Providing a Foundation for Deductive Reasoning: Students' Interpretations when Using Dynamic Geometry Software and Their Evolving Mathematical Explanations

A key issue for mathematics education is howchildren can be supported in shifting from `because it looks right' or`because it works in these cases' to convincing arguments which work ingeneral. In geometry, forms of software usually known as dynamicgeometry environments may be useful as they can enable students tointeract with geometrical theory. Yet the meanings that students gain ofdeductive reasoning through experience with such software is likely to beshaped, not only by the tasks they tackle and their interactions with theirteacher and with other students, but also by features of the softwareenvironment. In order to try to illuminate this latter phenomenon, and todetermine the longer-term influence of using such software, this paperreports on data from a longitudinal study of 12-year-old students'interpretations of geometrical objects and relationships when using dynamicgeometry software. The focus of the paper is the progressivemathematisation of the student's sense of the software, examining theirinterpretations and using the explanations that students give of thegeometrical properties of various quadrilaterals that they construct as oneindicator of this. The research suggests that the students' explanations canevolve from imprecise, `everyday' expressions, through reasoning that isovertly mediated by the software environment, to mathematicalexplanations of the geometric situation that transcend the particular toolbeing used. This latter stage, it is suggested, should help to provide afoundation on which to build further notions of deductive reasoning inmathematics.This revised version was published online in September 2005 with corrections to the Cover Date.     

West Nile Virus: Using Adapted Primary Literature in Mathematical Biology to Teach Scientific and Mathematical Reasoning in High School

This paper promotes the use of adapted primary literature as a curriculum and instruction innovation for use in high school. Adapted primary literature is useful for promoting an understanding of scientific and mathematical reasoning and argument and for introducing modern science into the schools. We describe a prototype adapted from a published article on a mathematical model of the spread of the West Nile virus in North America. The prototype is available as a web-based resource that includes supplemental pedagogical units. Preliminary feedback from use of the prototype in two classrooms is described and a sketch of an ongoing formal evaluation is provided.     

Using Propensity Scores for Estimating Causal Effects: A Study in the Development of Moral Reasoning

The purpose of this study was to illustrate the use of propensity scores for creating comparison groups, partially controlling for pretreatment course selection bias, and estimating the treatment effects of selected courses on the development of moral reasoning in undergraduate students. Specifically, we used a sample of convenience for comparing differences in moral reasoning development scores among students enrolled in intergroup dialogue, service learning, psychology and philosophy courses with those of an introductory sociology course. Adopting a propensity score approach included reviewing the empirical literature for its guidance in substantiating the reasons for including pretreatment variables (i.e., pretreatment course-taking behaviors, race, sex, political identification, need for cognition, major, age, pretreatment moral reasoning scores) in our analysis, measuring these variables, and reducing them into a single composite propensity score for each student in our analytic sample. This score then served as the basis for creating a new comparison group and for allowing us to estimate unbiased (or less biased) course-related treatment effects on moral reasoning development. Implications for higher education researchers are discussed.

义务教育阶段学生数学符号意识发展水平的实证研究

数学符号意识是我国义务教育阶段学生的一种数学核心素养,在国际数学教育中,各国也非常重视学生数学符号意识的培养。通过测评,得出以下结论:义务教育阶段学生数学符号意识发展水平随着年级的增长不断升高,具体可以划分为四个发展水平,即经验观察水平、本质内化水平、理性辩证水平、结构普适水平,并在四个分析层次上逐渐分布均衡。     

让教辅书成为大学生自主学习的好帮手——全新版《大学英语》教辅书对大学生自主学习的冲击及其对策

文章对目前大学生使用全新版《大学英语》教辅书情况进行了调查和分析,指出了学生利用教辅书进行自主学习存在的问题,并提出了相应建议和对策,以引导学生科学合理地使用教辅书,使其真正成为学生自主学习的好帮手。     

高等代数与解析几何两课合并的可行性分析及内容编排方案

阐述了高校数学专业高等代数与解析几何这两门基础课在教学内容方面的重复与联系之处 ,对这两门课程合并教学进行了可行性分析 ,提出了两门课程合并内容编排的原则和方案     

Scientific Reasoning,School Achievement and Gender: a Multilevel Study of between and within School Effects in Finland

The relationships between reasoning and school achievement were studied taking into account the multilevel nature (school- and class-levels) of the data. We gathered data from 51 classes at seven schools in metropolitan and Eastern Finland (N = 769, 395 males, 15-year-old students). To study scientific reasoning, we used a modified version of Science Reasoning Tasks, tapping control-of-variable schemata. Analyses were conducted by MLwiN2.10 multilevel modelling. The present results showed that the intra-class correlation coefficient (ICC) of schools for scientific reasoning is 7% and that the corresponding ICC of classes is 10%. Whereas the first finding confirms earlier PISA results, the second finding provides new insights into class variation within schools. In practice, class composition seems to be an efficient solution to meeting the differing needs of individual students.     

