the top ten grossing films of all time does not necessarily mean it is one of the most critically-acclaimed films of all time (I’m talking about you Jurassic World).

The level of challenge in books is crucially important, but so too is reading for pleasure.

All of the statistics used in this blog are taken from the most recent WKAR report for 2019. You can access it here – http://whatkidsarereading.co.uk/

I wrote another blog a while back about engagement ideas for reading. You can find it here – https://mrmorgsthoughts.wordpress.com/2019/03/10/engagement-with-reading-ideas-to-implement/

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education

Reading – Deep Dive Questions

Below is a list of questions OFSTED may ask your literacy or reading lead, as well as pupils and class teachers. This list has been formulated based on what I think they might ask in line with the new framework and what other teachers have reported from their inspections under the new framework. There may be repetition among them as there is a lot of overlap and some may be rewording of others.

NB: It is not set in stone that they will ask these specific questions. This is all guesswork, but it is a guideline for you to help you prepare for a deep dive into reading.

General questions for subject leaders:

  • How do you make sure early reading is a priority?
  • How often do teachers read to children? And for how long?
  • How do you make sure that when teachers are reading it is engaging for children? How do you support teachers in doing this?
  • How do you pick the books that children read? Are they linked to topics? Age-appropriate?
  • How do you help parents to foster a love of reading at home?
  • How do you ensure children are fluent and accurate readers? What about in key stage 2?
  • How do you ensure children’s books that you use help children to practise the sounds they have learnt?
  • How do you improve children’s reading fluency?
  • What books do children take home? Do they pick or do you pick? If you pick, how do you choose them?
  • How often do children change these books? Do they get to change them independently?
  • Do parents get involved with children reading these books at home? How do you know?
  • What is your action plan for developing reading this year? What are you trying to improve upon?
  • How do you make sure children have a love for reading? In class and at home?
  • What do you do to engage children in reading?
  • With older children, how do you know they are reading at home?
  • If parents can’t read themselves, how are you supporting them to help their child read at home?
  • How are the lowest 20% supported with reading?
  • How is reading taught in key stage 2?
  • What whole school reading policies do you have? Is sending reading books home a whole school thing? Is there reading homework? How often?

Questions around phonics:

  • Phonics check – if your results are good, how are you achieving that? If they need improvement, what do you plan on doing to make results better?
  • What is your termly plan for what you want children to know with phonics leading up to the screening check? What about afterwards in Year 2? Year 3?
  • How much time do children spend learning phonics?
  • When do you start teaching phonics? Why then?
  • How many sounds will your children know by the end of the term? Do you have an outline/plan for this?
  • Think about where we are in the year now – Where are the children up to? Which children are not at this point? Why? What are you doing to remedy this? Can you show me what they know? (read with children here potentially).
  • What images and movements do you use to convey the sounds, digraphs etc?
  • How do you know which children are not on track? How do you assess? How regularly?
  • What support is in place for these children to catch up?
  • How do you ensure children build strong phonics knowledge?
  • Are your KS2 teachers phonics trained? How are they supported to use phonics in their teaching?

Pupils:

  • What is your favourite book you’ve read at school this year?
  • What books have you taken home? How often do you take them home?
  • Does your teacher read aloud to you? When? How much?
  • Do your parents read with you? Do you parents know you have reading books that you take home?
  • Do you enjoy story time?
  • Do you read in other subjects?

Hope this of use.

 

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education

The Literacy of Numeracy Part 2: Explicit Vocabulary Instruction

This is the 2nd part of my ‘literacy of numeracy’ blogpost series. The first analysed the language used in SATs tests and suggested tips you can use in the classroom to help prepare children for the tests based off of the analysis. You can find part 1 here – https://mrmorgsthoughts.wordpress.com/2019/02/24/ks2-maths-sats-language-analysis/ and a free downloadable version with a PowerPoint you can use in class here – https://www.tes.com/teaching-resource/ks2-maths-sats-language-analysis-12076440

 

I originally delivered this current blog as a 30-minute speech at an education conference and have tried my best to trim it down.

Introduction

In this blog series, I have been titling the posts under the umbrella phrase – ‘the literacy of numeracy’. I want to begin by clarifying what I mean by that. This phrase concerns itself with the disciplinary literacy of mathematics. Put more simply, ensuring each child is numerically literate by teaching them how to interpret visual symbols, graphs, charts, diagrams as well as individual terms and word problems. I believe language is the principle factor in developing this literacy within children and that the teaching of reasoning and problem solving in its current form can be very ineffective, when it relies on basic strategies like the use of RUCSAC and circling and underlining keywords.

Following a more language-specific method can prove to be more fruitful, as mathematics presents a lot of issues through its frequent variety of representation (e.g. 500g, 0.5kg and 1/2kg), but often the language used remains consistent. Maths can be considered as an additional language, in which it has its own specific terms and syntax. Enumerated below are just a few language obstacles children face in our classrooms:

  1. Their knowledge of synonyms usually linked to one of the four calculation types (take instead of subtract, product instead of answer, altogether rather than add)
  2. Their understanding of superlatives (biggest, largest, tallest, smallest)
  3. Words that can have different meanings outside of a mathematical context (round, product, factor, prime)
  4. Words other than superlatives that suggest comparison (between, more/less than, each, share, in order, sorting, put in the correct place)
  5. Their understanding of the difference between the right answer and the wrong answer (best estimate, explain why Jack is not correct, write the correct symbol in each box, circle the improper fraction that is equivalent)
  6. Verbs implying mathematical meaning (remaining, left, combine, collect, spend)
  1. Compression of vocabulary through nominalisation and noun phrases – prime number, improper fraction, roman numeral, perpendicular and parallel lines, 3D shape
  2. Abstract nouns – circumference, multiplication, area, perimeter

 

I emphasise this idea of maths as its own language, because as a maths SATs marker this year, I saw countless children incorrectly answer Reasoning Paper 2 Q18 (pictured below) because they indicated that ’95 goes into 5′ and ’87 goes into 3′. In my two years of SATs marking, I have seen far too many marks lost to inarticulation. Interestingly, in the 1068 responses to Paper 2 Q18 I marked, I only saw 1 child use the term ‘composite’. Naturally, you did not need to use this term to explain the answer correctly but I thought it was indicative of a wider issue: the lack of explicit vocabulary teaching in mathematics. Somebody once said that, “you shall know a word by the company it keeps”. While this may be true in fictional texts, these context clues aren’t always as evident in the world of maths. While normal vocabulary instruction often permits the use of analogy or synonym, the opposite is true in teaching the vocabulary of maths – where a singular definition is required and needs to be precise. Naturally, synonyms are still rife in maths (e.g. multiply, times), but the focus must be on teaching specific maths vocabulary, in order for children to be able to reason and problem solve freely without difficulty, especially as the style of language and vocabulary used in the non-fiction texts of the maths classroom are different in nature to the fiction texts children usually read.

 

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Making it Accessible for All

As should be our intent for all our teaching, we must make the learning accessible for all in the classroom: our use of language is how we achieve this. Typically, the language that children read is more difficult than the language we use in our interactions with them. Therefore, there are two effects I believe to be present in the classroom. Firstly, the Dunning-Kruger effect, where children think they understand, but are unable to accurately communicate their thoughts and reasoning. Secondly, we as teachers suffer from the ‘curse of knowledge’, because we are experts transferring knowledge to novices, and we naturally overestimate their background knowledge and starting points. A consistent approach based around keywords is needed to combat both of these effects successfully. After all, the underlying fabric of maths teaching is to develop cognitive growth and the ability to reason, not to simply stack pieces of knowledge on top of each other.

 

Are the children that Alex Quigley defines as ‘word poor’ ever able to achieve mastery or greater depth? Language is an inevitable obstacle for them. This can be in part attributed to the fact that too much academic vocabulary remains implicit (e.g. explain, estimate, identify). These words require explicit vocabulary instruction, like any other word being learnt in any other subject. The language of the classroom and our everyday language are intertwined and should be more distinctly separate. For example, we may say that ‘we take from here and put it there’ rather than ‘we transfer from the hundreds column into the tens column’. We cannot successfully construct and convey the meaning of mathematics if we rely so heavily on language from everyday usage. The use of keywords is a simple way to combat this, as it allows for a manageable consistency; understanding can then be mapped and revisited more easily and it makes retrieval far simpler. As a year 6 teacher, I always thought about this approach when considering the transition to secondary school. The use of keywords in specific topics is likely to be consistent between our lessons in primary and secondary, whereas the use of individual and personal colloquialisms will not necessarily pervade.

