Connecting Mathematics and Science in Undergraduate Teacher Education Programs: Faculty Voices from the Maryland Collaborative for Teacher Preparation

The study reported in this paper investigated perceptions concerning connections between mathematics and science held by university/college instructors who participated in the Maryland Collaborative for Teacher Preparation (MCTP), an NSF-funded program aimed at developing special middle-level mathematics and science teachers. Specifically, we asked (a) “What are the perceptions of MCTP instructors about the ‘other’ discipline?” (b) “What are the perceptions of MCTP instructors about the connections between mathematics and science?” and (c) “What are some barriers perceived by MCTP instructors in implementing mathematics and science courses that emphasize connections?” The findings suggest that the benefits of emphasizing mathematics and science connections perceived by MCTP instructors were similar to the benefits reported by school teachers. The barriers reported were also similar. The participation in the project appeared to have encouraged MCTP instructors to grapple with some fundamental questions, like “What should be the nature of mathematics and science connections?” and “What is the nature of mathematics/science in relationship to the other discipline?”     

Mathematical building-blocks in engineering mechanics

A gamut of mathematical subjects and concepts are taught within a handful of courses formally required of the typical engineering student who so often questions the relevancy of being bound to certain lower-division prerequisites. Basic classes at the undergraduate level, in this context, include: Integral and Differential Calculus, Differential Equations, and Matrix (or Linear) Algebra. Focusing on but one sub-discipline within engineering, namely, Mechanics, the author attempts to expose the sheer pertinence of each of the aforementioned mathematical subjects as they unavoidably have materialized in various forms throughout his teaching experiences; specifically, an example is drawn from each of the following classes: Advanced Structural Analysis, Analysis of Plates and Shells, Fracture Mechanics and Fatigue, and Composite Materials. While comprehensiveness is not the aim of this article, the sampling of themes that are expounded upon?–?rudimentary to all disciplines of science and engineering?–?unearth such a commanding cross section of mathematical topics in their wake to warrant special consideration by every conscientious student.     

Improving student learning in calculus through applications

Nationally only 40% of the incoming freshmen Science, Technology, Engineering and Mathematics (STEM) majors are successful in earning a STEM degree. The University of Central Florida (UCF) EXCEL programme is a National Science Foundation funded STEM Talent Expansion Programme whose goal is to increase the number of UCF STEM graduates. One of the key requirements for STEM majors is a strong foundation in Calculus. To improve student learning in calculus, the EXCEL programme developed two special courses at the freshman level called Applications of Calculus I (Apps I) and Applications of Calculus II (Apps II). Apps I and II are one-credit classes that are co-requisites for Calculus I and II. These classes are teams taught by science and engineering professors whose goal is to demonstrate to students where the calculus topics they are learning appear in upper level science and engineering classes as well as how faculty use calculus in their STEM research programmes. This article outlines the process used in producing the educational materials for the Apps I and II courses, and it also discusses the assessment results pertaining to this specific EXCEL activity. Pre- and post-tests conducted with experimental and control groups indicate significant improvement in student learning in Calculus II as a direct result of the application courses.     

数学建模课内容和教学方法的探讨

拟就以下内容进行了探讨 .(i)该课程究竟应该讲什么内容、怎样讲 ,才能使学生在较短的时间内 ,掌握数学建模的基本知识和基本方法 ;(ii)该课程怎样与数学实验更好地结合起来 ,以培养学生的动手能力 ;(iii)该课程应采用什么样的教学手段和教学方法 ,才能加大课堂信息量 ,加强直观性和趣味性等 .我们的解决方法是 :(i)以介绍建立数学模型为主 ,按数学知识内容的不同来选取数学模型的典型案例 ,通过案例介绍 ,使学生学会怎样建立模型 .(ii)适当介绍数学软件包 ,让学生掌握运用软件包来求解模型能力 .(iii)做大作业 ,教员给出题目 ,学生自己收集资料、讨论、上机求解 ,最后写出报告 .(iv)开展多媒体教学 ,对主要的教学内容进行模块化教学 ,将建模分成 1 4个专题 ,做成 1 4个多媒体课件     

信息与计算科学专业应用型人才培养模式的研究

分析了信息与计算科学专业课程教学的特点和存在的教与学的矛盾.并以《高等代数》为试点,在教学实践中试行教学改革,积极探索教学与实际相结合与计算机信息有机结合的教学模式,在应用型人才培养方面取得显著成效.对信息与计算科学专业应用型人才培养有一定的借鉴作用.     

