河北省城镇居民收入现状与收入水平预测

通过对河北省城镇居民收入水平现状,历年收入结构变化,收入增长特征的实证分析,建立了城镇居民收入水平预测模型,为提高居民收入、合理调控收入差距提供科学的依据.     

Pre-service science teachers’ perceptions of mathematics courses in a science teacher education programme1

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers’ opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were ‘difficult’ because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers’ lack of knowledge in terms of teaching mathematics.     

Adolescent girls’ construction of moral discourses and appropriation of primary identity in a mathematics classroom

This qualitative study examines the way three American young adolescent girls who come from different class and racial backgrounds construct their social and academic identities in the context of their traditional mathematics classroom. The overall analysis shows an interesting dynamic among each participant’s class and racial background, their social/academic identity and its collective foundation, the types of ideologies they repudiate and subscribe to, the implicit and explicit strategies they adopt in order to support the legitimacy of their own position, and the ways they manifest their position and identity in their use of language referring to their mathematics classroom. Detailed analysis of their use of particular terms, such as “I,” “we,” “they,” and “should/shouldn’t” elucidates that each participant has a unique view of her mathematics classroom, developing a different type of collective identity associated with a particular group of students. Most importantly, this study reveals that the girls actively construct a social and ideological web that helps them articulate their ethical and moral standpoint to support their positions. Throughout the complicated appropriation process of their own identity and ideological standpoint, the three girls made different choices of actions in mathematics learning, which in turn led them to a different math track the following year largely constraining their possibility of access to higher level mathematical knowledge in the subsequent schooling process.     

Writing as a Tool to Demonstrate Mathematical Understanding

In this study, I examine how using a writers' workshop model in mathematics creates a space for students to write about their mathematical thinking and problem solving and how their writing impacts instruction. This case study of one classroom with one teacher spanned 6 weeks and included 18 implementations of an adapted version of the Writers' Workshop (WW) in a fourth‐grade mathematics class. On a biweekly basis, the data were reviewed and changes made to the model. The analysis of the students' writing revealed (a) their understandings and misunderstandings of the mathematical content, (b) their readiness for more challenging tasks, and (c) their connections to prior knowledge. Students used writing to demonstrate their understanding of mathematics and show their mathematical processes. In some cases, examining only the numerical work failed to illuminate the students' understanding, their writing provided deeper insight. Students recognized writing as a tool for learning; this was evident in interview responses.     

Novice facilitators’ changes in practices: From launching to managing discussions about mathematics teaching

Novice facilitators of professional development (PD) programs for mathematics teachers often face challenges in leading productive discussions and achieving the goals of these programs. Although research in this area is gradually accumulating, not much is known about how novice facilitators address these challenges and change their practices accordingly. This paper presents case studies of two novice facilitators of PD programs in two different countries. The analyses look at their work over one year, to illustrate the changes in their practices while managing discussions. The results show that although the facilitators operated in different contexts, their practices and their processes of change resembled, suggesting that these processes are not idiosyncratic. We argue that novice facilitators’ changes in practices correspond to changes in their resources, orientations, goals, and identities and that PD program teams can support these changes.     

A survey of mathematics undergraduates' interaction with proof: some implications for mathematics education

Proving is an essential activity in mathematics but there are serious difficulties encountered by mathematics undergraduates in engaging with proof in the intended way. This article presents an initial analysis of (i) a quantitative study of a large sample of UK mathematics undergraduates which describes their declared perceptions about proof, and (ii) a qualitative study of a subsample of these students which analyses their actual proof perceptions as well as their actual proof practices. A comparison is also made between their publicly declared perceptions of proof and their personal proclivities in proving.     

Children with mathematical difficulties cope with modelling tasks: what develops?

This study investigates the participation and knowledge growth of children with mathematical difficulties as they work in groups with their classmates on a year-long sequence of modelling tasks. It involves observations of a class of 23 fifth graders, 9 of whom were identified as having difficulties in mathematics. All the students worked for 8 months on a sequence of 12 modelling task in heterogeneous groups. The findings show a gradual growth in modelling competencies and mathematical knowledge of the students with mathematical difficulties together with an increase in their contribution to the group. The growth in modelling competencies involved their ability to analyse situations and the growth of mathematical knowledge was evident in offering mathematical ideas during group work and in a better posttest performance. Student reflections indicated their awareness of these changes and of the appreciation of their ideas by their peers.     

Undertaking data analysis of student outcomes as professional development for teachers

The study reports on collaborations with practitioners to examine the results of students’ performances on high stakes tests as a means to strengthen practitioners’ knowledge of probability and statistics and to empower their conduct of investigations on student performance. Four issues are summarized: the development of their statistical reasoning, their understanding of the meaning of and relationships among the concepts of validity, reliability and fairness as applied to testing, their introduction to the history of testing and its relationship to science, society and cultural inequality, and their reports of independent inquiries. Data on performance on pre- and post-tests demonstrate growth in teacher reasoning and in their professionalism in raising important issues about testing     

Volume, surface area and inward injectivity radius

We show some relations among the volumes of domains in Euclidean spaces, their surface areas and the inward injectivity radii from their boundaries. In particular, we give an estimate for the upper bound of the ratios of their surface areas and volumes by means of inward injectivity radii. The upper bound seems to depend on their topological structures.

