The Deadly Sins Of Maths

A Twitter conversation alongside Ben Ward got me thinking virtually a display idea...


There are but about misconceptions in addition to mistakes that come upwards up fourth dimension in addition to fourth dimension again. Last calendar week I laid upwards a lovely Don Steward quadratics homework for my Year 11s in addition to was dismayed to run across a reveal of them exercise this:
(x + 2)2 =  x2 + 4
When I returned the homeworks I talked to the whole shape virtually this mutual mistake. I told them that it makes me outcry every fourth dimension I run across it in addition to thence they must never ever exercise it again! When I asked them why it was wrong, they were able to explicate what had happened in addition to nation me the right agency to exercise it (phew!).

When I adjacent location mutual misconceptions inwards my students' work, I'm going to nation the perpetrators that they've committed ane of the deadly sins of maths, in addition to signal them inwards the direction of a classroom display. Making a large bargain virtually these mistakes (in a half-jokey agency that volition stick inwards their heads) is a skillful agency to lower the run a hazard of students repeating the same error inwards an exam!
You tin download my posters here (there are xx posters to pick from - you lot may non concord alongside all my choices). I've likewise made a US-friendly version (using the discussion math instead of maths) which you lot tin download here.

Some of these posters volition brand students halt in addition to mean value - it mightiness non hold upwards obvious to them what the error is.

In our didactics nosotros should endeavor to preempt mutual misconceptions - this is where clever questioning in addition to well-written resources come upwards into play. But sometimes nosotros can't run across mistakes coming - this is why effective mark in addition to feedback are essential.
These days mark doesn't cause got to hold upwards handwritten - websites similar Hegarty Maths can exercise it for you.

If you're looking for resources for highlighting in addition to tackling mutual misconceptions, hither are a few starting points:

#Christmaths16

I'm real excited to portion the details of this year's Christmaths event, which takes house inward London on Th 22nd Dec 2016.

#christmaths15 was a neat success (read close it here). We had an afternoon of CPD alongside bright speakers followed yesteryear food, drinks, puzzles as well as a quiz.

I know that many maths teachers are looking forwards to the opening of the novel maths gallery at the Science Museum, as well as thence I decided to organise a dissimilar type of Christmas effect this year. Here's the plan:

3pm - 5pm
: Group catch to Mathematics: The Winton Gallery. Explore this exciting novel gallery inward the companionship of beau maths teachers.

5pm - 7pm: We volition get got exclusive purpose of the Media Space Cafe at the Science Museum where you lot volition hold upward treated to a drinking glass of fizz as well as a mince pie. The Big Fat Christmaths Quiz volition return! Tickets for this reception are exclusively £12. There are 130 spaces available as well as I hold back these to become chop-chop as well as thence mass now!

From 7pm: If anyone fancies a flake of festive socialising, we'll hold upward going circular the corner to The Hereford Arms afterwards. This isn't ticketed as well as thence you lot tin but determine on the twenty-four hr current if you'd similar to come upward along.

For amount details of the effect as well as to purchase tickets catch christmaths.co.uk. Please invite your friends as well as colleagues along too! All welcome.




Going Well...

I'm struggling amongst workload at the minute but I'm taking a quick intermission from the marker together with UCAS references to portion 3 things that are going actually good this year.

1. Low Stakes Quizzes 
I started doing regular multiple selection quizzes amongst my Year 10s final twelvemonth together with right away loved it (I wrote almost it here). I've never done anything earlier that's given me so much insight into my students' agreement together with the effectiveness of my teaching. My Year 10s ended upward beingness taken yesteryear a PGCE pupil for a pregnant role of the twelvemonth so the quizzes stopped, but I possess got reintroduced them this twelvemonth amongst the same cast (now Year 11) together with ane time to a greater extent than I'm reminded of how awesome these quizzes are.

