Directionality of The Equals Sign: A Case Study Using Logarithmic Properties

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, log (MN)= log (M)+ log (N)) with bidirectional flexibility, and subsequently wondered if the “direction” that students are presented mathematical properties has an impact on their ability to use the properties successfully. The authors studied this phenomenon in 11 undergraduate, introductory-level mathematics courses (College Algebra and Precalculus) by presenting logarithmic properties in different “directions” and seeing what effect that had on students’ ability to apply the logarithmic properties successfully. Our results indicate that, despite careful classroom discussion of the meaning of the properties and sustained problem solving activities, the “direction” that the properties are presented to the students does have an effect on their ability to use the properties successfully.