How to make mathematics relevant to first-year engineering students: perceptions of students on student-produced resources

Many approaches to make mathematics relevant to first-year engineering students have been described. These include teaching practical engineering applications, or a close collaboration between engineering and mathematics teaching staff on unit design and teaching. In this paper, we report on a novel approach where we gave higher year engineering and multimedia students the task to ‘make maths relevant’ for first-year students. This approach is novel as we moved away from the traditional thinking that staff should produce these resources to students producing the same. These students have more recently undertaken first-year mathematical study themselves and can also provide a more mature student perspective to the task than first-year students. Two final-year engineering students and three final-year multimedia students worked on this project over the Australian summer term and produced two animated videos showing where concepts taught in first-year mathematics are applied by professional engineers. It is this student perspective on how to make mathematics relevant to first-year students that we investigate in this paper. We analyse interviews with higher year students as well as focus groups with first-year students who had been shown the videos in class, with a focus on answering the following three research questions: (1) How would students demonstrate the relevance of mathematics in engineering? (2) What are first-year students' views on the resources produced for them? (3) Who should produce resources to demonstrate the relevance of mathematics? There seemed to be some disagreement between first- and final-year students as to how the importance of mathematics should be demonstrated in a video. We therefore argue that it should ideally be a collaboration between higher year students and first-year students, with advice from lecturers, to produce such resources.     

Applications of a sequence of points in teaching linear algebra,numerical methods and discrete mathematics

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, Using a sequence of number pairs as an example in teaching mathematics. Math. Comput. Educ., 39 (2005), pp. 198–205; Y. Shi, Case study projects for college mathematics courses based on a particular function of two variables. Int. J. Math. Educ. Sci. Techn., 38 (2007), pp. 555–566) have presented some interesting examples which can be used in teaching high school and college mathematics classes. In this article, we further discuss a few interesting ways to apply this sequence of points in teaching college mathematics courses such as linear algebra, numerical methods in computing, and discrete mathematics. In addition to using them in individual courses, these studies may also be combined together to offer seminars or workshops to college mathematics students. Studies like these are likely to promote student interests and get students more involved in the learning process, and therefore make the learning process more effective.     

Next Generation Science Standards: A National Mixed‐Methods Study on Teacher Readiness

Next Generation Science Standards (NGSS) science and engineering practices are ways of eliciting the reasoning and applying foundational ideas in science. As research has revealed barriers to states and schools adopting the NGSS, this mixed‐methods study attempts to identify characteristics of professional development (PD) that will support NGSS adoption and to improve teacher readiness. In‐service science teachers from across the nation were targeted for the survey and responses represented 38 states. Research questions included: How motivated and prepared are in‐service 7–12 teachers to use NGSS science and engineering practices? What is the profile of 7–12 in‐service teachers who are motivated and feel prepared to use NGSS science and engineering practices? The study revealed that teachers identified engineering most frequently as a PD need to improve their NGSS readiness. High school teachers rated themselves as more prepared than middle school and all teachers who use Modeling Instruction expressed higher NGSS readiness. These findings and their specificity contribute to current knowledge, and can be utilized by districts in selecting PD to support teachers in preparing to implement the NGSS successfully.     

Reforming Elementary Science Teacher Preparation: What About Extant Teaching Beliefs?

A common maxim in the educational profession is that one teaches the way one is taught. Indications are that preservice teachers' beliefs, attitudes, and practices may be linked to previous experiences. Calderhead & Robson (1991) underscored this concern by asserting that teachers use good teachers as models for developing their own images as teachers. Others have argued that the images held by teachers are used as frames of reference for their own teaching practices. In this article, preservice teachers' perceptions of themselves as science teachers are examined. The assertion is made that a long history of stereotypical science learning experiences — in elementary school, high school, and college — powerfully impacts the way in which elementary preservice teachers understand the nature of science and come to believe science should be taught. In the current study, the images and perceptions preservice teachers bring to science methods courses (as evidenced in drawings of themselves as science teachers at work) are identified and ways these images and perceptions may have been formed and how they can be reinforced or modified during a science methods course are discussed.     

