# Before, then, now – modelling additive reasoning

One of the parts of the NCETM’s Calculation Guidance for Primary Schools is the ‘Before, Then, Now’ structure for contextualising maths problems for additive reasoning.  This is a very useful structure as by using it, children could develop deep understanding of mathematical problems, fluency of number and also language patterns and comprehension.

The first stage is to model telling the story.  We cannot take for granted that children, particularly vulnerable children in Key Stage 1, will know or can read the words ‘before’, ‘then’ and ‘now’.  Some work needs to be done to explain that this is the order in which events happened.  Using a toy bus, or failing that, an appropriate picture of a bus, we would talk through each part of the structure, moving the bus from left to right and modelling the story with small figures:

Before, there were four people on the bus. Then, three people got on the bus. Now there are seven people on the bus.

The child could then retell the story themselves, manipulating the people and the bus to show what is happening.  For the first few attempts, the child should get used to the structure but before long we should insist on them using full, accurate sentences, including the correct tense, when they are telling the story.

I have chosen a ten frame to represent the windows on the bus, which enables plenty of opportunity to talk about each stage of the problem in greater depth and to practise manipulating numbers.  For example, in the ‘Before’ stage, there were four people on the bus: if the child could manage it, it would be interesting to talk about the number of seats on the bus altogether and the number of empty seats.  By doing so, they are practising thinking about number facts to ten and building their fluency with recall of those facts.   The task could easily be adapted to use a five frame or a twenty frame.

The next stage could be to tell children a story and while they are listening, they model what is happening with the people and the bus.  After each stage, or once we have modelled the whole story, they could retell it themselves.  Of course, the adult would only tell the ‘Before’ and the ‘Then’ parts of the story as the child should be expected to finish the story having solved the problem.

When the child is more fluent with the language and they understand the structure of the problems, we can show them how it looks abstractly.  For the ‘Before’ part, the child would only record a number – how many on the bus.  For the ‘Then’ part, we would need to show the child how to record not only the number of people that got on or off the bus but the appropriate sign too – if three people got on they would write +3 and if two people got off they would write -2.  Finally, for the ‘Now’ part, they would need not only the number of people on the bus but the ‘is equal to’ sign before the number.  Cue lots of practise telling and listening to stories whilst modelling it and writing the calculation.

A more subtle level of abstraction might be to repeat the same problems but rather than the child modelling them using the bus and people, they could use another manipulative such as multi-link cubes or Numicon.  They could also draw a picture of each stage – multiple representations of the same problem provide the opportunity for deeper conceptual understanding.

The scaffolding that the structure and the multiple representations provide allows for some deeper thinking too.  In the problems described so far, the unknown has always been the ‘Now’ stage or the whole (as opposed to one of the parts). It is fairly straight forward to make the ‘Then’ stage unknown with a story like this:

Before, there were ten people were on the bus.

Then, some people got off the bus.

Now, seven people are on the bus.

This could be modelled by the teacher, who asks the child to look away at the ‘Then’ stage.  Starting with ten people on the bus and using a ten frame is a deliberate scaffold – deducing how many people got off the bus is a matter of looking at how many ‘empty seats’ are represented by the empty boxes on the ten frame in the ‘Now’ stage.  A progression is to not use a full bus in the ‘Before’ stage – it is another level of difficulty to keep that number in mind and calculate how many got on or off the bus.

Another progression is to make the ‘Before’ stage unknown.  The child will need a different strategy to those already explained in order to solve this kind of problem.  Then story would have to be started with: ‘Before, there were some people on the bus.’  Of course, the adult would not show the child this with the bus and toy people, but they would show the completed ‘Then’ stage: ‘Then, four people got on the bus.’  Finally, the adult would model moving the bus to the ‘Now’ stage and completing the story: ‘Now, there are eleven people on the bus.’  The child would have to keep in mind that four people had got on and now there are eleven, before working backwards.  They would have to be shown that if four had got on, then working out how the story started would mean four people getting off the bus.  They could be shown to run the story in reverse, ending up with seven people on the bus in the ‘Before’ stage.

This task has the potential to take children from a poor understanding of number facts, calculating and knowledge of problem structures to a much deeper understanding.  The familiar context can be used as a scaffold to build fluency and think hard about complex problems with varied unknowns.

# Suspense: a Talk for Writing unit (Phase 3: Invention)

This post follows on from the first and second in this series which talk through a successful Talk for Writing unit on suspense writing.

