Productive failure in learning the concept of variance

Instr Sci (2012) 40:651672

DOI 10.1007/s11251-012-9209-6

Manu Kapur

Received: 21 April 2011 / Accepted: 7 March 2012 / Published online: 22 March 2012 Springer Science+Business Media B.V. 2012

Abstract In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were rst asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical formulation of variance taught to them, PF students generated a diversity of formulations for variance but were unsuccessful in developing the canonical formulation. On the posttest however, PF students signicantly outperformed DI students on conceptual understanding and transfer without compromising procedural uency. These results challenge the claim that there is little efcacy in having learners solve problems targeting concepts that are novel to them, and that DI needs to happen before learners should solve problems on their own.

Keywords Problem solving Productive failure Multiple representations

Mathematics Classroom-based research

Introduction

Proponents of direct instruction (DI) bring to bear substantive empirical evidence against unguided or minimally guided instruction to claim that there is little efcacy in having learners solve problems that target novel concepts, and that learners should receive DI on the concepts before any problem solving (Sweller 2010; Kirschner et al. 2006). Kirschner et al. (2006) argued that Controlled experiments almost uniformly indicate that when dealing with novel information, learners should be explicitly shown what to do and how to do it (p. 79). Commonly cited problems with unguided or minimally guided instruction

M. Kapur (&)

Curriculum, Teaching and Learning, Learning Sciences Laboratory, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singaporee-mail: [email protected]

Productive failure in learning the concept of variance

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include increased working memory (WM) load that interferes with schema formation (Sweller 1988), encoding of errors and misconceptions (Brown and Campione 1994), lack of adequate practice and elaboration (Klahr and Nigam 2004), as well as affective problems of frustration and de-motivation (Hardiman et al. 1986).

Consequently, this has led to a commonly held belief that there is little efcacy in having learners solve novel problems that target concepts they have not learnt yet. Perhaps this...