Archive for the ‘Conferences’ Category

L3 Mathematical Studies AQA

1 Year or 2 Years?

On Thursday I hosted a Virtual Community for AQA on Developing the Teaching of L3 Mathematical Studies, concentrating on the 2A option. (Unfortunately 15 minutes in, the tech company hosting the platform had a fire alarm and we were stuck on a chat screen, so 45 minutes were spent type chatting to the delegates, having a general chat about the course – the VC will be rescheduled, hopefully for early December. Really looking forward to connecting to other teachers again).

However, we had managed to get to the part where we discussed advantages and disadvantages of the 1 year or 2 year course. We currently run it as 2 years, but I’m looking to change to a one year course with more lessons per week, as we’ve finished all the teaching and it’s a long time to keep enthusiasm for revision from November until May! The contributions from everyone at the VC were very valuable, and having seen other teachers query this, would like to share here. I’ve anonymised the comments, but haven’t edited any of them. From the poll, most teachers in the VC taught over 1 year, hence the imbalance of comments!

Question: What have you found the advantages of 1 year course?  

I don’t know. I only joined the school in September and there was no other option.  

Level 3 results available when doing UCAS, 

Students can focus on other A levels in year 13 

Students who study psychology but gained a 4 in maths. Pupils are more likely to engage with a 1 year course. 

Only funded for 1 year 

Doesn’t clash with other A’Level exams 

Great to have the extra qualification 

We have a mixture of Y12 and Y13 students, including those who did not do well enough with A level in Y12.  

The real life applications have been invaluable to students  

Students studying psychology have a pre requisite of Core Maths if they do not achieve a grade 6 or above at GCSE so helpful for that 

Financial maths is invaluable preparation for uni 

I’m actually delivering as CPD to other members of staff so the advantage for doing it over 1 year is that they’re able to get it ‘under the belt’ quicker 

Can be useful if students are dropping from 3 A’Levels to 2 or are resitting a year but keeping one of their original ones to fill in time on timetable 

Doesn’t interfere with the pressure on Students in Year 13. Students find the financial maths both interesting and very helpful. 

Question: What have you found the disadvantages of 1 year course?  

The exam is set too early (mid May) so less time to revise 

Lots of content to get through 

Fitting everything in can be a challenge 

Time 

Time pressure 

Getting everything done in time, not alot of time to review learning  

Not enough time 

Why did they move the exams back to May? Last summer they were in June. 

Agreed. Time is a bit tight, especially as I’m in a UTC where we lose lessons here and there for things like careers related days. 

Exams have usually been late May, they were only pushed back because of lost learning time due to covid, This mirrors the previous Use of Maths AS Level which it replaced. 

Question: What have you found the advantages of 2 year course?  

More time in teaching 

Extra exam paper practice 

I teach Deaf children and they need a lot of help understanding the vocabulary. 2 years allow me to take time to cover the langauge as well as the maths.  

Question: What have you found the disadvantages of 2 year course?  

Very thin content wise 

Difficult to plan 

Not knowing how long it takes to teach each part of the content 

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Conferences, Core Maths

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Mathsconf21

Hopefully this will be a short but informative post! MathsConf21 – my aim was to present but with moving to a new school and going full time I chickened out. But I did get to go to 5 very informative workshops which I can share all about.

Thanks, as always, go to Mark McCourt and his team at La Salle for allowing this affordable and relevant CPD to happen, and to all the amazing teachers who give up their Saturdays to help each other. This is the true meaning of a community. And where La Salle never fail to deliver, this time they outdid even themselves. A big announcement was on the cards, and oh wasn’t it big!  Here’s the link: autograph

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I am quite excited about learning how to use Autograph properly and sharing especially with my Year 12 students.

There were 5 workshops throughout the day I attended. Rather than write about them, this time I’m going to upload my sketch notes, inspired by the amazing @olicav and @MrsHawthorne maths. These are available as a pdf download here.

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I enjoyed being able to bring another puzzle to the tweet up at lunchtime. This conference it was @mathequalslove link to the Fisher maths puzzle Crazy 8s (here) which both exasperated and delighted some willing folks! We will be starting a puzzle club at our school soon and I’m sure the students will get loads of fun, and build lots of resilience, from some of Sarah’s puzzles she shares.

And finally mathsconf wouldn’t be the same without the opportunity to meet up with some lovely Twitter friends the evening before and during the day, and meeting new people as well. As always, a brilliant day – hopefully see you at the next one!

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Conferences

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ResearchEd Rugby 2019

IMG_8415Another Saturday in June and another education conference, and another gorgeous setting, this time in Rugby.  The stairs are important – they’re the two spiral flights we went up and down to get to the maths room.  Most times when I go to a conference, my exercise is considerably lacking on that day, but ResearchEd Rugby even managed to account for step rate too!  There was a good maths line up, which is where I spent most of the day, but I did venture out to a couple of other sessions, so I’ll start with the one I was most excited to go to, and come onto the maths afterwards. (As always, apologies if I’ve misinterpreted anything, or just got it wrong).

