Mathematical Flexibility: Aspects of a Continuum and the Role of Prior Knowledge

Abstract

Psychologists and mathematics educators have long viewed flexibility as critical to students’ mathematical development. In this paper, we focused on the multidimensional nature of flexibility to better understand how preference, knowledge, and use of effective methods for solving algebra problems are related. In Study 1, we identified research-based aspects of flexibility with algebra and assessed students on them following a two-step equations unit. Results indicated that certain aspects of flexibility develop prior to others and that prior knowledge of algebra plays a significant role in that development. Study 2 confirmed and elaborated on these results using a larger sample size. Implications for theory and for supporting flexibility in classrooms are discussed.     

Private and Public Schooling in Ghana: A Census and Comparative Survey

A census and survey of schools in the district of Ga, Ghana, explored the nature and extent of private education, and compared inputs to public and private schooling. Three quarters of all schools found were private, with almost as many unregistered private as government schools. Several important differences between registered and unregistered private schools were noted, including age, fee levels charged, teacher salaries and class size. A range of inputs, such as teacher activity, availability of desks, chairs, libraries, toilets and drinking water, were used to compare inputs to government, unregistered and registered private schools. Some conclusions are explored about the potential role for the private sector in helping meet “education for all” targets.     

Juvenile sex offenders: development and correction

This paper addresses the developmental nature of sexually abusive behaviors as they apply to juvenile male sexual offenders. Socialization and sexual victimization are discussed. Three case histories elucidate and support the discussion of the development of victim offending. Significant treatment issues of juvenile male sexual offenders center around the sexual assault cycle which provides a framework for sexual offenders to conceptualize and understand the cognitive, behavioral, psychological, and situational factors which have resulted in their offense(s). Although sexual offenders and sexual offenses are each unique, the sexual assault cycle offers a means of addressing essential commonalities in the treatment of juvenile sexual offenders. Sexual offender specific treatment is viewed as essential for decreasing the risk of further sexual offenses, and thus decreasing the incidence of sexual victimization.     

Effects of curricular activity on students' situational motivation and physical activity levels

The purpose of this study was to examine (a) the effects of three curricular activities on students'situational motivation (intrinsic motivation [IM], identified regulation [IR], external regulation, and amotivation [AM]) and physical activity (PA) levels, and (b) the predictive strength of situational motivation to PA levels. Four hundred twelve students in grades 7-9 participated in three activities (cardiovascular fitness, ultimate football, and Dance Dance Revolution [DDR]) in physical education. ActiGraph GT1M accelerometers were used to measure students' PA levels for three classes for each activity. Students also completed a Situational Motivation Scale (Guay, Vallerand, & Blanchard, 2000) at the end of each class. Multivariate analysis of variance revealed that students spent significantly higher percentages of time in moderate-to-vigorous PA (MVPA) in fitness and football classes than they did in DDR class. Students reported higher lM and IR toward fitness than DDR They also scored higher in IR toward fitness than football. In contrast, students displayed significantly lower AM toward fitness than football and DDR Hierarchical Linear Modeling revealed that IM was the only positive predictor for time in MVPA (p = .02), whereas AM was the negative predictor (p < .01). The findings are discussed in regard to the implications for educational practice.