Sunday, 27 October 2013

Maths Education and Unintended Consequences

I should emphasise that this post expresses only my own personal views.

That policy decisions can have unintended consequences is well illustrated by events in maths education in England over the last fifteen years.

First, the introduction of Curriculum 2000 created a modular A-level syllabus in which AS-levels became stepping-stones on the way to the full A-level.  In principle I think this was a thoroughly good thing.  But it had a disastrous effect on mathematics in higher education.  With module exams a few months after students had moved from GCSE into A-level study, the gulf proved too great, AS-level results were spectacularly awful, the number of students taking A-level maths plummeted because potential candidates were discouraged by their results at AS-level, schools and colleges advised students not to study maths post-GCSE, applications to study maths at University dropped substantially, and University departments closed because they could not recruit enough students to be viable.  It took a decade for mathematics in higher education to recover.

There was also the unintended consequences of the GCSE data-handling coursework.  The country needs more statisticians, and it needs citizens with basic understanding of descriptive statistics.  So the introduction of a significant statistical assignment - the data-handling coursework - was largely welcomed by the statistics community.  It would give students more knowledge of this important subject and encourage more to study statistics at university.

But it didn't work out that way.  Students found the coursework time-consuming and tedious.  It put them off statistics!  Numbers taking statistics at university, whether as a subject in itself or as an option in business or science degrees, fell as a result.  University statistics departments have shrunk.  The GCSE data-handling coursework did a huge amount of damage to statistics.

As another example, consider the inclusion of mathematics GCSE in the government's schools league table data for five GCSEs at grade A-C.  The maths community was delighted when the old league table measure, just the proportion of candidates getting five A-C grades regardless of subject, was changed to require that the five GCSEs must contain Maths and English.  The feeling was that this would lead schools to put more effort into Maths GCSE.  But a consequence has been that many schools have been putting their students in for maths GCSE as early as year 9, and at every opportunity thereafter until they get the C pass, even if they have not covered most of the curriculum.    If a student can scrape enough marks for a C, they then drop the subject so that they can focus on the other GCSEs: so they may never cover a large part of the GCSE curriculum.  This is extremely damaging for students (and may have prevented many potential mathematicians from taking A-level maths).  Fortunately the government has now acted to prevent this abuse, but it is another example of unintended consequences.

So with this history of apparently desirable initiatives having adverse outcomes, I am nervous about the proposal for a new maths qualification for 16-18-year-olds.  Like many others, I believe the more maths people study, the better; I regret the English system which means that so few students study mathematics post-16; and I welcome the opportunity to allow post-16 study of mathematics for those who will benefit from a less intensive course than A-level (such as those who did not obtain A* or A at GCSE but who have the potential to gain from developing further mathematical understanding).

But there are dangers.  Where are the teachers going to come from?  Will resources move from A-level teaching to the new exam?  Worse, will students who would otherwise have taken A-level maths prefer the less intensive course?  Could the new mathematics exam lead to another drop in A-level numbers and impact on further study?  Are some of the potential top mathematicians of the future going to find themselves unable to study maths at university because they made a poor decision, or their school or college advised them badly, at 16?

The new maths exams should provide an opportunity for many to gain useful training in a subject that will benefit them throughout their lives.  But, once again, there is potential for unintended consequences which could damage maths education in England.