| Technology use and a focus on 21st century skills, coupled with recent adoption of Common Core State Standards for Mathematics, marks a new challenge for mathematics teachers. Communication, discourse, and tools for enhancing discourse (NCTM, 1991, 2000) play an integral role in successful implementation of technology and mathematics standards.;Dynamic geometry environments represent a tool that has the potential to enhance the discourse within mathematical discussions. Also, Stein, Engle, Smith and Hughes (2008) described five practices for orchestrating productive mathematical discussions intended to help teachers incorporate student thinking into classroom discussions. The 1:1 laptop learning environment provides a context that has the potential to examine the intersection of classroom discourse, pedagogical practices, and technology use.;This study examined the nature of mathematical discourse, extent to which teachers used the five practices, examined design and technology features of pre-constructed dynamic geometry tasks and how teachers use them, and explored the combined influence of discourse, the five practices, and technology use on level of cognitive demand when teachers implement pre-constructed dynamic geometry tasks. The study followed a qualitative, multicase observational research design, where a purposeful sample of three teachers represented individual cases. All participants taught Algebra 1 in two high schools within the same 1:1 computing, high needs school district during the study.;The conceptual framework combined the Mathematical Task Framework (Smith & Stein, 1998) and the five practices for orchestrating productive mathematical discussions into a dynamic model characterizing task implementation and use of the five practices in 1:1 computing classrooms. The Task Analysis Guide (Smith & Stein, 1998), Sinclair's (2003) design principles for pre-constructed dynamic geometry sketches, and the IQA for Academic Rigor: Mathematical Rubric for Potential of the Task were used to evaluate the potential level of cognitive demand of pre-constructed dynamic geometry tasks. Participants were observed for three teaching sets (Simon, Tzur, Heinz, Kinzel, and Smith, 2000), and excerpts of the video that included use of pre-constructed dynamic geometry tasks served as episodes for analysis. Discourse was analyzed using a modified version of the Oregon Mathematics Leadership Institute Classroom Observation Protocol and Boaler and Brodie's (2004) question types. Drijvers, Doorman, Reed, & Gravemeijer (2010) teacher technology orchestration types were utilized to describe how teachers used pre-constructed dynamic geometry tasks during implementation. The five practices served as codes for interview, group planning, and classroom observation data to characterize the extent of teachers' use of the five practices. The triangulation of discourse, technology use, and use of five practices was compared to the IQA for Academic Rigor: Mathematical Rubric for Implementation of the Task to evaluate the implemented level of cognitive demand of the pre-constructed dynamic geometry tasks.;Findings indicated that teachers relied on teacher to whole class as the predominant mode of mathematical discourse. Questions and statements were the most common type of mathematical discourse, and questions were used slightly more often than statements. Higher level questions were posed more often than lower level questions, but teachers' incorporation of the five practices varied greatly. In terms of technology use, teachers most often orchestrated the pre-constructed dynamic tasks by discussing the screen or explaining the screen. Teachers used sliders and hide/show buttons to focus student attention and facilitate development of mathematical concepts. Given that pre-constructed dynamic geometry tasks adhered to design principles, two themes emerged for level of cognitive demand; 1) when teachers employed higher level questions/statements in conjunction with a discuss the screen technology orchestration type the implemented level of cognitive demand remained high and 2) when teachers employed lower level questions/statements in conjunction with an explain the screen technology orchestration type the implemented level of cognitive demand decreased. |
