Using Variables in School Mathematics: Do School Mathematics Curricula Provide Support for Teachers?

This study employed content analysis to examine 3 popular middle-grades mathematics curricula in the USA on the support they provide for teachers to implement concepts associated with variables in school mathematics. The results indicate that each of the 3 curricula provides some type of support for teachers, but in a varied amount and quality. More specifically, whereas the University of Chicago School Mathematics Project (UCSMP) curriculum provides support for teachers on several aspects of using variables in school mathematics, the support found in the Connected Mathematics 2 and the Math Connects curricula focused mainly on one conception of variables—namely, the use of variables as quantity that varies in the Connected Mathematics 2 curriculum and the use of variables as specific unknowns in the Math Connects curriculum. Overall, the UCSMP curriculum provides the most support for teachers, followed by the Connected Mathematics 2 curriculum, with the Math Connects curriculum recording the least support for teachers to enact variable concepts. It is worth pointing out that, although the 3 curricula collectively provide guidance for teachers to implement variable ideas within meaningful real-world contexts, the supports identified in the respective curriculum were not sufficient in addressing all of the areas that are essential for teaching the many concepts associated with variables in school mathematics effectively. Recommendations for curriculum developers and for international researchers with interest in the roles of variables in school mathematics are provided.     

自聚焦克尔类电介质中非傍轴光束调制非稳的研究

Propagation stability of non-paraxial beam in nonlinear Kerr media is investigated with a linear stability method.Both theoretical analysis and numerical simulation show that modulation instability(MI) gain spectrum has three different distribution features determined by the times of incident power P0 and the non-paraxial parameter a. Furthermore,the corresponding criterion is put forward to distinguish the three different distributions.     

Large amplitude free vibration of a flexible panel coupled with a leaking cavity

This paper addresses the effect of leakage on the natural frequencies of a large amplitude vibrating panel backed by a cavity, which has not been considered in many other related studies. The structural-acoustic governing equations are employed to study this nonlinear problem. An elliptical integral method, which was recently developed for the nonlinear panel cavity problem, is introduced here to solve for the structural-acoustics responses. The present results agree reasonably well with those obtained from the classical harmonic balance method. Modal convergences of the nonlinear solutions are performed to verify the proposed method. The effects of vibration amplitude and leakage size are studied and discussed. It is found that (1) the edge leakages in a panel cavity system significantly affect the natural frequency properties, and (2) the edge leakages induce a low frequency acoustic resonance.     

Exploring Relationships Among Belief in Genetic Determinism,Genetics Knowledge,and Social Factors

Genetic determinism can be described as the attribution of the formation of traits to genes, where genes are ascribed more causal power than what scientific consensus suggests. Belief in genetic determinism is an educational problem because it contradicts scientific knowledge, and is a societal problem because it has the potential to foster intolerant attitudes such as racism and prejudice against sexual orientation. In this article, we begin by investigating the very nature of belief in genetic determinism. Then, we investigate whether knowledge of genetics and genomics is associated with beliefs in genetic determinism. Finally, we explore the extent to which social factors such as gender, education, and religiosity are associated with genetic determinism. Methodologically, we gathered and analyzed data on beliefs in genetic determinism, knowledge of genetics and genomics, and social variables using the “Public Understanding and Attitudes towards Genetics and Genomics” (PUGGS) instrument. Our analyses of PUGGS responses from a sample of Brazilian university freshmen undergraduates indicated that (1) belief in genetic determinism was best characterized as a construct built up by two dimensions or belief systems: beliefs concerning social traits and beliefs concerning biological traits; (2) levels of belief in genetic determination of social traits were low, which contradicts prior work; (3) associations between knowledge of genetics and genomics and levels of belief in genetic determinism were low; and (4) social factors such as age and religiosity had stronger associations with beliefs in genetic determinism than knowledge. Although our study design precludes causal inferences, our results raise questions about whether enhancing genetic literacy will decrease or prevent beliefs in genetic determinism.     

‘Research as dialogue’ and cross-cultural consultations: confronting relations of power

In this paper, we discuss methodological issues that emerged as we worked through a small empirical research project, ‘Engaging Aboriginal students in education through community empowerment’. Recent national policy statements (see, for example, MCEETYA 2000, NBEET 1995) argue the importance of education/research that keeps the locus of control within the Aboriginal community as a means to further the goal of self-determination and improve educational outcomes. In keeping with these recommendations, our project aimed to challenge assimilationist frameworks and sought to ‘empower’ members of the local Aboriginal community through participation in the project.     

Fostering scientific understanding and epistemic beliefs through judgments of promisingness

The evaluation of promisingness is central to knowledge building and knowledge creation but remains largely unexplored. As part of a design-based research program to support promisingness judgments, the present study implemented an intervention in a sixth grade science class, with the goal of exploring the potential of promisingness judgments to foster scientific understanding and epistemic beliefs. Aided by a Promising Ideas Tool and pedagogical supports designed for this intervention, students explored the concept of promisingness, judged the promisingness of their community ideas, and engaged in iterative cycles of idea refinement. Results indicated that students were capable of improving their understanding of promisingness and making promisingness judgments deemed sensible by domain experts. The conceptual understanding and epistemic beliefs displayed by students improved over the course of the intervention, and such improvement happened in tandem with students’ understanding of promisingness. The implications of this exploratory study and future research are discussed.