Abstract
Facilitating meaningful mathematical discourse in an online setting can be a challenge for instructors. The purpose of this chapter is to analyze an instructor's discourse interventions to encourage mathematical discourse in online asynchronous discussions in an analysis course for secondary mathematics teachers (SMTs). The SMTs were required to participate in the discussions and encouraged to ask/answer questions, share/compare their ideas, and explain their thinking/answers. Instructor responses were analyzed using both Mazzolini and Maddison's four categories of response the respect to instructor intervention—(1) question, (2) answer, (3) mix of answer and question, and (4) other—and Simonsen and Banfield's five recurring categories—(1) resolve, (2) validate, (3) redirect, (4) expand, and (5) withhold. With respect to instructor intervention, the author suggests mainly withholding from responding and to use expand, redirect, question, or mix if necessary to encourage mathematical discourse.
TopBackground
“Mathematical discourse includes the purposeful exchange of ideas through classroom discussion, as well as through other forms of verbal, visual, and written communication (NCTM 1991, 2000).” The discourse in the mathematics classroom allows students to share ideas and clarify understandings, construct convincing arguments, develop a language for expressing mathematical ideas, and learn to see things from other perspectives. Facilitating this type of mathematical discourse to online settings can be just as challenging as it is to create in traditional classrooms. In traditional classrooms, the teacher’s role in facilitating discourse is to engage students in sharing mathematical ideas, orchestrate student approaches and solution strategies, and ensure progress towards mathematical ideas (NCTM). Students who take mathematics courses that use asynchronous communication are essentially forced to engage in some level of mathematical discourse as a requirement of the course (Simonsen & Banfield, 2006). The role ofthe online instructor, however, impacts the facilitation of the discourse.
At one time, the role that instructors should play was thought to be “ambiguous and largely untested’ (Easton, 2003, p. 87). Other researchers, however, propose that an instructor should take the “Socratic approach” (MacKnight, 2000) or play a more active role earlier in the course’ (Gold, 2001) or play the “’sage on the stage’ (Mazzolini & Maddison, 2003), or take a constructivist approach (Chinnappan, 2006; Gold, 2001; Shackelford & Maxwell, 2012). Literature on the role of online instructors in fostering discourse also encourages creating and facilitating learning environments that are collaborative, inquiry-based and student centered (Carey, Kleiman, Russell, Venable, & Louie, 2008; Chinnappan, 2006; Zhou & Stahl, 2007).
Key Terms in this Chapter
Mathematical Discourse: Discussions in mathematics where students articulate their understanding of concepts.
Posting: A message or comment or question that a student or instructor places on an online discussion board.
Conscious Construction: Reflecting on mathematical discussion and providing a meaningful contribution.
Teaching Modules: Activities designed to help teachers connect real analysis content, secondary mathematics, and teaching secondary mathematics.
Instructor Intervention: An instructor’s response or lack of response to a student’s post usually to a discussion board.
Asynchronous Communication: Exchange messages via computer and often with a time lag.
Forum: An online discussion consisting of messages and responses.