There always seems to be a conversation about what should be in a knowledge retrieval session in a lesson in maths, and I am definitly on one side of the fence. If i ramble enough, maybe some insight will unscramble from my brain.

For me this is all linked to mixing up the daily review and the weekly and monthly review (step 1 and step 10 of  Barak Rosenshine’s principles in action). But it’s the purpose of these reviews that I feel are often lost. If I look at them each in turn then hopefully i can untangle the purpose and how to use them effectively.

The Daily review for me has two key purporses. To remind students what they were learning the previous lesson and to get it fresh in their mind so they can make links with today’s work, and allow the teacher to notice any misconceptions or knowledge gaps that need to be addressed before they can succeed with the current days work.

Let me go back to the series theme of this blog (when i remember to post). The previously on recap is a carefully chosen series of bit of information to give you the context, and to remind you of key facts that you may need to know.

This is genearlly what happened last episode but other key information (Katherine becoming free for example) from several episodes ago which is important for the context of this episode.

The weekly / Monthly review is totally different. This is more of a pub quiz, checking the learning and finding out what people know. I don’t mean that in a belittleing way. It’s important, and helpful to help retention of information and reinforcing to long term memory, as well as allowing a teacher to know where people’s gaps are and what hasn’t been retained and allowing reteaching or reframing.

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The problem I have is that combining them together may make things easier for a teacher, but it is not helping the cognative load of students. It would be like starting a an episode of vampire diaries telling you random unrealted facts about series 1. This may help you in the long term remember more about the key characters and stick in your memory, but it is going to confuse you in the next episode.

Planning my Knowledge Retrieval

Imagine I am teaching a lesson on addition of fractions. I think about my previous lesson (equivalency and simplification) and then I think about the key information that the students need for today’s lesson from prior learning (addition, multiplication, multiples, LCMs)

I also want to make sure that they understood the last topic on Percentage of an amount, to check it has gone into long term memory

Combined Knowledge Reterieval

I see this a fair bit. People do 5 questions on perentage of an amount and 5 questions on LCM and multiples. They have ticked their Rosenshine box of Daily and Monthly review and got it out of the way, so they can start the lesson To be fair, the more able students can probably cope with this, but the cognative load for some of our students is too much. We have gone through percentage of an amount, they have thought hard about what they did, they got some right, it is gone through by the teacher. They now have a lot of percentage of an amount facts and thought in their head and they think “the teacher must have told me this for a reason – it must be useful” So as we teach the lesson they are using some of their working memory thinking about percentage of an amount. Again, it is like being told an irrelivent fact in the “previously on” which you then keep thinking with be relevant so you make assumptions about it linking in and get confused on the plot.

The other issue is what does a teacher do if the class don’t understand the percentage of an amount work. Do they leave the students with the misunderstandings… in which case what was the point, they are just reinforcing these misconceptions or do they stop and teach it again. This means the students have a break in the flow of the fractions lessons to pick up earlier errors, again potential causing issues, and if students didn’t understand it the first time why would a non planned lesson be better?

I have real issues with this combined knoweldge retrieveal between short term and long term for this reason.

Splitting up your Retrieval

By having your knowledge retrieval at the start of the lesson focused on what students need to know, you are allowing them to hone in on the key information needed that lesson. It allowed the teacher to address the important misconceptions and if they need to spend the whole lessons reteaching these concepts it’s a natural flow with the curriculum sequencing still.

But, what about the weekly/monthly review? Is it not important?

No, of course it’s important. Knowing what your students haven’t absorbed, allowing for spaced practice to move it to their long term memory, being able to reteach and address misconceptions is important. But, for me the time to do this is at the end of a lesson. Plan to finish one lesson a week early. Have a knowledge recall quiz. Spend time going through the answers and spending that time looking at them. THe students will be in a routine… they can pack away their learning for the day and then mentally prepare for a quiz. If a large error is found and you realise that the class hasn’t understood a concept you can use this information to plan a lesson to address this at a suitable time.

So looking at my adding fractions example. I teach my lesson on adding fractions, i then pack away and have a knowledge retrieval quiz. I realise studnents are strugling with percentage of an amount – I go through the answers quickly but tell them not to worry, we will revisit. I then plan after i finish adding fractions we will have a recap lesson on percentage of an amount (and maybe link to fractions of an amount) to allow them to revisit.

Anyway – those are my thoughts anyway. I will leave you with a video that explains the musical themese for every wandavision episode – cos it’s really interesting.

