I realise it’s not long since the last version of this list, but #mathscpdchat tonight is about bloggers so I thought I’d do an update. The following blogs are written by UK education bloggers who…]]>

I realise it’s not long since the last version of this list, but #mathscpdchat tonight is about bloggers so I thought I’d do an update.

The following blogs are written by UK education bloggers who are listed as having maths (or something including maths) as their subject. If any have been missed, please update the spreadsheet here. Obviously not all the blogs are actually about maths. Apologies that it won’t include any blogs I’ve discovered only since the main list of bloggers was last updated.

………Experimental Blog

…to the real.

@SPorterEdu

A Maths Teacher Writes

Adventure Time with D & Co.

Blog

Bodil’s blog

cavmaths

Christian Bokhove

David’s Denkarium

Emaths – Blog

f(maths)

FE Culture

Filling the pail

Flying Colours Maths

Frank Chalk

garethmetcalfe

GCSE Maths Stuff

Great Maths Teaching Ideas

iTeachMaths

joining up the maths

justmaths.co.uk/

Magical MathsMagical Maths

ManYana Ltd

MathedUp!

Mathematics, Learning and Technology

mathematicsandcoding

Maths Directory…

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I thought I understood A-level Maths until I started teaching it. As @magicalmaths tweeted the other day, we learn some of what we see or read and rather more of what we discuss or…]]>

I thought I understood A-level Maths until I started teaching it. As @magicalmaths tweeted the other day, we learn some of what we see or read and rather more of what we discuss or experience for ourselves, but none of it compares to how well we learn by teaching others. If you’re looking for the ideal training course to equip you to teach A-level Maths, you need to go back to the A-level Maths classroom, but this time stand at the front.

I was very proud of my own A-level results, but have become increasingly convinced that there is a yawning gulf between being able to get the best grade at A-level and being able to teach others to do so.

It’s now more than 5 years since I started teaching and the main difference between me now and NQT me (other than his gloriously unkempt facial hair and his lack of a wife…

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Although I took away many ideas, there is one in particular which I have incorporated into my teaching and this is what I would like to share with you today.

When pupils are working in groups, I explain at the start that I expect every member of the group (there are usually four) to be contributing, I expect them to communicate well with each other and I expect them to stay focused on the task.

At the end of the lesson, we count how many each group have and the pupils get rewarded in proportion to the number of counters (at first I used to just give rewards to the groups with the most counters, it depends on the class and the lesson). We have a ‘house point’ system at my school so I give out house points as a reward (they can buy chocolate in the reward shop for 10 house points so they love it!) and it seems to keep them on task.

I shared this idea at CPD at school and had really positive feedback from another teacher who tried it with a particularly chatty class – apparently it was the best lesson she’d had with them as they were eager for the counters so they stayed focused and worked hard. As it worked for her, I thought it might work for some of you

*This story can also be found at http://staffrm.io/@mrsmartinmaths*

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There are lots of times in a lesson where my pupils need to make the transition from working on a task to focusing on me.

Today, I overheard a conversation between my head of department and our newest PGCE student about the fact that before she said anything, she needed to get their attention and this was her first challenge upon which she would be judged (more so by the children than the observer!).

The list of options is long:

– Count down from five (especially effective if you supplement with visual finger counting down, also attempt to use vocal intonation to let them know the end is nigh!)

– Ask for attention (raising of voice may be needed)

– Raise your hand, hope to God they notice

– Turn the lights on and off

– Clap twice

– Ring a bell

– Blow a kazoo.

Well I’m pleased to say that I’ve found a method that I’m incredibly happy with and I thought I’d share it. I’d go so far as to say it’s my party trick which I’m desperate to show off when another adult is in the room.

In the first few lessons with my new classes, I train them to notice when I am standing in a particular spot. This spot happens to be the place I would naturally gravitate towards when I want their attention, by the board, at the front. “When I stand in this particular spot” I would say with great importance, “I expect you to look this way and listen”. At first, we’d practice in a comedy way so they’d be working on a task and I would walk towards the spot, the volume would go down, I’d smile at them and then divert my path at the last minute (very Simon Says). They kept an eye out for me and, sure enough, as soon as I stood firmly in the spot, they were looking towards me and listening.

How do they know I really want their attention? I stand up as tall as I can, concentrating on my posture and sweep the room with my eyes, focusing on those who haven’t yet noticed, hoping they’ll feel the glare (usually someone near them gives them a quick poke!).

My classes and I get on really well with this because I never use my voice to get their attention and I always praise them for refocusing quickly. It works for me in my school context where I do have the massive pleasure of working with wonderful kids. I’m not saying it’ll work in all contexts, but if you’ve never heard of it, at least now you have one more strategy to add to the lengthy list.

