Strategy use in mental subtraction determines central executive load

A dual task method was used to examine the relationship between strategy use and working memory load during subtraction problem solving. Undergraduates mentally solved subtraction problems alone and while performing secondary tasks that involved the central executive of working memory. Analyses revealed that a central executive task involving response selection and input monitoring (CRT-R task) interfered more with subtraction problem solving than a task that involved only input monitoring (SRT-R task). Additional analyses showed that the CRT-R task interfered more when participants used a nonretrieval (counting) strategy than a retrieval strategy. These findings suggest that the response selection subcomponent of the central executive is involved during both retrieval-based and non-retrieval-based simple subtraction problem solving but is involved more during the latter.     

Selection of consultees in school mental health consultation

To further understanding regarding the selection of teacher consultees, 15 mental health consultants completed a questionnaire. Consultants ranked teachers in their school consultation placements on ability to meet academic and socioemotional needs of children, receptivity to change, and likability. Next, after indicating which teachers they would most and least like to work with, consultants rated the teachers on nine 5-point rating scales. In general, results indicate that most preferred consultees, in comparison to least preferred consultees, are perceived as less needy of assistance around issues concerning children and lessons, more responsive to consultation, and more likable. It appears that teachers most in need of assistance are not selected for consultation.     

The association between children's numerical magnitude processing and mental multi-digit subtraction

Children apply various strategies to mentally solve multi-digit subtraction problems and the efficient use of some of them may depend more or less on numerical magnitude processing. For example, the indirect addition strategy (solving 72–67 as “how much do I have to add up to 67 to get 72?”), which is particularly efficient when the two given numbers are close to each other, requires to determine the proximity of these two numbers, a process that may depend on numerical magnitude processing. In the present study, children completed a numerical magnitude comparison task and a number line estimation task, both in a symbolic and nonsymbolic format, to measure their numerical magnitude processing. We administered a multi-digit subtraction task, in which half of the items were specifically designed to elicit indirect addition. Partial correlational analyses, controlling for intellectual ability and motor speed, revealed significant associations between numerical magnitude processing and mental multi-digit subtraction. Additional analyses indicated that numerical magnitude processing was particularly important for those items for which the use of indirect addition is expected to be most efficient. Although this association was observed for both symbolic and nonsymbolic tasks, the strongest associations were found for the symbolic format, and they seemed to be more prominent on numerical magnitude comparison than on number line estimation.     

Use of indirect addition in adults' mental subtraction in the number domain up to 1,000

This study examined adults' use of indirect addition and direct subtraction strategies on multi-digit subtractions in the number domain up to 1,000. Seventy students who differed in their level of arithmetic ability solved multi-digit subtractions in one choice and two no-choice conditions. Against the background of recent findings in elementary subtraction, we manipulated the size of the subtrahend compared to the difference and only selected items with large distances between these two integers. Results revealed that adults frequently and efficiently apply indirect addition on multi-digit subtractions, yet adults with higher arithmetic ability performed more efficiently than those with lower arithmetic ability. In both groups, indirect addition was more efficient than direct subtraction both on subtractions with a subtrahend much larger than the difference (e.g., 713 - 695) and on subtractions with a subtrahend much smaller than the difference (e.g., 613 - 67). Unexpectedly, only adults with lower arithmetic ability fitted their strategy choices to their individual strategy performance skills. Results are interpreted in terms of mathematical and cognitive perspectives on strategy efficiency and adaptiveness.     

Adaptive procedures in psychophysical research.

As research on sensation and perception has grown more sophisticated during the last century, new adaptive methodologies have been developed to increase efficiency and reliability of measurement. An experimental procedure is said to be adaptive if the physical characteristics of the stimuli on each trial are determined by the stimuli and responses that occurred in the previous trial or sequence of trials. In this paper, the general development of adaptive procedures is described, and three commonly used methods are reviewed. Typically, a threshold value is measured using these methods, and, in some cases, other characteristics of the psychometric function underlying perceptual performance, such as slope, may be developed. Results of simulations and experiments with human subjects are reviewed to evaluate the utility of these adaptive procedures and the special circumstances under which one might be superior to another.     

