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White Rose Maths - online quizzes

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Comprehensive stuff that will really help!

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Do Now's, exit tickets etc - linked to WR SoL

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Hello and welcome! I am a maths teacher who has taught for 2 years in the UK, 5 years in an international school in washington DC, and is now teaching in an international school in new york. i teach…

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Form Time Ideas - Tutor group activities

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Ideas and activities to keep your tutor group engaged during form time. A fresh set of activities is generated each time you visit.

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Maths Genie - Free Online GCSE and A Level Maths Revision

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Maths Genie is a free GCSE and A Level revision site. It has past papers, mark schemes and model answers to GCSE and A Level exam questions.

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Entries tagged Interwoven Tasks from Interwoven Maths

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All of the entries posted on Interwoven Maths tagged Interwoven Tasks

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Pearson Edexcel Resources

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If you have any questions or issues about the emporium, please contact us via our support portal. Please select the following so that your query reaches us. Customer type: Teacher & Department Heads - Issue Type: Systems, Tools and Services - Category: Maths Emporium.

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Registers, seating plans etc

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Class Charts is super fast behavior management software, creating school seating plans in seconds. Link our behavior & seating plan software with SIMS, Powerschool & more

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5-a-day GCSE 9-1

Numeracy 5aday - broadly designed for students aiming for Grades 1, 2 and 3.

Foundation - broadly designed for students aiming for Grades 3 and 4.

Foundation Plus - broadly designed for students aiming for Grades 4, 5 and 6.

Higher - broadly designed for students aiming for Grades 6 and 7.

Higher Plus - broadly designed for students aiming for Grades 8 and 9.

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The Corbettmaths 5-a-day for the 9-1 GCSE.

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Login: whatleyj@testvalley.hants.sch.uk
Password: Fantastic123!

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early career framework: log in to the site

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Early Career Framework: Log in to the site

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Login: winchesterd
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Mrs Maunder Altrincham Grammar School for Girls

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Welcome to CSUK:Teacher High Quality Resources For Hard Working Teachers Cathryn Armer Northleigh House School “We’ve mainly used the CSUK resources to help teach GCSE OCR Computer Science, although Schemes of Work for Key Stage 3,4 & 5 is included in the one price. They comprehensively cover every…

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Loads of careers info that uses maths

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This is Numberphile. We mainly post videos about mathematics and just numbers in general.

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Discover Mathigon, the Mathematical Playground. Learning mathematics has never been so interactive and fun!

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Controlling Focus - 5 Practical Ways to Remove the 'Blur' of Learning from the Classroom.

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"Memory is the residue of thought"

Daniel Willingham, Why Don't Students like School?, 2011

"PAY ATTENTION!" How many times have we heard this yelled across a classroom to a unyielding year 10 who just won't focus in the task in hand? Worse still, how many times have we asked a student a question, they get it wrong or say the infamous "Don't know sir" and we reply with "Well, weren't you paying attention?!". I have no doubt you have seen, or done, these in your teaching practice. Sometimes we say 'teacher-y' things like that without even thinking about. They have become habit. But how many times do we stop and think during our lessons, what do I want my students to focus on right now? Do they know to focus on this? How do they know? Removing the 'blur' of the learning by providing explicit foci for students can help improve engagement and learning over time.

To illustrate this, I want to draw your attention to whether you are sitting or standing? If you're sitting, can you notice the pressure of the chair on your back and bum? Were you aware of it before? Probably not. Another great example is, when was the last time you blinked? Bet you just blinked. The purpose of this if that if we don't explicitly direct our students focus or attention on to what we want them to think about, how are they going to understand what we are trying to teach them? I would completely understand if someone said that this was obvious, and it is. But ask yourself, when did you last think explicitly about what your students are thinking right now in your lesson? An example I used in a recent staff briefing was the following image.

Tree Illusion (adapted from https://www.peacequarters.com/see-first-image-identifies-hidden-self)

Let's say I showed this image to a class of students and provided the following facts:

This is an example of an organism

This organism can have a variety of colours

This is a marine organism

Most organisms of this type of gills

How many of the class would think the tree or the lioness or the gorilla have got all these biological features? How many would know I was referring to the fish at the bottom? Without me explicitly highlighting the fish at the start, the staff would get lost in the 'blur' of unclear focus. I then showed the following image and asked staff which of the organisms had caught their attention.

Tree Illusion (adapted from https://www.peacequarters.com/see-first-image-identifies-hidden-self)

What do the experts have to say?

The need to explicitly control and direct attention is well documented in educational research and I want to share a few choice references to evidence why I feel so strongly this is a vital tool to help students and teachers in the classroom.

Adam Boxer's CogSciSci Bath '2020' keynote presentation - At recent CogSciSci event in Bath, Adam Boxer shared some very insightful advice on how to improve all explanations. One of his golden nuggets was to direct attention of students explicitly to what you wanted them to think about. This can be done by starting with a blank canvas and modelling a process or diagram in real time which allows students to have their attention directed to exactly what you are doing. This was a real eye-opener for me and will forever change how explain things from now on. All of Boxer's ideas are covered in his new book.

Tom Sherrington's Model of Learning - Tom has an extensive library of blogs and information on his website, one of which is the following image, found here.

How we learn. Accessed from https://teacherhead.com/2020/10/04/teaching-for-understanding-schema-building-and-generative-learning/

This image shows the importance attention has on the learning process. Before any working memory can be activated and committed to long term memory, there must be a direction of attention to the specific part of the environment. Without drawing the students attention to what's important, how will they know what is important?

There are many other links, such as Daniel Willingham's Why Don't Students Like School?in which Willingham illustrates that if we don't direct attention and force students to think about what we want them to think about, they won't learn what we want them to learn. Remember, " Memory is the residue of thought". In Teach Like a Champion 3.0, Doug Lemov introduces the idea of directing attention and is the fudemental basis of track the speaker, written about in TES by Ian Taylor. Focus also features in Nimish Lads adaptation of the MARGE approach, the A is for attention. there is 100's of other sources but I feel these are the most powerful currently to me and my practice.

5 Practical ways to remove the blur from student focus

Here are some methods I try to use to explicitly direct focus and attention, making students think about what I want them to think about.

Provide resources that are clear. This can be slides, worksheets, booklets or handouts, all should contain a clear focus image or small amount of text to allow students to clearly see the intended focus

Minimise distractions. This can be from other students port behaviour, the teachers worry of a silent classroom and so the teacher fills the silence with more instructions or thoughts or anything else that could distract from the learning. Use behaviour management techniques to reduce peer distractions. Feel free to use a timer to provide yourself a well earned break in talking whilst the students focus and think about what you want them to think about.

Use appropriate models. Use models that students are familiar with and that don't over complicate the concept being taught. The parallels should be easily understood and the model should not distract from the concept.

Explicitly direct student attention with a gesture or emphasis on the board. I (am now going to) do this by using Adam Boxer's suggestion to start with a blank canvas. Show the blank canvas of a board and draw the concept live, using whiteboards, mini-whiteboards under a projector and a graphics tablet. This is such a powerful and captive way to explain something and is much more effective then sticking it in a PowerPoint.

Use questioning to drive students thinking towards a goal. Using cold calling, and it's the many variations, you can ask students questions to refocus attention but don't use this to much during an explanation as you can ruin the narrative of your explanation.

I hope to have shown why I think explicitly directing students attention is vital for all teachers, in all subjects and all phases, and why it's such a fundamental arrow in our pedagogical quiver. Thank you for reading, please give me your feedback and thoughts on Twitter via @DrB_SciTeacher.

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Controlling Focus - 5 Practical Ways to Remove the 'Blur' of Learning from the Classroom.

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"Memory is the residue of thought" Daniel Willingham, Why Don't Students like School?, 2011 "PAY ATTENTION!" How many times have we heard this yelled across a classroom to a unyielding year 10 who just won't focus in the task in hand?

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Science teacher on whole-school pedagogy.

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A collection of research and resources

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Evidence Informed Teaching A Collection of Resources

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Closing the Vocabulary Gap Resources | The Confident Teacher

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You can sign up to my Substack newsletter - The 3Rs - What I'm writing, reading, and research and resources I am interested in HERE.

Below are the free resources created to accompany my 'Closing the Gap' series.

CLOSING THE WRITING GAP RESOURCES

If you want to grab a copy of the book to accompany the resources you can grab a copy at Amazon UK HERE and Routledge

CLOSING THE READING GAP RESOURCES
CTRG Book Club Discussion Questions
If you want to grab a copy of the book to accompany the resources you can grab a copy at Amazon UK HERE and Routledge .

CLOSING THE VOCABULARY GAP RESOURCES

If want to grab a copy of the bestselling Vocabulary book, you can grab a copy from Amazon UK HERE and Routledge . Also, you can now get an audiobook now to - see Amazon UK .

