高职数学教学中数学文化的融入探索与实践

文章借鉴了一些本科院校开设数学文化课的经验,结合高职院校的实际情况,提出了在开设高职数学课的同时进行数学文化的融入,以及如何在高职数学教学中寻找数学文化的融入点,结合具体实例探索如何挖掘若干数学题材中的文化意义,并将其融入到高职数学教学中去,把传授数学知识和揭示数学文化相结合,从而提升学生的人文素养和创新精神。     

Use of comics to enhance students’ learning for the development of the twenty-first century competencies in the mathematics classroom

Abstract

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (1) several sets of comic strips expounding all related mathematical concepts in a lively way; (2) tiered practice questions for learning reinforcement; and (3) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and 11 students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.     

初中数学“章起始课”的探索与思考

在数学课程标准研制与修订中,一个重要的改进是强调整体把握课程,掌握课程的知识、方法、思想体系,促进学生核心素养、数学核心素养的发展。在数学教学中,如何上好数学“章起始课”的探索和实践是一个重要的抓手。围绕章起始课的教学要遵循六条基本原则:统领性、整体性、逻辑性、发展性、温故性、激趣性。     

Some Characteristics of East Asian Mathematics Classrooms Based on Data from the Timss 1999 Video Study

In this paper, characteristics of mathematics classrooms in the East Asian countries¹ of Hong Kong and Japan are discussed based on an analysis of the data of the TIMSS 1999 Video Study. The data shows that although students in these East Asian countries did not talk a lot in the classroom, they were exposed to more instructional content. The mathematics problems they worked on were set up mainly using mathematical language, and compared with the problems solved by students in other countries, the problems took a longer duration to solve and more proof was involved. According to the judgement of an expert panel on the Hong Kong lessons (Japan did not participate in this part of the study), more advanced contents were covered and the lessons were more coherent. The mathematics presentations were more developed, and the students were more likely to be engaged in the lessons. In sum, the overall quality of the teaching in this East Asian country was judged to be high. The findings show that high quality teaching and learning can take place even in a teacher directed classroom. It is argued that these East Asian classroom practices are deeply rooted in the underlying cultural values of the classroom and the wider society. The paper ends by drawing some implications of the study for the mathematics education community in other cultures.     

Teacher Actions to Maximize Mathematics Learning Opportunities in Heterogeneous Classrooms

The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class.     

Self-Study of a Teacher's Journey toward Standards-Based Mathematics Teaching

The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university. The shared analysis helped him learn to involve his students more directly in their own learning. A major lesson learned was that understanding the potential value of a problem-solving approach to teaching mathematics does not guarantee corresponding changes in the classroom. Two vital elements of lesson development emerged as focal points for self-study. After first learning how to prepare worthwhile mathematical tasks, the teacher also learned the importance of implementing effective questioning strategies to help students think more deeply about the mathematics they were learning.     

高职院校电气系各专业数学课程设置的探讨

本文从高职院校电气系各专业对数学课程需求情况的调查分析入手，提出了电气系数学教学的构想。指出高职数学教学必须贯彻“必需够用”的原则，采用适合高职特点的教学方法：结合专业，讲清概念；减少不必要的理论推导；提倡数学工具的应用。     

以就业为导向高职数学课程改革的探索

高职教育培养的是“应用型”高技能人才。因此,“以就业为导向”的高职数学教学应以“服务专业、注重应用、培养能力”为原则,优化教学内容,针对高职生的特点改革教学方法,采用现代化的教学手段,理论知识与实践教学相结合,建立能力考核为主的评价体系,注重培养学生运用所学的数学知识分析和解决实际问题的能力,提高学生的就业能力。     

让学生获得基本数学思想方法

数学的思想方法是数学的生命和精髓,忽视其教育价值,将缺乏后继的生长点。＂渗透＂难以承担作为教学目标的＂思想方法＂的教学任务,唯有＂把握内涵,跨越渗透;着眼目标,拓展途径;落实过程,循序渐进;讲求策略,系统运作;综合运用,触类旁通＂,方可实现教学目标,确保学生获得适应社会生活和进步发展所必需的＂基本思想＂。     

后现代教育理念视野下的数学教师教学行为

后现代教育理念对数学教育目的观、课程观、教学观的反思和批判产生一定的影响。关于数学教学观的反思主要体现于数学教学行为的改变：构建数学认知结构,强调学生个体的＂意识的建构＂;呈现静态知识方式,创设学生个体的＂认知的情境＂;重构思维发展模式,塑造学生个体的＂茎块式思维＂;培养问题质疑能力,强化学生个体对＂问题的反思＂;突破师生交往方式,注重师生之间的＂对话的互动＂。     

Teachers’ beliefs and practices related to mathematics instruction

Beliefs and practices related to mathematics were assessed for 21 fourth- through sixth-grade teachers. At the beginning and the end of the school year teachers’ beliefs about (1) the nature of mathematics (i.e., procedures to solve problems versus a tool for thought), (2) mathematics learning (i.e., focusing on getting correct solutions versus understanding mathematical concepts), (3) who should control students’ mathematical activity, (4) the nature of mathematical ability (i.e., fixed versus malleable), and (5) the value of extrinsic rewards for getting students to engage in mathematics activities were assessed. (6) Teachers self-confidence and enjoyment of mathematics and mathematics teaching were also assessed. Analyses were conducted to assess the coherence among these beliefs and associations between teachers’ beliefs and their observed classroom practices and self-reported evaluation criteria. Findings showed substantial coherence among teachers’ beliefs and consistent associations between their beliefs and their practices. Teachers’ self-confidence as mathematics teachers was also significantly associated with their students’ self-confidence as mathematical learners.     

