Approaches and practices in developing school mathematics textbooks in China

In this study, we aim to examine and discuss approaches and practices in developing mathematics textbooks in China, with a special focus on the development of secondary school mathematics textbook in the context of recent school mathematics reform. Textbook development in China has its own history. This study reveals some common practices and approaches developed and used in selecting, presenting and organizing content in mathematics textbooks over the years. With the recent curriculum reform taking place in China, we also discuss some new developments in compiling and publishing high school mathematics textbooks. Implications obtained from Chinese practices in textbook development are then discussed in a broad context.     

Education for Operational Research. A Practitioner's Viewpoint

University education for operational research in Britain is making great and welcome strides forward, but there has been little open discussion of its aims in relation to the advance of the profession. Progress in operational research, and in its application to the really worth-while problems of industry in particular, depends primarily on strengthening the industrial operational research group in its “front line” role. We need a research study of the teaching and practice of industrial operational research, in relation to effectiveness. We need “collaborative” programmes of operational research education in which the university and the industrial operational research group each contribute, in a man's training over a period of years, in the ways in which each is most competent. We need emphasis on “breadth” as well as “depth” in operational research education, and greater attention to the mutual contributions of operational research, teaching and practice, and the teaching and development of management. An impressionist sketch of a programme which might meet these needs is put forward for discussion of principles and feasibility.     

Socio-economic and cultural mediators of mathematics achievement and between-school equity in mathematics education at the global level

This paper aims at identifying and understanding how and to what extent socioeconomic and cultural factors mediate mathematics achievement and between-school equity in mathematics education among countries. First, under the assumption that equity and quality of education are independent constructs, the construct of equity-in-quality in mathematics education is developed. Second, the 18 countries that were identified in the previous work of the author Jurdak in (Toward equity in quality in mathematics education. Springer, New York, 2009) as being diverse in mathematics education will serve as study cases to illustrate, compare, and contrast the mediatory role of socio-economic and cultural factors in mathematics achievement and between-school equity in mathematics education. The results show that the differences in mathematics achievement and between-school equity in mathematics education at the country level are associated with, and can be accounted for in some cases, by socioeconomic and cultural factors.     

角蛋白16和17在部分表皮肿瘤中的表达和意义

目的 研究角蛋白16 和17（K16、K17）在部分表皮肿瘤中的表达和意义。方法 采用免疫组化法检测K16、K17在正常皮肤、脂溢性角化病、日光性角化病、皮角、基底细胞癌、鳞状细胞癌中的表达。结果 K16、K17 在正常皮肤表皮各层呈阴性表达;在脂溢性角化病表皮各层中除了角质层外大多呈阳性表达;在日光性角化病表皮K16 均不表达,K17 除了角质层外在其他各层也不表达;K16 在皮角表皮棘层呈强阳性表达,但在其他各层均呈阴性表达,K17 在皮角表皮各层基本呈阳性或强阳性表达;在基底细胞癌中,K16、K17除了在棘层呈弱阳性表达外,在其他各层均呈阴性表达;在鳞状细胞癌中,K16 在基底层呈阴性表达,但在其他各层及K17 在表皮全层均呈阳性或强阳性表达。K16 除基底层外在肿瘤表皮其他各层表达比较差异均有统计学意义（均P＜0.05）;K17 在表皮各层表达差异均有统计学意义（均P＜0.05）。结论 K16、K17的表达状况可为表皮肿瘤的鉴别诊断提供病理学方面的依据。     

政府花费改变对经济影响的理论分析

本文采用无限期内生时间偏好率模型,研究了政府花费对经济的影响.指出长期的政府花费增加可以使资本存量水平上升,消费水平下降和债券持有量上升;同时,短期分析表明政府花费增加可以减少初始投资率,增加政府债务率水平;但短期的政府花费增加同样导致资本存量水平上升,消费水平下降和债务水平的增加.     

Exploring gender factors related to PISA 2003 results in Iceland: a youth interview study

Students’ mathematical achievement in Iceland, as reported in PISA 2003, showed significant and (by comparison) unusual gender differences in mathematics: Iceland was the only country in which the mathematics gender gap favored girls. When data were broken down and analyzed, the Icelandic gender gap appeared statistically significant only in the rural areas of Iceland, suggesting a question about differences in rural and urban educational communities. In the 2007 qualitative research study reported in this paper, the authors interviewed 19 students from rural and urban Iceland who participated in PISA 2003 in order to investigate these differences and to identify factors that contributed to gender differences in mathematics learning. Students were asked to talk about their mathematical experiences, their thoughts about the PISA results, and their ideas about the reasons behind the PISA 2003 results. The data were transcribed, coded, and analyzed using techniques from analytic induction in order to build themes and to present both male and female student perspectives on the Icelandic anomaly. Strikingly, youth in the interviews focused on social and societal factors concerning education in general rather then on their mathematics education.     

