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.     

Self-belief does make a difference: A reciprocal effects model of the causal ordering of physical self-concept and gymnastics performance

Abstract

A large body of research in support of the reciprocal effects model of causal ordering demonstrates that prior academic self-concept predicts subsequent academic achievement beyond what can be explained in terms of prior achievement. Here we evaluate the generalizability of this support for the reciprocal effects model to a physical activity context in which achievement is reflected in gymnastics skills on a standardized gymnastics performance test evaluated by expert judges. Based on the responses of 376 adolescents collected at the start (T1) and end (T2) of a gymnastics training programme, there is support for a reciprocal effects model in which there are significant paths leading from both T1 gymnastics self-concept to T2 gymnastics skills and from T1 gymnastics skills to T2 self-concept. Although there were gender and age effects (girls and older participants had better gymnastics skills, boys had higher self-concepts), multiple group structural equation models indicated that support for the reciprocal effects model generalized over responses by boys and girls. In summary, self-concept and performance are both determinants and consequences of each other.     

New Books Briefly Noted

Abstract

Little research has investigated the observational learning process from a developmental perspective. The purpose of this study was to extend previous research by considering two factors: performance versus learning and sequencing versus form scores. Children 'N = 60) comprising two age groups (5-0 to 6-11 and 8-0 to 9-11 years) were randomly assigned to verbal rehearsal only, model only, or model plus verbal rehearsal conditions. The task was a 6 part motor skill sequence in which proper sequencing and quality of form were assessed. A 2 × 3 × 4 (age group by model type by trial blocks) repeated measures MANOVA revealed a significant three-way interaction. Older children performed equally well under any of the model type conditions during both performance and learning. For younger children, a model plus rehearsal was superior to rehearsal only on sequence and form at performance and learning and superior to model only on sequence scores during the first two performance trial blocks. Model only and model plus rehearsal conditions were equally effective on form scores. These results suggest that age differences exist in the modeling of motor skills under conditions varying in model type, sequence and form scores, and performance and learning phases.     

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.     

Children with mathematics learning disabilities in Belgium

In Belgium, between 3% and 8% of the children in elementary schools have mathematics learning disabilities (MLD). Many of these children have less developed linguistic, procedural, and mental representation skills. Moreover, a majority of the children have been found to show inaccurate prediction and evaluation skills in Grade 3. MLD often become obvious in elementary school. Whereas some children are retained, others are referred to special education. During the last 10 years, the number of children in special education and the number of children with learning disabilities who are following a special guidance program in general education (inclusive education) have increased. Children in Belgium with MLD can get therapy for about 2 years. Nevertheless, many problems continue unresolved even in high school and adulthood.     

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.