Epistemological beliefs concerning the nature of mathematics among teacher educators and teacher education students in mathematics

Beliefs constitute a central part of a person’s professional competences as beliefs are crucial to the perception of situations and as they influence our choice of actions. The present article focuses on epistemological beliefs about the nature of mathematics among future teachers and their educators at university and post-university teacher-training institutions in Germany. The data reported are part of a larger sample originating from the MT21 study [supported by the National Science Foundation through a grant to W. S. Schmidt and M. T. Tatto (REC-0231886). MT21 started in 2003] which explores and compares mathematics teacher education in Bulgaria, Germany, Mexico, South Korea, Taiwan, and the United States. In this article, we examine the structure and level of beliefs concerning the nature of mathematics for teacher education students in Germany both at the beginning (n = 368) and the end of their education (n = 286) as well as their educators (n = 77) in three academic disciplines (mathematics, mathematics pedagogy and general pedagogy). In the first part of the article, the literature on epistemological beliefs and their structure will be reviewed. In the empirical part, analyses on the level and the structure of beliefs for our samples and subsamples will be presented. Relations between educators’ and students’ beliefs will be explored.     

Towards an Organizational Model of Attitude Change

Building on the growing literature that views organizations as complex adaptive systems, this paper proposes a general model to analyze the relationship between organizational context and attitudes. In particular, we focus on how the system of formal and informal communication channels that characterize an organization and the timing of information flows affect the dynamic process of attitude change. We also use a stylized version of the model to illustrate how the general framework is able to generate insights that are relevant to particular situations.     

The Social Embeddedness of Academic Online Groups in Offline Networks as a Norm Generating Structure: An Empirical Test of the Coleman Model on Norm Emergence

This paper analyzes two questions. First, under which conditions does a norm emerge in academic online groups that prescribes members to help others during group discussions? Second, what effects does such a norm, and other social conditions, have on the contributing behavior of researchers during online discussions? It is argued that the Coleman model (1990) on the emergence of norms points to an important condition that facilitates the realization of such a norm. According to the Coleman model (1990) a dense network among members of a group tends to strengthen a group norm. The paper makes a distinction between different kinds of academic online groups. The criterion of the distinction is the extent to which within the membership a highly integrated research community exists. An online group with a highly integrated research community is called to have a high degree of social embeddedness of its online communication in offline networks. It is hypothesized that a high degree of embeddedness has a number of effects. A higher degree of embeddedness leads to a stronger help-prescribing norm. The stronger the norm the more researchers send online answers to questions of their co-members during public online discussions. Furthermore, a high degree of embeddedness increases the answering behavior of researchers directly because it provides opportunities to gain reputation within the academic community through contributing to the discussion. The study makes use of data that consist of a combination of survey data and observed data of the communication behavior of researchers in about 50 international academic emailing lists. The results provide evidence for the expected effect of embeddedness on the strength of the norm and for the effect of embeddedness on the answering behavior of researchers. The strength of the help-prescribing norm indirectly influences the answering behavior.     

Seeking mathematics success for college students: a randomized field trial of an adapted approach

Many students enter the Canadian college system with insufficient mathematical ability and leave the system with little improvement. Those students who enter with poor mathematics ability typically take a developmental mathematics course as their first and possibly only mathematics course. The educational experiences that comprise a developmental mathematics course vary widely and are, too often, ineffective at improving students’ ability. This trend is concerning, since low mathematics ability is known to be related to lower rates of success in subsequent courses. To date, little attention has been paid to the selection of an instructional approach to consistently apply across developmental mathematics courses. Prior research suggests that an appropriate instructional method would involve explicit instruction and practising mathematical procedures linked to a mathematical concept. This study reports on a randomized field trial of a developmental mathematics approach at a college in Ontario, Canada. The new approach is an adaptation of the JUMP Math program, an explicit instruction method designed for primary and secondary school curriculae, to the college learning environment. In this study, a subset of courses was assigned to JUMP Math and the remainder was taught in the same style as in the previous years. We found consistent, modest improvement in the JUMP Math sections compared to the non-JUMP sections, after accounting for potential covariates. The findings from this randomized field trial, along with prior research on effective education for developmental mathematics students, suggest that JUMP Math is a promising way to improve college student outcomes.     