Oliver Caviglioli

I first heard of dual coding from Peps McCrea, @PepsMccrea, a couple of years ago at the Maths and Science ResearchEd in Oxford.  My takeaway then was within powerpoint presentations, and that the brain couldn’t process written text and speech at the same time, so it is better to have a visual on the presentation to go with the speech.  This made complete sense, and since then, I’m much more aware in CPD sessions when there’s a large amount of text on the presentation, that I cannot read it whilst trying to listen properly to what is being said.

Last year I prepared some revision powerpoints for our year 10 form tutors, and dual coding came into play in two forms.  Firstly, as a revision technique from the LearningScientists.org, as one of the six strategies for effective learning, but secondly in the design of the powerpoint.  Similar, when I prepared CPD at the start of the school year about the challenges faced with reading and the new GCSEs, I was very conscience of dual coding, and tried to make the presentation as visual based as possible.

But now was the chance to hear from the expert, and as I tweeted, @olicav did not disappoint.  Oliver’s session was very practical based, in that he presented two problems and a solution, with audience participation!  I therefore didn’t write much in notes, but then Oliver has a very comprehensive website, olicav.com, where all his diagrams he presented are available (the quote below was also downloaded from there).  Spoiler alert though, the summing up for me was:

OliCac John Sweller Quote

  • Speech and text is linear
  • Schema isn’t linear – we think in diagrams
  • Text by itself has a computational inefficiency
  • Visual and text are separate but associated, and using both together gives double the chance to process and remember (John Sweller’s dual mode presentation)

The example that Oliver used for the computational inefficiency of text greatly resonates with me for some of those longer maths questions where there is so much information to pick apart.  I’m already very much a fan of a diagram or picture, but maybe I need to consider raising the importance of this earlier on for students, even spend time just trying to turn questions into diagrams as an exercise in itself.

The final part was our participation in a recount and redraw exercise.  Oliver (as the teacher) modelled, via a mind map diagram, and explained, via speech, a history of Corsica.  We, as the student, copied the diagram as Oliver was explaining it.  The student then recounts the diagram to a peer, tracing the elements and elaborating on what they have written as they go.  Finally, the student redraws the diagram from memory, noting that the retrieval practice would be even more effective if the student did this again a day later and a month later.

Mark Lehain

First of all, Mark is an absolute gentleman, and was very kind in giving his time after the presentation! Mark, @lehain, was talking about behaviour, and from the point of view of a Head Teacher, how teachers can help SLT.  Some highlights that I took from Mark were:

  • Parents and teachers for excellence – a group that believes that every school child should have an excellent education, and that the key characteristics of those schools that deliver this are excellent behaviour, a challenging curriculum, rigorous testing and enriching extra-curricular activities.
  • Recommending Tom Bennet’s Creating a Culture, and in particular the 8 principles of designing a culture.
  • Differences of opinion between SLT and teachers may be there because of different experiences, different values or different analyses of situations.
  • If you asked “What is the point of education”, there would be different responses.  So if we can’t agree on the why, then we’re probably not going to agree on the how.  However, we need to disagree well (we’re all a team, working together for the students, and we all have feelings).

The point about disagreeing well particularly resonated for me in the way some educationalists respond on Twitter.  I think I would respond so much more if we could all disagree well (or maybe I just need to be 10% braver)!

Don Steward

Now the maths bit! I love Don Steward’s resources.  They are so thoughtful of the maths, the connections and the applications, so it’s a real pleasure to explore some maths with Don.  Don took one of the Edexcel ratio questions from this year as a starting point to explore ratio.  The question involved a ratio of counters, which when other counters (of both types) were added, the ratio changed.  This was a lovely practical session, where it’s just great to have some time to explore some maths.  We looked at the different methods to solve this question, and the links between.  A snapshot of the session includes:

  • Establishing what a ratio is (and it being ok to ask students the obvious questions)
  • Using scaling to answer the question (testing it out with values and seeing what works)
  • Introducing a multiplier to a ratio when introducing ratio (so 4:3 would be 4k:3k) and therefore allowing an algebraic solution
  • Graphing ratios and linking to vectors to move from one graph to another – this developed could be developed into a vector method to solve the problem, and also links to a simultaneous equation method
  • Developing the question to find the possible number of counters added to change the ratio, which led to sequences and nth term
  • The work of Van Hiele, the avoidance of fractions and the proportion matrix
  • The ICAAMS project, where year 8 students were given 2 questions, which both use the same method, but had a large variance in success rate.IMG_8390

I’ve been teaching proportion with year 8s this week, and a started using Don’s resource on proportion boxes, as I wanted students to be able to understand that proportion was a multiplicative relationship, and that relationship can go either way.  So I’m going to give these two questions to my year 8s and hope that the work we’ve done will make some difference to their success rate with the first question compared to the second.

