Convergence of Sequences and Series 2: Interactions Between Nonvisual Reasoning and the Learner’s Beliefs about their own Role

This paper examines the work of students who, when reasoning about real analysis, do so almost exclusively by means of verbal and algebraic reasoning, and tend not to incorporate visual images into their work. It examines the work of students from two parallel courses of introductory real analysis, whose reasoning ranges from those who introduce definitions appropriately and work with them competently, to those who cannot recall definitions and appear to manipulate notation without regard for its reference. It presents a theory that relates the differences to students expectations regarding their role as learners of mathematics. Throughout, the argument is illustrated with interview data from which the theory was inductively generated.     

Cognitive Empathy and the Transition to Independent Graduate Study in Mathematics

Thirteen Ph.D. students took part in interviews focussed on the nature of their own learning of mathematics. In analysing these interviews an unexpected category emerged concerning the students awareness of others as having particular types of learning goal. In this paper we explore the three levels which we discerned within this category and link them to the notion of cognitive empathy. We suggest that differences in ones own cognitive style are linked to differences in the ability to empathise with those who have alternative learning goals. We also consider how these two features – cognitive style and cognitive empathy – may come to be linked.     

Defining attitude for science educators

A distinct and complex definition of attitude is evolving within the literature. A mental readiness to respond and a correlational consistency between attitude and behavior—although controversial and in need of further study and analysis—remain viable subcomponents within the definition. Most agree that evaluation is the heartbeat of attitude. The impact of social influence on attitudes is becoming increasingly important. Attitudes are learned and not inherited.     

Prediction and prevention of child abuse and neglect

Utilizing an interview, a questionnaire, and observations during labor, delivery, and the postpartum period, a sample of one hundred mothers was identified as at high risk for abnormal parenting practices. These mothers were randomly divided into a “High-Risk Intervene” group (N=50) and a “High-Risk Nonintervene” group (N=50). The “Intervene” group received comprehensive pediatric follow-up by a single physician, a lay health visitor, and/or a public health nurse in the home. The “Non-intervene” group received routine care, although the results of these screening procedures were shared with the physicians and nurses responsible for their ongoing care. Another group of 50 mothers, who delivered during the same time period and who were assessed as low risk in terms of abnormal parenting practices, served as controls. When the children were approximately two years old (mean age 26.8 months), 25 families in each of the three groups were chosen at random for detailed evaluation.     

The assessment of teaching in higher education: A critical retrospect and a proposal

Evaluation of college and university teaching is considered in the context of growing demands for accountability of educational institutions and particular roles of faculty in achieving goals for which these institutions are believed to be accountable. In the first of two papers,^* three contemporary aprroaches to evaluation of teaching in higher education are critically reviewed. All three of these approaches-assessment of learning outcomes, assessment of teacher characteristics and analysis of pedagogical behaviors-are found to be defective on logical, theoretical and empirical grounds. A common thread of deficiency is the absence of a coherent theoretical framework for analysis of teaching and phenomena associated with teaching. Specific defecs are analyzed in each of the three approaches as well as in the ubiquitous methodology of rating of teaching performance. In analysis of evaluation by assessment of learning outcomes, teaching is shown to be neither necessary nor sufficient to subsequent learning outcomes. Assessment of teacher characteristics fails to identify those characteristics peculiarly indigenous to teaching as a generic activity. Analysis of pedagogical behaviors fails to distinguish critical teaching acts from more general teacher characteristics interpretable in terms of teacher personality. Furthermore, no adequate basis is provided for normative interpretation of data pertaining to pedagogical behaviors. The use of rating scales to provide data about teacher characteristics or pedagogical behavior rests on assumed rather than demonstrated validity of results. Evidence of validity or meaningfulness is replaced by evidence of consistency which is often spurious. The first paper concludes with an outline of requirements for a more constructive approach to the task of teacher evaluation. In a second paper, an outline of a theory of teaching is sketched which conforms to these requirements. Realization of this theoretical structure in teaching assessment report forms is described. Tentative conclusions from trial use of forms-in-development and recommendations for additional data sources are discussed in terms of their potential contribution to improvement in teaching.     

Child sexual abuse: a case study in community collaboration

OBJECTIVE: This is an exploratory study that describes the process and outcomes of a Midwestern US community's approach to case management of child sexual abuse. METHOD: Data were abstracted from 323 criminal court files. Specific information gathered included child and suspect demographic data, law enforcement and CPS involvement, child disclosure patterns and caretaker responses, offender confession, offender plea, trial and child testimony information, and sentences received by offenders. Both case process and outcome variables were examined. RESULTS: In this community, criminal court records reflect a sex offense confession rate of 64% and a sex offense plea rate of 70%. Only 15 cases went to trial and in six the offender was convicted. CONCLUSION: Communities can achieve successful outcomes when criminal prosecution of sexual abuse is sought, but the child's testimony is not necessarily the centerpiece of a successful case. In this study, desired outcomes were a consequence of the collaborative efforts of law enforcement, CPS, and the prosecutor's office, which resulted in a high confession and plea rate.     

The failure of the public schools and the free market remedy

A Summary The replacement of the existing system of publicly operated schools by a market of private ones-supported by government vouchers—would probably yield mixed results. On the one hand, some parents would have greater choices among schools and some schools would have to be productive in order to survive in the competitive framework. The increase in consumer choice and the resultant competition among schools would be likely to lead to greater educational benefits for many students and their families (private benefits) than those which they receive under the present monopolistic system.On the other hand, the schools are also expected to fulfill certain social functions. It is in these that a market approach to schooling is likely to yield poor results. For example, basic schooling represents the primary device for equalizing opportunities among racial and social groups. Yet, advantaged children would probably receive far better schooling under the market proposal than would disadvantaged ones, and it is likely that this disparity would lead to larger future inequalities in opportunity between the children of the middle class and those of the poor. Further, it is not clear that a set of largely autonomous schools could provide the common set of values and knowledge necessary for the functioning of a democratic society. Finally, it is likely that the market proposal would increase racial and social stratification of students among schools. Whatever the success of the market in meeting consumer preferences, it would be offset by the market's failure to satisfy the social goals of basic schooling.Fortunately, we are not limited to choosing between the traditional educational bureaucracy on the one hand or an unmitigated free market for educational services on the other. There are several ways to create competition within a public school system. Jencks, Sizer, and Coleman have suggested particular plans based upon the competitive framework, and the proposal for community schools represents a more general framework in which the competition of the market place might be used to advantage. The time is ripe to experiment with at least one of these plans for the children of the ghetto. Do we have any buyers? Henry M. Levin is a research associate with the Economic Studies Division of the Brookings Institute. He has written on economic and educational matters in the Saturday Review, the Journal of Human Resources,and other publications. He is currently organizing a Brookings conference on the community school.     

Sociocultural input facilitates children's developing understanding of extraordinary minds

Three- to 5-year-old (N = 61) religiously schooled preschoolers received theory-of-mind (ToM) tasks about the mental states of ordinary humans and agents with exceptional perceptual or mental capacities. Consistent with an anthropomorphism hypothesis, children beginning to appreciate limitations of human minds (e.g., ignorance) attributed those limits to God. Only 5-year-olds differentiated between humans' fallible minds and God's less fallible mind. Unlike secularly schooled children, religiously schooled 4-year-olds did appreciate another agent's less fallible mental abilities when instructed and reminded about those abilities. Among children who understood ordinary humans' mental fallibilities, knowledge of God predicted attributions of correct epistemic states to extraordinary agents. Results suggest that, at a certain point in ToM development, sociocultural input can facilitate an appreciation for extraordinary minds.