SEED projects 2017 – Writing, Writing Everywhere

Writing reflective scripts on overcoming misconceptions and difficulties in mathematics

Dr Igor’ Kontorovich (Faculty of Science)

A familiarity with students’ misconceptions and difficulties with particular concepts has strategic importance in teaching. School teachers and university lecturers are expected to use this familiarity when conveying disciplinary content, communicating with students and designing evaluations. But how do they get familiar with students’ misconceptions and difficulties? In many cases, this knowledge emerges from anecdotal evidence, personal retrospections on their own learning, and speculative envisioning of students’ thinking. These sources are confined by the gap between experienced educators and beginner learners, and while they can provide insightful ideas for assisting students, they tell us little about how students overcome these struggles by themselves.

This project aimed, firstly, to collect data on students’ learning struggles in Mathematics, and, secondly, to provide students with opportunities to share their successes in overcoming their own misconceptions and difficulties. Seventy-four students from a Stage One Maths course participated in the project. Students on this course combine university studies with secondary school, which makes their learning experience particularly challenging and valuable. As part of their regular homework assignments, the students were asked to script a fictional dialogue between student-characters on one of the course topics that the script-writers experienced as challenging

Originally, script-writing was introduced to provide prospective teachers with an opportunity to plan for instruction and develop their professional competency in anticipation of students’ responses. Script-writing has also been used to evaluate students’ understanding of concepts and theorems. The innovation of this project is in using script-writing as a metacognitive tool that allows students to reflect on their learning experiences.

Overall, the students accumulated 156 scripts where they reflected on a rich variety of issues in relation to proving and the limit concept. While many of the issues have already been documented as challenging in prior educational research (e.g., an attempt to prove a statement through an example), this project showed that students are not only capable of making mistakes but they can also notice and encapsulate them in a creative form.