My weekly quizzes possess got twenty minutes to run inwards the lesson (we create it every Friday), summation almost twenty minutes to score later the lesson. The quizzes don't possess got long to brand when I'm planning my lessons - lately I've only been using the snipping tool to possess got questions from Diagnostic Questions (shhh, don't tell Craig!). You tin persuasion my quizzes here.

I plow over each pupil a flat (A, B or Not Yet) together with anyone who scores 100% gets a sticker (they dear that!). The quizzes are opened upward mass so there's no stress for students - inwards fact they dear them (I learn a cheer when I tell it's fourth dimension for the quiz!) together with they are ever excited to encounter their score inwards the side yesteryear side lesson. For me 'it's similar I'm looking at the freaking Matrix' (in the words of Nathan Kraft inwards this post almost vertical whiteboards!). Seriously, this is ane of the best things I've ever done.

2. Folders
My Year 11s at nowadays work band binders instead of practise books. It's brilliant. I bespeak to write a dissever ship service almost how this plant because there's lots to say. Loads of people told me it wouldn't work, mainly because the folders would chop-chop buy the farm disorganised (which may still happen - we're exclusively 3 weeks in), but I've designed a proficient laid of resources that minimise the direct chances of messy folders. I'm pretty confident that it volition proceed to run well. Watch out for a ship service almost this!

3. Times Table Rock Stars
I'm non certain I'm allowed to seat photos of my students on my blog, but if I could together with then you'd encounter the happy faces of my Year 7s absolutely loving Times Tables Rock Stars (whilst wearing wigs together with sunglasses!). All Year seven teachers at Glyn at nowadays possess got ane lesson inwards an information technology Room every fortnight to run a Times Tables Rock Stars lesson. I create the newspaper version amongst my cast too, summation I've only launched an later schoolhouse 'Rock Gods' monastic tell for groovy Year 7s. H5N1 publish of teachers possess got also laid other classes (Year 8 to Year 10) together with it seems to last going good all round. My students happily sit down at that spot for a amount hr enthusiastically practising times tables, together with I learn to hear to stone music so it's win-win...!

So that's 3 things are going peculiarly good for me this year. Are you lot trying anything novel that seems to last working? Please tweet me or comment below.






#Mathsconf8

I had a nifty fourth dimension at #mathsconf8. Thanks to Mark McCourt too La Salle Education for organising to a greater extent than or less other fantastic trial for maths teachers.

Friday night
We had a big turnout at the pre-conference drinks on Friday. It was lovely to grab upward alongside people I've non seen inwards a while. Workload was a mutual give-and-take betoken - sometimes it's helpful to allow off steam close the challenges of the project every bit good every bit sharing the highlights.

The best piece of job of the eventide was our Pringles Enigma machine activity! When nosotros visited Bletchley Park over summertime nosotros were treated to a display of a existent Enigma machine past times Tom (@TeaKayB). At the fourth dimension Tom mentioned that it's possible to brand an Enigma machine out of a Pringles underground too therefore nosotros invited him along to #mathsconf8 drinks to demonstrate us how! Here's what I came upward with, assisted past times @JoLocke1 (it works! We were able to decrypt a message). 
Kim (@MsKmp) didn't bring a Pringles underground merely managed to brand her Enigma machine out of a vino bottle! If you're interested inwards having a become at this activity, all the instructions too materials are here.

At the pre-conference drinks I also chatted to Craig Barton. I was interested to listen that he has relaunched his website mrbartonmaths.com. For a resourceaholic similar me, this is exciting news! I'm looking forwards to exploring all the resources that Craig has pulled together. For every topic he has provided specifications, videos, worksheets, diagnostic questions, lessons, rich tasks, interactive resources too probing questions. Amazing.

Saturday
The conference was brilliant. I thoroughly enjoyed my solar daytime too went habitation feeling inspired.

