Use of Manipulative Devices: Elementary School Cooperating Teachers Self-Report

This study looked at elementary (K-6) cooperating teachers' self-reported familiarity with, availability of, and use of 11 common manipulative devices and their perceptions about factors to consider when using manipulative materials to teach mathematics. The study found limited use of manipulatives by this select group of teachers and a pattern of diminishing use through the grades.     

A Comparison of Concrete and Virtual Manipulative Use in Third‐ and Fourth‐Grade Mathematics

The primary purpose of this classroom experiment was to examine the effectiveness of concrete (hands‐on) manipulatives as compared with virtual (computer‐based) manipulatives on student review of fraction concepts in third grade and introduction of symmetry concepts in fourth grade. A pretest–posttest design was employed with a sample of 91 third‐grade students and 54 fourth‐grade students who were randomly assigned to complete a lesson using either concrete or virtual manipulatives. Students used a variety of manipulative materials during the lessons. Results of the posttest suggest that student learning was unchanged by lesson condition.     

Science and Mathematics Equity Issues at a Local School District Level

Many reports to the nation have revealed differences in the educational experiences of males and females. This is especially true in mathematics and science where females are not receiving the necessary educational background to develop the skills and understanding required to be citizens and employees in today's technological world. As a result, females are underrepresented in science, mathematics, and engineering professions. This study compares one school district's data with the data in national reports and then attempts to analyze what factors exist in the community and school district that reinforce and perpetuate inequitable situations for females. This study also provides a model for other school districts to conduct a self-study of gender equity education issues.     

Special Issue Article: A Look at Technology's Role in Professional Development of Mathematics Teachers at the Middle School Level

In last month's issue of School Science and Mathematics, Glenda Lappan addressed the dilemma of supporting teachers in continuing to grow professionally in four domains: Learning more mathematics content; improving their pedagogical skills; improving assessment skills; and addapting the curriculum to the needs of their students. Though it is clear that this kind of learning is best done in the context of what is going on in the classroom, teachers' schedules and other problems make it difficult to implement a coherent classroom based, professional development program. In this article, two more knowledge domains are added to this mix: the ability to (a) use technology and (b) teach with technology effectively. Since the process of learning and teaching is a dynamic one, the author describes his vision of the classroom as a laboratory where teachers get to practice and improve in these six areas and get feedback from an audience of their peers. Reflections are based on a current project in Paterson, New Jersey where the author helps middle school teachers use computer software to improve their mathematics teaching and learning.     

贮雾器与定量手控吸入器配合使用中的数学模型

本文针对支气管哮喘病雾化吸入疗法中的贮雾器与定量手控吸入器配合使用问题 ,通过机理分析 ,利用差分方程建立最优吸入次数的数学模型 ,给出合理的吸入次数及药物剂量结果 .     

Mathematics,manifest: a review of Mathematics: the Winton Gallery at the Science Museum

Mathematics: the Winton Gallery strives, like any exhibition concerning mathematics, to make meaningful contact between the abstruse realms of mathematics and the viewing audience. Unlike many other exhibitions, this is here accomplished by displaying a rich range of objects that demonstrate the essential role of mathematics in the world by emphasizing connections to the viewers’ existing cognitive environments. Through a focus on the ways that mathematical work affects and informs our human world, the exhibition succeeds in connecting a mathematical way of thinking with the lives of the viewing public in a complex and profound way, in exchange for their efforts and attention. While an approach which places the interweave of life and mathematics at its centre may invite worries about the representation of pure mathematics or whether such a strategy insulates the viewer from an understanding of ‘real’ mathematics, what this exhibition does is to offer a sense of the mind-set that underscores mathematical work. By revealing the implications of this mode of thought, the exhibition encourages the audience to understand their own lives and world in a more mathematically-oriented way, while also encouraging them to understand mathematics in terms of the ways their human world is already formed.     

浅谈数学教学过程中逻辑、形式与直觉方法的表现

本文结合教学实际 ,分析了如何利用数学的逻辑思维、直觉思维、形式化思维的规律指导工科高等数学和工程数学的教学     

Perceived Helpfulness and Amount of Use of Technology in Science and Mathematics Classes at Different Grade Levels

Use of technology in science and mathematics classes has been increasing, but there are differences in the amount of use of and students' perceptions of its helpfulness across grade levels and subject areas. Technology was reported as used only occasionally. Technology was used most often to understand or explore in more depth concepts taught in class. The second most frequent use was as a tool of investigation or assessment. The lowest reported use of technology was as tool of communication. Students in middle school classes perceived technology as less helpful than did students in elementary or high school classes. Students in mathematics classes perceived technology as more helpful than did students in science classes. Girls perceived technology as more helpful than did boys. Additionally, teacher and student perceptions of amount of use varied with teachers reporting more use than students.     

未确知数学在决策中的应用

以不确定性信息处理的数学理论为基础,分析某欲建水库方案是否可行为例,说明了未确知数学在决策中的应用,同时本文还给出了未确知决策的一般公式.     

Technology Use in the Teaching of Mathematics and Science in Elementary Schools

Principals from 80 elementary schools, in predominantly rural Western Pennsylvania, completed and returned a 22-item questionnaire designed to assess the nature and extent of technology use for the teaching of elementary mathematics and science within their buildings. Technologies included calculators, microcomputers, overhead projection panels, videotape, and interactive video. Microcomputers were being used in at least some elementary grade levels for mathematics or science instruction in 84% of the schools. Teachers used microcomputers more frequently in mathematics (82.5%) than in science instruction (55%). Principals reported a lower frequency of calculator use with 63.3% of the schools having some grade levels where calculators were used in mathematics lessons, and 21.5% of schools in science lessons. Further analyses of data suggest that microcomputer and calculator use is more common in the intermediate grades (3–6) than in the primary grades (K-2).     

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.