After innovating twice, children were well immersed in the text type, they had fully internalised the Writers’ Toolkit and were ready to invent their own suspenseful story. After watching a film clip from Harry Potter, we discussed and boxed up the main events and discussed the key moments which contributed to the intended effect – making the audience think something bad was going to happen.

Just like during innovation, we then worked with the children to create save-boxes (banks of ideas) which could be used in their writing. We chose different elements of the Writers’ Toolkit on which to focus and again, we focused on the different sentence structures we had learned during this and previous units. The result was banks of sentences in both children’s books and on the working wall, ready to be transferred into planning:

A key moment after this was the transferral of these ideas and construction of new ones into a plan for writing. We placed sentences from save it boxes into the relevant section of the boxed up plan and then deliberately crafted new sentences using the structures on which we had been focusing, always with the intended effect in mind. What children were left with were detailed plans, which prepared them very well for writing.

We modelled writing, making explicit use of the plan and the toolkit to encourage the same kind of ‘writerly’ behaviour in the children. Support staff worked with small groups of children crafting one sentence at a time, making deliberate use of their plan throughout.

As with innovation lessons, each writing lesson during the invention phase would involve children either self or peer assessing their work. This might involve children choosing a successful part of their writing and a bit to improve which they would then independently or collaboratively edit. This develops their metacognitive skills. It could also involve children placing post-it notes onto their writing to identify which parts of the toolkit they have used, which provides the teacher with an assessment of a child’s understanding and internalisation of the toolkit:

Final pieces of writing from children of all abilities were successful: children had made conscious, deliberate use of the Writers’ Toolkits in order to achieve an indended effect. With the effect in mind, children had learned how to craft effective and highly accurate sentences through their familiarisation with and practice of various sentence types and structures.

# Suspense: a Talk for Writing unit (Phase 2: Innovation)

This post follows on from the first in this three-part series which talks through a successful Talk for Writing unit.

Following on from the imitation work of reading as a reader activities and then reading as a writer during toolkit construction (all explained here), we then began to create save-it boxes – banks of sentences which would be drawn upon in innovation sessions. After teachers had picked specific parts of the toolkit on which to focus, children looked through other texts and ‘magpied’, innovated and invented their own sentences which could be used during writing. Save it boxes generated collaboratively by the teacher and the class were then displayed on the working wall whilst children also had ideas saved in their literacy books, ready for writing.

After working on Writers’ Toolkits and save-it boxes as well as all of the sentence work that had been completed throughout the unit thus far, children were well prepared to innovate. During this unit, we used post-it notes to plan our innovated writing. Simply placing post-it notes with our new ideas over the original text map ensured sentence structures were maintained – the key to innovation. Children then created their own ‘post-it note plan’ ready for writing their version of the story. Teachers ensured that the different sentence types on which we had focused were explicitly modelled and picked from our banks of ideas on the working wall.

Each day during the innovation and invention phases we included short bursts of grammar or sentence work, usually as a ‘Jumpstart’ activity (a quick starter to a lesson). In the main, these were based on elements of their writing from the previous day that we had identified as needing focused work.

Having planned their writing in detail using the scaffold of the original text map, children then wrote a number of paragraphs per day. In this suspense unit, children wrote two lots of three paragraphs. During shared writing sessions, teachers made explicit reference to the Writers’ toolkit, modelling the writer’s thought processes by talking aloud the intention behind the various language choices made. We modelled from both the long and short versions of the focus text.

During every writing session, children related their analysis of their own work back to the toolkit – to the intended effect on the reader. In the image above, the class have been encouraged to self assess by identifying a particularly successful section of their story and to then explain how they wanted to make the reader feel at this point in their writing. As with shared writing, this meta-cognitive process requires clear modelling and explanation by the teacher. However, after their immersion in the suspense genre, their reading as a writer work and their subsequent internalisation of the Writers’ Toolkit, children were well prepared to relate their analysis of their own writing back to the intended effect. As well as highlighting a successful section of their story, children were also encouraged to identify a sentence or two which they felt could be made even better. After careful modelling of this process by the teacher, children would then have a second attempt at this part of their writing.

To give the children the opportunity to write an entire text in a single lesson we then planned a second innovation, changing the setting of the story. Writing was planned in the same way using post-it notes. Again, teachers and children made intentional use of the different sentence types we had worked on both in this unit and previous ones. Therefore, although children were sticking to the general structure of the text, they dropped in extra sentences where appropriate and effective. In their second innovation, many children were confident enough to move further away from the focus text, which in turn prepared them well for inventing.

