Socially Distanced Diagnostic Assessments

I hope everyone has had a restful summer and is looking forward to getting back to school and the kids.

Whenever we are looking to teach, it is useful to get a gauge of what our pupils can already do and where they have gaps, misconceptions or content they may not have been taught yet (or forgotten).  To help with this I’ve amended the format for the diagnostic assessments so these can be delivered at a ‘social distance’ without the need for the problem cards and other materials.  With such a gap between when pupils were last ‘formally’ in school, it may be more useful than ever to get an accurate gauge of where they are to help them move forward.

All the content is on the new Shared Drive which you can request access to here.  Additional content will be added over time.  Please use your Highland Google login details when requesting access (e.g. firstname.lastname@millburnacademy.org.uk)

If you haven’t already accessed the diagnostic assessment online training, we strongly suggest you do this before using the assessments so you have a better understanding about the rationale behind them, how to implement them and how to interpret the information.  A guide to this training can be found here.

Direct links to the diagnostic assessments that have been put into a socially distanced format can be found here:

The multiplication and division assessment and the fractions assessment have not been included as we are in the process of updating them.

 

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Summer Reading Ideas

I have just finished writing a long list of book suggestions for someone on Facebook so I thought I might as well post it on here in case anyone else is looking for some teaching related summer reading ideas!

The list comes from quite a wide range of places and includes different approaches to teaching maths and some that are linked to commercial products.  I’m not advocating any single approach or commercial product but do feel that reading widely and comparing different viewpoints and research is really useful to get the full picture.

I’ve written a very brief blurb about each to give you a bit more information.  There are also a couple that aren’t directly related to maths but are still very relevant.

In no particular order, here they are:

Mathematics in the Early Years:

Big Ideas of Early Mathematics (Erikson Institute)

  • It’s easy to read with a mix of practical ideas and thoery.
  • This has some really nice ideas for the Early Years with content also relevant for P2.  It gives a good sense of some of the important foundations for maths (that are perhaps sometimes overlooked or rushed) and may help people understand why some struggle later on and how enriching Early Years maths education may help prevent future maths difficulties.
  • It is written by the people behind the Erikson Institute Early Math Collaborative which is a brilliant website.

Learning and Teaching Early Math: The Learning Trajectories Approach (Clements and Sarama)

  • It’s easy to read.  The book is structured so the first section in each chapter is theory based.  This is followed by a table which has a progression in learning from 1-2 years old to 8 years old (this varies a little depending on the area).  The progression also has some activity suggestions.
  • It is written by the people behind the Learning Trajectories website.
  • It’s quite a lot more expensive than some of the other books on this list (but is very useful).

Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education

  • It’s easy to read with a mix of practical ideas and theory.
  • It is linked to a series of other books all related to Cognitively Guided Instruction (see below) but this one is specifically related to the Early Years.
  • If you’re not already on it, there is a Cognitively Guided Instruction In Scotland Facebook page as well.  This was set up by Dr. Lio Moscardini.

Teaching and Learning Early Number (Edited by Ian Thompson)

  • It’s easy to read but it’s probably more theory based than some of the others mentioned above.  It does have practical applications though.
  • It’s good for getting you to think about the ideas that are important for teaching maths.
  • It’s a little different from the others as each chapter is written by a different author.

Teaching Mathematics 3 – 5 (Sue Gifford)

  • It’s easy to read but it’s probably more theory based than some of the others mentioned above.  It does have practical applications though.
  • It’s good for getting you to think about the ideas that are important for teaching maths.
  • Sue Gifford writes a lot of the articles on the NRICH website related to Early Years Education.

General Primary Maths:

Children’s Mathematics: Cognitively Guided Instruction

  • Also part of the Cognitively Guided Instruction series (CGI) series of books.
  • It is good if you want a general overview of CGI at a range of levels.
  • It’s easy to read with lots of practical ideas for application.

Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School

  • Also by some of the authors of the other CGI books.
  • Excellent if you want you, as a practitioner, want to understand more about the properties of behind some of the operations and therefore support your pupil’s to better understand this.
  • It will support you to get your pupils thinking more mathematically and go far beyond just answering pages of sums and having these marked as either right or wrong.
  • It’s probably a bit heavier going than some of the others but still easy to read (in my opinion) and very worthwhile!

