Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and postulates. To assess the extent to which these disagreements may exist among high school science and mathematics teachers, a 14-item survey of the meanings and roles of the above terms was constructed and administered to a sample of science and mathematics teachers. As expected, the science teachers performed better than the mathematics teachers on the NOS items (44.1 versus 24.7%, respectively) and the mathematics teachers performed better than the science teachers on the NOM items (59.0 versus 26.1%, respectively). Nevertheless, responses indicated considerable disagreement and/or lack of understanding among both groups of teachers concerning the meanings/roles of proof and disproof and several other key terms. Therefore it appears that these teachers are poorly equipped to help students gain understanding of these key terms. Classroom use of the If/and/then/Therefore pattern of argumentation, which is employed in this paper to explicate the hypothesis/conjecture testing process, might be a first step toward rectifying this situation.     

Linking Mathematics and Psychological Science

Abstract

We describe a successful collaboration between mathematics and psychological science faculty members to create a learning community for our students that linked sections of introductory mathematical reasoning and psychological science courses. The students in our learning community were in their second or third semester. The learning community is designed so that, throughout the semester, students regularly move across the border between the two linked disciplines by completing common assignments, including a group project. We modified our existing course topics and frameworks to be intentional about building connections between the courses.     

Connected Knowledge in Science and Mathematics Education

While the traditional meaning of connected knowledge is valuable in some school subjects, it does not address the main activities of knowledge acquisition in subjects such as physics and mathematics. The goal of this article is to analyze the relationships between the concepts “learning for understanding” and “connected knowledge”, a central theme in feminist epistemology. In learning for understanding, the learner forms multiple, intricate connections among the concepts she is studying in school, between school concepts and her everyday concepts, and between school concepts and their wider context. Viewing connected knowledge as tightly related to understanding has several important implications. It brings connected knowledge into the central learning activities that take place in school science and mathematics, and gives it a high status. It contributes to our understanding of gender‐related patterns in thinking; and it may form a unifying theoretical framework for many studies and projects in the field of gender fair education.     

计算机科学中的数学──谈计算机专业数学的学习

本文讨论数学,特别是离散数学,在计算机科学中的重要性,它是计算机科学中基础理论的核心.以及在教学过程中就其内容及其与计算机实际应用进行讨论.     

Mathematics and Science Learning Opportunities in Preschool Classrooms

Research Findings: The present study observed and coded instruction in 65 preschool classrooms to examine (a) overall amounts and (b) types of mathematics and science learning opportunities experienced by preschool children as well as (c) the extent to which these opportunities were associated with classroom and program characteristics. Results indicated that children were afforded an average of 24 and 26 min of mathematics and science learning opportunities, respectively, corresponding to spending approximately 25% of total instructional time in each domain. Considerable variability existed, however, in the amounts and types of mathematics and science opportunities provided to children in their classrooms; to some extent, this variability was associated with teachers' years of experience, teachers' levels of education, and the socioeconomic status of children served in the program. Practice or Policy: Although results suggest greater integration of mathematics and science in preschool classrooms than previously established, there was considerable diversity in the amounts and types of learning opportunities provided in the preschool classrooms. Affording mathematics and science experiences to all preschool children as outlined in professional and state standards may require additional professional development aimed at increasing preschool teachers' understanding and implementation of learning opportunities in these 2 domains in their classrooms.     

Narrative Pedagogies in Science, Mathematics and Technology

Despite years of research, there remains serious concern regarding the engagement of students in science, mathematics and technology education. In this paper, the authors explore how narrative pedagogies are used in science, mathematics and technology in order to make the subjects meaningful. The paper focuses specifically on the role and aesthetic nature of narrative as a pedagogical approach in these school subjects and between school sectors. Case study methodology was used to compare the findings of two independent studies investigating the role of narrative-based pedagogies in mathematics and science (first author) and technology (second author). Based on this comparison, this paper proposes two perspectives on narrative-based pedagogies that deal with the connection of students with the subject: inward-looking that situated the learner within the story generated around artefact creation, and outward-looking that situated the stories of the content into students’ lifeworlds. The use of this comparative lens enabled a higher level of analysis that could not have been achieved by each research programme, generating a broader narrative that provided deeper insight into the teaching and learning experience.     

数学是模式的科学

数学是模式的科学，数学模式的诸多特征反映了数学科学的特点。     

科技奖励国际论坛 第四讲——数学与科技

由于促进中国与其它国家的科技交流而得到中国政府的表扬，本人深感荣幸。     

科学发展观与数学教育——GH数学教育方式的基本精神和特征

"科学发展观"是引领我国经济社会发展全局的重大战略思想.如何在数学教育中贯彻科学发展观,是数学教育界广泛关注的热点问题.设计"高效和谐的数学教育方式"(GH)的初衷,就是在数学教育中,落实科学发展观."GH数学教育方式"是在"MM教育方式"实验研究的基础上设计的,是它的一个新发展.     

Achievements in Mathematics and Science in an International Context

Starting from educational aims that emphasise tolerance and understanding, the focus of this article is to analyse how difference is constructed in students’ informal relations, by enactments of bullying and sex-based and racist harassment. The article also discusses how young people themselves and teachers reflect on these kinds of processes. These questions are explored using data obtained from different perspectives: 1) ethnographic observations in secondary school classes of 7th graders; 2) interviews of the students in these classes (about 13 years of age); 3) interviews of the teachers that taught these classes; and 4) follow-up interviews of the same young people at the age around 18. The findings suggest that students’ individual diversities are sometimes constructed to “different-ness” in everyday life at school. “Different-ness” might be used as a reason for bullying, racism, or sex-based harassment. In schools this is not effectively addressed by teachers.     

谈文科高等数学的教学

从数学与哲学、语言学、史学、美学等学科密切联系的角度,阐述了数学的人文价值;通过对数学学科的发展和应用方面的论述明确了高等院校文科专业开设高等数学的重要性.分析了当前文科学生学习高等数学的心理状况,提出关注数学精神的培养、加入数学史的教学内容及采取形式多样的教学形式等改进文科高等数学教学的建议.     

数理统计学源流及应用

系统论述了数理统计学的产生原因、发展过程及其应用,并指出数理统计学在数学教育中应有的地位。     

组合数学的科学艺术表现

阐述了组合数学的发展历程、科学艺术地位、研究内容和特点 ,介绍了青海省高校在该领域的研究成果 ,展示了组合理论对当代经济建设的作用     

Physics and Mathematics as Interwoven Disciplines in Science Education

The relationship between physics and mathematics is reviewed upgrading the common in physics classes’ perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.     

用数学知识解答科学问题

数学是一门工具学科，在各学科中都有广泛的应用，在小学科学课和中学物理课中更是经常用数学方法来解答相关问题。对于有些问题，甚至用小学的数学知识就能很快解答出结果。如果数学知识运用得当，有时也能起到事半功倍的作用。     

关于学科数学与科学数学

作为学科的数学和作为科学的数学,除了难度、深度上显而易见的差别外,在活动的任务、内容特点、存在形式等方面也有着本质上的不同.另外,它们之间的相互影响、相互作用又是十分显著的.正确认识二者的关系,对建立正确的数学教学观有重要的指导意义.     

用数学知识解答科学问题

数学是一门工具学科,在各学科中都有广泛的应用,在小学科学课和中学物理课中更是经常用数学方法来解答相关问题。对于有些问题,甚至用小学的数学知识就能很快解答出结果。     

Defining Computational Thinking for Mathematics and Science Classrooms

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include “computational thinking” as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.