 

Implementation

For me, this approach was born out of necessity. Working memory was becoming worse with each new class and the SATs were becoming increasingly hard following the introduction of the new curriculum – there seemed to be an increased demand on retrieval ability and the old level 6 questions were now arguably integrated at the back of the reasoning papers. I wanted to create an approach that was easy for teachers to remember and easy for them to implement. I ended up with two simple questions that we wanted the children to ask themselves:

  • What does the question want us to find out? (i.e. how many litres left, a fraction of the shape etc)
  • What do we have to do in order to find that answer? (i.e. subtract from the total, change to equivalent fractions etc)

The idea of these two questions is to blur the traditional gap between the words on the page (questions) and the words in our head (thought process) and we can achieve this through explicit vocabulary instruction. Research shows that children who are exposed to explicit vocabulary teaching benefit 3 times more than those who are not. In that sense, reasoning and problem solving activities must be treated as their own genre of reading that requires comprehensions skills taught around it (see part one of the blog for more on that). In order to do so, we must place an increased focus on both academic (e.g. estimate, identify) and subject-specific (e.g. numerator, multiple) vocabulary, like we do so readily in other subjects.

Children from Year 2 up can be taught to write down their reasoning justifications. Within these, they should be encouraged to use keywords to demonstrate their knowledge of them and how they exist within their own mathematical concepts. This should be done frequently, with at least one opportunity for it every lesson (e.g. a starter or plenary, responding to a further learning question from your marking).

In assessing children’s knowledge of keywords, Cronbach’s (1942) dimensions of word knowledge is a useful guide. It is also very informative as to how we should plan and deliver our lessons:

  1. Generalisation – the ability to define a word
  2. Application – the ability to apply the word in appropriate situations
  3. Breadth – the ability to know and recall different meanings of the word
  4. Precision – the ability to recognise exactly in what situations the word does and does not apply
  5. Availability – the ability to use the word in our thinking and in our speech

Here is a basic example of a child in my class using the keywords they have been taught to confidently explain their reasoning (isosceles):

 

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We know isosceles has two sides the same length which means they are equally spaced out. And the difference in the y is (6,8) (32, 18) so we have to add another 10 to the y which is 28. The whole answer is (6, 28).

Children need to be provided with the opportunity to reason frequently and our lessons can allow this through both verbal (answering questions aloud, discussions etc) and written opportunities (writing down their reasoning, independently attempting problems etc). The former being more important lower down the school (EYFS, Year 1), as younger children’s listening and speaking skills are superior to their written and reading skills. But no matter how good the opportunities we provide are, the only way this can be truly successful is for us to have the ability to improvise and respond effectively to whatever children say to us. That sounds easier said than done, and it is, but I believe as long as we have a depth of subject knowledge and are well aware of the common misconceptions children have, then we can improvise fairly effectively.

When it comes to introducing and teaching the definitions of words, I have found it effective to change definitions regularly so that children weren’t reliant on memorising a single definition and had to constantly access prior knowledge each time a new definition was formulated – for example, this could include blacking out words in a definition or providing different accompany examples to ones they have previously seen. But definitions aren’t enough. We need rich instruction. Here are just a few examples of things we can do to provide this alongside our definitions:

  • use of pictorial representation
  • etymology
  • morphology
  • root words (vertere = to turn)
  • links to other words and concepts (vertex, inverse, convert and vertical – what is the link?)
  • examples and non-examples
  • keywords in lesson objectives (and discussing these LOs)
  • frequent reasoning opportunities that use keywords and encourage children to use the keywords

Further comments about the use of keywords:

  • We should employ a specific focus on visual representation alongside them, as often a child’s lack of vocabulary can hinder them in understanding new words being taught to them and it can make it hard for them to break down even the simplest of definitions. It is often these children that argue they ‘cannot do maths’ when simply they are unable to use mathematical language to explain their thoughts.
  • Discussion of keywords is of the utmost importance because we must create an atmosphere where all answers want to be heard – right or wrong. We cannot develop understanding and take children to the next level without knowing if they misunderstand first.
  • We must make the work accessible for the children who struggle more – do not give a year 6 child year 4 work. Give them year 6 work that is pitched at their level (more pictures, breakdown of keywords used, methods explicitly stated alongside keywords etc).
  • If the meaning of keywords is only ever presented by the teacher and not negotiated with the class, then children will never consciously construct meaning for themselves. Meaning is derived from the context within which the language is being used, and the dialogue between teacher and child is what frames this.

 

Here is a picture of a slide that I might typically show at the start of a lesson to my class. It includes a pictorial representation of the definition as an example, the root word and a part blacked out to challenge their thought on what the definition is:

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I’ll end this blog with Charles Darwin’s very apt description of mathematics – “A mathematician is a blind man in a dark room looking for a black cat which isn’t there”. Language is the light that can help to cure the blindness, illuminate the room and put the black cat right in your hands.

I plan on carrying on this series by writing about mastery in maths and what a perfect lesson might look like, with reference to what has been said above.

Contact me on Twitter if you have any questions – @MorgsEd

 

 

 

 

Categories
education

Ideas for engaging children and fostering their love of reading

Below I have bullet-pointed different ideas you can implement in class and school-wide to increase engagement with reading and therefore foster a love of reading too. They are in no particular order. They are ideas that can be implemented with little cost or effort (for the most part).

  • When reading in class together, children follow along with a ruler (idea taken from @solomon_teach)

This ensures all children stay on task and that they do not get distracted. If they lose pace, they can check with the person next to them and get back on track quicker.

  • Don’t use reading as a punishment

You are killing any pleasure or joy for reading if children are doing it as a punishment. Find an alternative for them to do.

  • Hold a book club at lunchtimes or before/after school

This can be done with any type of text. I’ve done it previously with a group of boys uninterested in reading with football match reports, annuals and magazines.

  • Put a sticker inside the front cover of the book for children to put their name in

This is great for instilling a sense of ownership for a class text. Children feel more responsible for the book and take greater care of it. Also much easier identifying who it belongs to! Can even go one step further and allow space on the sticker for the child to leave a review (idea taken from @MrCFoyle as pictured below). Imagine the influence that can have on a younger child, if they see one of the children they look up to has read and enjoyed the book!

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  • Let them see you read every day (other than in lessons)

This can easily be done at the start or end of the day. If your school sets early morning work as children come in, then sit there reading. I do this every day. Children come in quietly as they can see I’m reading. Once they finish their short task, they pick up a book and start reading also. They do not need to see you reading children’s fiction necessarily – at the moment, my class see me reading Closing the Vocabulary Gap by Alex Quigley. This could also be at the end of the day, where you read to the class as a whole.

  • Take an interest in what they are reading

Ask children questions about their book. Ask them about the author’s style, whether it is part of a series or not, who their favourite character is, what it is about etc. The list of possible questions is endless. Sometimes, if it is a task that children can get on with independently without much teacher input needed, I wander around the room picking up the book they have on their table and simply read a few pages of it. Occasionally, I  read the chapter they have just read and ask them what they think is going to happen next and discuss it with them, throwing in my own ideas.

  • Never discourage their choice in a book

We are all aware that David Walliams does not write the most challenging texts, but neither did Roald Dahl. The fact of the matter is that children enjoy reading them so we should let them read them. Instead, ensure your class texts have a suitable level of challenge. For your top readers, make them aware that David Walliams’ books are fine to read, but that they should also challenge themselves with other more difficult books (for which you can make suggestions!)

  • Class teacher swap

Once a half term or term, send teachers into a different classroom to read. We trialled this for world book week and the whole school loved it. Children have asked for it to happen again. It was great for us as teachers to be able to share our favourite books, especially outside of the key stage we teach in.

  • Reading in assembly

Ensure all teachers do this occasionally for the same reasons as above! Normally, we have 3 teachers that do all assemblies. For world book week, everybody read in assembly except those 3. Again, children loved it. We scanned in the books to show on the projector along with questions to get children guessing.

  • Communicate that giving up on a book is OK

Sometimes books simply aren’t interesting enough to us and we give up after a few chapters. We should allow children to do the same – both individually and as a class. In my NQT year, we read Cosmic as a class. The class hated it. That doesn’t mean it is a bad book; it just wasn’t suitable for that class. I explained that to them and we stopped reading it.

  • Let them have a say in what you read

Do a class world cup of books (idea taken from @MrBoothY6) to help you choose what book to read next. If they liked a book by an author, why not read another book from the same author? You could give children a choice of a few books, wrapped up with only a few words written on them to entice them. Have a class vote and decide what you are going to read next. Idea taken from @SadiePhillips pictured below:

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  • Have a variety of texts in your book corner

Plenty of affordable magazine and children’s newspaper subscriptions exist –  FirstNews, Amazing Magazine, Phoenix Magazine. You can buy classics 2nd hand for pennies online!

  • Let children get comfortable when they read

You may have beanbags, sofas and cushions in your book corner, but can that space fit more than 5 children? Let the children slump on the tables, put their feet up, lay their heads in their arms – whatever makes them comfortable. Do we sit upright on uncomfortably hard, plastic chairs when we read at home?

  • Children only read half a page out loud

When reading together as a class, let children only read half a page. This gives the less confident readers the confidence to read out loud but also means the less engaged have to pay attention, as you could ask them to read at any point. Reading half a page also ensures a lot more children are heard reading every day.