Choral Counting and Counting Collections: Transforming the PreK – 5 Maths Classroom

  • Also from the authors behind other CGI books.
  • It’s great if you want to get a bit more detail about how to introduce Choral Counting and Counting Collections into your classroom.
  • It’s easy to read with lots of practical applications.

Books related to fractions:

Developing Fractions Knowledge (Hackenberg, Norton and Wright)

  • This is quite heavy going but it is very interesting and very useful and will probably give you a lot more in depth knowledge about how to teach fractions effectively.
  • It’s written by some of the same people behind other Maths Recovery books (but in my opinion is not quite as easy to read as the others).
  • As well as the theory side of things, it also includes questions for assessment purposes and activities – these could be easily implemented into your classroom.

Extending Children’s Mathematics: Fractions and Decimals – Innovations in Cognitively Guided Instruction

  • As the title suggests, this is another in the CGI series and is written by some of the same authors as the other books but specifically related to fractions and decimals.
  • It’s easy to read and has lots of practical applications as well as understanding the progression in learning.
  • It complements the Maths Recovery book above well.

Books related to Mastery:

Mastery, although it’s been around for a very long time seems to have made a bit of a resurgence recently.  From some of the things that I’ve seen/read on the internet, a lot of people appear to be reading the headlines and taking quite a superficial look at it.  Here are a few books if you want to find out more.

Teaching for Mastery (Mark McCourt)

  • It’s easy to read and gives an overview of the background behind mastery.
  • There is content related to both primary and secondary.
  • Mark McCourt is behind LaSalle Education and Complete Maths.

Mastery Learning: Theory and Practice (Edited by James Block)

Implementing Mastery Learning (Thomas Guskey)

Although I’ve read work by both authors/editors above, I haven’t read these books but someone has kindly let me borrow them.  I’ll update this with more information when I’ve read them.

Books related to Mindset:

I feel that people often take the headlines of some of the information shared on Mindset and as a result it’s often implemented in quite a superficial way.  (In a similar way to the comments I had about Mastery.)

Mindset (Carol Dweck):

  • Not specifically related to maths but a very interesting read about ‘mindset’ in general.

The Elephant in the Classroom and Mathematical Mindsets (Jo Boaler):

  • Both explore ‘mindset’ specifically from a maths perspective.
  • They are both easy to read and provide an interesting read.
  • Both, but more so the Mathematical Mindsets book has practical ideas that you could use in the classroom.  There are a mix of activities for both primary and secondary.
  • Jo Boaler is behind the YouCubed website.

Other:

The Number Devil:

  • This is actually a children’s book.  It would be good for upper primary or the first few years of secondary.
  • It is about a boy who hates maths and then meets ‘The Number Devil’ in his dreams who transforms the boys perceptions of mathematics.  It explores quite a lot of common areas in mathematics in an engaging way.
  • It would be a good read as a class novel and to explore some of the ideas along the way.
  • As an adult, I enjoyed reading it.

Closing the Vocabulary Gap (Alex Quigley):

  • This is not specifically related to maths but definitely has connections and is very relevant from a Closing the Poverty Related Attainment Gap point of view.
  • It has lots of practical applications across a range of subjects.
  • It would be suitable for both primary and secondary.
  • Alex Quigley did a podcast on the Mr Barton Maths Podcast if you wanted to listen to that instead or before deciding whether to read the book.
  • The book in my opinion provides a lot more detail than the podcast though but the podcast was a great starting point.

Make It Stick (Brown, Roediger, McDaniel):

  • This book is basically about memory and how we learn.
  • It’s easy to read and is absolutely fascinating (in my opinion).  I couldn’t put it down.
  • There are huge implications in terms of how a lot of teaching is usually carried out… and how it could be organised/structured much more effectively.
  • This has implications for your own learning (as an adult) as well as how we teach our children.

I could go on, there are many more wonderful books that I could mention but that list is probably long enough as it is.  I’ll maybe write another list later in the year as an update!

They are all great in my opinion, it’s quite hard to choose where I’d start as they are all quite different.

If you do read any, then leave a comment below to share what you thought of it.
If there are any that I haven’t included but you think should have been on the list, I’d love to hear your thoughts.

