Representational Effects in a Rule Discovery Task

Representational Effects in a Rule Discovery Task Frederic Vallee-Tourangeau, Andrea Krusi Penney and Teresa Payton Psychology Research Unit, Kingston University Kingston-upon-Thames, UNITED KINGDOM KT1 2EE f.vallee-tourangeau /a.kruesi /t.payton@kingston.ac.uk Abstract In the Wason (1960) rule discovery task reasoners must infer a rule that governs the production of number sequences. The task instructions are designed such that reasoners’ initial hypotheses are invariantly narrower than the correct rule. The inferential challenge lies in discovering the scope of these initial hypotheses. The traditional task departs from real- world hypothesis testing in at least one significant respect: The task is never presented in a manner that offers a rich external representation of the problem. The study reported here examined representational effects by developing task isomorphs which offered either an external, physically manipulable, representation of the problem space or a graphical presentation of the simple linear relationships between adjacent numbers in a sequence. Compared to a control condition, these task isomorphs lead to a significantly higher incidence of successful rule discovery, and encouraged the creation of a significantly more heterogeneous set of number sequences. Further, control participants had to produce 50% more number sequences than participants who worked with a rich external representation before discovering the rule. Keywords: Reasoning; distributed cognition. Introduction Wason (1960) created a simple inductive inference context which cast light on reasoners’ ability to discard plausible but overly narrow hypotheses. Wason’s 2-4-6 task consists of discovering the rule that governs the production of sequences of three numbers, or triples. To do so, participants create new number sequences that are then classified as either conforming or not to the rule. In Wason’s original task the rule is ‘any increasing sequence’. Before formulating their first test triple, participants are given the following crucial but misleading piece of information: the triple 2-4-6 conforms to the rule. This information implicitly identifies a set of triples that is narrower and more structured than the set of all conforming triples (Klayman & Ha, 1987). The salient features of the 2-4-6 example, namely evens and constant increments, constrain the initial hypotheses formulated by reasoners just as Wason (1960) intended. New sequences motivated by such initial hypotheses (e.g., 8-10-12) will unfailingly receive positive feedback since they are predicated on features that are sufficient but not necessary to produce triples that receive positive feedback. The challenge in this task thus lies in discovering the boundaries of such initially plausible hypotheses by formulating sequences that fall outside their scope, such as 1-19-33 for example. Solving the 2-4-6 task is hard. In Wason’s (1960) original study, 80% of participants failed to announce the correct rule at their first attempt. Subsequent replications have reported similarly low rates of success (e.g., Mahoney & DeMonbreun, 1977; Tweney, Doherty, Worner, Pliske, Mynatt, Gross, & Arkkelin, 1980; Wason, 1968). Two features characterise the hypothesis-testing output of most participants: indolence and narrow-mindedness (Vallee- Tourangeau, Austin, & Rankin, 1995). That is, participants produce few triples before announcing their best guess and those triples form a very homogenous set, which includes relatively few triples that increase by variable increments or that receive negative feedback. This rather grim reasoning profile has been consecrated into textbook wisdom (e.g., Poletiek, 2001; Schustack, 1988; Sutherland, 1992). Two research avenues can be explored in an attempt to shed light on the poor rule-discovery performance in the 2- 4-6 task. The first focuses on properties internal to the reasoners (cf. Stanovich & West, 2000). Wason himself enjoined future researchers to identify reasoners with a ‘disposition to refute’ (1960, p. 139). Vartanian, Martindale, and Kwiatkowski (2003) suggested that individual differences in creativity predicted successful rule induction in the 2-4-6 task. The second focuses on properties of the external environment. The aim is to determine whether variations in the physical presentation of the task encourage different degrees of diligence and creativity, and hence result in different degrees of success (Duncan, 1998). The research reported here stems from this latter perspective. Representational Effects Despite the simplicity of the 2-4-6 task, the inferential challenge of identifying the scope of a hypothesis and establishing its generalizability mirror features of real-world hypothesis-testing (Gorman, 1995). However, unlike real- world hypothesis testing the external representation of the dimensions of the triple space and the actual number sequences is nonexistent or impoverished. Rule discovery behaviour proceeds primarily on the basis of the reasoner’s internal representation of the problem. The extent to which the representation of the problem is distributed between the reasoner’s mind and the environment is limited to the written record of triples tested and feedback received. In this important respect the inferential context of the original Wason task is relatively atypical of real-world hypothesis testing. Scientific hypothesis testing, for example, is a process shaped by artefacts and methodologies favoured by researchers that encourage and constrain the nature of the