     

Discrete finite element characterizations of source fields for volume and boundary constraints in electromagnetic problems

The consideration of electromagnetic field sources in potential formulations necessitates the definition of source fields. Such source fields are first defined for both volume and boundary constraints in static electromagnetic models. Then, automatic procedures are proposed to conveniently and efficiently characterize discrete source fields, with regard to their use in finite element formulations, their supports, their direct expression requiring no pre-computation, and their associated constraints. Two application examples are proposed to illustrate the approach.     

Coordination in Dynamic Social Networks Under Heterogeneity

People often make choices or form opinions depending on the social relations they have, but they also choose their relations depending on their preferred behavior and their opinions. Most of the existing models of coevolution of networks and individual behavior assume that actors are homogeneous. In this article, we relax this assumption in a context in which actors try to coordinate their behavior with their partners. We investigate with a game-theoretic model whether social cohesion and coordination change when interests of actors are not perfectly aligned as compared to the homogeneous case. Using analytical and simulation methods we characterize the set of stable networks and examine the consequences of heterogeneity for social optimality and segregation in emerging networks.     

Combinatorial Gelfand Models for Semisimple Diagram Algebras

We construct combinatorial (involutory) Gelfand models for the following diagram algebras in the case when they are semi-simple: Brauer algebras, their partial analogues, walled Brauer algebras, their partial analogues, Temperley-Lieb algebras, their partial analogues, walled Temperley-Lieb algebras, their partial analogues, partition algebras and their Temperley-Lieb analogues.     

Behind the Masks: Identifying Students' Competencies for Learning Mathematics and Science in Urban Settings

Three mathematics and science educators reexamine and reflect on their teaching within the context of the American Association for the Advancement of Sciences (AAAS) and National Council of Mathematics' call to make math and science education accessible to all. The paper highlights the importance of teachers reflecting on their teaching practices in order to create opportunities for their students especially those in the urban setting. The educators argue that teachers' reflection on their teaching can cause them to recognize and validate their students' ways of knowing as they identify the students' hidden/concealed abilities that are often masked by their behaviors. The educators discuss their experiences and highlight the lessons that they learned about ways to prepare teachers to successfully teach math and science students in urban settings. Culturally responsive pedagogy and cultural competency are critical skills that teachers need to develop in order to teach all children, especially those in the math and science classroom in the urban setting.     

Changes in Student Attitudes Regarding Science When Taught by Teachers Without Experiences With a Model Professional Development Program

This study focuses on two main issues concerning changes in student attitudes toward science study and their perceptions of its usefulness in their lives. Information has been gathered concerning how student attitudes toward science have changed for teachers and schools not involved with any funded professional development project. Pretesting and posttesting were administered with such “control” groups at the same intervals corresponding with the data collected from students with teachers enrolled in five funded Professional Development projects over the 1981–2008 interim. The grade levels used by the National Assessment of Education Progress in their 1977 assessment of science were used; it focused on students in grades 3, 7, and 11. The results indicate a steady decline in student positive attitudes concerning their science study as grade levels increase. Conversely, the student perceptions of the usefulness of their science study as related to daily living, further science study, and for potential careers remained much the same over the 30‐year interim is a second focus. Generally, results indicate that traditional teaching and major use of textbooks cause increasingly negative student attitudes about science while not producing major changes in their perceptions of its usefulness in their lives.     

拟共形映射的重值

本文建立了一个关于拟共形射重值的基本不等式,应用它研究了涉及其重值的亏量关系,充满圆及Ｂｏｒｅｌ方向。     

Morgan-Mercer-Flodin模型和Weibull模型的拟合

Morgan-Mercer-Flodin模型和 Weibull模型是两个著名的四参数 S形生长模型 .在一定的正则变换下 ,它们的隐函数方程及未线性化参数与拐点特征之间的联系都非常相似 .从而可用完全相同的方法对它们的未线性化参数初始值进行搜索 ,以拟合隐函数曲线的 GNL法对它们进行最小二乘拟合 .还用实例对这种算法进行了验证 .     

Mathematics in engineering programs: what teachers with different academic and professional backgrounds bring to the table. An institutional analysis

ABSTRACT

In this paper, we examine how differences in the academic and professional backgrounds of engineering teachers shape their personal relationship to the use of mathematics in engineering practices, and whether these differences affect some of their practices. The analyses herein are based on an institutional perspective and employ Chevallard's anthropological theory of the didactic (ATD). We interviewed two teachers in an engineering programme to identify specific elements of their practice that could be attributable to the mobilisation of knowledge and skills derived from their distinct academic backgrounds and experience. The results indicate that the teachers mobilise different tasks, techniques, and technologies in many of their practices, and that they take different approaches to using mathematics and applying rigour.     

Australian teachers’ views of effective mathematics teaching and learning

Thirteen Australian teachers who had been nominated by their professional mathematics teachers’ associations as excellent teachers of elementary school mathematics were interviewed on their beliefs about mathematics, mathematics learning and mathematics teaching. In particular, they were asked to discuss the characteristics of effective teachers of mathematics and excellent mathematics lessons. In spite of their differences in location, experience and teacher education, the teachers displayed a lot of consistency in their responses and in their lists of characteristics. While this group of teachers cannot be claimed to be representative of Australian teachers, they have provided a snapshot of what is regarded as effectiveness in mathematics education in Australian elementary schools.     

Expert Assessment of Examination Grades

This paper investigates the abilities of a group of experts to produce subjective probabilities on the likelihood of their students obtaining various grades in their final-year examinations. We examine the calibration of these experts, and how their ability to forecast depends on experience and assessment procedures. We find that these well-motivated and statistically literate assessors, working in their field of expertise, still suffer from the types of assessment problems noted in previous studies on more naive subjects.