  • Dedicate time to reading

Every teacher’s timetable is full. It always is. But dedicating time to reading is of the utmost importance. That doesn’t necessarily mean a specific slot in your timetable (although I would strongly advise having this), but including it in other lessons. In PSHE, why not read a text with a bully in it to get the anti-bullying message across? In History, why not read through a historical source and base the lesson around that? Or a piece of fiction set around the same time and fact check it (The Boy in the Striped Pyjamas comes to mind)? If you have a spare 30 minutes after a school trip or assembly or after anything, why not read more of the class text?

  • Don’t always write from something you’ve read

Writing in literacy lessons doesn’t always have to be from a class book. It is important that children read a text for pleasure without having to do any real work around it. Question them yes, but don’t insist on a diary entry here and a newspaper report there. In my experience, I’ve found that reluctant readers are just as reluctant in doing the writing pieces based around the class book. By forcing them to constantly do writing based off a text, we are pushing them further away from enjoying reading. They will always associate reading with work. Instead, use more videos, pictures and experiences for your writing stimuli.

  • Watch and read author interviews about your class book

If your class text is very famous and popular, you’re likely to be able to find some videos about it on YouTube where the author is discussing it. Newsround occasionally have authors on and love4reading regularly have author Q&As in the blog part of their website (as pictured below):

 

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  • Contact authors and illustrators on Twitter

There are plenty of authors and illustrators on Twitter who are happy to respond to teachers. Come up with questions as a class that you want to ask. As you can see below, SF Said (Varjak Paw series) very kindly (and very quickly!) responded to questions I put forward for the Year 3 class at my school.

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  • Pre-teach vocabulary before you read together as a class

Define all the vocabulary in the upcoming chapter before you read it as a class. This helps those with weaker vocabulary understanding to be able to access the text too.

  • Invest in a text for every child

I understand this is an ideal situation, but when reading a class text, it works best when every child has their own copy. Speak to your SLT about funding this – we funded it this year through the money made from the book fair. If funds are tight, then you can always buy a copy between two for upper KS2 classes.

  • Build up reading stamina

If you have reluctant readers, start with shorter class texts and slowly build the stamina up. If the book is 300 pages long, it is going to take too long to read and they will lose interest. There are plenty of great children’s books that have short chapters and are sub 200 pages.

  • Test reading speed daily for 1 minute

With the less confident readers, test their reading speed every day for 1 minute using the same text for a week. This can help to improve their reading speed and therefore open up space in their working memory.

  • Watch the TV show/Film adaptation of the book

After we finish a book, we watch the film or TV adaptation of it together. Children are always excited to watch it and it creates great discussion about what was left out and kept in from the book. We recently read Skellig. The class loved the book but thought the film was terrible – this prompted great discussion about how scriptwriters/directors might interpret texts differently to how we do!

  • Sign up to a review website like Goodreads

You could write class reviews about a book and add books to your class wishlist. You can even find similar texts to read!

  • Dressing up for World Book Day (in pyjamas!)

A lot of families simply cannot afford a costume for their child – why not let children come in to school in their pyjamas? This is more inclusive and you can relate it to the fact that reading before bed time is a great activity. You could encourage children to bring in their slippers to wear in the classroom as well as their favourite teddy (so they have an audience to read to!)

  • Let children choose what text you read at the end of the day

When the children come into class in the morning, let them vote for which picture book they want you to read at the end of the day. One child = one vote! Simply use cubes, two books and two boxes. A wonderful idea shared by @_missgould on Twitter.

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  • Have a school vending machine where children can get books!

This incredible idea comes from @DaveShawICT. He bought the vending machine for just £40 online. Children who read at home x3 a week enter a raffle and then win a token which they can use in the machine. What a great idea! Some schools do a similar thing with old buses and turn them into a libraries.

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I will look to update this blog with other ideas that I hear of!

Contact me on Twitter if you have any great ones to share – @_mrmorgs

Categories
education

The Literacy of Numeracy Part 1: KS2 Maths SATs Language Analysis

The Literacy of Numeracy Blog Series Part 1: KS2 Maths SATs – A Language Analysis

I have uploaded this to TES for free so you can download it and share it however you please – https://www.tes.com/teaching-resource/ks2-maths-sats-language-analysis-12076440

I intend on writing a series of blogs focused on the ‘literacy of numeracy’ because I believe that mathematical vocabulary is of the utmost importance to a child becoming a fluent and confident mathematician. Part 1 focuses on how we can teach children to approach the language used in the reasoning papers in the KS2 SATs. Whether it be their ability to understand a teacher’s spoken input or a written word problem, a child will not be able to comprehend in depth without secure understanding of vocabulary (in the same way a child would not be able to comprehend a text in literacy if there were too many unfamiliar words). Let me say from the outset: this does not mean using RUCSAC or getting children to circle words, it means explicit vocabulary teaching so that a child can see a word and instantly recognise its meaning, the context within which it manifests itself and the calculation that is required.

Currently, the maths SATs are split into three tests: an arithmetic test and two individual reasoning papers that follow a problem solving focus. This explicit separation of the tests should encourage us as teachers to teach towards the different tests separately, despite the fact the skills required for both are often inextricably linked. Indeed, the arithmetic paper holds no vocabulary that children must decipher and is instead purely number-based. But, the reasoning papers place a great emphasis on assessing a child’s knowledge of specific mathematical terms. Often the less fluent mathematicians struggle with the last few questions in a reasoning paper. In my experience, those children have often had no idea what the question is asking them to do because of their lack of mathematical vocabulary. We must approach these tests as if they were a reading test; children must have a depth of vocabulary if they are going to be able to approach them confidently and successfully. This can prove problematic for a number of reasons, as I have enumerated below. A child could be tested on a variety of things:

  1. their knowledge of synonyms usually linked to one of the four calculation types (take instead of subtract, product instead of answer, altogether rather than add)
  2. their understanding of superlatives (biggest, largest, tallest, smallest)
  3. words that can have different meanings outside of a mathematical context (round, product, factor, prime)
  4. words other than superlatives that suggest comparison (between, more/less than, each, share, in order, sorting, put in the correct place)
  5. their understanding of the difference between the right answer and the wrong answer (best estimate, explain why Jack is not correct, write the correct symbol in each box, circle the improper fraction that is equivalent)
  6. Verbs implying mathematical meaning (remaining, left, combine, collect, spend)

NB: Any reference to 2015 in this blog is in reference to the Sample Papers released in 2015 so as not to confuse with the 2016 actual SATs papers.

To start, I will analyse the frequency of certain terms that I noticed appeared a lot. Naturally, if a child does not understand what a term means in one context, then their ability to understand it in another could be just as unlikely. Below is a frequency table to indicate how many times certain terms have been used from the 2015 sample papers onward. Obviously, there are other terms that have appeared more than once, but these were terms that I noticed were appearing enough to be significant to changing our classroom practice. I will now analyse each of these terms individually with implications for our class practice.

Frequently-occurring terms

Frequency

2015

2016 2017 2018

Total

Correct (sometimes not correct)

5

4 4 6

19

‘Equivalent’ or ‘equal’ or ‘equally’

3

4 2 4

13

‘Missing’  (as in digit, number etc)

2 4 7 5

18

‘Cost’ and ‘costs’ and ‘price’

10

10 5 6

31

‘Each’

10

12 11 13

46

‘Total’ and ‘altogether’ and ‘together’

4

7 5 3

19

‘How many’ and ‘how much’

11

4 14 11

40

 

Analysis of frequently-used terms

‘Correct’ – naturally, it may be obvious why a term like this has appeared so much. However, there are some interesting points to be made about how it is used and what this means for our classroom practice. It has been used for children to identify the right answer by using the wrong one:

  • 2015 Paper 2 Q6 – the watch is twelve minutes fast…what is the correct time?

Five times it has been used for children to demonstrate their reasoning for why somebody is correct or indeed incorrect:

  • 2015 Paper 2 Q18 – Dev says “The pie charts show that more girls than boys liked milk chocolate best”. Dev is correct. Explain how you know.
  • 2017 Paper 2 Q20 – Adam says, 0.25 is smaller than 2/5. Explain why he is correct.
  • 2017 Paper 3 Q12 – Adam says, I have four times as many balloons as Chen. Explain why Adam is correct.
  • 2018 Paper 2 Q9 – The cricket world cup has been held every four years since 1992. Adam is not correct. Explain how you know.
  • 2018 Paper 3 Q14 – Jack says the triangle is equilateral. Explain why Jack is not correct.

Implications for class practice: in each of the statements above, children were required to either prove or disprove a statement. Therefore, we need to teach children to approach these questions so that they can argue for or against the statement being made. If Adam is correct in saying 0.25 is smaller than 2/5, then children must understand they have to prove this statement to be true. If Adam is not correct in saying that the Cricket World Cup has been held every 4 years since 1992, then children must be aware that they are looking for mathematical evidence to disprove his statement (i.e. a gap between two of the World Cups post 1992 where there has been a difference of either less or more than 4 years). Sounds obvious, doesn’t it? But how well do all children in our class answer these questions so that their answers are right beyond scrutiny?

