“With Percentages the 100 is Always in the Denominator”: From the Field to Pre-service Teachers

Abstract

The ubiquity of the subject of percentages in our everyday life demands that math teachers and pre-service math teachers demonstrate a profound knowledge and thorough understanding of the concept of percentages. This work, which originated from one specific lesson in an 8^th grade math class, studies the conceptual understanding and problem-solving strategies of 17 pre-service math teachers. We exhibit and analyze the pre-service teachers’ misconceptions and their inefficient or false problem-solving strategies. We identify two main misconceptions. The first we name “In percentage problem is 100 always the denominator?” and the second “One can handle percentage problems using the same techniques as in numerical problems” (or Over-transferring of numerical problems). We hypothesize reasons and explanations for these misconceptions. The frequent use of percentages in everyday life and in sciences demands a sound knowledge of the subject. This paper aims to describe a process that began with a mathematics lesson in an 8^th grade. As an outcome of attending the lesson and the discussions that followed, we investigated 17 pre-service mathematics teachers' conceptual understanding and problem solving strategies associated with percentages. The research sample is not random. These are 17 pre-service teachers that we met in the course of our work with them. Because of the small size of the sample, no statistical analyses were performed beyond calculating the frequency of the events.