Happy reading whatever you decide to go with!

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Highland Numeracy Progression Summary Documents

The information outlined below is now contained within its own page.  The page HNP Summary Documents is organised as a sub-page of the Highland Numeracy Progression main page (see image below).  All updates to these documents will appear there.

HNP Summary Documents Blog Page.png

The following materials (see images below) have been put together as a summary of learning for each stage.  These should be used alongside the main Highland Numeracy Progression document.

We encourage all practitioners to read the HNP Summary Documents: Overview and Rationale before using the documents so you understand these documents better and use them appropriately alongside other resources we have available.

These are ‘live’ documents which means additional supporting documentation and resources will be added on an ongoing basis.  As such, we suggest you use them online (or regularly check that you have the most up to date version) rather than download them.

The documents below include Early*** and First*.  We will add the documents for the other stages as and when they have been finalised.  Click on each image below to be taken to a PDF of the document.

HNP Summary Document: Overview and Rationale

HNP Summary Documents Overview and Rationale

 

 

 

 

 

HNP Summary Documents: Early Level

Early*** HNP Summary Document   

HNP Summary Documents: First Level

 First* HNP Summary Document

These documents are also available on the Highland Digital Hub:Highland Digital Hub

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Training Slides and New ‘CPD’ section on the blog

CPD Slides:

Firstly, for all those who were asking for the ‘slides’ from the live sessions we have been delivering these are now up on the Highland Digital Hub.

You’ll see that they have been organised so that the slides and the recorded session are above/below each other with a PDF of the slides above and the recorded session below.  I’ve tried to group them so that connected sessions are together so they are easier to find.

Screenshot 2020-06-21 at 21.20.49

We have two more slides still to add (Counting Collections and Making Sense of Fractions: Equal Sharing Problems), I hope these will be up by the middle of the week.

New CPD Section on the Blog:

As the blog is our main location for all materials related to Numeracy and Mathematics in Highland, we have also created a CPD section so you can go to the recordings straight from the blog.

You can find this in the ‘Menu bar’ at the top with all the other pages.

If you click on ‘CPD’ or ‘CPD Overview’ this will take you to a page detailing all the CPD currently available.

Alternatively, you can select one of the categories from the drop down menu that appears when you hover over ‘CPD’ (see image below).

We plan to continue adding to this so the collection will grow over time.

Screenshot 2020-06-21 at 21.11.02

All CPD has been organised into these categories.
Where there is a lot of cross-over, some sessions will appear in more than one category.
When you are on a category sub-page, you can click on the ’tile’ you are interested in and this will take you directly to the recording of that live CPD session (see image below).Screenshot 2020-06-21 at 21.21.38

We hope you find this useful and it allows you to access training more easily.

A polite request when using the content:

The content can be used freely for non-commercial/non-profit educational purposes only.

It is freely available to all practitioners however we ask that you acknowledge the amount of time, effort, background reading and research along with practical experience of using these ideas in classes; that goes into putting this training together and ask that you don’t take the training and rebrand it as your own.
We have tried to acknowledge the sources of our information where possible/applicable.

We are only human, so if you spot any mistakes please let us know so we can fix them.

We also love a good discussion so if you disagree with any of the content, we’d love to discuss this further and hear your point of view.

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CPD: More Live Sessions

We will be putting on some more live sessions for the final two weeks of term.  The details of these are below.  The sessions outlined here are aimed at Early Level and so would be particularly relevant to teachers in the Early Years, EYPs, Childcare Managers and PSAs however in the interests in understanding the importance of progression in learning we would recommend these sessions to all staff.

We may decide to run an additional session (or two) at other levels as well.  If this is the case, I will post an update on the blog to let people know.

Part of the Early Years Series:

Real World Use of Maths (EARLY LEVEL)

Date: 22.06.20
TIme: 2pm

Aims:

  • Raise awareness of just how much maths goes on in everyday life!
  • Reflect on how we can notice and extend this learning for children. 
  • Consider how using maths in everyday life can be a focus for engaging with families.
  • Recognise how much more there is to maths than purely focussing on numbers and deliberately planned activities. 
  • Identify an aspect of your practice you would like to develop/improve.

