初中数优生、数困生的数学学习投入研究

通过对208名初中数优生、数困生的问卷调查,考察两类初中生数学学习投入的特点及其影响因素。结果表明：（1）数困生的数学学习投入显著低于数优生;数优生与数困生的数学学习投入有不同的变化趋势：数优生的学习投入一直维持在较高水平,而数困生的学习投入随年级的升高在逐渐下降;数困生的情感投入水平比认知投入、行为投入更低;数学学习投入的性别差异不显著。（2）社会支持、数学观和数学自我效能感对数优生、数困生的数学学习投入均具有显著影响;社会支持对数学学习投入既具有直接影响,同时也具有间接影响;数学观和数学自我效能感在社会支持和数学学习投入之间起着中介作用。     

Guest Editor's Introduction: Analyzing Tools: Perspectives on the Role of Designed Artifacts in Mathematics Learning

Concentrating the attention on one aspect makes it leap into the foreground and occupy the square, just as, with certain drawings, you have only to close your eyes and when you open them the perspective has changed. (Calvino, 1983, p. 7)     

社会视角下对学生数学教学信念的研究

从社会视角来看,学生数学教学信念可以分成如下几部分:对于作为活动中介的学校数学的信念;对于活动中自我的信念;对于活动中教师与学生角色的信念;对于活动以及活动中社会规范和数学社会规范的信念.学生的数学教学信念是在数学课堂教学的社会活动中产生和发展的.数学课程改革应该重视培养学生形成新的数学教学信念.     

Mathematics and Mathematics Education as Triadic Communication? a Semiotic Framework Exemplified

The article investigates in the first part critically dyadic and essentialist understanding of signs and utterances in mathematics and mathematics education as opposed to a triadic view. However even Peircean semiotics, giving priority to triadic, dynamic sign may face challenges, such as explaining the sign as a pragmatic act and how signs are related to context. To meet these and other hurdles an explicit communicational, pragmatic and triadic view, found in parts of the works of Bühler, Bakhtin, Habermas, and Halliday, is developed. Two basic principles are combined and established in a theoretical framework. Firstly, whenever uttering, there will exist in any semiotic sign system, dynamic reciprocity and simultaneity between expressing through form, referring to content, and addressing as an act. Secondly, meaning will be created by the dynamics between given and new in utterances and between utterances and contextual genres. The latter principle explains how meaning merge in communication dynamically and create the basis for a discursive understanding of semiosis and hence even learning at large. The second part exemplifies each of the three main aspects and the dynamics of utterance and genre and given and new by excerpts from a textbook in mathematics education. The concept ‘positioning’, in use for operationalisation, is explained in relation to main principles of the framework. The article ends focusing crucial implications for validation when moving from a dyadic to a triadic understanding of mathematics and mathematics education.     

数学学习与数学迁移

数学的初始学习对迁移来说是重要的,对学习经验相当程度的熟悉有助于迁移.过度情境化的知识不利于迁移,而知识的抽象表征有助于促进迁移.迁移完全是主动、动态的过程,并非是一类学习经验的被动结果.所有的新学习都包含了先前学习的迁移,这对设计促进学生学习的教学有着重要的意义。     

Communicating Mathematics on the Internet: Synchronous and Asynchronous Tools

Communicating and collaborating online are becoming common requirements in education. The specialized notations and symbols necessary for some content areas where mathematical expressions are part of the conversation require that users select appropriate communication tools. The purpose of this article is to describe tools that can be used for online, asynchronous or synchronous communication involving mathematical expressions.     

Communicating to Learn Multivariable Calculus: Students' Blackboard Presentations as a Means for Enhancing Mathematics Learning

This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the benefit of themselves and their peers. The intervention appears to have incentivized students to engage with and learn mathematics contents in an effective way, and it also helped the mathematics teacher to reflect on, adapt, and develop his teaching strategies. To conclude, it would seem that both students and teachers in mathematics have much to gain from giving students opportunities to develop their own voice in learning contexts otherwise relying on books and lectures.     

