数学文化在中学数学教学中的渗透

广义的数学文化是指数学本身就是一种文化.狭义上说,数学文化指数学的思想、精神、方法、观点、语言及其形成和发展过程.当前对数学文化认识所存在的误区主要有:不少人认为数学文化就是数学史,有些人认为数学文化就是介绍一些数学趣题,更多的人认为数学文化也就是数学本身.在中学数学教学渗透数学文化的途径有:在各章引言中渗透数学文化;在新课引入时渗透数学文化;在讲述概念时渗透数学文化;在定理公式证明时渗透数学文化;在思想方法中渗透数学文化;在例题教学中渗透数学文化;在数学的实际应用中渗透数学文化.     

Causal Connections Between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of children's mathematics skills, but there is limited causal evidence supporting this link. To address this research gap, 47 Head Start children were randomly assigned to a mathematical language intervention group or a business-as-usual group. Over the course of eight weeks, interventionists implemented a dialogic reading intervention focused on quantitative and spatial mathematical language. At posttest, students in the intervention group significantly outperformed the students in the comparison group not only on a mathematical language assessment, but on a mathematical knowledge assessment as well. These findings indicate that increasing children's exposure to mathematical language can positively affect their general mathematics skills. This study is an important first step in providing causal evidence of the importance of early mathematical language for children's general mathematical knowledge and the potential for mathematical language interventions to increase children's overall mathematics abilities.     

关于奥数与小学生数学思维能力发展冲突的思考

近年来,小学“奥数”越来越热。小学生做奥数题是否真的有利于小学生的数学思维能力发展,这一问题成为一些教育界人士与家长关心的重要议题。文章认为,大面积的小学生“奥数”培训热,降低了小学生数学学习的兴趣,不利于提高小学生的数学能力。小学数学教学应该把提升小学生的数学素质作为基本出发点,促进小学生的数学思维能力发展。     

数学实验融入高等数学教学的探讨

随着时代发展和科技的进步,迫切要求大学生掌握数学技术,也就是在学习过程中,把数学知识与计算机技术结合起来,使二者的学习相互促进.实现这一目标的最基本方法是把数学实验融入到数学教学中去.笔者在实验融入数学教学实践的基础上,通过对教学对象的实际问卷调查,运用层次分析法对实验融入数学教学模式和传统数学教学模式进行定量比较与评价.结果显示实验融入数学教学模式优于传统教学模式,该教学模式值得进一步研究和加强.     

文化视角下的数学教育

在数学新课程标准中,数学文化作为新增加的一个独立板块被明确提出。新课程标准倡导广泛开展数学文化活动,这促使我们重新认识数学文化,并从文化的角度来认识数学教育。在探究数学文化的定义、数学文化的历史观、哲学观和美学观的基础上,从数学文化的角度对数学教育进行尝试性探索,加强对数学课程、数学的教与学的认识。     

培养中学生数学思维的尝试

中学生数学思维培养是数学教学的重点.本文介绍了我的一些看法与做法.     

Mathematical Problem Solving with Technology: the Techno-Mathematical Fluency of a Student-with-GeoGebra

This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nature of young students’ spontaneous mathematical problem solving with technology. The empirical data comprise digital records of her approaches to two problems from a web-based mathematical competition where she resorted to GeoGebra and an interview where she explains and describes her usual problem solving activity with this tool. Based on a proposed model for describing the processes of mathematical problem solving with technologies (MPST), the main results show that this student’s solving and expressing the solution are held from the early and continuing interplay between mathematical skills and the perception of the affordances of the tool. The analytical model offers a clear picture of the type of actions that lead to the solution of each problem, revealing the student’s ability to deal with mathematics and technology in problem solving. By acknowledging this as a case of a human-with-media in solving mathematical problems, the students’ efficient way of merging technological and mathematical knowledge is portrayed in terms of her techno-mathematical fluency.     

