华罗庚的数学“双基”教学思想及其启示

华罗庚在几十年学习、研究、教授、普及数学和指导师生数学教与学中形成的数学教育思想是珍贵的财富,对于研究中国数学教育的优良传统和开展数学课程改革都具有重要的指导意义.华罗庚认为,数学教学的基本要义是让学生在打好"双基"中走向创造,为此,数学教学要重视"双基"教学,使学生对"双基"达到"懂"、"识"、"熟",并通过自学、独立思考、历经成功和失败、加强训练等"双基"教学方式使学生在打好"双基"中学会创造.     

数学教学中几何直观应用探研

小学生的思维以具体形象思维为主,对抽象知识的理解和接受能力还比较弱。在数学教学中,教师可巧妙借助几何直观,使抽象的问题形象化、具体化,从而降低学生的学习难度,提高教学效率和教学质量,提升学生数学核心素养,为学生终身学习奠定坚实基础。文章结合教学实践,对数学教学中几何直观应用进行探研。     

高职学生数学价值观的培养

高职学生数学价值观的培养是提高数学课程教学效果的主要内容之一,只有在充分认识和理解数学价值观的前提下,才有可能对学生的数学价值观进行培养,从而进一步提高学生学习数学课程的积极性。培养途径包括：在使用中学习,在学习中使用,以培养数学的应用价值;教学方法和具体教学内容有机融合,以培养数学的人文价值;突出教师主导学生主体作用,健全思维监控机构,以培养数学的思维价值;抽象与具体结合,应用与探究学习结合,以培养数学的科学价值。     

6+1教学法在高等数学教学中的研究

针对部分学生认为学习高等数学枯燥乏味,甚至产生厌烦、逃避的情况,提出6+1高等数学教学法.6+1高等数学教学法改变了传统高等数学教学中"教师讲、学生听"的教学模式,且与"学生为主体,教师为主导"的现代教学理念相吻合.通过"导""议""展""评""理""研""思"七环节,激发学生学习高等数学兴趣,培养学生的自主学习意识,提高学生的高等数学逻辑思维和探究能力.     

多元表征:探寻数学智慧课堂的一把密钥

将多元表征渗透到数学课堂教学中,一方面可以调动学生多感官的认知因素,促进知识的理解,培养学生的数学思维以及促进学生数学智慧的生长;另一方面通过对问题进行多元化的表征,为学生解决数学问题提供了新的平台,从而有助于提高学生对问题多角度的解释能力和创新能力。数学中多元表征的教学策略为:精深挖掘资源,探索数学表征的多元化;运用教育机智,达到多元表征的最优化。但要注意,多元表征不是每堂课都适用,也不是每个学生都能在课上得到最大的收获。     

A response to strategies and tactics through participatory action research in a developmental mathematics course

This paper explores the value of participatory action research in a community college developmental mathematics course. The authors used the framework of critical mathematics education in order to understand the critical conversations of students about their learning experiences, and also to help the instructor of the course develop the curriculum that attended to student experiences. The authors also draw on Michel de Certeau’s ideas about strategies and tactics to understand how students responded to their past learning experiences. Data results from the study show that students can gain a better understanding of their own learning and subsequently develop deeper content knowledge when they are more involved in the teaching and learning process. Lastly, the authors conclude that as adult learners grow in their understanding of the learning processes and of the content being presented, participatory action research can play an important role in the entire development of thinking and intellectual engagement.     

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.     

Teachers’ assessments of students’ learning of mathematics

This paper reports a study of the classroom assessment practices of 12 sixth form college mathematics teachers in Malta. It explores the extent to which these teachers are knowledgeable about their students’ learning of mathematics and the implications that this has for their classroom practices. It reveals that these teachers’ knowledge of their students’ understanding of certain mathematical concepts is fairly limited. It then goes on to discuss this phenomenon in terms of a process that can hinder rather than promote learning. The research illuminates the position of teachers who appear to lack certain detailed information about their students which, it can be argued, could inform more effective teaching strategies. The paper concludes by exploring possible implications for similar situations where learning could be enhanced by more effective classroom assessment strategies and their use to inform future teaching and learning activities.     

初中数学课堂中分层教学的点滴策略初探

由于初中生学习能力和生活环境的不同,他们对数学知识的理解和掌握也各不相同。要想使不同层次的学生都得到提升,需要初中数学教师采用分层教学法,尊重学生的个体差异,突出学生的主体地位,结合实际学情,达到整体推进的效果。本文从五个方面分析初中数学课堂教学分层的策略,旨在提升初中数学教学质量。     

The effect of manipulatives on mathematics achievement across different learning styles

The current study investigates the influence of manipulatives used in combination with traditional approaches to mathematics education and how varying amounts of time spent on manipulative use influence student achievement across different learning styles. Three learning environments were created that incorporated varying proportions of traditional teaching approaches and manipulative methods. In one of the learning environments, the teacher used strictly lecture- and exercise-based teaching activities, which are more conducive to abstract learning. Abstract learners showed higher academic performance compared with concrete learners in the environment where only traditional methods were used. For the other two environments, which utilised varying combinations of manipulative tools and traditional methods, the differences in the mathematics achievement levels among students of varying learning styles were not statistically significant. The study also showed that concrete learners demonstrated higher performance in mathematics when manipulatives were used than did their counterparts in the environment where only abstract activities were used; however, in the third learning environment, increasing the amount of manipulative use did not provide an extra benefit to concrete learners.     

