At a meeting of the Dublin Branch of the Irish Maths teachers on Thursday 4th October .The members were asked for comments of the 33 members attending 30 were very critical of all aspects of project maths 3 (from pilot schools) were in favour.
The following is an extract of some of the suggestions.
Detail of Syllabi:
1.1 Much more detail needed in the syllabi. The current syllabi are inadequate. There are holes in them. For example, for 2013 there is no mention of the Binomial Theorem but in other parts of the course it is needed, along with de Moivre’s Theorem. It was added in for 2014.
1.2 Items get added into the successive syllabi without us being explicitly told about them; e.g. graphing of a+bSincA.
1.3 A: Does the lack of detail mean that anything and everything can be included through the use of “scaffolding”, even if not explicitly mentioned in the syllabi. For example, the single word “simulation” has been used to justify the inclusion of the Central Limit Theorem.
Content of Syllabi:
Too much stats & probability on LC, both HL & OL. This topic is very time consuming to teach.
1.1 Removal of some parts of the calculus has caused some concern. : A possible solution may be to postpone the introduction of Strand 5. .
1.2 Financial maths should be removed and replaced with vectors. It was pointed out that teachers may have overreacted/panicked a bit following an overemphasis at training days.
Students should be given an option to study either financial maths or vectors, rather than both.
Length of Syllabi:
1.1 Some items appear short and simple to teach initially but turn out to be very time consuming. E.g. types of functions, present values.
1.2 Already long and yet there is deferred material.
1.3 Some choice is wanted, especially if it makes the syllabus shorter.
Structure of the Exam Paper
The exams are not balanced to match the way the syllabi are balanced. They don’t seem to assess what has been taught. Large sections of the course can be omitted. Some sections of the course are overrepresented, e.g. statistics.
Exam has no integrity. 2012 paper 2 no integrity, 2013 no integrity at all? Marks per question part need to shown on the exam paper for integrity of exam.
Marking Scheme:
Aimed at the mediocre student? The “lottery” element means that these students can be lucky and achieve a C grade. Similarly, the best students are highly likely to be unlucky in some part of the 2 papers. This bad luck is heavily penalised resulting in a B grade. Thus there is very little to distinguish the best from the mediocre.
Experiences:
Exams should not be such a devastating experience for students. This opinion was voiced to the SEC previously but the devastation is still being experienced. The unpredictability regarding how a “mad” question will be marked can be devastating. This can impact on the students’ answers to the other question on the same paper, the second paper and also impact on their preparation for other exams. In addition students lack of confidence in their expected results can influence their CAO choices. They may decide to change their preferences prior to the results becoming available
There are many areas of concern among teachers at 2nd and 3rd level but all agree that the reduction of the content of the calculus syllabus is a step too far .
All of the following have been removed at Higher level ;
Parametric Differentiation,Implicit Differentiation,Differentiation of sinx and cosx from first principles. Maclauren Series hence finding the value of Pi.Proof of the sum,product and quotient rules from first principles.
All the following have been removed from Integration :
Integration by substitution , integration of powers of sinx and cosx , integrals which give inverse sin and inverse tan , volumes of rotation,integration by parts.
The following have been removed from Ordinary level Differential Calculus:
Product Rule,Quotient Rule and chain rule , graphs of cubic functions
Projectmaths.com urges teachers and other to ask the Minister to abandon the introduction of Strand 5 until a proper syllabus on Differential Calculus has been agreed.
Postponing strand 5 will not affect anybody as it will not be examined in non pilot schools (everybody) until 2014
Another Topic which should also be abandoned is financial maths and its place should be taken by vectors.
Project maths.com has examined the marking schemes used for the 2010,2011,2012 Project maths exam taken by the pilot schools.We have assumed that a student answered all questions but only achieved the low partial credit (attempt mark)in each question.The low partial credit is given for any attempt but the value of the low partial credit changes from scale to scale it can be worth as little as 3 marks (scale 5B,5C) or 6 marks (scale 10B) to 15 marks (scale 25C).
The following diagram shows the percentages achieved by students in Pilot Schools who attempted every question and were awarded the low partial credit in each question. The results are compared to students in non pilot schools who achieved the attempt mark in each question .It is very clear that the Pilot school students could have achieved as much as 56% (2011) by just getting the low partial credit for all questions whereas the regular schools students could achieve a maximum of 33% by attempting every question. This is clearly unfair to the to the 8,000 regular ,to reward the 318 students in the pilot school students so handsomely.
Year  Student getting only Low partial credit in all questions  Student getting only low partial credit in all questions  Students achieve attempt mark in all questions 
Paper 1 (PilotSchool)  Paper 2(Pilot school)  Paper 1/Paper 2
(Regular school) 

2010  46%  33%  
2011  55%  58%  33% 
2012  55%  49%  33%(paper 1) 
While much of the attention has been paid to Higher Level maths and the generous marking scheme .Projectmaths.com decided to take a look at the marking scheme for the 2012 Ord Level Maths exam examined in the 24 pilot schools.
A student who just received the low partial credit for every question on Paper 1 got 155 marks out of 300 = 52%
This is nearly a C grade for taking 1 step in the right direction. So what does a student need to do to get the low partial credit?
Here are some examples .
(i)Effort at differentiation Q9a(i) : (2)Some correct substitution into formula for V.
(iii)Any Correct relevant step Q1c:Some correct substitution into roots formula Q2c.
(iv)Plots correct x or correct y coordinate Q5a: (v)Some correct substitution Q7a;
This was done for only one reason to make the project maths look better than the regular maths.
We have to agree with Mícheál Mac an Airchinnigh’s view that Mathdep should serve as a facilitator of reasoned discussion of mathematical issues.
Stewart Griffin’s piece is well written and researched as far as we can see. It is interesting that it has been criticised for its comments on Mathematical Studies but, in point of fact, the main thrust of the piece is a critique of Project Maths.
Project Maths claims to shift the emphasis on teaching mathematics to solving real life problems. At the same time the syllabus removes much of calculus, linear algebra and vectors, replacing these with Euclidean geometry and more probability and statistics.
We are puzzled at the lack of response in so far as most mathematicians to whom we have spoken seem to take a dim view of Project Maths. Apparently open debate of Project Maths is frowned upon. What is the opinion of the silent majority?
We have yet to obtain a satisfactory response to the following questions:
Why change the didactic methodology and the syllabus at the same time? How is it possible to evaluate the effect of the change in methodology if the syllabus is simultaneously changed. Why not leave the syllabus unchanged and aim to reconsider it at a later time when the effects of the change in teaching methodology have been evaluated? Is this not in fact bad didactic practice?
Why remove the particular topics (calculus, linear algebra, vectors) from the syllabus when these are at the heart of real life applications? For example, maximisation and minimisation problems, relative velocity etc.
Why remove mathematical topics from the syllabus which are key to the mathematics most used in third level courses (science, engineering, business)?
What effect will the new syllabus have on Irish students seeking places in universities in Britain and the rest of Europe? Why have we moved so out of line with Britain and the rest of Europe in removing key topics from the leaving certificate syllabus? Do we know something that the rest of Europe does not?
Why was the new syllabus, with a claimed emphasis on real life problems, designed by people who have no interest in solving such problems? Is this the reason for the “contrived” problems which Griffin mentions?
Eugene Gath,
Alan Hegarty,
John Kinsella,
Natalia Kopteva,
Sarah Mitchell,
Stephen O’Brien.
Mathematics and statistics, UL.