Another instance of how the term ‘correct’ has been used is in questions where children must put in missing values in order to make a calculation correct:

  • 2015 Paper 2 Q10 – write the two missing digits to make this long multiplication correct
  • 2015 Paper 3 Q11 – write the four missing digits to make this addition correct
  • 2016 Paper 2 Q3 – write the three missing digits to make this addition correct
  • 2017 Paper 2 Q3 – write the missing numbers to make this multiplication grid correct
  • 2017 Paper 3 Q1 – write the missing number to make this division correct
  • 2018 Paper 3 Q4 – write the three missing digits to make this addition correct

Implications for class practice: children must remember that they will not be given transfers (carrying over) in these questions (as in the first three Qs above) and that they must put them in themselves. If missing ‘digits’ are required, children must remember to only put 1 digit from 0-9 in the box. Each of these questions also relies on the child’s ability to apply the inverse calculation to check their answer. Whether it is any of the four calculations mentioned in questions above, each time the child could have used the inverse to check the answer was correct. As in, when using the inverse, did they get the same missing digit that they have put in to solve the question? Just as with the reasoning questions containing the term ‘correct’, children can use their ability to prove and disprove to guarantee they arrive at a right answer. In order for their assumed missing digits to make this calculation correct, children must revisit it from start to finish after putting their answers in to check it works – they should be taught to go through the usual motions of that specific method (i.e. start from the right in column addition etc).

The term ‘correct’ may also apply to putting in missing values or symbols to make a statement correct

  • 2016 Paper 2 Q7 – write the two missing values to make these equivalent fractions correct
  • 2018 Paper 2 Q10 – write the correct symbol in each box the make the statements correct

Implications for class practice: the same as above. Check after putting something into a box if it does indeed make the statement ‘correct’.

Lastly, ‘correct’ has often been used in questions where children are given a value or symbol and they must put it somewhere to make something else correct:

  • 2015 paper 3 Q13 – here are four fraction cards…use any three of the cards to make this correct <…<…<
  • 2016 Paper 2 Q1 – Ali puts these five numbers in their correct places on a number line…write the number closest to 500
  • 2016 Paper 2 Q5 – Write each number in its correct place on the diagram
  • 2018 Paper 2 Q10 – Write the correct symbol in each box to make the statements correct
  • 2018 Paper 2 Q16 – Tick the methods that are correct.

Implications for class practice: the overarching principle related to all of these correct questions? Children must be able to determine what is incorrect too. We can practise this daily by giving them conjecture to prove or disprove. This can be done with any topic! Sam believes…..Is he right? Why? Whenever possible, get children to write a sentence that includes a calculation in their answer to support it, as shown in these mark scheme answers from previous reasoning questions:

 

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‘Equally’ – There have been three instances of the term ‘equally’ so far – all linked to division:

  • 2015 Paper 2 Q16 – they share the cost equally
  • 2017 Paper 3 Q2 – they share the money equally
  • 2017 Paper 3 Q16 – Adam and Chen share the rest of the leaflets equally

Implications for class practice: Children need to be aware that when they see the term ‘equally’ that they are required to perform a division. They must understand that division is the splitting of a value into groups of equal size.

 

‘Equal’ – this has been used twice to demonstrate equal size in parts of shapes: shading in fractions of shapes and widths of rectangles. Perhaps more interestingly, it has been used the remaining three times to demonstrate an answer was needed, all to do with the recognition of place value:

  • 2015 paper 3 Q12 – two decimal numbers add together to equal 1
  • 2016 Paper 2 Q8 – circle two numbers that add together to equal 0.25
  • 2016 Paper 3 Q19 – circle two numbers that multiply together to equal 1 million

Implications for class practice: In decimal questions like this, it would be wise to advise children to put in placeholders to help them see the place value more clearly. As in this question below from 2016, if children put a placeholder next to 0.2 to make it 0.20 then the answer may have been more obvious and may have prevented careless errors like circling 0.23 and 0.2  – children must also be aware that equal can be used as a synonym for answer.

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‘Equivalent’ – naturally, all questions involving ‘equivalent’ required children to demonstrate their knowledge of equivalent fractions through their times tables knowledge. Twice this has included children representing equivalent fractions in shaded shapes:

  • 2015 Paper 2 Q4 – match each shape to its equivalent fraction
  • 2018 Paper 2 Q4 – these diagrams show three equivalent fraction…write the missing values

The other three times required children to demonstrate their knowledge of how fractions can be equivalent to each other (both proper and improper) and the equivalence between fractions, decimals and percentages:

  • 2016 Paper 2 Q7 – write the two missing values to make these equivalent fractions correct
  • 2018 Paper 2 Q7 – tick the two numbers that are equivalent to 1/4
  • 2018 Paper 2 Q13 – circle the improper fraction that is equivalent to 6 7/8

Implications for class practice: Children need to be confident in their understanding of equivalence between two forms. Whether that is between proper and improper fractions, or between fractions and decimals or percentages, the important knowledge required is times tables. If children are confident in their knowledge of times tables, the use of multiples and factors to find equivalence becomes a lot simpler. When asked to compare fractions with shapes, it is important to get children to write out the shaded part of shapes as fractions so that the equivalence becomes more obvious.

 

‘Missing’ – this term has come up with a variety of calculations attached – mostly attached to a division (5 times). More importantly, there were 10 instances when the term ‘missing’ should have indicated to children that they needed to use the inverse operation to solve.

  • 2015 Paper 3 Q2 – write the missing number in the boxes
  • 2015 Paper 3 Q14 – the number in a box is the product of the two numbers below it. Write the missing numbers
  • 2016 Paper 2 Q18 – write the missing number
  • 2016 Paper 3 Q1 – the numbers in this sequence increase by 14 each time. Write the missing numbers
  • 2017 Paper 2 Q3 – write the missing numbers to make this multiplication grid correct
  • 2017 Paper 2 Q5 – complete this table with missing numbers. One row has been done for you
  • 2017 Paper 3 Q1 – write the missing number to make this division correct
  • 2017 Paper 3 Q21 – the numbers in this sequence increase by the same amount each time write the missing numbers
  • 2017 Paper 3 Q24 – calculate the missing length on cuboid B
  • 2018 Paper 3 Q1 – write the missing numbers

Implications for class practice: children need to be taught to use inverse operations to be able to check their answers but also for the use of finding missing values. When the missing value is in the calculation and not the answer, like in 2016 Paper 2 Q16 and 2017 paper 3 Q1, children must learn to use the inverse to help them solve the calculation. NB: This is also an important skill for the arithmetic paper as missing values are appearing more frequently. This may also appear in context without the term ‘missing’ as shown below from 2015 Paper 3. The necessity for the inverse operation, however, is still present:

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‘Missing’ – this has also come up in another context a few times. Children are asked to write in the missing digits for a column subtraction, addition or multiplication.

  • 2015 Paper 2 Q10 – write the two missing digits to make this long multiplication correct
  • 2015 Paper 3 Q11 – write the four missing digits to make this addition correct
  • 2016 Paper 2 Q3 – write the three missing digits to make this addition correct
  • 2018 Paper 3 Q4 – write the three missing digits to make this addition correct

Implications for class practice: these questions to do not put the transfers in for the children. Children must be taught to treat these like they would a normal written calculation, going through step by step and putting in the transfers themselves. This should be obvious to children as it might ask the child what you add to 9 to make 1; if a child is aware of transfers, they will know they are adding 2 to 9 and it is actually making 11 with a transfer into the next place value column (have a look at the question example below). It is important children work through some missing digit calculations in class to help them for these questions but also to cement their understanding of how these methods work. Another thing children could be taught is to write out the calculation to the side afterwards and see if they get the same answer with the digits they have put in – or even use the inverse to check their answer!

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‘Cost’ – Naturally, this appears in the context of money every time. What is interesting with this term is that it often indicates a multi-step approach to solving the question. Even more intriguing is that one of those steps almost always included division. Below, I have listed all the ‘cost’ questions: next to each I have determined whether it needed a multi-step (MS) approach and followed this by the calculations needed to solve.

  • 2015 Paper 2 Q8 – Cost = number of cakes x 20p + 15p for the bag. How much will a bag of 12 cakes cost? (MS – multiplication and addition) NB: the 2nd part to this question required the inverse as it gave children a cost and they had to work backwards!
  • 2015 Paper 2 Q16 – Five children together buy one large pizza and three small pizzas. They share the cost equally. How much does each child pay? (MS – multiplication, addition and division)
  • 2015 Paper 2 Q19 – One gram of gold costs £32.94. What is the cost of half a kilogram of gold? – (MS if children realised it would be easier to do 2 steps rather than one by doing x32.94 x 1000 and then divide it by 2)
  • 2016 Paper 2 Q19 – Strawberries cost…Sugar costs…10 glass jars cost…Calculate the total cost to make 20 full jars of jam. (MS – multiplication and addition)
  • 2018 Paper 2 Q18 – Jacob went to four concerts. Three of his tickets cost £5 each. The other ticket cost £7. What was the mean cost of the tickets? (MS – addition and division)

Implications for class practice: children must be confident in their ability to divide decimal amounts using short division. This includes any ‘cost’ that is presented to them in whole pounds like in 2018 Paper 2 Q18, which required children to divide £22 by 4 to find the mean. Those not fluent in their division of decimals presented an answer of £5 r2 rather than the correct £5.50. Children must also be aware that money questions involve a multi-step approach more often than not (normally the 2 mark ones!)

