A Novice Teacher Researcher’s Action Research Project: Posing Problems to Promote Concepts of Graphs in Calculus

Abstract

A novice mathematics teacher researcher (TR) conducted an “interactive action research” (AR) to determine what problems would be most beneficial to teach her students about creating graphs based on a function’s attributes. After a number of trials that included adjusting her goals, the TR successfully designed problems appropriate for her goals. This paper describes the problem-posing process the TR used to derive the problems, and which include the four steps described in the literature: i) plan the problem, ii) pose it, iii) solve it, and iv) organize and complete it (see Guveli, 2015) plus an additional overall step added by this author, v) develop awareness of common perceptions (and misconceptions) that students have with respect to graphing. The contribution of this study is twofold. The first is the theoretical model of a five-step AR process, which can be used to guide TRs when conducting a mathematics posing problem AR: mathematical objective, source of inspiration, concerns related to formulation, mathematical uncertainties, and decisions taken. The second is that it demonstrates how TR’s formative assessment of the student’s solutions can improve her problem-posing heuristics and guide her to adjust her didactic goal(s). In addition, this paper documents her professional development on two aspects: developments and transitions in her thinking, and her development in skills required for reaching a didactic or mathematical goal. As part of a participatory action-research project, students at the vocational upper-secondary Natural Resource Use programme in Sweden were introduced to infrared cameras in their courses. Students were video recorded as they used infrared cameras in the investigation of pigs’ physiology and health in the school’s pig house and explained generated infrared images in whole-class dialogue, together with involved teachers and researcher. Students found that a pig’s injured leg has high temperature, but also, more surprisingly, udder abcesses with lower temperature than the surrounding healthy udder tissue. Students and teachers expressed excitement in explaining the results. From the perspective of seeing vocational education as a kind of cognitive apprenticeship, students’ investigations and dialogue with the teachers and researcher are characterised as an example of authentic activity in a community of learners, where expertise was distributed across all participants.