Spatial Awareness (EARLY LEVEL)

Date: 25.06.20
TIme: 2pm

Aims:

  • Raise awareness around spatial awareness, spatial ability, spatial reasoning, spatial  relationships & spatial understanding. 
  • Consider how spatial awareness supports flexible thinking in maths.  
  • Improve confidence to recognise and identify activities that can support the development of spatial awareness and the concepts involved. 
  • Identify an aspect of your practice you would like to develop.

Curiosity, Creativity and Confidence (EARLY LEVEL)

Date: 29.06.20
TIme: 2pm

Aims:

  • Develop practitioner confidence to explore open-ended enquiry and encourage children to lead their own learning.
  • Practitioner confidence to support children to make and test predictions and develop understanding of concepts.
  • Identify an aspect of practice to develop.
  • Recognise the links between positive relationships and children’s confidence, curiosity and creativity within maths.

 

Just a reminder that the recordings for all our sessions can be found on the Highland Digital Hub.

Lots of people have been asking about the slides for training sessions.  I will write a post (hopefully later today) to confirm these are all up on the digital hub.

We are also working on creating a CPD page on the blog so that all the training can be more easily accessed directly from the blog.  Again, I’ll post about that when it has been finalised.

 

 

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CPD: Additional Live Sessions

Here is an updated list of all the live CPD sessions that we have going on in the next few weeks.

Sessions that were already publicised but have not yet been delivered are listed in red. 

New sessions not previously listed are in blue.

Session details will be updated on the main Highland CPD site as well as the Digital Hub shortly.

If you have missed any sessions, you can find recordings on the Highland Digital Hub

Session: Diagnostic Assessments Part 2: Review and Q&A
Date: 25.05.20
Time:
Option 1:
11:00 – 11:30/11:45
Option 2: 17:30 – 18:00/18:15

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN
This session is aimed at people who have completed the self-paced online learning course for the diagnostic assessments and focusses on Part 2 of the course – the Knowledge Assessments

Session Aims:

  • Review some of the common issues that occur when undertaking the assessments
  • Review how to support learners to make their next steps in learning based on the assessments
  • Making sense of how the assessments can inform your day to day formative assessments
  • Reviewing how the knowledge assessments and addition and subtraction assessment can be linked to provide a more holistic overview.
  • General Q&A

Session: Using Story Problems to support understanding in Multiplication and Division at Early and First Level
Date: 26.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims:

  • An introduction to using a word problem approach to teaching multiplication and division at Early and First Level
  • Explore the rationale for using word problems to support understanding of multiplication and division
  • Understand the structure of word problems and how you can use this to support planning, teaching and learning including:
    • Multiplication Problems
    • Quotitive Division Problems (Measurement/Grouping)
    • Partitive Division Problems (Sharing)
  • Understand how to overcome common barriers associated with using word problems
  • Understand how differentiation and challenge can be supported through the use of word problems

Notes:
It will be useful if you have familiarised yourself with the attached Teacher Guide on Cognitively Guided Instruction.  This will be on the Digital Hub
This session sits well alongside the introductory sessions to multiplication and division at Early, First and Second Level.  You will get the most out of the session if you have also attended these other sessions.

A second session will be run looking specifically at extending these problems for pupils working at Second Level.

Further sessions will also be run that explore using this approach with addition and subtraction as well as with fractions.

Session: Understanding the properties of multiplication and their application at First Level, Second Level and beyond…
Date: 27.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, Primary, Secondary, ASN
Although not directly relevant to ELC staff, EYPs may find this useful to see the progression in learning.

Session Aims:

  • Explore the properties of multiplication including:
    • The Commutative Property
    • The Identity Property
    • The Distributive Property
    • The Associative Property
  • Learn to identify how these fundamental properties underpin the strategies that pupils use to solve multiplication and division problems.
  • Understand how these strategies underpin learning not just at First and Second Level but are fundamental for algebra in Secondary School.

Notes:
This session supports the introductory sessions on multiplication and division at First and Second Level.

