Development of computer play pedagogy intervention for children with low conceptual understanding in basic mathematics operation using the dyscalculia feature approach

This study describes the development of a basic computer-based play pedagogy intervention using a dyscalculia-remedy-oriented approach such as repetition and number orientation manipulation, and the investigation of its effect on children displaying dyscalculia characteristics. This computer play was evaluated in a group of 50 seven-year-old Malaysian children, who were low achievers in mathematics subject and were divided into control and intervention group. The intervention group engaged with the newly developed computer play for an hour per day for five consecutive days, while the control group attended normal classroom learning for the same time period. Overall post-test scores indicated that children from the intervention group performed significantly better than the control group after the five-day intervention period by 57.9%. Number disorientation and arithmetic operation confusion, which are common amongst the children displaying dyscalculia characteristics, were also significantly reduced after the intervention. This implies that the children benefitted from the computer play.     

Examining the effects of writing on conceptual and procedural knowledge in calculus

It has been claimed that writing to learn mathematics (WTLM) may benefit students' conceptual understanding as well as their procedural ability. To investigate this claim, we collected data from students in two sections of an introductory calculus course. In one of the sections, students used WTLM activities and discussed the activities after completing the writing; in the other section, students used similar activities that did not involve writing but engaged them in thinking about the mathematical ideas and in discussing the activities. The errors from the in-class and final exams of both groups of students were categorized and analyzed for information about the students' conceptual and procedural understanding. We found no significant differences between the WTLM group and the non-writing group, which suggests that the real benefit from writing activities may not be in the actual activity of writing, but rather in the fact that such activities require students to struggle to understand mathematical ideas well enough to communicate their understanding to others. This revised version was published online in July 2006 with corrections to the Cover Date.     

教育爱——一个被忽略了的教育学核心范畴

“教育爱”在教育实践过程中具有相当的重要性,也理应是教育学中的一个核心性范畴,但在当今的教育学理论中却鲜少对此的直接探讨。“教育爱”是教师在教育过程中对学生所施予的一种爱,因其明确的教育性意向而具有相对独特的内涵。结合一些经典的爱的理论论述,可以使我们进一步明确爱的实质内涵及“教育爱”的独特特征。     

寓"理解"于数学概念

数学概念理解是对数学概念内涵和外延的全面性把握,其特点主要有以下几方面:数学概念内涵理解的多样性,数学概念外延理解的丰富性,数学概念表述理解的抽象性,数学概念符号理解的系统性,数学概念应用理解的多变性,数学概念定义理解的逻辑性.根据不同特点的数学概念所对应的理解过程和方式可将数学概念分为叙实式数学概念、推理式数学概念、变化式数学概念和借鉴式数学概念4种类型.     

研究性数学、教育数学与数学教育

数学可分为研究性数学和教育性数学。研究性数学主要注重科学逻辑的序,而教育性数学则注重科学逻辑的序与认知心理的序之间的完美结合,后者即“教育数学”。教育数学是在研究性数学基础上的再创造、再提高,教育数学对数学教育改革具有深远的意义。     

被忽视的重要教育议题:校服的多重教育功能

校服具有重要的教育功能,人们对校服所承载的独特教育功能也都寄予厚望。校服蕴含了多重教育功能:一是教育秩序的强化功能,二是良好道德的涵育功能,三是审美追求的化育功能,四是健康心理的培育功能。我国当前的校服教育功能发挥地还并不充分,存在三多三少的问题,需要加强质量监管、兜住质量底线,注重校服设计、强化审美化育,助推校服产业、做大民族品牌。     

“悟是光”概念结构的认知分析

＂悟＂概念是一类比较常用的语汇。以汉语和英语为语料,剖析＂悟＂概念生发于＂光＂概念的认知根源,进而对＂悟是光＂概念结构生成过程中人类的隐喻化和范畴化发展机制进行了详细说明,旨在依托认知规律,对概念的隐喻化取象和范畴化拓展路径提供进一步的实践操作性借鉴。     

中学生数学解题表征的一次调查测试

问题表征是指问题或任务在问题解决者头脑中是如何呈现、如何表现出来的．问题表征依赖于人的知识经验，也受到注意、记忆和思维的影响．中学生问题表征处于3个不同水平：(1)程序性表征；(2)发展的表征；(3)概念性表征．经常要求学生解释数学表达式的意义，是促进学生概念性理解的重要手段．     

数学理解的层次性及其教学意义

数学理解有不同的程度、层次,这些层次包括:零层次、常识性层次、逻辑性层次、观念性层次和无尽的层次.数学理解层次的主要特点有不连续性、整体功能性、两种循环性和两种依赖性.在数学教与学中提高数学理解层次的途径有亲历知识的生长过程,参与数学研究,以及进行哲学思考.     

