Programming: Sheep and Goats

Prof Richard Bornat and Saeed Dehnad gave a fascinating EIS seminar yesterday on New Insights into Learning and Teaching Programming. Here is the abstract:

Historically a high proportion (round 30%, sometimes up to 50%) of novice programmers fails to learn to program, and the level of achievement amongst the successful is often disappointing. Until recently the reasons for this miserable state of affairs were mysterious. Now we have some insight, we have a test which reveals important differences between novices, and two potential explanations. The gloomy explanation is that there is a 'geek gene'; even if that is true, we may be able to identify the geeks. The hopeful explanation is that there is something peculiar about programming courses, which elevates difficulties into show-stopping obstacles; if true, we have at last identified one such obstacle, we can hope to identify others, we can diagnose those who are stuck and we may at last be able to do something about it.

They have devised some tests to be given to first year students before and during a programming course. The tests are based on asking students to interpret programs and visual representations of system states in a way that identifies students that can induce the rules of a machine. The test identifies those that cannot work out the rules, those that can work out a consistent set of rules that happen to be wrong, and those that get the correct set of rules.

I find this very persuasive since I noticed a change in my own programming abilities after being introduced to the SECD machine over 20 years ago. The SECD machine is for a particular language, but I hold to the principle that expert programmers have a facility for working with algebraic representations of system executions  on a variety of abstraction levels. Essentially, such machines support a data representation of current states, and both past and future actual and possible system executions. That is to be contrasted with axiomatic and denotational semantics that seem less oriented to humans than to mathematics, and with other forms of operational semantics such as SOS or program interpreters where complete executions are not conveniently modularized.

The results of Bornat and Dehnad are also interesting because they can explain the often observed student learner division between sheep (those that can program) and goats (those that cannot). The claim is that introductory programming courses build topic on topic and that any programme of learning that has this feature will exhibit polarity in student results. Whilst offering no solution, it was observed that organizing programming courses for mixed ability might solve the problem of losing students at the initial hurdles.