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Fifteen thousand students were affected back in June by mistakes contained in a question on paper two in Higher Level Maths. With results due out tomorrow morning, and a report for Education Minister Ruairí Quinn nearing completion, teacher Eamonn Toland – managing director of TheMathsTutor.ie – reminds us what happened, and outlines how the State Examinations Commission can make sure it never happens again.
THE MAIN ISSUE was that the trigonometry question was set out with too many items of information, thus creating a scenario that was not mathematically possible. In effect, examiners attempted to describe a triangle using a set of measurements that can’t actually co-exist in a single triangle. This meant that the question was fundamentally flawed. Students answering the first question posed about this scenario could arrive at different answers using legitimate mathematical methods. Follow-on questions would also be impacted. (For a video overview of the problem, click here).
So, how does this affect students?
Well, the stronger students would have found it unusual to be provided with four measurements to describe a triangle. Of course a triangle has three angles and three side lengths, but usually you’d expect to be given two side lengths and an angle, or two angles and a side length, and that would be enough to figure out the other measurements. Being given four measurements should set off alarm bells, especially for a strong higher level student.
Because of this, students might have chosen to solve the first part of the question using very basic trigonometry, and have then decided to quickly check their answer by using the same method but going at it (literally) from another angle. If they did this, they would be very puzzled, because they would arrive at two different answers. They might waste time trying to understand what was going on, and it could throw them off their stride.
Furthermore, the answer to part (a) feeds into part (b), so this student would be feeling very uncomfortable with the dilemma as to which answer was correct.
Not all students would be affected. Some might not realise the implications of being given four measurements instead of three, and would proceed to find the answer to the first part, and not do any further checks. They could then proceed to use their answer in solving part (b).
Note 1: the Irish language version of the paper did not include one of the measurements, namely the 36 degrees angle at H. Because of this, their question 8 was legitimate. However, this ‘omission’ was noticed, and ‘corrected’ verbally by means of an announcement by examiners before the exam began. This meant that Irish language candidates then became embroiled in the same problematic scenario.
Note 2: There’s a second error in the question, in that an exterior angle is effectively described in the text description as being 124 degrees, but it is the interior angle which is labelled as such in the diagram. It is highly likely that most students would have gone with the diagrammatic description, but it’s still not acceptable to have this kind of error, especially as different students have different ways of processing information. This could have been another source of confusion.
The SEC could do one of several things:
There are problems with all of these approaches. Too ‘soft’ an approach is unfair to students who are genuinely strong on trigonometry, as it effectively levels everyone’s marks for this question. Too ‘hard’ an approach could penalise all students unfairly, including the very best students as mentioned in scenario (c).
None of these approaches can compensate the students who spent extra time on this question, or who lost momentum or confidence in the exam due to this question.
The SEC has stated that the official marking schemes will be available by the end of August, in time for students to view their scripts. However, they may release a statement before then, due to the notoriety of this particular incident.
Anecdotally, there has been a mixed reaction: Most students, parents and teachers have been rightfully upset that this question could be set with these significant errors, not to mention other errors seen in other exam papers, including maths, this year. A lot of students have said that they hadn’t realised that there was an error in this trigonometry question, and as such were unaffected on the day. However, they are still concerned about how the question will be marked.
Some other students experienced unease at the question having too much information, but in the exam situation, took it at face value and did not necessarily investigate too deeply. Others did the check and became confused when they got two different answers. This caused a delay and upset during their exam.
How can this be prevented from happening again?
Exams are drafted and set by a team, including at least one drafter and one setter, and possibly assistant setters. These are answerable to a chief examiner who has ultimate responsibility for setting the exam. The setting process includes proof-reading, review and revision in accordance with SEC procedures.
Human error is always possible in any endeavour. Although the exams are set by a team of subject matter experts, it’s important that the quality assurance process be well designed, and fully complied with.
It is difficult to understand how so many errors have slipped through this year, particularly in maths. To avoid this in future, there should be more clarity and accountability in the process.
A report is being prepared for the Minister regarding the mistakes made in setting exams this year. We hope that there will be no more such mistakes, particularly in maths, from 2014 onwards. Irish students must be able to trust that their exams are based on valid and fair questions ongoing.
