An Onto-Semiotic Analysis of Combinatorial Problems and the Solving Processes by University Students

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of combinatorial reasoning. We finally analyze the implications of the theoretical model and type of analysis presented for mathematics education research and practice.     

Discrimination reversal learning in newts

The results of field research suggest that, contrary to being behaviorally inflexible, some amphibians may have the ability to respond effectively to changing environments. The performance of seven newts (Triturus viridescens) was studied across 20 successive reversals of a spatial discrimination problem in a dry T-maze. Submersion in shaded water served as reinforcement for correct responses. The subjects showed a decrease in mean errors across reversals and across ordinal trials within sessions. These results are discussed in terms of the importance of using biologically relevant methodologies in the study of comparative animal learning.     

The acquisition of a running response as a function of odor buildup,squad rotation,and introduction of naive subjects

A three-phase experiment was conducted in which rats received a double-alternation schedule of reward and nonreward. During Phase 1, the baseline period, double-alternation behavior was displayed earlier and more strongly by subjects run last in the daily sequence. This finding suggests that both reward and nonreward odor cues are cumulative over subjects. During Phase 2, a subject-rotation procedure was initiated; that is, each day the last subject in the previous day’s running sequence was moved to the first position in the sequence, etc. Rotation to the first position in the group led to an immediate disruption of responding. During Phase 3, two naive rats were inserted at the beginning of the running sequence and two at the end. The results, which showed that the naive animals placed at the end of the sequence acquired the patterning response much faster than those placed in the beginning positions, are interpreted as reflecting preparedness to respond to such intensified odors.     

Classically conditioned heart rate and respiratory-motor activity in newborn and neonatal pygmy goats

Classical discrimination conditioning of heart rate (HR) and respiratory-motor (RM) activity was examined in 16 newborn (average age = 1 day) and 8 neonatal (average age = 2 weeks) pygmy goats over 4 days of conditioning involving an electric shock US and auditory CSs. On the 4th day, one-half of the animals in each group received a low to moderate dose of ethanol to test the resistance of the CRs to drug effects. Discriminated conditioning of RM activity but not HR occurred in the newborn group, indicating an absence of close coupling between skeletal-motor activity and HR at this early age. While the newborn group failed to show recognizable HR reactions to the CSs during the 4 days of testing, it did show a long-latency brady-cardia UR beginning at 2 days of age that may have been secondary to baroreceptor reflex actions. The neonatal group displayed conditioning of both HR and RM activity. The similar latencies of the two types of CRs during the CS suggested that they may have been related to each other. However, the fact that the RM CR developed a day before the HR CR, combined with the observation that ethanol modified the HR CR but not the RM CR, supports the view that there was considerable independence between the two types of CRs.     

Inescapable shock interferes with the acquisition of a low-activity response in an appetitive context

This study investigates the effects of exposure to inescapable shock on the acquisition of a low-activity appetitive response using a trial procedure. Inescapable shock was found to interfere with the acquisition of a nose-poke response to obtain food as compared with animals exposed to either escapable shock or no shock. In addition, general activity levels were measured separately during the trial and the intertrial interval during the appetitive test. Inescapably shocked animals were less active during the trial component than were either the escapably shocked or the nonshocked animals. However, no differential levels of activity were observed during the intertriai interval component of the appetitive test. The relevance of these findings for both the learned helplessness and the learned inactivity hypotheses is discussed.     

The Long Decay Model of One-Dimensional Projectile Motion

This article introduces a research study on student model formation and development in introductory mechanics. As a point of entry, I present a detailed analysis of the Long Decay Model of one-dimensional projectile motion. This model has been articulated by Galileo (in De Motu) and by contemporary students. Implications for instruction are discussed.

---

Teacher engagement in core components of an effective,early childhood professional development course: Links to changes in teacher–child interactions

This study built on prior research regarding the effectiveness of the National Center for Research in Early Childhood Education (NCRECE) course by exploring the individual course components. Core aspects of course engagement and performance were described and examined in relation to improvements in the observed quality of teacher–child interactions. Teacher characteristics were also examined as predictors of course engagement and performance. A sample of 150 preschool teachers participated in a semester-long, credit-bearing, college course designed to improve the quality of their emotional, organizational, and instructional interactions with children. Teachers’ participation and performance in the course were high on average. Teachers’ skill level in accurately and specifically explaining other teachers’ instances of effective teacher–child interactions was related to improvements in their own observed teacher–child interactions. Finally, teachers with an early childhood major and those endorsing child-centered beliefs displayed better skills in detecting other teachers’ high-quality interactions with children. Results are discussed in relation to designing more effective early childhood professional development programs.     

Göttingen in retrospect

Participant assessment is one of the processes which can be used to evaluate the success of educational exchange programs. This study was conducted in 1972 with University of California students who attended the University of Göttingen, Federal Republic of Germany, during the 1965–66 academic year. Participants were asked about their subsequent use of language, as well as their assessment of the academic, intellectual, personal, social and cultural dimensions of the program. This paper reports the results of the Göttingen questionnaire and, hopefully, contributes to a better understanding of the kinds of enduring student benefits that can result from an educational experience abroad.