Peter E. Langford

A Longitudinal Study of Children's Understanding of Logical Laws in Arithmetic and Boolean Algebra

ABSTRACT Methodological problems involved in testing knowledge of logical laws in arithmetic and Boolean algebra are discussed. A longitudinal study of childrens knowledge of such laws that explores one solution to these methodological difficulties using two scoring criteria is described. Groups of tasks that are mastered in a definite order are identified. Factor analysis of items at their maximum level of variation was undertaken. Theoretical explanations for the results are explored.

A Representational Communication Approach to the Development of Inductive and Deductive Logic

Publisher Summary This chapter is taken up with presentation of some detailed work on deductive reasoning with syllogisms. It is followed by a brief digest of work on inductive reasoning using conditionals and other logical expressions. Approach to the deductive logic of syllogisms arose from a number of sources: the philosophy of mathematics and logic contained in the later writings of Wittgenstein; discontent about the way psychologists have construed the learning of mathematical concepts by mathematics educators, especially Freudenthal. In addition, socialization also influences aspects of representations and their use. The chapter draws a clear distinction between mathematics and logic as conceived by most mathematicians and logicians and performance in the deductive reasoning tasks used to study deductive reasoning by psychologists. The most notable developmental trends in the interpretation of logical expressions during adolescence occur for conditionals. Insofar as adolescents and adults are able to give anything like a correct interpretation of conditionals, this tends to resemble the biconditional interpretation, “X is B if and only if X is A.” One explanation for such conversion relies on discourse presuppositions.

A New Way of Scoring Moral Judgement Interviews

Abstract Two studies of the categorization of justifications for the morality of the actions of others are reported. Justifications were categorized using a scoring scheme not previously reported. Results showed that a reasonable degree of inter‐rater reliability could be achieved and that developmental trends detected were robust with respect both to interviewers and interview content, although interview content had an expected and comprehensible effect on the frequency of items within content categories. Results were interpreted within the context of a model of the development of moral reasoning that emphasizes the influence of the social focus of the interviewee and the process by which individuation occurs towards either a secular or a religious view of morality. The notion that a more differentiated individuation may also occur within each of these categories was explored, as were, shifts from paternalism to autonomous decision‐making in thinking about some areas of social life.

EVALUATION STRATEGIES FOR SOME NONSTANDARD CONDITIONALS DURING ADOLESCENCE

380 adolescents and young adults between the ages of 11 and 29 years participated in three experiments in which they were asked to evaluate both universally quantified nonstandard and standard conditionals using items of information bearing upon them. Subjects found it much easier to avoid a biconditional interpretation with the nonstandard than with the standard conditionals, which throws doubt on the explanation of desire for symmetry of biconditional conversion. It was argued, from data of other studies, that a modified version of the Piagetian view that biconditional conversion occurs as a result of a desire to avoid the complications of dealing with three factors explains most cases of such conversion in adolescence. Results also confirmed that it is more profitable to analyse performance on tasks of this kind using a two-stage model of interpretation and information use previously developed to explain performance with standard universally quantified conditionals than to view such tasks as providing truth-table values. Such an analysis was extended to the nonstandard conditionals studied in the present paper. The origins of the dramatic differences in information-use strategies adopted by adolescents for standard and nonstandard conditionals remain unclear.

Refining A non-Kohlbergian decision-making approach to the production of justifications for moral judgements

This paper reports two studies primarily designed to refine understanding of the influence of interview topic on the proportions of major types of justifications for moral judgements encountered during moral judgement interviews. It was assumed that subjects will tend to report the use of information that supports their decisions when a definite decision is made and will report all kinds of relevant information when they are uncertain what to decide. It was suggested that for situations to which a well-known moral rule applies, when the rule is upheld, the rule will influence such proportions as different rules are valued for different reasons. When such a rule is rejected, the nature of the reason suggested for rejecting the rule will influence such proportions. When subjects are uncertain whether to support or reject a rule, such proportions will be influenced by both the rule and the reason suggesting rejection. These predictions were broadly verified, which was interpreted as supporting the suggested analysis of the influence of these aspects of the interview topic on proportions of major types of justification.

A Non‐Kohlbergian Approach to the Development of Justifications for Moral Judgements

Summary Two studies are reported that used a non‐Kohlbergian approach to categorising justifications for moral judgements by subjects from 7 to 15 and from 7 to 21 years, respectively. The first study showed that some developmental trends suggested by earlier studies for the 12‐21 year period could be replicated, while others in the age range 7‐11 years were established. These are interpreted as supporting a social focus and language use rather than a cognitive limitation view of the growth of moral reasoning. There were also appreciable differences in the balance of justification types elicited by different topics, possibly due to variations in perceived degree of personal control in different situations. The second study showed that Colby & Kohlbergs method of categorising moral justifications confounds form of justification with content and masks underlying developmental trends in justification types. The educational implications of the findings are discussed.

Do Senior Secondary Students Possess the Moral Maturity to Negotiate Class Rules

Abstract Two studies are reported using written question sheets to assess attitudes to and moral reasoning about class rules among a total of 117 senior secondary school students and 87 trainee teachers. The studies confirmed the prediction of the multidimensional control model of the development of moral reasoning of Langford (1991a, b; 1992a, b) that the moral reasoning of such students about this topic is much more mature than predicted by Kohlbergian theory, their most important source of information for making moral decisions in this area being the general welfare of students and teachers. Other detailed predictions of the multidimensional control model were also, in the main, verified. It was found that, although the great majority of senior secondary students thought we ought to have those class rules that are necessary to protect the right of others to learn, there exist a small minority whose main aim is revenge upon schools and teachers and a rather larger minority who are not even prepared to u...

Evaluation of conditional and biconditional hypotheses in information-use tasks during adolescence.

This article describes three studies of the evaluation of conditional and biconditional hypotheses by adolescents and young adults in the age range 11-29 years. Patterns of responding were in accordance with the predictions of the two-stage model of such tasks proposed by Langford (1992). Conditionals and biconditionals gave rise to similar response patterns, suggesting that they are interpreted in similar ways. Conditionals and biconditionals involving changes in variables were more difficult than those involving individual events. The mention of a second possible antecedent to the consequent had little influence on the tendency to convert conditionals to biconditionals. This contradicts the notion that discourse presuppositions are the major source of such conversion. The most plausible alternative explanation is the Piagetian view that individuals seek to avoid the complications of dealing with three factors.

The Assessment of Moral Autonomy within a Multidimensional Approach to the Development of Moral Reasoning

Abstract Four studies are reported using both a questionnaire and an interview focussed on the questionnaire items to assess the development of moral autonomy in a total of 720 respondents from 12 to 21 years of age. The studies were intended to extend the analysis of the development of moral autonomy offered by an existing multidimensional model of the development of moral reasoning. Results showed the need to add a dimension of individual differences to the single dimension currently used to describe autonomy‐related developmental changes in the content of judgements. A further dimension, indexing individual differences in use of justification types was also identified. It was found that justifications for moral judgements were more theoretical than in a Kohlberg‐style interview. A content‐related categorisation of justifications revealed a substantial connection between justification and judgement content.

Arithmetical word problems: Thinking in the head versus thinking on the table

The paper presents an alternative explanation for the pattern of relative difficulty of arithmetical word problems to that suggested by Riley et al. (1983). Their view is based on the assumption that all symbolic manipulations take place internally. It is argued that for many problems much of the manipulation is accomplished externally.