“Do we teach subjects or students?” Analyzing science and mathematics teacher conversations about issues of equity in the classroom

Teachers involved in a Master's level course in diversity participated in virtual, synchronous, anonymized discussions around issues of ethnic and racial diversity, gender, and stereotypes that could impact their students’ participation in fields related to science, technology, engineering, and mathematics (STEM). Guided by theoretical frameworks from Social Cognitive Career Theory (SCCT) and Critical Race Theory (CRT), a convenience sample of 14 science and mathematics teachers participated in a series of virtual chats using open‐ended questioning and facilitated by two university instructors. Using conversation and critical discourse analyses, three primary themes emerged: understanding of issues related to stereotypes, encouragement of females and minorities to pursue careers in STEM, and the place for diversity discussions in science and mathematics classrooms. The teachers felt burdened by curricular and administrative constraints that inhibit their ability to participate in thought‐provoking critical conversations. The paper concludes with a discussion of ways teachers can assist in the STEM career identity development of their underrepresented females and students of color and calls for research that combines the key findings in SCCT and CRT to build confidence and capacity for teachers to effectively confront issues of racism, sexism, and stereotyping in science and mathematics classrooms.     

Interpretations of National Curricula: the case of geometry in textbooks from England and Japan

This paper reports on how the geometry component of the National Curricula for mathematics in Japan and in one selected country of the UK, specifically England, is interpreted in school mathematics textbooks from major publishers sampled from each country. The findings we report identify features of geometry, and approaches to geometry teaching and learning, that are found in a sample of textbooks aimed at students in Grade 8 (aged 13–14). Our analysis raises two issues which are widely recognised as very important in mathematics education: the teaching of mathematical reasoning and proof, and the teaching of problem-solving. In terms of the teaching of mathematical reasoning and proof, our evidence indicates that this is dispersed in the textbook in England while it is concentrated in geometry in the textbook in Japan. In terms of the teaching of mathematical problem-solving and modeling, our analysis shows that it is more concentrated in the textbook from England, and rather more dispersed in the textbook from Japan. These findings indicate how important it is to consider ways in which these issues can be carefully designed in the geometry sections of future textbooks.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

Problem solving and Working Mathematically: an Australian perspective

This article reviews “problem solving” in mathematics in Australia and how it has evolved in recent years. In particular, problem solving is examined from the perspectives of research, curricula and instructional practice, and assessment. We identify three key themes underlying observed changes in the research agenda in Australia in relation to problem solving: Obliteration, Maturation and Generalisation. Within state mathematics curricula in Australia, changes in the language and construction of the curriculum and in related policy documents have subsumed problem solving within the broader category of Working Mathematically. In relation to assessment, research in Australia has demonstrated the need for alignment of curriculum, instruction and assessment, particularly in the case of complex performances such as mathematical problem solving. Within the category of Working Mathematically, recent Australian curriculum documents appear to accept an obligation to provide both standards for mathematical problem solving and student work samples that illustrate such complex performances and how they might be assessed.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan

This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual knowledge and procedural knowledge of fractions in Taiwan and the United States. Participants were preservice teachers (N = 49) in a teacher education program in the United States and comparable Chinese preservice teachers (N = 47). Results indicated that Chinese preservice teachers performed better in procedural knowledge on fraction operations than American preservice teachers. No significant differences were found for conceptual knowledge on fraction division. Further, the correlation in this study showed that for Chinese and American preservice teachers, the relationship between conceptual and procedural knowledge of fraction operations was weak.     

Conception of expert mathematics teacher: a comparative study between Hong Kong and Chongqing

This paper reports the similarities and differences in how “expert mathematics teacher” is conceptualized by mathematics educators in Hong Kong and Chongqing, two cities in China which share similar but different cultural and social backgrounds. Thirty-seven mathematics education researchers, school principals with mathematics education background, and mathematics teachers were interviewed on their perceptions of expert mathematics teacher. It is found that in both cities an expert mathematics teacher should have a profound knowledge base in mathematics, teaching, and students; strong ability in teaching; and a noble personality and a spirit of life-long learning. As for differences, an expert mathematics teacher should have the ability to conduct research, mentor other teachers, and have profound knowledge of examination and educational theories in Chongqing. These attributes were not found in Hong Kong. These similarities and differences are discussed, and relevant social and cultural factors in the two contexts are examined.     

Progress and stagnation of gender equity: contradictory trends within mathematics research and education in Sweden

During the last decade women in Sweden have reduced men’s lead in participation in mathematics education and in professional careers as mathematicians. However, the development is uneven and slow overall. In some areas and at the highest levels women have increased their participation only marginally. Why, one may ask, is progress so slow after almost 20 years of active work from the Women and Mathematics movement in Sweden and within a society in which gender equity is highly valued at the societal and political levels? The development is described in quantitative measures going back 20 years. Several concrete and successful initiatives from the last decade intended to “de-gender” mathematics and to involve women and men alike in mathematics are described. In contrast a gender-blind position or a view of women as problems in mathematics seems to reign within some influential bodies.     

On linear functions of certain noncentral versions of independent gamma variables

A general Laplace transform and its inverse and their generalizations are considered in this article. This inverse contains the density functions of quadratic expressions in nonsingular as well as singular normal variables and a non-central version of linear functions of gamma variables, among others. Various representations of the inverse in power series, in gamma series, in Laguerre polynomials, in hypergeometric functions and in zonal polynomials are also discussed.     

