求分项分式的各项分子的系数的新方法

本文提出并证明了一组求分项分式的各项分子的系数的公式,称之为公式法.从而大大简化了分式分项的计算,简化了有理真分式的积分运算.     

一类特殊的纯循环连分数的收敛性判定

纯循环连分数的收敛性是一个很复杂的问题,实二次无理数的无限简单连分数一定可以表为一个循环连分数,循环连分数一定收敛于一个实二次无理数.但对于一般的循环连分数,无法计算出这个收敛值.这里介绍一种使用特征方程的方法,来计算一类特殊的纯循环连分数的收敛值,针对这类特殊的纯循环连分数的收敛性做了一个定量的结论.     

Learning at every age? Life cycle dynamics of adult education in Europe

Adult learning is seen as a key factor for enhancing employment, innovation and growth. The aim of this paper is to understand the points in the life cycle at which adult learning takes place and whether it leads to reaching a medium or high level of educational attainment. We perform a synthetic panel analysis of adult learning for cohorts aged 25–64 in 27 European countries using the European Union Labour Force Survey. We find that investment across the life cycle by cohorts older than 25 still occurs: participation in education and training as well as educational attainment increase observably across all cohorts. We also find that the decline with age slows down, or is even reversed for older cohorts, for both participation in education and educational attainment. Finally, we can identify cross-country differences in approach. In Nordic countries, adult learning is achieved primarily through participation in education and training without adding to formal educational attainment. In central Europe, adult learning occurs primarily in the form of increasing educational attainment. In Ireland and the UK, a combination of both approaches to adult learning is observable.     

Study of fractions in elementary mathematics textbooks from Finland and Taiwan

This study examines the different ways in which fractions are dealt with in two elementary mathematics textbook series: Kang Hsuan (KH) in Taiwan and Laskutaito in Finland. The results showed that the total number of fraction questions in Laskutaito is higher than that in KH and that Laskutaito highlights the basic definition of fractions to help children develop higher levels of reasoning. Fraction questions in Laskutaito were presented with a number of pictorial representations to clarify the concepts. Laskutaito includes more symbolic representation of questions. Moreover, the questions posed in the Laskutaito reflect real-life situations, whereas the questions posed in KH do not connect with real life. The implications of this study are discussed and suggestions for future studies are made in this paper.     

健美操对中年人健康的影响

健美操是一项集锻炼、娱乐、陶冶、交往、休闲、欣赏于一体的综合性体育活动,是非常适合中年人需求特点的一项运动,对中年人的身体健康和心理健康都有着积极作用.本文通过1年对39名中年人参加健美操活动情况的追踪调查,从生理、心理、音乐和社会的角度研究了健美操活动对中年人身心健康的影响.     

试论生物学教学中语言能力的培养

学生在生物学知识语言中表达欠准确，是生物学教学中的“老大难”问题。这在各类测试中增大了过失性失分。怎样提高学生的生物学语言表述能力是学生能力提高的重要一环。本从概念字的生物学取意、知识点关键词的分析、各表述形式的转换、语言表述的强化四个方面作了探索。     

Coping,confidence and alienation: the early experience of trainee teachers in English further education

Summer 2009 saw the introduction in England of the Masters in Teaching and Learning (MTL). Funded in full by the Training and Development Agency for Schools, the MTL aims to improve the quality of teaching and to raise standards in schools. In this paper we discuss what the MTL might mean both for in‐service teacher education and initial teacher training. We explore issues relating to the structure and delivery of MTL including the tension between standardisation and personalisation of its content as well as the lack of focus on research and the costs of this to its reputation and appeal of the qualification. Furthermore, we question the extent to which newly qualified teachers are ready to benefit from undertaking the MTL and consider how availability criteria may give rise to equity issues. With these concerns in mind we discuss the future of the MTL and whether this Labour initiative will have a chance to prove itself under a Conservative‐led coalition government at a time of severe austerity.     

Back to the Drawing Board

Teachers can conduct action research by taking what they are doing in their classrooms and leveraging it to help drive the performance of the school community. The authors present the action research process, mirrored with an in-depth example, and the opportunities to become teacher leaders. Sample action research questions are provided to help teachers generate their own ideas. Also, guiding questions at each stage of the action research process support teachers and help refine their thinking.     

Tracing the development of representational flexibility and problem solving in fraction addition: a longitudinal study

The study models the development of students’ multiple-representation flexibility and the use of problem-solving strategies and representations in fraction addition. A test administered three times, with breaks of 3–4?months between successive measurements to 108 students at a transition within primary school (Grade 5–6), 132 students at a transition from primary to secondary education (Grade 6–7) and 148 students at a transition within secondary school (Grade 7–8). Multivariate analysis of variance for repeated measures and dynamic structural equation modelling were carried out in order to analyse the data. Findings suggested that students’ performance improve through measurements. Dynamic modelling provided evidence for the strong interrelation between representational flexibility and problem solving at the three measurements. The results indicated the students’ established pre-existent knowledge and the important role the initial state of the aforementioned cognitive parameters plays on their advancement. Didactical implications are discussed.     

Diophantine方程a^4x（x＋1）（x＋2）（x＋3）=y（y＋1）（y＋2）（y＋3）

设a是大于1的正整数.本文运用初等数论方法证明了:方程a4x(x+1)(x+2)(x+3)=y(y+1)(y+2)(y+3)无正整数解(x,y).