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Closing the Gap Resources | The Confident Teacher

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You can sign up to my Substack newsletter - The 3Rs - What I'm writing, reading, and research and resources I am interested in HERE. Below are the free resources created to accompany my 'Closing the Gap' series.

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We have recently launched a new website. Many of the old links won't work and it could be a while before all the links to our site via search engines are up-to-date. If you have arrived here expecting specific content as a result of the link you clicked or the search you made, please try the search tool above - you should quickly find what you're looking for.

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Welcome to the teacher area of the website. Here you will find a wide range of resources to support teaching and learning of Mathematics. You can navigate the teacher area using the menu on the left-hand side of the page.

Classroom Resources

Planning Resources

In school support

The PDST Post Primary Maths Team will continue to deliver high-quality support for the 2022 - 2023 school year. We will be delivering a suite of workshops for Maths Teaching and Learning and carrying out school visits to support Maths departments. For more information see the links below:

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Welcome to the teacher area of the website. Here you will find a wide range of resources to support teaching and learning of Mathematics. You can navigate the teacher area using the menu on the left-hand side of the page. The PDST Post Primary Maths Team will continue to deliver high-quality support for the 2022 - 2023 school year.

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What can cognitive science tell us about how to design learning experiences?

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The cognitive load of a learning resource is the balance between task demand (how hard it is and how long it takes) and available resources (students' prior knowledge and the resources they have to hand).

If the cognitive load is too high, students become overwhelmed and disengaged.

If it's too low, they won't be challenged.

Design features can either enhance a learning resource or add unnecessary cognitive load.

David Didau explains how to get the balance right.

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What can cognitive science tell us about how to design learning experiences?

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Educational consultant and writer David Didau explores some key theories about learning - as well as debunking some widely-held beliefs along the way.

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One-page CPD summaries

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Latest Blogs

Teaching place value and not just about base ten.

...because all counters are double sided! A blog about how I use double sided counters in teaching directed number arithmetic

How I've tried to implement a few ideas from Mark McCourt's phasing learning model, in particular the practise phase

So, what is a MathsConf and why do I like them so much?

Some of the more technical details behind how I create my sketchnotes.

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Teaching place value and not just about base ten. ...because all counters are double sided! A blog about how I use double sided counters in teaching directed number arithmetic How I've tried to implement a few ideas from Mark McCourt's phasing learning model, in particular the practise phase So, what is a MathsConf and why do I like them so much?

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Colour me scientific: Two free fun colour-me-in downloads | New Scientist

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Colour me scientific: Two free fun colour-me-in downloads | New Scientist

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Never heard of a querkle or a spiroglyphic? No worries – just get your colouring pens and follow the simple instructions to reveal two iconic images of science

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Maths Hubs Programme Annual Report 2024/25 published

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Big banks of questions on topics

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Suitable for KS3 and GCSE and for all exam boards (Edexcel, AQA, OCR etc)

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How big are things compared to other things?

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Universcale lets you see and understand the relative size of the full range of known objects in our universe. How is your grasp of the sizes of such things? Nikon's opto-electronics technologies let people explore realms beyond the range of the naked eye.

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5 Evidenced Based Papers All Teachers Should Read (Updated)

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I first wrote this post over two years ago. In the intervening period two updated versions of the papers I included - Great Teaching & Cognitive Load Theory - have been written. I thought it was time to update the post. The title is written as a statement; arguably it should be a question. These would be the 5 key papers I think all teachers - from ITT to Headteachers - should read.

Some of the papers are pretty lengthy so you may wish to just read one at a time and return to this post for the next one, when you are ready. It is best to discuss the papers with others; collaboratively develop your depth of understanding and then work hard at implementing, within the classroom and staff room, until practices are systemic or fluent. The papers could inform a whole series of "evidence based" discussion groups in your school.

None of these papers are particularly new. Arguably, teachers are best working with evidence from researchers that is well established, has stood the test of time and been implemented in various contexts. Working with the latest evidence is fraught with difficulty. Not least, as soon as you have read one paper about the positive impact of a certain intervention, theory or way of working another new paper gives an opposing view. Let the researchers battle it out, produce evidence and counter evidence and argue their way through the fog. Wait until there is a clarity and collectiveness of view before engaging. Most teachers are simply too busy to do otherwise.

It's worth noting how experts in their field are much happier to embrace uncertainty than Twitter is, Professor Robert Coe, when talking about great teaching, said, "We don't know as much about it as we'd like to. We get glimpses at the moon through a cloudy sky - snippets that give insight. We try and bind them together, but we have a precarious grasp of something that is very complicated". Gone is the binary certainty of my Twitter time line and in comes a nuanced deep understanding. We must acknowledge degrees of certainty and uncertainty; it mustn't paralyse us rather enable us to approach any evidence with an understanding of its limitations.

Experts can also bring common sense to suggestions about implementation. My favourite example is in the Dunlosky et al paper where they comment on the "low utility" of highlighting texts as a way of learning. However given the widespread adoption of the process, rather than banning it on pain of death, they suggest, "Future research should be aimed at teaching students how to highlight effectively, given that students are likely to continue to use this popular technique despite its relative ineffectiveness."

Evidence doesn't replace experience; both work alongside each other developing, deepening and enriching each strand of professional life in a symbiotic relationship. The five papers I originally blogged about were used to stimulate discussion at regular senior leadership team meetings, over a period of months. Read them one at a time; come together and chew over what they mean and the implications for implementing. Encourage people to "play" with the ideas before seeking more formal implementation. It's often better to have an organic growth process rather than a full scale imposition.

So here are the five papers:

Great Teaching Toolkit: Evidence Review (2020) by Coe et al (Updated paper)

This would be my starter paper for discussion. It grounds you in what great teaching might be and how teachers can become great or at least much better. This more recent publication from Evidence Based Education (June 2020)is an update of the Coe et al (2014) paper What Makes Great Teaching? The 2020 paper identified "four priorities for teachers who want to help their student learn more":

Understand the content they are teaching and how it is learnt

Create a supportive environment for learning

Manage the classroom to maximise the opportunity to learn

Present content, activities and interactions that activate their students' thinking

Great Teaching Toolkit: Evidence Review (2020) by Coe et al

The paper looks at each of these components of great teaching in turn, referencing the work of Sweller et al., Rosenshine & Dunlosky (see below). Each of the four priorities are then broken down into constituent elements. For example, the first priority looks at the need for teachers to have a deep and fluent knowledge of the content they are teaching; know common pupil misconceptions & sticking points; know how to sequence the content and know a variety of activities, explanations and assessments to support pupils' learning. The fourth prioritiy focuses on activating students thinking through the use of: structuring, explaining, questioning, interacting, embedding and activating with references to the original works and examples provided to aid understanding.
Cognitive Load Theory - Sweller
Arguably the most important theory for teachers to know, according to Dylan Wiliam. The paper discusses five components that make up our human cognitive architecture and five compound effects that provide underpinning principles that govern the other simpler Cognitive Load Theory effects. The simpler effects I chose to divide into scaffolding learning effects and presenting information effects (this division is not contained within the paper). The links in this paragraph are to a set of PDFs providing an overview of key aspects of the paper; the images for the PDFs are below.

The paper requires reading, re-reading and considerable thought. As the authors lament, "Our knowledge of many of the characteristics of working memory, long-term memory and the relations between them had been well-established for many decades ... this knowledge has had a limited impact on the field of instructional design with most instructional design recommendations proceeding as though working memory and long-term memory did not exist." There is much that still requires conversion from theory into considered, purposeful and consistent classroom practice.
Principles of Instruction - Rosenshine
This is an interesting and detailed paper. The paper is built around principles rather than specific practices. Each principle has a useful "Research Findings" and "In the Classroom" section. It's one for classroom practitioners. Tom Sherrington has brought it alive in a wonderful little book published by John Catt Ltd.

Improving Students' Learning With Effective Learning Techniques: Promising Directions From Cognitive and Educational Psychology - Dunlosky et al
The paper provides a review of the ten learning techniques; each one is set out using the same format: a description of the technique and why it is expected to improve student learning; an exploration of its "generalizability" in different contexts; links to any research and any identified issues with implementation. Whilst it is worth reading the whole paper, for busy teachers the high utility techniques - practice testing & distributed practice - are worth reading first. These techniques are a common thread through many of the papers and emphasise the need for pupils to remember not just encounter, many aspects of the curriculum.

Developing Great Teaching - Teacher Development Trust
If we want great teaching and learning in the classroom then we need great professional development in the staff room first and foremost. Too much professional development is quite literally a waste of time. Substantial effective professional development of teachers is a precursor of effective implementation and supporter of significant improvements in pupil outcomes. Eight key elements of effective professional development are explained within this paper.