Processing speed and mental retardation: Deadline procedures indicate fixed and adjustable limitations

Brewer and Smith (1984) showed that control mechanisms mediating speed-accuracy regulation contribute to retarded-nonretarded differences in processing speed, with poorly controlled trial-to-trial RT adjustments underlying the greater RT variability of retarded individuals. In Experiment 1, response deadlines controlled processing time, thus minimizing the influence of such control mechanisms. The obtained speed-accuracy relations showed that retarded subjects were unable to match nonretarded subjects' accuracy when responding as rapidly, thus indicating structural limitations on processing speed. The results of Experiment 2 showed, however, that significant adjustments to retarded subjects' processing speed--exceeding those produced by practice--are achievable. Extended training at a short deadline led to tighter control of RT adjustments, with substantial improvements in mean RT when subjects transferred to a self-paced RT task.     

Dissemination of effective mental health treatment procedures: Maximizing the return on a significant investment

While much is known about the efficacy of evidence-based practices, it is currently less clear how to implement these practices into the broader mental health system. Dissemination and implementation research will play a critical role in addressing this uncertainty. This commentary reviews the most recent and compelling research related to these topics while advocating a broader and more defined perspective of dissemination for future research. Three of the authors' most pressing questions are proposed and explored.     

Prevalence of severe behavior disorders in persons with mental retardation and treatment procedures used in community and institutional settings

A statewide survey of moderate and severe behavior disorders in persons with mental retardation in institutional and community settings was conducted. Information on the treatment procedures used and the adequacy of available resources in both settings was also gathered. Results indicated that community staff had considerably less experience than institutional staff in dealing with serious behavior disorders exhibited by persons with substantial cognitive and physical impairments. The types of aberrant behaviors with the highest prevalence rates showed differences in the institutions and the community. The largest differences in prevalence rates for severe behavior disorders in the two settings occurred for aggressive and self-injurious behaviors. Community staff thus had appreciably less experience than institutional staff in designing interventions for severe aggressive and self-injurious behaviors. About half of the identified individuals in both settings received psychotropic medications. Institutional staff were most likely to use restrictive behavioral procedures than community staff. Findings indicated that the most restrictive procedures were used primarily with only certain severe behavior disorders. Subjective ratings of the overall effectiveness of interventions were lower by community than institutional staff. The usefulness of the obtained data base for statewide planning in the area of behavioral supports is discussed.     

Developmental differences in mental rotation.

A reaction time paradigm was used to investigate developmental differences in ability to rotate and compare imaginal representations. Third grade, fifth grade, and college students (ages 9, 11, and 20 years, respectively) were required to determine whether a letter of the alphabet was presented in its backward or normal position. Letters were presented at 0, 60, 120, 180, 240, or 300° orientations from upright. Subjects were given no advance information about a test letter, or they were given identity and orientation information. In the no information condition, reaction time increased for all age groups as a function of the departure in orientation of the test letter from an upright position. In the advance information condition, reaction time remained uniform across orientation for only the college subjects. The developmental implications of these findings are discussed.     

Simple mental addition in children with and without mild mental retardation.

The speeded performance on simple mental addition problems of 6- and 7-year-old children with and without mild mental retardation is modeled from a person perspective and an item perspective. On the person side, it was found that a single cognitive dimension spanned the performance differences between the two ability groups. However, a discontinuity, or "jump," was observed in the performance of the normal ability group on the easier items. On the item side, the addition problems were almost perfectly ordered in difficulty according to their problem size. Differences in difficulty were explained by factors related to the difficulty of executing nonretrieval strategies. All findings were interpreted within the framework of Siegler's (e.g., R. S. Siegler & C. Shipley, 1995) model of children's strategy choices in arithmetic. Models from item response theory were used to test the hypotheses.     

An evaluation of in vivo desensitization and video modeling to increase compliance with dental procedures in persons with mental retardation

Fear of dental procedures deters many individuals with mental retardation from accepting dental treatment. This study was conducted to assess the effectiveness of two procedures, in vivo desensitization and video modeling, for increasing compliance with dental procedures in participants with severe or profound mental retardation. Desensitization increased compliance for all 5 participants, whereas video modeling increased compliance for only 1 of 3 participants.     