Jo Morgan

It is always a pleasure to listen to Jo, @mathsjem, on whatever topic she is talking about, because you can guarantee that she knows that topic in depth before she presents it. Jo also gives some great nuggets of practice or exploration and takeaways, which again her multiplication session delivered brilliantly.  Highlights:

  • A method for any single digit multiplication greater than 5×5 (and a chance to prove why it works).
  • Jo’s thoughts on why timetables fluency is important (and I completely agree that although we can and do teach students how to work out timetables without having to know them off by heart, this is no good when the reverse is required, eg for simplifying fractions or factorising).
  • A review of different multiplication methods from Smile’s “Multiplication makes sense” and an explanation as to why the Russian Peasant Method works.
  • A presentation on the column method, and an argument against each of the reasons given for it to be a “formal written method”.  This was not having a go at the column method, just the reasoning given at the time.

Thanks Jo!

Tom Francombe

I hadn’t heard Tom speak before, but I am more than familiar with his book, Practising Mathematics, that I have open on my desk at home pretty much constantly!  As Naveen, being a victim of the train problems, was unable to make her session later on, Tom stepped in and did two sessions.  Part one was more about the theory, whereas part two was a chance to try some practice.

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Who knew there were so many types of practice? Although Tom started with deliberate practice, he explained how really this is unfeasible in the classroom, as it involves immediate feedback on mistakes and altering the practice in light of this.  So his talk was more about purposeful practice, an in-between of naive practice and deliberate practice.

Tom talked about fade feedback, which I hadn’t heard of as a term before, but in practice are techniques that I do use in the classroom.  As the term suggests, fade feedback reduces the level of feedback that a student receives when solving problems, but based on how the problem is prevented.  So the structure could look like the following:

  • Initially give the answers, in “show that…” style questions
  • Then have answers available to match
  • Structure questions so the answers have some sort of commonality (Don’s resources have some good examples of this)
  • No answers available.

Tom also spoke about organising practice, comparing blocked practice and interleaving, and within the interleaving, either mixing different questions (such as multiplying fractions and finding areas of kites), or mixing topics within the question (finding areas of kites with lengths as fractions). This is an important area of contemplation for me at the moment.  I use spaced practice in my BBQ starters for KS4, and my homework and quizzes for KS3, but I don’t interleave in “main” classwork, unless it’s part of revision.  Yet, as Tom pointed out, in maths we have to choose our strategies before we use them, which is not addressed in blocked practice.  This isn’t to say blocked practice doesn’t have a place, and Tom emphasised that with first learning, blocked practice would be more suitable.  This is definitely an area I need to think more on!

IMG_8409When presenting some of the possible ideas of practice tasks, Tom’s purpose was to find tasks that can develop fluency, but also allow for mathematical reasoning. He indicated that the research said that these tasks were as effective as straight forward exercise tasks, but they can be more motivating and enriching. IMG_8416We had a go at a few of these; this Pythagoras task adds another dimension to your normal “square, square, add or subtract, square root” type questions, and the multiplication task (which I’ve used before) gave us chance to explore some reasoning.

Pete Mattock

The great thing about attending one of Pete’s session (as well as his presentation) is that we get to play!  This time, Pete, @MrMattock, brought his algebra tiles along.  I’m very much a newbie with manipulative, only really having access to multilink cubes.  I did make my own +1/-1 counters this year for teaching negative numbers, which I loved using!

However, Pete’s session wasn’t actually about manipulative, they were just a bonus.  Pete was talking about the concepts of Teaching for Mastery (as described by the NCETM), Rosenshine’s Principles of Instruction and Sweller’s work on Cognitive Load Theory. Pete suggested that rather than look at them as three separate entities, we can find the overlaps between them, as then we’d be looking at the overlaps between high performing jurisdictions (Teaching for Mastery), high performing teachers (Rosenshine’s Principles of Instruction) and how the memory works (Cognitive Science).

I made the mistake here of listening and doing so much, that I didn’t write any notes! Pete gave some lovely examples of how these three concepts (is that the right word to describe them?) are used together, but I don’t trust myself to recall these accurately enough to describe (sorry Pete!).

 

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Conferences

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MathsConf15 Takeaways

With exam marking starting, I’ve only got chance for a quick blog about MathsConf15, mainly giving me a chance to organise my thoughts, but if anyone else can take something away then that is a bonus!  No Friday night socialising for me this time, which meant not much chance to catch up with the lovely folks I’ve got to know during mathsconfs.  So I’ll dive straight in!

Workshop 1 – Core Skills: Defining the basics

Ben Rapley took us on a a tour of how they have included a focus on improving core skills alongside their scheme of work in his department.  Through departmental discussions, they selected 7 key topics that are essential, and regularly used in multistep problems: Fractions, decimals, percentages, ratio, negative numbers, brackets and equations (this was stage 2; stage 1 topics were: addition, subtraction, multiplication, division, number properties, place value and collection like terms).