‘Cost’ – multi-step cost questions also appeared regularly asking for the price of one item:

  • 2017 Paper 3 Q14 – 3 pineapples cost the same as 2 mangoes. One mango costs £1.35. How much does one pineapple cost? (MS – multiplication and division)
  • 2017 Paper 2 Q19 – Amina posts three large letters. She pays with a £20 note. Her change is £14.96. What is the cost of posting one letter? (MS – subtraction and division)
  • 2016 Paper 3 Q8 – Olivia buys three packets of nuts. She pays with a £2 coin. This is her change. What is the cost of one packet of nuts? (MS – subtraction and division)
  • 2016 Paper 2 Q9 – 6 pencils costs £1.68. 3 pencils and 1 rubber cost £1.09. What is the cost of 1 rubber? (MS – division and subtraction)
  • 2015 Paper 3 Q10 – A bag of 5 lemons costs £1. A bag of oranges costs £1.80. How much more does one orange cost than one lemon? (MS – division and subtraction)

Implications for class practice: children need to be taught that to find the cost for one individual item (among a group of the same item as seen above), that they must use division and divide by how many of the item there are. If the question is asking you to find the cost of a singular item from their change, you must subtract first before dividing. Children need to understand that change is a remaining amount after having paid, so it will always involve subtracting the cost from the money handed over – this is perhaps best explained with manipulatives and volunteers.

‘Each’ – searching for this term produced quite interesting results. ‘Each’ most likely puts an image of division or multiplication in our heads, but what do children think of when they hear it? In the majority of questions below, ‘each’ indicated that multiplication was the required calculation:

  • 2015 Paper 2 Q2 – 4 children each take 7 sheets
  • 2015 Paper 2 Q4 – A fraction of each shape is shaded. Match each shape to its equivalent fraction
  • 2015 Paper 2 Q7 – in the circles, write a multiple that belongs to each set
  • 2016 Paper 2 Q10 – each diagram below is divided into equal sections. Shade three-quarters of each diagram
  • 2016 Paper 3 Q11 – each box contains 6 bags of marbles. Each bag contains 45 marbles
  • 2017 Paper 2 Q11 – 20 minutes plus an extra 40 minutes for each kilogram
  • 2017 Paper 2 Q13 – Jack buys 12 single stickers for 99p each
  • 2017 Paper 2 Q18 – A cat sleeps for 12 hours each day…a koala sleeps for 18 hours each day
  • 2017 Paper 3 Q2 – they get £16 each. How many friends in the group?
  • 2017 Paper 3 Q16 – William and Ally take 450 leaflets each
  • 2018 Paper 2 Q8 – each large box has 48 chocolates. Each small box has 24 chocolates
  • 2018 Paper 2 Q18 – three of his tickets cost £5 each
  • 2018 Paper 3 Q20 – Ken collects 2, 3 or 4 eggs each day from his hens

Of course, if it routinely involves the use of multiplication, then there was the odd occasion it was used for the inverse operation of division:

  • 2017 Paper 2 Q19 – the postage costs the same for each letter…what is the cost of posting one letter?
  • 2018 Paper 3 Q7 – each box holds six eggs. The farmer has 980 eggs to pack. How many boxes can the farmer fill using 980 eggs?

And the odd occasion where both multiplication and division were required – unsurprisingly, these were both worth 2 marks for the 2 operations:

  • 2015 Paper 2 Q16 – Large pizzas cost £8.50 each. Small pizzas cost £6.75 each. Five children together buy one large pizza and three small pizzas. They share the cost equally. How much does each child pay?
  • 2018 Paper 3 Q13 – A box contains 2.6 kg of washing powder. Jack uses 65 grams of powder for each wash. How many washes did Jack do?

‘Each’ also indicated just as frequently that children were required to give more than one answer. These questions also included the use of multiplication occasionally. If so, I have written (M) in brackets next to the question. There was only one use of ‘each’ throughout all the papers that only needed one answer:

  • 2015 Paper 3 Q1 – write one number in each box (M)
  • 2015 Paper 3 Q4 – write the name of each month where they collected more than £50
  • 2015 Paper 3 Q6 – Use a card to complete each calculation (M)
  • 2016 Paper 2 Q5 – write each number in its correct place on the diagram
  • 2016 Paper 3 Q1 – the numbers in this sequence increase by 14 each time
  • 2016 Paper 3 Q4 – each shape stands for a number. Work out the value of each shape (M)
  • 2016 Paper 3 Q14 – complete each sentence using a number from the list below
  • 2017 Paper 2 Q12 – tick each shape that has the same number of faces and vertices
  • 2017 Paper 3 Q17 – in each box, circle the number that is greater
  • 2017 Paper 3 Q21 – the numbers in this sequence increase by the same amount each time
  • 2018 Paper 2 Q10 – write the correct symbol in each box to make the statements correct
  • 2018 Paper 2 Q21 – she gives each shape a value…calculate the value of each shape (M)
  • 2018 Paper 3 Q1 – the numbers in this sequence increase by the same amount each time (M if children realised it was the 7x table but addition was more obvious)
  • 2018 Paper 3 Q3 – write a digit in each box to show Layla’s number

Implications for classroom practice: children need to be taught that the term ‘each’ most likely indicates either multiplication or division, as it is splitting a value or values into groups. It is important to also show it to children in a sequence context (e.g. increases by 14 each time above) so that they understand how ‘each’ can be used in different questions.

 

‘Total’ – as expected, ‘total’ is used often to delineate an answer. More importantly, it almost always indicates the use of addition is needed at some point to solve the question:

  • 2016 Paper 2 Q4 – What is the total of the numbers of people living in Formby and in Telford? (addition)
  • 2016 Paper 2 Q19 – Calculate the total cost to make 20 jars full of jam. (multiply then addition)
  • 2017 Paper 3 Q9 – What is the total number of hours for English on this timetable? (addition)
  • 2017 Paper 3 Q18 – A square number and a prime number have a total of 22 (addition)
  • 2018 Paper 3 Q6 – The total number of lions and tigers is 10 (addition)

Only one question didn’t require any addition. Although multiplication is repeated addition!

  • 2016 Paper 3 Q11 – How many marbles does the shop order in total? (multiply)

Another point to make is that when ‘total’ was used alongside shape, as in the questions below, it meant children working backwards to find individual values:

  • 2016 Paper 3 Q4 – Each shape stands for a number. Total 100…total 96…Work out the value of each shape.
  • 2018 Paper 2 Q21 – Amina is making designs with two different shapes…total value is 147…total value is 111…calculate the value of each shape.

Implications for class practice: ‘total’ has appeared frequently in a 2 mark question format and once in a 3 mark question. Children must understand that, although commonly it indicates use of addition, it has been used for multiplication also. If ‘total’ appears alongside shape again, children must use the given ‘total’ to identify individual values that would then add up to make the ‘total’ provided.

 

‘Altogether’ – In each instance below, ‘altogether’ has been used to show a total, whether that be through combining two values or a single value:

  • 2015 Paper 3 Q4 – How much money did they collect in February and March altogether?
  • 2015 Paper 3 Q9 – What is the mass of these six coins altogether?
  • 2017 Paper 2 Q1 – Altogether, how many children don’t walk to school?
  • 2017 Paper 2 Q14 – Altogether, 12 seeds grew. (in the text before the question)
  • 2018 Paper 2 Q8 – How many chocolates did Ken buy altogether?
  • 2018 Paper 3 Q6 – There are 20 big cats in the zoo altogether. (in the text before the question)
  • 2018 Paper 3 Q20 – In the first 20 days, Ken collects 57 eggs altogether. (in the text before the question)

Implications for class practice: ‘altogether’ has popped up in both the text before the question and in the question itself. Children need a solid understanding of what ‘altogether’ means so that they can understand it in both contexts. In each of the questions where ‘altogether’ was in the text before the question, it was establishing a value children had to remember in order to solve the question (i.e. knowing the 20 big cats made the entire pie chart, knowing Amina had 12 seeds grown for her ratio and that Ken already had 57 eggs so the following amount he collected had to be added to the 57 he already had). In the examples where ‘altogether’ was in the actual question, each time children were combining two or more values to find an answer (money in February and March; mass of three 10p coins and three 5p coins; children who don’t walk to school from Year 2 and Year 6; large boxes and small boxes of chocolate). If children can identify this difference in usage, answering the questions in which ‘altogether’ appears should become a lot easier.

