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Mira Randahl 《International Journal of Mathematical Education in Science & Technology》2013,44(7):881-896
The aim of this article is to present and discuss some results from an inquiry into mathematics textbooks authors’ visions about their texts and approaches they choose when new concepts are introduced. Authors’ responses are discussed in relation to results about students’ difficulties with approaching calculus reported by previous research. A questionnaire has been designed and sent to seven authors of the most used calculus textbooks in Norway and four authors have responded. The responses show that the authors mainly view teaching in terms of transmission so they focus mainly on getting the mathematical content correct and ‘clear’. The dominant view is that the textbook is intended to help the students to learn by explaining and clarifying. The authors prefer the approach to introduce new concepts based on the traditional way of perceiving mathematics as a system of definitions, examples and exercises. The results of this study may enhance our understanding of the role of the textbook at tertiary level. They may also form a foundation for further research. 相似文献
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通过开展应用数学教学活动和开办《应用数学学校》的多年实践 ,我校学生结合实际学习和应用数学知识的意识和能力不断提高 ,在上海市数学知识应用竞赛和美国大学生数学建模竞赛中连续取得好成绩 ,为了争取把这项工作做得更好 ,我们作了进一步思考和打算 相似文献
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Temple H. Fay Sarah Duncan Graham 《International Journal of Mathematical Education in Science & Technology》2013,44(1):65-79
Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model using Hooke's Law, the motion of each weight is described by a fourth-order linear differential equation. A nonlinear model is also described and damping and external forcing are considered. The model has many features that permit the meaningful introduction of many concepts including: accuracy of numerical algorithms, dependence on parameters and initial conditions, phase and synchronization, periodicity, beats, linear and nonlinear resonance, limit cycles, harmonic and subharmonic solutions. These solutions produce a wide variety of interesting motions and the model is suitable for study as a computer laboratory project in a beginning course on differential equations or as an individual or a small-group undergraduate research project. 相似文献
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This article explores the values that come to the fore when preservice mathematics teachers (PTs) 1 engage in critical discussions about the role of mathematical models in society. The specific model that was discussed was the Body Mass Index (BMI) 2. From the analysis of the PTs’ discussions of the BMI from a mathematical and societal point of view several mathematical and mathematics educational values were identified such as openness, rationalism, progress, reasoning, evaluating, and problematizing the instrumental understanding of mathematics. In addition, critical thinking about mathematics in society as emphasized in curricula in the three countries involved in the study, was identified with four categories of complementary pairs. Knowing the mathematical and mathematics educational values underpinning PTs’ discussions and their connection to critical thinking is important for successfully engaging with the role of mathematics in society. 相似文献
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Employing data from the National Center of Educational Statistics' High School Longitudinal Study and utilizing critical race theory and intersectionality as theoretical frameworks, this article interrogates the relationship between mathematics identity and math success for a nationwide sample of Black secondary school students. More specifically, hierarchical regression modeling is employed to examine the relative impact of math identity, demographic variables, and school/parent social capital variables on the math grade point averages of this sample. The article ends with a discussion of specific steps for teaching mathematics that put the identity of those from traditionally marginalized communities at the center of mathematics instruction. Thus making experiences, histories, culture, and abilities essential elements of students' learning, that are to be supported and built upon. 相似文献
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David A. Yopp 《The Journal of Mathematical Behavior》2011,30(2):115-130
The paper examines the roles and purposes of proof mentioned by university research faculty when reflecting on their own teaching and teaching at their institutions. Interview responses from 14 research mathematicians and statisticians who also teach are reported. The results suggest there is a great deal of variation in the role and purpose of proof in and among mathematics courses and that factors such as the course title, audience, and instructor influence this variation. The results also suggest that, for this diverse group, learning how to prove theorems is the most prominent role of proof in upper division undergraduate mathematics courses and that this training is considered preparation for graduate mathematics studies. Absent were responses discussing proof's role in preparing K-12 mathematics teachers. Implications for a proof and proving landscape for school mathematics are discussed. 相似文献
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Lutfi Incikabi 《International Journal of Mathematical Education in Science & Technology》2017,48(6):864-875
Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers’ opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were ‘difficult’ because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers’ lack of knowledge in terms of teaching mathematics. 相似文献
