A chronometric analysis of simple addition.
ABSTRACT Considers a number of models that specify how children and adults solve single-digit addition problems. It is shown that the most adequate of these for children's response latencies is a model that assumes the existence of a counter with 2 operations: setting and incrementing. The child adds 2 digits, m and n, by setting this counter to max (m,n) and then incrementing it min (m,n) times. This model also accounts for adults' latencies, though with a drastically reduced incrementing time. Some theoretical issues raised by this reduced time are considered, and an alternative model is suggested which assumes that adults usually use a memory look-up process with homogeneous retrieval times, but occasionally revert back to the counting process used by children. (2l ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
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ABSTRACT: A model of scanning based on separate sensory and short-term stores was suggested and tested. The experiment used a probe recognition method, with set size varied from 1 to 8 and a fast presentation rate. A masking procedure was used to vary the number of items available in a possible sensory store. Although conditions were such as to maximize the chances of detecting an effect, none was found: the possible size of the sensory store had no effect on reaction time whatsoever. Other aspects of the data lent little support to a serial exhaustive scanning model, but a previously proposed parallel processing model fared better. Finally, not only was the function for positive probes steeper than that for negative probes but also there was a crossover effect as well. This crossover is not without precedent and may indicate the need for consideration of both accuracy and latency in high-speed scanning studies.Memory & Cognition 01/1974; 2(1):27-33. · 1.92 Impact Factor
Article: Learning numerical progressions.[Show abstract] [Hide abstract]
ABSTRACT: Learning of simple numerical progressions and compound progressions formed by combining two or three simple progressions is investigated. In two experiments, time to solution was greater for compound vs simple progressions; greater the higher the progression's solution level; and greater if the progression consisted of large vs small numbers. A set of strategies is proposed to account for progression learning based on the assumption S computes differences between integers, differences between differences, etc., in a hierarchical fashion. Two measures of progression difficulty, each a summary of the strategies, are proposed; C1 is a count of the number of differences needed to solve a progression; C2 is the same count with higher level differences given more weight. The measures accurately predict in both experiments the mean time to solve 16 different progressions with C2 being somewhat superior. The measures also predict the learning difficulty of 10 other progressions reported by Bjork (1968).Memory & Cognition 01/1974; 2(1):121-126. · 1.92 Impact Factor
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ABSTRACT: A number of previous studies have interpreted differences in brain activation between arithmetic operation types (e.g. addition and multiplication) as evidence in favor of distinct cortical representations, processes or neural systems. It is still not clear how differences in general task complexity contribute to these neural differences. Here, we used a mental arithmetic paradigm to disentangle brain areas related to general problem solving from those involved in operation type specific processes (addition versus multiplication). We orthogonally varied operation type and complexity. Importantly, complexity was defined not only based on surface criteria (for example number size), but also on the basis of individual participants' strategy ratings, which were validated in a detailed behavioral analysis. We replicated previously reported operation type effects in our analyses based on surface criteria. However, these effects vanished when controlling for individual strategies. Instead, procedural strategies contrasted with memory retrieval reliably activated fronto-parietal and motor regions, whilst retrieval strategies activated parietal cortices. This challenges views that operations types rely on partially different neural systems, and suggests that previously reported differences between operation types may have emerged due to invalid measures of complexity. We conclude that mental arithmetic is a powerful paradigm to study brain networks of abstract problem solving, as long as individual participants' strategies are taken into account.NeuroImage 02/2014; · 6.25 Impact Factor