Session: An Introduction to Multiplication and Division at Second Level
Date: 28.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims: 

  • Extend understanding about the difference between grouping and sharing.
  • Explore the relationships between multiplication and division.
  • Explore the progression with multiplication and division at First Level including:
    • Use of the area model to support multi-digit multiplication and division and an awareness of how this extends into work at Third Level and beyond the BGE.
    • Supporting understanding of other mental strategies
  • Explore how different concrete materials and visual representations can support understanding.

Notes:
This is the third in a three-part series on An Introduction to Multiplication and Division.  We recommend that to get a better grasp of the progression, you attend all three sessions and not just the level you are currently teaching.

Session: Using Counting Collections in Primary School
Date: 02.06.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs, ELC, Primary, Secondary, ASN

Session Aims:

  • To explore counting activities for ALL primary children.
  • Revisit the Counting Principles
  • Skip counting with materials
  • Using counting to develop deeper understanding of grouping and place value
  • Linking counting collections to multiplication and division
  • Counting collections of mixed values
  • Counting with decimals and fractions.

Notes:
This session supplements other sessions at Early, First and Second level and connects to a wide variety of areas including counting, addition and subtractions, multiplication and division, fractions and decimals.

Session: Number Patterns and Relationships in Primary School
Date: 03.06.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs, ELC, Primary, Secondary, ASN

Session Aims:

  • Explore how we can build on children’s natural curiosity around counting and numbers.
  • Explore how we can create opportunities for ALL pupils to notice and wonder about number patterns and relationships.
  • Explore Choral Counting at First and Second Level.
  • To generate ideas for teacher observations to guide our next steps.
  • To support planning of number patterns and relationships.

Notes:
This session supplements other sessions at Early, First and Second level
It is a follow up to the session on Counting Collections.

It connects to a wide variety of areas including counting, addition and subtractions, multiplication and division, fractions and decimals.

Session: Using Story Problems to support understanding in Addition and Subtraction at Early and First Level

Date: 04.06.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims:

  • An introduction to using a word problem approach to teaching addition and subtraction at Early and First Level
  • Explore the rationale for using word problems to support understanding of addition and subtraction.
  • Understand the structure of word problems and how you can use this to support planning, teaching and learning including:
    • Joining and Separating Problems
    • Part-Part Whole Problems
    • Comparing Problems
  • Understand how to overcome common barriers associated with using word problems
  • Understand how differentiation and challenge can be supported through the use of word problems

Notes:
It will be useful if you have familiarised yourself with the attached Teacher Guide on Cognitively Guided Instruction.  This will be on the Digital Hub
This session sits well alongside the sessions on:

  • Counting Collections
  • Number Patterns and Relationships
  • Story Problems for Multiplication and Division

A second session will be run looking specifically at extending these problems for pupils working at Second Level.
Further sessions will also be run that explore using this approach with fractions.

Session: An Introduction to Measure in Primary School
Date: 08.06.20
Time: 14:00 – 15:00

Target Audience:
Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims:

  • Develop an introductory awareness of how children build up an understanding of measure from birth to the end of primary school
  • To explore length as an attribute in further detail
  • To make links to other areas of the mathematics curriculum
  • To explore some practical activities that could be used to further pupils understanding

Session: Making Sense of Fractions through Equal Sharing Problems at Early, First, Second and Third Level
Date: 09.06.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN
Session Aims:

  • An overview of some of the difficulties pupils might experience with fractions.
  • Explore how equal sharing problems can support pupil understanding of fractions even with pupils at Early Level.
  • Understand the progression in strategies that pupils may use to solve equal sharing problems involving fractions.
  • Understand how these problems can be tailored to explore other concepts in fractions such as:
    • Comparing size of fractions
    • Developing a measurement concept of fractions
    • Equivalence
    • Mixed numbers and improper fractions
    • Addition and subtraction of fractions

Notes:
This session will be part of a wider series of sessions on fractions.
You may find it useful to have attended previous session on using story problems to make sense of multiplication and division and addition and subtraction.

Session: Using Story Problems to support understanding in Multiplication and Division AND Addition and Subtraction at Second Level
Date: 10.06.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, Primary, Secondary, ASN
Although not directly relevant to ELC staff, EYPs may find this useful to see the progression in learning.