This blog post is taken from my story on http://staffrm.io/@mrsmartinmaths

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One of my concerns is that math in my classroom is not as inquiry based as I would like it to be. My students and I just began a unit on Geometry. I gave the…]]>

Lovely blog on an Inquiry Maths lesson. Innovative ways of getting pupils to reflect.

One of my concerns is that math in my classroom is not as inquiry based as I would like it to be. My students and I just began a unit on Geometry. I gave the pretest and for the most part, students had a spattering of knowledge and the test was completed with much hair pulling and cries of “Man! I KNOW this….but….I forgot!”. When we went over the paper, I could see a collective “aha” from the majority of the students as they started to dust off the vocabulary sitting at the back of their minds. So, what to do?

I did some scouring of the internet and came up with a couple of really interesting reads: Angle Measurement – An Opportunity for Equity, and Inquiry Maths: A Parallel Lines Inquiry.

After reading these articles, the next day my students and I sat with the pretest and…

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We’re not happy with the spiral approach. They ‘learn’ every year and many of them forget every year. Maybe not completely, but there are definitely backwards steps that are too big.

So we’re moving towards a ‘mastery’ scheme of work approach, as outlined by Bruno Reddy here. Here’s how Bruno’s post looks in my head.

There are so many things to think about and I *really* love a list so here’s what’s in my head at the moment.

- Teaching for deep understanding. We will need to teach in a more relational way than we currently do. Possibly more use of manipulables (as suggested by the Primary commentor on my previous post).
- Questions. Loads of them. We’ve decided we’re not going to be afraid of doing absolutely loads of practice (hence the title), so we’re going to need plenty of questions.
- Enrichment and connection making. We’re incredibly aware that there is a huge range of ability in year 7 when they join. This year, they went from a level 1 to a level 6 on entry. We’re a bit nervous about stretching the high ability (or, to be honest, we’re nervous about them getting bored and their parents complaining). However, we truly believe that they need the most solid of foundations if they are going to get a fantastic grade at A-Level maths (whilst we get plenty of excellent GCSE grades, the A-Level grades really sort them into the ones who ‘get it’ and the ones who ‘learnt how to do it’.
- Assessment. Our school expect us to assess once per half term and to report on this with a ‘green sheet’, on which we write their WWWs and EBIs for that assessment. Currently, we’re thinking an Alfie test might be the way forward so that the ‘green sheet’ will automatically be filled out for us and pupils can get instant feedback without huge loads of marking. This means we can focus our time on planning those relational lessons we’re going to have to get used to teaching. I’d be creating an assessment using past SATs questions based on the topics covered that half term. It’s not ideal as we’d rather move away from SATs but it feels like the best we’ve got for now and it should help us achieve what we want at the moment.
- Homeworks. We really like idea of the fortnightly 30 mark homeworks outlined in Mr Barton Maths’ blog on creating a new scheme of work. 20 marks from the current topic, 10 marks from all other topics, to remind pupils of previously learnt skills.
- Reporting (meeting the school requirements). We have to complete ISMs (reports) showing a pupils’ NC level four times during the school year. We’re going to have to think about this because, for now, our school is sticking with levels.
- SLT on board. This one is crucial, but will take some doing. We will no doubt get parental ‘inquiries’ about our new way of doing things, but we’re doing the right thing and if SLT support us, then we’ll be fine.

Wish us luck.

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In light of the changes to KS3 and KS4, and as a result of some feelings we’ve had, for some time, about the way we teach maths, it’s going to drastically change (I hope).

However, before that change takes place, I think it is worthwhile to stop and look at what we have right now: things that work, things that could work and things that didn’t work.

Here’s a snapshot of the first half term for year 9 – drum roll for the snazzy spreadsheet please…

Let me decipher it for you a little.

- We change topics every couple of weeks – because that’s what we’ve always done.
- School policy is to do a ‘green sheet’ assessment once per half term where we mark and give written feedback to pupils on a green WWW/EBI sheet (this should be revisited after three weeks to check progress). It didn’t work for us last year when we were doing end of topic tests and then moving on, so in this scheme of work I decided we would do a ‘cumulative’ assessment each time, so we could show progress on previous learning. Also, I wanted to regularly revisit previous topics in an attempt to stop pupils forgetting!
- FIG Friday: Functional, Inquiry or Groupwork. This is something I am proud of. One lesson per fortnight is either a lesson with a functional theme, or an Inquiry Maths lesson (see http://www.inquirymaths.com) or a groupwork lesson of some sort. It means that all our pupils get to do something a little different on a regular basis, even if that’s not their teacher’s normal style.
- Maths OD (here’s my display board)