Does Time Matter in Improving Mathematical Discussions? The Influence of Mathematical Autonomy

Facilitating students’ transition from less to more mathematically productive engagement in discussions is an important area of investigation. Research on mathematical whole-class discussions has consistently identified facilitating students' mathematical autonomy as a central component of this transition. Additionally, research commonly infers such transitions take time to manifest. The present study examined students' perceived mathematical autonomy and perceived engagement in mathematical discussions over a half year of school. Using hierarchical linear growth-curve modeling, the authors found that although it may take time for students to transition into more mathematically productive engagement in discussions, it may be the development of their mathematical autonomy, rather than mere exposure over time, that facilitates this transition.     

开放性数学网络教学交互系统设计

提出一种开放性数学网络教学交互系统的设计方案.网络数学教学平台集成了数学知识库,数学工具库,网络数学实验和交流平台,讨论了各部分的功能及设计思路.结合大学数学建模课程的教学讨论平台的设计和应用,提升使用者的学习和实践技能,进一步提高大学生综合研究的能力.     

中学生数学学习能力的调查

通过对提高中学生数学学习能力的调查分析 ,得到 :学生的数学学习能力总体水平不高 ;心理健康、身体健康、学习方法、学习热情、朋友关系、与老师关系、家庭环境、学校环境与数学学习能力呈正相关 ;按数学成绩分类 ,学生的数学学习能力有一定的差异性。因此提高中学生数学学习能力是实施数学素质教育的有效途径     

矩阵在数学建模中的应用举例

矩阵作为一种认识复杂事物的简捷工具已经被广泛应用在各个学科领域中,在数学建模中也有许多应用。本文就数学建模中使用矩阵的情况做一些举例、小结,最后给出一个典型的数学模型。     

浅谈数学物理方法的教学改革

数学物理方法是物理系物理学专业的一门重要的基础课,为后续专业课程提供了必要的数学工具。该文提出了如何在数学物理方法教学中进行教学改革,以得到更好的教学效果。     

A framework for analyzing the collaborative construction of arguments and its interplay with agency

In this report, we offer a framework for analyzing the ways in which collaboration influences learners' building of mathematical arguments and thus promotes mathematical understanding. Building on a previous model used to analyze discursive practices of students engaged in mathematical problem solving, we introduce three types of collaboration and discuss their influence on the building of mathematical arguments and student agency. The framework is exemplified using data from a study of the development of mathematical reasoning in an urban sixth-grade informal after-school program.     

Problem solving in Swedish mathematics textbooks for upper secondary school

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their difficulty level, and (d) their context. Based on an analysis of 5,722 tasks from the area of calculus, it is concluded that the textbooks themselves contain very few tasks that can be defined as mathematical problems, and that those that are mathematical problems are found at the end of a chapter at the most difficult level, and are presented in a pure mathematical context. Implications are discussed.     

马克思价值转形问题上中国人数学解法的无效创意

转形问题长期陷入数学求证困境,所得到的各种结果与中外研究者所投入的时间和精力不能成正比。本文列举的中国人的三种解法,各有其特点。既要识别真伪性,也要识别合理性与不合理性。三种解法都以"西方构思"为本源,做出一点点创新(新的未必就不是伪的或不合理的),但都没有突破"西方构思"的基本框架。西方学者刻意追求数学证明,往往又止步在证伪"两个等于"。数学求证有一定的局限性。突破其局限性,不是数学技巧问题,而是数学思维问题。但是,改变数学思维终归替代不了从数学求证转换到非数学求证。     

Integrating Mathematical Learning During Caregiving Routines: A Study of Toddlers in Swedish Preschools

