Dumbed down markschemes?

May 22, 2015 1 comment

Today I was working through the June 2014 Edexcel M1 paper for my year 13s, noting down thought processes etc and I arrived at this question:

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It’s quite a nice, general bouncing ball question that takes into account many of the rules of mechanics. When I finished the question I checked it against the markscheme so I could jot down where each mark came from and on part E I received a bit if a shock.

The weight of the ball is given as is the distance it’s dropped from and the distance it bounces to. In earlier parts of the question you have been asked to calculate the final speed of the bit before the first bounce and the initial speed after. Part E asks for the time between the ball being dropped and the second bounce. I split it into to, used s = ut + (1/2)at^2 (u=0, s=2,a=9.8) to find the time it took to drop, then the same equation for the time between bounces (this time s=0, u= the value already calculated, a=(-9.8)). A simple question, a simple solution and a nice answer. The markscheme, however, says this:

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I don’t understand why they have felt the need to work out the time between the first bounce and the top then double it. It’s a valid mrthod, granted, but surely looking at the whole motion is sensible as acceleration is constant?

Worryingly, in the notes there’s no other solutions offered and I was left wondering if examiner’s might miss that thus method is not only correct,, but actually more sensible.

Which way would you have done it? Do you think I’m correct thinking mines the mire logical sensible way?

Revenge of the real life questions

May 21, 2015 4 comments

Last year I wrote this piece discussing some of the worst pseudo-contexts that I’d come across in maths exams. You know the ones, the ridiculous made up contexts that are supposed to give a real life twist to a question but Ard actually anything but. Well this year’s C2 Edexcel A Level paper has two of the worst I’ve ever seen!

Exhibit A

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Aaaaaaaarrrrrrggggghhhhhh!!!!!!

“Figure 1 shows a sketch of a design for a scraper blade. The blade OABCDA consists of an isosceles triangle COD joined along its equal sides to sectors OAB and OCD of a circle with centre 0 and radius 8cm. Angles AOD and BOC are equal. AOB is a straight line and is parallel to the line DC. DC has length 7cm.”

There are a few issues I have with this question. Firstly we have a whole paragraph that is entirely unnecessary! The only purpose this paragraph would serve was to test the ability to sketch or visualise but this us completely negated  by the diagram. One of my year 12s asked, “what’s the point in that writing on the sectors question? It just described the picture.” I had to agree.

That wasn’t the worst bit though, the worst bit is there at the beginning .

“Figure 1 shows a sketch of a design for a scraper blade”

I can imagine the examiner’s meeting now: “I’ve got a great sectors question, it uses area, arc length, cosine rule, sine rule for area…. it’s a classic.” “Great, but we said that was going to be a real life question this year.” “Oh b@#@##ks, what can I do?” “Just make it about a scraper blade!”

What even is a scraper blade, and why do we need this question be about one?! This was actually a great question, or would have been if it had only one of the picture or the paragraph and no stupid mention of a scraper blade.

Exhibit B

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“A solid glass cylinder, which is used in an expensive laser amplifier, has a volume of 75pi cm^3.
The cost of polishing the surface area of this glass cylinder is £2 per cm^2 for the curved surface and £3 per cm^2 for the circular top and base areas. Given that the radius is r cm…”

Show that the cost is, then find the minimum.

This question is pseudo-context at its worst. A part for an expensive laser amplifier will be the required size for said amplifier. It will need to fit abd as such it’s length and radius will be far more important that it’s volume, do there’s no way at all that they would design the laser around the minimum cost of polishing a cylinder with a certain volume! Why would you create such a convoluted, nonsensical, bogus context?! If you want to ask questions in context fine, but please make it a believable one!

Formative Assessment

May 5, 2015 2 comments

My current MA assignment is on Formative Assessment and as you might imagine the topic has been at the forefront of my mind recently. It’s a topic I’ve touched on before, and one I’ve wrestled with throughout my entire career.

When I was a trainee teacher I heard the term AfL constantly, I knew it stood for “Assessment for learning”, but I knew very little else.  I remember being shown a video of Dylan Wiliam running a classroom experiment where they removed grades from marking and replaced hands up questioning with lolly sticks. An interesting video, not least because the top achieving girl stole the stick with her own name on!

During my teaching placement I heard on more than one occasion “you need more AfL, use lolly sticks or whiteboards”, I heard comments like “that’s a good card match, and it covers your AfL”, once I heard “get them standing up to cover your AfL”. None of this helped. I still managed to finish my PGCE with only a slim grasp on what AfL even was.

