The Heisenberg-Gabor uncertainty principle defines the limits of information resolution in both time and frequency domains. The limit of resolution discloses unique properties of a time series by frequency decomposition. However, classical methods such as Fourier analysis are limited by spectral leakage, particularly in longitudinal data with shifting periodicity or unequal intervals. Wavelet transformation provides a workable compromise by decomposing the signal in both time and frequency through translation and scaling of a basis function followed by correlation or convolution with (...) the original signal. This study aimed to compare the accuracy of predictive models in mental arithmetic in time and frequency domains. Analysis of the author's response time at mental arithmetic using a soroban was modeled for two periods, an initial period, and a return period both separated by an interval of 370 days. The median response times in seconds was longer for all tasks during the TI compared to the TR period, for addition [CTAdd 62 vs 50 s] and summation [CTSum 68 vs 57 s]. Response times were longer for errors regardless of the study period or task. There was an increasing phase difference for the addition and summation tasks during the TI period toward the end of the series 49.65o compared to the TR period where the phase difference between the two tasks was only 2.05o, indicating that both tasks are likely demonstrating similar learning rates during the latter study period. A comparison between time and time/frequency domain forecasts for an additional 100 tasks demonstrated higher accuracy of the maximum overlap discrete wavelet transform model, where the mean absolute percentage error ranged between 5.48 and 8.19% and that for the time domain models [autoregressive integrated moving average, generalized autoregressive conditional heteroscedasticity ] was 6.16–10.80%. (shrink)

The study of everyday numeric thinking in adults directs our attention to several aspects of number cognition that have received almost no attention in the experimental cognitive science literature, namely the influences of socially situated artifact use on numeric processing. The current studies explore numeral recognition and conceptualisation processes in business people who engage in different types of numeracy practices; orally based numeracy practices which involve very little use of written records compared to paper-based numeracy practices. Ethnographic observations of Lebanese (...) business people were conducted to gain a detailed understanding of the socio-cognitive demands in orally-based paperless and paper-based business settings. These observations were in turn used to design experimental reaction time studies which investigated currency based numeral recognition and conceptualisation processes. The results of the numeral recognition and priming studies clearly illustrate that the use of artifacts in everyday numeracy practices influences numeral recognition and conceptualisation in a way that suggests tight linkages between the visio-spatial processes involve in recognizing numerals embedded in cultural artifacts and the semantically based processes involved in the conception of these numerals. The relevance of the current findings for the main models of adult numeric cognition and for research on everyday numeracy will be discussed. (shrink)

Previous accounts of how people develop expertise have focused on how deliberate practice transforms the cognitive and perceptual representations and processes that give rise to expertise. However, the likelihood of developing expertise with a particular tool may also depend on the degree to which that tool fits pre‐existing perceptual and cognitive abilities. The present studies explored whether the abacus—a descendent of the first human computing devices—may have evolved to exploit general biases in human visual attention, or whether developing expertise with (...) the abacus requires learning special strategies for allocating visual attention to the abacus. To address this question, we administered a series of visual search tasks to abacus experts and subjects who had little to no abacus experience, in which search targets and distractors were overlaid atop abacus “beads.” Across three studies, we found that both experts and naïve subjects were faster to detect targets in semantically relevant components of the abacus, suggesting that abacus training is not required to exhibit attentional biases toward these components of the abacus. This finding suggests that the attentional biases that scaffold numerical processing of the abacus may emerge from general properties of visual attention that are exploited by the design of the abacus itself. (shrink)

Do AI programs just make it quicker and easier for humans to do what they can do already, or can the range of do-able things be extended? This paper suggests that cognitively-oriented technology can make it possible for humans to construct and carry out mental operations, which were previously impossible. Probable constraints upon possible human mental operations are identified and the impact of cognitive technology upon them is evaluated. It is argued that information technology functions as a cognitive prosthetic enhancing (...) human intelligence and planning capabilities. Boundaries and constraints which Kant, Whorf, and many post-modernist theorists have seen as intrinsic to human cognition now cease to apply. (shrink)

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based learning—particularly how actions generate new internal structures that support problem-solving—are not understood. We develop a model of the way manipulations generate internal traces embedding actions, and how these action-traces recombine during problem-solving. This model (...) is based on a study of two groups of sixth-grade students solving area problems. Before problem-solving, one group manipulated a tangram, the other group answered a descriptive test. Eye-movement trajectories during problem-solving were different between the groups. A second study showed that this difference required the tangram's geometrical structure, just manipulation was not enough. We propose a theoretical model accounting for these results, and discuss its implications. (shrink)