Timothy C. Rickard

The calculating brain: an fMRI study

To explore brain areas involved in basic numerical computation, functional magnetic imaging (fMRI) scanning was performed on college students during performance of three tasks; simple arithmetic, numerical magnitude judgment, and a perceptual-motor control task. For the arithmetic relative to the other tasks, results for all eight subjects revealed bilateral activation in Brodmanns area 44, in dorsolateral prefrontal cortex (areas 9 and 10), in inferior and superior parietal areas, and in lingual and fusiform gyri. Activation was stronger on the left for all subjects, but only at Brodmanns area 44 and the parietal cortices. No activation was observed in the arithmetic task in several other areas previously implicated for arithmetic, including the angular and supramarginal gyri and the basal ganglia. In fact, angular and supramarginal gyri were significantly deactivated by the verification task relative to both the magnitude judgment and control tasks for every subject. Areas activated by the magnitude task relative to the control were more variable, but in five subjects included bilateral inferior parietal cortex. These results confirm some existing hypotheses regarding the neural basis of numerical processes, invite revision of others, and suggest productive lines for future investigation.

Sleep does not enhance motor sequence learning.

Improvements in motor sequence performance have been observed after a delay involving sleep. This finding has been taken as evidence for an active sleep consolidation process that enhances subsequent performance. In a review of this literature, however, the authors observed 4 aspects of data analyses and experimental design that could lead to improved performance on the test in the absence of any sleep consolidation: (a) masking of learning effects in the averaged data, (b) masking of reactive inhibition effects in the averaged training data, (c) time-of-day and time-since-sleep confounds, and (d) a gradual buildup of fatigue over the course of massed (i.e., concentrated) training. In 2 experiments the authors show that when these factors are controlled for, or when their effects are substantially reduced, the sleep enhancement effect is eliminated. Whereas sleep may play a role in protection from forgetting of motor skills, it does not result in performance enhancement.

On the cognitive structure of basic arithmetic skills: Operation, order, and symbol transfer effects.

In 2 experiments, college Ss practiced extensively on single-digit multiplication and division problems (e.g., = 6 × 9; 42 = × 6) and were tested on both practice problems and several altered versions of those problems, which were constructed by changing the required operation, operand order, or arithmetic symbol. There was strong positive transfer to test problems that had exactly the same elements (the numbers and the required operation) as a practice problem, regardless of whether other factors such as operand order or symbol were changed, but little if any positive transfer to test problems that did not have the same elements as a practice problem. An identical elements framework is used to interpret these results and implications for existing computational models of arithmetic fact retrieval and for the development of arithmetic skill are discussed

Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty

Recent behavioral investigations indicate that the processes underlying mental arithmetic change systematically with practice from deliberate, conscious calculation to automatic, direct retrieval of answers from memory [Bourne, L.E.Jr. and Rickard, T.C., Mental calculation: The development of a cognitive skill, Paper presented at the Interamerican Congress of Psychology, San Jose, Costa Rica, 1991: Psychol. Rev., 95 (1988) 492-527]. Results reviewed by Moscovitch and Winocur [In: The handbook of aging and cognition, Erlbaum, Hillsdale, NJ, 1992, pp. 315-372] suggest that consciously controlled processes are more dependent on frontal lobe function than are automatic processes. It is appropriate, therefore to determine whether transitions in the locus of primary brain activity occur with practice on mental calculation. In this experiment, we examine the relationship between characteristics of event-related brain potentials (ERPs) and mental arithmetic. Single-digit mental multiplication problems varying in difficulty (problem size) were used, and subjects were trained on these problems for four sessions. Problem-size and practice effects were reliably found in behavioral measures (RT). The ERP was characterized by a pronounced late positivity after task presentation followed by a slow wave, and a negativity during response indication. These components responded differentially to the practice and problem-size manipulations. Practice mainly affected topography of the amplitude of positivity and offset latency of slow wave, and problem-size mainly offset latency of slow wave and pre-response negativity. Fronto-central positivity diminished from session to session, and the focus of positivity centered finally at centro-parietal regions.(ABSTRACT TRUNCATED AT 250 WORDS)

Some tests of an identical elements model of basic arithmetic skills.

: Two experiments tested an identical elements model of the organization of basic arithmetic skills (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994). This model assumes a distinct abstract representation for each unique combination of the basic elements (i.e., the operands and the required operation) of a problem. Participants practiced multiplication and division problems and were then tested on various altered versions of these problems. Experiment 1 confirmed the prediction of no positive transfer when the presented elements of a test problem do not exactly match those of a practice problem. Experiment 2 confirmed the prediction that there is complete transfer when the elements of the test problem match exactly with those of a practice problem. Experiment 2 also confirmed that there is both perceptually specific and nonspecific speed-up with practice. Implications for number processing and arithmetic are discussed.