Eamonn Toland is founder and Managing Director of TheMathsTutor.ie, and leads a team of mathematicians, teachers and technologists who have created Ireland’s leading e-learning system for Project Maths.
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Not mentioned i the article is the 67% DISAPPROVAL rating for Inda Kenny, and that was BEFORE his response last night to the biggest mobilisation of the Irish people in the history of the state i.e. falling back into primary school teacher mode to talk down to us and threaten us like we’re a class full of disobedient 9 year old schoolchildren.
After that display, if the poll was held today his rating would be somewhere between that kid on love/hate who shot the cat and the ebola virus.
Incidentally, just heard Mary Lou McDonald state on RTE that after hearing Enda Kennys threats she will now NOT pay the water charge. The rest of SF need to do the same NOW.
Biggest mobilisation of the Irish people in the history of the state? – maybe you’re too young to remember the marches against the Iraq war.
The Iraq war march drew 150,000 (largest estimate I’ve seen, please correct me with a relevant link if thats incorrect)
Yesterdays estimates were 170,000+
Like i said, feel free to correct me.
Ha ha ha ha ha ha RTE ha ha ha ha ha ha ha Indo ha ha ha ha ha Irish Times, Newstalk, the Journal. Political propaganda fail…….
@WereJammin Totally agree, SF in power will solve all our problems.
The Irish Independent ‘journalists’ must have had a A Clockwork Orange brainwashing camp. The newspaper has become a parody and they react like spoiled brats when anyone criticises them, zero decorum. Very sad that all of the staff at that newspaper studied hard to work in journalism only to end up being a mouthpiece for Fine Gael and he who shall not be named. The paper just reads like one big long rant from front to back, and of course some trashy celeb nonesense scattered in between.
Last week the headline was “bad news for sf…” This week the headline is “despite the maria cahill controversy…” and then a reminder of that story again. I need not say more.
The article didnt even exist a few minutes ago despite being all over social media and radio since yesterday and even twip!
@ Ruairi: At the same time the “Bad news for SF” article was on here, the following was on the BBC
http://www.bbc.com/news/uk-northern-ireland-29771610
“Irish polls suggest little change in Sinn Féin support
The first opinion polls to be published in the Republic of Ireland since allegations were made by Belfast woman Maíria Cahill suggest the claims made little impact on Sinn Féin’s support.
The Red C/Sunday Business Post poll has the party down three percentage points to 20%. That is within the poll’s margin of error (+/- 3%).
A second poll, conducted by Behaviours and Attitudes for the Sunday Times, has Sinn Féin support unchanged at 19%.”
This news broke last night and The Journal are only putting the story up now.. The Journal even had time to fit another Mairia Cahill story in this morning with the comments section closed as usual..
You see Ruairi, we have a very fair minded media NOOOOT including “Journal.ie from whom I expected more
Looks like there is no such thing as bad publicity for Sinn Fein.
Which also means 4 out of 5 SF voters are either satisfied or have no opinion either way.
Poor spin, by the way.
1 out of 5, Enda would take that any day.
I’ve told FG people this over and over but they can’t accept it: ”Dancing on the PIRA/North/Shady dealings card energizes your base but it energizes THEIR base way more and just makes swing voters roll their eyes thinking it’s the same punch and judy show”.
They live in a bubble where everyone they know thinks SF are loony and FF ‘destroyed the country’ that’s just your bubble though. People should make it a point, esp in politics, to talk to people who disagree with them, it gives you way more perspective. When you’re a politico pick the lowest box total where you got your smallest no1s and canvass that area right after the election and instead of lecturing them on how they just don’t realize your party is great for them, try listeing to them and asking them what you would have to do to get their support.
There is no point living in an echochamber where everyone thinks the same as you.
It seems the writer wrote this article through gritted teeth, scraping twitter to find anything to put a negative spin on the poll results. No mention of the other leaders popularity ratings to compare to Adams, when even after the two week tirade against him no other leader is more than 2 percentage points higher than him in satisfaction ratings.
This poll shows the depth of anger against the three establishment parties and the most satisfying trend I can see from the polls is the stagnation of FF, long may it continue!
You’ve gotta hand it to Meehawl, handing over Mairia Cahill to Enda and letting him run downhill with the fallout. Lets see what sweets and treats the troika of FG/FF/LAB will give us to win us back, if they ever can.