论学习的研究范式与视界

影响人的学习的最重要因素是什么?不同的教学理论对此给出了大相径庭的答案,这是因为它们各自对学习本身持有不同的视界,有的看重预期的学习结果,有的聚焦影响学习过程的各种方法,还有一些则抓住了学习发生的条件.有八种对教育传播与技术领域的理论发展一直产生影响,并且仍在产生强烈影响的最流行研究范式,它们分别是完形心理学、行为主义和新行为主义、发展心理学、文化—历史学派、信息加工理论、认知符号理论、认知资源理论和社会建构主义.一般来说,研究总是在某个特定的范式框架内进行的,但是研究者应该认识到,范式本身会对研究方法和结果产生很深的影响.更重要的是,研究者应该对各种不同的理论与范式持开放的心态,因为新的发现总是出现在不同范式之间的交叠磨合处.     

儒家学习观与数学学习

我国数学教学背后有着优秀的文化传统,这一传统的主导主流——儒家思想在教育方面有许多瑰宝.儒家关于学习的论述既有一定的理论性,又有方法论的意义,深刻影响着我国学子的数学学习.努力使这一传统中的宝贵经验得以继承和发扬,对搞好当今的数学课程改革有着重要意义.     

发展性数学学习方式的思考

数学学习过程是一个混合体,是一个选择的过程,围绕怎样选择,又是一个研究、体验、反思的过程,数学学习充满选择性、研究性、体验性和反思性.简要论述了数学学习方式的特点、数学学习模式.     

多模态时代教与学的符号学意蕴

传统的教育形式单一,符号史与模态史的演进,推动教育领域的模态从单一走向多样。在书面语占统治地位的既往历史中,页面占据主导地位。现今,随着计算机技术的发展,屏幕越来越占据主导地位,图像、动画等成为交际的多媒体,教学话语的多模态性已经成为一个重点研究领域。多模态是基于多媒体的多通道意义构筑形态。在符号教育时代,课堂教学很少再有满堂灌的情形,代之以音乐、图画、动画、口语、姿势、味道、空间、动作等多种模态教育教学形式。未来以大数据、人工智能、虚拟现实等要素自由组合的多模态将构成一个生动活泼的符号系统,在多元切换中实现表情达意、沁人心脾、润物无声、春风化雨。     

East-West Perspectives on Elder Learning

This paper describes and conceptualizes the meaning of lifelong learning from two cultural perspectives—East and West. It examines the different principles underpinning lifelong learning that explain why and how elders in the two cultures engage differently in continued learning. Finally, it discusses the cultural impact on elder learning by examining the reasons, choices and processes used by elders in the two different cultural contexts as they conceptualize, experience, and negotiate ongoing lifelong learning.     

Mathematics and Mobile Learning

This paper argues for an approach to mobile learning that leverages students’ informal digital practices as resources for designing mathematics classrooms activities. We briefly describe two exploratory designs along these lines, one featuring the use of photos taken by students outside class and the other centered on their recording and analyzing videos of motion. We then present a case study analysis of two students working through portions of these activities in class and discuss the potential of the approach as well as challenges associated with its implementation.     

数学学习中的心理问题探析

数学是一门积累性很强的学科,其学习过程并不简单。对某些学生来说,数学的学习是痛苦和乏味的。因此学生在学习数学的过程中出现了很多问题,从而产生了一定的心理障碍。本文通过对数学学习的心理障碍进行探讨,详细分析了各种容易出现的心理障碍及其产生的原因,并对学生克服学习数学的心理障碍的方法进行了探讨和总结。     

论数学学习中数学知识的生成性

数学教与学的实践证实了建构学说的论断:数学学习的过程就是数学认知结构的形成和发展的过程,是数学知识的生成过程,数学知识在生成过程中的各种特点倍受关注.     

关于当代国外数学教育观的综述

本文对当代国外数学教育家所主张的数学文化观、大众数学观、数学意义建构观、数学层次序列观、数学智力结构观、数学实验活动观以及数学情感育德观作了全面综述,揭示了其对我国当前的中小学数学新课程及教学改革的启发意义。