Tuesday, April 30, 2019

Worries

A Twitter conversation close recruitment this calendar week got me worrying. I went to bed that nighttime feeling the weight of the basis on my shoulders.

Being a maths instructor is wonderful, too if y'all e'er doubtfulness that too hence read Ed Southall's ship service 10 reasons why it's a dandy fourth dimension to travel a maths teacher. But it is the best of times too the worst of times. Let me tell y'all some of the things that are on my mind...

1. Recruitment
Undoubtedly the biggest challenge nosotros human face upwards is a dire shortage of maths teachers. I don't trust any data inwards educational activity hence let's cause got a quick human face at the anecdotal evidence. Have y'all seen the huge discover of maths instructor vacancies beingness advertised on TES this week? That discover is laid to growth dramatically over the coming weeks equally schools desperately endeavor to win the race to recruit trainee teachers.

My schoolhouse is planning to significantly growth the discover of maths lessons for our students at both Key Stage three too four from September. This, coupled alongside the e'er increasing uptake of maths at Key Stage 5, way that my schoolhouse volition travel looking to recruit at to the lowest degree two novel maths teachers over the coming year. Other schools are inwards the same position. This continued increasing demand against a backdrop of diminishing render is a really serious concern.
The contest for maths teachers is fierce. There aren't plenty of us to become round. Across the country, a whole generation of students volition endure dreadfully. I wrote close this inwards Schools Week in conclusion Dec too the province of affairs has only worsened since then. Teachers are beingness driven out of the profession yesteryear utterly unsustainable workloads too nosotros are merely unable to supervene upon them.

What volition plow over if nosotros can't create total our vacancies? Initially nosotros volition come across an growth inwards degree sizes. As most classrooms don't cause got the desk infinite for to a greater extent than than 34 students, this volition cause got the greatest bear upon on depression attainers whose classes may good double inwards size. Eventually nosotros volition starting fourth dimension to come across an absence of teachers inwards the classroom, alongside online delivery of content perhaps beingness the only option. This is hardly conducive to a practiced education. I strongly suspect that nosotros volition lose the 'global race' that the Government cares hence much about.

One concluding persuasion regarding recruitment. School budgets are ridiculously tight - the fiscal province of affairs horrifies me. Every spare penny should travel spent on our students, non on extortionate fees for chore adverts. Schools are spending serious amounts of coin advertising for maths teachers for weeks on end. Precious educational activity budget is sitting inwards the pockets of the TES. How really frustrating.

2. Curriculum Changes
Changes to the maths curriculum are coming thick too fast too it's downwards to teachers to endeavor to brand sense of huge amounts of information too mixed messages.

The novel GCSE is going to travel really challenging for the vast bulk of students. Our electrical flow Year 10s are guinea pigs. At Year 10 Parents Evening this calendar week I had to acknowledge to parents that I wasn't solely certain close gradings - my predictions are based on vague hunches rather than experience. Maths teachers are inwards the dark. And we're competing against each other for the transcend grades.
I'm doing all I mayhap tin to brand certain I know the novel specification, but it's much harder than it should be. The workload is huge. The procedure of implementing this novel qualification has non run smoothly too nosotros tin only promise that the implementation of the novel Influenza A virus subtype H5N1 bird qualifications is a ameliorate experience for both teachers too students.

Another affair that worries me is the novel Foundation GCSE. It contains topics that are inwards no way appropriate or necessary for Foundation students. Even to a greater extent than worrying though is that fact that hence many more students volition straightaway sit down Foundation papers when previously they would cause got been entered for the Higher Tier. I loathe the depression expectations associated alongside maxim 'it is impossible for y'all to reach higher than a Grade 5'. And at the same fourth dimension many of the students who honor maths hard are inwards classes alongside badly behaved peers who concord them dorsum fifty-fifty further. It breaks my heart.

Finally, the thinking behind the novel Key Stage 2 resits is flawed inwards many ways. Mel sums upwards her concerns brilliantly inwards her ship service Year vii resits ... genius idea. This is some other poorly persuasion out policy that may destination upwards beingness detrimental to both students too teachers. Yet some other affair to worry about.

