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Analysis of students' knowledge in relation to the factorial.

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Bibliographic Details
Title: Analysis of students' knowledge in relation to the factorial.
Authors: Thomas, Charlott1 (AUTHOR) charlott.thomas@uni-potsdam.de, Kapp, Felix2 (AUTHOR), Pöhler, Birte1 (AUTHOR)
Source: Frontiers in Education. 2026, p1-15. 15p.
Subject Terms: *Curriculum, *Teaching methods, *Educational attainment, *Cognitive Strategy Instruction, *Mathematics education, Factorials, Combinatorics
Geographic Terms: Germany
Abstract: This study investigates students' knowledge of the factorial at the end of their school career (aged 17–18), as the factorial represents a central combinatorial idea. Therefore, 161 students were given tasks designed to assess different aspects of their factorial knowledge: interpreting the exclamation mark in factorial notation (primarily factual knowledge), solving combinatorial tasks (primarily procedural knowledge), and formulating their own word problems (primarily conceptual knowledge). Furthermore, it is well known that mathematical performance differs across school types (Gymnasium and Gesamtschule in Germany) and course types (basic course and advanced course). To investigate whether these differences can also be observed in the domain of combinatorics, this study compares students from different school types and different types of courses regarding their success in solving the tasks. Our study confirms that many students struggle with tasks involving factorials and shows that performance depends strongly on the types of school and course. These findings highlight the importance of developing instructional approaches tailored to specific student groups that aim to enhance students' comprehensive understanding of factorials and combinatorics. [ABSTRACT FROM AUTHOR]
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Database: Education Research Complete
Description
Abstract:This study investigates students' knowledge of the factorial at the end of their school career (aged 17–18), as the factorial represents a central combinatorial idea. Therefore, 161 students were given tasks designed to assess different aspects of their factorial knowledge: interpreting the exclamation mark in factorial notation (primarily factual knowledge), solving combinatorial tasks (primarily procedural knowledge), and formulating their own word problems (primarily conceptual knowledge). Furthermore, it is well known that mathematical performance differs across school types (Gymnasium and Gesamtschule in Germany) and course types (basic course and advanced course). To investigate whether these differences can also be observed in the domain of combinatorics, this study compares students from different school types and different types of courses regarding their success in solving the tasks. Our study confirms that many students struggle with tasks involving factorials and shows that performance depends strongly on the types of school and course. These findings highlight the importance of developing instructional approaches tailored to specific student groups that aim to enhance students' comprehensive understanding of factorials and combinatorics. [ABSTRACT FROM AUTHOR]
ISSN:2504284X
DOI:10.3389/feduc.2026.1678978