Session Aims:

  • A review of the different word problem types.
  • A review of the underlying structure of the problem types:
    • Joining and Separating
    • Part-Part Whole
    • Comparing
    • Multiplication
    • Quotitive Division
    • Partitive Division
  • Extending the word problems to support learning at Second Level including multi-step word problems

Notes:
It will be useful if you have familiarised yourself with the attached Teacher Guide on Cognitively Guided Instruction. This will be on the Digital Hub
This session builds on the two sessions already presented at Early and First Level:

  • Using Story Problems to support understanding in Multiplication and Division at Early and First Level
  • Using Story Problems to support understanding in Addition and Subtraction at Early and First Level

The session will make most sense if you have attended these sessions.
The sessions will explore the use of strategies explored in other sessions but in the context of word problems.

Session: Making Sense of Factors, Multiples and Primes
Date: 11.06.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, Primary, Secondary, ASN
Although not directly relevant to ELC staff, EYPs may find this useful to see the progression in learning.

Session Aims:

  • Reviewing the importance of language and the use of graphic organisers such as Frayer Models
  • Using concrete materials to support conceptual understanding of multiples, factors and primes.
  • Exploring connections to other areas of the mathematics curriculum to support understanding of multiples, factors and primes.

Notes:
This session builds on the sessions relating to multiplication and division as well as the Language of Maths.
The session will make most sense if you have attended these sessions.

 

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Fractions Project – What a week!

I was very fortunate last week to be working with an amazing group of P5 pupils from Newton Park Primary School in Wick who volunteered to be part of a project I’m working on.

The lockdown and the current situation we find ourselves in has many downsides, many of which will sadly be long-lasting and/or irreversible.  At the moment, everyone is trying hard to make the best out of a bad situation, myself included, and this week I was excited about the following:

  • Despite being unable to leave the house I can work with a group of children who live 3 hours away – I’m in Inverness, they are in Wick but they could have been anywhere in the world.
  • It has reinforced to me that rich learning discussions, while definitely not as easy, are definitely still possible in our current circumstances.  Although the discussions themselves required a device, the work the pupils did in between sessions was using pen and paper – no device and no parental support required.
  • It also reinforced that you can spend 45 minutes discussing the intricacies of a single problem.
    • As a child, you’ll likely learn far more than solving a page full of calculations.
    • As a teacher, you’ll likely learn far more about the child’s understanding than seeing their page full of answers.
      You don’t need to spend as long as this (45 minutes)… this was partly, again, down to the rationale behind doing the project and so the extended discussion was useful for us.

For anyone interested this was the format of our week:

Day 1: Introductions

  • The children did not know me.  I am not their teacher although I do work with and visit the school several times a year.
  • Set the first problem which had three levels of difficulty.
  • After the Google Meet, children worked on the problem independently (pupils were asked not to get help from parents and siblings) and sent pictures of their strategies to me via their teacher.

Days 2 – 5:

  • Using Google Meet, Google Slides and Google Canvas, we compared the different ways they had solved the problems and had in-depth discussions about potential misconceptions that arose and the pros and cons of the different strategies that people had used.
  • A new problem was set that had two levels of difficulty.  Children completed these independently and sent their work to me via their teacher for discussion the following day.

The purpose of the sessions was to support work that we are currently doing around developing The Highland Numeracy Progression (and Northern Alliance Progression) further to include a major update on fractions.  The work will then feed into both face-to-face teacher training and an online module that teachers can work through at their own pace.

The work is fascinating and we think teachers will find it incredibly beneficial when it’s released.

We recorded all the sessions with permission from the parents and pupils with the intention to use them for the purposes outlined above.

Here is a sample of the pupils’ work from a few different days of the project.  At some point, videos will accompany this

Take a look at the work yourself and reflect on:

  • What do the pupils understand
  • What is missing and therefore may reflect a gap in understanding and knowledge?
  • How does the work develop over the week?

The images themselves are incredibly rich but the discussions that accompanied brought everything up a level.

The progression in questioning and the numbers selected were carefully chosen, in part based on the responses that pupils gave but also to try and explore some of the ideas that we were particularly interested in… we are not suggesting that this is a sequence that you would typically follow.

A note on the levels of difficulty:
With each problem (see examples below) children are told to insert the first number in brackets into the first space and the second number into the second space.  The same problem is therefore used but has three levels of difficulty to it.