Similarly, my NQT year started without any real ideas, but I started to get to grips when my mentor discussed mini whiteboards and how she’d seen people not use them properly, having pupils wave them as soon as they have an answer. I began to realise their use, and gain a better understanding.

As time progressed I became more reflective and I began to think more about the formative assessment I used. I realised that even though I was doing the assessment right, ensure whole class answers were shown together etc there was no point, as it didn’t affect what I was doing. I was using whiteboards to check understanding but teaching the lesson the same. To be effective, surely the plans have to change.

This realisation rocked my perception a little. Up until this point I had thought that ensuring lessons were thoroughly planned was they key. I now realise that willingness and ability to divert from those plans is. If the students can all do, without prompting, the subject of the lesson when it starts, there’s no point teaching them. But similarly, there’s no point moving on after they’ve done something once as they will not retain that information. Formative Assessment must be constant and effect the lesson, you should be checking baselines, checking they have the skills and knowledge to attempt a task, checking they are practising those to ensure retention.

The same principles apply to written feedback, the longer it goes the more useless it becomes. If you mark every two weeks, at the end of a topic say, and a learner has picked up a misconception you have missed in lesson 1 then there’s a strong likelihood that there’s going to be an issue all through. That’s why checking work in class, as it’s being completed, is imperative. That way you can catch the issues as they happen and correct them on the spot.

There’s a lot of research and writing out there on Formative Assessment, and currently I’ve only just brushed the surface, but I’m adequately intrigued to see what others have said.

An End to GCSEs?

April 24, 2015 1 comment

This article was originally published on Labour Teachers here.

This week Tristram Hunt postulated in the Guardian that a Labour government may look to phase out GCSEs all together. if you didn’t catch the article, have a look here.

It’s an interesting article, and I have to say I like some of the things he’s saying. Firstly, he’s ruling out radical quick reform. This is something that has been playing on my mind, after 4 years of Gove’s fast paced reformation I feel we need time to let it embed. We haven’t assessed the new GCSEs or A Levels yet and won’t for a few years, and I feel it is right to let this take place given the work that is already underway. I happen to think the new maths curricula are in fact better than the old ones so am looking forward to teaching the new content. I am happy, though, that there are plans afoot to restore the AS /A level link.

The second thing I liked about Tristram’s comments was that he feels there is a wider discussion to be had, and that the education agenda needs to be thought through in a long term manner. This is something Gove never really seemed to think. With him it was reform, reform, reform. Some good, some bad, all fast. It felt like consultations were being hidden because they were being done over the six week summer holidays where many involved in education are refreshing themselves ahead of the new academic year. Tristram seems committed to taking views from all stakeholders and working with the sector, rather than imposing on it.

Finally, there is the proposal itself. An end to the current model and a total overhaul of everything we know! It’s a scary prospect, but also an exciting one.

I’ve written before about vocational education and our repeated failure, as a nation, to get it right. Maybe this is how we can. Instead of single subjects the suggestion is that students would leave with a baccalaureate. This could be academic or vocational and both would be equivalent.

The ins and outs aren’t fleshed out in the article, but I would envision a core section (possibly covering the old “three Rs”, basic history, hopefully some political education) and then a wide selection of options. I believe other countries run similar types of programmes. I’d imagine it gives a lot of scope for choice.

I do have reservations though, and I would certainly need more information before I could definitely say I agreed with the proposal. It’s unclear when students would sit it. We’ve seen a requirement introduced for young people to be in education or training up until 18, but if the baccalaureate was assessed at 18 would those choosing apprenticeships and the such from 16 leave school with nothing? Would study towards a baccalaureate be a requirement for said apprenticeships? Or would young people need to stay in school until 18? What exactly would the baccalaureate look like? How would we ensure the technical baccalaureate and the academic one hold the same footing? All in all, an interesting development that opens a much wider conversation.

What do you think about these proposals? Do you think this could be the way forward, or would you prefer to keep the system as is? I’d love to know!

Equal Products

April 23, 2015 2 comments

I come across a lot of puzzles and other maths things online and often save them for later, this evening I came across this little puzzle:

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The numbers 2,3,12,14,15,20 and 21 may be divided into two sets so that the product of the numbers in each set is equal. What is that product?

I had saved this over a year ago, and cannot remember where I got it from, but I can see why. It’s a lovely little question that I intend to use as a starter next week and see how my classes get on.

How I approached it

Before you read on have a go at it yourself. Go on, you know you want to……..

