Tootfinder

Examining Gender Differences in the Impact of Instructional Clarity on Year 9 Students' Mathematics Interest in New Zealand: A Multi-Group Comparison of 2019 TIMSS Data
Huayu Gao, Tanya Evans, Gavin T. L. Brown
https://arxiv.org/abs/2508.13502

Examining Gender Differences in the Impact of Instructional Clarity on Year 9 Students' Mathematics Interest in New Zealand: A Multi-Group Comparison of 2019 TIMSS Data
Grounded in Social Cognitive Career Theory (SCCT), this study explores how teacher instruction clarity impacts Year 9 students' mathematics interest through the mediating roles of confidence and value, with a focus on gender differences. Structural equation modelling applied to the 2019 New Zealand TIMSS dataset (2,594 girls and 2,651 boys) supports the SCCT framework. While confidence and value have similar mediating effects for boys, confidence plays a more pivotal role for girls. Gender diff…

Friezes and continued fractions
Evgeny Smirnov
https://arxiv.org/abs/2508.17074 https://arxiv.org/pdf/2508.17074 …

Friezes and continued fractions
We explore basic properties of number friezes, due to Conway and Coxeter, and their relations to decompositions of rational numbers into continued fractions, Farey sequences, and the modular group acting on the hyperbolic plane. These are notes from a mini-course for undergraduate students given at the 19th Summer School ``Modern Mathematics'', Dubna, Russia, July 18-29, 2019.

Collaborative Preferences for Learning Mathematics: A Scale Validation Study
Sang Hyun Kim, Tanya Evans
https://arxiv.org/abs/2508.12199 https://arxiv.org/…

Collaborative Preferences for Learning Mathematics: A Scale Validation Study
Collaboration within mathematics has been established as being effective in providing students with crucial opportunities to develop critical thinking, effective communication, and teamwork skills. By engaging in group problem-solving and shared learning experiences, students may gain deeper insights into mathematical concepts and learn to approach challenges from multiple perspectives. However, there remains a need for a reliable instrument to capture students' preferences for collaboration. T…

Cyclic Equalizability of Words and Its Application to Card-Based Cryptography
Kazumasa Shinagawa, Koji Nuida
https://arxiv.org/abs/2507.04916 https://

Cyclic Equalizability of Words and Its Application to Card-Based Cryptography
Card-based cryptography is a research area to implement cryptographic procedures using a deck of physical cards. In recent years, it has been found to be related to finite group theory and algebraic combinatorics, and is becoming more and more closely connected to the field of mathematics. In this paper, we discuss the relationship between card-based cryptography and combinatorics on words for the first time. In particular, we focus on cyclic equality of words. We say that a set of words are cy…

Homotopy classification of closed polygonal lines: results and problems
E. Alkin, O. Nikitenko, A. Skopenkov
https://arxiv.org/abs/2508.16287 https://arxiv…

Homotopy classification of closed polygonal lines: results and problems
In this text we expose (as a sequence of problems) basic cases of some fundamental ideas and methods of mathematics. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal lines in a subset of the plane. Although these ideas and methods are parts of topology, they are used in many other areas including computer science. This text is expository and is accessible to mathematicians not specialized in …