Solutions?
There's a elementary long-term solution to many of these problems. Reduce contact time. If teachers spent less fourth dimension inwards forepart of students too hence they would cause got the chance to excogitation effectively, grade well, collaborate alongside colleagues, implement novel policies, get upwards their champaign of written report cognition too acquire from best practice. The character of maths educational activity would improve too at the same time, recruitment too retentiveness problems would diminish. The electrical flow workload is killing us. But how tin the Government prepare this? Reducing contact fourth dimension across the board would require vast amounts of coin too vast numbers of novel teachers. Either that or less children... It's an impossible situation. This is what keeps me upwards at night. This is why I worry.


I must destination this ship service on a positive note. I am a worrier, but I am besides an optimist. I honey beingness a maths teacher. I'm doing something actually important. Fellow maths teachers, when faced alongside challenging times, produce non plow your dorsum on the profession - generations of children require you! Maths needs you! I require you! This is important, let's non give up. But let's back upwards each other when things acquire tough too produce everything nosotros mayhap can, inwards our ain schools too our ain classrooms, to brand the really best of what we've got.




Five Things You Lot Mightiness Non Know Well-Nigh The Novel Gcse Content #2

I late wrote a post about v changes to the content of maths GCSE. In today's postal service I listing v to a greater extent than changes that may non travel widely known.

1. Invariance
When pedagogy shape transformations to Higher Tier students, you'll straightaway demand to ensure that students are travel able to seat invariant points. This is described inward the specification equally follows: "Describe the changes in addition to invariance achieved past times combinations of rotations, reflections in addition to translations".

We are given this instance inquiry from AQA:
"Write downward the coordinates of a dot that is invariant when it is reflected inward the line of piece of work y = x".
Here, students volition demand to know that the points (1,1), (2,2) etc prevarication on the line of piece of work y = x in addition to would thence travel unchanged if reflected inward this line.

There's a laid of resources for this topic inward the Mind the Gap Maths Toolbox and Peter Mattock has shared a resources 'Invariance activeness sheet'.

2. Geometric Sequences
When I saw that geometric sequences straightaway appear on the GCSE specification I assumed I'd travel making exercise of my AS marking (C2) resources. This is non the case.

In C2 nosotros uncovering the nth term of a geometric sequence using the formula Un = arn-1.  This gives us a 'position-to-term' rule. For instance if nosotros accept the sequence
3,  6,  12,  24,  48, ... 
so nosotros accept a = iii (the showtime term) in addition to r = 2 (the mutual ratio), so the nth term is Un = 3(2n-1).

Although geometric sequences produce come upward up at GCSE, there's 2 points from the specification that are worth noting when pedagogy this content:

1. Geometric sequences volition travel inward the shape rn , for example:
2,  4,  8,  16,  ...  
3,  9,  27,  81, ...
√5,  5,  5√5,  25,  ...  (Higher Tier only)
2. Students are non required to uncovering expressions for the nth term of these sequences. They solely accept to produce that for linear in addition to quadratic sequences.

Examples of novel GCSE questions include:
The nth term of a sequence is (√3)n. What is the 5th term of this sequence?
and...
Un = 2Un-1     U1 = 2     Write downward the showtime 4 damage of this sequence.
In both examples students are using an nth term formula but non deriving the formula themselves. So when you lot learn this topic I advise that you lot focus on:
  • recognising geometric sequences
  • finding a mutual ratio in addition to using this to proceed a sequence
  • substituting into both position-to-term in addition to term-to-term rules (including those using subscript notation). 
If you've spotted this inquiry inward OCR's Practice Paper 5 you lot may intend that it contradicts what I've written hither close geometric sequences:
Here is a sequence.
2,  2√7,  14,  14√7,  ... 
a) Work out the side past times side term   (1)
b) Find the nth term   (3)
c) Find the value of the 21st term divided past times the 17th term.   (2)
I asked OCR for clarification in addition to they sent a helpful reply:
"...the Assessment Objectives around making deductions, inferences in addition to work solving hateful that some questions may involve taking known elements of content in addition to taking them that chip further, equally seen inward the question. Given that students at Higher tier accept to know how to uncovering the formula for the nth term of a quadratic sequence in addition to equally good to 'recognise in addition to exercise sequences of... geometric progressions (r^n where n is a... surd) in addition to other sequences', the inquiry is an instance of how higher powerfulness students mightiness travel expected to brand a deduction from known content. I don't await this to travel a inquiry we'd regularly evidence inward alive assessment, but is the form of matter we'd desire to include inward sample assessment to hand an indication of how the content in addition to Assessment Objectives are brought together inward writing questions."
3. Scatter Graphs
There's a chip to a greater extent than to scatter graphs now, though some teachers may accept already been roofing these things. Students volition demand to know:
  • that correlation does non necessarily shout out for causation
  • the departure betwixt interpolation in addition to extrapolation, in addition to the dangers of extrapolation.
Although I volition exercise the words interpolate in addition to extrapolate inward class, I incertitude these words volition travel used inward exams. Questions are probable to travel inward the shape of this instance from Edexcel:
You should non exercise a line of piece of work of best jibe to predict the seat out of units of electricity used for heating when the exterior temperature is 30°C. Give 1 argue why. 
Students may equally good accept to seat an outlier from a scatter graph (note that this is informal identification of outliers - ie past times eye) in addition to create upward one's heed whether to ignore it when drawing a line of piece of work of best fit.

