An epistemological analysis and educational reflection on the expression ‘all sequences’

This study analyzes how pre-service mathematics teachers interpret the expression ‘all sequence {aₙ}’ as it appears in questions on sequences in the Korean College Scholastic Ability Test (CSAT). It also investigates how the difficulties they encoun ter in this interpretive process are related to the epistemological characteristics of universal quantification. To this end, individual and focus group interviews were conducted with four pre-service mathematics teachers enrolled in a teacher education program. Their interpretative tendencies were analyzed within a theoretical framework based on philosophical perspectives on universal quantification—particularly the contrast between intuitionism and formalism. The findings reveal that prospective teachers tend to interpret the word ‘all’ in a collective sense and frequently misunderstand sequences as mere sets of values rather than as functions. Furthermore, They recognized that the expressions “all” and “each” represent different problem situations, and made different judgments on universally quantified statements that are mathematically equivalent. This study suggests the need for logical and philosophical training on universally quantified expressions within mathematics teacher education programs.