The role of understanding in solving word problems

Word problems are notoriously difficult to solve. We suggest that much of the difficulty children experience with word problems can be attributed to difficulty in comprehending abstract or ambiguous language. We tested this hypothesis by (1) requiring children to recall problems either before or after solving them, (2) requiring them to generate final questions to incomplete word problems, and (3) modeling performance patterns using a computer simulation. Solution performance was found to be systematically related to recall and question generation performance. Correct solutions were associated with accurate recall of the problem structure and with appropriate question generation. Solution “errors” were found to be correct solutions to miscomprehended problems. Word problems that contained abstract or ambiguous language tended to be miscomprehended more often than those using simpler language, and there was a great deal of systematicity in the way these problems were miscomprehended. Solution error patterns were successfully simulated by manipulating a computer model's language comprehension strategies, as opposed to its knowledge of logical set relations.     

Industrial and Organizational Psychology Programme at the University of Colorado at Denver

This article describes the Industrial and Organizational Psychology Programme at the University of Colorado at Denver (CU-Denver). First, we provide an overview of the programme's most salient characteristics and objectives. Next, we summarize five ongoing research programmes being conducted at CU-Denver: (a) Social Power and Influence in Organizations, (b) Personnel Selection, (c) Applied Research Methods, (d) Training Evaluation, and (e) Cognitive Assessment. For each research programme we describe (a) primary questions addressed, (b) selective recent findings, and (c) current projects and future directions. Finally, we describe the role and current activities of the Centre for Applied Psychology     

Alcohol First Use and Attitudes Among Young Children

We describe the attitudes and first use of alcohol by children, grades 3-6, who participated in the Bogalusa Heart Study, 1993-94. Questionnaire data reflected that more than one-third of the children had experimented with alcohol at the time of the study. The dominant environmental factor in experimentation was family modeling, and the dominant personal factor was curiosity, regardless of race, gender, or grade. Most children believed that alcohol use can lead to accidents, that drinking has negative social consequences, and that alcohol use hurts only if done to excess. Indications are that young children generally have negative attitudes regarding alcohol use, and that public and family alcohol education efforts need to be more specific about deleterious effects of even low levels of alcohol use in the young.     

Inside the Black Box, with apologies to Pandora. A review of Ulric Neisser's Cognitive Psychology

It behooves us, as good citizens of the science of psychology, to shirk no area of psychology as long as we can apply scientific method to it. The research in cognitive psychology is certainly interesting, on the whole well executed, and very challenging. It is well within the scope of a behavioristic approach. It merely awaits more attention from behaviorists.     

Positive und negative Rückmeldung bei Alternativdiskriminationen

Zusammenfassung Die Untersuchungen befassen sich mit dem Einfluß der verbalen Rückmeldungen richtig und falsch auf das Erlernen von Alternativdiskriminationen in Blank-trial-Experimenten. Dabei wird insbesondere die Wechselwirkung der Rückmeldungskombinationen (richtig/fehlende Rückmeldung vs. falsch/fehlende Rückmeldung) mit der Rückmeldungsproportion untersucht. Die Rückmeldungsproportion ist definiert als das Verhältnis der Anzahl der S-R-Verbindungen einer Lernliste, auf die eine verbale Rückmeldung erfolgt, und der Anzahl der S-R-Verbindungen, bei denen die verbale Rückmeldung fehlt. Die Rückmeldungsproportion wird zwischen 119 und 191 systematisch variiert. Unsere Experimente ergeben u. a., daß bei kleiner Rückmeldungsproportion die Kombination richtig/fehlende Rückmeldung und bei großer Rückmeldungsproportion die Kombination falsch/fehlende Rückmeldung die Lernleistung erhöhen. Dieser Befund wurde nach theoretischen Annahmen über die Lernstrategie der Vpn erwartet. Eine alternative theoretische Interpretation der Befunde wird nach einem Zusatzexperiment verworfen. Insgesamt bestätigen die Untersuchungen, daß (a) die relative Wirksamkeit von Rückmeldungskombinationen stark von den jeweiligen experimentellen Randbedingungen abhängt, daß (b) von einer automatischen Wirksamkeit verbaler Rückmeldung keine Rede sein kann und daß (c) theoretische Annahmen über die kognitive Verarbeitung verbaler Rückmeldungen und über entsprechende Lernstrategien für die Interpretation der untersuchten Lernvorgänge erfolgversprechend sind.

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Positive and negative feedback in discrimination between alternativesFeedback proportion and learning strategy

Summary This study is concerned with the influence of the verbal feedback modes of right and wrong on the acquisition of alternative discriminations in blank-trial experiments, with special reference to the interaction between the feedback combinations (right/non-feedback as against wrong/non-feedback) and feedback proportion is investigated. Feedback proportion is defined as the ratio of the S-R connections of a learning list succeeded by verbal feedback to the S-R connections succeeded by non-feedback. Feedback proportion was systematically varied between the ratios of 119 and 191.Results showed that at a low feedback proportion learning score is increased with the combination right/non-feedback while in contrast at a high feedback proportion learning score is increased with the combination wrong/non-feedback. These results are in accordance with theoretical expectations on learning strategies of Ss. An alternative interpretation was not confirmed by the results of an additional experiment.In general, our investigations showed that (a) the relative effectiveness of feedback combinations is strongly dependent on the particular experimental conditions; (b) an automatic effect of verbal feedback cannot be assumed; (c) a cognitive interpretation of verbal feedback effects in terms of learning strategies seems very promising.

     

On a hitherto unexploited extension of the finitary standpoint

P. Bernays has pointed out that, in order to prove the consistency of classical number theory, it is necessary to extend Hilbert's finitary standpoint by admitting certain abstract concepts in addition to the combinatorial concepts referring to symbols. The abstract concepts that so far have been used for this purpose are those of the constructive theory of ordinals and those of intuitionistic logic. It is shown that the concept of a computable function of finite simple type over the integers can be used instead, where no other procedures of constructing such functions are necessary except simple recursion by an integral variable and substitution of functions in each other (starting with trivial functions).     

Der Mensch in der Masse

Ohne ZusammenfassungPrivaat docent aan de Gemeente Universiteit van Amsterdam     

Beitrag zu den Grundlagenproblemen in der Wahrscheinlichkeitsrechnung

Zusammenfassung Es wird gezeigt, daß man zwei Gruppen von Erscheinungen unterscheiden muß, solche, bei denen bestimmte Voraussagen unter Angabe gabe des größten Fehlerintervalles Sinn haben, und solche, bei denen bestimmte Voraussagen leer sind. Über die zweite Gruppe von Erscheinungen können jedoch Wahrscheinlichkeitsvoraussagen gemacht werden, das sind solche Aussagen, die nicht exakt, sondern nur praktisch bestätigt oder widerlegt werden können. Am Beispiel des Roulette wird gezeigt, wie man aus einigen Wahrscheinlichkeitsaussagen über die Erscheinungen beim Roulette unter Zugrundelegung von gewissen Rechenvorschriften weitere Wahrscheinlichkeitsaussagen über dieselben Erscheinungen gewinnen kann. Aus der praktischen Bestätigung der abgeleiteten Wahrscheinlichkeitsaussagen ergibt sich die Berechtigung für die Anwendung der gennanten Rechenvorschriften. In Verallgemeinerung der Erscheinungen bei dem Roulette wird die Definition eines Kollektivs in Wahrscheinlichkeitsaussagen gegeben.