“The Case of the Case of Benny: Elucidating the Influence of a Landmark Study in Mathematics Education”, 2014-09 (; backlinks):
We report the most common purposes for citing 1973’s “Case of Benny”.
The case is most frequently cited to support the claim that students have idiosyncratic conceptions of mathematics.
A common purpose for citing the case is to support the claim that correct answers to not imply correct understanding.
The case is viewed by many as exemplary qualitative (case study) research.
The case is used to support the claim that there are serious difficulties with behaviorist-based learning systems.
Stanley Erlwanger’s “Case of Benny” is seen by many as particularly influential in the mathematics education research community.
This paper reports the results of a study designed to describe the nature of that influence.
Through an analysis of academic references to the Case of Benny from the past 40 years, 5 primary purposes for citing the case were identified. These purposes revolve around the themes of student mathematical conceptions, the relationship between correct answers and understanding, the value of qualitative research, the impact of a behaviorist-based curriculum, and students as sense makers.
The paper concludes by using these themes to reflect on the past 40 years and to look ahead to the future of research in mathematics education.
…Benny’s classroom success was made possible through a fascinating confluence of conceptions of mathematics and curricular design. Benny knew there were multiple equivalent representations for the fractions he was working with (he used the example of the equivalence of 1⁄2 and 2⁄4). He also knew that the answer key for his tests had a single correct answer for each problem. What 1973 uncovered was that Benny had combined these conceptions into “an incorrect generalization about answers” (pg5), one that allowed him “to believe that all his answers are correct ‘no matter what the key says”’ (pg5). Thus, rather than interpreting his wrong answers as wrong, he interpreted them as correct but in the wrong form. He then played a game, a “wild goose chase”, (pg6) of looking for patterns in the correct answers and “rules” that would allow him to get those answers frequently enough to get at least 80% on his mastery tests. He thus maintained numerous rules for working “different” kinds of problems, even though frequently these rules contradicted each other and resulted in numbers that actually were not equivalent. This game he played led “him to believe that the answers work like ’magic, because really they’re just different answers which we think they’re different, but really they’re the same”’ (pg8).