Is this just another post about a teacher during the Covid-19 posting about what they’re doing during “remote teaching”. Probably. Actually, there is not real point to this post. But I haven’t written for 6 months and also am feeling a bit down about education (because of the situation we’re in at the moment)

Look, this is Season 6 of Buffy, where the bad guy has is 3 nerdy kids who seem to be able to use Zoom. . and when all my friends are posting on facebook about how they’re “home schooling” and then doing cooking and fun games and watching tv programmes – the rational person in me knows they are doing their best and working round difficult circumstances – but the frustrated teacher in me wants to throw something at the computer screen. And then I read twitter how people are doing loads of CPD, looking after children and delivering live lessons… or then others who are taking up new hobbies and not doing any work (seemingly) and I am in wall to wall meetings.

So, what am I doing. Like many Maths teachers I’m using Hegarty Maths. The problem is that my students don’t like engaging with it… they claim to struggle with the videos (but I know generally when they put them on, don’t take notes, and then have a go by guess work for the most part)

I am not a fan of homework. I think that homework shouldn’t be practicing skills, because if people practice skills wrong then you are building in misconceptions into your learning. I prefer knowlege based homeworks where they learn facts which they can bring to the lesson. A student who does 30 homework questions who isn’t going to want to go back and re-do them – and worse, they have practiced this skill wrong and you’ll have to do 60 right to be able to correct that (i’m better at chosing random numbers than cognative science). Hegarty Maths is good… becuase it tells you straight away if you’re wrong (or if you can’t round in the case of many of my students) . Which is great, it gets round this issue, but because i’ve never used it before and never really appreciated homework my students aren’t as well trained as working from home as they should be.

This also means that the student’s aren’t used to doing the videos, of watching a stranger (and they do hate people they don’t know speaking to them) tell them how to do maths. So what i’ve done is to work around that. I’ve probably made more work for myself, and I’m not sure that many of my students are engaging – but my bottom set year 10s (there are 6 of them in total and they are all awesome) but all but 1 have had a go, have messaged me and spoke to me about the work, have sent me maths gifs (which isn’t helpful, but it’s good connection). They may not learn a lot – but knowing that I care about their learning is probably just as important.

What I’m doing

A 20 minute video for every lesson. These started as an hour – but there’s no need. 20 minutes gives me a chance to do some knowlege retrieval, for them to hear my voice and to show breif notes. Then I complete the Hegarty task on paper as a visualiser. Basically, I’m modelling what I want them to do. My videos are not as good as Colin Hegarty’s – but they have one thing that his don’t. They have me doing it – and for many of my students who are feeling as long , that means a lot. The students can layout their books like mine, they can watch me do the work and then they can do it themselves. Since I’m mainly doing revision rather than new content, it also means the way I show them is the way they’re used to which jogs their memories about the way it is done – which helps. The doing the work, the tracking, the marking is all done via Hegarty. I put the work up on Google Classroom because show my homework (although good) has a dreadful way of showing the work. Great for normal times… shows them when it’s due, but unfortuantly, we want them to see when it was set – which it doesn’t do well… calendar view on a laptop works, but not on the app.

Look – this might be season 6. This might be the battle of the nerds, a laboured love affair between Spike and Buffy, no Angel (due to social isolation), but we have Dark Willow, we have Once More with Feeling and we have the realisation that Buffy may not have been in hell to come. So we need to learn lessons about our practice for when we go back. Especially since Season Seven has Faith and Caleb to look forward too.

How I will change my practice

I will probably use Google Classroom as standard. Not as a learning aid, but as a way to catalogue what i have taught, and to support people who are ill. To put copies of worksheet up there and keep a track of the work I set. Mainly because I shouldn’t need it – but if a student ins ill and off for a long time then having a resource that they are used to is key.

Most importantly I will use Hegarty properly. They will write out the questions in a book that I’ll look at – and I will be massively strict about making sure it’s done, to train them into workign through it. Because if we don’t train our students how to use these resources and allow them to see the benefit, then what’s the point. Will I use it for the work I’m doing in class – maybe. But probably I’ll use it for recapping previous work, to make sure that they are still remembering it properly rather than new content. new content isn’t best learnt at home, but allowing to reinforce prior knowlege and help memory of those skills is great.

Mainly though, I’m going to stop kicking myself that I’m doing a bad job at the moment. Stop judging others and comparing myself to them – and just do what I can do, for my students and for myself. It’s a bad season, but is that a reason to give up… or keep going and see what comes next.