Institutional Norms and Policies That Influence College Mathematics Professors in the Process of Changing to Reform‐Based Practices

This case study was an investigation of the role of the institutional culture of a university in the process of changing to reform‐based practices for two college mathematics professors. A framework is presented for identifying and analyzing institutional norms and policies that are present and those lacking in supporting faculty efforts toward reform. The primary categories considered in the framework are the teaching and learning context, the professional community, and the university's reward system. This framework is applied to the cases, and findings indicate that institutional norms in the forms of priorities for how time is allocated to professional responsibilities (as part of the teaching context), and colleagues and administrators who understood and shared the professors' goals for reform (as part of the professional community) strongly influenced the professors' efforts toward change. Additionally, a reward system that recognized efforts to improve teaching and learning was critical in establishing a culture that promoted change. However, despite the fact that both professors were in the same mathematics department, the nature of the influence of these factors was not uniform. The institutional culture indeed had multiple layers that required examination for each professor's individual context. The findings help highlight the importance of institutional context for both K‐12 and college level teaching and learning. The nature of these influential factors and the institutional layers were discussed for each case, along with implications for other institutions.     

L’enseignement des mathématiques dans l’enseignement secondaire maghrébin

The goal of this talk is to study the following questions. Does the mathematics teaching in the secondary schools in the Maghreb prepare to University studies and more specifically does it initiate students to modern science and technology? Is anyone able to understand mathematics or is mathematics only accessible to the happy few Is it a means of selection? Is mathematics omnipresent in our modern society? What relationship can one hope to find between mathematics and other disciplines? Has mathematics evolved to such an abstract and formal state that it seems difficult relate it to any other topic? All these questions are discussed in relationship with the particular problems in the Maghreb, namely the mathematics program as taught today in these countries.     

What is effective mathematics teaching? A study of teachers from Australia, Mainland China, Hong Kong SAR, and the United States

What is effective teaching in mathematics? How do teachers in Australia, Mainland China, Hong Kong SAR and the US view effective teaching in mathematics? What are the similarities and differences in the views of teachers from the East and West on effective teaching? This paper provides theoretical and methodological bases for addressing these questions, which are dealt with in empirical studies described in the papers of this issue.     

Development and Implementation of an Integrated Mathematics/Science Preservice Elementary Methods Course

If integration of mathematics and science is to occur, teacher preparation programs at colleges and universities must provide leadership in developing and modeling methods of teaching integrated content. This paper describes the development and implementation of an integrated mathematics/science preservice elementary methods course at the University of Connecticut. In planning the course several questions were addressed: (a) What does integration of mathematics and science mean? (b) What content should be taught in an integrated mathematics/science (IM/S) elementary methods course? and (c) How should an IM/S elementary methods course be taught? An important element of the course involved enlisting an exemplary elementary teacher who was released from her classroom one day per week to co-teach the methods class. Establishing a definition of integration proved to be one of the most challenging aspects of course development. The authors determined that most difficulties in integration of disciplines result from attempts to “force” the integration. As the team struggled with the philosophical, theoretical and logistical problems in the development of the course, it became apparent why integration has not been more widely implemented. It is believed this model can be adapted to allow for integration of all content areas. Plans are currently underway to incorporate social studies into the methods class for Fall of 1993.     

Humans-with-media and continuing education for mathematics teachers in online environments

This paper begins by situating online mathematics education in Brazil within the context of research on digital technology over the past 25?years. I argue that Brazilian research on technology in mathematics education can be divided into four phases, and then present an example that ??blends?? aspects of the second and third phases. Phase two can be characterized by research with software designed to address traditional mathematics topics, such as functions, while the third phase is characterized by online courses. The data presented show creative solutions for a problem designed for collectives of humans-with-function-software. The paper is analyzed from a perspective that emphasizes the role of different technologies as teachers and professors collaborate to produce knowledge about the use of mathematical software in regular face-to-face classrooms. A model of online education is presented. Finally, the paper discusses how technology may change collaboration and teaching approaches in continuing education, as it allows for greater integration of online learning with teachers?? classroom activities in schools. In this case, the online platform plays an active role in the learning collective composed of humans-with-media.     

