Using Open-response Tasks to Reveal the Conceptual Understanding of Learners—Learners Teaching the Teacher what they Know about Trigonometry

Abstract

This article reports on using open-response questions to reveal the level of, and change in, conceptual understanding of a small sample of Grade 11 learners of trigonometry in a South African high school. The investigation used learner response sheets in a regular classroom with the teacher as researcher. Combining the idea of concept image and concept definition with Sfard’s ideas of interiorisation, condensation and reification as the conceptual framework, the research indicated that open-response questions can reveal the conceptual knowledge of learners. The findings suggest that the fullness of learners’ conceptual knowledge is reflected by the degree to which a learner’s articulation of the concept image matches the concept definition. In contrast to the predetermined data derived from multiple choice or short answer questions, open-response questions provide glimpses of learners’ conceptualisation of trigonometric constructs. The power of this pedagogy allows teachers to learn what their learners know.

Keywords:

• Concept definition and concept image
• learner conceptions
• open-ended responses
• trigonometry

ORCID

Pieter van Jaarsveld http://orcid.org/0000-0002-6131-3348