用实数完备性证明闭区间上连续函数的有界性

用实数完备性定理（区间套定理、确界原理、单调有界定理、柯西收敛准则）,直接证明了闭区间上连续函数的有界性,从一侧面反映了实数完备性的6个基本定理是互相等价的。     

关于曲线E：y^3=x^4＋x上的有理点

对于高次曲线上的有理点及整点的确定是数学上一个比较难理解的问题。研究并给出曲线E：y^3=x^4＋x上的所有有理点及整点,证明了曲线E：y^3=x^4＋x的两个定理。     

辅助函数法在一些数学问题中的应用

辅助函数法是处理和解决数学问题的一种重要思想方法。在高等数学解题中,往往不是直接对问题本身进行求解,而是根据问题以及所给的已知条件,巧妙地构造一个适当的辅助函数,从而间接有效的解决问题。     

High school students' evolving alternative conception related to the volume of gas: A Lakatosian perspective

The purpose of this case study, informed by a Lakatosian perspective, is to identify how an alternative conception that originates in present learning but is related directly to subsequent learning contexts can be constructed. Before the study, one of the authors found by accident that a student who had learned about Avogadro's principle and chemical reaction in South Korea constructed an alternative conception related to the volume of gas. Later, we identified seven Korean high school students with the alternative conception through a test and analyzed their underlying understandings qualitatively through interviews. The results show that they had a scientific conception—core conception—and intuitive assumptions about implicit information of external representations—implicit assumptions—in common. The students' implicit assumptions could be divided into three types again: core assumption, auxiliary assumption, and context-inducing assumption. The core assumption, like the core conception, played a significant role in constructing the alternative conception (hard core), while the auxiliary assumptions were incomplete implicit assumptions to protect the alternative conception (protective belt). The context-inducing assumption was an implicit assumption bringing the context of the subsequent curriculum, and the core conception and the core assumption could be interpreted in this induced context. At the end of the study, the implications related to learning progressions were discussed.     

质数及其判定

介绍了质数及质数个数是无穷的判断方法,结合同余式与不定方程的求解中与质数形状有关的问题进行了归纳总结,有助于克服判断一个整数是合数还是质数以及质数的形状这个数论学习难点.     

一类具有分布时滞的退化中立型微分系统的周期解

利用不动点定理讨论了一类具有分布时滞的退化中立型微分系统：E（t）d/dt[x（t）＋∫0-τB（s）x（t＋s）ds]=A（t）x（t）＋∫（t,x（t-r（t）））的周期解。得到了周期解存在的充分条件．     

Student-centred and teacher-centred learning environments: what students think

This contribution explores the relationship between teacher-centred and student-centred learning environments from a student's perspective. Three different views with respect to this relationship can be retrieved. The balance view suggests that the more teacher-centred a learning environment is, the less student-centred it is and vice versa. The transactional view stresses the continuous renegotiation of teacher- and student-roles. The independent view argues that teacher- and student-centredness are independent features of learning environments. Results from three survey studies of higher education students’ conceptions of quality education are discussed. While the practice-oriented literature regularly seems to adopt a balance view, factor analyses did not reveal evidence for the balance view in any of these studies. In students’ minds student-centredness and teacher-centredness seem to be mutually reinforcing features of high quality education. From a curricular point of view, and especially with regard to teacher training, the results warrant to argue for the development of so-called powerful learning environments rather than for the transition from teacher-centred towards student-centred learning environments.     

'There's no way this kid's retarded': teachers' optimistic constructions of students' ability

Historical research in the field of autism has suggested that judgements regarding the ability of students with autism should be made carefully, taking into consideration the person with autism's difficulty with communication, movement and performance in general. Although the historical literature has urged professionals to proceed with caution regarding judgements about ability, a haphazard understanding of people with autism as retarded prevails. This qualitative study analyses the experiences of four teachers who, within the context of the inclusive classroom, resist interpreting non-verbal students with autism as mentally retarded and seek to form a new understanding of ability. The following themes will be discussed: (1) finding situations where students demonstrate competence, (2) rethinking performance and understanding, and (3) expecting struggles.     

‘Go over there and look at the pictures in the book’: an investigation of educational marginalisation,social interactions and achievement motivation in an alternative middle school setting

The middle years of school represent a time of educational turbulence, serving to marginalise some students from educational opportunities. Much research has focussed on individual cognitive factors influencing educational engagement, with less attention directed towards social interactions. Theoretically positioned within an expectancy–value model of achievement motivation, this study draws on the lived experience of a 12-year-old student within an alternative school in South Australia, Australia, to explore how social encounters may contribute to educational marginalisation. Findings from a narrative case study employing a semi-structured interview suggested that connections exist between social influences, such as interactions with teachers and peers, and subsequent achievement motivation. This study suggests that social interactions are critical determinants to an individual's educational engagement, affecting educational ability, expectancy and value beliefs.     

Effects of the WhyTry social skills program on students with emotional and/or behavioral problems in an alternative school

Social skills training (SST) is an evidence-based intervention to help increase social competence for students with emotional and behavioral disorders (EBD), but there is limited research that addresses SST for students identified as experiencing EBD at alternative campuses. A mixed methods design was utilized to examine SST at an alternative campus for students identified as experiencing EBD. Pre-intervention data were collected for students' attendance, grades, office disciplinary referrals, and behavioral rating scales, after which the WhyTry SST program (Moore 2008 Moore, C. 2008. The WhyTry Program, Salt Lake City, UT: WhyTry.  [Google Scholar], WhyTry, Salt Lake City, UT, USA) was implemented. Following the intervention, the same data were collected. Non-parametric statistics guided the quantitative analysis, because of the small population being studied. Differences from pre- to post-intervention were examined. Students exhibited significant differences from pre- to post-intervention in the number of office disciplinary referrals and several areas on the behavioral rating scales. Triangulation methods drove the qualitative data collection through observations, student interviews, and teacher interviews. Insight into motivation and perceptions was gained through the qualitative analysis.