Already, I’m liking this workshop! I’m currently working on building more number sense into our scheme of learning from year 7, and the stage 1 topics, except for collecting like terms, were pretty much the same as what I had!

Ben’s department created a core skills development ladder for each of the 7 topics.  Looking at brackets on our table, you realise how quickly the ladder could be enormous! But as Ben said, these are organic creations which change as you use and need to tweak them.img_4380.jpg

The next part was about the assessments.  For Ben’s department, they do 1 assessment per half term, and everyone on stage 2 (from year 7 to 11) do the same assessment.  This is an interesting idea, and the question was asked about motivation for some students who may score poorly on it.

The assessment lasts 1 and a half hours and has 15-20 questions per topic – a question for each sub-part of the ladder.  The 2nd half of the lesson is self-assessment, and here Dylan William’s quote about the research comes into play, where students that self-assessed progressed more than those that peer assessed or had their work teach assessed.  The next lesson was feedback, often whole class verbal and modelling target questions.  Every lesson after that had starters related to the targets.

The assessment set up is a big step away from ‘normal’ termly assessments, being one mark per skill, and total fluency without context or multisteps.  The big takeaway for me here though, is the excel spreadsheet used to generate the questions!  I need to do a bit of work, but currently I have weekly quizzes for years 7 and 9 (I don’t currently teach 8) and daily starters for year 10, which if I could press F9 and do some of the amazing things the spreadsheet does, then it would be such a time saver!!!  I was almost drooling when Ben explained that you choose your click on the questions and they appear in a worksheet, which could also be changed to a project view.  Might be watching a few ‘Excel how to’ videos over the holidays.

Ben finished with talking about interleaving the core skills throughout the scheme of work; again something that I am looking at with the number sense work for Year 7, with the example of using fractions when calculating perimeter or area.  This is something I also want to think more about within my teaching, so that it’s not just the weekly quizzes or daily starters that cover topics taught, but they’re intertwined throughout future learning.

Workshop 2 – Procedures are not the enemy

I hadn’t realised when I went to Andy Elwell’s  workshop that he was the creator of Method Maths.  I hadn’t come across it before this year, but have been very impressed with how the year 11 were using it to practise, practise, practise this year!

Andy started with a tour of how multiplication is taught from year 1 to year 6.  The stand out point of this was the journey from concrete, with lots of manipulative, to more abstract (ie just written) in Year 6.  Andy then demonstrated the number of steps needed to complete a column method multiplication, compared to the lattice method. img_4403.jpg
The immediate murmuring was about how the lattice method does not help students understand the place value in multiplication and it was just learning a procedure.  However, Andy was ready for this, and showed a neat justification of why the lattice method works, by rotating a multiplication grid.  The question to consider is, why don’t we let students use easier methods, as long as we keep it conceptually connected justifiying why they work?  So my first takeaway – should we teach our year 7s the lattice method when they arrive, alongside why it works?

img_4406.jpgThe next idea was a game changer for Andy, and I love it!  I wouldn’t even call it a procedure, but more making Pythagoras’ Theorem a bit more concrete, rather than the abstract algebra workings.  I (and I’m sure many do) introduce Pythagoras looking at the square of the sides of the right angled triangle.  Well why not draw squares next to each side and put the square value in?

We were now starting to get, on what Andy believed to be, more controversial ground.  The DM method!  And I’d agree, if it was introduced as a process with no understanding, it would be controversial.  So what is it?!  img_4408.jpgThe DM method is basically a procedure to use for any maths that can be set up in proportional grids  From ratios, to map scales, equivalent fractions to even inverse proportion.
And all it is is “divide, multiply”.  But of course there is a justification – dividing establishes scale factor and multiplying applies the scale factor.  This is definitely something that I want to explore.

The final idea we unfortunately didn’t get to explore as much as was possible in the workshop, but again is something I’d like to revisit, even if just for my interest.  Andy has stopped starting trigonometry with SOHCAHTOA, but introducing trig using the Sine Rule.

Plenary Session – From Fermat to The Simpsons

How amazing to have Simon Singh, mathematician (background is mainly Physics), author, and one of the writers of The Simpsons to deliver a midday plenary session.  Simon talked to us about some of his books: The Bible Code (and how for every prediction found in the Bible Code, one is also found in The Moby Dick Code!); Fermat’s Last Theorem; The Simpsons and their Mathematical Secrets (which I’ve read and enjoyed).  It was a pleasure just to listen to Simon and his enthusiasm about his work.

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Simon also mentioned some of the maths projects that he’s running for schools.  For post 16s there is “Who wants to be a mathematician” – more can be found at http://goodthinkingsociety.org; and for KS4 Top-Top Set and Parallel https://parallel.org.uk, which is well worth an investigation.