The solar daytime kicked off alongside Mark McCourt talking us through the 1089 activity. I've heard of this activity earlier merely non looked at it inwards detail. I actually enjoyed doing the maths (even inwards base of operations seven!) too tin give the axe view that this would brand a vivid lesson for students. I hope to usage it at schoolhouse at to a greater extent than or less betoken this year.

I also enjoyed the speed dating session where I picked upward a brace of first-class resources.

The get-go session I attended was Kris Boulton's beak on Engelmann. I saw the get-go piece of job of this beak at researchED Maths too Science inwards June which I wrote close here.  Kris continued to beak close Engemann's ideas, including examples of how Kris has applied these ideas to his teaching. I detect all of this actually interesting, too it does brand me enquiry whether I usage the most effective method of instruction.

It was interesting to view a snapshot of Kris' planning procedure for a sequence of lessons.
Thanks to @MathsWebb for this photo

I enjoyed watching videos of Kris' teaching inwards action, too was pleased that he spoke close the means he handled a student's negative demeanor (I don't recollect plenty teachers speak close the challenges nosotros human face upward alongside regard to demeanor management, too therefore this was refreshing to hear). The most hitting matter Kris did inwards his video was stay still when solving a pair of simultaneous equations on the board. I ever beak through what I'm doing stride past times step, too I wonder if my talking distracts students from next what I'm writing. I demand to recollect close this.

At the intermission I bought a calculator! It's probable my Influenza A virus subtype H5N1 marking students volition hold out using these adjacent yr too therefore I'm going to start using it straightaway to ensure I'm good practised past times adjacent September.

The mo session I attended was close mastery too was delivered past times Mark McCourt, a thoroughly entertaining too knowledgeable speaker. If you're interested inwards what Mark has to nation close mastery, read his recent spider web log shipping service 1089 activity. I've heard of this activity earlier merely non looked at it inwards detail. I actually enjoyed doing the maths (even inwards base of operations seven!) too tin give the axe view that this would brand a vivid lesson for students. I hope to usage it at schoolhouse at to a greater extent than or less betoken this year.

I also enjoyed the speed dating session where I picked upward a brace of first-class resources.

The get-go session I attended was Kris Boulton's beak on Engelmann. I saw the get-go piece of job of this beak at researchED Maths too Science inwards June which I wrote close #MasteryFail too expect out for his adjacent shipping service too.
  

At tiffin it was nifty to view too therefore many teachers enjoying the maths activities at the Tweet Up.

After tiffin I attended a session on champaign of written report cognition past times Ed Southall. I learnt lots from this session - my favourite matter was the word discorectangle (also known every bit a stadium). I learnt close the etymology of the word integer (not touching / standing alone).  I also learnt the divergence betwixt an oval too an ellipse (an ellipse has 2 lines of symmetry) too lots of other lovely snippets of maths knowledge. I dear learning novel things close my subject. You tin give the axe download Ed's slides here.

All 3 sessions I attended were excellent.

I presented inwards the in conclusion slot of the day. My session was close novel higher GCSE topics. I promised that I'd percentage my slides too therefore yous tin give the axe usage them to deliver preparation at school.
  • Here is the version I presented at the conference.
  • Here is the 'uncut' version which has lots of additional information. If you're presenting to your region I recommend using this i (split over 2 or 3 sessions).
  • Here are the GCSE questions that I used every bit a starter activity.

Links tin give the axe hold out industrial plant life inwards the slides themselves or inwards the notes section. I hope these slides are helpful, delight allow me know if I tin give the axe clarify anything.
Thanks to @letsgetmathing for this photo

I actually enjoyed catching upward alongside Twitter friends too coming together lots of novel people. Thanks to Mark McCourt for promoting my #christmaths16 trial which yous tin give the axe purchase tickets for here.

If you've non been to i of La Salle's maths conferences before, create come upward along to Bristol on 11th March or London on 24th June. Tickets volition hold out available through mathsconf.com.

