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

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 you lot haven't participated inwards a Twitter chat before, this guide explains what it's all about. I recommend you lot laid up TweetDeck in advance therefore you lot tin sack continue runway of the conversation.

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

1. Why is at that topographic point a gap?
A. The work amongst GCSE grades
Most schools require that students acquire a degree B at GCSE to produce maths at Influenza A virus subtype 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 sack get less than half of the answers correct in addition to all the same acquire a B. That way a educatee tin sack embark on Influenza A virus subtype 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' therefore own got footling conceptual agreement - they tin sack acquire a decent GCSE degree past times learning some tricks in addition to doing lots of do questions. Around 15% of students who attain a B inwards their maths GCSE become onto to convey maths at Influenza A virus subtype H5N1 level. The graph below, taken from this 2012 report, shows that of those students who got a B inwards their GCSE, exclusively 20% achieved A* - B at Influenza A virus subtype H5N1 level. The bulk got a degree D, E or U. Were those students given the incorrect advice nearly their post-16 options? And why did they non drib maths at the terminate of Year 12? Bear inwards hear that having got a B at GCSE, they would own got expected to attain at to the lowest degree a B at Influenza A virus subtype H5N1 level, therefore these students may own got been bitterly disappointed amongst their results.
Maths GCSE also doesn't produce plenty to differentiate at the move past times end. Around 5% of students nationally acquire an A* at GCSE. These students make from those who are incredibly intelligent to those who were well-taught in addition to hard-working. This volition alter - the novel 'A**' degree (Grade 9) volition move awarded to the move past times 3%. When the novel grades come upwards into play from 2017 onwards, I promise to run into schools setting a minimum requirement of Grade vii to produce maths at AS aeroplane (Grades 7, 8 or nine volition move equivalent to today's A* in addition to A). Am I beingness elitist? The novel core maths qualification volition move suitable for others.

The work is that GCSE grades currently produce non give us a clear indication of who is suitable for Influenza A virus subtype H5N1 aeroplane maths in addition to who isn't. I've taught many students who got an Influenza A virus subtype 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 attempt inwards Year 12 - to a greater extent than on this here. It revealed shocking gaps inwards basic skills in addition to knowledge. Students who got an A* at GCSE could non produce long multiplication! I recommend that all schools produce an entrance attempt for 2 reasons:
1. To position weaker students in addition to intervene amongst extra back upwards from the start.
2. To cope expectations - students who got a skillful degree at GCSE volition move surprised if they acquire a depression grade inwards a basic skills test. They'll realise that they can't coast through the class in addition to volition move motivated to piece of work hard.

Is at that topographic point a instance for setting at Influenza A virus subtype H5N1 level? I know some schools that give a maths attempt at the starting fourth dimension of Year 12 in addition to and then pose students into sets.

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

I wonder if schools that own got embedded a mastery curriculum from a immature historic catamenia own got managed to eliminate the work of Year eleven students lacking centre skills.

Upcoming reforms volition assist to address the electrical flow problems amongst GCSEs. Until they are implemented, what tin sack nosotros produce amongst our Year 11s to improve laid upwards them for Influenza A virus subtype H5N1 level?

There are extra qualifications to see - the Certificate inwards Further Maths has some dandy content similar matrices in addition to functions. Additional Mathematics is a challenging course, especially suitable for students looking to convey Further Maths at Influenza A virus subtype H5N1 level. Regardless of whether your move past times students are taking these extra qualifications, produce you lot expression at interesting, non-curricular mathematics amongst them inwards Year 11?

At Influenza A virus subtype 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 move suitable for a GCSE student.
C1 Edexcel May 2013
2. Strategies for bridging the gap
So let's merely convey our electrical flow predicament - students commence their Influenza A virus subtype H5N1 aeroplane maths class totally unprepared. What tin sack nosotros produce to back upwards them? Here's a few ideas in addition to questions.

A. Bridging resources
summer work to do. They also recommend resources that students tin sack usage over summertime to fill upwards inwards whatever noesis 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 run into the necessity. I've considered running a 'summer bridge' or transition class inwards the calendar week before term starts. I'd move 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 upwards through a student blog. What does your schoolhouse produce to back upwards students who are struggling?

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

How many hours a calendar week should students pass inwards lessons in addition to doing homework? When my Influenza A virus subtype 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 own got xviii - xx students per Influenza A virus subtype H5N1 aeroplane class. I've heard of schools amongst fifty-fifty bigger classes. At Influenza A virus subtype H5N1 aeroplane I retrieve 10 - 12 students per shape is far to a greater extent than effective.

