Adults' strategies for simple addition and multiplication: Verbal self-reports and the operand recognition paradigm.

Abstract

Accurate measurement of cognitive strategies is important in diverse areas of psychological research. Strategy self-reports are a common measure, but C. Thevenot, M. Fanget, and M. Fayol (2007) proposed a more objective method to distinguish different strategies in the context of mental arithmetic. In their operand recognition paradigm, speed of recognition memory for problem operands after solving a problem indexes strategy (e.g., direct memory retrieval vs. a procedural strategy). Here, in 2 experiments, operand recognition time was the same following simple addition or multiplication, but, consistent with a wide variety of previous research, strategy reports indicated much greater use of procedures (e.g., counting) for addition than multiplication. Operation, problem size (e.g., 2 + 3 vs. 8 + 9), and operand format (digits vs. words) had interactive effects on reported procedure use that were not reflected in recognition performance. Regression analyses suggested that recognition time was influenced at least as much by the relative difficulty of the preceding problem as by the strategy used. The findings indicate that the operand recognition paradigm is not a reliable substitute for strategy reports and highlight the potential impact of difficulty-related carryover effects in sequential cognitive tasks.

From domain-specific to domain-general? The developmental path of metacognition for strategy selection

“…This plethora of studies indicates that participants' performance and agerelated changes in cognitive performance depend on strategies. Yet, despite extensive research seeking to understand how people choose among strategies on a given item (e.g., Metcalfe, & Campbell, 2011;Thevenot, Fanget, & Fayol, 2007), participants' ability to monitor their chance of selecting the better strategy in the future (i.e., prospective judgment) or to estimate their level of confidence associated with a selected strategy (i.e., retrospective judgment) has been examined neither in the arithmetic domain nor in the memory domain. As four decades of studies -mainly in the memory domain -have established that the influence of metacognitive processes on cognitive performance is exerted through the implementation of effective strategies (e.g., DeMarie, Miller, Ferron, & Cunningham, 2004;Geurten, Lejeune, & Meulemans, 2016;Nelson & Narens, 1990; see Dunlosky & Metcalfe, 2009 for an overview), it is surprising that so little has been done to investigate how accurate participants are in estimating whether they selected (or will select) the most effective strategy on a given item.…”

Time‐resolved and spatio‐temporal analysis of complex cognitive processes and their role in disorders like developmental dyscalculia

“…While key regions like occipital visual areas or the motor area are activated as expected, not many of the regions that code for the various intermediate cognitive subprocesses show a response similar to controls. Because the behavioral results suggest otherwise, with subjects with DD performing the task at par with their peers, we assume that this discrepancy is rooted in the interindividual differences of brain recruitment and in the established (hardwired) individual neuropsychological strategies for arithmetic problem solving (Cho et al,2011; Metcalfe and Campbell,2011). Such spatial incompatibilities between functional maps are not addressable through conventional voxel‐based analysis methods operating in a normalized brain space.…”

Differential recruitment of brain networks in single-digit addition and multiplication: Evidence from EEG oscillations in theta and lower alpha bands

“…Since operands are suggested to be encoded into visuospatial Arabic code in single-digit addition and verbal code in multiplication, it is still A C C E P T E D M A N U S C R I P T 5 unclear whether the recruitment of brain functional network is modulated by arithmetic type during the early encoding stage, related to the control of attention and stimulus encoding. Additionally, some research has suggested that both arithmetic operations are solved by direct retrieval of arithmetic facts Campbell, 2015, 2016), whereas some research has argued that single-digit multiplication depends on direct fact retrieval but single-digit addition is solved by procedural strategies (Fayol and Thevenot, 2012;Metcalfe and Campbell, 2011;Uittenhove et al, 2016). If the latter assumption is valid, greater recruitment of executive function will be observed for single-digit addition, due to the fact that numerical information will be manipulated in effortful procedural manipulation (Geary et al, 1999).…”