# Volume 21, Numbers 1 & 2 (February 2024)

"A culture is not a self-enclosed world. It is not an identity, but a system of differences held together by history. Not being self-complete, it opens out to other possibilities. Then one finds the other within oneself." - J.N. Mohanty

## Editorial

Horocycles, Horoscopes, Horizons…: A Review of Petra Mikulan & Nathalie Sinclair’s (2023) Time and Education

Bharath Sriraman

## Articles

The Field Q and the Equality 0.999. . . = 1 from Combinatorics of Circular Words and History of Practical Arithmetics

Benoit Rittaud and Laurent Vivier

Seeing Pascal’s Mystic Hexagon from a Different Angle

Anderson Norton

Stepping Stone Problem on Graphs

Rory O'Dwyer

The Tradition of Large Integers in Historical Arithmetical Textbooks

Franka Miriam Bruckler and Vladimir Stilinovic

An Active Learning Activity for the Construction of a Finite-Field Slide Rule for Undergraduate Students

Marco Abrate

Productive Struggle in Mathematical Modelling

Piera Biccard

An Examination of the Factors and Characteristics that Contribute to the Success of Putnam Fellows

Robert A. J. Stroud and Thomas C. DeFranco

Displaying gifted students’ mathematical reasoning during problem solving: Challenges and possibilities

Attila Szabo, Ann-Sophie Tillnert, and John Mattsson

The construction of figured numbers in GeoGebra software using algebraic properties

Francisco Evamar Barros, Francisco Regis Vieira Alves, Paula Maria Machado Cruz Catarino, and Renata Teofilo de Sousa

Tagging Opportunities to Learn: A Coding Scheme for Student Tasks

Janet Heine Barnett, Cihan Can, and Daniel E. Otero

The spirit of mathematical modeling – a philosophical study on the occasion of 50 years of mathematical modeling education

Peter Frejd and Pauline Vos

The Chain Rule Does Not Have to be a Pain Rule

Elizabeth Beeman, Jennifer Runge, Lauren Holden, Devon Maxwell, and Yi-Yin (Winnie) Ko

On the Even Distribution of Odd Primes: An On-Ramp to Mathematical Research

James Quinlan and Michael Todd Edwards

An Analysis of Graduate Teaching Assistants’ Noticing Skills During Calculus and Physics Tutoring Scenarios

Lindsay Borger, M. J. Camarato, and Molly H. Fisher

Today’s mathematics student: Take two

Carmen M. Latterell

Investigating Problems Posed by Pre-Service Mathematics Teachers for the Four Operations in Fractions

Yasemin Kiymaz

On Convincing Power of Counterexamples

Orly Buchbinder and Rina Zazkis

Going off on a Tangent: An Inclusion-Exclusion Identity

Aloysius Bathi Kasturiarachi