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This study explores the use of Desmos in creating artworks out of the four conic sections discussed in Pre-calculus, namely: circle, parabola, ellipse, and hyperbola. This performance task was designed to give senior high school students an opportunity to integrate their creativity in arts and their knowledge of conic sections to produce their own artworks using a graphing calculator. Description of the performance task, concepts underlying its design, and examples of Desmos artworks produced by Grade 11 students are presented in this paper. Moving forward, mathematics educators could use this information as a springboard for designing performance tasks that integrate mathematics, art, and technology. [ABSTRACT FROM AUTHOR]

This pilot study is anchored on the theory of grounding in communication by Clark and Brennan (1991), who argued that discourse requires a conscious and consistent effort from its participants to coordinate the content of what they intend to convey so that they can establish common ground or shared understanding. This coordination process is known as grounding. Due to the fast-expanding use of online environments in facilitating mathematical discourse, a question arises as to whether or not common ground can be reached during online mathematical discourse and what evidence indicates so. As part of an ongoing dissertation project, this pilot study therefore aimed to seek evidence of grounding in an online mathematical discourse to determine whether or not common ground has truly been established by the teacher and students. Using the aforementioned theory as an interpretive lens and following a qualitative research design, four (4) video-recorded class sessions of an online graduate course in Combinatorics were observed to answer the posed research question. The course was conducted once a week through a video conferencing platform, with each class session lasting for three hours. It was composed of one (1) teacher and three (3) graduate students, who were all pursuing a PhD in mathematics education at a private university in Manila, Philippines. A multimodal conversation analysis (MCA), which involved a transcription of the recordings and an inductive examination of the transcripts, was subsequently carried out to identify the emergence of evidence of grounding. The analysis showed that positive evidence of grounding was present in the online mathematical discourse in Combinatorics. This evidence came in the form of acknowledgements, adjacency pairs, and continued attention. For instance, the teacher posed questions from time to time to check the students' understanding, to which the students responded either verbally or using embodied and material resources (e.g., head nods, hand gestures, and virtual gestures). Hence, it was concluded that the teacher and students consciously and consistently worked their way towards updating and establishing their common ground during the online mathematical discourse. The findings of this study provided a guide for assessing whether or not shared understanding is achieved between teachers and students as they engage in an online mathematical discourse. [ABSTRACT FROM AUTHOR]