Showing posts with label #mathscpdchat. Show all posts
Showing posts with label #mathscpdchat. Show all posts

Thursday, October 24, 2019

Bridging The Gap To A Level

At 7pm on Tuesday seventh Oct I'm hosting a Twitter chat on the topic of bridging the gap from GCSE to AS level. Please bring together inwards using #mathscpdchat. If yous haven't participated inwards a Twitter chat before, this guide explains what it's all about. I recommend yous laid up TweetDeck in advance thus yous tin proceed rail of the conversation.

In grooming for this chat, this ship service outlines some of the issues that I desire to discuss. First I'll facial expression at why there's a gap, thus I'll facial expression at some possible strategies for bridging it. I'm actually keen to hear others' ideas on Tuesday.

1. Why is at that spot a gap?
A. The work amongst GCSE grades
Most schools require that students acquire a degree B at GCSE to produce maths at H5N1 level. This yr your AS aeroplane classes volition comprise a mix of students who got anything from 48% to 100% inwards their maths GCSE. This lower jump mightiness surprise you. Yes, students tin get less than half of the answers correct together with yet acquire a B. That agency a educatee tin embark on H5N1 aeroplane maths amongst absolutely no agreement of algebra, or no thought how to add together 2 fractions without a calculator.

Students are oft 'taught to the test' thus direct keep picayune conceptual agreement - they tin acquire a decent GCSE degree past times learning some tricks together with doing lots of exercise questions. Around 15% of students who attain a B inwards their maths GCSE become onto to bring maths at H5N1 level. The graph below, taken from this 2012 report, shows that of those students who got a B inwards their GCSE, alone 20% achieved A* - B at H5N1 level. The bulk got a degree D, E or U. Were those students given the incorrect advice well-nigh their post-16 options? And why did they non driblet maths at the terminate of Year 12? Bear inwards hear that having got a B at GCSE, they would direct keep expected to attain at to the lowest degree a B at H5N1 level, thus these students may direct keep been bitterly disappointed amongst their results.
Maths GCSE also doesn't produce plenty to differentiate at the transcend end. Around 5% of students nationally acquire an A* at GCSE. These students arrive at from those who are incredibly intelligent to those who were well-taught together with hard-working. This volition alter - the novel 'A**' degree (Grade 9) volition endure awarded to the transcend 3%. When the novel grades come upwardly into play from 2017 onwards, I promise to come across schools setting a minimum requirement of Grade vii to produce maths at AS aeroplane (Grades 7, 8 or nine volition endure equivalent to today's A* together with A). Am I beingness elitist? The novel core maths qualification volition endure suitable for others.

The work is that GCSE grades currently produce non give us a clear indication of who is suitable for H5N1 aeroplane maths together with who isn't. I've taught many students who got an H5N1 or A* at GCSE but went on to acquire a D, E or fifty-fifty a U at AS level. Why did they of a abrupt halt beingness 'really good' at maths?

Last yr I introduced an entrance essay inwards Year 12 - to a greater extent than on this here. It revealed shocking gaps inwards basic skills together with knowledge. Students who got an A* at GCSE could non produce long multiplication! I recommend that all schools produce an entrance essay for 2 reasons:
1. To position weaker students together with intervene amongst extra back upwardly from the start.
2. To create produce expectations - students who got a skillful degree at GCSE volition endure surprised if they acquire a depression grade inwards a basic skills test. They'll realise that they can't coast through the course of instruction together with volition endure motivated to piece of work hard.

Is at that spot a instance for setting at H5N1 level? I know some schools that give a maths essay at the start of Year 12 together with thus set students into sets.

B. The work amongst GCSE content
I did some analysis of the marks available on final year's higher Edexcel GCSE papers. This is what I found:
  • Approximately 40% of the questions tested skills that are absolutely essential for AS marrow maths eg fractions, algebra, arithmetic, Pythagoras
  • Approximately 35% of the questions tested marrow maths skills that are taught ane time to a greater extent than at AS aeroplane eg surds, indices, trigonometry, simultaneous equations, inequalities, quadratics together with coordinate geometry. 
  • Approximately 25% of the questions tested applied topics (eg statistics) or topics that don't come upwardly up at H5N1 aeroplane (eg loci, transformations).
H5N1 educatee tin easily acquire a degree B amongst rattling few marrow skills.

