I’ve written before about the nature of Russia’s equivalent to our A level examination. Yesterday evening, I came across a tweet by Danny Brown (@dannytybrown) linking to this blog post he has written – essentially arguing that the form of the assessment can too heavily influence our approach to teaching. Included in the post is a sample Core 1 paper with some excellent problems for students to get their teeth into. Take a look now if you haven’t already seen this!
I don’t know the full ins and outs of the German system but essentially their equivalent to A level is the Abitur. In Mathematics, there are separate papers for calculus, analytical geometry and statistics. Moreover, these papers can be taken at the Grund- or Leistungs level (somewhat akin to Maths and Further Maths).
What I find most interesting about the nature of the assessment is how the calculus paper keeps a common theme throughout. I’ve exemplified this with a past paper from Hessen to which I’ve added brief translations of the questions: Hessen LK A1
The paper tests differentiation, integration, transformations of graphs etc but all based around a single family of curves. (How often at A level do we even talk about families of curves?!) There is also a locus question, looking at how the maximum point moves with the parameter. Believe it or not, there’s even an element of the f-word.. functional maths. Interpreting a graph of weight-gain in puppies!
How to Assess A level Maths?
To be honest, I think the question about how best to assess is much akin to how best to teach. A lot of investigation and research and experimentation could be carried out and never yield conclusive results. What’s most important, and I believe this is Danny’s point, is that assessment should not be the single-minded focus of classroom teaching. We need students to be doing mathematics, doing it often, and in doing so explore a variety of challenging and thought-provoking problems.