数学软件在高职高专数学教学中的应用探讨

在高职高专数学的教学过程中把数学内容与数学软件进行有机结合是数学教学最有效的教学模式,介绍了数学软件在教学中的作用,说明了在教学过程中如何把数学知识和数学软件有效地结合起来,加强了数学教学的实用性,从而提高学生在专业学习、实际工作与生活过程中使用数学的能力．     

Unraveling the culture of the mathematics classroom: A video-based study in sixth grade

Changing perspectives on mathematics teaching and learning resulted in a new generation of mathematics textbooks, stressing among others the importance of mathematical reasoning and problem-solving skills and their application to real-life situations. The article reports a study that investigates to what extent the reform-based ideas underlying these mathematical textbooks impact the current teaching of mathematics. Two problem-solving lessons were videotaped in 10 sixth-grade classrooms and a coding scheme was developed to analyze these lessons with regard to three aspects of the classroom culture that are assumed to enhance students’ mathematical beliefs and problem-solving competencies: (1) the classroom norms that are established, (2) the instructional techniques and classroom organization forms, and (3) the set of tasks students are confronted with. Two instruments were administered to measure students’ beliefs about learning mathematical word problem solving, and to assess their problem-solving processes and skills. The results indicate that some reform-based aspects seemed to be easier to implement (e.g., a strong focus on heuristic skills, embedding tasks in a realistic context) than others (e.g., the use of group work, an explicit negotiation of appropriate social norms).     

Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem solving

In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning mathematics via problem solving. Two novice MTEs worked with an experienced MTE and reflected on the process of learning to teach via problem solving and supporting PTs in developing deep understandings of foundational mathematical ideas. Taking a position of inquiry as stance, we examined our experiences teaching mathematics content courses for PTs via problem solving. We found that all of the MTEs used and developed some MKTT through (a) understanding and deciding on the mathematical goals of both the individual lessons and the two-course sequence as a whole, (b) choosing and facilitating tasks, and (c) using questions to scaffold PTs learning and engage them in mathematical processes such as making conjectures, justifying their reasoning, and proving or disproving conjectures.     

ICT as a Change Agent of Mathematics Teaching in Swedish Secondary School

There is a common assumption that computers will change the conditions for mathematics teaching. In this article the author discusses how the computer as a change-agent may influence the conditions, methods and results in everyday mathematics teaching. The empirical material is collected through interviews with eighteen teachers in lower secondary school. The author has also participated in all computer-aided lessons given by two teachers during one year. That means 700 possible computer-aided lessons. Teaching of mathematics seems to have such a strong tradition that the computer as a change-agent is relatively weak. The fact is that the computer is assimilated into an old tradition of methods and contents. A great deal of the computer-aided lessons give attention to drilling pupils with different types of drill-program where they can learn mathematical procedures. In some lessons laborative work is pursued with the intention that the pupils computer-aided learn mathematical concepts.     

大学数学学习障碍的成因与对策

高等教育大众化以来,感觉数学学习困难的大学生人数逐渐增多,部分学生产生厌学情绪。理清这些大学生学习困难的原因,制定相应的教育策略,营造良好的学习氛围,进行因材施教,是当前大学数学教学改革的一项重要课题。导致学生学习障碍的主要原因：一是教学内容的衔接问题,二是教学方式的转变问题,三是思维方式的转变问题,四是外部环境的影响问题。大学数学教学要以学生为中心,不断改进教学方法,加强与中学内容的衔接,将数学思想、数学方法和数学建模思想融入课堂教学,构建和谐的数学教学文化理念,将数学文化融入课堂,激发学生的学习积极性,着力提高大学数学教的水平和学生学的质量,真正为学生的全面发展奠定良好的基础。     

经验学习理论对数学活动经验教学的启示

学生数学活动经验对于学生数学学习活动的开展、数学思想方法的领悟等方面有着十分重要的作用。经验学习理论对学生获得数学活动经验的教学具有重要的启示：为学生提供有层次性的、数学本质一样的、广泛的活动情境及足够的替代性经验,让学生经历参与、反思、内化等数学活动的全过程,及时反省、评价、抽象和运用在该过程中获得的经验,并利用“社会”因素,积极干预学习风格的不良影响,有助于学生获得充足的数学活动经验。     

如何突出经济数学的教学特色

结合数学与经济学之间的联系,将经济问题转化为数学问题,用数学方法对经济学问题进行分析.从课程目标、学习重点来说,经济数学教学与高等数学的教学有很大的区别.从经济数学教学的课程体系、方式、方法等方面对如何激发学生学习经济数学的兴趣,培养学生的数学思维,从而提高他们的数学应用能力进行一定的探讨.