以《常微分方程》课程为例浅谈教学也是一种学术

为社会发展培养高素质的人才是高校教师的主要职责,这需要学校、乃至教师在教学理念、教学手段和教学形式、培养模式和教学研究等方面进行全方位思考,还应加强教学学术发展的制度保障,促进教学与科研的协调发展．本文以常微分方程课程为例,阐明教学与科研一样也是学术这一观点。     

关于空间解析几何的学术形态和教育形态

空间解析几何知识需要形式化的表述,而学生掌握空间解析几何知识需要经过思考,需要追根求源．作为教师,必须善于将空间解析几何的学术形态转化为教育形态,激发学生的学习兴趣和主动性．结合自己在空间解析几何教学实践中的体会,给出了一些实例．     

Development of an attitude-towards-using-mathematics scale for high-school students and an analysis of student attitudes

ABSTRACT

This research has been carried out in two stages and has two main objectives. The first aim of the study is to develop a Likert-type scale which is used to determine the attitudes towards the use of mathematics in real life. The second aim is to examine the attitudes of high school students about the use of mathematics in real life according to different variables used in the developed scale. The research was carried out according to the correlational research method, and the participants comprise the sample of 340 and 356 students for the scale development and implementation stages of the study, respectively. As a result of the research, a structure consisting of 23 items and three sub-factors was determined for the scale. In the second stage of the study, it was observed that the student attitudes were at the level corresponding to the ‘undecided’ option of the scale, and they differed significantly according to gender and grade level variables. In addition, it was found that there was a positive and significant relationship between the students’ attitudes towards the use of mathematics and their mathematics achievement.     

A study of the difficulties experienced with mathematics by engineering students in higher education

This paper describes a study undertaken to investigate the problem of the lack of mathematical expertise demonstrated by polytechnic engineering students. The study is based on a multiple‐choice diagnostic mathematics test, designed for the purpose, which was taken by incoming engineering students over a period of five years. The test aims to identify particular areas of difficulty. These difficulties are analysed and suggestions are made regarding their cause and alleviation. It has been confirmed that there is cause for concern at the overall mathematical ability of the students and it has been possible to identify certain areas of mathematics which appear to be difficult to a large proportion of students. It has also been possible to identify some of the common errors made by students in certain topic areas. Some suggestions have been made regarding the implications for teaching.     

Teachers learning the registers of mathematics and mathematics education in another language: an exploratory study

Many mathematics teachers around the world teach in a language different from the one in which they studied or completed their teacher education. Often these teachers must learn both the registers of mathematics and of mathematics education to teach in the additional language. This paper examines the factors that help teachers to learn these registers in Māori, the Indigenous language of New Zealand. Many of these teachers are second-language learners of the Māori language and attended English-medium schools and teacher-education programmes. After a brief discussion about the key role of language in teaching mathematics, this paper examines data from teachers at two Māori-immersion schools and a professional development facilitator. The analysis provides initial understanding of the factors that support or hinder their learning of the mathematics registers. Finally, a research agenda is suggested for further investigation of this issue.     

Kaizen teaching and the learning habits of engineering students in a freshman mathematics course

Which are the teaching methods that actually contribute to the learning of mathematics? The answer to this certainly is the holy grail of didactic and pedagogy, and should be supported by large scale statistical evidence. Our article aims at providing an initial step into this direction by first illustrating a teaching paradigm that is suited for the generation of large scale data sets: based on industry best practice quality assurance standards we introduce the Kaizen teaching paradigm which enforces Kolb’s reflective learning cycle on the students’ side. Second, we present and analyze the data we obtained through our pilot implementation at a engineering freshman mathematics course in the Sultanate of Oman. These emphasize the effectiveness of Kaizen teaching and once again show the necessity of continuous learning. A practice that seems to be forgotten in traditional university engineering courses due to the mere size of the audience. In particular it seems that a Markovian estimator for students’ performance may have to be considered.     

