Project Maths – backwards or forwards?

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Project maths was initiated to tackle concerns about the general standards in maths achieved by students in Ireland. It is intended to bring about higher levels of achievement nationally through a revised syllabus and teaching approach.

I am one of the many people who are far from convinced that is likely to go any distance in achieving its aims. The more I learn the more astonished and dismayed I become about aspects of the project. Dumbing down of the leaving cert maths course under Project Maths has repercussions for other subjects and courses.

The Department of Education’s Circular Number 0059/2011 concerning the Applied Mathematics for Examination at Leaving Certificate in 2012 and subsequent years  states that “as a consequence of the introduction of Strand 5 (Functions) in the Leaving Certificate Mathematics syllabus from September 2010 in the 24 initial schools in Project Maths, it is necessary to introduce changes to the Applied Mathematics syllabus in the Leaving Certificate course for examination in 2012 and subsequent years for all candidates. Although integral calculus is included in both mathematics syllabuses, the range of integration techniques required is significantly reduced under Project Maths. There are other changes/omissions which also affect Applied Mathematics, but the principal concern arises in respect of integration for Higher Level candidates .

While the Applied Mathematics syllabus states that ‘knowledge of the relevant parts of the Mathematics course is assumed’, candidates for the LC Applied Mathematics examination in 2012 and 2013 will have followed different mathematics courses, depending on whether or not they were in one of the initial schools for Project Maths. For the LC Applied Mathematics examination in 2014 and subsequent years all candidates will have followed the Project Maths syllabus. There are a number of topics which are treated differently, or omitted (such as vectors), under Project Maths and which impinge on those studying Applied Mathematics. Of these, a general technique referred to as “integration by substitution”, which arises for Higher level candidates, is the most significant. The remainder can be dealt with as part of the Applied Mathematics course – in fact, they are usually taught by the Applied Mathematics teacher before they arise in mathematics class. The specific integration item referred to here would add significantly to the workload in Applied Mathematics if it were to be taken on ab initio.

Although there is significant choice in the Applied Mathematics exam, this particular topic/question is a popular one. It also provides a good example of applying in a realistic context what otherwise might be a difficult concept to grasp.
To minimise the effect of the changes, the following arrangement has been agreed by the Department, the National Council for Curriculum and Assessment, and the State Examinations Commission.

In the Leaving Certificate Higher Level Applied Mathematics examinations of 2012 and subsequent years, any differential equations that arise will not require the use of “integration by substitution” in their solution. They may require integration of functions of the following forms, and sums or differences of these:

– xn
– sin nx, cosnx, sin2 nx, cos2nx;
– functions of the form:
1/(x+a),  1/(a^2+x^2), 1/SQR(a^2-x^2)

This is an extract from the current (old) mathematics syllabus, with the particular requirement in relation to integration by substitution omitted.

Under this arrangement, all candidates in the 2012 and 2013 examinations would have experienced the same relevant parts of the mathematics course in respect of integral calculus and therefore any disadvantage in relation to this would be removed. As all Leaving Certificate Mathematics candidates will have followed the Project Maths syllabus in 2014 and subsequent years this arrangement will continue to apply until revision of the Applied Mathematics s.” (End of statement in circular).

Others are concerned about the effect of omissions from the new syllabus on the level of preparedness of students to undertake third level courses. The following is part of the text of an advertisement by The Dublin Institute for Advanced Studies in the Irish Independent, (July 12th).

“Due to recent changes in the Leaving Certificate mathematics curriculum, the amount of calculus taught has been severely reduced. As this subject is essential for preparation to third level courses in Mathematics, Science, and Engineering (as well as Economics) and in order to give students with an aptitude for mathematics the opportunity to prepare themselves better for further study, a 10-week course on Mathematical Calculus will be given” “on Saturdays before Christmas.”

Apart from the dumbing down of the course, the feedback I have received from students who did Leaving Cert maths this year was that they felt additional stress because of the uncertainty of what type of questions would appear on paper two and because they had no idea of how the marking scheme would work. And despite all the hype and publicity many did not know the differences between the old and new syllabus. If there was a 360 degrees appraisal system in place whereby the students were to mark the effectiveness of the Project Maths implementation the scores would be very low indeed.

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