I wonder if schools that direct keep embedded a mastery curriculum from a immature historic menstruum direct keep managed to eliminate the work of Year xi students lacking marrow skills.

Upcoming reforms volition aid to address the electrical flow problems amongst GCSEs. Until they are implemented, what tin nosotros produce amongst our Year 11s to improve laid upwardly them for H5N1 level?

There are extra qualifications to reckon - the Certificate inwards Further Maths has some peachy content similar matrices together with functions. Additional Mathematics is a challenging course, especially suitable for students looking to bring Further Maths at H5N1 level. Regardless of whether your transcend students are taking these extra qualifications, produce yous facial expression at interesting, non-curricular mathematics amongst them inwards Year 11?

At H5N1 level, students oft fighting amongst the alter inwards the way questions are worded. Perhaps nosotros should start looking at these kinds of questions earlier. For example, the interrogation below is from a C1 newspaper but would endure suitable for a GCSE student.
C1 Edexcel May 2013
2. Strategies for bridging the gap
So let's merely bring our electrical flow predicament - students commence their H5N1 aeroplane maths course of instruction totally unprepared. What tin nosotros produce to back upwardly them? Here's a few ideas together with questions.

A. Bridging resources
summer work to do. They also recommend resources that students tin usage over summertime to fill upwardly inwards whatever cognition gaps - hither are a few examples:
In my experience, urging students to produce piece of work during the summertime preceding Year 12 isn't especially effective because students merely don't come across the necessity. I've considered running a 'summer bridge' or transition course of instruction inwards the calendar week before term starts. I'd endure interested to hear from teachers who produce this.

B. Intervention
At my schoolhouse nosotros run compulsory remedial sessions inwards the Autumn term for students who don't produce good inwards their entrance test. We also offering an optional weekly Help Club to all students all yr round. When I was Key Stage v Coordinator I offered additional back upwardly through a student blog. What does your schoolhouse produce to back upwardly students who are struggling?

C. Course structure
Does your schoolhouse offering students flexibility over modules? Which applied modules piece of work best? We notice that M1 is also hard for many of our Year 12s (except those taking Physics) thus is best tackled inwards Year 13. The planned changes to H5N1 aeroplane maths volition standardise the course, removing the chemical constituent of choice.

How many hours a calendar week should students pass inwards lessons together with doing homework? When my H5N1 aeroplane teaching hours were cutting from 4.5 to 4 hours a calendar week due to budgetary constraints, my students suffered.

How large are your classes? At my schoolhouse nosotros currently direct keep eighteen - xx students per H5N1 aeroplane class. I've heard of schools amongst fifty-fifty bigger classes. At H5N1 aeroplane I shout upwardly 10 - 12 students per degree is far to a greater extent than effective.

D. Delivery
How produce yous organise the delivery of the course of instruction content? Do 6th shape classes direct keep to a greater extent than than ane teacher? What fellowship produce yous tackle the modules in?

At the start of Year 12, how much fourth dimension produce yous pass re-teaching GCSE topics such equally algebra, surds, indices together with quadratics?

Do yous direct keep whatever item strategies for teaching H5N1 aeroplane lessons? Any item resources?

E. Effort
How produce yous encourage students to piece of work hard? Do they produce equally much exercise equally they need to? At my schoolhouse nosotros laid out our expectations together with outline the back upwardly available inwards a student handbook.

My students are given Alps estimates equally targets to piece of work towards, but these are based purely on GCSE grades together with inwards my persuasion (partly for reasons outlined above), they are meaningless without instructor input.
Target setting (source: FFT)
Summary
I've made an infographic to summarise my thoughts together with questions well-nigh the path to H5N1 level. On Tuesday I desire to focus on 2 primal questions:

1. What structures should nosotros direct keep inwards position at Key Stage 4 to aid our students laid upwardly for H5N1 level?
2. What back upwardly tin nosotros offering during Year 12 to ensure students hitting the terra firma running together with don't autumn behind?

I facial expression frontward to hearing your ideas. If yous can't participate inwards Tuesday's chat thus delight part your ideas inwards the comments subdivision below.

_________________________________________________________

Update: 6/10/14
All 4 posts comprise lots of skillful ideas together with insightful reflections.

Thanks also to @paulsuvs for pointing me inwards the direction of these National Transition Matrices which supply interesting information well-nigh the grades achieved at AS level. 



