Using peer and self-assessment to develop modelling skills with students aged 11 to 16: A socio-constructive view

Eight Welsh secondary schools participated in an action research project which developed approaches to teaching and assessing mathematical thinking skills involved in practical modelling situations. The development of the metacognitive and strategic skills necessary for successful modelling is discussed from a socio-constructivist perspective as a process of acculturation as well as cognitive construction. Learning to model involves socialization into the consensual realities of a wider mathematical culture and the teacher plays a pivotal role in the generation of this consensus through the legitimization of linguistically expressed subjectivities. Assessment is an integral part of this process. Participation in peer and self-assessment was found to involve the student in a recursive, self-referential learning process which supports the explicit development of metacognitive skills.     

Measurement Problems

History teaches the continuity of science; the developments of tomorrow have their genesis in the problems of today. Thus any attempt to look forward is well begun with an examination of unsettled questions. Since a clearer idea of where we are going smoothes the path into the unknown future, a periodic review of such questions is prudent. The present day, lying near the juncture of the centuries, is well suited for such a review. This article reports 16 unsolved problems in educational measurement and points toward what seem to be promising avenues of solution.     

Faculty dynamation: Guided empowerment

Dynamation is the integrative process whereby the sum total of all learning, knowledge, experiences, and feelings are brought to bear on productive, creative action and problem solving. In this paper, we describe some of the benefits of dynamation, outline a general approach to it-including the importance of friendship (the core of the empowerment process)- and explain several key incentives that will encourage faculty, through dynamation, to engage in growth activities. Throughout the article we discuss ten techniques developers can use. Our focus is on informal facilitator-enhanced (guided) empowerment. That is, we look at growth that is likely to result when developers work with faculty with the goal of growth, change, and development.Richard L. Weaver II is a professor in the Department of Interpersonal and Public Communication at Bowling Green State University. Darrell Mullins is an assistant professor in the Communication Department at the University of Wisconsin at Whitewater. Howard W. Cotrell is an associate professor in the Instructional Media Center at Bowling Green State University. Thomas A. Michel is an assistant professor in the Graduate School of Business at Fordham University, Bronx, New York.     

Two studies of low income parents' involvement in schooling

An interview and an intervention study are reported. Interview findings extend research on the positive relationship of parent involvement to school success. That is, although most of the low income families reported low-moderate participation, a postive relationship was found between parent involvement and school adjustment as early as kindergarten. With respect to negative valuing and barrier interpretations of low participation, the data support the latter; all but a few parents reported positive attitudes toward school involvement, while the majority indicated significant barriers. In comparing Latino and non-Latino groups, the former reported more barriers. Within the Latino group, parents whose children had made a good school adjustment indicated the most participation. Non-English proficient parents reported more barriers than those proficient in English but comparable degrees of involvement. In the intervention study, a simple strategy resulted in more treatment than control parents attending a school event. Differences in attendance were related to ethnicity and language.This work was carried out in conjunction with a dropout prevention demonstration project conducted as a collaborative effort of the School Mental Health unit (Janelle Munn, Director) and Dropout Prevention unit (Pete Martinez, Director) of the Los Angeles Unified School District and the School Mental Health Project at UCLA (Howard Adelman and Linda Taylor, Co-directors). Partial support for the project came from the U.S. Department of Education. The authors, of course, assume full responsibility for the contents, but we want to take this opportunity to acknowledge the contributions of participating schools and project staff (especially Mary Beth DiCecco and Alison McAlpine). And although she declined author credit, this work could not have been accomplished with the many contributions of Linda Taylor, the project director. We would also like to thank Regina DeWitter, Teresa Gonzales, Kathy Eides and the many other UCLA students who assisted in various phases of the research.     