Five papers can never represent the totality of what is important in the classroom. Much of what is above deals with the technical aspects of teaching. They have been selected because they are arguably more within our control than many other factors which also impact significantly on the great venture that is education. The impact of socio-economic factors, importance of school culture and impact of relationships also require thought and detailed work. They are all part of a greater whole.

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5 Evidenced Based Papers All Teachers Should Read (Updated)

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I first wrote this post over two years ago. In the intervening period two updated versions of the papers I included - Great Teaching & Cognitive Load Theory - have been written. I thought it was time to update the post. The title is written as a statement; arguably it should be a question.

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Mathematics is not just the currency used to "get to college." It has many uses and opens many doors in this world. But which doors does it open? Making Sense of the World Understand finance and ma...

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The EEF is an independent charity dedicated to breaking the link between family income and educational achievement.

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Using the Rasch Model to Analyse Multiple Choice Questions

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Using the Rasch Model to Analyse Multiple Choice Questions

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This is the final post in my week long series on assessment and reporting at Paradigm Trust schools. Monday: Exploring Comparative Judgement Data With Charts Tuesday: Communicating Assessment Score…

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Deep Dive Mathematics Inspection - Mr-Mathematics.com

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At the start of February my school had a full OFSTED inspection under the new framework. In this blog I will share my experience of the deep dive mathematics inspection as head of department.

Preparing for a Deep Dive Mathematics OFSTED inspection

At around 4.30 pm the day we were told OFSTED were coming all the staff got together to find out the plan. The Head of Mathematics, Science and English would each have a full day of the inspection dedicated to their deep dive with one inspector assigned to each department.

I had already done a great deal of preparation for the deep dive from the trial inspection last June. This meant I could spend time before the inspection offering advice to my teachers about their lessons. This helped to settle their nerves and gave me an overview of what my team were teaching the following day.

The Deep Dive Interview

My day began with the Deep Dive interview at 9 am. My first question was, "Tell me about the issues you have encountered since you have worked here. I did not like the question. My response was to share the joys I have encountered since I have worked here and the challenges my team and I have overcome to experience them.

I discussed redesigning the curriculum so mathematics could be taught through problem solving and students had more opportunities to apply their learning rather than recite it.

Teaching Mathematics through Problem Solving

I was quickly interrupted and asked to explain how we teach mathematics through a problem-solving approach. I explained that when students have understood the concept of the learning objective, they begin connecting it to other areas of mathematics. We regularly expose students to questions that require them to link multiple topics together within a single problem. We give them the time to make sense of the problem, come up with a method, refine the method and attempt a solution. Students share their solutions with the teacher and their peers and amend when necessary.

Teachers rarely give students the help they want, or at least, think they want. Instead, we give them the help we know they need. Often, this is simply time or someone to read the problem out loud to. Of course, we provide guidance to students who are struggling but this is in the form of clues and prompts rather re-teaching.

Vision or real life?

The inspector asked if I was describing a vision or what really happens in the classroom. I explained I was describing both. I am realistic enough to know not all these these things happen every lesson. However, they underpin our practice and I knew he would see enough evidence of this in the observations to see how effective teaching mathematics through a problem solving approach can be.

The inspector wanted to see if the department's long-term plan and schemes of work reflected the approach to teaching that I had described. Thankfully, I had bought these with me to the interview. The inspector was impressed with the linked resources, mostly to the lessons on Mr Mathematics and problem-solving questions.

I explained the schemes of work are used as a basis for discussion during every faculty meeting when we talk about and share additional resources for the forthcoming topics. We discuss which problem solving questions are suitable for the different ability classes and whether to use them as a plenary to assess learning or as a starter in the next lesson to review prior learning.

Implementing the Mathematics National Curriculum

Next, we discussed the implementation of the mathematics curriculum. I explained we have a two-year key stage 3- and three-year key stage 4. The inspector questioned whether Key Stage 3 was long enough to ensure enough preparation for GCSE in Year 9. I explained my Key Stage 3 leader has completed a thorough audit of what students are taught in Key Stage 2 and ensured no time is wasted in Year 7 or 8 repeating the same topics.

The Learning Visits

The inspector said he was excited to see teaching mathematics through a problem-solving approach in action. I was excited to show him. As we walked towards the maths corridor, I explained he would see happy students, either solving problems or being taught how to do so.

I observed two Year 7 lessons with the inspector. We remained in each lesson for about 10 minutes. It was obvious from the work on the board the teachers had clearly modelled several examples on for the students before we arrived. One class were applying multiple angle properties within a single problem and the other were solving worded problems with fractions.

Pupil Premium Students

As part of the deep dive mathematics inspection the inspector wanted to talk with specific students who were identified either as pupil premium or gifted and talented. I was grateful the teachers had all this information to hand so I could quickly direct the inspector to the correct student. He chose a couple of students from each class that he wanted to talk to later in the day as part of the student panel.

The inspector had planned to observe the maths department again after break time. I felt we needed to show more evidence of how we challenge students through great questioning as well as supporting them through our precise modelling. It was important for inspector to see us teach using the approach I had described in the interview earlier in the day.

Learning Visit - Part 2

I was teaching top set Year 11 circle theorems. The inspector observed the first 15 minutes of the lesson where the students were challenged to prove the angle at the centre is double the angle at the circumference. I guided class through with subtle prompts and a range of open questions. The students were amazing. Every single student showed creativity, fantastic algebra skills and progress. The inspector left the room a minute before the first student completed the proof.

The Deputy Headteacher carried out the rest of the learning visit for the next two lessons while I taught my class. I was told the lessons went very well and the inspector got to see how other teachers support and challenge their students through a range of carefully scaffolded questions and prolonged thinking time.

Immediately after the learning walk I spent the next 15 minutes urgently collecting all the books the inspector had asked for on his learning walk. I collected an additional 10 books which I wanted to present to the inspector in my next meeting. He had not asked for these, but they showed evidence of how we teach maths through problem solving. I hoped I would be allowed to present them.

Book Look and Student Panel

With all the exercise books in hand, I was asked to wait outside the inspector's room for my next meeting. The inspector was interviewing the students he had asked to meet during the two learning walks. I have no idea what the students were asked, or how they responded.

Shortly after the students left, I was asked to meet the inspector again. We looked through some books together and had a short conversation about the marking policy which he appeared to approve of. However, I could tell he was looking for something which he was yet to find. I asked if I could present evidence of problem solving in the student's books. This is what he had been looking for.

Look at these books

As we went through the books, I took every opportunity to highlight the scaffolding of questions, the diagrams that showed a mathematical model, working that was crossed out and replaced and linking of multiple of topics within a single problem. This is what my teachers do daily and there was ample evidence to present.

It was clear at this point the inspector had found what he was looking for as he began making copious amounts of notes on his laptop. When he had finished making notes the inspector told me he was excited by what we do here in maths. He said, the maths team understand and embrace the essence of the curriculum and he could see clear evidence of students enjoying their lessons.

Relief and pride

I felt immediate relief that we had shown a true version of ourselves and pride in our courage to teach to our values no matter what. We are not the finished article and there is much more to be done. But we are a team and we are getting better every day. As the inspection has yet to be published, I am not allowed to state our final grade. On a separate note, there will be a school party later this year.

My team and I have worked tirelessly over the past two and a half years to give the students a better deal. We have done this, not for the school but for our students and ourselves. To have our hard word acknowledged in such a way is a tremendous lift for all of us.

Getting through the Deep Dive Mathematics Inspection

Finally, as I have done this twice now, I would like to offer some practical advice to all Heads of Mathematics in preparing for their Deep Dive.

Have a substantial breakfast the day of the deep dive and if you drink coffee or tea take a flask to work. . There was no time for me to eat during the day.

Have your schemes of work and curriculum plans to hand all day.

Ensure your teachers have seating plans to hand. These need to include details of who are your gifted and talented, pupil premium and other sub-groups.

Most importantly,

Do not be afraid to argue your point. I disagreed with several comments the inspector made and I was able to present lots of evidence to prove the points I needed to.

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About Mr Mathematics

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Deep Dive Mathematics Inspection - Mr-Mathematics.com

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At the start of February my school had a full OFSTED inspection under the new framework. In this blog I will share my experience of the deep dive mathematics inspection as head of department. At around 4.30 pm the day we were told OFSTED were coming all the staff got together to find out the plan.

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The Golden Ratio Is Cool, but Could We Interest You in the Silver Ratio?

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The Golden Ratio Is Cool, but Could We Interest You in the Silver Ratio?

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Here’s how the math works. (And there’s more where that came from.)

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What we mean when we say "Anyone can do math"

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We need to unpack the phrase, and attendant phrases, that are so popular today, and that are in some ways so radical and unintuitive that we both believe and disbelieve them at the same time.

