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.     

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.     

‘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.     

汇率干预中的多点自由边值问题的数值计算方法

1IntroductionIt is i mportant for the economic development of acountry to maintain the stabilization of exchange rate,so the intervention of exchange rate has become thetopic of the main concerns of the economic and math-ematical circles[1-5].To maintain the stabilization ofexchange rate,many countries use target zone re-gi mes,that is,the central banks intervene in the for-eign exchange market such that the exchange ratestays within the interval[a,b].There are fixed costand cost proportional …     

Investigation of iodine concentration in salt,water and soil along the coast of Zhejiang,China

Objective: We aim to describe the environment iodine concentration in salt, water and soil along Zhejiang Province coast in the China foreland. It will be helpful for us to judge whether this area is insufficient in iodine and universal iodized salt is necessary or not. Methods: We collected iodized salt samples, drinking water samples (tap water in the towns, and well water or spring water in the villages), water samples from different sources (ditches, lakes, rivers) and soil samples through random sampling in June, 2005. Salt, water and soil iodine was detected by arsenic-cerium redox method. Statistical analysis was expressed as mean±SEMby Windows SPSS 13.0. Results: (1) The iodine concentration in salt was 27.9±4.33 mg/kg (n=108). (2) Seventy-five water samples were collected. The water iodine value was 0.6～84.8 μg/L (mean of 11.66 μg/L). The watershed along the Qiantang River has significantly higher iodine content than the water in Lin'an in mountain area (P＜0.01). The iodine content and mean iodine content of tap water, well or spring water and natural water sources were 4.30±2.43 μg/L (n=34), 23.59±27.74 μg/L (n=19)and 12.72±10.72 μg/L (n=22) respectively. This indicated that among environmental water sources, the ditch iodine content was the highest with river water iodine being the lowest (P＜0.01). (3) Soil iodine value was 0.11～2.93 mg/kg (mean of 1.32 mg/kg).Though there was no statistical difference of soil iodine in different districts (P=0.131), soil iodine content correlated positively with water iodine content. Conclusion: Iodine concentration in salt accords with national policy of adding iodine in salt. Foreland has more iodine in water than mountain area. The data reflected that water and soil iodine in foreland area was not high, which suggests universal iodized salt should be necessary. Environment iodine has relatively close association with pollution.     

Development of a Clinical Practice Model for Serving Clients with Fetal Alcohol Spectrum Disorder

There is a lack of systematic research on the training of clinicians toward providing counselling services and support to individuals with Fetal Alcohol Spectrum Disorder (FASD). The aim of this qualitative project was twofold: (1) to develop and pilot a clinical consultation process that would address clinicians’ reported need for greater communication and information sharing in serving clients affected by FASD; and (2) to build a model of FASD-informed clinical counselling practice by examining this consultation process and by capturing the experiences of clinicians who were involved. Findings from focus groups and meeting minutes are reported with respect to the model’s focus on reflection, communication, and action.