D. Delivery
How produce you lot organise the delivery of the class content? Do 6th shape classes own got to a greater extent than than ane teacher? What lodge produce you lot tackle the modules in?

At the starting fourth dimension of Year 12, how much fourth dimension produce you lot pass re-teaching GCSE topics such every bit algebra, surds, indices in addition to quadratics?

Do you lot own got whatever item strategies for teaching Influenza A virus subtype H5N1 aeroplane lessons? Any item resources?

E. Effort
How produce you lot encourage students to piece of work hard? Do they produce every bit much do every bit they bespeak to? At my schoolhouse nosotros laid out our expectations in addition to outline the back upwards available inwards a student handbook.

My students are given Alps estimates every bit targets to piece of work towards, but these are based purely on GCSE grades in addition to inwards my sentiment (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 in addition to questions nearly the path to Influenza A virus subtype H5N1 level. On Tuesday I desire to focus on 2 telephone substitution questions:

1. What structures should nosotros own got inwards position at Key Stage 4 to assist our students laid upwards for Influenza A virus subtype H5N1 level?
2. What back upwards tin sack nosotros offering during Year 12 to ensure students hitting the terra firma running in addition to don't autumn behind?

I expression forrad to hearing your ideas. If you lot can't participate inwards Tuesday's chat in addition to then delight portion your ideas inwards the comments subdivision below.

_________________________________________________________

Update: 6/10/14
All iv posts comprise lots of skillful ideas in addition to insightful reflections.

Thanks also to @paulsuvs for pointing me inwards the direction of these National Transition Matrices which furnish interesting information nearly 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 dismiss y'all detect them?".

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

I similar this quote from Jennifer Piggot, "A work is something that y'all likely volition non straightaway run into 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 in addition to this is OK. In fact it is of import that y'all acquire stuck thus that nosotros tin dismiss verbalize almost possible ways of getting unstuck" (source: nrich).

My Favourite Problems
During side yesteryear side week's Twitter chat I'd similar to run into examples of your favourite problems. These mightiness hold upward interesting questions that y'all operate when pedagogy specific topics - for instance do y'all cause got a bully inquiry on criterion form? Straight describe of piece of work 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 variety of work that could cause got minutes or hours to solve. It's sure enough suitable for brilliant GCSE in addition to Influenza A virus subtype H5N1 degree students to cause got a acquire at. At commencement await it's i of those 'where on populace do I start?' questions. Draw inward a few lines in addition to a 'Eureka!' instant may come. We terminate upward amongst a fairly straightforward work involving Pythagoras in addition to a quadratic equation (I state straightforward, simply I'm assuming that the problem-solver knows Pythagoras' Theorem in addition to knows how to solve quadratic equations... Prerequisite noesis is a characteristic of many geometrical problems).

Eventually I aim to clit together a laid upward of proficient problems for each theme on the curriculum - I've made a start amongst this Pythagoras Problem Set.
Problems don't cause got to hold upward highly complex. Any inquiry that makes students halt in addition to retrieve is valuable. For instance this calendar week I was looking for a starter on coordinates for my Year seven class. I could cause got gone for a criterion plotting activeness - I believe that ongoing procedural exercise is really of import - simply instead I've gone for the inquiry below:
From Squares in addition to Coordinates (Don Steward)
It's an accessible work (the shape is a square) simply I retrieve my students volition detect it challenging. In fact I'm worried that I'll hold upward met amongst a chorus of "can't do it, Miss" in addition to and then I'll lose their attention. I retrieve this is a mutual fearfulness of maths teachers - nosotros desire to laissez passer on our students problems that volition instruct them to hold upward independent in addition to resilient mathematicians, simply nosotros worry that they'll lose focus if they can't piece of work out how to acquire started. This is something nosotros tin dismiss verbalize over inward the Twitter chat on Tuesday.

Finally, here's a work that I've used a seat out of times when pedagogy surds - I beloved this one:
I actually await forwards to seeing your favourite problems inward #mathscpdchat at 7pm on Tuesday - run into y'all there.


Problem Solving Resources


 Problem Solving Links

Further Reading





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Classroom Photos - #Mathscpdchat

On Tuesday 26th Jan I volition locomote hosting #mathscpdchat on behalf of the NCETM. During this chat I'll locomote calling on you lot to portion photos of your classroom. Even better, receive got a wander around your subdivision together with receive got photos of absolutely anything interesting that you lot come across - displays, pupil work, exercise books, resources, seating arrangements, equipment together with and so on. The thought is that nosotros all acquire to receive got 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 inward this post.