Finally, cheers to superstar Rob Smith for running the tuck store too doing an amazing project of raising coin for charity throughout the day. Every conference should bring a tuck shop!





5 Maths Gems #64

I haven't written a gems postal service inward a long time! I've been also busy at work. So I've got a big listing of resources as well as ideas from Twitter, plenty to produce amount iii or 4 posts. Let's brand a start...

1. New GCSE Resources
Teaching novel GCSE? Edexcel stimulate got come upward to our rescue yesteryear launching a ready of resources for novel GCSE topics. There's loads of useful stuff hither including worked examples, exercises amongst answers, as well as extension material. Sixteen topics are covered include functions, iteration, Venn diagrams as well as geometric progressions.
Extract from 'N15 Bounds (Foundation as well as Higher)'

2. Fractions Task
Thanks to @MaxTheMaths for sharing this lovely fractions task. This is taken from Buzzard Publishing's Arithmekit Bundle (@BuzzardPublish). Check out CanDoMaths.org for to a greater extent than resources similar this.
3. MathsFrame
It's been a long fourth dimension since I terminal taught Year 7. Now I've got a depression attaining Year seven flat I'm going to start adding lots of novel resources to my resource libraries (for instance I've of late added house value as well as addition). With my Year seven flat inward mind, resources from mathsframe.co.uk (@Mathsframe) stimulate got caught my eye. There's over 200 complimentary resources hither - they're aimed at head schools only secondary teachers may notice them useful too.
Extract from Year vi fractions assessment

4. Inspect the Spec
Craig Barton has been writing a keen ready of 'Inspect the Spec' posts on TES. If you're instruction novel GCSE, you'll notice these posts helpful. They comprise data almost what's inward the GCSE specification (what's changed as well as what's the same) along amongst recommendations of TES resources. 

5. Number Line
Megan Guinan (@MeganGuinan1) get-go tweeted almost this tool ages ago, only it's taken me a spell to notice a occupation for it. I of late used the zoomable issue line from mathsisfun.com to assist explicate decimal house value to my Year 7s. Now I realise it volition endure useful for quite a few topics. My Year 7s were 'wowed' yesteryear it as well as asked me to proceed zooming inward (forever!). Then they realised it could also zoom out to demo actually big numbers. It's e'er keen to meet kids getting excited yesteryear numbers!

Update
In instance y'all missed them, hither are my most recent posts:

I've straight off sold one-half the tickets for #christmaths16. There's yet sixty tickets left only demeanour inward hear that the get-go sixty tickets sold inward alone ix days then I recommend that y'all mass straight off then y'all don't immature lady out! Visit christmaths.co.uk for to a greater extent than information.

I'll exit y'all amongst this lovely flick from an onetime maths textbook. Thanks to @john_overholt for sharing this.
The XXth Century Arithmetic published inward 1903




New Gcse: Capture-Recapture

If your schoolhouse plans to role Edexcel for GCSE from 2017 together with therefore you lot may get got spotted the capture-recapture method inwards the Higher Tier specification:
Source: Edexcel GCSE (9 - 1) Mathematics Teaching Guidance

Here's the sampling content inwards to a greater extent than detail:

Source: Edexcel Content Exemplification FAQs

It's worth noting that both Edexcel together with AQA listing stratified sampling every bit a topic that has been removed from GCSE. However, this comes amongst a caveat - both sampling together with proportional reasoning create characteristic inwards the ix - 1 GCSE, therefore it would last reasonable for exams to include a stratified sampling query fifty-fifty if students haven't been explicitly taught this topic (as long every bit the query doesn't role the give-and-take 'stratified' without explaining its meaning). So my advice - whatever board you're using - is to expect at a few stratified sampling questions amongst your GCSE class, whether inwards a statistics lesson or a ratio together with proportion lesson.

Stratified sampling is a slap-up chance to role proportional reasoning, every bit is the capture-recapture method. If you've taught Edexcel's GCSE Statistics together with therefore you'll already last familiar amongst capture-recapture, but I'll explicate it hither inwards instance you've non seen it before.