Anyone can do math

Everyone is a mathematician

You're good at math (and don't know it)

There's no such thing as a math person. Everyone can do math!

And so on. These are correctives, and important ones, to another, earlier set of problematic (and faulty) axioms, that assumed the world is divided up into "math people" and "I'm-not-a-math-person" people. There are multitudes who believe they can't do math when they suffer only from corrosive classroom experiences. But too unthinking an embrace of these taglines is problematic too.

The current excitement around growth mindset in classrooms around the world is meant, partly, to prevent math class from being a place where you get identified as a person who either has or doesn't have the "math gene" (another discredited concept), and sorted accordingly into the appropriate track. Then students who are fast and know their facts are fast-tracked into more challenging and interesting mathematics, while folks who are slower or don't have the facts down are placed in lower, slower tracks, and get the message that they don't belong in the subject.

And yet we have a way of overcorrecting. Growth mindset is effectively a positive and useful outlook, but right now there's a risk it gets overapplied (and under-understood) and becomes another educational fad that backfires in implementation.

When we say anyone can do math, what do we actually mean?

If we're saying that everyone is equally talented mathematically, then we're lying. And kids know this. You know it too. There are people who have unusual insights or abilities in mathematics. Some (e.g., Ramanujan, Nash, Turing, Johnson) get their own movies. And speaking of movies, that anyone can do math line has a counterpart in the movies, in Pixar's Ratatouille. There, the line is anyone can cook.

"Not everyone can become a great artist- but a great artist can come from anywhere"
Ego, from Ratatouille

Ego's parsing of the phrase anyone can cook is not obvious, and it's not really the primary meaning of the phrase. The truth is, there are really three meanings all wrapped up there: anyone can learn to have the joy and pleasure of cooking in their life, even if they don't become a master chef. Some people will get serious about it. And the visionaries who change the way we think about the art can come from anywhere - lock them out of the field and we all suffer.

This is what we have to mean when we insist that anyone can do math. For it to be more than an empty platitude, or a blatant falsehood, we have to be precise.

What does anyone can do math really mean?

Everyone is capable of mathematical literacy. In other words, everyone has the capacity to learn the foundational mathematics that allow them to understand and participate in our (increasingly data-heavy) world. Everyone is capable of doing arithmetic, understanding fractions, percents, basic algebra and graphing, basic probability and statistics, and should be able to read a graph in a newspaper or hear a statistic on the radio without getting flustered. They should know that they have the ability to understand the vast majority of the math that surrounds them in the world if they decide to put in the work. This means they should have the numeracy to participate as citizens in our society, and also to pursue the career path of their choice. (It is shocking how many people literally give up on their dreams because it requires them to take too many math courses.)

Everyone deserves to see some beautiful ideas of mathematics. Just like we send students on field trips to museums and have them read great poems and novels, part of their human inheritance is exposure to breathtaking mathematical ideas. (I've written about this extensively before, but if you feel like spending twenty minutes on a specific example, check out a 3blue1brown video, like this one on Hilbert Curves.) The fact that people respond with panic rather than wonder is a sign that we're doing something wrong.

A great mathematician can come from anywhere. We all have biases about what mathematicians are supposed to look like, and also what students who are "good at math" are supposed to look and act like. We need to teach like anyone and everyone in our classroom could have a gift for math that's about to manifest... because they just might, and we may never know unless they're given the opportunity.

This is what I mean when I say that anyone can do math. Not that everyone is equally talented (which is a lie), or equally interested in the subject (another lie). I used to say that Math for Love was dedicated to giving people a chance and a reason to fall in love with mathematics, but I know full well that not everyone will, which is fine.

What we should all be shooting for is a world where everyone is mathematically literate, and where fear or anxiety around mathematics doesn't prevent people from doing the things they dream of doing. Everyone should see some beautiful mathematical ideas and know what it feels like. And if we can do that, we'll also see great mathematical arising from all corners or our society and classrooms. Because there are kids who have a gift for or love of mathematics who we're not reaching yet.

Not everyone is equally gifted in mathematics. But there are reasons to teach like everyone could be.

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What we mean when we say "Anyone can do math"

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We need to unpack the phrase, and attendant phrases, that are so popular today, and that are in some ways so radical and unintuitive that we both believe and disbelieve them at the same time. Anyone can do math Everyone is a mathematician You're good at math (and don't know it) There's no such thing as a math person.

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Directory of all lessons

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On our shared area of teams

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Website

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We use cookies to help provide a better website experience for you, and help us to understand how people use our website. Our partners will also collect data and use cookies for ad personalisation and measurement.

Clicking "Accept" will allow us and our partners to use cookies, learn more in our cookie policy or to change your cookie preferences, click "Manage".

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Maths resources for teachers | White Rose Maths

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Find the free maths schemes and all related teaching resources for each of the year groups. View our Maths resources from White Rose Maths.

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Craig Barton now doing CPD!

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Welcome to Tips for Teachers - the site that helps you supercharge your teaching one idea at a time.

There are over 100 tips below, each available in audio and video.

But the fun does not stop there. You can also:

Order my Tips for Teachers book

Access on-demand or face-to-face Tips for Teachers CPD

Sign up for the free Tips for Teachers newsletter

Become a Patreon to get lots of lovely goodies

I really hope you find this site useful

Tips for Teachers - Top 5s

These collections of tips are all taken from my Tips for Teachers book

Habits and routines

Build habits, not one-off things - Harry Fletcher-Wood - audio - video

Willpower is overrated - Peps McCrea - video

Consistency before challenge - Peps McCrea - video

Be aware of the Valley of Latent Potential - Craig Barton - video

Don't just describe a routine, justify it - Craig Barton - video

Don't just introduce a routine, retrieve it - Craig Barton - video

Teach students what to do when they are stuck - Tom Bennett - audio - video

Beware the distraction addiction - Jamie Thom - audio - video

Interruptions leave a wake - Peps McCrea - video

Behaviour and relationships

Validate introverts - Jamie Thom - audio - video

Three reflections on behaviour in schools - Ollie Lovell and Craig Barton - video

Teach behaviour lesson one - Femi Adeniran - audio - video

Use the school behaviour policy - Tom Bennett - audio - video

Use non-verbal gestures for better behaviour management - Mark Roberts - audio - video

Students need to know you are in charge of the classroom - Tom Bennett - audio - video

Be clear and follow through - Charlie Burkitt - audio - video

Think creatively when attempting to improve engagement/performance of boys - Jon Mumford - audio - video

Enjoy the kids' company - Charlie Burkitt - audio - video

To develop resilience you need both high challenge and high support - Bradley Busch - audio - video

Teach students how to behave in a supply or cover lesson - Tom Bennett - audio - video

Teach students how to have the right equipment - Tom Bennett - audio - video

Make detention work fit the crime - Dylan Wiliam - audio - video

Ban mobile phones - Bradley Busch - audio - video

Some behaviours are more important than others - Kieran Mackle - audio - video

The means of participation

Checking for understanding

Be aware of student bias - Sarah Donarski - audio - video

Three reasons students don't know the answer - Ollie Lovell and Craig Barton - video

Check for understanding - Ollie Lovell - audio - video

Always build from what they know - Sarah Cottingham - audio - video

Always check for understanding - Clare Sealy - audio - video

No hints before a check for understanding - Ollie Lovell + Craig Barton - video

Planning the checks for understanding - Craig Latimir - video

Ask a question at the end of every lesson that every student should be able to get right - Daisy Christodoulou - audio - video

Planning the end of a lesson - Craig Latimir - video

Consider lengthening wait times to maximise retrieval - Bradley Busch - audio - video

How to ensure questioning involves all pupils - Jade Pearce - audio - video

The Tick Trick - Ollie Lovell and Craig Barton - video

Ask students to make a pre-topic mind map - Alex Quigley - audio - video

Use talk cubes to encourage students to contribute - Emma Turner - audio - video

Start with whoever got 8 out of 10 - Tom Sherrington - audio - video

Use Post-it notes to find out what they don't understand - Mark Roberts - audio - video

Play "Just a minute!" - Alex Quigley - audio - video

Provide explicit scaffolds for verbal responses - Tom Sherrington - audio - video

Pick the student least likely to know - Sammy Kempner - audio - video

Foster cross-class accountability - Tom Sherrington - audio - video

Trick your students to test if they really understand - Sammy Kempner - audio - video

Depressurise learning - Chris Such - audio - video

Responsive teaching

Don't forget the "respond" part of responsive teaching - Jo Morgan - audio - video

Planning responsive teaching - Craig Latimir - video

Modify your lessons as you go - Jake Gordon - audio - video

Responsive teaching: what to do when some students understand, and some don't - Craig Barton - video

Don't let "Don't know" be the end of the conversation - Dylan Wiliam - audio - video

End every conversation with the student saying something smart - Michael Pershan - audio - video

