The Effect of Using Prediction Questions in the Middle School Algebra Classroom

This paper presents prediction as an instructional means to develop students’ mathematical understanding and reasoning. In order to determine the effect of using prediction questions, data from two middle school algebra classrooms taught by the same teacher were gathered during one school year. According to the state test results, the two classrooms were considered comparable at the beginning of the study. During the school year data were collected while two algebra units were taught: in one classroom prediction questions were posed and discussed at the launch of each lesson, and no prediction questions were exposed to the other classroom. After each of the two units, students were given a unit assessment evaluating students’ mathematical understanding and reasoning on linear and exponential relationships. These unit assessment data show that the treatment classroom outperformed the non-treatment classroom, which indicates that students with prediction questions developed better mathematical understanding and reasoning. Introduction The importance of understanding and reasoning in the teaching and learning of mathematics has been recognized by the mathematics education community all over the world, and yet developing students’ ability to think and reason mathematically has not been a trivial task. This paper highlights an initiative to utilize prediction questions as a means of helping students develop mathematical understanding and reasoning. Prediction is an aspect of reasoning to which researchers in mathematics education have paid less attention compared to other aspects of reasoning, such as justification. Our analysis of the U.S. state standards revealed that prediction was the most prevalent reasoning expectation across grades as well as content strands (Kim & Kasmer, 2006). This suggested that prediction could be an important component of reasoning that could be easily pursued at all grade levels and in all mathematics content strands. It also implicated the sound rationale to investigate the potential of prediction in the mathematics classroom for the development of mathematical understanding and reasoning. As such, we began to explore to what extent and in what ways prediction questions could help students develop understanding and reasoning in the context of middle school algebra. Related Literature Prediction is a type of reasoning that can lead to a generalization of patterns and also be derived from a generalization (Kim & Kasmer, 2007). Peirce’s (1998) notion of abduction supports the importance of prediction in developing knowledge. According to Peirce, abduction is forming a prediction without any positive assurance, is the only way in which people are introduced to a new idea, and makes a logical connection between deduction and induction. In various disciplines, prediction has been investigated as a means of helping students’ learning. In reading education, a body of research has investigated prediction in the area of reading (e.g., Block, Rodgers, & Johnson, 2004; Palincsar & Klenk, 1991). In such research, students were asked to make a prediction in a reading activity using questions, such as “what do you know about this character that helps you predict what he or she will do next? ” and “given the situation in the story, what will possibly happen next? ” The results revealed that asking students