Workshop 3 – Problem Solving

Claire took us on a tour of problem solving and some of the research around it. sh65me8yrwcl6bnvdk4mw.jpgShe looked at some of the definitions that have been given about problem solving and shared what what I thought was a great summary: challenging for individual learners; involves a strategy for solving that is not immediate or obvious and involve independent thought and creativity.  Problem solving is another of my projects in our department, as we develop our SHAPED problem solving (taking the SHAPED genius of my HOD to implement it effectively to improve problem solving – hopefully more on this to come).

Claire looked at the why of problem solving and what we have to consider when problem solving with out students – some really useful considerations: cognitive load of the students; surface and deep structures (I really like the idea of trying to sort problems into similar groups, where there are multiple groups possible); growth mindset; generic problem solving skills (and whether there are any??!! but also identified the work of Polya’s 4 stages, which is what we’ve also used in our SHAPED problem solving) and topic specific problem solving skills.

Workshop 4 – Variation in mathematics

“Reflect, Expect, Check”

A treat of a workshop to finish, with Craig Barton, Jess Prior and Ben Gordon doing a triple act on how they’ve used variation theory in their teaching.  Craig began, introducing 4 ways in which he uses variation theory: by example, by rule, by pattern and by demonstration.  Then it was over to Jess to explain how she uses variation by example as an intelligent practice exercise.  I love these!!  I’ve started using them with some of my classes after reading Craig’s book, but without the full “reflect, expect, check” experience.  However, they have already allowed questions and discussions about what is happening.  The point is, instead of having unrelated practice questions, change one thing each time, so that the students have the opportunity to think about what’s changed and what effect this will have.  At this point, it’s worth pointing out that from Craig’s point of view, this is one tool to use whilst giving student a wide diet of maths.  I was so engrossed, I didn’t even get any pics! But Jess has very helpfully written in far more detail on her blog here at minimallydifferent.wordpress.com.
bnGYSwsoRsq7U%XscstCbQBen then took the baton to talk about variation by rule, and how he introduces concepts through examples and non-examples, but by varying one thing at a time in his examples.  Again, I’ve done some of this, but not to the extent of only changing one thing!  And it was hard to come up with the examples and non-examples as my list.  Ben’s example of mode from a table was seamless, and his demonstrations of actually how to do it with the class were very useful.  A silent introduction whilst students concentrate on the examples, cold calling for reasoning, insisting on correct language, and then class calling!

Both Jess and Ben came across as if they’d been hosting workshops to a packed lecture theatre alongside “famous” maths teachers for years, and not that it was their mathsconf debut!  Craig then finished off with the other two variation methods, firstly making sure that if you are to use a pattern that to make sure it doesn’t become a pattern filling exercise, you leave a “gap of understanding” for students to identify the pattern, see what is happening, and use to predict the results.  Finally with regards to variation by demonstration, the key point was to keep the initial diagram for a reference point.  I really need to learn how to use geogabra!

Of course, Craig these days does not finish a workshop without an announcement, and true to form, there was an announcement at the end of this one.  Craig, Jess and Ben have created a new website called variation theory.com.  This will become a collaborative website with all things variation!

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Final thoughts

If you haven’t been yet, you must go to a mathsconf.  The CPD for maths teaching is amazing and the willingness to share in second to none.  I was very excited to hear that mathsconf17 will be in my home town of Sutton Coldfield!  Asking Mark whereabouts, he couldn’t remember but suggested I do a workshop.  I had the intention before, but expressed how all that I know is what I’ve read about and heard about from other more expert people than me!  Yet the kind Kris Boulton suggested to make that the basis of my workshop, as many other teachers won’t have read these, or heard about them.  So, watch this space!

 

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Conferences

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Mathsconf14

A quick overview of the mathsconf14 sessions I went to, with my takeaways and links to the blogs of the speakers, who obviously put it much more eloquently than I can, which is why they were presenting!

First though, a little aside about the night before and the friendships formed over the conference.  I started going to mathsconfs by myself, and still do.  However, I do  not feel like I am by myself when I attend as the good folks of mathsconfs are always very welcoming, and I hope I am now passing that on to new folks.  As well as wonderful CPD, mathsconf brings together maths teachers who are passionate about their subject and want to talk about it (amongst other things of course!).

Andrew Taylor delivered another informative key note message at the start of the day, and following some speed dating, during which @AMercerMaths shared with me the Teach Like a Champion mat.  I’m part way through TLAC 2.0, and have listened to @MrBartonMaths podcast with Doug Lemov and it is always good to be reminded of the many ideas that Doug has seen and written about.