Metacognitive activities in text-studying and problem-solving: Development of a taxonomy

This article describes the construction of a hierarchical taxonomy of metacognitive activities for the interpretation of thinking-aloud protocols of students in secondary education, who studied texts on history and physics. After testing an initial elaborate taxonomy on a restricted number of protocols by multiple raters, it appeared that the interrater correspondence was well below par. The categories in the taxonomy were too highly specified. Categories were combined and tested on new protocols in a cyclic fashion. The revised taxonomy was then used for coding 16 history protocols and 16 physics protocols. Frequencies of occurrence of metacognitive activities were obtained, as well as judgements of the quality of the metacognitive activities of the participants. There is a reasonable correlation between the frequency method and the quality method for coding thinking-aloud protocols. Also, there is a substantial covariation of the number of metacognitive activities across both tasks.     

Phonological Awareness and Rapid Automatized Naming Predicting Early Development in Reading and Spelling: Results from a Cross-Linguistic Longitudinal Study

In this study, the relationship between latent constructs of phonological awareness (PA) and rapid automatized naming (RAN) were investigated and related to later measures of reading and spelling in children learning to read in different alphabetic writing systems (i.e., Norwegian/Swedish vs. English). 750 U.S./Australian children and 230 Scandinavian children were followed longitudinally between kindergarten and 2nd grade. PA and RAN were measured in kindergarten and Grade 1, while word recognition, phonological decoding, and spelling were measured in kindergarten, Grade 1, and Grade 2. In general, high stability was observed for the various reading and spelling measures, such that little additional variance was left open for PA and RAN. However, results demonstrated that RAN was more related to reading than spelling across orthographies, with the opposite pattern shown for PA. In addition, tests of measurement invariance show that the factor loadings of each observed indicator on the latent PA factor was the same across U.S./Australia and Scandinavia. Similar findings were obtained for RAN. In general, tests of structural invariance show that models of early literacy development are highly transferable across languages.     

Argumentation and Conceptualization in Context: a Case Study on Sunshadows in Primary School

I will analyse the individual and collective activities of fourth grade students while trying to explain a schoolfellow's mistake in the use of a geometrical schema (shared by the class) of the sunshadows phenomenon. The study aims at detecting productive links between context-related argumentation, mathematical modelling (here concerning sunshadows) and conceptualization (inclination of a straight line to a plane), as well as discussing their relevance for mathematics education. This revised version was published online in July 2006 with corrections to the Cover Date.     

从视频研究透视课堂教学对学生学习的影响及其路径——基于GTI视频研究上海数据的实证分析

教学的有效性是教育研究的一个核心议题,而相关的课堂教学研究大多基于间接性的课堂数据,使得教师效应长期处于“黑箱”状态.本研究利用OECD发布的全球教学洞察(GTI)视频研究对教师和学生的课堂行为进行的教学视频观测而生成的实证数据,聚焦中国上海的初中数学课堂,探析特定的教师课堂教学实践对其学生的学习兴趣、自我效能和成绩的...     

Changes in and Stability of Cardiovascular Responses to Behavioral Stress: Results from a Four-Year Longitudinal Study of Children

This study examined the changes in and stability of cardiovascular responses to behavioral stress among 132 children in a 4-year longitudinal study. Children's heart rate and blood pressure were measured at rest and while performing 3 tasks: serial subtraction, mirror image tracing, and isometric exercise. This procedure was followed at study entry when children were in grades 2-12 (ages 6-18 years) and at follow-up when children were in grades 6 through post-high school (ages 11-21 years). Results showed that blood pressure and heart rate responses during the tasks were reliable across time for all measures except heart rate responses during isometric exercise. Systolic blood pressure responses to all tasks increased with age for boys, but not for girls. These results support the notion that cardiovascular responses to behavioral stress are a stable individual difference variable.     

Language factors associated with achievement grouping in math classrooms: a cross-sectional and longitudinal study

The study examines the effects of classroom achievement grouping (AG) practices on the early mathematics performance of language-minority students and compares their mathematics achievement to that of English-speaking majority students. Using a nationally representative database of the USA, both cross-sectional and longitudinal analyses were done. In the cross-sectional analyses we explored the direct effect of grouping practice on students performance, while in the longitudinal analysis we looked at the growth trajectory in mathematics learning. The results of cross-sectional analyses indicated that the effect of AG was negative on the math achievement in 1st and 5th graders. The longitudinal analysis showed a significant negative effect of AG for English Language Learners (ELL). The paper provides the basis for practical guidelines for the grouping practices in mathematics.     