Right, good, now you can see if I went about it the same way!

My first thought was that all the fun could be taken out of this by using a calculator, typing all the numbers in and pressing square root. So when I set it I will be adding the line “and which numbers are in each set”, and this is what I set out to find.

Firstly I set out the numbers in terms of their prime factors:

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Then I tallied up the prime factors:

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From this I knew that the product must be 2x2x2x3x3x5x7 which is 2520.

This, of course, answers the original question but I wanted each set. I looked at the numbers and the first think I noticed was tgat 14 and 21 had to be in separate sets, as they had 7 as a factor. I also needed to split 15 and 20, my intuition suggested that 20 and 21 should be in separate boxes, but it was easy to spot that the 2s and 3s, wouldn’t work out so I placed them together and fit the rest on around them.

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A nice little puzzle, I wonder how my classes will find it.

It’s election time again

April 21, 2015 5 comments

It’s election time again, and we all know what that means….. BAD GRAPHS!!!! Last year, in the run up to the locals, we had some classics and this time is no different.

Let’s start with a positive, an example for others to look at:

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Amazing isn’t, despite the fact that he’s running for parliament, Jamie Hanley (@jamiehanley) – Labour candidate Pudsey, has managed to buck the trend and include a fully correct bar chart!! Dave Gale (@reflectivemaths) did point out that technically the claim “Can’t win here” is invalid, and should in fact read “statistically extremely unlikely to win here” or something similar. But that doesn’t take away from the excellent bar chart.

Now for some crimes:

Exhibit A

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These two came through my door, both from Greg Mulholland (@gregmulholland1) the Liberal Democrat defending the constituency. The first error, I’m sure you’ll notice, is that the numbers are different on both leaflets despite them claiming to be from the same set of election results! The second error is that the tiny gap between the Lib Dem and the Labour bars is supposed to signify around 700 people (on one, 800 on the other!) and that massive gap between the Labour and Conservative bars is supposed to be 1200 on the top and 1600 on the bottom. So the biggest it should be is twice the gap between Lib Dems and Labour, as you can see it is considerably more than this. The third error is that the aforementioned gaps between the Labour and the Conservative bars is supposed to signify between one third and one fifth of the total size of the Conservative bar, but as you can see it is actually considerably bigger on both bars. The final error is the one Dave mentioned above, the claim “Can’t win here” is technically wrong. If one of my pupils turned this in I’d be fuming!

Here’s what they should look like:

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Exhibit B

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This classic was sent to me the other day and is from a Liberal Democrat leaflet in Bristol West, where Stephen Williams is the candidate and is trying for reelection. This is a terrible example. Firstly, the gap between Lib Dems and Labour is, as the numbers state, 10% and the gap between Labour and conservative is 20%, so clearly the gap in the bars should reflect this and the Labour bar should be considerably nearer the Conservative bar. However, this is clearly not the case in this picture. Next, the gap between the Labour and Conservative bar should be less than half the size of the Conservative bar, it isn’t! And again, Dave will be screaming about that all too familiar slogan. Another terrible effort. Here’s what it should look like:

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Exhibit C

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This was sent to me by a friend, it’s from literature relating to the local elections that are currently being held and is from the Lib Dem candidate (Martin Hughes) in the Horsforth Ward of Leeds City Council. Error 1, as you can see, numbers wise the difference between Lib Dem votes and Conservative votes is 157 and the difference between Conservative votes and Labour votes is 216, these numbers are fairly similar, but the gap on the bar chart suggests the Tory Labour difference to be roughly 4 times that of the Lib Dem Tory difference. And 216 is very definitely not 4 times 157. Error 2: the 605 vote difference between Labour and UKIP is shown by a gap that is much bigger than the entire UKIP bar which represents 1059, a considerable amount of votes more! And again, there’s that slogan. Another terrible bar chart, and here’s the correct version:

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Exhibit D

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Greg again, it’s no wonder that Colin Beveridge (@icecolbeveridge) has started referring to this sort of graph as a “Mulholland”, every leaflet that comes has another crime against statistics contained in its midst, perhaps Greg should read Colin’s book? This one is particularly telling, firstly we have a question of validity, the data is ten years old. There has been a general election since then so why use 2005 data? It fits the narrative, the leaflet is aimed at trying to convince Conservative voters to vote tactically and the information from the last election would tell them that actually the Conservative candidate came second. As you can see above though, the landscape has changed and the aggregated results (whichever version is true!) in the last local do suggest a similar landscape to 2005. Why hasn’t he used those again? I can only conjecture that it is because he wanted to use percentages somehow as a general as turnout is much higher it seems closer? Secondly we have the fact that there is a 4% difference between Labour and Lib Dems and a 6% difference between Labour and Conservative, this should show as a similar difference in bar heights (the difference Labour to Conservative should be 1.5 times the Labour Lib Dem difference), as you can see the difference is nothing of the sort and 6% appears to be ten times the size of 4%. Then there’s the Tory bar, apparently representing 27% yet smaller in size than the aforementioned 6% gap. And to top it off, that slogan again! Here it is, but correct:

