Re-mythologizing mathematics through attention to classroom positioning

With our conceptualization of Harré and van Langenhove’s (1999) positioning theory, we draw attention to immanent experience and read transcendent discursive practices through the moment of interaction. We use a series of spatial images as metaphors to analyze the way positioning is conceptualized in current mathematics education literature and the way it may be alternatively conceptualized. This leads us to claim that changing the way mathematics is talked about and changing the stories (or myths) told about mathematics is necessary for efforts to change the way mathematics is done and the way it is taught.

Feeling number: grounding number sense in a sense of quantity

Drawing on results from psychology and from cultural and linguistic studies, we argue for an increased focus on developing quantity sense in school mathematics. We explore the notion of “feeling number”, a phrase that we offer in a twofold sense—resisting tendencies to feel numb-er (more numb) by developing a feeling for numbers and the quantities they represent. First, we distinguish between quantity sense and the relatively vague notion of number sense. Second, we consider the human capacity for quantity sense and place that in the context of related cultural issues, including verbal and symbolic representations of number. Third and more pragmatically, we offer teaching strategies that seem helpful in the development of quantity sense coupled with number sense. Finally, we argue that there is a moral imperative to connect number sense with such a quantity sense that allows students to feel the weight of numbers. It is important that learners develop a feeling for number, which includes a sense of what numbers are and what they can do.     

Kinematic differences of elite and high-performance tennis players in the cross court and down the line forehand

This study identified and compared the full body kinematics of different skill levels in the forehand groundstroke when balls were hit cross court and down the line. Forty-three three-dimensional retro-reflective marker trajectories of six elite and seven high-performance players were recorded using an eight-camera 400 Hz, Vicon motion analysis system. The six highest horizontal velocity forehands with reliable kinematics of all participants were analysed for each specific situation (a total of 156 analysed shots). Significant differences (p < 0.01) and large effect sizes were observed between elite and high-performance players in linear velocity of the shoulder (2.0 vs. 1.2 m/s), angular velocity of the pelvis (295 vs. 168 °/s), and angular velocity of the upper trunk (453 vs. 292 °/s) at impact. The elite group showed a tendency towards higher racquet velocities at impact (p < 0.05). No significant differences were found in angular displacement of the racquet, hip alignment, or shoulder alignment at the completion of the backswing; nor did angular displacement vary significantly at impact. Irrespective of the group, different shoulder, hip, and racquet angles were found at impact, depending on the situation. The results should assist coaches when striving to improve their players' forehand.     

A comparison of the Rescorla-Wagner and Pearce models in a negative patterning and a summation problem

In two experiments, we examined two related conditioning problems previously investigated by Red-head and Pearce (1995a) and Pearce, Aydin, and Redhead (1997). Experiment 1 involved an A+, B+, C+, AB+, AC+, BC+, ABC2 discrimination. The Rescorla-Wagner model predicts that response to AB, AC, and BC will be greater than that to A, B, and C at asymptote, whereas the Pearce model makes the opposite prediction. In Experiment 2, we investigated the responding to a novel ABC compound in groups trained with either A+, B+, C+ or AB+, AC+, BC+. The Rescorla-Wagner model predicts greater response to ABC in the group trained with A+, B+, C+ than in the group trained with AB+, AC+, BC+, whereas the Pearce model makes the opposite prediction. In contrast to the findings of Redhead and Pearce (1995a) and Pearce et al. (1997) in pigeon autoshaping, our findings in rabbit eyelid conditioning support the Rescorla-Wagner model.     

Using Student Journals for Course Evaluation

The evaluation of courses has become more important than ever in the higher education sector. Information is commonly collected from students on their perceptions of a course using questionnaires, discussions or interviews. This paper discusses the use of a student learning journal as a means of collecting data on the effectiveness of a course. Students in a graduate diploma course at the University of Technology, Sydney use learning journals to record and reflect on their development as a teacher/trainer over one semester. The evaluator of the course obtains qualitative data from the journals regarding students’ perceptions of the course content, structure, activities and assessment. The main advantages of this technique include the longitudinal perspective it gives on students perceptions of a course and also that it provides information on the whole course, particularly on whether whole course outcomes are being met. Collecting information from student journals also has the advantage that the data were not written specifically for course evaluation. Issues regarding validity, confidentiality and data analysis using student journals are addressed in this paper as is the place of this technique in a quality assurance scheme for a course.     

Exploring the relationship between school discipline referrals and delinquency

There is a growing concern about violent and destructive behaviors of youth that require intervention by juvenile justice and youth‐serving agencies. This concern has led many to conclude that schools and community agencies must increase efforts to prevent juvenile delinquency and to provide programs that will facilitate rehabilitation, education, and vocational training for youth already involved. A clear understanding of the nature and range of behaviors that result in juvenile crime is needed in order to develop programs and interventions that can be expected to lead to beneficial changes for youth and for society as a whole. The purpose of this article is to describe the relationship between school behaviors and youth characteristics in school (e.g., discipline referrals, teacher nominations, nomothetic ratings) and referrals to juvenile authorities (e.g., illegal behaviors). We describe a strategy of using teacher nominations, school discipline referrals, and community arrest data to predict delinquent and violent behavior in youth. We outline data from a group of socially maladjusted middle school youth to illustrate the relationship between the two data sources and recommendations for identification and treatment of youth at risk for delinquency and antisocial behavior. © 2001 John Wiley & Sons, Inc.