International Group for the Psychology of Mathematics Education (PME)

Proceedings of the International Group for the Psychology of Mathematics Education · Volume 1

Idiosyncratic Metaphors in a Mathematical Investigation: the Sieve of Eratosthenes

Everton Lacerda Jacinto, Rina Zazkis

Simon Fraser University

49th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2026Helsinki27 July 2026 - 1 August 2026pp. 883–890ISSN 2790-36482026Scopus conference code 336559
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Abstract

We engaged undergraduate liberal arts students in investigating patterns within the Sieve of Eratosthenes, a historical method for finding prime numbers in a given interval by crossing out multiples of primes. The investigation used a digital application in which numbers appeared in a grid, and changes in grid width produced different visual displays of prime and composite numbers. The participants examined how the grid width related to the appearance of primes in specific columns and described their approaches and conclusions in the form of a dialogue between interlocutors, referred to as “scripting journeys.” The reported research examines how participants use metaphors to articulate and develop their reasoning within a mathematical investigation.

Keywords

Mathematical InvestigationWriting DialoguesIdiosyncratic MetaphorsThe Sieve of Eratosthenes

Recommended citation

Lacerda Jacinto, E., & Zazkis, R. (2026). Idiosyncratic Metaphors in a Mathematical Investigation: the Sieve of Eratosthenes. In Krzywacki H., Hähkiöniemi M., Haataja E., Hannula M.S., Hästö P. (Eds.), Proceedings of the International Group for the Psychology of Mathematics Education, Volume 1 (pp. 883–890). Psychology of Mathematics Education (PME). ISSN 2790-3648.
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