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Exhibit E

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Here we have a superb example of a terrible misleading bar chart. It’s from Liberal Democrat literature in Lewisham East (where the candidate is Julia Fletcher). As you can see from the graphic, the Labour bar is largest, followed by the Lib Dems who are fairly close then the tories who are much further behind. But hang on, look at those percentages! The Labour bar represents 43%, the Lib Dem bar 28% and the Conservative bar 23%, the Lib Dem bar should be much nearer the Conservative bar than the Labour bar! And both Lib Dem and Tory bars should be around half the size of the Labour one. And again we see that slogan. Another shocking effort, and here’s another correct version:

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Exhibit F

As I’ve been writing this post I’ve just received this link to this crime against statistics!

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And I’m sure you’ll agree it’s immense. This one is from a Lib Dem leaflet in Wantage, where Alex Meredith is the candidate. They have tried to get by on a technicality, using a broken blue bar to show that the Tory share is broken, but that negates entirely the need to include the bars at all, they are there to be a visual representation of the proportion of votes, but using a broken bar makes a mockery of this as the ammended heights suggest a close race, when actually the blue bar should be almost double the size of the yellow. Even with this technicality the bar is still wrong, as the rest bar should be half the size of the yellow bar but infact it’s less than one third. And yet again, Dave’s favourite slogan has reared it’s head. A terrible effort, here’s how it should look:

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While writing this post I asked people to send me any bar chart crimes that had come through their doors on election material, I particularly asked for non Lib Dem ones, yet the masses that came in all seemed to be theirs. I am beginning to worry that no one in one of the parties that has held government office for the last 5 years can grasp a basic bar chart. I’d be seriously worried if year sevens were making these mistakes. What’s worse is that there are tons of free websites that will do it for you, I used meta-chart for these. Or perhaps it’s just their policy to use misleading bar charts on their flyers. I am always on the lookout for crimes against statistics, so please do send me any you find, be they election related or not.

A Political Education

April 19, 2015 Leave a comment

This post was first published here on Labour Teachers on 19th April 2015

Monday is the last day you can register to vote, which means I have spent a large portion of the week checking in with my year 13 class and my year 13 form group that they have registered. This has led to various discussions around politics, how they can decide who to vote for etc. It seems a lot of young people take on the political views of their parents. I was pleased to hear a number of them had actually downloaded the manifestos of the major parties and we’re using them to help them decide. I was shocked, however, at how many of them knew very little about any of it.

One asked if she could vote for Barack Obama. One asked if we were choosing a new queen. One thought Ed Miliband was the prime minister at the moment. There were many others like this and they echoed conversations I’ve had in previous years too. When one young lady asked who I thought our next president would be another year 13 overheard and joined the conversation. He was very knowledgeable about the political spectrum and the democratic process and it was quite refreshing to hear him explain the ins and outs of it rather than having to explain it myself.

As the conversation drew he said: “the thing is sir, there are far too many people who know nothing about it. It’s arguably the most important part of life. Why isn’t more taught about it in schools?”

I don’t have an answer. I don’t know much about citizenship, but I thought that this was something that fell under that banner. The current provision clearly isn’t helping engage young people with the process and it clearly isn’t helping to enhance their understanding of politics. I am a firm believer that we need to be giving our learners the knowledge they need to make these decisions, and that means we need to increase this aspect of their education.

Maybe the citizenship curriculum is too wide and/or the time allocated is too small meaning teachers cannot give each topic the time it deserves? Maybe it’s not seen as important by schools because it doesn’t fall into the same category of core subjects as others? Perhaps if it were made a requirement that all students study it to GCSE and it were given double weighting on progress 8 similarly to English and maths then it would be seen as more important by schools? Perhaps it needs a revised curriculum and a rebranding? Perhaps it suits the political classes to keep the majority uneducated on politics and it’s importance? One thing is for sure, there are far too many people leaving school without a sound knowledge of these matters.

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