Mathematics educators accept that if students demonstrate procedural knowledge - how to get to an answer in mathematics - it does not necessarily imply that these students understand why the procedure works (e.g. Tall, 1992; Rittle-Johnson & Alibali, 1999; Hiebert, 2013). In contrast, if students have conceptual knowledge, we consider they do understand these principles. Conceptual knowledge can be described as "Explicit or implicit understanding of the principles that govern a domain and of the interrelations between pieces of knowledge in a domain" (Rittle-Johnson & Alibali, 1999, p. 175). One of the ways that students demonstrate conceptual knowledge is by procedural flexibility, where students have "knowledge of multiple ways to solve problems and when to solve them" Rittle-Johnson & Star, 2007). Tall and Vinner (1981) defined conceptual understanding of ;the necessary procedures as the concept image, the "total cognitive structure that is associated with the concept" including ''all the mental pictures and associated properties and processes" that are "built up over the years through experiences of all kinds, changing as the individual meets new stimuli and matures" (p. 152).

Item Type:	Refereed Conference Paper
Keywords:	student limit derivative
Research Division:	Education
Research Group:	Curriculum and pedagogy
Research Field:	Mathematics and numeracy curriculum and pedagogy
Objective Division:	Education and Training
Objective Group:	Learner and learning
Objective Field:	Learner and learning not elsewhere classified
UTAS Author:	Reaburn, R (Dr Robyn Reaburn)
UTAS Author:	Oates, G (Associate Professor Greg Oates)
UTAS Author:	Dharmadasa, K (Dr Kumudini Dharmadasa)
UTAS Author:	Brideson, M (Dr Michael Brideson)
ID Code:	125889
Year Published:	2018
Deposited By:	Education
Deposited On:	2018-05-15
Last Modified:	2019-02-13
Downloads:	0