The labour silence has been deafening. Afraid their Official IRA connections might sneak out. A quick google of a certain ministers husband makes interesting reading
Thats not who i was referring to!
oooh Sam, please tell, I’m hovering over the Google button!
Look towards real capital. South of Tipperary.
Denis I think Enda took the baton off mehole.
FF massive op to get back into power if the lose their dinosaurs. Thanks to Enda of course.
Just goes to show how inept and useless Enda Kenny and FG ae. they use an alleged rape victim to conduct their own political “kangaroo court” under privilege as well as getting their propaganda mouthpieces at the Independent to spew out some of the most ridiculous drivel since Völkischer Beobachter and they still can’t stop Sinn Fain!!!
While I have no doubt that some politicians have tried to capitalise on the Cahill case, it’s actually distressing that a lot of Sinn Féin supporters are perfectly happy to completely ignore Adams’ and SF’s role in the whole affair, not to mention the rest of their recent shady past. SF have done a wonderful job of casting themselves as the victim, which I find disgusting quite frankly.
History records plenty of sleaze and murders committed by civil war parties. Can we please see some balance to the debate.
@ Search Eagle, i think you’re missing the point that people saw straight through Kenny and Martins pathetic attempt at political ping pong at the expense of the said victim. Also Ms. Cahill probably has her own agenda here.
@Denis No I’m not missing the point. The point I was making is that a lot of people seem perfectly fine with the fact a victim of such an act was treated with such contempt by SF/GA, whose response has repeatedly been to smear her until they’ve been forced to backtrack.
@History records plenty of sleaze and murders committed by civil war parties.
Absolutely correct. But what current members of FF, FG, Labour, AAA, Greens et al. are linked to and/or apologists for murders and bombings. That is large part of the reason that a lot of the Irish electorate have no time for SF, myself included. I’m not willing I’m afraid to simply brush aside the horrors of the Troubles, and those who are, to put it mildly, apologists for the atrocities committed.
And I’m completely consistent. I wouldn’t want Pearse or any of the other people who thought that violence was a preferable course to democratic means in my government either.
Pesky rape victim
There is so much support for Sinn Fein because of the way Enda and co brought out mairia Cahill as soon as Sinn Fein got power and the people see that. M Martin knew about this 2 years ago! Why wasn’t it brought up then? Because Sinn Fein had no power at that time so now they had to act fast, something so horrible that people would be disgusted by and turn people from supporting Sinn Fein backfired on then FF,FG,LAB they only have themselves to blame. Bye bye
“There is so much support for Sinn Fein because of the way Enda and co brought out mairia Cahill”
Edna was so outraged by the idea of a kangaroo court that he decided to try and set up his own by inviting the four accused to meet with him behind closed doors. You couldn’t make it up really. He and the rest of FG & Labour must take people for absolute fools if they believe the public can’t see straight through them.
I didn’t agree with Mary Lou McDonald when she said she was going to pay her water charges. I am happy that she has now changed her mind after Kenny’s speech last night trying to bully people into paying. There is huge anger and that is unlikely to abate with only 16 months before the general election.
@Brendan i wonder what the climb down words will be when those that advocate not paying the charges – then have to pay the pay the charges. Those that are on group water schemes already pay – business already pays and they also pay rates (is this correct?)… whether we like it or not water is utility… and countries like Ireland already pay separately for water.
Karma for the Sindo. 26 articles last week on Sinn Fein. Their obsession knows no bounds now their poll has sickened them all at that disgraceful rag. Up thr Shinners!!
Will this popularity end up with them winning the next Election? I’m sceptical. People always like to rebel before an election campaign and support the ‘outside’ parties, but almost always flock to the usual ones at the polling stations.
No I doubt that’s even on their agenda, they’ll be a senior partner in a coalition. SF will be hoping the born-to-rule parties will continue this attack politics because more they do it the better SF polls as the voters see right through it.
Thats true derek. A lot of people are uneducated when it comes to voting and vote for the name they know. Sf need to work on getting transfers from other left leaning candidates
I still can’t see them getting the votes necessary to be a senior partner. People are fickle and scared when it comes to election time and I doubt that SF will get more than FG. They definitely won’t be junior partner as FG, FF and Labour have all said many times they’d never go into a coalition with SF, and the other alliances haven’t a hope of getting more than FF, FG or Labour either.