Rephrase to amaze - Mark Roberts - audio - video

Diagnostic Questions - the perfect exit ticket? - Craig Barton - video

How to design good multiple-choice questions - Kate Jones - audio - video

Share photos of students' work - Jake Gordon - audio - video

Planning lessons

The crucial role of curriculum - Ollie Lovell + Craig Barton - video

Lesson planning mistakes - Craig Latimir - video

Lesson planning principles - Craig Latimir - video

The first thing to think about - Craig Latimir - video

Make question planning part of lesson planning - Dylan Wiliam - audio - video

Focus on explanations, not resources - Femi Adeniran - audio - video

Plan sequences not lessons - Jemma Sherwood - audio - video

Backwards plan. ALWAYS backwards plan! - Ollie Lovell - audio - video

Be super clear about what you want children to learn - Clare Sealy - audio - video

Do less, but better - Harry Fletcher-Wood - audio - video

We should all be focussing on doing fewer things and greater depth - Mary Myatt - audio - video

Review every lesson plan in terms of what the student is thinking about - Daisy Christodoulou - audio - video

Plan for error - Emma Turner - audio - video

Take a low effort, high impact approach to task and question design - Kate Jones - audio - video

Teach what you mean to teach - Jemma Sherwood - audio - video

Focus on the concepts and the Big Ideas in our curriculum - Mary Myatt - audio - video

Learning doesn't start in Year 7 - Craig Latimir - audio - video

Examples and modelling

Beware the curse of knowledge - Sarah Cottingham - audio - video

Set out the big picture - Tom Sherrington - audio - video

We know more and remember more when we've heard it in a story - Mary Myatt - audio - video

Planning the exposition - Craig Latimir - video

Planning the modelling - Craig Latimir - video

Mind your modes - Peps McCrea - video

Question, don't tell - Sammy Kempner - audio - video

Use explicit instruction for novice learners - Jade Pearce - audio - video

Model techniques live - Jo Morgan - audio - video

Try teaching from anywhere in the room - Jake Gordon - audio - video

Begin your explanations as a series of questions that everyone can answer - Michael Pershan - audio - video

Use, where possible, dialogic teaching - Sarah Donarski - audio - video

Encourage students to say "stop!" if they are confused during an explanation - Emma Turner - audio - video

Avoid the Split-Attention Effect during worked examples - Craig Barton - video

What you say matters - Jemma Sherwood - audio - video

What you don't say matters - Jemma Sherwood - audio - video

Don't ask students to listen and read simultaneously - Craig Barton - video

Explicitly teach the skills an expert in your domain uses - Craig Latimir - audio - video

Use visual aids, including props and online tools to bring explanations alive - Jo Morgan - audio - video

Reduce clutter from everything students see and hear - Jake Gordon - audio - video

Beware of seductive details - Craig Barton - video

Use examples, not definitions, when teaching & assessing - Daisy Christodoulou - audio - video

Get used to asking "what if" after explaining something - Michael Pershan - audio - video

Provoke curiosity in our students - Mary Myatt - audio - video

Use related examples and non-examples to explain a concept - Craig Barton - video

Further thoughts on the Myth of Copying Things Down - Ollie Lovell and Craig Barton - video

Hone your public speaking - Jamie Thom - audio - video

Feign enthusiasm when necessary - Chris Such - audio - video

Student practice

Planning the practice phase - Craig Latimir - video

Teach in small chunks and fool kids into doing lots of work initially - Femi Adeniran - audio - video

Make sure students know whether they are right or wrong, and don't wait until it's too late - Jo Morgan - audio - video

Provide answers so pupils can check their work in real-time - Femi Adeniran - audio - video

Set occasional open-response tasks - Tom Sherrington - audio - video

Two frameworks for learner-generated examples - Craig Barton - video

Use SSDD Problems to improve students' practice - Craig Barton - video

How to help students avoid "silly" mistakes - Craig Barton - video

Memory and retrieval

Data and assessment

To make good use of data, compare to other subjects - Adam Boxer - audio - video

Know how to effectively assess - Sarah Donarski - audio - video

Stop talking about grades - Mark Roberts - audio - video

Homework

To make homework more effective, integrate it with classwork - Adam Boxer - audio - video

My favourite homework activity - Craig Barton - video

Rebrand homework as practice - David Goodwin - audio - video

Marking and feedback

Improving as a teacher

Observations and coaching

How to observe a lesson - Adam Boxer - audio - video

How to give a colleague feedback - Adam Boxer - audio - video

Diagnosis in coaching - Ollie Lovell and Craig Barton - video

Develop competing hypotheses when observing teaching and learning - Ollie Lovell and Craig Barton - video

Leadership and culture

Health and well-being

Maintain perspective - Harry Fletcher-Wood - audio - video

Remember the tortoise and the hare - Jamie Thom - audio - video

Tackle the negativity radio - Jamie Thom - audio - video

How to get better sleep - Ollie Lovell and Craig Barton - video

The secret to a happy life - Craig Latimir - audio - video

End the day on a positive - Ollie Lovell and Craig Barton - video

Maths, Maths, Maths!

Use the same questions, with different numbers - Sammy Kempner - audio - video

Use calculators with students from the earliest opportunity - Jo Morgan - audio - video

The power of a slideshow for teaching mathematics - Ollie Lovell and Craig Barton - video

Doing maths is not the same as teaching maths - Jemma Sherwood - audio - video

Practice, practice, practice...not until you can get it right but until you cannot get it wrong - Julia Smith - audio - video

It ain't what you do, it's the way that you do it...and that's what gets results - Julia Smith - audio - video

Fluency in the four operations is a cornerstone of developing mathematical understanding - Julia Smith - audio - video

How to deal with students who say they hate maths or are no good at maths - Julia Smith - audio - video

Reading, literacy and oracy

Micro-tips

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All the Tips for Teachers from the videos and podcasts in one place. Click on a tip to hear the podcast / watch the video!

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All subjects by key stage - Oak National Academy

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Free online lessons across a variety of UK school curriculum subjects

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Great practice, reverse fading and deeper questions

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Maths Teaching Resources | Dr Austin Maths

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Dr Austin Maths is a free-to-use Maths teaching resources website, focussing on quality resources for KS4 IGCSE and GCSE Maths.

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Spreadsheet

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Worksheets and more with excellent wb versions

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Maths for Primary and Secondary

Resources for students and teachers

Access hundreds of quizzes and other interactive activities that will help you enjoy and improve your maths whether you are at school or at home. There are thousands of carefully designed questions to improve maths knowledge and help develop fluency in important maths skills. These activities, developed for ks1 up to GCSE, have been helping students to better their target grades for more than ten years.

You can access the activities for free, but if you sign up for an account activities will be grouped together by topic and your scores for the interactive games and quizzes will be saved so that you can keep track of your progress.

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Popular with both teachers and students, the questions in these free maths resources are carefully crafted and include the answers. They are designed to help students to take the first steps in each topic, then strengthen and extend their knowledge and skills. The resources include revision questions for KS2 SATs and GCSE.

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User: TestValleyMaths
Password: TVSmaths1!

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Go Teach Maths: Handcrafted Resources for Maths Teachers

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Homepage - Go Teach Maths: Handcrafted Resources for Maths Teachers

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Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes.

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Provided by the British Army

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STEM challenge provided by the British Army

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Quizzes created by other teachers in Microsoft forms

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Amazing mathematical tasks. My new favourite go to resource for worksheets.

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Links from Craig Barton's book

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Links from Reflect, Expect, Check, Explain

Here you will find the links to all the sequences, diagrams and activities described in my book: Reflect, Expect, Check, Explain.

The best way to view an image in high-resolution is to right-click and select open image in new tab.
The best way to save an image is to right-click on it, select copy image, and then paste it into a PowerPoint, Word document, etc.

If you have not yet read the book, then it is available from Amazon or John Catt Educational
My other books, including How I wish I'd taught maths, can be found here

Contents

Many of the research papers quoted throughout the book and detailed in the References section can be accessed here

The easiest way to access the podcast episodes quoted in the text is to visit the Mr Barton Maths Podcast homepage

When running a workshop, the most common questions I am asked concern where I get my clicker and my PowerPoint egg-timer from. I am not sure what that says about the quality of my content. Anyway, here you go:

Logitech Spotlight clicker
PowerPoint egg timers

The five stage process for running Intelligent Practice sequences in the classroom:

The double-pause of questioning:

Student Prompts whilst they work on an Intelligent Practice sequence:

Two possible student templates for them to record their answers in:

My model of a Learning Episode:

The Atomisation process:

The five stages of the Example-Problem Pair process:

Your Turn prompts:

Student prompt cards for each stage of the Example-Problem Pair process:

Suzanne Stoppard kindly created and shared a Word version of these Prompt cards where all the cards are the same size and editable here

My process for asking Diagnostic Questions:

My Extension Prompts for Diagnostic Questions:

Prompts for student-generated sequences::

A structure for teacher trying sequences:

A structure for teacher writing their own sequences:

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Reflect, Expect, Check, Explain book links from Mr Barton

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Links from Reflect, Expect, Check, Explain Here you will find the links to all the sequences, diagrams and activities described in my book: Reflect, Expect, Check, Explain. The best way to view an image in high-resolution is to right-click and select open image in new tab.