# Suspense: a Talk for Writing unit (Phase 1: imitation)

Our recent Talk for Writing unit on suspense in Year 6 has been the most successful of the year. A number of factors have contributed to this: children internalised the text well and this happened early in the unit; we focused heavily on sentence accuracy, ensuring that there was daily opportunity for children to practise writing accurately; children internalised and were able to recall the writers’ toolkit and therefore it was used well by all in the writing phases. This series of three posts will be an overview of what our Talk for Writing unit looked like, including snapshots from planning, our working walls and children’s work.

To begin with, we assessed the children’s writing within the genre of suspense. Children were given a context and we had a class discussion about content so that they were well prepared to write. Image, video and sound were used to create an atmosphere and immerse them in the genre. This writing provided us with an overview of children’s individual writing needs within the genre whilst also highlighting any general needs across the class and year group which could then be planned for.

We prepared children for reading the focus text by exploring the context of the story and by introducing and discussing any unfamiliar vocabulary that they would encounter. Image and video are used regularly at this stage to ensure children have a grasp of difficult concepts. This vocabulary was then used to create a set of speed words for the unit. Speed words were practised daily as part of the warm up for each imitation lesson. Children working on a shorter version of the text had a differentiated version of the speed words, based on the vocabulary in their story. After daily practice, it  means that decoding and word comprehension are not a barrier to reading, even for children working below expectations.

Once children had a sound understanding of the vocabulary they would encounter, the differentiated versions of the focus text were then introduced. Most of the class worked on the main version, whilst children whose reading and writing levels are below expectation and those who struggle to write accurately, worked on the shortened and simplified version of the text. We then introduced the text map as soon as possible. Children experienced daily rehearsal of sentences and paragraphs from the text. The class teacher’s role here is key – we modelled reading behaviours such as re-reading and ‘going over bits’ in order to perfect retelling. We focused on the intended effect of our suspense text throughout our daily retelling – in this case ‘to make the reader think something bad will happen’. Knowing the intended effect at this stage helped both teachers and children when we came to creating writers’ toolkits later in the imitation phase.

Children who would find the writing need of this too challenging completed a colour coding alternative.

To follow the work on adverbials, children completed sentence work which focused on innovating adverbials in a sentence. This not only prepared them for the next phase of innovation but also provided us with valuable time to work on sentence accuracy. Following the structure of sentences from the focus text by innovating early in the unit contributed towards their internalisation of a variety of grammatical structures.

Children then completed AF2 questions about the focus text. Those working beyond age-related expectations worked on a mixture of AF2 and AF3 questions. Having completed the bridging activity on adverbials, children were well prepared for success in this activity.

As children are immersed in oral rehearsal of the text, work on ‘talking the text’ is valuable. In this unit of work, children annotated with codes we generated together on how best to read the text aloud. Like our daily retelling of the text,  focusing on the intended effect in this activity – making the reader think something bad is going to happen – was crucial. This is what a child’s work from this activity looked like:

Alongside retelling, once children had a good grasp of the text, they would also ‘quick write’ it. This involved them writing 1-2 paragraphs accurately per day using the picture prompts from the text map. Children working on the shortened version of the text would ‘quick write’ in this structure:

Here , sentences have been structured so that they are seperate and therefore easier to follow.

During the imitation phase, quick activities focusing on grammar were dropped into lessons. These were usually based on children’s needs which either came to light during their pre-assessment or during their daily sentence work. Activities are either jumpstarts (quick activities at the beginning of lessons) or dedicated lessons focusing on new grammatical concepts.

After picking out and selecting various sentence types for our focus text, part of the imitation phase involved deconstructing, discussing, modelling and practising these, in preparation for writing. Children and teachers created save-it boxes of sentences which could then be drawn upon during innovation and invention.

As well as introducing new sentence types, we also dropped in short activities which revised old sentence types so that children were building a repertoire of tools for their writing. Revision of previously covered sentence structures were all within the context of the new unit and the new story.

