Kindergarten children's symbolic number comparison skills relates to 1st grade mathematics achievement: Evidence from a two-minute paper-and-pencil test

Basic numerical skills provide an important foundation for the learning of mathematics. Thus, it is critical that researchers and educators have access to valid and reliable ways of assessing young children's numerical skills. The purpose of this study was to evaluate the concurrent, predictive, and incremental validity of a two-minute paper-and-pencil measure of children's symbolic (Arabic numerals) and non-symbolic (dot arrays) comparison skills. A sample of kindergarten children (M_age = 5.86, N = 439) were assessed on the measure along with a number line estimation task, a measure of arithmetic, and several control measures. Results indicated that performance on the symbolic comparison task explained unique variance in children's arithmetic performance in kindergarten. Longitudinal analyses demonstrated that both symbolic comparison and number line estimation in kindergarten were independent predictors of 1st grade mathematics achievement. However, only symbolic comparison remained a unique predictor once language skills and processing speed were taken into account. These results suggest that a two-minute paper-and-pencil measure of children's symbolic number comparison is a reliable predictor of children's early mathematics performance.     

Valuing practice over theory: How beginning teachers re-orient their practice in the transition from the university to the workplace

This paper is about the experiences of beginning teachers in turning theory learned in universities into practice in the workplace. The research is situated in the context of a pre-service teacher education programme that explicitly and deliberately seeks to bridge the theory-practice gap in teacher education. The paper argues that, despite long-standing awareness of the theory-practice gap as a central issue faced by beginning teachers, attempts by teacher educators to address this issue remain thwarted. The argument draws on interview and focus group data collected via a study of 1st year graduate teachers of an Australian pre-service teacher education programme. The theoretical perspective of symbolic interactionism is used to focus on the meanings that graduates have of their experiences of turning theory into practice. The data suggest that prospective teachers during pre-service training value both the theory that they learn on campus and the practice that they observe in schools. However, once they become practitioners, they privilege the latter. Upon entry to the workplace, graduates come to associate good practice with that of the veteran teacher, whose practice and cache of resources they seek to emulate.     

Exploring the phase space of a system of differential equations: different mathematical registers

We describe and analyze a situation involving symbolic representation and graphical visualization of the solution of a system of two linear differential equations, using a computer algebra system. Symbolic solution and graphical representation complement each other. Graphical representation helps to understand the behavior of the symbolic solution. Together with it, the symbolic solution and its analysis are needed to understand the graphical representation and to overcome the limiting constraints of the CAS. The study described in this paper points out the importance of flexibility in building connections between different mathematical registers, together with the fact that the balance between the usage of symbolic representations and of graphical representations can be very different from one student to the other. Research supported by Israel Science Foundation, grant number 1340/05.     

Numerical issues in backstepping control: Sensitivity and parameter tuning

The backstepping-based adaptive tuning functions design is a control-scheme for uncertain systems that ensures reasonably good stability and performance properties of the closed loop. The complexity of the controller makes inevitable the use of digital computers to perform the calculation of the control signal. This paper addresses the issue of the numerical sensitivity of this control scheme. It is shown that while the increase of the design parameters may be desirable to achieve a good transient performance, it harms the control signal as this increase introduces large high-frequency components due to the numerical errors. The presented results suggest that it is necessary a certain compromise between the choice of the design parameters and the numerical precision of the tools involved in the control design. This compromise can be quantified by explicit expressions.     

Symbolic convergence and special communication theories: Sensing and examining dis/enchantment with the theoretical robustness of critical auto ethnography

This study answers 4 research questions as it explicates the SCT's ability to explain how special communication theories come into being as the product of rhetorical visions that contain the norms, conventions, and customs for exemplar participation in a specific communication style. This study demonstrates that the concept of rhetorical vision yields insights into the creation, rise, and potential for demise of a style‐specific, special theory of communication named the critical autoethnography special theory (CAST). The study reports that the CAST itself is a symbolically created product of the critical autoethnographic rhetorical vision (CARV). The study's findings indicate that CARV's life‐cycle is congruent with those of other rhetorical visions and would predict that the CARV may well implode upon itself as it contains the seeds of its own destruction.     

The Communication of Community Collaboration: When Rhetorical Visions Collide

Recently, community coalitions have grown in size, scope, and popularity in response to increasing demands for community-based involvement. Despite this trend, little is known about the ubiquitous role communication plays in the creation of community coalition missions, goals, and enactment practices. In addition, few studies have focused on the symbolic discourse of vital, active community groups. This study examines how coalition members have symbolically converged around a shared vision, which has unintentionally affected group sustenance. Fantasy theme analysis identifies two distinct visions in competition with one another, highlighting possible group dysfunction and decline. This communicative analysis of the group's symbolic life, coupled with a practical look into group effectiveness, bridges the gap between functionalist and interpretive approaches to studying organizational groups.     

Mathematica软件在《数学分析》中的应用

从求解不等式、极限、导数、微分、不定积分、定积分及绘图等方面介绍了Mathematica软件在《数学分析》中的应用。研究表明,将Mathematica应用于《数学分析》中,能够使学习变得更直观、更容易,对提高学生学习的积极性有明显促进作用。     

Discursive Constructions of the Meaning of “Family” in Online Narratives of Foster Adoptive Parents

Framed by relational dialectics theory, discursive constructions of the meaning of “family” were examined in 100 online foster adoption narratives. Parental narratives manifested struggles between biogenetic and discursive constructions of “family,” identified here as the discourse of biological normativity (DBN) and discourse of constitutive kinning (DCK). The DBN reinscribes the dominant cultural and foster care system preference for biogenetically connected families. The DCK resists the DBN, maintaining that enacted behaviors and shared affections, rather than shared genetics, constitute legitimate families. Contrapuntal analysis revealed a high degree of polemic interplay; both discourses competed to be centered rather than marginalized through the discursive practices of negating, countering, and entertaining. Implications for theorizing definitions of family and studying families in context are discussed     

英语介词教学反思

英语介词的使用频繁,用法灵活,搭配能力很强,是词汇学习中大家所公认的一大难点。探讨介词意义分析,隐喻,搭配、翻译和功能可促进介词教学效果。