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Teacherhead blog on 3 impactful strategies

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When I'm invited to support schools and colleges with CPD around teaching and learning - or I'm simply asked to nominate my favourite high-impact strategies - these three strategies are what usually come to mind as key areas to focus on. Cold Calling; Think Pair Share and Check for Understanding.

They work incredibly well in themselves and even better in combination - in my experience.

Where teachers have all three working really well, there are numerous benefits:

every student is involved in all questioning exchanges; everyone feels warmly invited to take part - it's inclusive and challenging at the same time.

every student can rehearse their thinking, engaging in generative recall and self-explanation, working out what they know and don't know; there's plenty of space for uncertainty and tentative first steps.

there's a depth to classroom exchanges, beyond the surface of short responses; we can get into the details.

the teacher gets good information about student learning for them to base dynamic decisions on during the lesson: it makes instructional teaching highly interactive and as responsive as it should be.

Before you cry 'common sense', 'obvious' or do your ' teachers do this already ' eye-roll, I'd just invite you to take a mental walk with me on my travels around schools. The truth is, it just isn't absolutely solid common practice for these things to be done really well - separately or in combination. It's actually very patchy - despite all the benefits that follow. Sometimes teachers don't do any of these things routinely... and it shows. So, I advocate these strategies because I see so much mileage in improving teachers' default practices in relatively straightforward ways.

Cold Calling

Essentially this means 'no hands up and no calling out'; the teacher chooses students to respond and establishes the routine that this could be anyone for any question. You ask everyone the question, pause, giving thinking time and then warmly invite someone to give their answer or share their thoughts.
(To the whole class): What are the main factors that made this a significant change?
Pause
Jonah... what were you thinking?
Then you engage with Jonah's response and, after a brief exchange, invite someone else to contribute. It keeps everyone involved, thinking; it stops some people dominating and it prevents the habit of opting out - that students develop in a hands-up classroom. In the right spirit, this a highly inclusive strategy - but it also embeds high expectations about engagement with the material in hand.

(If you don't like the name, you really just need to get over that - or call it something else. Don't let it be a barrier to actually doing it!)

Think Pair Share

On its own, Cold Calling isn't enough. Why? Mainly, it is because it is a sampling process - although everyone can be thinking about the questions, you only get to hear a few responses from a whole class; this means that not everyone gets the opportunity to rehearse their thinking out loud. It is just so powerful to enable everyone to have a chance to think their ideas through by sharing them with a talk partner. The process of verbalising your ideas tells you a lot about gaps in your own understanding - try it! Do you have the conceptual framework, the vocabulary, a way to put ideas into a sequence? Pair share provides everyone with this opportunity - in a little safe bubble of two where you may admit to uncertainty and doubt much more readily than you would alone. (I've written about this more extensively here.)

Where pair-share is rare, it's just so much harder for all students to express uncertainty; it's also more difficult to make sure everyone can rehearse using ideas, words, explanations. Some don't.. they never really fully explore ideas in detail and they mask their struggles. There needs to be some simple routines around it:

Everyone has a talk partner pre-established (especially important in a socially distanced space but important any time.)

The talk should have a goal; a focus -eg to list five advantages or to decide which of two options is better or to formulate a clear explanation of a concept as if for a younger student.

The talk should have a time limit; knowing how long you have helps to gauge the depth and intensity of the discussion.

Pairs should know they will be cold-called after their discussions - so that everyone knows they could be asked to share their ideas, no opting out.

Ideally you would circulate during pair talk. That will need to wait until classrooms return to normal but think-pair-share can still be a big part of a socially distanced classroom.

Check for Understanding

The final piece in the trio of ideas is Check for Understanding. This is important for numerous reasons - feeding in and out of Cold Calling and Think Pair Share. If teachers routinely sample students' understanding after any exchange, comparing answers and exploring differences, more students are rehearsing their thinking and the teacher gets a much better idea of how the learning is going. It takes numerous forms:

Michael, what did you understand from what Safiya was saying about the poem?

Samira.. I've explained the main points in the narrative.. let me check, what did you understand the main points to be?

John.. run through the instructions for the task for us.. what are we all going to do? (practical, activity, homework....)

Daisy - tell us what you understood was happening in the last chapter of the story?

Steph - let's have your version; how do can we work out this angle from the information in the diagram? And Melissa - what was Steph's method again? What could you do instead?

Check, check, check. Then compare and contrast. Can we learn from each other's responses?

These three strategies weave in and out of each other continually. Everyone is included. Everyone is connected . Everyone is thinking. Everyone is exploring their own schema looking for gaps, making links. Everyone is thinking. (Oops I said it twice.) And the teacher is getting a rich wash-back of feedback from the class: levels of fluency, knowledge gaps, insights into students' thought processes... It's dynamic, responsive, inclusive. This is great teaching.

In my experience each of these elements can require some work - a conscious choice on a teacher's part to change their habits: to cold call instead of taking hand up; to make pair-share a frequent, punchy, productive, disciplined thinking activity; to check for understanding instead of using the ineffective alternatives like ' is everyone ok yeah?'. It takes effort and real sustained intent to make these switches. Don't diminish the challenge this can present for some people; it's easier said than done. The pay-off is significant but it all starts with the determination to make the changes.

How's it going for you?

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Top Three! High-impact, inclusive questioning strategies.

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When I'm invited to support schools and colleges with CPD around teaching and learning - or I'm simply asked to nominate my favourite high-impact strategies - these three strategies are what usually come to mind as key areas to focus on. Cold Calling; Think Pair Share and Check for Understanding.

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Shortcut to links going through "Cold Call", "No opt out" etc

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You searched for cold call - Teach Like a Champion

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Popsicle Sticks and 'Hands Down' are not Cold Call: Key Differences & Why They Matter

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Teacherhead blog on how to do this

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It's very hard to change your practice. We're all so busy, very often it is difficult to create space to fully explore a set of ideas and to deliberately adapt our teaching routines to absorb something new. At the same time, we're often bombarded with initiatives and issues to address. It can be overwhelming. I've been thinking about the possibility of stripping down each initiative or development area to something very simple; one idea that captures the spirit of a wider set of strategies. This would be the thing where you could say if you do just one thing, do this. A Silver Arrow is one that you allow to penetrate your armour; it changes what you routinely do.

There isn't a definitive research-informed list; I'm presenting a set of ideas that I think make good Silver Arrow contenders based on my own teaching. You will have your own set of arrows that carry that message: if you do just one thing, do this. Here is mine:
1. Behaviour Management: Signal. Pause. Insist.
Effective classroom management is multi-faceted but if you can do this, you can do anything. A class is full of students talking - on entry or after an activity or discussion:

Signal: You give the agreed signal for attention

Pause: You wait, adopting an assertive stance and position in the room, scanning for eye contact;

Insist: You insist on full attention. Michael...Suki... I need you looking this way and listening. ....Thanks.

You now give the instruction or direction you want to give. You do not do anything until you have full attention; you expect it, you insist upon it, so it happens. Signal. Pause. Insist.

( A Bill Rogers Top 10 Behaviour Strategies)
2. Questioning: 'In your pairs, discuss' + dialogue
Instead of 'hands up', you ask students to discuss their answers in pairs for a short period and then you call individuals to respond, reporting back on their discussion. You then engage in a dialogue with the respondent, exchanging three or four responses to probe more deeply.

What were you saying in your pair? (Reporting back a rehearsed answer or state of confusion)

Why do you think that might be the right answer?

Can you link that to what James said earlier?

Does that happen all the time or just in this case? And so on.

( The Washing Hands of learning: Think, Pair, Share)
3. Literacy: 'Say it again properly'; saying it is a rehearsal for writing it.
The whole-school literacy strategy could be reduced to this: Every time students give a verbal answer and before they are asked to write anything, ask them to re-form their intial responses into well-constructed sentences using the key words and phrases you've discussed. Do it relentlessly, every time.

What does the graph tell us?

First attempt: It goes up.

Second attempt: The speed on impact increases as the mass of the trolley increases.

4. Marking and Feedback: Close the gap.
Think about all marking and feedback as a short plan of action. Once you regard marking as a plan for the feedback a student will act upon and nothing more, it helps to keep it in perspective and have more impact. Only give feedback at the level and frequency that it is practical to be acted upon. This needs to be linked to giving time for redrafting and for acting on feedback during lessons, as well as for homework - directed improvement and reflection time or DIRT.