In recent years the interest in preschool mathematics has increased. However, studies seldom focus on children under the age of three and research is scarce on the early use of mathematics observed in natural settings. This article reports a study of mathematical possibilities during diaper changing in a preschool setting. A diaper change can be a communicative moment when the child can experience mathematics with a professional preschool teacher, but it can also be a moment of mechanical routine with no pedagogical context. The intention of the study presented here was to investigate the mathematical potential preschool teachers described in relation to diaper changing and to examine the ways this potential was put into action. Both similarities and differences emerged regarding the mathematical potential preschool teachers described in relation to diaper changing and the mathematical content that they were observed to communicate. The results show that it is possible to communicate mathematical content in a pedagogical way during diaper changes, making this routine a learning opportunity for children. However, the results also show variations in the observed range and context of such communication, and therefore the potential for mathematical learning during diaper changes seems to differ widely.     

Mathematical language and mathematical abilities in preschool: A systematic literature review

It is well established that early general language during preschool is critical for children's mathematical abilities. In an attempt to further characterize this association between language and mathematics, an increasing number of studies show that one specific type of language, namely mathematical language or the key linguistic concepts that are required for performing mathematical activities, is even more critical to children's mathematical abilities. The purpose of this systematic review is to summarize the evidence on mathematical language and mathematical abilities. We focus on preschool children as nearly all of the existing work has been done at this age. We first explain how mathematical language has been defined across studies, and report how it has been evaluated in studies in preschool. Next, we present the results of our systematic review. Following the PRISMA guidelines and after a critical appraisal, we ended with a set of 18 papers that were all of sufficient methodological quality. In these studies, mathematical language was defined as terms that are about numbers and operations on numbers (e.g., nine), but also included linguistic terms that do not directly refer to numbers, yet are important to understand mathematical concepts (i.e., quantitative and spatial terms such as fewest and middle, respectively). Some of these studies evaluated children's performance on mathematical language tasks, while others evaluated the mathematical language input provided to the child by their (educational) environment (teachers/parents/interventionists). Mathematical language correlated positively with children's mathematical abilities, concurrently and longitudinally. It also directly affected children's mathematical abilities, as was shown by intervention studies. We discuss potential directions for future research and highlight implications for education, arguing for more support for teachers and parents to improve the use of mathematical language in the classroom and in home settings.     

Measuring the mathematical quality of instruction

In this article, we describe a framework and instrument for measuring the mathematical quality of mathematics instruction. In describing this framework, we argue for the separation of the mathematical quality of instruction (MQI), such as the absence of mathematical errors and the presence of sound mathematical reasoning, from pedagogical method. We argue that conceptualizing this key aspect of mathematics classrooms will enable more clarity in mathematics educators’ research questions and will facilitate study of the mechanisms by which teacher knowledge shapes instruction and subsequent student learning. The instrument we have developed offers an important first step in demonstrating the viability of the construct.     

数学建模培训课程体系设计探讨

数学建模培训的目标是培养学生应用数学解决实际问题的能力.对参与数学建模培训的学生的能力要求主要包括:对数学学科的宏观驾驭能力,分析和解决问题以及数学建模的能力,数学模型的求解能力以及对计算机工具和数学软件的使用能力,数学迁移能力和创新能力等.数学建模培训课程体系设计包括以下几个阶段:准备阶段,建模预处理阶段,专题培训阶段及模拟和实战阶段.     

儿童数学认知策略研究新进展

认知策略是指向认知目标的一种心理操作,主体通过使用策略,可以达到解决问题的目的,关于儿童数学认知策略的研究是探讨个体整个认知策略发展的重要途径之一。儿童数学认知策略的特性主要表现为多样性和差异性、竞争性和适应性、突变性和渐进性。儿童数学认知策略的发展主要受教育环境、工作记忆、数学焦虑的影响。微观发生学的研究方法为儿童数学认知策略的研究提供了一个新的视角。目前儿童数学认知策略研究的新趋势主要集中在有意识和无意识之间的关系、影响儿童数学认知策略发展的内在因素和外在因素之间的关系、进一步扩大儿童数学认知策略的研究范围等方面。