Learning Mathematics

Authored by: Ann R. Edwards , Indigo Esmonde , Joseph F. Wagner

Handbook of Research on Learning and Instruction

Print publication date:  December  2010
Online publication date:  February  2011

Print ISBN: 9780415804608
eBook ISBN: 9780203839089
Adobe ISBN: 9781136882159


 Download Chapter



In 1973, Stephen Erlwanger published a groundbreaking article in the Journal of Children’s Mathematical Behavior reporting on a case study of one sixth grade student’s mathematical thinking. “Benny’s conceptions of rules and answers in IPI [Individually Prescribed Instruction] Mathematics,” or “Benny” as it came to be called, employed protocol analysis of clinical interviews to reveal the “rules” Benny had developed to operate on fractions and decimals. Benny was a successful student in IPI, a curriculum in which students individually progress through sequentially ordered behavioral objectives via continuous cycles of assessment and feedback. Erlwanger showed that while Benny demonstrated mastery on the IPI assessments using his rules, he had little conceptual understanding of fractions and decimals. Perhaps more importantly, he also argued that Benny’s “rules” could be seen as a sensible effort on the part of the learner to construct meaning out of instructional experiences that made little mathematical sense.

Search for more...
Back to top

Use of cookies on this website

We are using cookies to provide statistics that help us give you the best experience of our site. You can find out more in our Privacy Policy. By continuing to use the site you are agreeing to our use of cookies.