A unproblematic example
Try this question... it volition solely get got you lot a second.
I captured 50 fish from a lake. I marked a big cross on the dorsum of each fish amongst a permanent marker*... 
I pose the marked fish dorsum inwards the lake together with they happily swam away to bring together their friends. 
The side past times side solar daytime I captured twenty fish from the same lake. 10 of them had a cross on their back. 
Can you lot approximate the total population of fish inwards the lake?
*no fish were hurt, promise.

I'm sure you lot spotted that the proportion of marked fish inwards the bit sample was 0.5, together with nosotros tin assume the same proportion of marked fish inwards the whole population. Given that I marked 50 fish, nosotros tin approximate that at that spot are 100 fish inwards the lake.

A formula
If the numbers are less straightforward therefore the estimation can't last done mentally, it's slow to ready a formula to operate out the population. This is for certain non a formula that students volition postulate to memorise - it tin last deduced using proportional reasoning.
You tin run into that the formula on the left merely shows that proportion of marked fish inwards the population is equal to the proportion of marked fish inwards the sample. The formula on the correct has been rearranged to brand northward the subject.

Here's an instance from the Biology department of BBC Bitesize. It would last ameliorate if they had shown the proportional reasoning together with rearrangement procedure rather than exactly give a terminal formula.
Source: BBC Bitesize

The instance goes on to listing about assumptions - these are for certain worth discussing amongst your students.
  • There is no death, immigration or emigration (ie the population is closed)
  • The sampling methods used are identical
  • The marking has non affected the survival charge per unit of measurement of the animals 

We too assume that animals create non lose their marks, that marking does non touching the likelihood of recapture, together with that sufficient fourth dimension is left betwixt marking together with recapture for all marked individuals to last randomly dispersed throughout the population.

An essay question
So what mightiness this topic expect similar inwards a GCSE exam? Here's a question from Edexcel's 2014 Higher GCSE Statistics paper.
A scientist wants to approximate the pose out of fish inwards a disused canal. He catches a sample of thirty fish from the canal. He marks each fish amongst a dye together with and therefore puts them dorsum inwards the canal. The side past times side solar daytime the scientist catches twenty fish from the canal. He finds that iv of them are marked amongst the dye. 
(a) Estimate the total pose out of fish inwards the canal. (2)
(b) Write downwardly whatsoever assumptions you lot made. (2)

For business office b, candidates get got to lift 2 ideas, including something nigh the population beingness unchanged, or the thought of randonmess, or that markings rest unchanged.

For to a greater extent than essay questions, see Edexcel's Emporium together with expect under GCSE 1MA1 Practice Papers > Themed Papers.

Teaching ideas
I yell back this volition last quite a overnice topic to teach. Here are a few useful links:

Finally, here's a overnice video to present inwards your lesson - Johnny Ball estimates the pose out of dark cabs inwards London.






The Folder Experiment

I'm trying something novel alongside my Year 11s this year.

I ended upward inwards a chip of a mess alongside this degree final year. Their practise books overflowed alongside worksheets, inwards fact it got as well as therefore bad that at 1 betoken I was emailed yesteryear a bring upward complaining almost the amount of unloose newspaper her boy was carrying around. Some of my students tried difficult to proceed things tidy, merely my worksheet habit overwhelmed them as well as fifty-fifty the tidiest books buckled nether the pressure.

I know I'm non the alone instructor alongside this problem. Here are around of the causes:
1. I don't convey access to textbooks. I purpose printed resources (often Don Steward as well as MathsPad) inwards every lesson... I dear resources, inwards illustration you lot hadn't noticed.
2. I produce endeavor to display equally much equally I tin flaming on the board instead of printing it out (to salvage printing budget), merely most of my activities don't run equally good if non printed out.
3. I used to learn girls - most would crease as well as stick their worksheets beautifully (see motion painting below). I similar a shot learn boys... most aren't as well as therefore bothered almost keeping things neat.
4. I'm non especially skillful at reminding students to stick sheets inwards during the lesson.

