ORIGINAL ARTICLE Ben’ s perception of space and subitizing activity: a constructivist teaching experiment Beth L. MacDonald 1 Received: 6 March 2015 /Revised: 23 August 2015 /Accepted: 25 August 2015 / Published online: 4 September 2015 # Mathematics Education Research Group of Australasia, Inc. 2015 Abstract This 22-session constructivist teaching experiment set out to investigate a preschool student’ s number understanding relative to his subitizing activity. Subitizing, a quick apprehension of the numerosity of a small set of items, has been found to characterize perceptual and conceptual processes students rely on as their understand- ing of number develops. The purpose for this study is to investigate how a preschool student’ s, Ben, perceptual subitizing activity changed relative to the density of items and the development of his number understanding. Findings indicated that early on in the teaching experiment, Ben’ s perceptual subitizing activity was influenced by his primary reliance upon the perceived amount of space between items. Shifts in reason- ing when perceptually subitizing indicated physiological and experiential development in Ben’ s number understanding, as Ben described the number of items increasing when the perceived amount of space between items decreased. Number conservation was considered as relevant to these findings because Ben’ s explanation for why a number could increase or decrease mirrored similar logic when unable to conserve number. Implications of this study suggest nuances in number understanding development which can explain preschool students’ reliance upon a more refined set of perceptual subitizing. Keywords Subitizing . Conservation of number . Number understanding Number knowledge development was initially explicated as dependent upon a combi- nation of physiological development and experiential development (Piaget 1965). However, in the last 50 years, research findings indicate that young children are quite capable of constructing numerical knowledge well before the stages of development delineated by Piaget (1965) (Dehaene 2011). Number knowledge development has also been found to relate to subitizing, a quick apprehension toward number Math Ed Res J (2015) 27:563–584 DOI 10.1007/s13394-015-0152-0 * Beth L. MacDonald beth.macdonald@usu.edu 1 Utah State University, 2805 Old Main Hill, Logan, UT 84322-2805, USA