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Favourite Problems

On Tuesday 23rd June I'm hosting a #mathscpdchat entitled "Problem solving: what are 'good' problems? Where tin y'all respect them?".

What's a Problem?
Influenza A virus subtype H5N1 problem, inwards the mathematical sense, tin live on defined equally "an enquiry starting from given weather condition to investigate or demonstrate a fact, result, or law". The give-and-take originated inwards the belatedly 14th century,'a hard inquiry proposed for solution', from Old French problème, together with straight from Latin problema, from Greek problema 'a task, that which is proposed, a question' (source: etymonline).
A occupation from solvemymaths.com

I similar this quote from Jennifer Piggot, "A occupation is something that y'all belike volition non similar a shot run across how to tackle or which i time started volition challenge your thinking. This agency that at some betoken y'all are probable to acquire stuck together with this is OK. In fact it is of import that y'all acquire stuck hence that nosotros tin speak nearly possible ways of getting unstuck" (source: nrich).

My Favourite Problems
During adjacent week's Twitter chat I'd similar to run across examples of your favourite problems. These mightiness live on interesting questions that y'all purpose when didactics specific topics - for instance do y'all stimulate got a non bad inquiry on measure form? Straight business graphs? Sequences? Remember that we're focussing on problems equally opposed to resources, activities or worksheets.

Here's i of my favourite problems:
Source: Chris Smith's Newsletter, Issue 51
This is the form of occupation that could accept minutes or hours to solve. It's for sure suitable for vivid GCSE together with Influenza A virus subtype H5N1 score students to stimulate got a acquire at. At showtime expect it's i of those 'where on globe do I start?' questions. Draw inwards a few lines together with a 'Eureka!' instant may come. We terminate upwards amongst a fairly straightforward occupation involving Pythagoras together with a quadratic equation (I tell straightforward, only I'm assuming that the problem-solver knows Pythagoras' Theorem together with knows how to solve quadratic equations... Prerequisite noesis is a characteristic of many geometrical problems).

Eventually I aim to clit together a gear upwards of skilful problems for each theme on the curriculum - I've made a start amongst this Pythagoras Problem Set.
Problems don't stimulate got to live on highly complex. Any inquiry that makes students halt together with cry back is valuable. For instance this calendar week I was looking for a starter on coordinates for my Year vii class. I could stimulate got gone for a measure plotting action - I believe that ongoing procedural exercise is real of import - only instead I've gone for the inquiry below:
From Squares together with Coordinates (Don Steward)
It's an accessible occupation (the shape is a square) only I cry back my students volition respect it challenging. In fact I'm worried that I'll live on met amongst a chorus of "can't do it, Miss" together with and hence I'll lose their attention. I cry back this is a mutual fearfulness of maths teachers - nosotros desire to reach our students problems that volition instruct them to live on independent together with resilient mathematicians, only nosotros worry that they'll lose focus if they can't move out how to acquire started. This is something nosotros tin speak over inwards the Twitter chat on Tuesday.

Finally, here's a occupation that I've used a publish of times when didactics surds - I honey this one:
I actually expect forwards to seeing your favourite problems inwards #mathscpdchat at 7pm on Tuesday - run across y'all there.


Problem Solving Resources


 Problem Solving Links

Further Reading





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Wednesday, October 16, 2019

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

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Questions Close Practise Books - #Mathscpdchat

To me, exercise books are a agency to an destination - they are only a identify for students to jot downward workings inward lodge to solve problems. It is the act of practising that's important, non the written tape of that practice. I'd happily convey my students produce all their piece of occupation on scraps of newspaper that they throw away at the destination of the lesson.

"Oh but what virtually their notes? They'll request those for revision". I specifically say my students to revise for exams past times doing practise questions (past examination papers, workbooks etc). I say them to sentinel a video or inquire me for help alongside anything they exceed stuck on. I never say them to 'read their exercise book' for revision. So what value is at that spot inward spending fourth dimension together with attempt out focusing on the organisation together with presentation of classwork, if that classwork volition never last referred to again?

I'm deliberately playing devil's advocate here, but I produce think this is worth discussing. How of import are exercise books inward the pedagogy of mathematics?

Please bring together #mathscpdchat at 7pm on Tuesday 15th March to part your opinions.

I'm certain many of you lot volition convey a catch on the importance of good presented exercise books. I aspect that people volition utter virtually students taking pride inward their piece of occupation together with the advantages of a disciplined approach to setting out workings.