复杂思维下教育研究的挑战与应战

当前教育研究已取得了丰盛硕果，但也存在着诸多问题，复杂思维的冲击与挑战是一个不可忽视的致因。它对简单化的研究范式、经典性的研究内容和自然科学的研究方法都提出了质疑。在复杂视域下，理解、解释教育现象和预测教育走向，策略和方法研究成为教育研究的新的价值取向。     

xyZET: A Simulation Program for Physics Teaching

A simulation program, named xyZET, has been developed to support the teaching of physics and the preparation of interesting and challenging exercise material. xyZET offers a rich and complex user interface, which allows the development in 3D-space of numerous experiments in basic mechanics and electricity. It is also possible to visualize effects dependent upon relativistic changes of mass. In addition, the radiation of accelerated charge carriers can be demonstrated in accordance with the Linard Wiechert theory. A special learner mode has been implemented as an alternative to the normal working environment in which all the control elements are available to the user. In this learner mode, the program can be controlled by Java applets embedded in WEB pages. By clicking on active buttons, communication with the simulation program is established, using the TCP/IP protocol. This allows the learner to concentrate fully on the topic, and frees him or her from any control activity which might divert attention from the underlying science. Using xyZET and this external control feature a complete mechanics course has been developed, containing most of the traditional topics taught in 11th grade at German high schools (Gymnasium). The course material has been tested under classroom conditions and proven to be stable and effective. Further improvements can be expected if students have access to more powerful computers and more support and time is provided to allow exploratory and self-supported learning. xyZET was developed under UNIX and X-windows and runs on PC platforms under LINUX or Windows95/98.     

一种面向差错控制的认知观测系统模型--平面向量概念理解差错模式实证研究

结合认知理论和系统控制理论,构造了一种面向数学概念理解差错的观测分析模型,建立了对平面向量概念体系的理解进行实证研究的观测分析流程.通过对平面向量概念理解差错进行统计分析,认为数学概念学习中的理解差错,主要有两种模式:一类是概念模板差错,另一类是认知过程差错.基于观测分析,提出了改进设想:概念的表述;在练习中理解;重视教学的整体性;加强相关学科间的联系.     

A typology of undergraduate students' conceptions of size and scale: Identifying and characterizing conceptual variation

The importance of “size and scale” in nanoscience and engineering has been recognized by both scientists and science educators. A solid understanding of this concept is key to the learning of nanoscience. Students, however, have been reported to have considerable difficulty grasping this concept; yet little is known regarding their state of understanding. To address this knowledge gap, we conducted a series of studies that were aimed at exploring the different ways students conceive of “size and scale” in the context of undergraduate nanoscience and engineering courses. Informed by Variation Theory of Learning (Marton and Booth, 1997), we identified four major categories (with two sub‐categories within each) of student conception—fragmented, linear, proportional, and logarithmic. These conception categories, together with the aspects of variation that characterize and distinguish them, are summarized in a typology. In addition to serving as a diagnostic tool to describe students' understanding, this typology can also be used to guide the development of instructional interventions that facilitate students to move toward a more sophisticated understanding of “size and scale.” © 2011 Wiley Periodicals, Inc., Inc. J Res Sci Teach 48: 512–533, 2011     

关于数学教师的数学理解--基于一个成功的师范生培训案例的探析

传统的教学观念和教学方法影响了学生对数学活动的理解,由此导致许多学生害怕数学,甚至放弃数学.教师忽视数学理解是问题的主要原因,其中教师在教学观念和教学方法上的落后是导致其对数学知识的理解和把握不够深入的主要因素.解决问题的方法是建立高效的师资培训机制,在各级培训中强调对数学的深层次理解.     

美国“促进理解的数学课堂”简介及启示

公众的要求以及相关的研究成果使得促进理解的数学课堂的出现成为美国教育发展的必然。美国的"促进理解的数学课堂"无论在课堂讲授、作业选择,还是评价方式上都尽可能地体现理解的意义,促进学生的深层次理解。NCRMSE试图通过引导创设这样一种促进理解的数学课堂,让学生获得终身受益的数学理解能力,也即让学生获得终身需要的具有可持续发展功能的数学教育。     

试论数学理解的两种类型——从R.斯根普的工作谈起

数学学习中，理解无疑是首要的，学习在学习数学知识的过程中通常有2种含义迥然不同的数学理解模式。工具性理解和关系性理解。我们在教学实践中常常关注的是工具性理解，但我们希望学生获得的却是关系性理解，这是为什么？有益于促进学生真正理解数学的教学可以是什么样的？     

教育数学是具有教育形态的数学

数学有3种形态:原始形态、学术形态和教育形态.体现数学本质要做到返朴归真,平易近人,言之有理,感悟真情.实际教学中,数学本质常被“过度的形式化”与“教条式的教学改革”所掩盖.数学教学中,应反对“去数学化”的倾向,突出数学的文化本质,以本原问题驱动展现数学本质,利用数学史加深学生对数学本质的理解.     

教育研究范式:从二元对立到多元整合

20世纪的教育研究主要是科学和人文两大范式的争论,20世纪后期出现并可能成为21世纪主导的复杂科学,将改变教育研究范式的这种二元对立,走向多元整合的复杂性研究范式,实现教育研究方法论的根本性转换。     

脑科学在数学教育研究中的应用

20世纪90年来以来,许多脑活动测量的仪器得到发展.使用脑活动数据使得研究者有可能在不依赖学生自主解释其自身问题的能力的情况下,探查学生心理变化和学习困难水平.尝试使用真实课堂教学中的数学任务,测量学生问题解决过程的脑活动数据,进而获得了脑活动(含氧血红素浓度与去氧血红素浓度)与有关学习特征、理解过程之间的关系的初步结论,同时也为在数学教育研究中应用脑科学提供经验.