This more an indictment of the current govt. All the promises at the last election to on have been renaged on.
The promised reforms haven’t materialised. They are handing it on a plate to SF.
The cronyism of FG makes FF look like choir boys.
People are angry: sign up for a utility but they can’t tell what bill will cost???? No reward for water consumers who save water. There should be discounts.
FG need to get rid of kenny now. He might be a nice guy but as a leader a failure.
They need a dublin based leader. Give Varadkar a shot at it.
I think FF would go into coalition with Sinn Féin. A truly frightening prospect.
Bruce, I don’t think FG are too worried about the next election. Labour will get slaughtered because they are the smaller party and thus become a scapegoat. People are still angry at FF and won’t vote for them, and they’ll become fearful of SF once the campaign starts and all the big parties team up against SF and a whole host of IRA stuff gets ‘leaked’. Ok they renaged on election promises, but cmon, what party in any election in history hasn’t done that?
No more frightening that the current batch of fascists and siptu shitebags who are screwing the country.
They won’t be any partner in any Coalition, as while they’ll poll well with their politics of negativity & incredible budgetary economics, as the by-election results have shown, there is continuing deep mistrust of the current leadership (due to the continuing drip-drip of controversy after controversy, all badly handled) & they won’t get transfers required to be a singular compelling consideration for Coalition ie there will always be other options to get the main party over the line.
That combined with the rightful unease of the other parties at getting into bed with a partner with an unknown number of further skeletons in the closet will mean that SF won’t be in Government next time, unless they change leader & handle legacy issues more openly & transparently, without equivocation.
Yea that and the fact that even sf supporters would be thinking twice about gerry as taoiseach
God yes search eagle. The prospect of ff having a hand on the tiller again with their pompous rubbish. I wouldn’t put them in charge of a goldfish bowl. Their as bad as fg, cut from the same cloth.
I think fg and kenny have done irreparable harm this time especially their attitude towards the people and thats now seared into the minds and only staunch blue shirts will vote for them next election. This all plays into ff hands as we as an electorate are too afraid of change to vote in sf and the inevitable retelling of the past during a campaign especially from a fg fighting for their political lives will be too much for them to translate their popularity into votes . So that leaves ireland once again with a shower or c¥nts in power with the people grumbling and complaining but reaping what we sow.
Still a better love story than fg labour
Bruce, no point replacing a muppet with another muppet, Fine Gael and Labour will be wiped out at the next election, I think you are underestimating the anger over the Water Tax.
Fine Gael party???….
But sure Enda kenny thinks he’s a Dictator…..
You can’t water down the fact that he’s a 24 carrot w****r…..
I’m actually leaning towards the idea of Sinn Fein in power now only due to the main parties and medias fear of them in power
I guess the media would want to keep up the hype on Mairia Cahill, if they think it will help to wipe out SF. The journal has written 20 or more articles and a bit in this column on Mairia Cahill, what people hate is to have stuff rammed down them. They dont want to see the same story every day, give us a break and write something bad about Enda Kenny for a change. Nice to see SF gain some ground, SF and the Independents could be the next government, so talk nice about them.
I would like to know why The Journal took the unprecedented (to the best of my memory) step of closing comments on the Mairia Cahill stories, there’s more to that than just reporting the news. I’m not sure the sheer volume of articles on that case in any way reflect public interest in the story, but that’s their prerogative.
Sf and independents has to be better than ff fg and labour
Looking at the recent slant of Journal coverage of SF I’m wondering will they soon be part of the Sindo group?
Unless a man is vilified in the private news papers and media he can not be a true national statesman of the opressed
Thanks to the clown Enda kenny
Someone pass Cameron two paracetamol.
Typical Journal, Typical Media, Sinn Fein will be elected no matter what you print in your poor excuse for a newspaper.
Enda Kenny and Joan Burton are scu*bags
People are desperate for change and didn’t get last election but will the next one. God save us.
Surely sf have been around long enough to be due a go behind the wheel, after all some of them put their lives on the line for change
Who? I mean specifically for change in the Republic?
Dan the time on that tweet is 2pm yesterday before results were published, bit disingenuous to use it.