Strategy execution in cognitive skill learning: An item-level test of candidate models

This article investigates the transition to memory-based performance that commonly occurs with practice on tasks that initially require use of a multistep algorithm. In an alphabet arithmetic task, item response times exhibited pronounced step-function decreases after moderate practice that were uniquely predicted by T. C. Rickards (1997) component power laws model. The results challenge parallel strategy execution models as developed to date and they demonstrate that the shift to retrieval is an item-specific, as opposed to task-general, learning phenomenon. The results also call into question the entire class of smooth speed-up functions as global empirical learning laws. It is shown that overlaying of averaged item fits on averaged data can provide a sensitive test for model sufficiency. Strategy probes agreed with strategy inferences that were based on step-function speed-up patterns, supporting the validity of the probing technique.

A revised identical elements model of arithmetic fact representation

The identical elements model of arithmetic fact representation (T. C. Rickard, A. F. Healy, & L. E. Bourne, 1994) states that, for each triplet of numbers (e.g., 4, 7, 28) that are related by complementary multiplication and division problems, there are 3 independent fact representations in memory: (4, 7, x) --> 28; (28/7) --> 4; and (28/4) --> 7. In this article, the author reviews the evidence for this model, considers alternative accounts, and proposes a simple and empirically motivated revision to the model that (a) accommodates conflicting results, (b) provides a novel account of the ties effect, and (c) makes new and nonintuitive predictions for the factoring operation (e.g., factoring of 28 into 4 and 7). The author reports 3 experiments designed to test these predictions and discusses implications for arithmetic instruction.

Losing Their Configural Mind: Amnesic Patients Fail on Transverse Patterning

A configural theory of human amnesia is proposed. The theory predicts that amnesic patients will exhibit selective deficits on tasks that normal subjects perform by learning new configurations of stimulus elements. This prediction is supported by results for four amnesic patients who learned a nonconfigural control task but failed to learn the configural transverse patterning task even after extensive practice. Matched normal subjects easily learned both tasks. The theory provides unique and viable accounts of the central results in the human amnesia literature. Relations between the configural approach and other theories are discussed.

Sleep and Motor Learning: Is There Room for Consolidation?

It is widely believed that sleep is critical to the consolidation of learning and memory. In some skill domains, performance has been shown to improve by 20% or more following sleep, suggesting that sleep enhances learning. However, recent work suggests that those performance gains may be driven by several factors that are unrelated to sleep consolidation, inviting a reconsideration of sleeps theoretical role in the consolidation of procedural memories. Here we report the first comprehensive investigation of that possibility for the case of motor sequence learning. Quantitative meta-analyses involving 34 articles, 88 experimental groups and 1,296 subjects confirmed the empirical pattern of a large performance gain following sleep and a significantly smaller gain following wakefulness. However, the results also confirm strong moderating effects of 4 previously hypothesized variables: averaging in the calculation of prepost gain scores, build-up of reactive inhibition over training, time of testing, and training duration, along with 1 supplemental variable, elderly status. With those variables accounted for, there was no evidence that sleep enhances learning. Thus, the literature speaks against, rather than for, the enhancement hypothesis. Overall there was relatively better performance after sleep than after wakefulness, suggesting that sleep may stabilize memory. That effect, however, was not consistent across different experimental designs. We conclude that sleep does not enhance motor learning and that the role of sleep in the stabilization of memory cannot be conclusively determined based on the literature to date. We discuss challenges and opportunities for the field, make recommendations for improved experimental design, and suggest approaches to data analysis that eliminate confounds due to averaging over online learning. (PsycINFO Database Record

Transverse Patterning and Human Amnesia

The transverse patterning (TP) task (A B, B C, C A) has played a central role in testing the hypothesis that medial-temporal (and, in particular, hippocampal) brain damage selectively impairs learning on at least some classes of configural (i.e., nonlinear) learning tasks. Results in the animal and human literature generally support that hypothesis. Reed and Squire [Impaired transverse patterning in human amnesia is a special case of impaired memory for two-choice discrimination tasks. Behavioral Neuroscience, 113, 39, 1999], however, advanced an alternative account in which impaired TP performance in amnesia reflects a generic scaling artifact arising from the greater difficulty of the TP task compared to the elemental (i.e., linear) control task that is typically used. We begin with a critique of Reed and Squire, countering their conceptual arguments and showing that their results, when analyzed appropriately, support the configural deficit hypothesis. We then report results from eight new amnesic patients and controls on an improved version of the TP task. Despite substantial practice, accuracy of patients with bilateral hippocampal damage due to anoxia reached and maintained an asymptote of only 54% correct, well below the maximum accuracy obtainable (67%) in the absence of configural learning. A patient with selective bilateral damage to the anterior thalamic nuclei exhibited a TP accuracy asymptote that was near 67%, a pattern of two out of three correct consecutive trials, and a pattern of nearly always answering correctly for two of the three TP item pairs. These results are consistent with a set of unique and parameter-free predictions of the configural deficit hypothesis.