This study reports on the algebraic generalisation strategies used by two fifth grade students along with the factors that appeared to influence these strategies. These students were examined over 18 instructional sessions using a teaching experiment methodology. The results highlighted the complex factors that appeared to influence student strategy use, which included: (a) input value, (b) mathematical structure of the task, (c) prior strategies, (d) visual image of the situation, and (e) social interactions with the teacher and other student. Particular combinations of these factors appeared to increase the predictability of student strategy use. However, the complex nature of the factors influencing these strategies demonstrates the challenges that exist in encouraging students to move toward more sophisticated strategies.
This study compares the views of teachers and professional development facilitators about effective professional development (PD). We analyzed interviews with 72 teacher participants and 23 PD facilitators involved in nine science and mathematics PD projects. The teachers' themes for characterizing effective PD included classroom application, teacher as learner, and teacher networking. Similarly, the PD facilitators discussed effective PD as having classroom application and experiences for teachers as learners. In addition, PD facilitators shared the need to develop collegial relationships with teachers and improve teacher knowledge. These views correspond to some of the standards and recommendations described in policy and research documents on effective PD. Criteria of effective PD in these documents that the participants did not mention included: (1) challenging teachers' content and pedagogical content knowledge with transformative learning experiences, (2) encouraging teacher leadership for sustained support, and (3) focusing on student learning by instructing teachers on how to use student data to inform their teaching practice. Our findings have implications for designing PD that reflects the criteria of standards-based reform.
The purpose of this study was to determine if the Activities-specific Balance Confidence (ABC) Scale, Falls Efficacy Scale (FES), and Survey of Activities and Fear of Falling in the Elderly (SAFE) assessments measured fear of falling in the same manner (convergent validity) and to determine if they predicted those individuals who, based upon a previous history of falls, limitation of activity, and not leaving home, had an increased potential for falling (predictive validity). One hundred and eighteen individuals, 60 years of age and older, completed each of the assessments. They self-reported activity restriction, fall history, and the number of times they left the home each week. The convergent validity of each assessment was established by correlating each assessment tool with each of the others. Findings indicated the ABC and FES were highly correlated with each other, indicating they measured similar constructs, and both were moderately correlated with the SAFE, suggesting these assessments measured different constructs. The predictive validity of each instrument in relation to the frequency of falls, limitation of activity, and frequency of leaving the home revealed no individual tool could accurately predict any of these characteristics of the sample. As a result, no one test by itself was able to identify individuals who may be at risk and a candidate for an intervention program.
Numerous studies have identified depressive symptoms as antecedent to stressful experiences. However, the interrelations of depressive symptoms, personal resources, and coping as antecedents of stressful experiences are largely unknown. For this investigation, a prospective design was used to test a model estimating two categories of daily hassles at Time 2 in relation to depressive symptoms, self-esteem, gender, coping, and daily hassles at Time 1. Utilizing simultaneous equations, direct effects were observed for depressive symptoms, Time 1 hassles, gender, and avoidance coping in relation to category of hassles at Time 2. Depressive symptoms and avoidance coping were observed to be mediators for gender and self-esteem.
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