“In advance of today’s poll, some Sinn Féin officials appear to have jumped the gun somewhat, dismissing the findings before their publication.”
This isn’t complicated councillor, figure it out!
Yeah I read that wrong a
It’s to be expected. Sinn Fein target the lower income voter demographic, promising to extract even more tax from higher income voters and give it to them.
A solid strategy.
So long as the higher income bracket are happy to pay even more tax to support the state.
Well the higher income have a math problem, which is why throughout the world the top 1% have bought the politicians through donations and lobbyists, because the 99% will always outvote the 1%.
Only 4% of the Irish electorate make over 100k a year, so a plan that says we wanna third tax rate for income over 100k (so if you make 150k 25k in takex be taken out of the extra 50) then worst case scenario is all 4% vote for FG plus some who leigitmatly (or the bigger group) unrealisticially think they will earn more than that throw in another 10% that’s still 14% and those people, being high income, were probably always inclined to vote for a centrst rather than centre-left party anyway..so SFs tax policy isn’t gonna loose it people it hadn’t already lost.
Meanwhile Labours making the classic mistake the UK Labour and US Dems made: If I act right wing enough I’ll loose my lefty reputation…and all they’ve lost is their base.
We have a third tax rate for self employed on USC making over a 100k.
It is the unpopularity of the current leadership which is causing SF to shine. It will be brief and will not translate into any sort of victory at the polls in the future.The water debacle outweighs the IRA/ABUSE/ADAMS scandal at the moment and that is purely for financial reasons.Any fix to the water charges and the SF numbers will tumble.
Any chance of next weeks Lotto numbers?
Any chance of an opinion?
Alan
It was the unpopularity of ff that got fg elected last time.
If I was advising FG and Labour now, I’d tell them theres one easy way to totally undermine SF support, and they’d best do it. I’d tell them once Adams and the old IRA crowd are gone and someone like MLMD is in charge they will breach the middle class vote (esp after people realize they’re not communists but mainstream social democrats). I’d tell them that no FG led govt has ever been re-elected, and always needs Labour as a rocket booster to get into power, and that rocket booster is about to implode, that they need to regain their base from SF if FG are to see a second term. I’d tell them bashing SF on the north or the Cahill stuff only energizes the people already voting FG and does not push swing voters, it just looks like cheap mud slinging to them.
So what’s the way to get back support? Become the people you ran as in 2011. Labour threaten to walk without a new PFG, and in that should be:
-Abolition of water charges (via a huge allowance that will mean you’re only charged if you wontonly waste)
-Abolition of college fees and move to graduate tax system
-Go back to the Universal Health Care plan but with a simpler model, spend 2015 reforming the system and then aim to have UHI done in time for the next election, or at least started
-Make the tax system more progressive, phase out USC
You would rob the wind from SFs sails if you did that, luckily for them though, you’re just not that politically savvy.
Ryan, much too late for any of that, the damage has been done, Fine Gael and Labour are finished no matter what they do!
UHI?
Are you mad? I would need to find nearly 5k for my family according to Reillys estimates. Water charges are preferable to that.
If sinn fein IRA get voted in to government, I’m emigrating.
Start packing
F.G. not a chance.
F.F. not a chance.
S.F. not a chance.
It will be a combination of the three which is a scary thought.
Lab not a chance
The Shinners the most popular party in Ireland? Shouldn’t that be the most populist?
All aboard the handcart to hell, everybody, departing soon.
How can we believe this after the details about SF and IRA dealt with rape and abuse claims! Moving people around they’re worse than the what the Catholic Church did.
Media attacked both of those groups
There’s a large minority of people who are as morally bankrupt as the Sinn Fein party .
Handout culture trumps child safety and basic morals….
Everyone against sf has no face
It wasn’t SF who introduced handout culture in Ireland.
True Ger. But They’re making it policy…
They’re our ukip: Sinn Fein indeed.
Notice there is no margin of error comments this week as SF are up. Believe its around 3% so in reality they are up 1% if the shiners comments last week are correct
Ronan
Or they could be up 7% on 29% by the same logic.
Time will tell, I’m not convinced that much will change unless a new party comes along.
Any new party will probably be setup by the wealthy to take over from fg
have your say