Academic journal article Canadian Journal of Experimental Psychology

Numerical Cognition: Adding It Up

Academic journal article Canadian Journal of Experimental Psychology

Numerical Cognition: Adding It Up

Article excerpt

When Jamie Campbell invited me to present at the Banff Annual Seminar in Cognitive Science, it occurred to me that my experience in this field over the last 30 years could provide an interesting framework for this conference. Also, I assumed that many members of the audience would not be familiar with the field of numerical cognition. Accordingly, I provide a historical perspective, starting with the advent of "cognitive science," and then focusing on the development of research on numerical cognition from the late 1960s on.

The Cognitive Revolution

George Miller, writing in 2003 about events in the late 1950s, attributed the cognitive revolution to the failure of the principles and assumptions of behaviourism to explain findings in experimental psychology (Miller, 2003). In 1956, Miller published an article about the "special number 7" (plus or minus 2), in which he explored the idea that memory is limited in capacity (Miller, 1956). In the same year, Jerome Bruner, Jacqueline Goodnow, and George Austin published "A Study of Thinking" (Bruner, Goodnow, & Austin, 1956), which allowed problem solving as a mental activity to be a topic of study, and Noam Chomsky (1957) published a monograph on syntactic structures, which informs modern research on numerical representations. Miller (2003) claimed that these researchers "brought the mind back into experimental psychology" (p. 142).

Nevertheless, it took over 20 years for the domination of behaviourism in experimental psychology to be replaced by the study of cognition. Coincident with the birth of cognitive science, in 1957, the preeminent behaviourist B. F. Skinner published an influential book titled Verbal Behaviour (Skinner, 1957). The Journal of Verbal Learning and Verbal Behaviour published its first issue in 1962, and was only renamed the Journal of Memory and Language in 1984. Similarly, the birth and rise of "numerical cognition" caused researchers to move away from interpreting mental activities as "verbal behaviour." Instead, they focused on developing descriptions of cognitive processes that included memory, attention, language, and problem solving.

My own experiences in psychology started at the University of Alberta in 1979, just as the cognitive revolution was taking a firm hold in Western Canada. Several young psychologists who were trained in the new "information processing" approach were hired in a short period of time (e.g., Jeffrey Bisanz, Gay Bisanz, Peter Dixon, Alinda Friedman), and the first courses in "cognitive psychology" were offered at the graduate and undergraduate levels. Verbal learning was not yet consigned to history, as Willy Runquist still stomped the halls at the University of Alberta, and graduate students struggled through the mandatory course on learning (which seemed to be mainly about pigeons) with Don Heth, but it was clearly on the way out.

Numerical cognition is inherently a mental activity, with even overt behavioural evidence of number processing (e.g., verbal counting, finger counting) relying on a complex network of rules and concepts. The study of numerical cognition needed the cognitive revolution to gain a foothold in experimental psychology and eventually develop into a distinct field. Nevertheless, the field is still evolving. It was not until 2014 that researchers could choose the keyword numerical cognition for their presentations at the annual conference of the Psychonomic Society (known as Psychonomics). The journal Mathematical Cognition was published from 1995 to 1999, but failed to receive sufficient submissions. The online journal Numerical Cognition started accepting submissions in January of 2015, and given the growth of this field since 2000, I believe it will thrive. My personal analysis of the routes that researchers took toward the modern field of numerical cognition identified six main areas that have exerted an influence on the development of the field: (a) psychophysics; (b) information processing; (c) neuropsychology and, subsequently, cognitive neuroscience; (d) mathematics education; (e) psychometrics, specifically research on individual differences in cognitive abilities; and (f) cognitive development. …

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