Workshop 1: Naveen @naveenfrizvi – Engelmann Insights: Structuring Teaching for the Weakest Pupils

As I have the pleasure of teaching 2 nurture groups (and 1 almost nurture group) this year, it was a no brainer for me to go to Naveen’s workshop.  I’ve heard Naveen present a few times before, and I really like the thought she puts into the maths pedagogy she presents about.  This presentation was about her experience using Engelmann’s book Connecting Maths Concepts, using an example of teaching fractions and how Engelmann breaks it down into small, well structured and sequence steps.  The books are targetted for intervention groups, which is how Naveen has used it, but I did ask Naveen if the ideas could be used for whole class teaching of weaker students, to which she did say that the principles could be applied to whole class teaching.  Naveen is blogging about her presentation here.

My takeaways:

Connecting Maths Concepts uses scripts (remember it’s for an intervention group), but even without a script I should think more about the language I use and be careful about not using redundant language.  Say more in less words.

“Future learning never contradicts prior learning”. My immediate thought of this was about division with remainders.  For example, when first learning 5÷4, a student may be taught to write 1 r1. Then later on, they are taught not to write this any more, but 1 1/4. It may depend on sequencing of teaching, but why not teach 1 1/4 to begin with?

Engelmann Fractions

Pre-empt future misconceptions by thinking carefully about how you introduce earlier parts of the topics, as in the very first example of writing a fraction of a shape.  Use more than one whole unit to emphasise the denominator is the number of parts in one unit.

Show that equivalent fractions is actually multiplying by 1, but replacing the 1 with, for example, 3/3 instead of using arrows!

Workshop 2: Danielle @piximaths – Scaffolding in Maths Education

Anybody who looks online for maths resources should already know about @piximaths and her wonderful collection of resources that she’s built up over the years.  Danielle has also blogged about mathsconf14 here, and has included her slides for her presentation. It was good to have discussions on the table on how we would scaffold certain topics.  We went off on a tangent from the directed topic (adding fractions), but that just gave us more insights.  It was interesting how between us we thought of different ways to scaffold.

 My takeaways:

IMG_2208.JPGDanielle shared Alibali’s ideas for scaffolding, which reminds me not to always use the same method.

The most important part of scaffolding is to take it away.

To think about whole class scaffolding vs individual scaffolding – i.e. 1 worksheet which begins scaffolded and students can start at the appropriate point vs 3 worksheets with the same questions, where 1 is very scaffolded, then second has some scaffolding and the third is without scaffold (and the first two gradually take the scaffold away).

To further review the difference between scaffolding and differentiating by time.

Tweet-up

Petals Around The Rose tweet

The wonderful @MrMattock had got a few of us organised to run some puzzles and games at lunch time.  I kind of overran eating my lunch and chatting with Jo and Craig, but I finally arrived with the puzzle I first discovered on @mathequalslove blog here, Petals Around A Rose.  I’m sorry to Jess and @sheena2907, amongst others, who I annoyed with it, using it as an example of needing resilience.  Unfortunately it meant I didn’t get to see other Tweet-up puzzles, but it was lovely chatting to new people.

Workshop 3: Jemma @jemmaths – Building Effective Learning Strategies into a Maths Curriculum

I chose to go to Jemma’s workshop as this is what maths pedagogy is all about to me – using the most effective learning strategies.  In this session, Jemma elaborated on the article that she wrote for Learning Scientists here, which explains how she is embedding the six strategies of effective learning from the Learning Scientists into her maths curriculum at her school.

My takeaways:

Spaced practice: I love using Numeracy Ninjas every lesson for my Year 9 nurture group.  They’re all building up stickers on the front of their books and I’ve been really impressed with the progress some have made.  I also use BBQs (Bread and Butter Quizzes) for my year 10 and 11 groups, which means it’s never too long between returning to previous topics.

Interleaving: This is definitely an area I want to work on – bringing previous learning into next topics.  At the moment this only occurs on an ad-hoc basis, but it would be far more ideal if previous learning was planned into new topics.  Jemma describes beautifully how it works in her curriculum, which has the advantage that she designed the curriculum so that she could interleave.

Retrieval Practice: This is something I’ve started working on recently.  The BBQs, which I’ve been using for a few years now can be seen as a type of retrieval practice as well as spaced practice.  However, this term I’ve introduced weekly quizzes for my year 7 and year 9 groups.  They have a homework with “last week, last topic, a previous topic” questions, which we self assess and review in lesson every Thursday.  On the Friday they then do a quiz, with same questions, different numbers, and an added “this week” section. They must attempt if first of all without their books, but after about 10 minutes, if they have got to the end and have gaps, I allow them to look in their books.  I can definitely see improvements for some students, but we’re still early in its infancy, and I know for some I need to help develop their resilience and pride in their work as well.

Elaboration: As Jemma says, “sweat the small stuff”!

Concrete Examples: A given!

Dual Coding: Another area I want to read more into.  I’m aware that it’s representing with images or diagrams and not using additional text, but also that an image or diagram in conjunction with the spoken work is processed better than text that is read out. It is definitely an area I need to develop.

Workshop 4: Craig @MrBartonMaths – How I Wish I Taught Maths, 2 months on..

