A reminder of key mathematical pedagogy, mastery and Blooms Taxonomy.

The concrete-pictorial-abstract approach,clarifies that there are three steps necessary for our children to develop a deep understanding of a concept (Mastery). Reinforcement is achieved by going back and forth between these representations.

 Concrete representation - modelling a concept with concrete apparatus, at this stage children should be doing using manipulatives to support.
Pictorial representation - learning is moved on and key concepts are now represented in other ways such as drawing pictures/ diagrams. At this stage the children are 'seeing' using representations of objects to model problems.
Abstract representation  - maths is now modelled in a symbolic way using numbers, symbols.


https://makingeducationfun.wordpress.com/2012/04/29/concrete-representational-abstract-cra/

http://www.aveson.org/asl/singapore-math-faq


The concrete-pictorial-abstract (CPA) approach is at the heart of the Singapore Maths program in which the bar method is used to provide a powerful pictorial representation. Please watch the video for good introduction. 



A good interactive resource to support your teaching of the bar method are the 'Thinking Block' tools as shown below in which there is a great modelling tool. 

In a the most recent edition of "Teach Primary" Beth Budden, a teaching and assessment lead at John Ball Primary School in Lewisham, write an interesting article about how she uses Blooms Taxonomy to design the learning journey in stages and build a mastery approach.  In summary:

Stage 1: Remembering (fluency) - Retrieve an recall the required information. At this stage Beth talks about being aware of what the children already understand and where the gaps lie. It is about the children gaining confidence and growing efficiency with numbers.

Stage 2: Understanding - The children need to understand 'how to' and may need lots of practice.
Stage 3: Applying (problem solving) - The child needs to apply what they have learnt in context e.g real life maths. 
Stage 4: Analysing (reasoning)- at this stage the children need to be able to deconstruct what they have learnt through reasoning. The children should be able to write or verbalise their learning.
Stage 5: Evaluating - this stage is all about the children being able to make judgements about a process, understanding how they or a peer made an error and how to correct it.
Stage 6: Creating - creating their own questions/ problems, writing their own success criteria. The children should also be able to coach another children through the steps to complete the problem. 







Marking, feedback and next steps!

Schools are constantly reviewing and re reviewing marking policies, all schools mark differently, but many of us still spend hours of school time and our own time trying to keep up with marking and feedback demands. Sometimes we are our own worse animals finding it hard to let go of the the more detailed traditional marking. Here are a few tips that might help to cut your marking time down.

  • Experience has taught me that marking needs a lot of forethought and planning. Look at your timetable a week before and plan in which lessons you will complete detailed marking and which lessons can use another form of marking such as the suggestions below.
  • Use labels to save time. Many people have been posting on social media recently about using label machines but another alternative is to use label printer paper as shown in the picture below. Before or after the lesson you can type up your star/ wishes/ next steps onto a label, simply print off and stick into books.  You could use the same label template for all children or differentiate a number of ways to suit the abilities in your class. I normally put my next steps in red so it is obvious to the children.

  • Hand write stars, personal to the child, but use a bank of next steps preprinted on labels. These could be preprinted with titles such as reasoning, fluency and problem solving.
  • Photographic evidence – if the children are completing group work, practical activities, rough notes on whiteboards etc, you don’t have to always stick in their work. Take a photo and add to a word document with date, LO and at the bottom the next steps. To save time you can include three level of next steps, colour coordinated and children can choose the level of difficulty they would like to challenge themselves with.
  • QR code next steps – if you have ipads in class why not print of QR codes for next steps linking to a quiz or game for the children to complete building on previous learning.

  • Peer and self-assessment sheets which can be acknowledged by the teacher with a some tick.
  • Mark with the children, data has proven 1:1 feedback as being the most effective form of marking and feedback. If you can sit with a child and mark, simply mark with something along the lines of '1:1 feedback', 'chat time' or 'verbal feedback'.

  • Stampers – get a good set of stampers which can be used on ‘those days’ when you have 90+ books to mark.

  •  Supply teachers – get yourself a supply teacher stamp for those times you come back and find your books unmarked despite the pleading letter to mark work. We should not be spending even more time marking someone else’s work on top of the existing workload. 
  • Sometimes just a tick and an initial is all a piece of work needs, don't over complicate it :-).
  • Use TAs - if your wonderful TA has been working with a group why not ask them to mark the their books. Six books can save you a good chunk of time.

Maths in PE - Free resource

Working in a school that has Maths as a development area means we are continually thinking of new ways of using Maths in other curriculum areas to help our children embed/ revisit some of their core skills. This weekend I have been thinking about Maths in PE and have created some Maths themed PE warm up cards. Please feel free to download and use.