Three related posts: Marking in Perspective; Close the Gap marking; Improving the basics
5. Straight teaching: Objectives, explain, model, practice, check
I find this a useful model; it helps to make sure you've taught something properly.

Objectives: You know exactly which ideas you want to explore. The more precise the better.

Explain: You walk through the ideas and explain them using models, analogies and examples.

Model: You show your students how to apply the learning to a question or problem, modelling the strategies.

Practice: Students now try a few problems themselves; they test out their understanding.

Check: You use a range of feedback strategies to find out how they got on, adjusting the next cycle accordingly. Importantly, you need to be ready to diverge; some student will get it and will want to move on; some will need more consolidation.

Objectives, Explain, Model, Practice, Check. Each step is important.

Great Lessons 6: Explaining Learning objectives vs Tasks
6. Assessment: Set lots of tests - formatively.
Repeat after me: Tests are good. Once you embrace this idea, your students will shoot forward. Tests help with recall, developing long-term memory and serve a great way to tell you how well you have taught something. Micro-tests, self-assessed tests, multiple choice tests and single question long-answer tests all help to flush out misconceptions, areas of weak understanding - and develop memory. Take time to go over them, making sure that students learn from their mistakes.

Formative use of summative tests.
7. Gifted and Able: Teach to the top:
There are lots of strategies, but the Silver Arrow is the disposition: A total philosophy of G&T. Use assessment data to identify your three highest performing students. Imagine that their parents are hawkish and demanding; they (rightly) expect nothing but the best for their children. Do everything in your power to make them love you because their children are stretched and engaged - always. If you do that, the thing is - everyone's a winner. You are a winner, the top-end students are winners and - here is the clincher - everyone in the class is a winner too. Teach to the Top and everyone benefits.
8. Homework as Guided Study: "You are not doing it for me; you are doing it for yourself"
That is one of my all-time favourite teacher-clichés. Homework is Guided Study. You are giving students the tools to learn to study independently. They are doing this for themselves and not for you. That helps to put all kinds of things into perspective: the nature of the tasks; the resources you provide and expectations in relation to marking. As well as questions for practice and consolidation, activities such as pre-learning, making notes and research are all valid, helpful homework tasks. Activities that link into the next lesson are useful too - everyone brings in work that forms the starting point for the lesson. The key thing is to make sure students have the tools they need once they leave your classroom.
Great teachers set great homework 9. Hard Work: 10 minutes of silence.
Learning does not flow from engagement; engagement flows from learning. That's a good message to hold on to. Sometimes, after a whole series of activities and discussions, you just need students to get on with some work on their own. 10 minutes of silence is a great way to create an atmosphere of hard-working, heads-down endeavour. It's almost a treat after all the noise of a classroom exchange. You are making hard work a positive experience by showing students how much progress they make in a short focused burst. Crucially, the silence has to be a warm, peaceful silence; not the silence of discipline and dread.
Pedagogy Postcard #4: Working in Silence 10. Creative Opportunities: for open-endedness, respond in any format
To mix things up a bit and to give students some scope for making decisions about their learning, I like the open-format response strategy. If you have done some research, explored some ideas or finished a topic, it can generate fantastic responses if you ask students to capture their learning in any format they like: an essay, a Powerpoint presentation, a website, a video, a booklet, a 3-D artefact - whatever they like. This leads to a lovely range of responses that can be shared in different ways. There's nothing worse than a class of Powerpoint to schlep through - but the open format method usually yields enough variety to make it possible to see everything.

Students can explore a range of creative ideas to communicate their learning, learning some technical media skills in the process. Often I find that students need reassurance - Am I allowed to make a website? Yes, of course! You need to make sure the content is given due weight - it needs to be a rigorous piece of work. It helps to show them last year's stunning exemplars.

Give them permission to do whatever they like - but ask them to dazzle you.

Please add your own Silver Arrows in the comments below....

Thanks to @EducatingMiss for creating this infographic summarising this post:

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10 Silver Arrows: Ideas to penetrate the armour of ingrained practice

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Silver Arrows? It's very hard to change your practice. We're all so busy, very often it is difficult to create space to fully explore a set of ideas and to deliberately adapt our teaching routines to absorb something new. At the same time, we're often bombarded with initiatives and issues to address.

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Teacherhead blog on Bill rogers

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Behaviour Management: A Bill Rogers Top 10

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Behaviour Management Strategies from Bill Rogers Without doubt the greatest personal challenge I’ve faced as a teacher was moving from the Sixth Form college in Wigan where I started teaching…

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Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.

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Hegarty replacement + more!

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DrFrostMaths provides an online learning platform, teaching resources, videos and a bank of exam questions, all for free.

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Fun fact: The number 163 is prime, which we can prove simply by showing that it is not divisible by 2, 3, 5, 7, or 11. (Of those prime factors, the only one that's a little tricky to check is 7, but I can see that since 140 + 21 = 161 is a multiple of 7, the number 163 is not.). By the way ... why don't I have to check prime factors greater than 11? Howie Hua gives a nice little video explanation.

First, indulge me while I give a little plug for my own playful math project, a series of free math songs on my YouTube channel called Tunes that Count. We just released a new song about powers of 2 called The Power of Powers. Check it out!

Now, check out the great things I found below. Some are perfect little nuggets for use in classrooms or homeschooling. I also found some great math-art project ideas. Enjoy!
INTERNATIONAL DAY OF MATHEMATICS
March 14 was Pi Day, of course, but according to UNESCO it is also the International Day of Mathematics. One of the activities that was organized was a mathematics cartoon contest. Children and adults from all over the world entered, and you can see some of the selected cartoons in this gallery. Since the cartoons have no words -- only visuals and mathematical symbols -- the gallery is a testament mathematics as a universal form of communication. Below is one of my favorite of the cartoons, submitted by two students from Colombia.
FRENCH WEEK OF MATHEMATICS
Speaking of playful math....The French Ministry of Education sponsors a "week of mathematics" each year with a different theme in which it encourages people to create and share playful mathematics activities. This year, the "week" of mathematics ran from March 6 to March 15 and had the theme "Mathématiques à la carte." The contribution shown below is a clever game of vector dominoes by Jeux 2 Maths. For more details and for more games see their website. (Many of the games are so visual that you don't need to read French to understand them.) If you want to see more ideas, search for the hashtag #SDM2023 on Twitter.
HAPPY PALINDROME DAY!
NCTM reminded us with a tweet that March 20, 2023 was a palindrome day! Naturally that raises questions. I wonder how special that is? Do we get only one per year? Do we get one every year?

PLAYFUL CLASSROOM MATH Math for Love
A recent post from Math for Love helps teachers out with resources to plan a Family Math Night at their school. In general, I love games and puzzles where the rules are simple but the math is not. This blog post offers a nice sample of such games and puzzles. The image below shows one puzzle type (The Broken Calculator), which I think would be perfect for 4th or 5th grade. In fact, I loved the idea so much I created my own version for a 5th grade decimal unit. (For example, how would you make 0.364 without the decimal point and without a 3, 6 or 4? Tricky!)

Denise Gaskin's Let's Play Math

Denise has been sharing free games and activities from her collection of playful books. One of her books is called "Thinking Thursday: A new math journaling prompt every week!" From this book Denise recently shared the prompt, "Pick a topic you have learned in math. Write two correct statements and one false statement. Trade with a friend. Can you find each other's fibs?"

Here's an example of a more targeted prompt: "Tell me two truths and a lie about the median of a set of 5 numbers." If you try it yourself, as I did below, you'll see it's not so easy to write these kinds of statements. Open-ended tasks like this are great for differentiation within a classroom because students will each challenge themselves at an appropriate level.

A. The median of 5 numbers is always a number in the set.

B. The median of 5 numbers is always greater than the smallest number in. the set.

C. The median of 5 numbers does not change if you add 10 to the largest number.

Reflections and Tangents: Thoughts on Math, Education, and Technology

The Reflections and Tangents blog has done a series of posts using what they call the "Same and Different inquiry routine." The idea is that you present students with two similar mathematical situations, and (as the name suggests) ask students to brainstorm how the situations are the same and how they are different. The March 3 blog post gives an example from calculus, but you could really adapt the structure of the activity to any grade level at all. For a middle school classroom, you might ask, for example, what is the same and what is different about 3 different sequences.
@Mathgarden
This recent tweet by Sunil Singh sort of blew my mind. He shows a textbook illustration that extends Pascal's triangle upwards to include Row - 1, Row -2, and Row -3. Why didn't I think of this before? Extending the triangle would make a wonderful, playful activity for middle schoolers. For older students, it broadens the application of the binomial theorem to include negative exponents.
PLAYFUL MATH PROJECTS, PUZZLES, AND GAMES FOR MATH CIRCLES Playful Bookbinding and Paperworks
This blog is by an artist (Paula Beardell Krieg) who explores mathematics visually. In a recent post she turns a circle theorem about inscribed right triangles into an art project. Notice the visual impact of this drawing: In spite of the complexity and asymmetry of the drawing, many of the lines Paula created intersect in what appears to be the center of the circle. The drawing invites you to wonder why!
Julia Robinson Mathematics Festival activities blog
The Julia Robinson Math Festival is always a good source of playful activities. Their new blog for activities that are not quite ready for prime time is a great find. The most recent post on Modular Origami with Sonobe Units is a rich activity that could keep a math circle busy and engaged for a few sessions. The origami squares become building blocks to create polyhedra, which can then be explored geometrically (exploring structures) and algebraically (exploring numerical patterns).