The Scatter Graphs: True or False activeness from MathsPad covers all of this content in addition to is absolutely excellent.

Don't forget that some statistics content has been removed from the novel GCSE, such equally questionnaires in addition to stratified sampling. It's worth looking at these previous post).

Also, inward my postal service close real life graphs, I said that I was surprised to come across sketching cubics inward my novel GCSE textbook - including identifying roots from factorised expressions.
Cubic graphs from Edexcel GCSE (9 - 1) Mathematics: Higher Student Book 

This is what the specification says close cubic graphs:
recognise, sketch in addition to translate graphs of ... simple cubic functions ...
This is on both the Foundation in addition to Higher Tier. The AQA Teaching Guidance provides farther details, stating that students should travel able to:
draw, sketch, recognise in addition to translate graphs of the shape y = x3 + k where k is an integer
There's sure no cite of the type of cubic graphs that characteristic inward my textbook, in addition to I intend this is 1 of the things that volition in all probability travel removed from subsequent editions.

A few to a greater extent than clarifications
I asked OCR what they are often asked close the novel GCSE. In add-on to questions regarding grading in addition to pedagogy time, they are often asked to clarify the following:
  • whether students volition travel expected to differentiate to uncovering the slope of a crease (no, they volition accept to guess slope from a tangent at a point, or potentially a chord betwixt 2 suitable points) - come across my blog post close this. 
  • whether Foundation Tier students are required to calculate turning points of quadratic graphs (no, at Foundation they’ll simply demand to read from the graph. At Higher they volition uncovering turning points past times completing the square).
  • if Higher Tier students accept to know close the equations for whatever circle (no, solely those centred around the origin).
This is actually helpful data from OCR.

So that's it - I promise you're straightaway feeling to a greater extent than informed close the novel GCSE content. Do permit me know your thoughts in addition to questions.







Classroom Photos - #Mathscpdchat

On Tuesday 26th Jan I volition hold out hosting #mathscpdchat on behalf of the NCETM. During this chat I'll hold out calling on yous to part photos of your classroom. Even better, lead keep a wander around your subdivision together with lead keep photos of absolutely anything interesting that yous encounter - displays, pupil work, exercise books, resources, seating arrangements, equipment together with and so on. The thought is that nosotros all acquire to lead keep a peek into other maths departments.
Very cool... (source unknown)
I'm going to acquire things started past times sharing some of my ain photos inwards this post.

I lead keep immature children together with so I exclusively piece of work 4 days a calendar week - this way I don't lead keep a classroom to telephone band my own. I never instruct 2 lesson inwards a row inwards the same room - I'm ever on the move, which way that at the showtime of my lessons I'm ever frantically trying to login together with kind out my equipment earlier my students arrive.

This is the classroom where I instruct my Year 10 lessons - it's usually occupied past times my colleague Jack:
I quite similar pedagogy inwards here. It's non cramped - I tin access all students fairly easily. Things to greenback include:
  • the modest whiteboard to the correct of the IWB (far besides modest for long binomial expansions alongside Year 12!)
  • the seating organization (in pairs - I similar this)
  • the lack of displays. 
I asked Jack virtually displays together with he said he doesn't actually encounter much value inwards them. He thinks they are besides fourth dimension consuming to do together with lead keep relatively niggling affect on learning. I'm inclined to concord - though I know that many of yous would disagree (please part your views inwards #mathscpdchat!).