Student Motivation and Learning in Mathematics and Science: A Cluster Analysis

The present study focused on an in-depth understanding of student motivation and self-regulated learning in mathematics and science through cluster analysis. It examined the different learning profiles of motivational beliefs and self-regulatory strategies in relation to perceived teacher autonomy support, basic psychological needs (i.e. autonomy, competence, and relatedness), motivational regulations, and academic achievement. Grounded in self-determination theory, this study examined the learning profiles of 782 students from eight secondary schools in Singapore. The cluster analyzes revealed four distinct learning profiles, and they were compared in association with perceived teacher autonomy support, needs satisfaction, motivational regulations, and grades. Cluster profiling enables teachers to have better understanding of their students’ self-regulated learning so that they can apply effective teaching strategies to foster their motivation. The findings offer a perspective to secondary students’ psychological needs along with some insights into their perceived task value and self-efficacy in the contexts of mathematics and science.     

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。     

An Analysis of Prospective Teachers' Dual Roles in Understanding the Mathematics of Change: Eliciting Growth With Technology

We analyze the interrelations between prospective and practicing teachers' learning of the mathematics of change and the development of their emerging understanding of effective mathematics teaching. The participants in our study, who were all interested in teaching secondary mathematics, were mathematics majors who had significant formal knowledge of the fundamental concepts of calculus prior to taking our courses, but who often experienced and expressed procedural orientations toward the teaching of mathematics. To address this difficulty, we developed novel computer-based activities to challenge the participants' mathematical understandings and required them to use technology during short teaching episodes they conducted with younger students. To analyze our participants' understandings, we developed a framework that juxtaposes the roles of the participants as students and teachers, and their understanding of mathematics and of pedagogical strategies. Our analysis of the participants' views from these different perspectives enabled us to see simultaneously the intertwined development of subject matter insights and specific views of teaching. This revised version was published online in August 2006 with corrections to the Cover Date.     

中学生数学理解障碍及教学对策的探究

数学理解障碍是数学学习中不容忽视的一种障碍．从数学认知、教育心理学等层面来讲，中学生的数学理解障碍有认知型障碍，表象型障碍，联系型障碍，语言型障碍；克服这些障碍相应的教学对策有：帮助学生生成正确的数学表象；利用实物、模型等，增强学生对知识的感性认识；利用多媒体进行辅助教学；注重数学交流；加强学生对数学知识的自主探究与实际应用等来加深理解。     

Developing culturally responsive mathematics teachers: secondary teachers’ evolving conceptions of knowing students

Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the importance of culture in mathematics education. To contribute to what is known about supporting secondary mathematics teachers in developing a culturally responsive teaching practice, we studied the impacts of a graduate course called Culture in the Mathematics Classroom on 13 teachers enrolled in the course. The course was designed to guide secondary mathematics teachers in understanding and growing their capacity to enact culturally responsive teaching in their classrooms. The purpose of our research was to explore how teachers’ perceptions changed as a result of their engagement in the class with respect to understanding the role of culture in knowing and being responsive to their students. Specifically, we examined how each of the four course projects seemed to individually and collectively influence teachers’ thinking. Overall, teachers appeared to expand their cultural awareness and dispositions for cultural responsiveness that would support them in knowing and supporting their students in the manner of a culturally responsive teacher. Teachers did not, however, develop some more “advanced” understandings related to power and privilege in society. This study provides researchers and mathematics teacher educators with a potential analytic framework for understanding teacher change with respect to culturally responsive teaching.     

论数学概念的教学

在数学学习中，数学概念不清，学生在进行计算，证明，交流、推理时都会出现极大困难，然而，由于不少学生在以抽象思维能力为主的数学能力等诸多因素上的差异，导致了数学概念这个重点同时又成了数学教学的难点，本文从探讨数学概念教学困难的原因，数学概念的学习机制入手，为的是找出更加有效的教学策略，以促进数学课堂教学改革，实现高效教学。     

论中小学数学课程中的情境及其作用

作为一种数学学习资源,情境在数学教学中发挥着多种作用:激发兴趣,促进学生参与数学学习;揭示知识的产生背景,促进学生对数学的理解;启迪思维,引导学生探寻解决问题的策略;提供运用数学的机会,培养学生解决问题的能力;等等。深刻理解情境多方面的作用,有助于促进学生有意义的数学学习。     

新课标下数学实验教学策略的探索

数学是一门比较抽象的学科,需要学生具有一定的抽象思维。学生以形象思维为主,加强数学实验教学是一种有效的教学方式,能帮助学生理解知识形成过程,提升学生学习效果。教师要对新课标下数学实验教学策略进行探索,以增强实验教学的趣味性,突破教学重难点,提升学生数学学习能力。     

问题导学法在初中数学教学中的应用探究

问题导学法是随着教育教学改革不断深化而出现并且得到教师广泛关注和应用的一种新兴的教学模式。在初中数学教学课堂上应用这种模式,不仅能实现教学效率的提升,还有助于学生自主学习能力的强化,实现学生的综合发展和成长。因此,教师要在课堂上强调问题的设计,通过师生有效沟通以及课堂的回顾总结,使这一模式在数学课堂上得到更好的应用,同时给初中学生的数学学习和全面发展提供更大的帮助。