{'fraction_non_alphanumeric': 0.013452914798206279, 'fraction_numerical': 0.0, 'mean_word_length': 6.031496062992126, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Classroom Activities For Introducing Equivalence Relations

Abstract Equivalence relations and partitions are two interconnected ideas that play important roles in advanced mathematics. While students encounter the informal notion of equivalence in many courses, the formal definition of an equivalence relation is typically introduced in a junior level transition-to-proof course. This paper reports the results of a classroom teaching experiment comparing the effectiveness of traditional lecture versus in-class group activities in introducing equivalence relations. Student understanding was assessed using task-based interviews outside of class. Students involved in group activities made a stronger connection between equivalence relations and partitions. Furthermore, they were more flexible and successful in proving or disproving that a given relation formed an equivalence relation.