How Do Middle School Mathematics Teachers Conceptualize Open-Ended Questions?

Abstract

The study aims at examining middle school mathematics teachers' conceptions of open-ended questions. A questionnaire consisting of open-ended items was applied to 40 mathematics teachers. The teachers were asked to define the open-ended question in general and the mathematical open-ended question in particular and provide examples to exemplify their definitions. This study employs phenomenographic study aiming at revealing middle school mathematics teachers' conceptions and experience regarding open-ended questions in an exploratory manner. The findings show that the teachers explained the open-ended question through its form (appearance), the number of outputs, the process/method required, and its functionality. In addition, teachers defined the open-ended question mostly using non-mathematical terms, and they had particular difficulties defining the mathematical open-ended question. The teachers regarded questions with variable correct answers as open-ended, could not give examples of open-ended questions with infinitely correct answers, and some deemed closed-ended questions as open-ended. Although the participants were mathematics teachers, the examples they presented for the open-ended question were mostly from outside the field of mathematics. This study points out the fact that teachers need a guiding conceptualization of open-ended questions.