Counting problems in enumerative combinatorics are considered critical to solving problems in probability at the high school level and taught in undergraduate mathematics classes such as combinator...

The main goal of the research was to find out the connectivity between various representations of sets and attempt to clarify source of error when passing from one representation to another. A questionnaire which focused on the inclusion relation between sets, by switching this relation from the verbal, formal and verbal-logical to the visual representation, i.e. to Venn diagrams, was distributed to 120 pre-service teachers who had been learning a basic course in set theory, from two colleges of education. Our findings highlight the fact that the verbal representation was the easiest, in other words, the students succeeded more in switching from the verbal and the verbal-logical to the visual representation, more than in switching from the formal representation to the visual one. Moreover, the main sources of errors were: Non identification of the problem variable or subject; adding new condition enlarges the set; Partial visual attribution to Venn diagrams and the inclusion relation is not checked element-wise and there were some misconceptions that contributed to errors.

Article Free Access Share on Learning threshold functions with small weights using membership queries Authors: Elias Abboud Research Center, Ibillin Elias College, P.O. Box 102, Ibillin Research Center, Ibillin Elias College, P.O. Box 102, IbillinView Profile , Nader Agha Research Center, Ibillin Elias College, P.O. Box 102, Ibillin Research Center, Ibillin Elias College, P.O. Box 102, IbillinView Profile , Nader H. Bshouty Computer Science Technion, Haifa Computer Science Technion, HaifaView Profile , Nizar Radwan Mathematics Technion, Haifa Mathematics Technion, HaifaView Profile , Fathi Saleh Research Center, Ibillin Elias College, P.O. Box 102, Ibillin Research Center, Ibillin Elias College, P.O. Box 102, IbillinView Profile Authors Info & Claims COLT '99: Proceedings of the twelfth annual conference on Computational learning theoryJuly 1999 Pages 318–322https://doi.org/10.1145/307400.307483Published:06 July 1999Publication History 2citation232DownloadsMetricsTotal Citations2Total Downloads232Last 12 Months14Last 6 weeks3 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF