Comments on: School maths, from the distant past

By: Jack Webster

Jack Webster — Tue, 08 Sep 2009 15:58:58 +0000

By the way, Question 3 really does need that it is *not* differentiable at x=0. (As otherwise f[x]=0 is possible)

By: a.c.

a.c. — Tue, 08 Sep 2009 12:42:28 +0000

João, to have a justified true belief that it rains more in winter, it actually has to rain more in winter. That is, it has to be true.

There is pleanty of solid evidence about rainfall levels, so that we're not stuck at impressions, anecdotal evidence, and the like.

By: João

João — Mon, 07 Sep 2009 20:48:45 +0000

I don't think that you really need rigorous statistical analyses to have a, at least, justified and true belief that rains more in winter and here, as a teacher, you have a similar situation, particularly if you are not in an elite institutions and even more if you are in a state controlled one.

Anyway, what is "subjective" in the observation that, in mathematics courses for engineering students, the percentage of failed exams tripled over (roughly) the last five years, while both the scope and depth of the said exams narrowed to the incredible point that, in probability and statistics courses you are instructed (meaning: you don't comply, your contract won't be renewed) to avoid question with percentages, because they confuse the students?

Where is the subjectivity when, having taught discrete mathematics (for computer science students) for more than five years, I ended up with a syllabus with lenght less than a third of the original and with students that are unable to understand integer division? (because they are inured to pocket calculators since their first school years).

Besides, upon showing Prof. Smiths' questions to a former colleague today, I got the atonished reply: "they asked students to prove stuff?"

By: Simon Hewitt

Simon Hewitt — Mon, 07 Sep 2009 18:54:33 +0000

I get the impression that, even over the relatively short time since I did them, maths A-levels have become, if not exactly easier, certainly less wide-ranging.

By: Anonymous

Anonymous — Mon, 07 Sep 2009 18:45:46 +0000

A.C., while I agree that subjective impressions ought not to weigh heavily as evidence, I wonder what would constitute solid evidence as far as you're concerned? Also, it isn't quite fair to dismiss Joao's impressions as merely subjective – surely they fall into the category of expert testimony, which is perhaps the best we are able to expect on matters where questions of value are concerned.

By: Jack Webster

Jack Webster — Mon, 07 Sep 2009 18:40:43 +0000

This is supposed to the evidence with respect to A-Levels. See page 99ish.

Personally, I don't feel this proves anything as the tests they have done aren't really that likely to work, especially across different subjects.

For instance, many peoples who do mathematics can't write and spell. Many people who do history can't do even simple mathematics, and they haven't seem to have taken that into account.

(Perhaps for each subject the tests should have been combined in a sort of ax + by way and the constants a and b found by statistical magic?)

By: a.c.

a.c. — Mon, 07 Sep 2009 13:14:03 +0000

What, if anything, is the solid evidence that standards have declined? Subjective impressions are not enough, in my opinion.

By: João

João — Sun, 06 Sep 2009 21:46:15 +0000

Dear Prof. Smith,

Allow me add a few similar comparisons (I'm not in the UK):

(1) I taught mathematics for nearly 15 years (at university level); when I left, almost a year ago, the level of the exams (where I taught) was below the ones I took *before* entering university myself.

(2) I compared the exams I drafted during these years and the trend is unmistakable: downhill; as is the other, more objective, one: my marks, despite the lowering of the bar, were dropping even faster.

(3) I used, as a pastime, to answer a few interesting mathematical questions in sites such as Yahoo. I stopped for almost a year and return to take a peek a few weeks ago; someone might have warned me about the step.

The fact is, as you say, that is all too easy to be seduced with the impression that you're going to the dogs but, as far as mathematical and scientific knowledge is concerned, I don't have any doubts that things are going to the dogs.

Best Regards

J. Soares

By: notedscholar

notedscholar — Sat, 05 Sep 2009 19:09:57 +0000

I got very, very lost when they started talking about monkeys!!!

By: Jack Webster

Jack Webster — Thu, 03 Sep 2009 20:16:48 +0000

In my opinion:

That papers is significantly easier than current STEP, but significantly harder than current A-Level further mathematics.

I think it is hard to argue that the older A-Levels papers don't require more knowledge, but on the other hand it does require people to do more things to do with translating word problems into mathematical problems, which might be a more relevant skill 'for the real world'. It's certainly easier to pass the exam, but remember an E is a pass...