This study posed and studied a solution to a prevailing tension in online education: the online medium is fundamentally connective and yet students often report feelings of social isolation. The study compared two online interventions -- both into a student's fluency in the language of functions and graphs, a major focus of a student's transition from arithmetic to algebra. The "traditional" intervention had students perform auto-graded recall-based work common to current online education platforms, and experience didactic instruction. The "Functionary" intervention, meanwhile, had students perform communicative work, taking turns drawing and describing a graph with an online partner, and experience instruction in response to their need. These interventions were studied using a pretest-posttest 3 x 2 factorial design with three levels of the between-subject condition variable ("traditional," "Functionary," and "null") and two levels of the within-subject time variable ("pre" and "post"). Students were counterbalanced between conditions according to their pretest scores, which assessed their proficiency in various elements of precision in describing and drawing graphs. An analysis of variance determined that students perceived the Functionary intervention to be significantly more social than the traditional intervention. In the aggregate, both the traditional and Functionary interventions learned significant amounts, with neither learning significantly more than the other. An analysis of student descriptions of a graph revealed that the Functionary condition saw a significant increase over time in the number of students who used a correct coordinate. The other conditions didn't see the same gains. Aspects of Functionary's design may therefore be useful to instructors and instructional designers in both online and face-to-face classrooms. This study also revealed the challenges students faced taking up conventional mathematical notation, adding to our pedagogical content knowledge of the language of functions and graphs. Implications for instructional designers, math teachers, and math education researchers are discussed. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]