I'm certain people volition also convey views on when together with where to laissez passer on feedback. I solely laissez passer on feedback on homeworks together with assessments - my homeworks are e'er on worksheets, pregnant I never write straight inward my students' exercise books. In fact I rarely aspect at them. Does it matter? Some #mathscpdchat participants may convey views on the score of independence nosotros should laissez passer on students - how much should nosotros monitor their classwork books? Do you lot monitor the classwork of 6th cast students?

The pictures below present a good presented exercise mass together with a poorly presented exercise book. These are from 2 real dissimilar types of pupil - I wonder what you lot tin infer virtually each student.


If nosotros attention virtually presentation, how tin nosotros educate our students to introduce their piece of occupation well? At the kickoff of each schoolhouse twelvemonth I ready out my mass presentation expectations alongside each class. What produce you lot do?

How produce you lot bargain alongside worksheets? I piece of occupation a lot of worksheets (mostly Don Steward) together with I'm terrible at remembering to say my students to stick their sheets in. Their books are bursting alongside loose sheets. Perhaps band binders would last better.

On Twitter I've seen a make of ideas for exercise books including collapsible release lines, treasury tags together with raffle tickets. Do you lot produce anything that's 'a flake different'? Please share!

There are many interesting give-and-take points here. Please bring together #mathscpdchat at 7pm on Tuesday 15th March to part your opinions. I'd dearest it if you lot could part pictures of your students' exercise books too!





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#Mathscpdchat - Celebrating Don Steward

Please bring together me for #mathscpdchat at 7pm on Tuesday 24th May to explore Don Steward's fantastic resources.

Don's weblog Median has late passed its millionth stance thence this seems similar a expert fourth dimension to part our favourites from his vast collection of rich tasks. Join the chat to hash out which resources you've tried as well as which direct maintain worked well.

To start us off, hither are 3 of my favourites.

1. 'One wrong simplification'

I honey this fix of tasks. When I took over my electrical flow Year eleven flat inwards October, I gave them this activity inwards the offset lesson. At the fourth dimension they were working at GCSE flat B or C as well as it was of import for me to know how fluent they were amongst algebra. This activity is actually engaging - every bit my students got stuck in, I had the chance to circulate, assess their agreement as well as hash out mutual misconceptions. They constitute the delineate of piece of occupation accessible simply quite challenging, which fix the musical note for what their maths lessons amongst me would live on like.

This seem caught most of them out:
I'm certain you lot tin dismiss encounter what the mutual error is hither - most students incorrectly simplified this to 3 + 5n. This raises a useful tidings most grouping as well as brackets, or lack of brackets.

This activity also plant brilliantly every bit a warm-up on H5N1 flat induction day.

 2. Difference of Two Squares
Recognising as well as beingness able to factorise a departure of 2 squares is a useful science throughout GCSE as well as H5N1 level.

Give a pupil an algebraic fraction to simplify as well as you'll frequently detect that they direct maintain no thought what to create amongst a 4x2 - 9 inwards the numerator, fifty-fifty though they seemed to empathise how to factorise a departure of 2 squares when you lot previously taught it.

Don Steward has unopen to swell activities for pedagogy this topic, culminating inwards this awesome fix of challenging questions. I honey these.
This reminds me of unopen to other Don Steward delineate of piece of occupation - 'Mega difficult powers questions' which offers stretch as well as challenge for students learning fractional as well as negative indices. This delineate of piece of occupation plant good at H5N1 flat too.

I similar it that both of these tasks assistance students realise how much easier it is to operate improper fractions rather than mixed numbers or decimals.

3. Form as well as Solve a Quadratic
Forming equations comes upwards a lot inwards GCSE exams (particularly inwards Linked Pair GCSE, which is what I've been pedagogy this year). I'm non certain our students acquire plenty exercise of this - which is partly why thence many were stumped yesteryear Hannah's Sweets end year. Don Steward has a lovely fix of tasks for forming as well as solving quadratics.

Students frequently detect it actually difficult to know where to start on problems similar this thence careful questioning as well as scaffolding may live on needed.

In this post I've solely shared algebra resources, simply comport inwards hear that Don's resources are awesome for shape, measure, number, proportional reasoning, information as well as probability too. I volition part many to a greater extent than resources during the chat on Tuesday. See you lot then.





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