深思·启思·反思·沉思——关注学生数学思维，提高课堂教学效率

数学是思维的体操，数学活动的本质是学生的数学思维活动，忽视学生数学思维训练必然会导致数学课堂效率低下。尽管大多数学生都具备能进行有效数学思维的禀赋，但是现实中并非所有的学生都能利用这种禀赋，不少学生数学学习效率不高通常与他们思维习惯不好以及数学思维品质不高有关。     

聘文学使者 启数学思维

作为思维体操的数学，如何才能更好的启迪思维？笔者认为，有时不妨在小学数学课堂教学中聘请诸位文学使者，让“他们”为开启学生的数学思维尽一份绵薄之力。     

浅谈数学课件中的思维价值

数学课件以其生动、巧妙、直观的演示，把数学课堂引入了崭新的境地，令许多数学老师趋之若鹜。教师在使用多媒体上课时，只有把数学思维融入到数学课件之中，才能像春雨润物般渗透到学生内心，帮助他们优化思维方法和思维品质，取得在数学上的长远发展。     

培养学生数学创新思维的教学策略

数学思维按其智力品质可分为再现性思维和创新性思维两种。在数学教学中，培养学生数学创新思维的策略有：让数学创造进入课堂，激发学生数学创新思维的动机；展现数学思维过程，引导学生探索数学创新思维的规律；实施开放式数学教学，创设学生进行数学创新思维的情境。     

论高中学生的数学思维障碍

通过对高中学生数学思维障碍的成因分析,提出了要提高存在数学思维障碍的学生的解题能力,就要了解学生掌握的基础知识状况、思维方式,并重视对他们进行数学思想方法教育。     

探讨高中学生的数学思维障碍的成因及突破

在多年的数学教学中,笔者发现很多学生数学成绩不好,究其原因是他们数学思维存在着障碍,有些当然是来自于教学中的疏漏,更多的则来自于学生自身.研究高中学生的数学思维障碍对于增强高中学生数学学习能力有十分重要的意义,找到破除数学思维障碍的方法有利于数学教学质量的提高.     

试论数学教育中两个思维过程的教学

数学思维包括发现性思维和整理性思维，在数学活动中，它们相辅相成，互相补充，共同促进数学思维的发展，为有效解决学生数学学习中的问题，必须同时加强这两个思维过程的数学。     

关于数学思维训练教学的探讨

现代数学论认为，数学教学是数学思维的教学。思维活动的强弱，决定一个人的思维品质。在数学课堂教学中，探求问题的思考、推理论证的过程等一系列数学活动都以逻辑思维为主线，这是数学教学中实施思维训练的理论依据之一。     

研究思维水平的差异，注重创新思维的培养

提高数学能力是每一个数学教师在教学中关注的热点，而数学思维能力是数学能力的核心，在数学教学中注意随时观察学生的思维过程和现状，分析和研究他们思维水平的差异，有针对性地提高学生的思维能力，提升他们的思维水平，是数学教学研究中一个重要的课题。一、从下面例题的解法看思维水平的差异例：等差数例狖an狚的前m项和为３０，前２m项和为１００，则它的前３m项和为（）A．130B．170C．210D．260这是1996年全国高考试题。解法1：直接运用等差数列求和公式，设公差为d，由题设得，因此选C。解法2：先考虑一般情形，研究Sm，S2m，…     

依托动手操作学习 培养学生数学抽象思维能力

在数学教学中，教师要高度重视学生的动手和用脑的训练，以此助推学生数学学习的开展，促进他们进行智慧数学学习。基于此，教师要科学地研读教学内容，把握学生的学情，并通过真实的动手操作引导来点燃学生的抽象思维火花，丰厚他们的抽象思维认识，激发他们的抽象思维活力，发展他们的抽象思维能力，使学生的数学学习更有思维含量，从而不断提升其学习实效性。     

How to use (five) curriculum design principles to align authentic learning environments,assessment, students’ approaches to thinking and learning outcomes

In this article, we articulate five principles of curriculum design and illustrate their application in a third‐year undergraduate course for environmental and ecological scientists. In this way, we provide a practical framework for others wishing to enhance their students’ learning. To apply the five principles, we created a learning environment consisting of a broad range of learning resources and activities which were structured and sequenced with an integrated assessment strategy. The combined effect of this ensured alignment between the learning environment we created, the thinking approaches students used and the learning outcomes they achieved. More specifically, the assessment activities guided students by requiring them to recognise when their understanding was limited – and then to engage them in thinking approaches that would develop their understanding further. By providing a framework of thoughts, ideas and information, we sought to progressively enhance the sophistication of our learners’ thinking. Thus, the assessment required students to integrate, synthesise and construct their understandings in ways consistent with the discipline and the professional pathways on which they had embarked. We intend that this illustration will act as a guide to other academics to adopt the same principles in their teaching.     

高职学生学习驱动力情况分析与研究

高职学生学习驱动力不足的问题已成为高职院校提高教学质量,谋求内涵发展的障碍,对高职学生个性、品质、思维方式、未来发展也都将产生较大影响。从分析高职学生学习驱动力不足的原因入手,提出了对应的解决措施,旨在帮助高职学生树立正确的学习目标、养成良好的学习习惯、激发他们的学习驱动力。     

College Now Program: Successful Transition for Moderate Achievers

Do our students actually read and use the feedback we provide? If so, what purpose does it serve them? Although these should be concerns, if we provide the adequate tools and guidance on how to use our feedback, this question should not be a pedagogical burden. Ultimately, learning, thinking, and understanding are the products of good feedback to a student, which includes feedback that may not be as concrete as students would like. But concrete ambiguity may be the key in helping our students develop their thinking, as well as their writing.     

