ABSTRACT
Working memory is an organismic construct that captures the notion of a limited capacity to “keep in mind” information. Measuring the capacity of working memory has proven to be diffi cult, and there is no consensus in the literature about its limit – as the last epigraph suggests. This diffi culty may stem from failure to apply, or explicitly create, sensible principles for valid and direct (fundamental) measurement. Instead, research psychologists tend to use somewhat arbitrary ways of scoring without giving much attention to organismic processes that the numeric scoring represents. In this chapter we advance towards a solution of this problem by formulating an explicit organismic model of mental (i.e., voluntary, executive) attention – a construct often regarded as the maturational component of working memory. We discuss explicitly principles of fundamental measurement relevant for this measurement, and clarify the concept of functional units of processing (often called chunks) by discussing in detail the construct of organismic schemes, to show how “chunks” are explicated within a constructivist evolutionary epistemology. Then, after
discussing our model of mental attention, we present data supporting the fruitfulness of our approach. We begin with fundamental measurement, because this concept must be clear to see how our psychological approach can help to solve the working-memory measurement problem. Fundamental measurement (Suppes & Zinnes, 1963) uses a formal (often numerical) relational system to represent an empirical relational system. Such a representation is made possible by “the assignment of numbers to objects in such a way that the observed relations among objects are refl ected by the corresponding relations among the numbers assigned to them” (Coombs et al., 1970, p. 29). Thus objects from an empirical relational system, and stable functional relations amongst them, are mapped onto objects – often numbers – and relations of a formal relational system. When the direction of mapping can be reversed, that is, formal and empirical structures can represent/map each other, the mapping generated is an isomorphism. Notice that in fundamental measurement both the formal and empirical systems result from theory-guided rational choices or modeling: The characterization of the fi eld of study as an empirical relational system results from a constructive abstraction process in which “raw data of our experience are classifi ed and structured as objects and relations” (Coombs et al., 1970, p. 11). When both the empirical mapped structure and the formal-mapping structure are suitably confi gured by the researcher, one can defi ne fundamental measurement as an isomorphic mapping (Narens, 1985). Classic physical measurement generally is fundamental and extensive, in the sense that it is based on semantic-pragmatic procedures analogous to the arithmetical operation of addition: an empirical concatenation operation, that is, counting the reiteration of suitable displacements of a unit (such as a centimeter) over the length to be estimated, or the juxtaposition of objects in a balance, or the displacement of mercury over the thermometer’s metric scale. When such a concatenation operation is impossible, specialists talk instead of intensive measurement. Examples of intensive properties are heat, or degree of attention, or most other psychological qualitative variables. It is now well recognized that one does not need to have extensive measurement to produce interval scales (i.e., scales of measurement in which not only the values, but the intervals between values can be meaningfully compared and treated as invariant). The Coombs et al. (1970) quote in the epigraph emphasizes that theory is important for fundamental measurement. Furthermore, measurement of psychological organismic variables is particularly in need of theory, because organismic processes, being hidden, must be “invented” before they can be “discovered” and described via empirical experimentation and measurement (Pascual-Leone & Sparkman, 1980). In this sense we should talk of three facets of measurement, and not just two: The formal model and the empirical model, which respectively produce the measurement’s formal relational system and empirical relational system, and also the organismic or general theory, which informs and justifi es the procedure for measurement and the formal and empirical models. Also necessary is an explicit method of task analysis (based
on the general theory) that can coordinate formal and empirical models with the actual procedures of successful measurement. Crucial to fundamental measurement is the aptitude of the chosen formal relational system to epistemologically refl ect (or mirror in its functional structure) the functional structure in the empirical domain. Such epistemological refl ection emerges as functional invariant in the context of praxis (Gibson, 1979; Reuchlin, 1962; Ullmo, 1967) – and, when well defi ned, is an isomorphism. Consider an example in a simple perceptual domain: Imagine different human or animal faces and faces made with geometric shapes that replace eyes, nose, mouth, head. The term “face” is applied to all of them, because a similar relational pattern emerges under exploration, which the visual scanpaths basically preserve in each, as the gaze goes from one “face” feature to the other: This is the (functionally) invariant relational pattern of “a face.” We commonly express this idea by saying that each drawing refl ects the structure of a face. This purely perceptual functional invariant relates to the similar semantic-pragmatic interpretations (or perceptual cognition) that each drawing elicits, which justifi es the claim that symbols of a face embody an isomorphism between two systems, one more perceptual and the other more cognitive. The fi rst epistemological thesis of this chapter is that, if a suitable organismic theory and method of task analysis are available, it is possible to do fundamental measurement of a “hidden” organismic resource, which often is called endogenous effortful attention, that is responsible for developmental differences in problem-solving ability. This sort of attention has been called alternatively voluntary attention, focus of attention, executive attention, and (biogenetic component of ) working memory. We call it mental attention, and we contrast it with spontaneous attention (an effortless, often exogenous, perceptual or imaginal sort of attention that also occurs in mind wandering; Berger, Henik, & Rafal, 2005; Christoff, Gordon, Smallwood, Smith, & Schooler, 2009; Hopfi nger & West, 2006; Posner & Peterson, 1990). Mental attention grows with and regulates cognitive development. As a construct it may underpin what Binet (1910; Binet & Simon, 1905/2004) considered the root of developmental intelligence and judgement (Pascual-Leone & Johnson, 2005); what Spearman (1927) regarded as the organismic foundation of his g factor (Pascual-Leone & Goodman, 1979; Pascual-Leone & Johnson, 2005); what Piaget called operativity (e.g., centration and decentration of refl ective attention – his mental “fi eld of equilibrium”); and what James (1892/1961) called voluntary attention that monitors the stream of thought. Attention is an intensive, purely qualitative resource of humans and other mammals. We have long had the intuition (Pascual-Leone, 1970) that mental attention could be measured by the size of a set: the set of distinct schemes (semantic-pragmatic processes) that a person can endogenously activate and coordinate together to synthesize a distinct mental state (or a percept) as integrated totality. Indeed, mental attention (like William James’ [1892/1961] voluntary attention; or Husserl’s [1948/1973] intentional syntheses of
consciousness) appears to subjective experience as if it were a limited resource, which can only encompass, and simultaneously boost with activation, a small set of separate representational and operative schemes (relevant separate pieces of information). Restle (1959) proposed a metric for set-theoretical measures. In our case, however, because we propose a set-theoretical measure for mental attention, and units of information (i.e., schemes) are in the mind of the beholder, we must fi rst make available a method of metasubjective – mental if you will – task analysis, to demarcate task-relevant schemes needed for the acts of mental attention. In what follows we present a brief summary of the organismic general model informing our task analysis method. Then, to clarify the important concept of misleading situations, we give several examples of tasks measuring mental attention (M-tasks), outlining their task analyses and illustrating with some data. We discuss measurement of mental attention as a new form of additive conjoint measurement (Coombs et al., 1970) and illustrate the invariance of our M-measurement results across types of tasks as well as across age-group samples.
