In 1991, the National Council of Teachers of Mathematics (NCTM) published the Professional Standards for Teaching Mathematics in which they emphasized the importance of discourse in the teaching and learning of mathematics. While many acknowledge the important role discourse plays in the teaching and learning of mathematics, transforming the classroom to one in which students are active participants in classroom discussions does not occur automatically (Hufferd-Ackles, Fuson, & Sherin, 2004; Nathan & Knuth, 2003). The teacher needs to choose worthwhile mathematical tasks, identify appropriate tools to use, anticipate, monitor, select and sequence student work on those tasks, and then bring the class to an appropriate close (e.g., Stein, Engle, Smith, & Hughes, 2008). They need to be able to orchestrate the communicational processes (who is speaking, when, and how) as well as focus on the mathematical content of the conversations.

Because technology supports students’ conjecturing, problem solving, and exploration of mathematical tasks that can be of high cognitive-demand, and may also serve as an agent disruptive of current norms and practice (Rochelle, Pea, Hoadley, Gordin, & Means, 2000), this may affect the nature of the content of the discourse in which students engage. Also, since students are interacting with a computer as well as one or more students as they work on problems in pairs or small groups they may pose more questions to each other and to the teacher. A question that guided this study was, “In what ways does the inclusion of technology in a mathematics class influence the nature of mathematical discourse?” The purpose of this study was to characterize the nature of mathematical discourse when students were using technology and to contrast this to discourse that was typical in the class when technology was not used.

Methods

During the summer of 2010, twenty teachers from four different schools districts attended a one-week professional development workshop. The school districts were in different stages of implementing 1:1 laptop initiatives. The professional development workshop focused on assisting teachers in using a dynamic geometry software program, The Geometer’s Sketchpad ver. 5.0, to teach particular topics in the high school geometry curriculum (e.g., triangles, quadrilaterals, transformations). The summer workshop was followed by an online course that was taught during the 2010-2011 school year. These experiences are part of a larger 2-year professional development project. The data reported here were collected during the early stages of the teachers’ participation in the professional development experience. The data reported here were collected during the early stages of the teachers’ participation in the professional development experience.

The Oregon Mathematics Leadership Initiative (OMLI) Classroom Observation Protocol (RMC Research Corporation) was modified and used to gather more detailed information about discourse in the classroom when technology was and was not used. This instrument identifies the modes and types of mathematical discourse and the tools that were used. However, the purpose of this instrument was to focus on student discourse and it did not attend to discourse that was initiated by the teacher. Thus, the instrument was modified to allow researchers to code both student discourse as well as teacher discourse. The mode was used to identify who was participating in the discourse (e.g., teacher to student, student to student) and the type of discourse was used to identify the nature of the response or question during the interaction (e.g., explanation, prediction, justification, answer). The OMLI project assigned a number to each of the different types of discourse to suggest a ranking similar to the categorization of lower and higher-level questions identified by other researchers (e.g., Author2 & Other 2005; Moyer & Milewicz, 2002). Especially for this study, the tools that were used for the discourse were important to also note.

Three teachers were selected for more in-depth analysis based on teaching experience and technology usage. Mrs. Adams and Mr. Jones represented teachers at both ends of the teaching continuum and demonstrated facile use of various types of technology. Mrs. Smith represented a long tenure teaching, but initially demonstrated little aptitude for technology.  An iterative process was carried out on two of the six video-recordings until an agreement rate greater than 70% on the codes was reached. Then two coders analyzed the remaining four video-recordings individually.

Findings

For both Mrs. Adams and Mr. Jones the mode of discourse shifted when technology was used while it did not for Mrs. Smith. For Mr. Jones there was less teacher-to-whole class discourse and more teacher-student and student-teacher discourse. For Mrs. Adams there was a striking increase in the number of student-to-student discursive interactions when technology was used. However, it is important to note that while students were using technology they were often working in small groups or in pairs. It is possible that similar changes in the modes of discourse would be observed in non-technological settings when students are working in pairs or small groups, however Mrs. Smith used small groups both with and without technology, but this did not engender more student-student interactions. This is a question that could be further examined. Clearly the use of technology alone does not shape discursive practices, but may provide a supportive vehicle for doing so.

While changes in discourse modes were noted, changes in discourse types were not. While many have suggested that technology has the potential to support reasoning and sense-making activities that could foster justification and generalization discourse types, this was not observed. Research in non-technological learning environments suggests that teachers first build an environment that students feel comfortable interacting (modes) and then turn their focus to mathematics (types) (Silver & Smith, 1996; Wood, Cobb, & Yackel, 1991). As teachers transition into the second year and this becomes a more explicit focus for them it would be interesting to see if more dramatic changes become evident in the type of discourse that occurs within their classrooms.