IMG_2212Initially I wasn’t going to go to Craig’s workshop.  Not that I didn’t want to hear what he said, but more that I had already vacuumed up his book in a weekend of frenzied reading, and have listened to many of his podcasts with the experts from which Craig’s reading into the research had originated.  How glad I am I changed my mind!  Craig is a fantastic speaker and his depth of thought into maths teaching is inspiring.  I have no problem in recommending any maths teacher, new or experienced, read Craig’s book. Craig chose 5 areas of his book to talk about, elaborating on what he wrote in the book, and adding some special little nuggets in for us.

My takeaways:

I’ve got to try some goal free problems, especially with my year 11.  Get a problem, take away the actual question part (the goal) and replace it with “what can you find out”.

I’ve already started using example pair problems, but what I want to improve is the “show-call” part of the “Your Turn”, using my visualiser to show student responses and discuss the best parts of them and if there can be improvements.

IMG_2217Intelligent practice is something else I am striving towards.  At the moment, I attempt it rarely, but it is something that can become a powerful tool in students initial learning and understanding of a concept.  Craig’s example with product of prime factors blew my mind! I thought it was genius how the questions develop so students can start to expect a certain answer, and then check it with their learning.  And then every now and again a cognitive shock is thrown in when the answer isn’t what they expect and they look to see why, involving the hypercorrection affect (learning is more powerful when you are wrong about something you thought was correct).

Purposeful practice is another area that I’m trying to develop.  This is for when students have learned the concept, but need more practice, and is trying to get away from just having questions to practice and towards practicing with a purpose (surprisingly!).  I have already started looking at @colinfoster77 etudes which are ideal for purposeful practice.  This was where Craig introduced the first of his golden nuggets, as he announced that he had collated and added to his collection of venn diagram problems, which are great for purposeful practice, on a new website www.mathsvenns.com, and I’m really pleased to say it came with a lot of venn puns!

The CompanySame structure, different deep problems (SSDD problems) were something else Craig introduced in his book and has since developed.  These are problems which look the same, or are in the same context, but have different mathematical requirements for them, as on the example shown (this is one of mine!!).   In this case they are different types of percentage questions, but the mathematical concepts in each question does not have to be related.  Time for Craig’s second golden nugget – he has set up another website www.ssddproblems.com, to collate and share these problems.  All he asks is that you submit one (or more) of your own, based on a shape, an image or a context.

And finally…

From the bottom of my pedagogical maths teaching heart, I cannot thank the presenters enough for all that they do sharing their experience and response to research, and of course to Mark McCourt, @LaSalleEd for bringing it altogether and enabling such an event.

On a personal note, it was wonderful to meet up yet again with some twitter and mathsconf acquaintances who I hope I can now call friends.  And it was in discussion with these friends that I am starting to believe in myself and my pedagogy again after recently experiencing feedback from a 15 minute observation which left me crushed and devastated when told what I was doing was “wrong”, despite (but not being allowed to) being able to justify why I did each part.  Speaking with far more experienced maths teachers than me has given me my confidence back that I can keep developing my practice in order to help student learn maths in the most effective and long lasting manner that research is currently pointing towards.  I know I still have a lot to learn and to implement and I hope I can continue doing this to impact positively on my students.

 

 

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Conferences

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Mathsconf13

My sixth mathsconf, so it’s about time I blogged about the fab day organised by @Emathsuk and his team at @lasalle.

As often as possible I try to start mathsconf with the Friday night meet up.  It’s a great time to catch up with maths teachers we’ve met along the way and through Twitter, as well as meet new folks.  Despite a mix up with Julia, @Tesmaths, trying to meet in the foyer of the hotel, then realising we were in different ones, I made it up to All Bar One with Jo, @jolocke1.  We’d both started new schools in September, so lots to chat about.  At the bar I was chatting with @rach_2210 who was in Sheffield on her first mathsconf, and through our “where about do you teach” introductions, discovered we lived in the same town a couple of miles apart, and Rachel teaches at the school my 10 year old has put down as his preferred choice!  Small world! It was lovely to catch up with Jo, @mathsjem, and hear of her experience so far as head of maths.

So onto the mathsconf.  After introductions from Mark and Andrew Taylor of AQA, who talked about post 16, it was over to Matt Parker, @standupmaths, who as you can imagine, was an instant hit.  Not only was there lots of laughing out loud, but some neat maths too:

Choose a random 2 digit number, cube it and Matt will tell you the original number.  It’s all to do with expanding a trinomial and the affect on the 10a and b when cubing.  Going to have to explore this one a little more – but isn’t that the point – creating a hook to explore some maths.

Spreadsheet Picture

img_1070.jpgThen Matt introduced us to his favourite spreadsheet.  Just a spreadsheet with cells coloured in red, green or blue, but when you zoom out it’s a picture of Matt!  Here’s mine, created from Matt’s pixel spreadsheet downloader on his excellent website think-maths.co.uk.  Amongst other things there are downloads for building 3d fractals, including a festive fractal Christmas tree, and if you visit megamenger.com, you’ll find details on building the world’s largest menger sponge from business cards, along with all downloads and instructions.