Towards the end of the imitation phase, we collaboratively created writers’ toolkits. Teachers modelled identifying and analysing how the writers of suspense texts had achieved the intended effect. Children then worked in small groups to continue this with other extracts of text. This activity ensures that children are exposed to and talk about what good writers do and how to achieve similar effects in their writing. For children who wouldn’t be able to access this work and who still need to work on accuracy in writing, we devised activities such as this:

Here, children were exposed to the language of the toolkit that the rest of the class were constructing, but were also taking part in activities which met their needs as writers.

For the next couple of days and throughout writing phases, we practised recalling the toolkit because in order for children to write well, they need to be able to remember how to achieve certain effects. We blanked out the main wording of the toolkit, leaving only a short prompt. It was then covered with a sentence which shows the effect in action. For example ‘describe a sudden noise’ is covered with ‘A door banged’.  Daily practice recalling the toolkit ensured that it was internalised, just like the focus text.

The next two posts will describe the key moments from the innovation and invention phases.

# Growing Great Teachers – Which research group?

Penn Wood – Growing Great Teachers

Key Principles:

• Working on the ‘bright spots’ – building on existing strengths.
• The Pareto principle – 20% of teaching strategies yield 80% of the value.
• Deliberate practice – Focused, intentional practice supported by high quality feedback.
• Action research – experimenting with strategies to find out what works.
• Better never stops. All teachers need to improve, not because we are not good enough, but because we can be even better.

Teachers will come ready to think of a teaching sequence which has gone well.  Through discussion with year colleagues, using the coaching questions below, teachers will identify aspects of the teaching sequence that were good or better.  This will also provide some practice for teachers when coaching later in the action research cycle.

• Tell me about a time when behaviour for learning was great?  What did you do that supported them to do this?
• Tell me about a time when you could immediately respond to what a child said or their work with quality feedback?
• Tell me about the outcomes for different groups of children?  How did you meet their needs?
• Tell me about a time when you saw a real improvement in reading fluency /understanding?

These questions will help teachers to focus in on an area of strength that will then become the focus of a term’s CPD.   Teachers will develop on an aspect of good or better teaching in research groups, led by senior or middle leaders.  The groups are as follows:

• What are the most effective strategies for improving fluency and understanding?
• How can we create a positive climate for learning to read for pleasure and widely across the curriculum?

Modelling and explanations

• What are the most effective ways of authoritatively imparting knowledge?
• In what ways can our explanations develop children’s resilience and thirst for knowledge?

Meeting the needs of different groups of children

• How can we ensure that teaching strategies, support and intervention match individual needs accurately?
• How can we differentiate tasks so that more children attain the higher levels in national assessments?

Feedback and questioning

• How can we anticipate misconceptions, check for understanding and intervene to make a notable impact on learning?
• How can we use feedback and questioning to ensure that more pupils attain higher levels in national assessments?

EYFS

• What are the most effective strategies to secure the early acquisition of language?
• How do we increase the proportion of children meeting and exceeding national expectations?

Within these research groups, teachers will further discuss what worked well for them in their successful teaching sequences, with the aim of creating a toolkit for possible strategies.  This will be supported by short videos (available by logging into the school account), blog posts and books.

http://www.learningpt.org/pdfs/literacy/components.pdf

Modelling and explanations

http://www.education-consumers.org/CT_111811.pdf

http://wp.me/p3UXMS-2I

http://www.aft.org/pdfs/americaneducator/spring2012/Rosenshine.pdf

Meeting the needs of different groups of children

http://www.learningspy.co.uk/featured/deliberately-difficult-focussing-on-learning-rather-than-progress/

http://bit.ly/1iiwu1B

http://bjorklab.psych.ucla.edu/research.html

http://ow.ly/o8Anb

http://learninglab.psych.purdue.edu/publications/

Feedback and questioning

http://wp.me/p2uRcx-VJ

www.huntingenglish.com/2013/12/26/disciplined-discussion-easy-abc

wp.me/p43kJZ-4U

http://reflectionsofmyteaching.blogspot.co.uk/2013/10/can-i-be-that-little-bit-better.html?m=1

http://reflectionsofmyteaching.blogspot.co.uk/2013/11/can-i-be-that-little-bit-better-at.html?m=1

http://youtu.be/ag38OBjuMrQ

http://wp.me/p2uRcx-V9

http://feedbackasateachingstrategy.weebly.com/

http://www.learningspy.co.uk/featured/reducing-feedback-might-increase-learning/

http://meridianvale.wordpress.com/2014/01/25/what-if-feedback-wasnt-all-it-was-cracked-up-to-be/

The final part of the session will be for each teacher to settle on one strategy that they will experiment with in their classrooms over the next few weeks.  The research leader will ensure that each teacher in their working group leaves with a plan in place.