“泉州模式”的形成：社会资本视角的分析

社会资本是解释一个国家或者地区社会经济发展的重要因素。“泉州模式”的形成与发展是我国制度转型背景下泉州地方政府、人文传统、海外联系等因素共同作用的结果。特别是泉州社会资本在“泉州模式”形成过程中起了重要的作用。泉州侨乡的族缘社会资本、侨缘社会资本和业缘社会资本主要通过信任机制、信息机制和认同机制塑造了“泉州模式”“以侨资、侨力为依托”、“以股份合作制为主体”、“以国内外市场为导向”等特点。     

Growth in Students' Attitudes About the Utility of Science Over the Middle and High School Years: Evidence from the Longitudinal Study of American Youth

The purpose of this paper is to track changes in students' attitudes about the utility of science over the middle and high school years using data from the Longitudinal Study of American Youth (Miller, J. D., Hoffer, T., Suchner, R. W., Brown, K. G., and Nelson, C. (1992). LSAY code book: student, parent, and teacher data for 1992 cohort two for longitudinal years one through four (1987–1991). Northern Illinois University, Illinois. Latent variable growth modeling is the technique that was used to examine the growth in students' attitudes about the utility of science. The results of the present study show that the overall trend for students' attitudes about the utility of science is positive. This means that middle and high school students have fairly positive attitudes about the usefulness of science. It is clear from the present analysis that some of the important predictors of attitudes about the utility of science include science self-concept, teacher encouragement of science, and to a lesser extent achievement motivation and science activities. The effects of the peer and parent variables were found to be quite small and statistically nonsignificant. Also it was found that the time-invariant predictors were not statistically significant. Latent variable growth modeling allows one to examine change in attitudes and also examine the effects of time-varying and time-invariant predictors. Substantive and methodological implications of this technique are also discussed.     

课程:"跑道"变"在跑道上跑"——解读后现代课程理论对我国当前课程改革的启示

"课程"一词源于拉丁语,原意指"跑道"。后现代课程理论作为一种新的思维方式和新的视角,从课程的本质、课程目标与内容的选择到课程实施中的师生关系以及课程评价诸方面,都需要我们重新追问课程的内涵,对当前我国的新课程改革有着多方面的启示。     

Variations on Modernisation: Technological Development and Internationalisation in Local Swedish School Policy From 1950 to 2000

ABSTRACT

Since WWII, Sweden has had an international reputation for being modern and progressive, with schooling that provides equal opportunities for all children. Analysing local enactment of the national pursuit of modernisation in two contrasting municipalities, this paper offers new perspectives on Swedish education history beyond the image of schooling as a uniform national project. The concepts of technological development and internationalisation are applied to capture the ideas and visions inherent in this modernisation. The study demonstrates, through the example of the rural municipality of Tierp and the municipality of Stockholm, the complexity of the modernisation process and the interplay between divergent interpretations of national reforms and local enactment of modernisation.     

Nationalistic Education in a Post-colonial Age: the Impact of Study Trips to China and the Development of Hong Kong Students' National Identity

With the return of its sovereignty to the People's Republic of China (PRC) on 1 July 1997, Hong Kong attained a new political status as a Special Administrative Region. Hong Kong students, under British rule, had long been receiving de-politicised education, and a sense of belonging to China was limited to the cognitive domain of Chinese history. The ideal of promoting national identity, underpinned in the current civic education curriculum, is proving to be a difficult task. While much literature has documented how curriculumbased educational practices fail to instil students with such an identity, little study has been undertaken to suggest effective alternatives and to examine how they work. This paper reports a study investigating the impact of study trips on developing students' national identity. Through observation and interviews, it takes an in-depth look into students' experience, into how they identify with a Chinese identity. Results indicate that though the study trips help to nurture the cognitive and affective dimensions of national identity, there are limits and possibilities involved. This paper concludes with reminders which teachers should have taken into account when thinking of using co-curricular activities to address the legitimate need of fostering nationalistic education.     

Reading and writing from multiple source documents in history: Effects of strategy instruction with low to average high school writers

This study examined the effects of historical reasoning strategy instruction on 11th-grade students. Students learned historical inquiry strategies using 20th Century American history topics ranging from the Spanish-American war to the Gulf of Tonkin incident. In addition, students learned a pre-writing strategy for composing argumentative essays related to each historical event. Results indicate that in comparison to a control group (N = 79), essays written by students who received instruction (N = 81) were longer, were rated as having significantly greater historical accuracy, were significantly more persuasive, and claims and rebuttals within each argument became more elaborated. Importantly, students in the control group read the same primary and secondary source document sets, and received feedback on written essays on the same topics.     

Transforming practice in Design and Technology: evidence from a classroom-based research study of students' responses to an intervention on inclusive design

This article offers evidence from a classroom-based research study in English secondary schools which developed an innovative approach to teaching in Design and Technology based on inclusive design (also known as universal design). The research evidence highlights how creative, problem-solving approaches in Design and Technology can be used to provide authentic, engaging learning experiences for students. This study, entitled ‘Designing our Tomorrows', introduced secondary school teachers and students to the principles and practices of inclusive design through an intervention using specially designed resources. In this article, findings from the study's qualitative pre- and post-intervention interviews are presented to illustrate how this type of approach can stimulate students' creativity and understanding of design.