How Long Would It Take to Open a Padlock? A Study and Research Path with Grade 10 Students

We present the first implementation of a finalised study and research path (SRP) related to basic enumerative combinatorics. The SRP starts with a generating question about “How long would it take to open different kinds of padlocks?”. This paper describes the main steps of the SRP as implemented with secondary school students of grade 10. We want to stress some specific features of the SRP: the role of the empirical milieu and its enrichment through the collective construction of specific terminology; the students’ use of question-answer maps to organise and describe their inquiry; the experimental validation of the final answers; and the use of padlocks as models to solve combinatorics problems. We implemented the SRP in a secondary school with a long tradition in “active methodologies”. It is interesting to study these particular institutional conditions and their effects in the evolution of the SRP.