I don't yell upward that messy books are the worst affair inwards the world, merely I felt that at that spot was room for improvement.
Good sticking!

My solution is to hand a telephone binder to each student. I've ever had my H5N1 flat students purpose telephone binders merely I've never done it at Key Stage iv before.
So far, it's awesome. It's working actually well. I volition explicate hither what I'm doing, as well as written report dorsum after inwards the twelvemonth on whether it's all the same working well.

Worksheets
For each lesson I ready 1 double sided A4 sheet which includes a starter, infinite for notes, the principal classwork practise as well as an extension activity. If they request to a greater extent than infinite for notes or classwork, they convey a stack of newspaper at the dorsum of their folder.

The worksheets are similar a shot a good established routine. They hand my lessons a actually clear construction - this fits good alongside my pedagogy style. With a dedicated infinite for notes as well as examples, I'm seeing an improvement inwards their Federal Reserve notation taking (which was almost non-existent final year).


Revisiting Year 10 topics
My Year 11s convey ix hours of maths a fortnight (last twelvemonth Year eleven alone had six, as well as therefore this is a big improvement). Because I convey immature children I alone run iv days a week, important that 1 of their ix lessons is taught by around other teacher. In her lessons my students are given a 1 lx minutes Edexcel topic examine to run through (these tin flaming live downloaded from the Emporium) - these are kept inwards a separate department inwards their folder. So in 1 trial a fortnight my students are spending an lx minutes doing examination fashion questions on previously taught topics. This is skillful grooming for their upcoming mocks as well as allows me to larn on alongside pedagogy novel content.

Multiple choice quizzes
I wrote here almost the multiple choice opened upward mass quizzes that my Year 11s produce every week. I dear these! There's a department inwards their folder to proceed their marked quizzes. When they larn a quiz dorsum they tape their score on a tracking canvas as well as therefore they tin flaming easily encounter topics that request to a greater extent than work.

Marking
There's also a department inwards their folders for marked homeworks. This agency that when my Head of Faculty does a mass scrutiny she'll easily encounter the feedback I've given. In previous years my marked run oftentimes ended upward lost inwards a stack of unloose sheets, as well as therefore it looked similar I never did whatsoever marking.

I laid 1 assessed homework per fortnight that I grade as well as hand feedback on. This gives me a skillful feel of how each educatee is getting on and, along alongside the quizzes, ensures they larn regular feedback. Every other calendar week I laid a self-marking homework. My workload is far likewise heavy to grade homework every calendar week for every class.
Admin
My Year 11s convey an 'information' department inwards their folder which includes a topic checklist, topic timeline, progress information as well as examination information.

Considerations
So far I'm loving the switch to telephone binders. It's working actually well. My students' maths notes as well as classwork are good structured as well as organised. This volition live beneficial when they revise for their GCSEs. Although a few folders are getting a picayune chip messy (eg file dividers falling out), the bulk are inwards actually skillful shape. I produce worry that the folders mightiness overflow yesteryear May - maybe lever arch files would convey worked improve given the mass of run nosotros larn through.

This was a fairly pricey experiment for me (I'm reluctant to pass whatsoever of my ain family's coin on equipment for schoolhouse merely this cost me £40 for foldersfile dividers as well as paper). One modest setback is that I learn this degree inwards 3 dissimilar classrooms as well as most conduct to larn out their folders alongside me, which agency I convey to bear folders betwixt rooms at the halt of the day. Life would live easier (in many respects) if I were based inwards 1 classroom.

Overall my folder experiment is going actually well. I volition written report dorsum at the halt of the twelvemonth on whether I'll produce it in 1 trial again adjacent year!