The Mathematics Attitudes and Perceptions Survey: an instrument to assess expert-like views and dispositions among undergraduate mathematics students

One goal of an undergraduate education in mathematics is to help students develop a productive disposition towards mathematics. A way of conceiving of this is as helping mathematical novices transition to more expert-like perceptions of mathematics. This conceptualization creates a need for a way to characterize students' perceptions of mathematics in authentic educational settings. This article presents a survey, the Mathematics Attitudes and Perceptions Survey (MAPS), designed to address this need. We present the development of the MAPS instrument and its validation on a large (N = 3411) set of student data. Results from various MAPS implementations corroborate results from analogous instruments in other STEM disciplines. We present these results and highlight some in particular: MAPS scores correlate with course grades; students tend to move away from expert-like orientations over a semester or year of taking a mathematics course; and interactive-engagement type lectures have less of a negative impact, but no positive impact, on students' overall orientations than traditional lecturing. We include the MAPS instrument in this article and suggest ways in which it may deepen our understanding of undergraduate mathematics education.     

Strategic planning decisions in an R & D setting

Strategic planning, by nature, is concerned with the organization's interaction with its environment and is normative because it deals with organizational motives and self image. The salient problem confronting strategic planning is to reflect the abstract and implicit value system held by management within a disciplined and informed analytical methodology.The Gas Research Institute has developed a strategic planning process, centered upon the annual development of a projection of the U.S. energy/economic situation. The process, which requires collaboration of top management and analytical staff, brings current environmental data and sophisticated methodology to bear on the outlook for the gas industry and gas-related technologies, but it ensures that analytical judgements will be influenced and, if necessary, overriden by current management values. Contradictions between managament perceptions and objective analysis are raised and resolved in an explicit process.     

Impact of first-year mathematics study groups on the retention and graduation of engineering students

Many interventions have been proposed to improve the retention and graduation rates of engineering students. One such intervention is to use study groups for first-year college students; such groups provide a structured environment in which the students can learn course material from each other outside of class and can provide the students with a sense of community. In this paper, we report on the impacts fostered by study groups in first-year mathematics courses on the odds of retaining and graduating engineering students. Students who participated in the study groups are compared to students of similar academic preparation who did not participate in such groups. It is found that student participation in study groups is significantly associated with the higher odds of being retained in engineering studies through the first 3 years of college. The results reported here are not as certain for the effect of study group participation on 5-year graduation odds for engineering students and some possible reasons for this are discussed.     

Crossing minimization in extended level drawings of graphs

The most popular method of drawing directed graphs is to place vertices on a set of horizontal or concentric levels, known as level drawings. Level drawings are well studied in Graph Drawing due to their strong application for the visualization of hierarchy in graphs. There are two drawing conventions: Horizontal drawings use a set of parallel lines and radial drawings use a set of concentric circles.In level drawings, edges are only allowed between vertices on different levels. However, many real world graphs exhibit hierarchies with edges between vertices on the same level. In this paper, we initiate the new problem of extended level drawings of graphs, which was addressed as one of the open problems in social network visualization, in particular, displaying centrality values of actors. More specifically, we study minimizing the number of edge crossings in extended level drawings of graphs. The main problem can be formulated as the extended one-sided crossing minimization problem between two adjacent levels, as it is folklore with the one-sided crossing minimization problem in horizontal drawings.We first show that the extended one-sided crossing minimization problem is NP-hard for both horizontal and radial drawings, and then present efficient heuristics for minimizing edge crossings in extended level drawings. Our extensive experimental results show that our new methods reduce up to 30% of edge crossings.     