 

‘Together’ – Similar to ‘altogether’, this term has been used to show a combination of two values. Except for the first question below, each time it has explicitly told children the calculation needed (add or multiply). In the first question, children had to make the link that buying them together meant adding the costs together:

  • 2015 Paper 2 Q16 – Five children together buy one large pizza and three small pizzas
  • 2015 Paper 3 Q12 – Two decimal numbers add together to equal 1
  • 2016 Paper 2 Q8 – Circle two numbers that add together to equal 0.25
  • 2016 Paper 3 Q19 – Circle two numbers that multiply together to equal 1 million
  • 2017 Paper 3 Q3 – She multiplies them together

Implications for class practice: similar to that of ‘altogether’. The key point for children to remember with ‘together’ is that it means two values are being combined, whether that be adding or multiplying them is for the children to interpret in the individual context of the question.

 

‘How many’ – this is an interesting term that appeared 24 times across the 8 papers. There are a mixture of operations attached to them so I have put the operation needed in brackets after each question. There are five points to be made here. First, the vast majority of questions including the term ‘how many’ required children to perform multiplication or  division either to solve the entire question or for part of the question:

  • 2015 Paper 2 Q8 – How many cakes are in the bag? (subtraction then division)
  • 2015 Paper 2 Q20 – How many pages are there in Lara’s book? (division/multiplication – subtraction)
  • 2016 Paper 2 Q11 – How many days does the packet of oats last? (multiplication and division)
  • 2016 Paper 3 Q11 – How many marbles does the shop order in total? (multiplication)
  • 2017 Paper 2 Q11 – How many minutes will it take to cook a 3kg chicken? (multiplication)
  • 2017 Paper 2 Q14 – How many seeds did Amina plant? (multiplication)
  • 2017 Paper 2 Q16 – How many degrees does Layla turn through her dive? (multiplication)
  • 2017 Paper 3 Q2 – How many friends are in the group? (multiplication)
  • 2017 Paper 3 Q16 – How many leaflets does Adam get? (multiplication and division)
  • 2018 Paper 2 Q8 – How many chocolates did Ken buy altogether? (multiplication and addition)
  • 2018 Paper 2 Q15 – How many melons does the supermarket sell? (multiplication)
  • 2018 Paper 3 Q7a – How many boxes can the farmer fill using 980 eggs? (division)
  • 2018 Paper 3 Q12 – How many times larger is the United Kingdom? (multiplication)
  • 2018 Paper 3 Q13 – How many washes did Jack do? (multiplication and division)

The second point to make is that how many left questions always requires children to perform a subtraction at some point:

  • 2015 Paper 2 Q2 – How many sheets of paper are left in the packet? (multiplication – subtraction)
  • 2017 Paper 2 Q8 – How many toy cars were left in the toy shop at the end of June? (addition and subtraction)
  • 2018 Paper 3 Q7b – How many eggs will be left over? (subtraction)
  • 2018 Paper 3 Q11 – How many millilitres of water are left in Stefan’s bottle? (subtraction)
  • 2018 Paper 3 Q16 – How many pages are left for Amina to read? (division and subtraction)

Third, the use of ‘how many’ alongside a graph, timetable or chart meant children could get a mark for simple retrieval of information – they had to interpret the data in front of them. Twice this also required children to perform a calculation also:

  • 2016 Paper 3 Q9 – How many minutes does it take the 10:31 from Riverdale to reach Mott Haven? (retrieval)
  • 2017 Paper 2 Q1a – How many children don’t walk to school? (retrieval)
  • 2017 Paper 2 Q1b – How many more Year 6 children than Year 2 children walk to school? (retrieval and subtraction)
  • 2017 Paper 3 Q4 – How many degrees warmer was it at 3pm than at 3am? (retrieval and subtraction)

Lastly, ‘how many’ followed by a comparative or superlative term could mean performing a subtraction was necessary:

  • 2017 Paper 2 Q1b – How many more Year 6 children than Year 2 children walk to school? (retrieval and subtraction)
  • 2017 Paper 3 Q4 – How many degrees warmer was it at 3pm than at 3am? (retrieval and subtraction)
  • 2018 Paper 2 Q5 – How many degrees colder was Paris than Rome? (subtraction)

This question being the exception to the rule – however this question had the synonym ‘times’ which children should have realised meant to multiply:

  • 2018 Paper 3 Q12 – How many times larger is the United Kingdom? (multiplication)

Implications for class practice:  children need to be taught to find the operation required using the term ‘how many’. Usually, this indicates the use of multiplication or division but not always. Children must be able to identify that ‘how many left’ questions always require subtraction and that if ‘how many’ is linked to a chart, graph or timetable etc that they must use a ruler and a pencil to circle the correct information they are being asked to retrieve (to avoid them putting the wrong answer in the box). Finally, children need to be aware that ‘how many’ followed by a comparative (more) or superlative (warmer, colder, larger) is always asking them to compare two values: this may mean subtraction is required but not always. Either way, children should identify more easily through their understanding of that language that it means a comparison is needed.

 

‘How much’ – this term has appeared 16 times across the papers and every time in either a money or measurement context. Here are several examples of this:

  • 2015 Paper 2 Q8 – How much will a bag of 12 cakes cost? (money – multiplication and addition)
  • 2015 Paper 2 Q16 – How much does each child pay? (money – multiplication and division)
  • 2015 Paper 3 Q4 – How much money did they collect in February and March altogether? (money – addition)
  • 2015 Paper 3 Q18 – How much chocolate should he use? (measurement – division)
  • 2016 Paper 3 Q20 – How much money did Lara have to start with? (money – addition and multiplication)
  • 2017 Paper 3 Q10 – How much milk is left? (measurement – subtraction)
  • 2017 Paper 3 Q14 – How much does one pineapple cost? (money – multiplication and division)
  • 2018 Paper 3 Q8 – How much does Jack spend on his new bike? (money – multiplication and division)

Similar to ‘how many’, when ‘how much’ appears with a comparative or superlative term after it, it is indicated the use of subtraction is required:

  • 2015 Paper 3 Q10 – How much more does one orange cost than one lemon? (money – division and subtraction)
  • 2015 Paper 3 Q19 – How much larger is the area of the football pitch than the area of the rugby pitch? (measurement – multiplication and subtraction)
  • 2017 Paper 2 Q4 – How much higher is Mount Everest than the combined height of the other two mountains? (retrieval – measurement – subtraction)
  • 2017 Paper 2 Q13 – How much more does Jack pay than Ally? (money – subtraction)
  • 2017 Paper 3 Q5 – How much more money do they need to reach their target? (money – subtraction)

This was also true of the instances where the term ‘left’ appeared after ‘how much’:

  • 2017 Paper 3 Q10 – How much milk is left? (measurement – subtraction)
  • 2018 Paper 2 Q17 – How much orange juice is left over? (measurement – multiplication and subtraction)

Implications for class practice: the term ‘how much’ often presents itself in either a money or measurement context. It would be wise to introduce this into problems worked through as a class when learning these two topics. Children must also be confident in their ability to multiply or divide using decimal numbers, whether that be money (2015 Paper 2 Q16  – £6.75) or measurement (2018 Paper 2 Q17 – 0.225L). As was the case with ‘how many’, any instance of a comparative or superlative term following ‘how much’ indicates a comparison of values; with every instance so far showing a subtraction was needed. Just a side note on measurement questions while I remember. They always require children to convert between two units of measurement as they give two different units of measurement in each question (e.g. 2016 Paper 2 Q11 – 1.5kg and 50g / 2018 Paper 2 Q17 – 225ml and 8L). It is paramount children are confident in their knowledge of dividing and multiplying by 10, 100 and 1000. This is a necessary skill for the arithmetic paper too!

 

Comparative terms

These are terms that appear frequently in reasoning papers to indicate to children that comparison is needed at some point in the question for the answer to be found (e.g. Which cities have a population less than 50000 people? The child must find answers below 50000. They are comparing all the populations given with 50000 to see if they are lower or higher than that amount). Although this blog is only looking at language specifically, do not forget that comparison in mathematics can be shown through the use of symbols too with the use of inequality signs (< and >). These symbols have been used for 2 different questions (2015 Paper 3 Q13 and 2018 Paper 2 Q10) and both times children’s knowledge of them was assumed. Furthermore, the equals symbol (=) can be used for comparison to show that two statements or values are equivalent in value. Ensure children see this regularly!

 

Comparative term

Frequency
2015 2016 2017 2018

Total

‘Difference’ or ‘different’ 1 4 1 3

9

‘Than’

8 5 8 6

27

‘Less’ and ‘more’

3 4 5 2

14

 

‘Difference’ –  this term has always been used to show children that they need to perform a subtraction:

  • 2015 Paper 2 Q3 – What was the difference between the temperature in Oslo and the temperature in Berlin?
  • 2016 Paper 2 Q4 – What is the difference between the numbers of people living in Bedford and in Dover?
  • 2016 Paper 3 Q2 – What is the difference between the temperature on 1st January and the temperature on 8th January?

Implication for class practice: children need to understand that a difference is a comparison of a larger amount and a smaller amount through subtraction. Subtraction has the root word ‘tract’, meaning to ‘drag or pull from’- this can help children to remember to put the bigger number on top in the column method and take from it. Furthermore, notice how in each context above children had to interpret data from a table too. It would be wise to combine subtraction with data interpretation in your practice questions in class.