What are you doing for Sport Relief? - 18th - 20th March

Twinkl has teamed up with Sport Relief to produce a range of resources to support schools, including assemblies, videos and classroom activity packs.


Maths Mastery - White Rose Maths Hub Spring Assessments now out!


Assessment in Science/ Science Week

In the unknown world of 'Life without levels' we are all working very hard to find the best way of assessing our subjects. At my school we use School Pupil Tracker which is a good formative method of assessment but we also need to remember regular summative assessments too. The Primary Science Teaching Trust has produced a number of documents to support this and have also produced a very user friendly tool to audit current assessment provision, known as the TAPs Pyramid Model. 

 http://www.pstt.org.uk/SiteDocuments/doc/taps/taps-pyramid-final.pdf
http://www.pstt.org.uk/Files/Project_Files/ASAEPS%20teachers%20FULL1.pdf



Don't forget National Science and Engineering week

Why not take the opportunity to plan some observational experiments and link into Blooms Taxonomy questioning matrix.

https://sciencebob.com/try-some-lava-in-a-cup/
Real life science link - oil tanker spillage 
Describe what you can see.
Use your knowledge of states of matter to describe what you see.
Which liquid is heavier/ more dense? explain how you know.
Predict what will happen when.....
What do you know that might help us to understand what is happening...?
What would happen if we ...?
Explain what is happening
Discuss what you think might be happening.


Free Science Week activity packs


What exactly is mastery learning?

If I reflect on this year we all seem to have spent a large amount of it trying to understand what actually is meant by various terms and the difference between them; mastery, depth of learning, greater depth, maths mastery, secure, working towards, assessment without levels...... unsurprisingly, individuals and companies have all had a go at unpicking these terms with varying degrees of success and accuracy. It is not surprising there is confusion across schools. 

The 'Final report of the Commission on Assessment without Levels', published in September, defines mastery and clarifies it is not about working above and beyond but simply 'mastering' a skill or having a secure knowledge of a concept. Could we then argue that if a child is 'secure' with a skill they have therefore 'mastered' it?

Reasoning- the Welsh are doing it well!

Reasoning provides children with an opportunity for deeper understanding through communication. Individually or in groups, children learn to explain and defend their ideas and analyze the reasoning of others. Historically we have done this very well in English thorough "talk for writing" and thankfully we are now getting much better at providing "talk for maths" opportunities into our own lessons. Teachers are able to assess the children's knowledge through asking “good questions,” and deliver lessons to ensure each child understands how to use math skills through thinking, talking, and doing combined with elements of fluency, reasoning and problem solving. 
Having spent the last year or so such searching for the best reasoning resources to support my practice the Welsh have often offered the best. One of the most useful resources I have come across is their 'Reasoning in the Classroom' resource. Click the relevant year group and then support materials.



The Welsh Government has also written a document called 'Audit of existing resources to support the development of mathematical reasoning in the GCSE classroom' which although aimed at GCSE children has lots of resources to support primary school children and HA Y5/ 6. There is obvious NRICH and Kangaroo Maths but there are also lots of other useful links e.g tarcia support, I particularly like this 'Convince Me' tarcia. 


Although this resource is not Welsh I can't possibly write a reasoning blog without mentioning the Mastery Overview documents created by Maths Hub which are invaluable. I can't recommend this resource highly enough if you haven't already used it. 

Reasoning in EYFS

The following EYFS resources are well worth a look through.

NRICH

Early Years Maths
An old document but still has a lot of relevant advice

NCTM - EYFS magazine
Evidencing reasoning in books

If you are in a school where evidence in books is highly valued you have two options for capturing evidence of reasoning, the most obvious being taking a photo of the activity and annotating the picture with details of the task. Another nice way though is to add a QR code linking to a video of the reasoning activity. 
The easiest QR code creator I have come across is QRme.

On this site you can create a QR code linking to any web based document or a written note. I use Google Drive to save videos and then use the 'share' facility to capture the URL of the evidence. I can then simply copy it into the QR code creator website to create my unique QR code linking to the video. Once created I can copy the image and stick into Maths books for evidence. Anyone with a QR code reader can then watch the videos.



Michel Tidd explains how he believes Primary Progress will be calculated from 2016


Micheal Tidd (@MichaelT1979) has produced some interesting videos recently which can be found on his YouTube channel.


https://michaelt1979.wordpress.com/

Developing reasoning skills in class

I recently attended an amazing course led by @carpenter_rob, an Executive Headteacher of a number of South East London schools, who has a history of turning schools around, very quickly! The course was about mastery across the curriculum but as with all great courses I came away with a whole lot more. 