The effectiveness of resources created by students as partners in explaining the relevance of mathematics in engineering education

First-year engineering students often struggle to see the relevance of theoretical mathematical concepts for their future studies and professional careers. This is an issue, as students who do not see relevance in fundamental parts of their studies may disengage from these parts and focus their efforts on other subjects they think will be more useful to them. In this study, we surveyed engineering students enrolled in a first-year mathematics subject on their perceptions of the relevance of the individual mathematical topics taught. Surveys were administered at the start of semester when some of these topics were unknown to them, and again at the end of semester when students had not only studied all these topics but also watched a set of animated videos. These videos had been produced by higher-year students to explain where they had seen applications of the mathematical concepts presented in the first year. We notice differences between the perceived relevance of topics for future study and for professional careers, with relevance to study rated higher than relevance to careers. We also find that the animations are seen as helpful in understanding the relevance of first-year mathematics. The majority of students indicated that lecturers with students as partners should work collaboratively to produce future videos.     

Social choice and topology a case of pure and applied mathematics

The existence of a social choice model on a preference space P is a topological, even homotopical problem. It has been solved 50 years ago, under different terminology, by the author and, a little later, jointly with T. Ganea and P.J. Hilton. P must be an H-space and either contractible or homotopy equivalent to a product of Eilenberg-MacLane spaces over the rationals.     

基于简化的区间数据主成分分析的高校教师绩效分析

绩效分析是高校教师绩效管理中的重要组成部分.基于简化的区间数据主成分分析方法,以2008 2009年A大学经济管理学院的教师绩效评估数据为例,考察了两年内各岗位级别教师的整体绩效和变化情况,以及教师个人绩效在所处岗位级别上的动态变化情况.基于绩效分析的结果,对绩效管理决策提出了相关建议.     

影响农民工随迁子女学业成绩的潜变量因素及回归分析

采用调查研究与统计分析相结合的方法,描述并研究了影响农民工随迂子女学业成绩的潜变量因素.潜变量因素包括四个方面:外部环境因素(包括:父母期望、亲子关系和师生关系以及家庭流动性)、行为因素(包括:家庭支持和课余学习时间)、内部心理因素(包括:学习兴趣和自我认知)和学习经验(包括:学习焦虑、学习动机和学习态度).以Spss软件为工具,得到了以下结论:亲子关系和师生关系、家庭支持、课余学习时间、学习兴趣、自我认知、学习态度和学习动机都与学业成绩呈正相关关系,家庭流动性和学习焦虑都与学业成绩呈负相关关系,父母期望对学业成绩的影响很小.外部环境因素、行为因素、内部心理因素和学习经验对学业成绩均有预测作用.     

Reflections on the promise and complexity of mathematics coaching

If students are to develop mathematical proficiency, then mathematics teaching must both change and improve. In an effort to provide site-based professional development addressing the mathematical content and pedagogical demands that teachers encounter in reality of public schooling, many school districts are turning to elementary mathematics coaches. Knowledgeable coaches can have a significant positive impact on teachers, yet this study documents substantial variance in the amount of coaching delivered and in the nature of activity that coaches undertake within schools. Coaches are frequently responsive to the needs of individual teachers. If this support is primarily marked by shared teaching or provision of instructional materials, it may not transform either instruction or teacher knowledge. Similarly if coaches assume duties that primarily address an administrator’s needs, they will have less time to enhance a school’s mathematics program. Coaches need to engage teachers in fundamental dialogue about mathematical content, mathematical learning, and student understanding. It may be that this dialogue and the effectiveness of a coach’s work with individual teachers would benefit from a coach’s concurrent work with grade-level teams. When a coach leads a grade-level team through discussion of targeted goals and approaches, the coach may facilitate individual teacher learning while building collective learning. When coupled with the support of a principal, this partnership may foster instructional change across a school.