基于化学学科理解的教学——以“苯”为例

以“第一种人工合成染料苯胺紫”为素材创设情境,将煤、苯和染料苯胺紫等建立联系,由此引导学生探讨3个问题:“苯从哪里来”“如何确定苯的结构”及“如何解释苯的性质”,让学生在收获具体知识的同时,理解苯环结构的稳定性,了解苯的结构的研究历史背景以及苯环结构学说在有机化学发展史上的卓越作用。     

基于学科理解的“物质成分”大概念教学*

以“物质成分”大概念教学为例,基于学科理解,以探究物质成分的相关化学史为线索设计教学,引导学生在追溯“物质成分”相关概念、理论的发展过程中,逐渐建构物质成分的宏观、微观、宏微结合视角。并在解决探究物质成分的真实问题的过程中,培养学生基于证据进行推理的科学论证能力,通过认识视角的发展,体会科学理论是在不断发展和进阶的,初步建立科学发展观。     

Making sense of the traditional long division algorithm

This classroom scholarship report presents a group of elementary students’ experiences learning the traditional long division algorithm. The traditional long division algorithm is often taught mechanically, resulting in the student's performance of step-by-step procedures with no or weak understanding of the concept. While noting some initial difficulties, the class episodes in this article provide examples of internalization that highlight the active role of the learner in transforming concrete representations into an abstract algorithm. Several factors encouraged students to be deeply engaged in making sense of the long division algorithm: meaningful tasks based on a theoretically well-articulated curriculum, effective pedagogical measures, and dynamic class discussions.     

CFETR偏滤器靶板的概念设计与分析

基于以前的偏滤器研究,提出了中国核聚变工程实验堆(CFETR)偏滤器靶板的概念设计。在最差工况下进行的热工水力分析和力学分析表明,应力和温度都在允许范围内,验证了该设计模型的可靠性。该概念模型和对其所做的分析可以为以后的工程设计提供参考。     

Secondary school students’ levels of understanding in computing exponents

The aim of this study is to describe and analyze students’ levels of understanding of exponents within the context of procedural and conceptual learning via the conceptual change and prototypes’ theory. The study was conducted with 202 secondary school students with the use of a questionnaire and semi-structured interviews. The results suggest that three levels of understanding can be identified. At the first level students’ interpretation of exponents is based upon exponents that symbolize natural numbers. At Level 2, students’ knowledge acquisition process is a process of enrichment of the existing conceptual structures. Students at this level are able to compute exponents with negative numbers by extending the application of prototype examples. Finally, at Level 3 students not only extend the prototype examples but also reorganize their thinking in order to compute and compare exponents with roots, a concept which is quite different from the concept of exponents with natural numbers.     

Effective collaboration in the productive failure process

Productive failure is a learning design that encompasses problem solving prior to instruction and the learning that occurs during and after this process. In the mathematics education literature, there is a need for analyses of students’ interactions that occur as they collaborate during the productive failure process. In this paper, we contribute to this area by taking a closer look at students’ interactions that characterize an effective productive failure process. In analyzing video footage of two different groups of students working on invention tasks in a flipped mathematics classroom, we observed that the productive failure process seemed to work best in groups of students among whom the instructional design evoked students’ intellectual need and curiosity. These students also developed a set routine for solving problems whose solutions are difficult to find without prior direct instruction on the topic, which proved valuable on follow-up in-class and posttest problems.     

New architectures for constructed complex systems

This paper is an overview of our research program in intelligent systems. Our object of study is constructed complex systems, which are software and hardware systems mediated or managed by computers. We describe how biological systems provide stiff competition for constructed complex systems in the areas of autonomy and intelligence, robustness, adaptability, and communication. We describe our computationally reflective integration infrastructure, called ‘wrappings', and show how it can provide many of the necessary flexibilities. We also describe two directions of research in computational semiotics, which for us means the study of the use of symbols by computing systems. We describe our ‘conceptual categories', which are a method of knowledge representation that supports these flexibilities, and some new results on symbol systems, which leads to some new mathematical questions about what can be represented in formal systems and how they can be extended automatically. These are then combined to describe our architecture, which we are currently in the process of implementing.     

Scalar and vector line integrals: A conceptual analysis and an initial investigation of student understanding

This paper adds to the growing body of research happening in multivariable calculus by examining scalar and vector line integrals. This paper contributes in two ways. First, this paper provides a conceptual analysis for both types of line integrals in terms of how theoretical ways of thinking about definite integrals summarized from the research literature might be applied to understanding line integrals specifically. Second, this paper provides an initial investigation of students’ understandings of line integral expressions, and connects these understanding to the theoretical ways of thinking drawn from the literature. One key finding from the empirical part is that several students appeared to understand individual pieces of the integral expression based on one way of thinking, such as adding up pieces or anti-derivatives, while trying to understand the overall integral expression through a different way of thinking, such as area under a curve.     

Learning to teach high school mathematics: Patterns of growth in understanding right triangle trigonometry during lesson plan study

“Lesson plan study” (LPS), adapted from the Japanese Lesson Study method of professional development, is a sequence of activities designed to engage prospective teachers in broadening and deepening their understanding of school mathematics and teaching strategies. LPS occurs over 5 weeks on the same lesson topic and includes four opportunities to revisit one's own ideas and the ideas of others. In this paper, we describe one prospective teacher's growth in understanding right triangle trigonometry as she participated in LPS. This study is part of a much larger study investigating how prospective secondary teachers learn to teach mathematics within the context of LPS. Results of this study indicate that Image Saying, an activity for growth in understanding from the Pirie-Kieren model [Pirie, S., & Kieren, T. (1994). Growth in mathematical understanding: How can we characterize it and how can we represent it? Educational Studies in Mathematics, 26, 165-190], is critical to prospective teachers’ growth in understanding school mathematics. Multiple opportunities and contexts within which to share understanding of school mathematics led to significant growth in understanding of right triangle trigonometry which in turn led to growth in understanding of teaching strategies. That is, the results of this study indicate that growth in understanding school mathematics (what to teach) leads to growth in understanding teaching strategies (how to teach) as prospective teachers participate in LPS.     

Education campaign and family understanding affect stability and qualitative behavior of an online game addiction model for children and youth in Thailand

Online game addiction has become a large problem worldwide, and it could give negative impacts on children in many ways such as physical health, learning, emotion, and behavior. Online game addiction is mostly found in children and youth at the age of 15 to 24 years. Therefore, in this paper, we have developed a mathematical model of online game addiction to explore the effects of education campaign and family understanding on online game addiction in Thailand. Analysis of this model reveals two main equilibria, addiction‐free (AFE) and addiction‐present (APE) ones. Results show that the AFE is locally asymptotically stable when the value of basic reproduction number (R₀) is less than the unity; otherwise, there is a unique endemic equilibrium point, and it is locally stable when satisfies the Routh‐Hurwitz criterion. Further, the conditions of AFE to be globally stable are demonstrated. Finally, the results of sensitivity analysis and numerical simulation show that the effectiveness of both education campaign and family understanding is an important factor in reducing the value of R₀ and holds great promise for lowering the number of children and youth who addict to online game in Thailand.