That’s an exciting title, but I am having a bit of a break from curriculum thoughts for a bit. After an excellent days at Research Ed Northampton, my head is full of ideas I want to get down – but this is actually just a thought about my own practice.

I know that one of the issues in maths is that we (everyone – not teachers) are too concerned about answers. I know as a teacher I care about the process and the deeper understanding, but ask me a question in a CPD session and I’ll want to get the answer right first. There are loads of great things about this, and lots of correct answers is great for combatting maths anxiety. But – does it test understanding?

Anyway, I’m trying to change my own practice. I’m a good teacher, and I get good results but I am not sure I’m doing things right all the time. On some level hasn’t this bothered me becuase I get good results and the students I teach do well… but I want to do better. Anyway, I’m just writing here so I can record my thoughts – I don’t think anyone actually reads this other than me.

So, let’s take subtracting fractions with different denominators. I would have modelled how to do this and discussed the stages, and the layout I wanted. Asking questions for each step of my working.

What is the lowest common multiple of 3 and 5? 15

What do I multiply 3 by to get to 15? 5

What do I get if I multiply 1 by 5? 5

What do I multiply 5 by to get to 15? 3

What do I get if I multiply 2 by 5? 10

I’ve always done this nicely, with curly arrows between the fractions and layed out clearly. All modelled, with the students all being aware of the processes I use and the questions I ask myself. And it’s generally worked… but every time most students can replicate it – and often most of them can retain it. .. and some can

I want to get rid of the deminishing returns of their learning, and I know that’s how memory works, but if I can change my teaching so they’re not copying my method but they understand the method and can remind themselves then they can do it without being told by me.

Basically, I’ve turned me into an exam factory… and although I get good results I’m not happy with my teaching. I realise I’m opening myself up for judgement – but hey.

The other issue was when I ask students how to do it, they either can or can’t. The more able jump to the answer and any misconceptions (like cross multiplying and simplifying) are not picked up early enough by me. And ones that need the support say a number, or are walked through it and breate a sigh of relief knowing they are safe and can switch off.

Anyway, what I’m trying . (I’m not saying it’s better or perfect, but I’m a lot happier and it’s helpign for now. However, I won’t know if I students will get it into their long term memory more effectively until I give them time to forget. So, the key thing I’m trying is to get them to ask each other the questions as I go through.

So, I am modelling the questions with the first student. They work through it and tell me the answers, and then I do a new question on the board. I ask them to chose another student (or I chose for them if I want to select someone specific) and then I get them to ask the questions. I won’t let the other student say the answer too early, or miss out bits of learning. Once we have done that we chose another student and the new student asks the same questions. The students are gettign the questions right, because it is broken down and scaffolded for them.. but it’s coming from the students.

What I’m finding. The students are less worried about answering questions, because it is being broken down for them. I am focusing on do they know the process, not do they know the answer. The students are able to repeat the process and break down the problems better. Occasionally they get the questions wrong or the process wrong and we can talk about that… but I don’t have to worry about the answers being wrong (because if they are we can correct them but don’t have to discuss it – because we have dissucced the process)

I wonder how many Blogs are floating around the internet with one or two posts before updating regularly becomes consumed by the day to day business of teaching and learning takes over and they become ship wrecked, left stranded where a few passing strangers will see them and then leave them, forgotten.

It’s been quite busy for me, with house moving and getting my head round new job but I am back in the position to start thinking again. Not that my time has been wasted, I’ve been doing a lot of reading (and listening to the excellent Craig Barton podcast) ready to get my head round the first series of my maths curriculum. I’ve also done work with KS2 resources and materials to get my head round transition. On the other hand I haven’t unpacked all the boxes from my house nor fully reassembled IKEA furniture.

Series One: Addition and Subtraction

Series Overview. During this series I want to explore addition and subtraction, to introduce the characters that are needed for later serieses and to allow the audience to have a feel of the epic scale of the world which this series is set. I want it to build up, and somehow reach a finale where audience are excited about the next series (the one where we get to multiply as well)

Recurring Characters

In the olden days (so, about six months ago if I was writing a curriculum) I would have probably have taught discrete episodes. I would have made sure students knew place value, I would have done column addition and subtraction. I would have spoken about decimals. I would have taught about shapes and perimeter. And I would have had a lesson on rounding. There may also have a holiday special or two on the history of maths. But… they would have been no linkage. What I want to do is keep building on things. One reason for this is that the I want to reenforce the knowlege by makign students having to recall it and improving the retrieval strength of that information. But, I mainly want to get rid of that myth of “We’ve done this topic” and the idea that we can always expand on our prior learning.