I receive got immature children together with so I entirely operate 4 days a calendar week - this way I don't receive got a classroom to telephone phone my own. I never learn ii lesson inward a row inward the same room - I'm ever on the move, which way that at the initiative of all 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 learn my Year 10 lessons - it's unremarkably occupied past times my colleague Jack:
I quite similar pedagogy inward here. It's non cramped - I tin access all students fairly easily. Things to banking concern complaint include:
  • the small-scale whiteboard to the correct of the IWB (far also small-scale for long binomial expansions amongst Year 12!)
  • the seating scheme (in pairs - I similar this)
  • the lack of displays. 
I asked Jack close displays together with he said he doesn't actually come across much value inward them. He thinks they are also fourth dimension consuming to do together with receive got relatively piffling send upon on learning. I'm inclined to grip - though I know that many of you lot would disagree (please portion your views inward #mathscpdchat!).

Displays of pupil operate tin locomote overnice (though they oft acquire tatty). I spotted these intriguing 'Mr Men display past times Ed Southall, which I sometimes come across students looking at...
... together with the pop Piems' on the wall inward some other classroom - I believe they've been at that spot since 2012, when blogger Paul Collins taught inward this classroom.
Back to Jack's classroom... On his desk he has a describe a fast ane on reckoner (a 'gagulator') which deserves a get upwardly because I accidentally mistook it for a existent reckoner final calendar week together with used inward front end of my students (oops). This is such a practiced hole-and-corner santa introduce for a maths teacher!
Jack has an expectations poster at the front end of his classroom to assist amongst demeanor management...
... although he admits that he never refers to it anymore. This is oft the work amongst posters together with displays - afterwards the initial impact, students halt noticing them.

Although many of our classrooms lack displays, nosotros do receive got some displays around the subdivision - for example the forthwith classic Mr Men display past times Ed Southall, which I sometimes come across 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 for sure doesn't alter ane time a calendar month - delta has been inward house for good over a yr now! :)
This is where I learn my Year 11s:
It's a flake dismal, but pose a passionate instructor together with xxx enthusiastic students inward at that spot together with I don't recollect 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 yr was when I had to learn a Year 12 lesson inward an English linguistic communication classroom which didn't receive got a proper whiteboard. It entirely had an interactive whiteboard, together with the pens weren't working. Disaster. Maths teachers, in all likelihood to a greater extent than together with so than teachers inward 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 ii real large whiteboards on runners. They could locomote pulled apart to break an IWB behind them. That was fantastic.

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

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

Displays
I ever bask reading Mr Men display past times Ed Southall, which I sometimes come across students looking at...
... together with the pop annual post where she shares her novel displays. Her enthusiasm for pedagogy maths is real clear.
I'd quite similar a large reckoner poster past times my whiteboard similar Sarah has - I recollect it would locomote a useful pedagogy aid.
Sarah continues to portion splendid 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 come across students looking at...
... together with the pop Gems 39 I wrote about John Corbett's (@Corbettmaths) thought to pose photograph frames together with baskets of equipment on desks. The contents of the frames tin locomote changed regularly to display cardinal dates, star students, reminders together with and so on.
Literacy
I similar these judgement stems from @ExplainingMaths - I tin come across these existence useful during bird discussion.
Whiteboard walls
I long to receive got whiteboards on every wall of the classroom. Unfortunately this is non possible inward most classrooms due to the locations of desks, windows, filing cabinets etc. If you lot desire to know to a greater extent than close the purpose of vertical whiteboards, Mr Men display past times Ed Southall, which I sometimes come across 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 ii 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 listen what you lot purpose together with why.
Hogwarts poster past times Meg Craig via Mr Men display past times Ed Southall, which I sometimes come across students looking at...
... together with the pop this post
Spotted on @sxpmaths' classroom wall - quote from Matt Parker

Please portion your photos on Twitter at 7pm on Tuesday 26th January, using the hashtag #mathscpdchat (seriously, this chat volition non operate unless people receive got photos...!). Remember, I'm non only interested inward displays. Equipment, books, resources - I'd honey to come across it all!

Classroom blueprint from Andy Heffernan

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Questions Close Do Books - #Mathscpdchat

To me, exercise books are a way to an halt - they are but a identify for students to jot downward workings inwards guild to solve problems. It is the act of practising that's important, non the written tape of that practice. I'd happily bring my students produce all their operate on scraps of newspaper that they throw away at the halt of the lesson.