# Hassan’s internal number line

Hassan is a wonderful boy. He’s polite and has a great group of friends. But Hassan started Year 6 working significantly below his peers. His school history is of sustained underachievement with very little progress. He did not have an internalised number line with which to think about numbers, to the point where he could not reliably say which number out of two was biggest.

This post is an account of an intervention carried out by Amy Coyne. It is one of the most successful interventions I have seen and has resulted in vast improvements in Hassan’s ability to think about numbers. Here’s what happened:

These number cards were prepared: 53, 67, 54, 35, 76, 45

Two of the cards were presented to Hassan and, with the use of Numicon or dienes blocks or arrow cards, Amy modelled explaining which was the bigger number. Hassan picked this up fairly quickly, but to help him to retain this procedural knowledge, it was repeated little and often over the course of a few days.

A third card was added and Amy again modelled, using appropriate concrete equipment, how to order them. When he could consistently order three numbers, a further card was added until he could deal with ordering six cards. Using those six cards, Amy made seven different sequences:

53, 67, 54, 35, 76, 45

67, 35, 76, 54, 53, 45

76, 35, 67, 53, 45, 54

45, 53, 35, 76, 67, 54

54, 45, 76, 53, 35, 67

53, 54, 35, 76, 45, 67

45, 76, 54, 67, 53, 35

The cards were presented to Hassan in these orders, one set at a time, and Hassan was asked to order them. At first, with this slight change in task, he would place the numbers in fairly random order for each sequence. After completing each sequence, Amy ordered them with him, using concrete models when necessary. When Hassan was asked to read out the order, if he was incorrect, he often didn’t notice. However, when the sequence was read aloud to him, he could hear the error and would correct it.

This was repeated over several days for short periods of time. Sometimes this was in maths lessons and at other times it was not. The seven different sequences would be laid out in a straight line and he would pull the cards out and order them. As the days progressed, he could very quickly pick out card 35 and put it furthest left and also card 76 and put that furthest right – the smallest and greatest numbers. However the other cards in between were never placed consistently in order.

After a week of doing these sequences once or twice a day, he could order every sequence in the correct order. A new set of numbers was introduced: 12, 27, 45, 54, 59, 72

Hassan was very good at picking out the biggest and smallest numbers. The numbers in between were still more difficult for him. Amy modelled looking at the tens and units columns and this prompted him to order them correctly.

The cards were then mixed up, with more numbers being added one at a time to see if he could order them again. His confidence was growing and once he was happy with the order he had put them in, he was asked to read the numbers out to see if he could spot any errors himself. He often did and corrected them without Amy needing to intervene.

After a few days starting with six or more cards, he could reliably order them correctly every time. Next, some three digit numbers were added to make twelve cards overall. He was quickly able to deal with this progression. He was then given cards with multiples of ten to see if he could slot them into the correct places. He struggled a little with cards 10 and 20 but he placed multiples of ten more than twenty in the right places every time. If he needed to, he referred to a tape measure to check.

Once he was confident in ordering these numbers and could do it correctly every time, two numbers from the sequence were chosen. He was asked: ‘What are the smallest and biggest numbers that could go in the gap?’ This proved to be quite tricky for him and he would often say the number before the smallest card. This took him around a minute to process each time, and many answers were guesses. Amy modelled looking at a tape measure to find the two numbers (53 & 59). He then could see, using the tape, which numbers would come after 53 and before 59, and therefore the biggest and smallest that could go in the gap.

From here, Hassan is now working on adding and subtracting one digit numbers and multiples of ten from numbers in his card sets, with increasing success. Soon, the goal is that he can add and subtract any two digit number from any other.

Why this intervention worked, when other have failed

Spacing and interleaving

Regular short sessions, interspersed with other topics in maths lessons, with varied lengths of time in between those sessions has given Hassan time to internalise patterns of numbers and procedural knowledge for dealing with them.

Building knowledge of the number system

The more he practised recalling facts about numbers and procedures for how to think about them, the more successful he became. Each nugget of internalised knowledge enabled further memory development until he had internalised the basic number system.

Deliberate practice to mastery

The moment that Hassan understood and was successful did not signal the end of the intervention. It will continue until he never makes a mistake, even when tasks are altered.