| Investigating student knowledge in mathematics at the end of their first year of post-primary education in Ireland: a case study | 55$-$75 |
Abstract
This paper reports on performance data obtained as an integral part of a major research study on the effect of the transition from primary to post-primary education on Irish students' mathematics performance [V. Ryan, Making the Transition: A Student’s Mathematical Journey from Primary to Post-Primary School in Ireland, PhD. University of Limerick]. The data were obtained using a standardised test designed for use in Irish primary schools to assess student mathematical knowledge at the end of their first year of post-primary school. The results highlight significant underperformance across all curriculum strands of the official mathematics curriculum indicating an unsatisfactory grasp of mathematical knowledge at this stage of students' development. The item analysis also shows statistically significant differences in performance between male and female students. These findings are concerning in the context of major recent reforms of the national post-primary mathematics curriculum and targeted measures to avoid negative outcomes in mathematics as students make the transition from primary to post-primary education. In research terms, the end of year 1 in post-primary education is a neglected milestone in students' mathematics education that straddles a key period in students' mathematical journey when students negotiate academic and emotional transitions that affect their performance, attitudes and dispositions towards mathematics. This paper gives a recent appraisal of the mathematical knowledge of students entering year 2 of post-primary education in Ireland. It discusses factors affecting these student outcomes in mathematics in the context of the students' transition from primary to post-primary school/mathematics. Finally, it sheds light on a neglected mathematics milestone for students, and its potential to influence future student outcomes in mathematics.
Keywords: Transition in mathematics; Mathematics milestone; Mathematical achievement.
MSC Subject Classification: 97D60
MathEduc Subject Classification: D63
| Outcomes from an experimental teaching -- on two types of isoptics for curves with asymptotes | 76$-$84 |
Abstract
The paper presents the outcomes of a long-term individual educational trajectory for a team of secondary school students. The topic isoptic of a curve with asymptotes appears naturally when two viewpoints on isoptic are compared. The result about hyperbola hints that the curve with asymptote needs special attention when considering the locus of visibility, but not just the locus of points from which the tangents meet at a constant angle. The particular cases for the exponent and logarithm are studied. The proofs are based on calculations by a computer algebra system (CAS), and the illustrations are done by a dynamic geometry system (DGS).
Keywords: Isoptic; individual educational trajectory for a team; synthetic competence.
MSC Subject Classification: 97U40
MathEduc Subject Classification: D54
| A short and elementary proof of Brauer's theorem | 85$-$86 |
Abstract
A short and elementary proof is given of a celebrated eigenvalue-perturbation result due to Alfred Brauer.
Keywords: Brauer's theorem; eigenvalue; eigenvector; rank-one perturbation.
MSC Subject Classification: 97H60, 15A18
MathEduc Subject Classification: H65
| Pages dedicated to professor Milosav (Milo) Marjanović on the occasion of his 90-th birthday | 87$-$111 |
Abstract
Brief biography. Milo was born on August 24, 1931 in Nikšić, Montenegro, where he completed his primary and secondary education. He received a diploma in mathematics from the Faculty of Natural Sciences, University of Belgrade in 1955. He was employed at the same faculty as a teaching assistant in 1957 and at that faculty his entire career ran until 1997, when he was retired. (Some complementary biographical data can be found in The Teaching of Mathematics, XIV, 2, 2011). Milo wrote text-books and research papers on education at all levels, from primary school to university. A number of papers that he finds to be particularly representative for his work on education are shortly presented in this material, together with some of his recollections and chats.
| A glimpse into the theory of chessboard complexes | 112$-$128 |
Abstract
In this paper we review some of recent developments related to chessboard complexes and their generalizations. Focusing on explicit shelling constructions we have opportunity to present some surprising and exciting recent progress, to the necklace-splitting problem and to envy-free division.
Keywords: Shellable complexes; neckless-splitting problem; envy-free division; configuration space/test map scheme.
MSC Subject Classification: 05E45, 55M20, 55M25, 55U10, 91B32
MathEduc Subject Classification: 97K99