A bit like 4OD, it’s Maths On Demand. Pupils write on a post-it note to tell the teacher which topics they’d like to ‘see again’ – they stick them on their TV and the teacher plans a lesson around the requests. Essentially, it gives pupils the chance to make decisions about what they revise and they respond well to the lessons because they asked for them! (Of course you don’t need the display, I just like the visual representation). - The ‘objectives’ hyperlink links to another tab in the spreadsheet containing a topic ticksheet that looks like this:
- At the start of the topic, we use them as a discussion point with pupils to see what they already know. When we nicked them from SJB (thank you SJB!) they had three columns which pupil would tick, cross or dash, one for before the topic, one for after and one for how many questions they got right in the test. We used it in that format for a year but it didn’t work for us. We changed it to RAG at the end of the topic and that seems to be ok.
- Resource sharing: we have a shared resources folder and I’ve just linked the folders to the SoW so it’s always up to date. We probably don’t share enough though, but what’s in the folders could do with a good sort!

So, that’s what we’ve got now. It’s been alright for a first attempt, but I’m looking for something a little more sophisticated for my next try. Maybe something a little less busy (a bit like this one by Bruno Reddy perhaps: http://www.mrbartonmaths.com/blog/writing-new-scheme-work-part-3-advice/). Definitely something that works smarter not harder.

I like this tweet from Andrew Blair…

I feel like this could apply equally to a scheme of work. Less to it and more in it… room to explore and master.

I’ll keep you posted…

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It was our second lesson together, ever, and we were multiplying and dividing by powers of 10. Together, we constructed a place value grid on the board and worked out that if you divide by 100, the numbers move to the right, two columns. During the utterly thrilling session of Multiplying & Dividing by Powers of Ten Bingo, I noticed that some pupils were moving the numbers in the opposite direction to what we had decided on.

Why?

They were so used to moving the decimal point that, when we had discussed what direction they go in when you multiply or divide, they applied the direction to the decimal point instead.

At that moment I thought to myself “am I doing the right thing?”.

This class will always find maths a challenge. They will take their linear foundation GCSE at the end of year 10 in order to give them an early bash at it, followed by a re-sit in November of year 11 and then again in June of year 11. I have two years to help them get to grips with the subject and, here’s the crucial bit, I have the opportunity to help them attempt to get a C in Maths.

Should I teach them that the decimal point stays put and the numbers move? Or should I teach them to move the decimal point?

This throws up a massive question over the way I decide to teach these pupils for the next two years. I know that I could teach a ‘certain’ way in order to train them to answer exam questions, but this will be purely instrumental, tricks, rules, methods to follow.

My instinct was to teach relationally, especially as I have two years with them (for the past couple of years I have got yr11 bottom set when they arrived in yr11, so only had one year with them). However, when I realised they were so used to moving the decimal point, I wondered whether I wasn’t just making their life harder by insisting on drawing out the place value grid.

Or can I have a combination? Can I teach them about multiplication and division using a place value grid and then finish off with a “now you know how it works, here’s a quick trick to make your life easier”?

This decimal point dilemma has really got me thinking. What do I want? Pupils with a relational understanding, although this may take longer to achieve and therefore slow down the pace with which we cover content, or pupils who can follow methods and rules who may be able to answer exam questions through training and therefore be more likely to get a C and, thus, more likely to have choices in life. (I am torn, by the way, between ‘helping pupils to get a C in order to improve their opportunities in life’ and ‘not devaluing a C grade by training pupils to achieve it through following rules when they may not really understand it’. Some may say those pupils do not deserve to pass maths, but others may say it is those pupils who need our help more than anyone.)

It makes me uncomfortable and I’m not sure what I want. I know I want to do the best I can for them, so I’ll focus on building their confidence in maths and building trust and rapport with the class. I think I’ll have to work out what is right for them and what is right for us.

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All year I have been using maths songs to help them remember important formulae, such as the circle song, the area of a trapezium song, my cube number song (that I made up when I was 13, what a cool kid!) and one they got me to make up on the spot about stratified sampling to help them remember the definition (I’ve started taking requests!).

So, when they saw Gettin Triggy Wit It, their immediate response was “Miss, that was so good, can we make one?”. In that moment, I had to make a quick decision.

1. They could just be wanting to ‘waste time’ in making a video instead of doing more trigonometry…

2. They really loved that maths video and we already do maths songs, they want to make something ABOUT MATHS that cool that they can be proud of.

So I said, “Yes, yes we can!”

Next lesson, we split into three groups in order to come up with lyrics for three songs. The first, Y=MX+C to the tune of YMCA, is finished, I’m just waiting for the last 2 parental permission notes to come in before we go global (youtube). The second, about Pythagoras to the tune of Do Wah Diddy, is in the editing stage and the third, Transformations to the Cha Cha Slide has lyrics but filming may not happen as it was a little sketchy.

