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### Maths Grinds' Blog

Blogging and Mathing
6 Dec 2018

I’ll put my cards on the table from the start, I’m not a fan of the Project Maths Syllabus (the new Mathematics Syllabus in Ireland). There have been many voices discussing the advantages and disadvantages of the new Syllabus. And I don’t intend to add my voice to that chorus as what I have to say does not differ much from the anti-Project Maths camp anyway. What does interest me more is the “why”.

Plenty of views expressed talk about what is right and wrong with Project Maths but I want to understand the “why”, why change the Syllabus? I was curious firstly to the percentage of second level students that go on to third level. My view is that a certificate should provide students with either A) a closed learning experience (the contents are self-contained and everything must stand on its own feet, nothing is done to prepare further study, like making a movie with zero intention for a sequel).  Or B) an open learning experience (the contents are taught because their is an eye on what is down the road to learn, like a movie made with a sequel in mind and the “to be continued” at the end).

I could not find a table of percentage of students going into third level online but the Independent have a look-up facility on their website. You can look up the percentage of students from a particular school and a particular year going into a particular third level school. Here is my estimate (if I wanted to put in more time I could have been more accurate but the numbers I got matched with some known values, for example in Jan 2017 (referring to 2016) it was reported in the Irish Times that about 60% of students go on to third level – “about” is code for “nearly” because if it was more than 60% the author would have said “over 60%”. This matches nicely my 59% for 2016. Again the Irish Times reports in 2018 (so referring to 2017) that over 60% of students go on to third level. My table reports 60% whereas the true percentage the author does not mention could be up to 60.9% (otherwise he would have said 61%). So I believe my table to be correct up to one percentage point of error.

%Students going on to third level education from second level (estimate $\pm1\%$)

2009 2010 2011 2012 2013 2014 2015 2016 2017 2018
51% 53% 54% 59% 58% 58% 60% 59% 60% 56%

So clearly the Leaving Cert is an open preparation certificate as most students go on to third level – or at least it should be, but it is not. Students should be getting a more open education and indeed the old Syllabus provides this, particularly in the STEM Mathematical topics, such as Vectors, Matrices, Calculus, Group Theory and so on. So why did Mathematics at the Leaving Cert become closed off and self contained? Focusing on context based questions and problem solving (this is Mathematical Education code for solving contrived word based problems). In 2012 NCCA published a response to the anti-Project Maths debate and they list 3 key reasons for the need for change.

1. “post-primary mathematics education in Ireland featured a highly didactic pedagogy with mathematics being taught in a procedural fashion with relatively little emphasis on problem solving (Lyons, et al., 2003).
2. the ‘new’ mathematics curricular culture, with its elevation of abstraction as a core principle, had dominated post-primary mathematics teaching for the last forty years(Oldham, 2001).
3. over three cycles of PISA, Ireland had been ranked in the middle of OECD countries in mathematical literacy (OECD PISA reports in 2003, 2005, 2008).”

So clearly the change wasn’t to meet the future needs of the students who would benefit from a more preparatory course for third level – as more than half of students go onto third level. The three points are interesting because only one of them if valid (but as everyone knows three reasons must be given to make a case). Consider:

Addressing point 1:  A quick wiki result for those wondering what a didactic pedagogy is “A didactic method is a teaching method that follows a consistent scientific approach or educational style to present information to students“. This really is the best (and proper) way to teach Mathematics.

Addressing point 2:  Abstraction is the core principle of Mathematics, it is why it works so well in Science!! This is like critizing History because it looks at the past – but much worse!

Addressing point 3:  This is the only valid reason here. In 2008 Ireland scored 487 in PISA (the same as the USA). This is less than the OECD average Mathematics PISA score of 496. I find it interesting that Ireland’s 487 is more than some research powerhouses such as Israel’s 447. To me this tells me a snapshot of a countries middle school 15 year olds is not always good indicator of future Mathematical success for a country.

So I believe I have my answer. I think the one and only true reason for the change is to increase Ireland’s standing in international PISA ranking. We are gearing our system to optimize preparing for PISA and other international exams at the expense of the traditional pure third level STEM Mathematics. If you want some more evidence of this claim then have a look at this list of sample PISA Maths questions. Don’t they look very “Project Mathsy”?

My prediction: We will move up in our PISA ranking but down in our third level ranking of Mathematics (after a lag-time). And so far we our moving up in PISA (in 2015 Ireland scored 504 which was more than the OECD’s 490 average. I think we will move up a little more in the next PISA rankings and then plateau at the new higher level). But my prediction is also that after some more lag-time we will see a decline materialize in third level Mathematics and beyond (from 2021 onwards). How though, I do not know… but cracks will emerge.

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