The Setting for a lot of this series will be in Perimeter and Polygons, but also I want to have the use of different bases as a different setting… like Daenerys on the Dothraki Sea whilst the Perimeter is my Westeros. I want to talk about ordering, addition, subtraction, metric conversions, decimals. I want to show these in the practical sence each time looking at my perimeter in more detail, with more depth of knowlege – but then looking at how these skills are used in different bases and how these bases are/were used.

As I see it my series starts at place value and ends up looking at compound shapes, finding perimter and missing sides, with decimals and metric conversions – ready to look at area.

Place Value: Integers

Roman Numerals

Counting in other Bases

Rounding to 10s, 100s, Ones.

Metric Conversions

Addition and Subtraction of Integers

Addition and Subtraction in other bases

Perimeter of Polygons (Integers)

Place Value:  Decimals

Ordering Decimals

Addition and Subtraction of Decimals

Questions involving Money

Rounding to decimal places

Rounding to significant figures

Estimation

Perimeter of Polygons/Compound Shapes (Decimals)

I realise that is just a list of topics – the least helpful planning tool – but hopefully the progression can be seen where these topics are recapped throughout, with column addition and subtraction the key characters who are being used in different settings. I also like the links to future estimation by just hinting at it, like a sneak preview of a future character.

I’ve never watched Games of Thrones on TV… so I’ve been reading the books (or actually listening to the audiobooks) . It means i’m going through the excitment everyone else went through a while back. So apologies if this is influencing the way I describe maths at the moment .

At the weekend I had the privilege of going to CurriculumEd 2019, where I was inspired by such speakers as Christine Counsell, Sean Hartford, Claire Sealy, Mark Lehain and Tom Middlehurst.  The weekend solidified a load of the ideas on curriculum that had been going on in my head for the last year.  The title of the blog, S1 E1 Mathematics is my kind of tribute to Claire Sealy’s amazing talk on curriculum as a box set, and therefore my journey is really Series 1, Episode 1.  That’s obviously not true.  As a secondary teacher, by the time students get to us they are on about series 7, a lot of the major characters are established and they generally have an idea where the plot is going.  But S7 E1 didn’t have the same ring really.

Mainly, this blog is not preaching.  I do not know best, but I am eager to think and learn.  I have a load of ideas that may be right and may be wrong, but if I write them down then I can work out where my brain is going and it will inspire me to read more and learn from others.

I’ve been teaching since 2000, and spent a lot of that time involved in data and data systems. My thesis for my masters degree was as exciting as it sounds, “Implementing Data Analyisis systems in UK Secondary Schools.” I am pretty good at data too. I’ve worked as an Assistant Headteacher in several schools in that role and through it all I’ve come to an epifany. It’s pretty much pointless. There, I’ve said that data is pointless… or atleast whole school data is pointless.

What I’m saying is nothing new. What makes a difference is a good curriculum, high qualitily teaching and learning and then knowing your students. Whole school data analyisis is (to mix my metaphors) weighing the pig after the horse has bolted. I mean, it has its moments… and if you’ve got everything else right it’s a great tool. But the focus has to be on getting the curiculum right and creating a deeper understanding.

Why am I doing a blog? Why do I think I know better than other people? Well, that’s easy. I don’t. I have thought about this a lot personally, but I haven’t read a lot about it. I mean, I’ve done my reading and discussed it but not in the in depth levels I really need to. If I do a blog then that reminds me to read, to study and to think about what I’m doing. Do I expect other people to read this, maybe, but I doubt everyone will agree.

So, I guess the final part of this is what’s my big idea… the USP of this blog? Otherwise why would I bother. I think one of the big problems with many developments in maths are the fear that many people (including many SLTs) have of maths. I have heard it so many times (and said it myself), the … that won’t work in maths. Most of the time it’s not questioned. There isn’t the in-depth “Why won’t it work”. People just assume that maths cannot be taught like other subjects and we have some archaic laws that cannot be broken… because it has always been like that.

I’ve found that often, when you discuss maths with other maths teachers they are held back by the idea that things don’t work in maths, that we have too many discrete topics to get through, that we are a purely skills focused curriculum, that we don’t need literacy. This is where I talk about circles and half of the people in the room roll my eyes because they’ve heard it before.