Development of Scientific Thinking Facilitated by Reflective Self‐Assessment in a Communication‐Intensive Food Science and Human Nutrition Course

A one‐credit seminar on controversies in food science and human nutrition was a platform to introduce students to learning frameworks for thinking‐like‐a‐scientist. We hypothesized that explicitly engaging students in thinking about their thinking abilities within these frameworks would enhance their self‐perception of scientific thinking, an important general ability for food scientists. Our objectives were to assess thinking‐like‐a‐scientist using a student self‐assessment survey, and analyze their self‐reflections for evidence of such thinking. For students enrolled in one of the offerings of this course among 5 semesters from 2012 to 2014, differences in scores on a survey instrument for thinking‐like‐a‐scientist from the beginning to the end of the course showed gains in self‐assessed abilities (N = 21 to 22 students/semester). In each of the first 2 semesters in which we introduced thinking‐like‐a‐scientist frameworks, students thought they were better at defining problems scientifically by 13% to 14%. In the 3rd course offering, students’ self‐assessment of their abilities to seek evidence improved by 10%. In the 4th and 5th semester course offerings, students’ self‐assessed abilities to develop plans based on evidence improved by 7% to 14%. At the end of each semester, students’ self‐reflections on scientific thinking (N = 20 to 24/semester) included specific reference to asking questions (45% to 65% of reflections) and making plans based on evidence (26% to 50% of reflections). These data support the usefulness of self‐reflection tools as well as specific learning frameworks to help students to think about and practice thinking‐like‐a‐scientist.     

论评价思维及其对高校创新教育的意义

评价思维是对发散思维和聚合思维的超越,创新思维=发散思维 评价思维。培养大学生评价思维能力可以充分发展大学生创新能力,实现大学生创新能力由自我性向社会性的顺利转变,提高学生创新学习能力。高校应该从教师观念、教学和评价制度三个层面着手,遵循提高学生评价思维能力的必要性,培养学生的评价思维,并体现出其对创新学习的有用性。     

评价思维及其对高校创新教育的意义

评价思维是对发散思维和聚合思维的超越，创新思维一发散思维＋评价思维。培养大学生评价思维能力可以充分发展大学生创新能力，实现大学生创新能力由自我性向社会性的顺利转变，提高学生创新学习能力。高校应该从教师观念、教学和评价制度三个层面着手，遵循提高学生评价思维能力的必要性，培养学生的评价思维，并体现出其对创新学习的有用性。     

从算术到代数

从算术向代数过渡,是学生数学学习过程中极为重要的转变阶段.符号是代数不同于算术的典型特征,学生从算术向代数的过渡,是从对数的思考向对符号的思考的转变,是从算术思维向代数思维的转变,是思维层次从个别到一般、具体到抽象的飞跃.     

Exploring and enhancing spatial thinking skills: Learning differences of university students within a web-based GIS mapping environment

There is a dearth of research concerning the learning effects of web-based mapping tools on students with different learning characteristics. This study investigates the extent that different learning styles exert an influence on spatial thinking of students within a web-based GIS mapping environment. Thirty six sophomores utilized the tools over one semester in a course guided by a blended learning approach. A learning style inventory, a self-rating questionnaire and a survey were administered to these students to examine their learning styles, the development of their spatial thinking skills as well as factors influencing the enhancement of their spatial thinking skills. Results show that all learners have improved their spatial thinking skills after interacting with the GIS mapping tools. However, the visual and auditory learners have improved significantly more than the kinaesthetic learners (p = 0.024). The survey result from students shows that such differences may be attributable to the design of the web interface that matches the learning styles of the visual and auditory learners better than with that of the kinaesthetic learners. Our findings contribute to the current debate on students’ learning styles as well as to help instructional designers and educators optimize learning in spatial thinking through personalized learning design.     

思维课堂:意蕴与实践——基于深圳市南山区第二外国语学校的课堂文化建设

思维课堂有着深刻的内涵与丰厚的意蕴。它以学生为中心构建课堂教学的基础,以激活学生的思维凸显课堂教学的核心,以丰富的课堂活动作为提升思维品质的载体,实现问题导学与深度思维的统一、集体思维与个体思维的统一和教师研导与学生研学的统一。通过构建系统的实施策略和可行的操作模式,可拓展学生的学习与思维空间,提升思维品质与创新能力。     

基于三维图形思维拓展的三维动画课堂教学改革初探

目前国内的三维动画课程教学均以软件操作学习为主,过于重视三维技术的学习,忽略了对学生创造性思维的培养。所以,动画专业的课程教学需要进行有针对性的改革,并培养学生的艺术素养、激发学生的自我思考能力和三维图形思维拓展能力。文章通过对三维图形思维拓展概念的解读和三维课程课堂教学改革的初步探索,创造了三维图形思维拓展教学改革"三步走"的方法,分析了基于三维图形思维拓展的实践过程和效果,从而奠定了课堂改革的基础,确定了三维动画教学改革的方向。