Strategies in subtraction problem solving in children

The aim of this study was to investigate the strategies used by third graders in solving the 81 elementary subtractions that are the inverses of the one-digit additions with addends from 1 to 9 recently studied by Barrouillet and Lépine. Although the pattern of relationship between individual differences in working memory, on the one hand, and strategy choices and response times, on the other, was the same in both operations, subtraction and addition differed in two important ways. First, the strategy of direct retrieval was less frequent in subtraction than in addition and was even less frequent in subtraction solving than the recourse to the corresponding additive fact. Second, contrary to addition, the retrieval of subtractive answers is confined to some peculiar problems involving 1 as the subtrahend or the remainder. The implications of these findings for developmental theories of mental arithmetic are discussed.     

Verification of Donders' subtraction method

In an experiment on 6 young adults advance (precued) information of the correct choice response was utilized completely: (a) For precue-to-stimulus intervals (PSIs) clearly shorter than the difference between mean choice and simple reaction time (RT), median response latency (L) measured from precue onset was invariant; (b) For clearly longer PSIs, median RT was very near the value for simple RT. This precue-utilization effect would be expected if response actualization had been delayed until the response had been selected and if the requirement for discrimination and selection had no adverse effect on readiness to respond. Donders' (1868/1969) hypothesis in his initial application of the subtraction method, that choice and simple reactions are identical except for the serial insertion of discrimination and selection operations in the former, is thereby strongly supported. If this formulation is accepted, models that hold that response processing can overlap other processing stages may be considered valid only for response selection, not response actualization.     

Comparison of simultaneous prompting and constant time delay procedures in teaching sight words to elementary students with moderate mental retardation

Simultaneous prompting (a type of antecedent prompt and test procedure) and constant time delay were compared with four students with moderate mental retardation learning expressive sight words. A parallel treatments design across word sets and replicated across students was used. For acquisition, the simultaneous prompting procedures required fewer trials, sessions, and training time to criterion and resulted in fewer student errors during daily probe and training sessions. However, maintenance data indicated mixed results across the two procedures. Reliability data (both dependent and independent variables) revealed no differences between the two procedures in terms of the teacher's accuracy in recording student responses and implementing each procedure. Future research issues are discussed.     

Stimulus discriminability in free-operant and discrete-trial detection procedures.

Six pigeons were trained to discriminate different light intensities in four experimental procedures. Experiment 1 compared stimulus discriminability in a yes-no signal-detection task with discriminability measures obtained from two free-operant procedures. Discriminability estimates were significantly lower in the detection procedure. Experiment 2 showed this lowered discriminability to be a function of the delay between stimulus presentation and the availability of the choice-response keys in the standard detection task. In addition, reinforcement sensitivity was lowest when correct choice responses were intermittently, rather than continuously, reinforced.     

Concept-procedure interactions in children's addition and subtraction

A 3-week problem-solving practice phase was used to investigate concept-procedure interactions in children’s addition and subtraction. A total of 72 7- and 8-year-olds completed a pretest and posttest in which their accuracy and procedures on randomly ordered problems were recorded along with their reports of using concept-based relations in problem solving and their conceptual explanations. The results revealed that conceptual sequencing of practice problems enhances children’s ability to extend their procedural learning to new unpracticed problems. They also showed that well-structured procedural practice leads to improvement in children’s ability to verbalize key concepts. Moreover, children’s conceptual advances were predicted by their initial procedural skills. These results support an iterative account of the development of basic concepts and key skills in children’s addition and subtraction.     

Errors in children's subtraction

Many of the errors that occur in children' subtraction are due to the use of incorrect strategies rather than to the incorrect recall of number facts. A production system is presented for performing written subtraction which is consistent with an earlier analysis of the nature of such a cognitive skill. Most of the incorrect strategies used by schoolchildren can be accounted for in a principled way by simple changes in the production system, such as the omission of individual rules or the inclusion of rules appropriate to other arithmetical tasks. The production system model is evaluated against a corpus of over 1500 subtraction problems done by 10-year olds and is shown to account for about two-thirds of the (nonnumber fact) errors. It also provides an alternative, simpler interpretation of the subtraction errors analysed by Brown and Burton (1978). Some implications for teaching are discussed.