When I started taking an interest in university mathematics teaching back in 2003/4, I quickly became aware of a report “Measuring the Mathematics Problem” (2000; also the 1995 Tackling the Mathematics Problem). This describes a decline in standards of students entering university and looks to serve as a call to arms to take action to prevent further decline. The preface of this reads:

Evidence is presented of a serious decline in students mastery of basic mathematical skills and level of preparation for mathematics-based degree courses. This decline is well established and affects students at all levels. As a result, acute problems now confront those teaching mathematics and mathematics-based modules across the full range of universities.

This report is aimed, therefore, at those in Higher Education who teach mathematics-based modules and those involved with admissions. There is a need for each department to become attuned to the full extent of the problem as it affects their students. The diagnostic testing of new undergraduates is recommended as an effective means of achieving this goal.

The report is also aimed at those charged with responsibility for setting the A-level Mathematics curriculum. Following the many changes introduced in the early 1990’s we would suggest that now is the time to take stock.

Now, I think it is important work and I mean in no way to belittle such worthwhile endeavour, but recently I have come across a couple of sources which set such despair in some context.

Firstly, see the following quote:

Today as never before mathematics is assuming an importance in the lives of everyone. Never has science, of which mathematics is the basis, played such a great role in the development of modern society and in the solution of both peacetime and wartime problems of organization and production. Even more, perhaps, in a time when everything depends on education toward reason is mathematics the unparalleled agent of mental discipline and the embodiment of constructive and inventive thinking.

Unfortunately, these aspects of mathematics have been greatly neglected in the recent past. Most of us have been subjected to a routine mathematical training in high school. Some of us acquire a certain degree of mathematical skill in liberal arts colleges or engineering schools. Few of us, however, have any real understanding of mathematics and what it is all about. What is Mathematics? was written to fill that gap.

This is from the cover blurb for What is Mathematics? by Richard Courant and Herbert Robbins. I can’t tell if this was written in 1941, when the book was first published, or in 1960, when the edition I am holding was printed. (This book was revised in 1996 by Ian Stewart and is still available; it gets a review from Brian E. Blank in the Notices of the AMS in 2001.)

But we can do better than that. A few weeks ago, on the Math/Maths Podcast episode 4, Samuel Hansen read a little from a letter by Rev. John Toplis, written in Arnold, Nottinghamshire on October 13, 1804, entitled: “On the Decline of Mathematical Studies, and the Sciences dependent upon them” (as written up with commentary over at Skulls in the Stars). From this:

It is a subject of wonder and regret to many, that this island, after having astonished Europe by the most glorious display of talents in mathematics and the sciences dependent upon them, should suddenly suffer its ardour to cool, and almost entirely to neglect those studies in which it infinitely excelled all other nations … It is a very great disgrace for a nation like this, which can proudly boast of a superiority over all others in arts, arms and commerce, to suffer the sublimest sciences, which once were its greatest pride and glory, to be neglected.

So it seems mathematics is often (or continually?) considered to be in serious decline. Does this mean contemporary concerns about mathematics teaching are misplaced? We can’t say that, but it’s interesting to consider that generational differences, rather than decline, may be at work.

I notice this week in his Bad Science column, Ben Goldacre talks about decline in A-Level standards: “Are exams getting easier? Nobody knows“.

One of the few relatively consistent measures I know of (similar population, similar test, rigid controls), the SAT Math scores (at least until 2005 – the test was changed and is difficult to compare now) indicates a slight decline in the early 80s and then a steady increase.

http://www.collegeboard.com/prod_downloads/about/news_info/cbsenior/yr2007/national-report.pdf

Part of the “kids these days” syndrome is that curriculum is fluid, and what used to be taught only in college was moved to the high school. So what we call “algebra” and what someone growing up in the 50s calls “algebra” are two rather different things.

I believe the raw numbers of math-focused students has more to do with economics than anything — witness Japan’s difficulties recently in recruiting engineering students because they’re losing them to finance.

It has been thus in the past, and will be again. There are cycles. We’re in a much better state than we were eight years ago (in the UK) – look at the number of popular maths books, TV and radio, even Edinburgh Fringe shows – and the A-level results an duniversity numbers and the quality of graduates. Test results don’t help – the maths kids know, and the maths they need to know, has changed. While a few years ago university maths departments were closing, and newspapers were talking about the irrelevance of maths, now there’s much more appreciation of its value. We must fight to keep it that way!

I have the impression that teachers have been complaining for centuries that students nowadays don’t know as much as they used to. A search for references in the literature would give a nice paper, not in math, but in the humanities. The only thing that has not changed is that older people are older than young people, so I assume it is a characteristic of age.

The content of teaching changes fast enough that you can always find a measurement to support the argument for decline, if you are so inclined. Believe it or not, electrical engineering professors also think that their students don’t know as much as they used to. But any EE senior project nowadays is vastly superior to anything my buddies built 25 years ago, thus their allegation is patently nonsense. I guess that the conclusions about math decline are likewise an artifact of the way the measurements were taken.

I wrote a follow-on blog post, Shifting decline of mathematical preparedness?, in which I recommend reading Mathematics at the Transition to University: A Multi-Stage Problem? by Michael Grove.

I speak about this on Pod Delusion 114.