Matt finished off with a round up of websites and events.  I’m particularly hoping we’ll be able to take some year 11s to the mathsinspiration.com event in Birmingham in November.  Fingers crossed!

During speed dating I met Jack from Nottingham Uni Samworth Academy who showed me the spreadsheet they had made to support strategies for rewarding positive behaviour and effort.  It was just the thing to implement with a couple of my groups, as I was looking for ideas of how to record all the positiveness in the classroom.  Pete, @MrMattock showed us BBC Skillswise, the adults learning site, and the resources it had for older children who needed further support on the basics.  Clear resources without the gumpf!  I was also able to have a catch up with Bruno, @MrReddy, and was happy to share that one of my first responsibilities in my new department is to get TTRockstars properly up and running!

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This was my contribution – at the end of school on Friday, a year 8 lad was excitedly telling his form tutor all about the probability tree he created and what each of the parts meant.  He was in the nurture group, and the hook to get him engaged in probability trees was making it! All from my colleague Emily next door.

Onto the sessions, and first it was Sarah, @Schamings28, with Developing Resilient and Confident Mathematicians.  Perfect, as 3 out of my 4 teaching groups are nurture groups, and resilience and confidence are in short measure.  Sarah gave an inspiring workshop, clearly addressing the issues and giving excellent practical advice for taking back into the classroom straight away.  img_1076.jpgShe gave some excellent phrases to use to support confidence and resilience, as well as ideas for resources that get pupils practising resilience in low entry challenges which can then be used as a starting point to praise the process of resilience.  I would highly recommend Sarah’s workshop if she were to do another one.

Next was an overview of Richard Skemp’s work: Relational Understanding and Instrumental Understanding from Gordon, @gordon-brough.  I thought the effects of instrumental and relational teaching and learning was very pertinent. I have downloaded a copy of the paper so I can read through it again.

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Jonny’s, @studymaths session on Primes, Patterns and Purposeful Practice was a whirlwind of ideas to engage students in their maths learning.

img_1112.jpgFrom “tricks” for squaring n+0.5 two digit numbers, based on expanding brackets like earlier, to factor skyscrapers, HCF/LCM pyramids, the Ulan Sprial, Goldbach’s conjecture, happy numbers, Kaprekar’s routine, Sierpinksi triangle and Chaos Game to name a few, Johnny provided us with many ideas, with quite a few being being enable from his excellent mathsbot.com site.  It’s always great when you get an “aha, that’s perfect for when I teach …. next week” moment in a session, as well as a collective “wow” that came with the Chaos Game.  Jonny’s session slides can be found here.

Finally I went to see Amir, @workedgechaos, and was treated to a review of how he would and does implement turning research and “current thinking” into practice with his staff. Amir has been a head of department and is now an assistant vice principal. It is very true that there is so much out there at the moment that it can easily become overwhelming.  img_1123.jpgAmir took his big 3 – Bloom’s Mastery, Englemann’s Direct Instruction and Cognitive Load Theory and looked at the common themes.  He then boiled it down to Question, Model, Check, Praise and Retrieve.  It is, of course, a bit more detailed than that! You can find Amir’s slides and handout here. Amir shared with us an overview of a year’s scheme and how this was delivered each week.  For spacing and retrieval, I loved how a topic was spread over several weeks (but not taught over several weeks):

Week 1: Topic A

Week 2: Mini test on topic A

Week 3: DIRT on topic A

Week 7: Review lesson on content A

But it’s not only the speakers and workshops which give great ideas.  I happened to bump into Naveen and Dani, @Naveenfrizvi and @danicquinn, and got to ask a couple of questions I was intrigued about.  Firstly rolling the timetables and implementing it with a group, and secondly from Dani’s podcast with Craig Barton @Mrbartonmaths, where she said they differentiated by time, so lower groups went slower. I just couldn’t fathom how these groups could have the same expectations if they went slower.  The answer is obvious really – they have more time; more lessons!

I know I can’t do justice to some excellent workshops in such a short summary, but if it means that it interests someone to attend the next mathsconf14 in Kettering, March 10, then that’s great. A huge thank you to Mark and his team for another fantastic day of maths teaching CPD, and all the speakers who gave up their time to prepare and deliver such wonderful sessions.

Next for me is to give back and deliver a workshop myself, but for that I need to know I have something to offer that will be of interest to others and that’s worthwhile for teachers to give up their time for.

TMBrownhillsOh, and I almost forgot, I need to do a bit of shameless plugging of our #TMBrownhills on Saturday 18th November, featuring @teachertoolkit Ross McGill, author of Teaching Backwards @oteacher Mark Burns and many local teachers presenting on classroom practice.

 

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