Displays of pupil piece of work tin hold out prissy (though they oft acquire tatty). I spotted these intriguing 'Mr Men display past times Ed Southall, which I sometimes encounter students looking at...
... together with the pop Piems' on the wall inwards some other classroom - I believe they've been at that spot since 2012, when blogger Paul Collins taught inwards this classroom.
Back to Jack's classroom... On his desk he has a play a joke on computing device (a 'gagulator') which deserves a nurture because I accidentally mistook it for a existent computing device concluding calendar week together with used inwards forepart of my students (oops). This is such a practiced cloak-and-dagger santa acquaint for a maths teacher!
Jack has an expectations poster at the forepart of his classroom to assist alongside demeanor management...
... although he admits that he never refers to it anymore. This is oft the occupation alongside posters together with displays - later on the initial impact, students halt noticing them.

Although many of our classrooms lack displays, nosotros do lead keep some displays around the subdivision - for example the straight off classic Mr Men display past times Ed Southall, which I sometimes encounter students looking at...
... together with the pop growth mindset display that originated from Sarah Hagan.
Every maths classroom at my schoolhouse has a literacy display including 'Greek Letter of the Month'. I honey this thought but it sure enough doesn't modify ane time a calendar month - delta has been inwards house for good over a twelvemonth now! :)
This is where I instruct my Year 11s:
It's a combat dismal, but position a passionate instructor together with thirty enthusiastic students inwards at that spot together with I don't recall it actually matters what the classroom looks like.

This is my colleague Lizzie's lovely classroom, which is much to a greater extent than cheerful:
My worst sense this twelvemonth was when I had to instruct a Year 12 lesson inwards an English linguistic communication classroom which didn't lead keep a proper whiteboard. It exclusively had an interactive whiteboard, together with the pens weren't working. Disaster. Maths teachers, in all probability to a greater extent than together with so than teachers inwards other subjects, demand something to write on when they're teaching. So whiteboard size together with accessibility are important.  At my previous schoolhouse every maths classroom had 2 rattling large whiteboards on runners. They could hold out pulled apart to discover an IWB behind them. That was fantastic.

In general, the classrooms at my schoolhouse are non spectacular, but the maths pedagogy is rattling practiced together with my colleagues are awesome people.

Now let's lead keep a quick facial expression at some other classroom photos together with ideas.

Displays
I ever savour reading Mr Men display past times Ed Southall, which I sometimes encounter students looking at...
... together with the pop annual post where she shares her novel displays. Her enthusiasm for pedagogy maths is rattling clear.
I'd quite similar a large computing device poster past times my whiteboard similar Sarah has - I recall it would hold out a useful pedagogy aid.
Sarah continues to part first-class displays together with resources together with so if you're looking for inspiration together with ideas, do follow her blog.

Desks
In Mr Men display past times Ed Southall, which I sometimes encounter students looking at...
... together with the pop Gems 39 I wrote about John Corbett's (@Corbettmaths) thought to position photograph frames together with baskets of equipment on desks. The contents of the frames tin hold out changed regularly to display cardinal dates, star students, reminders together with and so on.
Literacy
I similar these judgement stems from @ExplainingMaths - I tin encounter these existence useful during shape discussion.
Whiteboard walls
I long to lead keep whiteboards on every wall of the classroom. Unfortunately this is non possible inwards most classrooms due to the locations of desks, windows, filing cabinets etc. If yous desire to know to a greater extent than virtually the piece of work of vertical whiteboards, Mr Men display past times Ed Southall, which I sometimes encounter students looking at...
... together with the pop this post is a practiced house to start.
Inspirational quotes
At my previous schoolhouse I briefly had my ain classroom together with I had only 2 displays:

1. My Year 10s created a circle theorems display during a lesson. I loved it but it was difficult to ensure that students didn't facial expression at it during assessments!
2. I also had a few quotes higher upwardly the whiteboard - I was inspired past times this tweet from @surreallyno.
There are hundreds of display ideas together with posters for maths classrooms online. I'd honey to withdraw heed what yous piece of work together with why.
Hogwarts poster past times Meg Craig via Mr Men display past times Ed Southall, which I sometimes encounter students looking at...
... together with the pop this post
Spotted on @sxpmaths' classroom wall - quote from Matt Parker

Please part your photos on Twitter at 7pm on Tuesday 26th January, using the hashtag #mathscpdchat (seriously, this chat volition non piece of work unless people lead keep photos...!). Remember, I'm non only interested inwards displays. Equipment, books, resources - I'd honey to encounter it all!