Effects of group rearing on the control exerted by an imprinting stimulus

Prior research suggests that group rearing may attenuate a young bird’s tendency to approach and follow an imprinting stimulus. The present work examined the effect of group rearing on a different measure of attachment, suppression by the imprinting stimulus of distress calling induced by abrupt reductions in group size. In Experiment 1, ducklings were reared in groups of 12 or 3 over Days 1–6 posthatch, and each group received a total of 3.5 h of exposure to an imprinting stimulus. Subsequent tests revealed that, when the groups of ducklings were separated into smaller subgroups: (1) the fewer the ducklings in a subgroup, the more distress calls emitted; (2) a given number of birds separated from a larger group emitted more distress calls than an equal number from a smaller group; and (3) regardless of the subgroup size, fewer distress calls occurred when the imprinting stimulus was present than when it was absent. A second experiment revealed that when a group of 12 birds was first confronted with an imprinting stimulus on Day 6 posthatch, they reacted with an increase in distress calling and corner huddling (an aversive reaction). After several hours of exposure to the stimulus, however, its presence exerted a powerful suppressive effect on distress calling. It is concluded that the social bonds between the members of a brood do not preclude the formation of a social attachment to an imprinting stimulus subsequently encountered.     

Acquisition of behavioral control by the auditory features of an imprinting object

Presentations of a visible moving object immediately suppressed ongoing distress vocalization in newly hatched ducklings, but presentations of only the auditory features of the object initially had no effect. However, as the ducklings received more and more exposure to the visible moving object, the object’s auditory features gradually acquired the ability to suppress distress calls themselves. These auditory features failed to develop suppressive properties in ducklings which received prolonged exposure to those features but never saw the object in motion. The gradual acquisition of behavioral control by the auditory features of a moving object is taken to represent the essence of the imprinting process.     

Flavor- vs. tone-cued shock avoidance

In a direct comparison, flavor-cued rats learned to avoid shock in a two-way shuttlebox as well as, or better than, tone-cued rats. These results stand in contrast to the prevalent view that rats encounter difficulty in forming flavor-shock, but not tone-shock, associations. In attempting to account for this contrast, we note that experiments revealing cue-modality specificity employ an aversion paradigm and record ingestive behavior. It is argued that both the paradigm and the dependent variable are inappropriate for assessing shock-avoidance learning, and that cue-modality specificity in such a setting reflects paradigm and response choice rather than a general characteristic of rats.     

Teachers' Interpretations of Effective Whole-class Interactive Teaching in Secondary Mathematics Classrooms

Prompted by ongoing concerns over standards of numeracy, eight mathematics teachers from four secondary schools in south Wales formed a teacher inquiry group to research the impact of introducing whole-class interactive teaching strategies into their own practice. Possible teaching approaches and activities were developed and agreed during group meetings. These were trialled by the teachers during their normal mathematics lessons. Lesson observations, interviews with teachers and discussions at the group meetings, however, indicated that the implementation of the approaches varied significantly across teachers. This paper analyses the variation in interpretations and teaching styles, and discusses their impact on the quality of the classroom discourse. The determining features discerned within the classroom dialogue included the extent to which pupils were encouraged to reflect on their mathematical knowledge, and the ways in which teachers were able to scaffold pupils' learning.     

A Bayesian Method for Evaluating Passing Scores: The PPoP Curve

In this note, we demonstrate an interesting use of the posterior distributions (and corresponding posterior samples of proficiency) that are yielded by fitting a fully Bayesian test scoring model to a complex assessment. Specifically, we examine the efficacy of the test in combination with the specific passing score that was chosen through expert judgment, or, in general, any external a priori criterion. In addition, we study the robustness of the test's efficacy with respect to choice of the passing score.     

Concurrent observations of barpress suppression and freezing: Effects of CS modality and on-line vs. off-line training upon posttrial behavior

In a conditioned suppression study with rats, CS modality (light vs. noise) and type of conditioning (on-line vs. off-line training) were manipulated. All rats were then tested on-line with only half the test trials reinforced. Some results and conclusions were as follows: (1) During initial training, suppression following reinforced noise trials was moderately strong at first but weakened over days; for the light, it was weak from the start. It was suggested that this strong influence of CS modality might complicate interpretations of posttrial suppression as a measure of US effectiveness. (2) During testing, posttrial suppression and freezing were greater following non-reinforced trials than following reinforced trials (US-omission effect), and this effect was stronger for noise than for light. Since noise also produced more freezing than light, this result favors the hypothesis that the US-omission effect is due to persistent CS-elicited freezing that is un-disrupted by a shock US. (3) Although noise produced more freezing, both noise and light produced similar barpress suppression. This result is consistent with the suggestion that noise and light acquire equal associative strength but elicit different defensive behaviors.