Wednesday, December 14, 2005

exam questions

So, the problem with setting numerical targets like "90% to get an A" is that then in order to fairly test the student population, that is to actually determine which students have know the material well and understand it in depth, you have to design an exam (or generally any gradable assignments) such that very good students actually can perform at that level.

Now, if you're using multiple choice exams, which are almost necessary for large introductory classes, then this is not so difficult, since it is straightforward to pitch the exam to whatever level the instructor wants. For other types, it is harder, you tend to either have short answer questions focused on factual and method testing, which tends to fail to probe in depth understanding, which is really what an "A" should reflect; or you grade leniently, which is always an option for non-multiple choice assignments.

Clifford over on Cosmic Variance has done a take on this. The "British style" of examining has some significant virtues that examining in the US system (at the ugrad) level makes almost impossible. (BTW, WTF do the Smurfs come on iTunes every time I blog this week, I don't have that many (Icelandic) Smurf songs... ah well, this time it is a version of "Walking in a Winter Wonderland". Surreal.)

So, the idea is that exams are long written questions, preferably you pick k out of n questions and have 30-60 minutes to do each question.
Each question is roughly in 3 parts. The first part asks for a definition, or a theorem, or some very basic point to set the students mind on the topic and test for elementary knowledge. Usually worth 30% of the total, if you don't get it you fail.

Second part is usually an extended calculation, preferably working with or from the first part. It is worth 40% of the total and takes work, skill and knowledge of the material. If you set the 1st/2.1 boundary at 70% then a student doing the first two parts correctly is borderline 1st but not quite (ie a B+/A- grade - English university grading is 1st; 2.1 or upper second, 2.2 or the lower second (AKA Tutu); 3rd and "ordinary" (non-honours pass) and Fail).
You provide heavy partial credit on the grading, so students who make progress but do not complete get a 2.2 or 2.1

So, the third part, worth ~ 30% of the total, is something related that was not in class or on the syllabus. It requires the student to use their knowledge to figure out something new on the spot under exam pressure. You do all the previous parts and that, you get a 1st.

Such questions are very hard to write. Good university departments have sets of them going back decades that are carefully mined and refined.

My all time favourite question was from an advanced ugrad "Waves and Fluids" class.
Started off asking for a definition/theorem on laminar flows.
Then we got a standard calculation for steady flow, using a geometry different from any class examples or homeworks.
Straightforward, somewhat technical, doable, took some time.

The third part of the question then asked us to solve the same problem for supersonic flow.
The class did not cover supersonic flows at all.
The solution, as it happens, fell out automatically once you realised what the differences were (a serious sign change for one term), and then the physical implications just fell out. As I recall, in particular, the lift changed sign!
Absolutely beautiful question.


Blogger yami mcmoots said...

My least favorite question of that type involved finding the normal modes of waves on a möbius strip. It had all the elements of applying one's knowledge to an entirely new problem, but none of the elegant real-world implications. Which also meant physical intuition was less than helpful...

6:13 PM  

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