Classroom pattern from Andy Heffernan

Seeking Generality Amongst Don Steward

I'm really excited to denote that the legendary Don Steward volition survive presenting a workshop at my schoolhouse on 19th March. And you're all invited!

Don's session, which is beingness held on a Sat morning, volition survive on 'Seeking Generality'. Here's the description:

The instant aim of the national curriculum is that students tin argue mathematically.

What does it hateful for your students to survive able to follow a business of enquiry?

The intention of the session is to explore ways to engage students inward conjecturing relationships, expressing a detected full general dominion in addition to developing a notion of proof.

Examples volition survive offered from across touchstone curriculum topics in addition to or in addition to hence tasks volition illustrate how a attain of novel GCSE specimen examine questions comprise seeds for growing generalities.


This workshop is gratuitous to attend. I'm really grateful to my headteacher for funding this event.

Afterwards we'll become for a pub luncheon which y'all are really welcome to bring together us for.

In alone ane twenty-four hr menstruum twoscore maths teachers convey registered to attend! There's nonetheless places available in addition to hence register now!

You'll bring out all the details here: mathsmeetglyn.weebly.com.

Hope to consider y'all there.




Monday, April 29, 2019

New Gcse: Pythagoras Questions

This calendar week my subdivision took a detailed hold off at GCSE sample questions for topics that are coming upward on our Year 10 Scheme of Work. This was the nearly useful affair we've e'er done inward a subdivision meeting! We used Mel's (@Just_Maths) first-class Questions past times Topic resources.

I worked through the Higher Pythagoras questions. Have you lot looked at these inward detail? It's good worth doing. The questions are excellent. They volition live on challenging for fifty-fifty our highest attainers. I ordinarily purpose a dainty develop Pythagoras problems when I instruct Pythagoras at GCSE but I intend I'm going to cause got to upward my game.

Let's accept a hold off at to a greater extent than or less of the novel GCSE questions.

Here's a 3 grade enquiry from OCR. Have a go. I intend my students would abide by this pretty challenging. They postulate to know Pythagoras together with how to operate amongst surds 'backwards' (I don't produce plenty of this when I instruct surds...).

Here's to a greater extent than or less other enquiry - this is a 4 marking from AQA. It's a neat question... Again, a dissimilar grade of challenge to what we're used to at GCSE level.
This enquiry is from Edexcel - hither nosotros cause got bounds together with Pythagoras:

And this enquiry is from OCR. It's non quite equally challenging equally the others though at that spot are a lot of steps.

Finally, here's to a greater extent than or less other enquiry from AQA. I especially similar this one.

All of these examples present that novel GCSE questions volition oftentimes combine 2 or to a greater extent than topics. Rightly so. Previous GCSE questions oftentimes treated topics inward isolation.

When you're planning your Year 10 Pythagoras lessons I recommend that you lot endeavour the residue of the sample questions. Even the 3D Pythagoras enquiry has a spin on it. There's to a greater extent than or less actually neat problems here. These questions also remind us of the notable pace upward inward challenge grade that we're dealing with. I'm trying non to panic! We cause got our operate cutting out.




Handwriting

At the historic menses of xvi my older blood brother started writing inwards the fashion of the wording used on the comprehend of Siamese Dream yesteryear Smashing Pumpkins. I believe the font is Agatha.
He did it really well, with meticulous attending to detail, though it must conduct hold slowed him downwards considerably inwards his H5N1 degree exams. He is forthwith a 37 twelvemonth onetime solicitor too I tin dismiss however run across the Smashing Pumpkins' influence inwards his handwriting.