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如何提高高等数学课堂教学的质量 总被引:2,自引:0,他引:2
数学的课堂教学过程是在教师的传授和指导下进行学习、掌握数学知识、技能、思想、方法的一种认识过程.影响数学课堂教学质量的因素是多方面的,本文仅就提高高等数学课堂教学质量谈几点个人的认识. 相似文献
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Jennifer Holm 《International Journal of Mathematical Education in Science & Technology》2013,44(5):563-574
A deep conceptual understanding of elementary mathematics as appropriate for teaching is increasingly thought to be an important aspect of elementary teacher capacity. This study explores preservice teachers’ initial mathematical understandings and how these understandings developed during a mathematics methods course for upper elementary teachers. The methods course was supplemented by a newly designed optional course in mathematics for teaching. Teacher candidates choosing the optional course were initially weaker in terms of mathematical understanding than their peers, yet showed stronger mathematical development after engaging in the extra hours the optional course provided. 相似文献
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试谈应用数学的发展——加强数学联系实际的学风(下半篇) 总被引:1,自引:1,他引:0
在高等数学中 ,怎样发展应用数学并在社会建设中起促进作用 ?本文就此问题提供少量素材和一份讨论意见。全文分四章 ,共十一节。前两章共四节对历史和现状作了回顾。第三章分四节 ,对科研情况进行了分析 ,涉及到数学的学科性质、过四关分类、工作困难、以及在抽样思维、逻辑推导和应用实践之间的相互关系。按照回顾与分析 ,本文指出 :在 2 0世纪 ,由于工业不发达 ,我国数学应用的基础薄弱 ;加上缺乏经验 ,我国数学联系实际的学风比较差 ,有待努力加强。第四章有三节 ,提出加强联系实际、发展应用数学的多种措施 ,并给出为了建成数学强国应该达到的定量标准 相似文献
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de Villiers (1990) suggested five roles of proof important in the professional mathematics community that may also serve to meaningfully engage students in learning proof: verification, explanation, systematization, discovery, and communication. We investigate written reflections on an end-of-semester assignment from undergraduates in an inquiry-based transition to proof course, where students reflected on instances during the semester when they engaged in the five roles of proof. We present the types of activities students recalled as influential to their engagement in the roles of proof (presenting, discussing, conjecturing, working on problem sets, and critiquing) and describe how students perceived these activities as influential to their engagement in the roles of proof. We provide student quotations highlighting these activities and offer implications for both research and practice. 相似文献
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Ole Skovsmose 《The Journal of Mathematical Behavior》2006,25(4):267-284
Three issues concerning the relationship between research and practice are addressed. (1) A certain ‘prototype mathematics classroom’ seems to dominate the research field, which in many cases seems selective with respect to what practices to address. I suggest challenging the dominance of the discourse created around the prototype mathematics classroom. (2) I find it important to broaden the school-centred discourse on mathematics education and to address the very different out-of-school practices that include mathematics. Many of these practices are relevant for interpreting what is taking place in a school context. That brings us to (3) socio-political issues of mathematics education. When the different school-sites for learning mathematics as well as the many different practices that include mathematics are related, we enter the socio-political dimension of mathematics education.On the one hand we must consider questions like: Could socio-political discrimination be acted out through mathematics education? Could mathematics education exercise a regimentation and disciplining of students? Could it include discrimination in terms of language? Could it include sexism and racism? On the other hand: Could mathematics education bring about competencies which can be described as empowering, and as supporting the development of mathematical literary or a ‘mathemacy’, important for the development of critical citizenship?However, there is no hope for identifying a one-way route to mathemacy. More generally: There is no simple way of identifying the socio-political functions of mathematics education. Mathematics education has to face uncertainty, and this challenge brings us to the notion of responsibility. 相似文献
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We conducted a multi‐year study of specialization in elementary mathematics and/or science, using data drawn from a local sample of teachers and a nationwide sample of principals. Using the theory of planned behavior, we compare and contrast teacher and principal views and decision‐making processes related to elementary content specialization (ECS). Survey data indicate that specialist models were conceived as a way to better meet students' academic needs while relieving some of the rigorous demands placed on elementary teachers in the context of new content standards. In contrast, self‐contained classrooms were retained in elementary schools largely due to beliefs that these traditional structures provide the best social and emotional stability for students. After presentation of survey findings, we use three local case studies to present ECS at different stages of maturity (from newly enacted to well‐established), with corresponding discussion of benefits, challenges, and lessons learned. Our case study data indicate that, while newly adopted ECS models tended to face the most challenges, there may still be critical model‐specific concerns at play even when specialization has been ongoing for decades. Our findings have implications for teachers and principals, as well as researchers and professional development providers. 相似文献