Day 1:

___ children in Mrs Ferrier’s class decide to share ___ banana loaf cakes.  If they want everyone to have the same amount with none left over, how much will they each get?

(6, 3)   (6, 5)  (5, 3)

Day 2:

At Toby’s birthday party, he has some chocolate logs for people to share.  If ___ children share ___ chocolate logs and everyone gets the same amount with none left over, how much will they each get?

(4, 3)  (8, 6)

*Is it better to share 4 chocolate logs between 3 people OR 8 chocolate logs between 6 people?  Explain your ideas.

Day 3:

Mrs Ferrier decides to do an art project with the class.  ___ children need to share ___ blocks of clay equally so everyone has the same amount and there is none left over.  How much clay do they each get?

(6, 4)   (6, 8)

Day 4:

The problem for Day 4 was a little bit different.  We asked the children to look at the work that had been created from the problem set on Day 3 where pupils had written different fractions for the same problem and the problem posed was:

  1. Does the fraction that each person has written match their drawing?  Explain your answer.
  2. Everyone solved the same problem but the fractions people wrote looked different.  The range of fractions recorded was then outlined as a reminder.
    Are these the same amounts or different amounts?  Explain your answer and use a drawing to show/prove your ideas.

    Are the fractions all written correctly or do any of them need to change?

 

This week, we’ll be doing more of the same but this time with a different year group and a different school.  I’m really looking forward to it.

I’m also looking forward to sharing the outcome, of what has been a huge piece of work, more broadly with others when we put out the updated progression and the accompanying CPD.

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CPD – Concrete Materials at Secondary School: Algebra Tiles

In addition to the sessions we’ve already published, Fiona Philips from Alness Academy will be presenting a session on Tuesday (tomorrow) and Wednesday on using Algebra Tiles with secondary pupils to support understanding.  Many Highland secondary teachers are already aware of this session but I’ve put it up here for any primary teachers who may also wish to attend.

As described below, although the content is mostly Third Level and above, it builds nicely on the work that we are promoting in Primary School and helps to emphasise that concrete materials are not just for younger pupils but for all pupils.

The session and link to the Google Meet can be found on the Highland Digital Schools Hub training calendar.

Session: Concrete materials in Secondary School: Algebra Tiles

Date/Time:
Option 1: 05.05.20     19:30
Option 2: 06.05.20     14:00

Target Audience: Secondary Teachers, Primary Teachers (exploring how concrete materials can be used with older pupils)

Session Aims:
Explore how algebra tiles can be used to help pupils make sense of:

  • Adding and subtracting integers
  • Multiplying out brackets
  • Factorising quadratic equations
  • Solving equations

Notes:
Although the content is mostly around Third Level and beyond, this may suit primary school teachers to see how concrete materials are also used in primary school.  Many of the ideas build on work that it is useful to do in primary school using Dienes Equipment which can build the foundation for the work explored here.

If you are attending the multiplication and division series run by Highland Numeracy, this would be an extension of where some of that work goes.

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CPD: Live Online Sessions

Great to see that some people have made a start on the self-paced diagnostic assessment course I posted about earlier in the week.  If you missed it, see this post here: CPD: Self-paced Online Learning   As well as continuing to notify people on the blog, any future self-paced learning will also appear on its own page on the Highland Digital Schools Hub

We’ve also just added several sessions to the Highland Digital Schools Hub Online Training Calendar.  Details of the sessions we’ve added are below.

The content would be appropriate for both teachers and PSAs.

Session: An Introduction to Multiplication and Division at Early Level

Date: 07.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims:

  • Recognise multiplication and division opportunities within real & play contexts at EARLY LEVEL
  • Explore word problems as a means of providing a meaningful CONTEXT to support understanding.
  • Identify the differences between grouping and sharing
  • Raise awareness of the need to work flexibly within the teaching model
  • Recognise the variety of language used at Early Level
  • Raise awareness of the links to other areas of maths e.g. patterns, language, addition/subtraction, number word sequences etc.
  • Explore and evaluate the range of resources we can use for multiplication & division.