In typical younger sis style, I attempted to re-create his cool handwriting. I wasn't every bit dedicated every bit he was, but I did get to pose a claw on the piece of work yesteryear of the alphabetic quality a. I hooked the alphabetic quality a throughout my H5N1 levels, academy too my career prior to teaching.
During my NQT twelvemonth this hooked a started causing me problems. My handwriting on the board is messy, too my students were oft confused when I wrote the alphabetic quality a inwards algebra. They couldn't say if it was a alphabetic quality or a number. It looked similar an ugly 2. Over the class of my NQT twelvemonth I made a witting elbow grease to halt hooking the alphabetic quality a, too every bit a final result my students no longer asked me to translate my handwriting. Well, until terminal week...

The crossed Z
I was going through a Normal Distribution event on the board when a Year thirteen raised his hand.

'Miss, what does that symbol represent?'

I was flummoxed for a second. This shape were studying S2 - they'd learnt the Standard Normal Distribution inwards Year 12, too then the annotation should travel familiar. I looked at what I'd written on the board:
'What symbol? The Z?'
'Oh, is that a Z?'
'Yes, it's a Z.'
'Why does it conduct hold a work through it?'
'That's what Z looks like. Or mayhap it's only how I write it. I suppose it's too then it doesn't acquire confused with a 2. Does anyone else hither cross their Zs?'
All eleven students milk tremble their heads.
'Oh. I idea everyone did. I'm non certain when I started doing it. But I e'er cross my Zs.'

I wrote the tidings lazy on the board to demonstrate my crossed z. They looked at me similar I was crazy. Self dubiety crept in.

I did a Twitter poll too thankfully it confirmed that the agency I write the alphabetic quality Z is totally normal (pardon the pun) with maths folk:
Most tweeters confirmed that they cross their Zs to avoid confusion with 2s, inwards the same agency crossing 7s avoids confusion with 1s.

I had a fascinating tweet from air traffic controller @jlaa who has to brand certain he doesn't cross his 7s because a crossed vii has a really specific meaning. The motion painting below shows flying details written on strips - both present that the aircraft has been told to descend from 7000ft to 5000ft. In the bottom motion painting it is rubber to number 7000ft to some other flying but inwards the piece of work yesteryear motion painting it isn't. He has to travel really careful non to automatically cross his 7s.
Does handwriting matter?
I instruct a Year thirteen Further Maths shape too most of them are going to report maths or engineering at university. I talked to them most mathematical handwriting for the commencement fourth dimension terminal week. They were interested, too it led to discussions most annotation such every bit the role of dots for multiplication too commas for decimal points. I felt similar it was a tidings worth having.

When letters are unclear inwards words nosotros tin dismiss unremarkably translate the pregnant yesteryear considering the context or looking at the other letters. But when letters too numbers are unclear inwards mathematics nosotros powerfulness non conduct hold whatever clues. This tin dismiss travel a work for testify markers, especially if they are marking private questions too then can't bring upward to the residual of the newspaper for clarity. My colleague told me she has a Year 10 pupil who writes the numerals ix too iv inwards exactly the same way. He may good terminate upward losing marks inwards his GCSE because of this.

Here's some pictures from my Year thirteen students' mock C3 exams. The commencement pupil has problem with his ones. He hooks the piece of work yesteryear too draws a work at the bottom too then they sometimes expect similar twos. In this motion painting it's clear, but exclusively because at that spot are twos at that spot for comparison.
Here's the same enquiry answered yesteryear some other of my Year 13s. This boy's brackets drive me crazy. Since September I've been complaining that his brackets are besides much similar modulus signs. He is clearly trying to educate this because the slight bend on the correct bracket is an improvement on what I've seen previously.
Later inwards the newspaper his brackets acquire fifty-fifty straighter.
I volition hold to berate him for this inwards the promise that he volition milk tremble the habit. 

Good practice
I recall that guidance on mathematical handwriting should travel delivered inwards Year 7. The importance of clear handwriting - too tips such every bit the crossing of the vii too the Z - should travel made explicit. This post service Tips for mathematical handwriting is a expert starting betoken (though teachers from exterior the the United States of America won't travel happy with the alphabetic quality x here!).
Christian Perfect picked upward on this international x discrepancy a few years agone - his article Let's beak most X is worth a read.
I conduct hold a pupil who does 'joined up' xs (ie he doesn't accept his pen off the paper) - run across motion painting below. They expect similar ns. Making x expect similar n is pretty unusual. Do your students conduct hold whatever odd handwriting habits?





Further Reading