Victor Giraldo

The introduction of real numbers in secondary education: an institutional analysis of textbooks

In this paper we analyse the introduction of irrational and real numbers in secondary textbooks, and specifically the propositions on how these should be taught, in a sample of Brazilian textbooks used in state schools and approved by the Ministry of Education. The analyses discussed in this paper follow an institutional perspective (using Chevallards Anthropological Theory of Didactics). Our results indicate that the notion of irrational number is generally introduced on the basis of the decimal representation of numbers, and that the mathematical need for the construction of the field of real numbers remains unclear in the textbooks. It seems that textbooks used in secondary teaching institutions develop mathematical organisations which focus on the practical block.

Research on Teaching and Learning Mathematics at the Tertiary Level: State-of-the-Art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry.

Topic Study Group No. 2: Mathematics Education at Tertiary Level

Research in mathematics education at the tertiary level has experienced tremendous growth over the last decades (Biza, Giraldo, Hochmuth, Khakbaz, & Rasmussen, 2016; Rasmussen & Wawro, 2017). Evidence of this growth includes the continued success of the Research in Undergraduate Mathematics Education conference in the United States, now at its 20th annual conference; the university mathematics research contribution to the Espace Mathématique Francophone since 2006; and since 2011 the working group on University Mathematics Education in the Congress of European research in Mathematics Education conference. In 2015 the Australian Mathematical Society established a Special Interest Group in Mathematics Education, which has among its goals the promotion of inquiry and discussion about tertiary mathematics education. The first biennial conference of the International Network for Didactic Research in University Mathematics took place in 2016. Furthermore, in 2015 the new International Journal of Research in Undergraduate Mathematics Education published its first issue. Reflecting this growth, a total of 64 papers and 23 posters were accepted for presentation at TSG 2. There were four main sessions with 14 papers, including two invited talks, one by Elena Nardi and one by Greg Oates. There were 50 short oral