 

‘Different’ – has always been used for comparison. In each instance, children had to notice the value of one thing before finding the value of another:

  • 2016 Paper 3 Q10 – Write the letter of the cuboid that has a different volume from Emma’s cuboid
  • 2016 Paper 3 Q17 – Four of the triangles have the same area. Which triangle has a different area?
  • 2018 Paper 2 Q21 – Amina is making designs with two different shapes…calculate the value of each shape.

In the most recent example (Q21 last year), the word ‘different’ would have helped children to notice that not only were the shapes ‘different’, but so too were their values. By focusing on the term ‘different’, children should have been able to establish that the shapes were different by having one less hexagon and the values were different by a gap of 36. By seeing the relationship between the two, the question becomes a lot easier to solve.

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Implications for class practice: children must understand that if they see the term ‘different’, it means they must compare two things from the question (e.g. shapes, values) and see how they are similar or different. This could be a difference numerically or in size or shape.

‘Than’ – unsurprisingly, ‘than’ was always used to show comparison as shown below:

  • 2015 Paper 3 Q10 – How much more does one orange cost than one lemon?
  • 2015 Paper 3 Q19 – How much larger is the area of the football pitch than the area of the rugby pitch?
  • 2017 Paper 2 Q13 – How much more does Jack pay than Ally?
  • 2017 Paper 3 Q20 – A rectangular tile is 3 cm longer and 2 cm narrower than the square tile.
  • 2018 Paper 3 Q3 – 2 so that it has a higher value than any of the other digits
  • 2018 Paper 3 Q12 – The area of the United Kingdom is larger than the area of Jamaica.

However, there is an interesting point to be made. When ‘than’ appeared in a question context including data (temperatures, money raised on a graph, animals in a zoo, number of children walking to school), the children simply had to interpret the data to either prove a statement right:

  • 2015 Paper 2 Q18 – The pie charts show that more girls than boys liked milk chocolate best…Explain how you know.
  • 2015 Paper 3 Q4 – Write the name of each month where they collected more than £50
  • 2018 Paper 3 Q6 – Tick the statements that are right…there are more cheetahs than jaguars...there are more than 5 jaguars.

Or interpret the data to be able to perform the calculation that the question wanted. Only once children had identified the necessary data could they perform the necessary calculations needed below:

  • 2015 Paper 2 Q3 – Which city was 4 degrees warmer than Kiev?
  • 2016 Paper 3 Q2 – On 22nd January the temperature was 7 degrees lower than on 15th January. What was the temperature on 22nd January?
  • 2017 Paper 2 Q1 – How many more Year 6 children than Year 2 children walk to school?
  • 2017 Paper 2 Q4 – How much higher is Mount Everest than the combined height of the other two mountains?
  • 2017 Paper 3 Q4a – How many degrees warmer was it at 3pm than at 3am?
  • 2017 Paper 3 Q4b – At 6 pm the temperature was 4 degrees lower than at 3pm. What was the temperature at 6pm?
  • 2018 Paper 2 Q5a – At midnight, how many degrees colder was Paris than Rome?
  • 2018 Paper 2 Q5b – Which city was 6 degrees colder at midnight than at midday?

Another conclusion that can be made is to do with the term ‘than’ being used to demonstrate that a value is less or greater than. In these instances, children should understand that their answer falls within a certain range (i.e. less than 100 means their answer cannot be 100 or above).

  • 2015 Paper 2 Q1 –                  is 20 more than 237
  • 2015 Paper 3 Q16 – Lara chooses a number less than 100
  • 2016 Paper 2 Q14 – Write all the common multiples of 3 and 8 that are less than 50
  • 2016 Paper 2 Q16a – Write the number that is five less than ten million
  • 2016 Paper 2 Q16b – Write the number that is one hundred thousand less than six million
  • 2016 Paper 3 Q13 – Lara chooses a number less than 20
  • 2017 Paper 2 Q2 – Circle the number that is 10 times greater than nine hundred and seven.
  • 2017 Paper 2 Q20 – 25 is smaller than 2/5

Implications for classroom practice: it is important to remember that ‘than’ can also be indicated through use of the inequality signs, also known as greater than < and less than > symbols. Children need to be taught that ‘than’ is used for comparison and that they must compare two or more values when they see the term. When learning about data interpretation, it is important for children to attempt questions that ask them which values are less or greater than each other (i.e. which subject do children enjoy more than English in the graph?) Again, any questions including data interpretation should encourage children to use a pencil and a ruler to single out the data they are being asked about, rather than accidentally looking at the wrong column or wrong bar in a bar graph etc. Finally, children must be aware that if the question states an answer is less or more than a certain value (e.g. 2106 Paper 3 Q13 – Lara chooses a number less than 20), then any answer that outside of the given range is impossible (i.e. any answer in this case that is 20 or above).

 

‘Less’ – this term has only occurred a few times and in two different ways. First of all, to show that an answer was below a certain amount:

  • 2015 Paper 3 Q16 – Lara chooses a number less than 100
  • 2016 Paper 3 Q13 – Lara chooses a number less than 20
  • 2016 Paper 2 Q14 – Write all the common multiples of 3 and 8 that are less than 50

Secondly, to show an answer is below a certain amount but through a subtraction as the choice of operation:

  • 2016 Paper 2 Q16 – Write the number that is five less than ten million
  • 2016 Paper 2 Q16 – Write the number that is one hundred thousand less than six million.

Implications for class practice: note what has already been said about terms of comparison; children need to remember their answer must meet the requirements given but also that less can indicate use of subtraction. I like to teach children this through the suffix ‘less’ which means without (e.g. heartless, careless). This helps them to remember a subtraction is needed, because now a number is going to be without a value it originally had.

 

‘More’ –  this has been used in questions that have a predetermined value from which the children have to base their answer. In each of the cases below, their given answer just had to satisfy the value given by being higher than it:

  • 2018 Paper 2 Q6 – There are more cheetahs than jaguars… There are more than 5 jaguars (tick if correct)
  • 2015 Paper 2 Q18 – “The pie charts show that more girls than boys liked milk chocolate best.” Explain how you know.
  • 2015 Paper 3 Q4 – Write the name of each month where they collected more than £50

Three times it has been used to demonstrate addition was required:

  • 2015 Paper 2 Q1 – 180 is 20 more than 160… is 20 more than 237
  • 2017 Paper 2 Q5 – 1,000 more
  • 2017 Paper 2 Q8 – 8,728 more toy cars were delivered

Perhaps the most important point to note is that when the term ‘more’ was coupled with either ‘how much’ or ‘how many’, it always indicated a subtraction was needed in order to find a difference between two values:

  • 2015 Paper 3 Q10 – How much more does one orange cost than one lemon?
  • 2017 Paper 2 Q1 – How many more Year 6 children than Year 2 children walk to school?
  • 2017 Paper 2 Q13 – How much more does Jack pay than Ally?
  • 2017 Paper 3 Q5 – How much more money do they need to reach their target?

Implications for class practice: the significant point for classroom practice here is that ‘more’ does not always indicate an addition like most children might assume. In every instance above, ‘more’ indicates one value being higher than another – this is the key thing to teach children. However, this could mean adding ‘more’ to make a value bigger or finding how much or many ‘more’ a value is and therefore using subtraction. Children need to see the term in both contexts to fully understand its use. Children must understand that ‘how many more’ or ‘how much more’ is trying to find a difference in values, by seeing which value is bigger and by how much; in every case, a subtraction is needed.

 

 

Superlative Terms

Superlative term

Frequency

2015 2016 2017 2018 Total

Warmer

1 1

2

Shortest

1

1

Largest

1

1

Nearest

3 2 4

9

Larger

1 1

2

Closest

1 1

Furthest

1

1

Lowest 2

2

Lower

1 1 2
Smallest 2 2 2

6

Earliest

1 1
Greater 2

2

Higher

1 2 3

Smaller

1

1

Latest 1

1

Longer

1

1

Narrower

1

1

Colder

2

2

Greatest

2

2

Total by year

7 10 15

9

 

What is immediately clear from the table above is that, although specific superlatives may not appear every year, the use of superlatives is prevalent throughout every set of reasoning papers each year (with an average of 10 being used yearly). In fact, although specific ones aren’t recurring often, it shows that the test makers are varying their use of superlatives as you can see with ‘colder’ and ‘greatest’, which both appeared for the first time last year. It is important that children are exposed to as wide a variety of superlatives as possible to avoid any confusion in understanding the question. In both instances that ‘greatest’ appeared last year, both questions were worth 2 marks and the term ‘greatest’ was used in the actual question:

  • 2018 Paper 3 Q15 – What is the greatest number of colours she can have in the design?
  • 2018 Paper 3 Q20 – What is the greatest number of eggs Ken can collect in March?

If children didn’t understand the term, then they lost out on 4 marks instantly. I remember the egg question being particularly tricky in my class even among the greater depth children!

