Mathematics in pre-service teacher education and the quality of Learning: the monty hall problem

António Domingos, Fernando Santos

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


If students acquire a new mathematical notion, according to Gray and Tall (1994), they pass through a proceptual divide. At a higher education institution in Portugal, students from different courses (education and business) came into contact with the Monty Hall problem in Statistics class. As a part of the learning environment the students have at their disposal all the technological apparatus they could use. The correct outcomes of two students (from the two courses) are analysed against the background of a model of analysis based on Tall's theory of the advanced mathematical thinking linked with SOLO taxonomy by Biggs and Collis (1982) and supported by Engeström (2001) third generation model of Activity Theory. In particular, the two different outcomes show that students can attain the same level, but may be operating in different levels: procedural thinking and proceptual thinking.

Mathematics in Pre-service Teacher Education and the quality of learning: The Monty Hall problem (PDF Download Available). Available from: [accessed Mar 28, 2017].
Original languageEnglish
Title of host publication12th International Conference on Technology in Mathematics Teaching
Place of PublicationFaro
Number of pages7
ISBN (Electronic)978-989-8472-68-7
Publication statusPublished - 27 Jun 2015


  • Advanced mathematical thinking
  • proceptual divide
  • probability
  • quality of learning
  • SOLO taxonomy


Dive into the research topics of 'Mathematics in pre-service teacher education and the quality of Learning: the monty hall problem'. Together they form a unique fingerprint.

Cite this