Leaving Cert Higher Level Maths Paper 1

[fisherpearse]

I'm just wondering what peoples reactions are to the LCHL Maths Paper 1 served up to students last Friday, and the subsequent response from the SEC etc. 

I realise many people here might not teach Maths but I also know there are a lot of intelligent, articulate people on this forum and others, who's opinions I value.

I think this 'blunder' and the response so far, is a symptom of wider issues in the education system and I'd like to keep the debate going among teachers now that the 'news cycle' seems to have moved on to the next topic.

If your not sure what I'm referring to here, have a listen to 'Liveline' from last Monday.

https://www.rte.ie/radio/radio1/clips/22262242/

Pearse

[Laurence Cuffe]

I’ve not followed the controversy in the media, but I am somewhat aware of it. I sat down yesterday evening, and worked my way through the paper.

I felt the questions were not well designed. 

As mathematicians, we love clever problems, where you suddenly have that Aha moment and see a fast way to the answer.

That kind of problem makes a very poor exam question, and there was too much of this kind of thinking at play here.

A good question should build incrementaly, getting harder as it develops, and each part should be answerable independently of the others.

Thats why we see question phrases such as show that the area = 15 square meters, rather than calculate the area.

I found the questions on paper one to be too long and too clever. 

Too long:  in terms of testing for math speed, not knowledge.

 Too long also, insofar as the phrasing of the questions was complex, and would pose problems for students with an element of dyslexia, or for students for whom english was not their first language. It would also pose difficulties for someone with visual issues.

I also felt that the questions had not been properly proof read for intelligibility. We have all written something, and been quite clear about what we meant, only to have others read different things into it, because they were not party to our thinking.

Q2 for instance, the second part is trivial, once you understand what is being asked. If phrased “Graph the function h(x)=g(x) -2” then I think most students would have had little problem.  As phrased, it was not so simple.

Q3(b)  Too clever. Its two minutes, if you see it, but could waste a lot of time if you don’t.

Q3(c) Students might struggle to get words on paper when it really only requires one short sentence.

q5(c) Whats with the symbols in the middle set?

Q7 Phrasing a mess. The mixed units are like a fingernail scraping on a blackboard to my applied math brain. Part (g) Was the question not long enough already?

There is a second issue here. I think the examiner is probably quite comfortable with physics and applied math. A student with a background in those subjects could do ok on this question, however, this gives them an advantage over students who do not do those subjects.

Q8 Too long.  

Q9 Yes, you had a lot of fun playing with this, and you want to show the world how clever you are.  Just too long here, and again too clever.

Q10 again, too long. One part or the other, but not both.

Thats my condensed opinion.

Normally I’m well impressed by the professionalism of the Exam commission, in question setting.

It was not the case here.

Best

Laurence Cuffe

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[Mark Lynch]

I agree with all of what Laurence had to say there but would like to add my some of my 20+ years of knowledge and experience to why this has happened. Prior to Project Maths, we had a well defined syllabus and 4 great text books for Higher Level Maths all written by brilliant people, Oliver Murphy, Maurice O'Driscoll, George Humphreys and Aidan Rowantree and it wouldn't matter which book you used, your results in any particular exam year would differ by less than 1%. 

Now since Project Maths, we have a hopelessly defined and unecessarily vague syllabus with dillusional aims and objectives. We saw what this produced in the early years of Project Maths exams in 2011 and 2012 and we are back to the same again after this year's paper 1 exam. We had a new examiner who wrote the 2013 exam, there was an impossible triangle on the paper 2 that year and the Product and Quotient rule( which were not on the syllabus for Ordinary level) were asked on the Ordinary Level paper 1 that year also, and if my sources are correct, he retired sometime in the last year or so. He seemed to be a safe pair of hands and nothing too wild showed up for many years and he seemed to be into touch with what was going on in our classrooms and the levels of what students of different abilities were capable of answering.

 Just to give you a simple example of how bad this syllabus is if you haven't looked at it, if you look at the last point on page 25 of the Project Maths syllabus for Coordinate Geometry 'solve problems involving a line and a circle', what is God's name does this mean? Has anyone got any idea of how much depth we need to go into? This is why the Project Maths books are all different and it's impossible to get a definite answer on anything from the NCCA, they struggle to understand that teachers may need clarity when asked anything. 

If you look at Project Maths marking scheme for the 2011 higher level leaving cert exam for pilot schools, q6 paper 1, the Financial Maths question, it has 7 parts, the first 3 parts, (a) (b) and (c) are all very doable, they get 40 marks. After that the question became very challenging, (d) (i) and (ii) are grouped together, get either part right you get 4 out of 5 and 3 out of 5 if you had any step right, writing down a formula in the tables booklet etc and the same with the last two parts (d) iii and é were grouped together. These marking schemes are a joke and the marks allocated to certain parts in no way reflects the level of difficulty and how long it's takes to do them. We will have all this grouping of parts of questions nonsense again this year. 

To conclude after my long rant, there is a simple solution to getting the exam right, you must get the syllabus right first and if the powers that be don't, we are faced with years of good hardworking students having their love of the subject eroded by shocking Maths papers.

Mark 

[Laurence Cuffe]

This is much appreciated. I think the idea of not putting the marks on the paper in advance does our students a disservice, and allows examiners to fudge the results after they’ve messed up so that it all comes out right in the end, in a statistical way.

For the poor student who has buried time in some long winded final part of a question, which requires as much effort as all the other parts combined, but only gets an extra two points, we have not played fair.

An exam with the allocated marks given would allow students to be strategic when they are tight on time.

My 2¢

Laurence Cuffe

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