As each superlative doesn’t appear too frequently I will group all the implications for class practice below in bullet point form:

  • ‘warmer’ and ‘colder’ and ‘lower’ – in each instance of their use, the context of the question was temperature. Perhaps less obviously, children needed to perform a subtraction to find a difference between two values. This can be tricky because it can include both positive and negative values so maybe the use of numberline should be encouraged.
  • ‘nearest’ – this has only ever appeared in a rounding context. Make sure children are confident in their ability to round well because in the three years it has popped up, it has been worth 2 marks each time. Ensure children hear the term ‘nearest’ regularly when teaching rounding.
  • ‘closest’ and ‘furthest’ – each of these has only appeared once, however it is important children understand this is testing their understanding of place value if it does pop up again. Children could label the values given with their place value columns or simply draw a place value grid and put all the numbers into it.
  • ‘larger’ – both times this has been seen the use of multiplication was needed
  • ‘smallest’ – each of the times this has appeared, children had to order values from ‘smallest’ to largest. Twice this has been decimals with different amounts of decimal places and once as fractions with different denominators. Children must understand that ‘smallest’ means finding the value that is the least biggest in comparison to the others, whatever representation the value is in.
  • ‘earliest’ and ‘latest’ – these have obviously only appeared in the context of time – make sure children hear them in your lessons on time!

Although not always true, superlatives ending in ‘est’ normally indicate children need to simply identify a value and could be solved mentally without any written method or long working out:

  • 2015 Paper 2 Q9a – Measure the shortest side accurately, in centimetres (sides already provided simply had to identify and measure)
  • 2015 Paper 2 Q9b – Measure the largest angle (angles already provided simply had to identify and measure)
  • 2016 Paper 2 Q1a – Write the number closest to 500 (numbers already provided)
  • 2016 Paper 2 Q1b – Write the number furthest from 500 (numbers already provided)
  • 2016 Paper 2Q2 – Put these houses in order of price starting with the lowest (prices already provided)
  • 2016 Paper 3 Q9 – What is the earliest time he can reach Tremont on the bus? (times already provided)
  • 2017 Paper 3 Q6 – Circle the latest time that William can leave London. (times already provided)

This is also true of the rounding questions as long as children are confident in their place value:

  • 2015 Paper 2 Q14 – Round 124,531 to the nearest 10,000…1,000…100
  • 2016 Paper 3 Q15 – Complete this table by rounding numbers to the nearest hundred
  • 2017 Paper 2 Q10 – Round 84,516 to the nearest..100…1,000
  • 2017 Paper 3 Q19 – He rounds his answer to the nearest 10

These two questions were the exception where children did need to perform calculations without being able to solve mentally. Both from last year and both with the use of the same term:

  • 2018 Paper 3 Q15 – What is the greatest number of colours she can have in the design?
  • 2018 Paper 3 Q20 – What is the greatest number of eggs Ken can collect in March?

Implications for class practice: it would be wise to inform children that an ‘est’ superlative often involves little working out and simply identifying a value provided. As long as children are aware of this, it may make these questions easier for them. We can teach children to search for this in context and therefore help them to approach these questions in a simpler manner.

Conversely, superlatives ending in ‘er’ normally (not always) indicated that working out was necessary in order to find the answer for those less fluent. Of course, if children were fluent and confident in their knowledge, some of these could be done mentally. I have indicated the questions that could be done mentally by putting (M) after each of those questions. However, I have ultimately decided to keep them all in the same list as a lot of children who aren’t fluent would have used working out to solve these questions:

  • 2015 Paper 2 Q3 – Which city was 4 degrees warmer than Kiev? (M)
  • 2015 Paper 3 Q19 – How much larger is the area of the football pitch than the area of the rugby pitch?
  • 2016 Paper 3 Q2 – On 22nd January the temperature was 7 degrees lower than on 15th January. What was the temperature on 22nd January? (M)
  • 2017 Paper 2 Q2 – Circle the number that is 10 times greater than nine hundred and seven. (M)
  • 2017 Paper 2 Q4 – How much higher is Mount Everest than the combined height of the other two mountains?
  • 2017 Paper 2 Q20 – Adam says 0.25 is smaller than 2/5. Explain why he is correct.
  • 2017 Paper 3 Q4a – How many degrees warmer was it at 3pm than at 3am? (M)
  • 2017 Paper 3 Q4b – At 6 pm the temperature was 4 degrees lower than at 3 pm. What was the temperature at 6 pm? (M)
  • 2017 Paper 3 Q17 – In each box, circle the number that is greater. (M)
  • 2017 Paper 3 Q20 – A square tile measures 20 cm by 20 cm. A rectangular tile is 3 cm longer and 2 cm narrower than the square tile. What is the difference in area between the two tiles?
  • 2018 Paper 2 Q5a – At midnight, how many degrees colder was Paris than Rome? (M)
  • 2018 Paper 2 Q5b – Which city was 6 degrees colder at midnight than at midday? (M)
  • 2018 Paper 2 Q12 – How many times larger is the United Kingdom? (M)
  • 2018 Paper 3 Q3 – 2 so that it has a higher value than any of the other digits…the remaining two digits so that 7 has the higher value. (M)

 

Synonyms

There is no ‘implications for class practice’ section here as the implications for our teaching practice is obvious: children need to be exposed to as many synonyms for the four different operations as possible because the reasoning tests always utilise a wide variety of synonyms. We must remember as teachers that some terms can be used for more than one operation and not take it for granted that children know this as well as we do.

This table only includes language that is explicitly clear in demonstrating the operation. It therefore avoids questions like this that are not explicitly clear for children in which operations they should use:

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NB: Where possible, this table only includes synonyms and not phrases or whole sentences that may also indicate operation. Emboldened words are terms that could be used for more than one operation or require two operations for solving (i.e. mean).

Operation

Synonyms and short phrases used in the 2015, 2016, 2017 and 2018 tests to indicate these operations

Addition

More than, twelve minutes fast, mean, altogether, add, together, total, increase, adds, combined, more, plus, add, and, sum, after

Subtraction

How many left, difference, how much more, subtracts, how much larger, difference between, takes, less than, lower than, change, how many more, how much higher, how many warmer, pours out, how many colder, decrease, different, before

Multiplication

Multiple, long multiplication, product, total, area, multiply, times, each, for every, ratio of, multiplies, factors, together, three-quarters, times larger

Division

 

 

Halfway, share equally, mean, half, divides, each, divided into equal sections, factors, multiple, how much is one or how much does one cost, one-quarter, three-quarters, scale, times larger

It is also worth mentioning that synonyms for ‘answer’ are often utilised (product, result, equal, remaining, left, left over). Children should also be aware of these.

 

The importance of past papers in teaching vocabulary and comprehension

No doubt using past papers is something all Year 6 teachers do. Rightfully so, it allows us to assess our classes and get a rough idea of what topics they struggle with and even the scores they might get on the day. But perhaps lesser known – and this is something that really benefitted my class last year during revision sessions – is that questions are often recreated in very similar (or exactly the same) contexts year on year. For this reason, it is very important that children see past questions regularly. Below, I have put questions from previous years that were similar to each other:

2015 Paper 2 Q4 and 2018 Paper 2 Q4

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2016 Paper 2 Q11 and 2018 Paper 3 Q13

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2018 Paper 3 Q1 and 2016 Paper 3 Q1 and 2017 Paper 3 Q21

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2015 Paper 3 Q21 and 2016 Paper 3 Q13

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2015 Paper 2 Q8 and 2018 Paper 3 Q15 and 2017 Paper 2 Q11

note that the 2nd part to all of these questions gave children an answer (cost, price and cooking time) with which they had to work backwards from using the inverse.

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2015 Paper 2 Q20 and 2018 Paper 3 Q16

 

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2017 Paper 3 Q1 and 2016 Paper 2 Q18

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2018 Paper 3 Q18 and 2017 Paper 2 Q23

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2016 Paper 3 Q11 and 2018 Paper 2 Q15

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Implications for class practice: children must regularly see past questions when attempting a certain topic to understand the contexts in which it often comes up. This will help to build their understanding of the tests and help them to comprehend them better. To help with this, you can find a lot of the old questions put into short early morning work/starter activities here thanks to @MrCJ248 on Twitter – https://twitter.com/MrCJ248/status/1098346220328767490

NB: There are many more examples of these but this blogpost is long enough as it is! I plan on putting all questions of a similar context into a PowerPoint for teachers to use as a revision session but I haven’t made it yet. It will able available for free on my TES profile – morganell.

 

To conclude, I will leave you with something that helped me a huge amount last year. @thirdspacetweet compiled together a list of all the maths topics in order of the frequency that they have appeared in recent years. This should help to define your revision sessions more clearly. The picture below was made before the 2018 SATs (can be found here – https://thirdspacelearning.com/blog/how-third-space-learning-teach-maths-2018/). If they do this again for the current SATs, I will update the blog:

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Thanks for reading. As usual, if you have any questions contact me on Twitter here  @_mrmorgs