An overview of the gender factor in mathematics in TIMSS-2003 for the Asia-Pacific region

This paper highlights the gender factor in the Trends in Mathematics and Science Study in 2003 (TIMSS-2003) of eight participating countries from the Asia-Pacific region: Chinese Taipei, Hong Kong-SAR, Indonesia, Japan, Republic of Korea, Malaysia, Singapore, and the Philippines (Chinese Taipei and Hong Kong-SAR will be referred to as countries in this paper.) in mathematics. The focus is on gender-related data encompassing the overall performance of students from the participating countries and their performance in the content and cognitive domains. At grade 8 level, the gender difference in the overall performance of students mirrored the international average and favored girls in all countries of the Asia-Pacific region (except in Japan and the Republic of Korea). The regional data also showed that, in general, the Philippines and Singapore can be considered to be at one extreme with gender differences favoring girls in both content and cognitive domains, and the Republic of Korea and to some extent Japan are at the other extreme with the gender differences favoring boys. At grade 4 level, girls from the Philippines and Singapore also performed better than the boys whereas the boys from Japan and Chinese Taipei did slightly better than the girls.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

Comparing the Development of Fractions in the Fifth‐ and Sixth‐Graders' Textbooks of Singapore,Taiwan, and the USA

This research examined the presentation of fractions in textbooks used by fifth and sixth graders in Singapore, Taiwan, and the United States. The specific textbooks examined were My Pals Are Here! Maths (MPHM) in Singapore; Kung Hsung (KH) in Taiwan; and Mathematics in Context (MiC) in the USA. Results show the problems posed in MiC put more emphasis on real‐life situations than KH textbooks in Taiwan and MPHM in Singapore. Designing materials that provide opportunities to connect mathematics content with applications in real life is consistent with recommendations from professional organizations. The activities in KH and MPHM tended to emphasize procedures, while the activities of MiC focused more on conceptual understanding and less on the development of procedures. An examination of the mathematics textbooks revealed that MPHM introduced and developed fractions the earliest among the three countries investigated and the content taught in MPHM was about one grade earlier than when the same content was experienced by students in KH and MiC.     

Scan Statistics on Enron Graphs

We introduce a theory of scan statistics on graphs and apply the ideas to the problem of anomaly detection in a time series of Enron email graphs. Previous presentation: Workshop on Link Analysis, Counterterrorism and Security at the SIAM International Conference on Data Mining, Newport Beach, CA, April 23, 2005. Carey E. Priebe received the B.S. degree in mathematics from Purdue University in 1984, the M.S. degree in computer science from San Diego State University in 1988, and the Ph.D. degree in information technology (computational statistics) from George Mason University in 1993. From 1985 to 1994 he worked as a mathematician and scientist in the US Navy research and development laboratory system. Since 1994 he has been a professor in the Department of Applied Mathematics and Statistics, Whiting School of Engineering, Johns Hopkins University, Baltimore, Maryland. At Johns Hopkins, he holds joint appointments in the Department of Computer Science and the Center for Imaging Science. He is a past President of the Interface Foundation of North America—Computing Science & Statistics, a past Chair of the Section on Statistical Computing of the American Statistical Association, and on the editorial boards of Journal of Computational and Graphical Statistics, Computational Statistics and Data Analysis, and Computational Statistics. His research interests are in computational statistics, kernel and mixture estimates, statistical pattern recognition, statistical image analysis, and statistical inference for high-dimensional and graph data. He was elected Fellow of the American Statistical Association in 2002. John M. Conroy received a B.S. in Mathematics from Saint Joseph's University in 1980 and a Ph.D. in Applied Mathematics from the University of Maryland in 1986. Since then he has been a research staff member for the IDA Center for Computing Sciences in Bowie, MD. His research interest is applications of numerical linear algebra. He is a member of the Society for Industrial and Applied Mathematics, Institute of Electrical and Electronics Engineers (IEEE), and the Association for Computational Linguistics. David J. Marchette received a B.A. in 1980, and an M.A. in mathematics in 1982, from the University of California at San Diego. He received a Ph.D. in Computational Sciences and Informatics in 1996 from George Mason University under the direction of Ed Wegman. From 1985–1994 he worked at the Naval Ocean Systems Center in San Diego doing research on pattern recognition and computational statistics. In 1994 he moved to the Naval Surface Warfare Center in Dahlgren Virginia where he does research in computational statistics and pattern recognition, primarily applied to image processing, text processing, automatic target recognition and computer security. Dr. Marchette is a Fellow of the American Statistical Society. Youngser Park received the B.E. degree in electrical engineering from Inha University in Korea in 1985, the M.S. degree in computer science from The George Washington University in 1991, and had pursued a doctoral degree there. From 1998 to 2000 he worked at the Johns Hopkins Medical Institutes as a senior research engineer. Since 2003 he is working as a research analyst in the Center for Imaging Science at the Johns Hopkins University. His research interests are clustering algorithm, pattern classification, and data mining.