Alternative ways to initiate students' intuition, and hence internalization, of why zero factorial is equal to one

TL;DR

This paper explores algebraic and statistical justifications for zero factorial being one, demonstrating their effectiveness in improving students' understanding through a survey at a university.

Contribution

It introduces alternative algebraic and statistical methods to help students grasp why zero factorial equals one, enhancing teaching strategies.

Findings

Students found the justifications useful for understanding zero factorial.

Preference was highest for the first algebraic justification.

Survey results indicate improved student comprehension and engagement.

Abstract

Zero factorial, defined to be one, is often counterintuitive to students but nonetheless an interesting concept to convey in a classroom environment. The challenge is to delineate the concept in a simple and effective way through the practice of justification, a familiar concept in mathematics and science education. In this regard two algebraic and one statistical justification using the squeeze theorem are presented. To assess the effectiveness of the justifications, a student survey was conducted at a comprehensive university incorporating the analysis of the pre- and post-presentation statements. They clearly present that the justifications are useful in giving credence to zero factorial equals one. Overall, the results from the online survey supports that the students preferred Justification 1. The justifications provide instructors alternative ways to initiate exploration of students' intuitive set up of comprehending unobvious facts like zero factorial equals one. For a range of learners with their varied abilities to perform various mental activities most closely associated with learning and problem-solving, the justifications as simple alternative methods offer the potential to raise the current level of cognitive skills to inspire differentiated paths of learning. These are evident from survey results noting the role of statistical thinking and techniques.