Early Family Math

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A math blog by Sian Zelbo for elementary and middle school. Emphasizes problem solving and mathematical reasoning.

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Inquiry Maths is a model of learning that encourages students to regulate their own activity while exploring a prompt (an equation, statement or diagram). Inquiries involve the class in questioning, conjecturing, generalising and proving and, when required, in listening to an explanation. In

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Similar to Variation Theory but with greater meta-cognition but not as substantial

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Posts about Completing the square written by berwickmaths

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Welcome to Goal Free Problems, a place to find and share goal free problems for use with pupils in class and revision

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NonExamples.com - Something that is not an example of a rule or definition already shown, used for a clearer explanation.

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User: testValley
Password: talentedCoach

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We believe that you have "Session cookies" disabled. You must enable these in order to access the eChalk subscription area.

If this is the first time you have seen this message, you may be able to correct this by closing all your web browser windows and tabs then reopening your web browser and revisiting our website.

To see our help section on how to enable cookies click here.

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Enter your login details to start using our mobile-friendly educational games, simulations and puzzles. We have over 1000 interactive resources all designed with a focus on learning through fun.

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Better than knowledge organisers (for maths anyway)

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About

Forget knowledge organisers, for the maths classroom it is all about Frayer Models!

Frayer Models are an excellent way to collate key notes and examples for pupils, to support in lesson work or retrieval quizzing.

​

All of the Frayer Models featured on the site download in Microsoft Word ™ and are fully editable to suit your classroom and your pupils.

Contact

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Frayer Models are a great resource for organising information for learners. Find lots of free maths Frayer models here.

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GCSE Maths Takeaway

GCSE maths revision resources have been sorted by topic and include the new GCSE specification.

Choose items from the menu that you feel you need to work on. Do the questions, use the videos if needed and mark your work. Once you feel you are ready, take the quiz. Aim to get full marks on the quiz questions and make sure you explain each answer (this will mean you are more likely to remember - which is the point of revision!) Have fun!

A special thank you to KESH maths, CorbettMaths and Mrbartonmaths for some of these resources.

Found this page useful? Please like/share by using the buttons below..

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GCSE maths revision resources have been sorted by topic and include the new GCSE specification. Choose items from the menu that you feel you need to work on. Do the questions, use the videos if needed and mark your work. Once you feel you are ready, take the quiz.

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Maths Gems resources

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Resourceaholic - free resources and ideas for teaching secondary school maths

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This website is my attempt to assemble a collection of high-quality, sequences of questions and examples using key principles from Variation Theory. By holding key features between questions and examples constant, together with the mathematical behaviour that I call Reflect, Expect, Check, Explain and the supporting role of the teacher, I believe we can help students better understand key mathematical ideas.

You can find out more about the site and the different types of sequences available by visiting the Introduction.

You can access all the sequences of questions and examples from the Topics menu above.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using these sequences effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the sequencers on the Variation Theory website are:

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Sequences and behaviour to enable mathematical thinking in the classroom - by Craig Barton @mrbartonmaths

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This SMILE collection contains eighteen resources of games, investigations, worksheets and practical activities supporting the teaching of shape and space.

The resources cover 3D, angle, angle properties, area and perimeter, circle measure, coordinates, combined transformations, drawing, measurement,...

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This SMILE collection contains eighteen resources of games, investigations, worksheets and practical activities supporting the teaching of shape and space. The resources cover 3D, angle, angle properties, area and perimeter, circle measure, coordinates, combined transformations, drawing, measurement,...

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In 2016, I attended #MathsConf7 in Leeds. The outcome? A to-do list longer than my arm as I intended to create a textbook of exercises of increasingly difficult questions to improve upon the standard…

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Rich Venn Diagram maths activities from Craig Barton @mrbartonmaths

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Personalised tuition for all, covering the whole of mathematics

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Almost 10 years after it started, the aim of this website remains the same: to get everybody enjoying their maths a bit more. Whether you are a teacher looking to plan a great series of lessons, or a student looking for some extra help with a topic, hopefully mrbartonmaths.com will have something fo…

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Do you enjoy thought-provoking questions? If so, this is the place for you.

These collections of activities are ideal for developing your subject knowledge and problem-solving skills.

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Collections of problems organised by topics found on the secondary school maths curriculum.

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Pearson Edexcel GCSE Maths Collection

Welcome to the Pearson Edexcel Diagnostic Question page!

These schemes cover Years 9, 10 and 11 (Higher and Foundation).

Make use of the questions in class, or set individual quizzes for homework. The questions are fantastic for whole class discussions, identifying key misconceptions and encouraging students to provide their reasons. See our series of In the Classroom videos for more on this.

We really hope you and your students find them useful.

To find out more about Pearson Edexcel's GCSE (9-1) Maths qualification, and all the accompanying free support material available, please click here.

Don't forget to register for the Maths Emporium. Email us at mathsemporium@pearson.com to be added to the mailing list.

To find out more about Pearson Edexcel GCSE (9-1) Maths resources, written specifically for GCSE (9-1) Maths, and take an innovative mastery approach to tackle the increase in demand, visit www.pearsonschools.co.uk/mathsgcseresources.

Once you are ready to get started, we first need to make sure that you've added students and teachers to Eedi. The fastest, most secure and easiest way to do this is to connect your school to Eedi using Wonde. This is a one-time task that connects your MIS to Eedi and means that students, teachers and classes will be automatically setup in Eedi and, if new students join your school or if some leave, those changes will be automatically reflected in Eedi. The whole process takes just a few minutes to complete. Super easy.

Disclaimer

You don't have to purchase any resources to deliver our qualification.

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Pearson Edexcel GCSE Maths Collection Welcome to the Pearson Edexcel Diagnostic Question page! These schemes cover Years 9, 10 and 11 (Higher and Foundation). Make use of the questions in class, or set individual quizzes for homework. The questions are fantastic for whole class discussions, identifying key misconceptions and encouraging students to provide their reasons.

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Visual 🤬 and quick activities.

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KS3 and KS4 secondary maths resources for every topic taught in Year 7, Year 8, Year 9, Year 10 and Year 11 all of which have been quality assured and hand picked by Craig Barton and the Tes Maths Panel, providing lesson presentations, activities, practice questions, homeworks and assessments

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Home Resources Games Portal Blog Contact

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SSDD stands for Same Surface, Different Depth. They are a special set of problems that may look the same at first glance, but require different mathematical ideas to solve them.

SSDD Problems have become one of my key strategies to use with my students to help them become better problem solvers.

You can search for different topics using the tags on the right-hand side (or below if using a mobile device), and you can find out more about SSDD Problems on this page.

My books

I have written two books about my use of these types of activities.

My 2020 book, Reflect, Expect, Check, Explain: Sequences and behaviour to enable mathematical thinking in the classroom, goes into detail about making the most of these activities in the classroom. You can order the book from Amazon, John Catt, or wherever you get your books.

My 2023 book, Tips for Teachers: 400+ ideas to improve your teaching, details my most recent thoughts on using SSDD Problems effectively. You can order the book from Amazon, John Catt, or wherever you get your books.

My online courses

I have an online course store which offers low-cost, high-quality CPD on-demand. Each course contains short videos, resources, research, activities and questions to reflect upon. The courses most suited to the questions on the SSDD Problems website are:

Supporting this website

I do not make any money from this website, so if you did want to support its future development - and hopefully learn more about the pedagogy underpinning these ideas - then I would be so grateful if you would consider:

Thanks so much for taking the time to read this - now go and enjoy the site!
Craig

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Same Surface, Different Deep Structure maths problems from Craig Barton @mrbartonmaths

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Used for GCSE Revision

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PixiMaths | Free Maths Teaching Resources | Homepage | Oakham

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Welcome to PixiMaths where you will find an assortment of resources as well as SOWs and assessments for the new 9-1 maths GCSE.

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Welcome to Corbettmaths! Home to 1000's of maths resources: Videos, Worksheets, 5-a-day, Revision Cards and much more.