Observation of Reform Teaching in Undergraduate Level Mathematics and Science Courses

This paper reports on initial results from an ongoing evaluation study of a National Science Foundation project to implement reform‐oriented teaching practices in college science and mathematics courses. The purpose of this study was to determine what elements of reform teaching are being utilized by college faculty members teaching undergraduate science and mathematics courses, including a qualitative estimate of the frequency with which they are used. Participating instructors attended summer institutes that modeled reform‐based practices and fostered reflection on current issues in science, mathematics, and technological literacy for K‐16 teaching, with an explicit emphasis on the importance of creating the best possible learning experience for prospective K‐12 science and mathematics teachers. Utilizing a unique classroom observation protocol (the Oregon‐Teacher Observation Protocol) and interviews, the authors (a) conclude that some reform‐oriented teaching strategies are evident in undergraduate mathematics and science instruction and (b) suggest areas in which additional support and feedback are needed in order for higher education faculty members to adopt reform‐based instructional methodology.     

Post‐financial meltdown: What do the services industries need from us now?

In 2008 the global economy was rocked by a crisis that began on Wall Street, but quickly spread to Main Street U.S.A., and then to side streets around the world. Statisticians working in the service sector are not immune, with many concerned about losing their jobs. Given this dramatic course of events, how should statisticians respond? What, if anything, can we do to help our struggling organizations survive this recession, in order to prosper in the future? This expository article describes some approaches that we feel can help service industries deal with aftereffects of the financial meltdown. Based on an understanding of current needs of the service industries, we emphasize three approaches in particular: a greater emphasis on statistical engineering relative to statistical science, ‘embedding’ statistical methods and principles into key business processes, and the reinvigoration of Lean Six Sigma to drive immediate, tangible business results. Copyright © 2009 John Wiley & Sons, Ltd.     

Ways of promoting the sustainability of mathematics teachers’ professional development

This paper deals with the sustainable effectiveness of professional development programmes. Based on a review of literature and research findings, the following questions are raised: What is regarded as an effective way of promoting mathematics teachers’ sustainable professional development? Which levels of impacts are aimed at? What are the factors promoting the effectiveness of professional development programmes? Regarding these questions, the article links theoretical considerations with research findings from a case study. A secondary mathematics teacher, taking part in a teacher professional development programme in 2002, was revisited in 2005 and 2010 to gather data regarding the sustainable impact of the programme. The case study’s results provide information about the teacher’s professional growth and lead to a discussion of implications for mathematics teachers’ professional development and teacher education in general.     

高等数学课程分层次教学理念的思考和举措

高等数学课程是高校所有专业的基础课程之一,对实现高校的人才培养目标起着十分重要的作用.本文遵循因材施教的原则,科学设计了分层次教学模式,对于开展分层次教学的意义和理论依据作了阐述,提出了分层次教学模式的组织与实施,并就教学内容、教学方法、考核模式的改革给出相应的实施方案.     

Preparing New Science Teachers for Urban Classrooms : Consensus Within an Expert Community

Preparing future science teachers for U.S. city classrooms is an important yet poorly understood process. The purpose of this study was to determine the philosophies and practices of university ‐based science educators associated with programs supplying teachers for metropolitan school systems. Through an iterative process of mailed questionnaires, 20 participants rated their views on issues pertinent to science teacher education. The responses to questionnaires were used in the creation of items for each subsequent round. The three rounds of questionnaires contained Likert ‐scale and open‐ended questions. For many issues, there was consistently high consensus among the expert panelists, including the presence of students for whom English is a second or new language, the importance of science education professors remaining connected to urban school issues, and practices often affiliated with reform (e.g., alternative assessment, nature of science). Several issues emerged as having low regard by the participants, including the role of student ethnicity on teaching strategies, providing instruction about reading strategies within science teacher preparation, and the value of professors having themselves taught science in urban settings.     

On the theoretical, conceptual, and philosophical foundations for research in mathematics education

The current infatuation in the U.S. with “what works” studies seems to leave education researchers with less latitude to conduct studies to advance theoretical and model-building goals and they are expected to adopt philosophical perspectives that often run counter to their own. Three basic questions are addressed in this article:What is the role of theory in education research? How does one's philosophical stance influence the sort of research one does? And,What should be the goals of mathematics education research? Special attention is paid to the importance of having a conceptual framework to guide one's research and to the value of acknowledging one's philosophical stance in considering what counts as evidence.