Notes:
This is the first in a three-part series on An Introduction to Multiplication and Division.  We recommend that to get a better grasp of the progression, you attend all three sessions and not just the level you are currently teaching.

 

Session: An Introduction to the Language of Maths (Part 1: Early)

Date: 12.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims: 

  • Raise awareness of maths language used within our daily interactions
  • Identify daily opportunities where we can develop maths language and enhance understanding
  • Improve confidence to use WORDS UP key messages for maths
  • Identify an aspect of our practice we would like to develop 
  • Agree next steps for our setting/class

Notes: 

 

Session: An Introduction to the Language of Maths (Part 2: Primary and Secondary)

Date: 14.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims: 

  • Explore how understanding etymology and morphology can help us make better sense of language and build connections.
  • Explore how the use of Frayer Models can improve understanding of mathematical language.

Notes: 

  • Frayer Models can be used for other subject areas too e.g. literacy, science, technology, geography etc. so these could be used across the curriculum – they are not exclusive to maths!
  • This is the second in a two-part introductory series on the Language of Maths.  We recommend that to get a better grasp of the progression, you attend both sessions and not just the level you are currently teaching.

 

Session: An Introduction to Multiplication and Division at First Level

Date: 21.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims: 

  • Extend understanding about the difference between grouping and sharing.
  • Explore the relationships between multiplication and division.
  • Explore the progression with multiplication and division at First Level including:
    • Skip Counting
    • Repeated Addition
    • Multiplicative strategies that involve known facts
  • Explore how different concrete materials and visual representations can support understanding.

Notes:
This is the second in a three-part series on An Introduction to Multiplication and Division.  We recommend that to get a better grasp of the progression, you attend all three sessions and not just the level you are currently teaching.

 

 

Session: An Introduction to Multiplication and Division at Second Level

Date: 28.05.20
Time: 14:00 – 15:00

Target Audience: Teachers, PSAs, EYPs.  ELC, Primary, Secondary, ASN

Session Aims: 

  • Extend understanding about the difference between grouping and sharing.
  • Explore the relationships between multiplication and division.
  • Explore the progression with multiplication and division at First Level including:
    • Use of the area model to support multi-digit multiplication and division and an awareness of how this extends into work at Third Level and beyond the BGE.
    • Supporting understanding of other mental strategies
  • Explore how different concrete materials and visual representations can support understanding.

Notes:
This is the third in a three-part series on An Introduction to Multiplication and Division.  We recommend that to get a better grasp of the progression, you attend all three sessions and not just the level you are currently teaching.

 

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CPD: Self-paced Online Learning

If you are looking to make better sense of the progression of children’s learning in numeracy as well as the types of strategies that they might use at different stages then the Highland Diagnostic Maths Assessment Training may be what you are looking for.

Target Audience:
While the primary audience is teachers, the course would also be suitable for PSAs.  It is not expected that PSAs undertake the assessments with pupils but it may be useful to support awareness and extend professional understanding of the strategies that pupils use and the progression of learning.

Suggested Access:
If possible, we suggest that you get together (virtually) with a group of individuals (from your school or otherwise) and arrange times to discuss the materials periodically, as you work through the course.  We feel that discussing the materials will allow you to get more out of the course.

The materials can, of course, be accessed independently if you prefer.

Duration and suggested schedule:
Part 1: 
This takes approximately 3 hours (the suggested times below are slightly longer as they include time for discussion with colleagues and a Review/Q&A session with a Development Officer).
We have put a suggested schedule below as we feel this will help people break the course up into manageable chunks.

You can see on Day 4 there is also an optional Q&A session with one of the development officers.

Screenshot 2020-04-29 at 08.44.38

Part 2: This takes approximately 4 hours (the suggested times below are slightly longer as they include time for discussion with colleagues).
We have put a suggested schedule below as we feel this will help people break the course up into manageable chunks.

Again, there will be an optional Q&A session on Day 4.

Screenshot 2020-04-29 at 08.44.53Polite Request:
If you undertake the course, we ask that you complete the pre-course questionnaire and the two post-course questionnaires (these are contained within the course).  We also request that you send your moderation recording sheets.  These aspects help us to evaluate the effectiveness of the course.  If you do not have a printer at home to print the recording sheet, a hand drawn version can be used.

 

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