In total, we spend four lessons making the videos, plus about four hours of my own time editing (that’s one video’s worth of editing so far). Was it a valuable use of class time? You could argue it both ways. It is true that they did not spend those lessons practising mathematical skills or learning new content. For me, though, a big part of teaching Maths is about rapport, between pupil and teacher and between pupil and subject. (So much so, that I wrote my PGCE final masters level essay on Teacher-Pupil Relationships and their effect on learning). I knew that the process of making a maths music video would have a massively positive effect on their view of maths (for the right reasons? Not sure).

The amount of time I spent editing the first video was massively appreciated by them and, when I showed the video in class, it received a round of applause from them, plus a sea of excited, proud and pretty chuffed faces.

Amazing maths? No. Worthwhile lesson? In my opinion… totally.You can now find our maths music videos at https://vimeo.com/mrsmartinmaths/videos or http://www.youtube.com/user/MrsMartinMaths/videos (the Vimeo link is the best quality).

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- Session 1: Codebreaking
- Session 2: Team Maths Challenge
- Session 3: Inquiry Maths

So, yesterday, I had an awesome day because I got to teach 3 double-lessons of inquiry maths to three different classes of pupils. At our school we have two parallel top sets, middle sets and bottom sets. Yesterday, the two parallel sets were combined to make two classes, each a mixture of pupils from each class. It was a great opportunity to teach some year 7 pupils that I do not get the chance to interact with on a daily basis.

Each group rotated around the 3 sessions, having a double lesson in each session.

The teachers running the sessions stayed with their activity, being the ‘experts’. I was the inquiry maths teacher, along with my Head of Department.

**How to choose the right prompt for the inquiry?**

Talking to Andrew Blair (creator of http://www.inquirymaths.com) confirmed what I already thought – the numberline inquiry was the best one to do with a class new to inquiry. However, as I have been doing inquiries with my top set all year, I had already done it with them, so we were forced to choose an alternative to use with the top set. I chose the parallel lines inquiry as I hadn’t done it before and it was incredibly open.

**Numberline inquiry**

The first class I had for this was the middle set year 7. As can often be the case with an inquiry (especially with a class new to inquiry), the start of the lesson felt a little lacking in pace – this is the first test for a new inquiry teacher as it can be tempting to start telling them what to do so that they are ‘doing something!’. I asked pupils for any comments or questions and they came up with the usual “the answer is always 2” and the not so obvious “why are the answers to the multiplications always even?” – fantastic!

As it was their first inquiry, I restricted them to choosing one of those two questions to inquire into as I felt those were the most mathematically valid. (NB I have, in the past, let pupils look into any question at all and this sometimes results in pupils doing something not very mathematical but has also resulted in pupils doing some great maths I wouldn’t have thought of – dilemma!)

**Highlights**** of the Numberline Inquiry**

One group decided to look into sequences and what happens if, rather than using the counting numbers, you go up in twos or threes, etc. Their findings are below:

For all pupils, they either practised something like multiplying negatives, decimals or long multiplication or thought about properties of sequences. Some groups Found that if they went up by 0.01 the difference was 0.002 and if they went up by 10 each time, the difference was 200. All fantastic stuff.

**Parallel Lines (or Straight Lines) Inquiry**

Pupils came up with questions and comments about the angles involved, the area of the ‘square’, whether or not it tessellated, the ratio of the lengths of the lines, how many lines there were and grid method multiplication. An interesting line of inquiry was to work out the bearings of the ‘paths’ that the lines traced out.

One group adapted the prompt by tilting a pair of lines and adding another transversal as below (described by Andrew Blair as a prompt to a guided rather than open inquiry, but the pupils came up with it themselves).

Although my top set were used to inquiry lessons, they found the straight lines inquiry much more challenging – perhaps because it is so open. I was disappointed that no-one thought about the equations of the lines and, if I were to do this inquiry again, I may consider running it around the time of a straight line graphs topic – although would this be me trying to engineer the outcome? Perhaps putting a co-ordinate grid behind it would have the same effect.

I struggle with the balance between allowing pupils the freedom and creativity to follow their own line of inquiry and guiding them towards mathematically valuable questions. Sometimes, they are unable to articulate exactly what it is they want to inquire into, so their questions seem uninteresting, but the maths that follows shows what they actually meant was something more sophisticated. On the other hand, it is depressing to watch a pupil come to a dead end whilst trying to answer a question which does not have an interesting answer.

I would argue that pupils ask better questions in the future if they are allowed the freedom learn from their mistakes. However, it is tough to justify the classroom time as I want them to be doing interesting maths as much as possible, so I have increasingly guided the class as to which questions to choose from. It’s a difficult one and I don’t have the answer.

What I do know, is that I thoroughly enjoyed the day and feedback from students suggest that they did too. I will end with a quote from a middle set year 7 girl: “Doing inquiry maths was the best maths lesson I ever had because it taught me how to think”.

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