 One of the most important messages I took away was about 'teaching' reasoning. Within class I have been working really hard on the  'reasoning' agenda, particularly in maths, expecting the children to 'explain the maths'. What I have been focusing on though is the maths when this actually the children have not had much instruction on how to structure their reasons.

 @carpenter_rob schools have produced these postcards for pupils, parents and teachers to help support the development of reasoning skills and next step questions. They are printed out on double sided postcards. The children use the speaking frames when answering questions, next steps and completing reasoning tasks in books.

 Parent reasoning cards
Learning reflection cards
KS2 reflection/ reasoning cards
Maths reasoning cards

I have since found this great resource on Twinkl. To make them part of all maths lessons, I put all of the cards onto one sheet of A4 and have stuck them into the front cover of our maths books to support next step answers and reasoning tasks.

Other resources I love are:

Tower Hamlets - Progression in language structures
Speaking and listening frames - source unknown
More - source unknown

Rob's blog http://www.robcarpenter.org.uk/ is well worth reading, there are many useful documents in the 'documents' section.

Sometimes the oldest are the best - Diamond 9

Over the last term have have been using the diamond nine concept more and more in all areas of school life. 

 "A Diamond Nine Diagram helps to prioritise and categorise key factors. The most important factors are placed towards the top of the "diamond 9 ". The least important factors are placed towards the bottom. Factors of equal importance are placed in the same row. Each factor can be colour coded for further sophistication." 
Class tools provide an interactive version of the template, allowing you to change the colour of the boxes and move each around as much as you like. There are also many templates available on-line. 

Potential uses

  • Whole school priorities - at my school we have been using the diamond 9 to communicate our school priorities with all of our staff. We prioritised our RAP priorities and have displayed them around the school for all to see in a simple and usable format. 
  • Literacy - persuasive arguments. I have recently been discussing deforestation with my children and looking at the reasons for and against. As part of their planning for a persuasive letter they have been using a diamond 9 format to prioritise their arguments which will then be used to inform the structure of paragraphs. 
  • Maths - Equivalents

Diamond 9 fractions and decimals sort

  •  Justifying reasons

  • Prioritising individual targets, class gap filling objectives

Mindfulness in schools

I have recently brought my newfound love of mindfulness into the classroom. I have quite an 'active' Y4 class and they have benefited greatly from completing short meditations after break times. Initially they were quite sceptical and some even resistant but they now ask for meditation time and can talk about how it helps them to focus, clear their mind and get ready for learning. I use videos on YouTube to lead meditations and particularly like the following (most are aimed at adults but the children enjoy them all the same).
Kate Beddow is a great person to follow and she has produced some great lessons based on the Pixar film Inside Out.

There are also some other lovely ideas on this Pinterest page linking the film with mindfulness

At my school we use an amazing resource called 'Focused for Learning', written by Kelly Green in the Gloucestershire Healthy Living and Learning team. It is well worth investigating if you would like to introduce mindfulness into your class.

Facebook is another create source of inspiration and here are a couple of pages I follow providing some useful information.



Michael Rosen - Don't mention the children


Nicky Morgan's message on Primary Assessments


In need of a 3D printer? This site allows you to find local printers for you to use.

I came across this website at the BETT show recently, I was looking for a 3D printer last year to use and I wish I had known about this site. It allows you to put in your location and it will provide you with the location of your nearest printer. Make sure you click "distance" when the search results come up as it defaults to "best match".

Developing a growth mindset culture in your classroom

How many times a day do you hear "I can't do it" "I'm not very good at this"? I believe that when I manage to change the mindsets of even the greatest self doubters the enjoyment of learning and the progress of my class will speak for itself. Over the last term this has been one of my biggest focuses and I have seen a change of attitude from a large number of class but there is still away to go. As normal I have drawn upon the tools that already exist and thought I would share them with you......
Twinkl has a great selection of resources

There are some great examples of displays on the search engines - this is one of my favourites (source unknown)


 Class Dojo is an amazing behaviour management tool but also as a means to encouraging a growth mindset culture. Within the site you have the option to edit the positive points to reflect growth mindset characteristics such as persistence and self belief. More recently they have also added some amazing growth mindset videos.

This is a great display to illustrate that making mistakes is not only part of learning it is an essential part of the learning process, problem solving and mastering skills.
Sarah Hagan (@mathequalslove)

Story settings

There are many great blogs about using different forms of visual stimuli to engage children with story settings and generally writing. Some of most impressive blogs are the Literacy Shed, Tim Rylands and Mr P, all of which promote the use of video games, apps, art, and 360 panorama's to inspire writing. One of my favourite sites to use is actually a visual tour of a wedding venue near me. The combination of audio and interactiveness makes it very effective to use in class. 

Mr P recently shared this site with an amazing range of 360 click and drag videos.
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