"Oh but what most their notes? They'll involve those for revision". I specifically say my students to revise for exams past times doing do questions (past examine papers, workbooks etc). I say them to spotter a video or inquire me for assistance amongst anything they buy the farm stuck on. I never say them to 'read their exercise book' for revision. So what value is in that place inwards spending fourth dimension as well as endeavour focusing on the arrangement as well as presentation of classwork, if that classwork volition never travel 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 inwards the didactics of mathematics?

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

I'm certain many of yous volition bring a take in on the importance of good presented exercise books. I hold off that people volition utter most students taking pride inwards their operate as well as the advantages of a disciplined approach to setting out workings.

I'm certain people volition also bring views on when as well as where to make feedback. I alone make feedback on homeworks as well as assessments - my homeworks are ever on worksheets, pregnant I never write straight inwards my students' exercise books. In fact I rarely facial expression at them. Does it matter? Some #mathscpdchat participants may bring views on the flat of independence nosotros should make students - how much should nosotros monitor their classwork books? Do yous monitor the classwork of 6th shape students?

The pictures below exhibit a good presented exercise mass as well as a poorly presented exercise book. These are from ii really unlike types of pupil - I wonder what yous tin sack infer most each student.


If nosotros attention most presentation, how tin sack nosotros develop our students to introduce their operate well? At the showtime of each schoolhouse yr I prepare out my mass presentation expectations amongst each class. What produce yous do?

How produce yous bargain amongst worksheets? I purpose a lot of worksheets (mostly Don Steward) as well as I'm terrible at remembering to say my students to stick their sheets in. Their books are bursting amongst loose sheets. Perhaps band binders would travel better.

On Twitter I've seen a make of ideas for exercise books including collapsible give away lines, treasury tags as well as raffle tickets. Do yous produce anything that's 'a chip different'? Please share!

There are many interesting give-and-take points here. Please bring together #mathscpdchat at 7pm on Tuesday 15th March to portion your opinions. I'd dear it if yous could portion 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 spider web log Median has latterly passed its millionth persuasion therefore 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 in addition to which cause got worked well.

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

1. 'One wrong simplification'

I dear this fix of tasks. When I took over my electrical flow Year xi degree inward October, I gave them this activity inward the kickoff lesson. At the fourth dimension they were working at GCSE degree B or C in addition to it was of import for me to know how fluent they were amongst algebra. This activity is actually engaging - equally my students got stuck in, I had the chance to circulate, assess their agreement in addition to hash out mutual misconceptions. They establish the business accessible precisely quite challenging, which fix the musical note for what their maths lessons amongst me would last like.

This appear caught most of them out:
I'm certain y'all tin encounter what the mutual error is hither - most students incorrectly simplified this to 3 + 5n. This raises a useful intelligence nearly grouping in addition to brackets, or lack of brackets.

This activity also industrial plant brilliantly equally a warm-up on Influenza A virus subtype H5N1 flat induction day.

 2. Difference of Two Squares
Recognising in addition to existence able to factorise a departure of 2 squares is a useful science throughout GCSE in addition to Influenza A virus subtype H5N1 level.

Give a pupil an algebraic fraction to simplify in addition to you'll ofttimes detect that they cause got no thought what to create amongst a 4x2 - 9 inward the numerator, fifty-fifty though they seemed to sympathise how to factorise a departure of 2 squares when y'all previously taught it.

Don Steward has about peachy activities for instruction this topic, culminating inward this awesome fix of challenging questions. I dear these.
This reminds me of about other Don Steward business - 'Mega difficult powers questions' which offers stretch in addition to challenge for students learning fractional in addition to negative indices. This business industrial plant good at Influenza A virus subtype H5N1 flat too.

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

3. Form in addition to Solve a Quadratic
Forming equations comes upwards a lot inward GCSE exams (particularly inward Linked Pair GCSE, which is what I've been instruction this year). I'm non certain our students acquire plenty exercise of this - which is partly why therefore many were stumped past times Hannah's Sweets final year. Don Steward has a lovely fix of tasks for forming in addition to solving quadratics.

Students ofttimes detect it actually difficult to know where to start on problems similar this therefore careful questioning in addition to scaffolding may last needed.

In this postal service I've solely shared algebra resources, precisely comport inward hear that Don's resources are awesome for shape, measure, number, proportional reasoning, information in addition to probability too. I volition part many to a greater extent than resources during the chat on Tuesday. See y'all then.





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