Problem-Solving Software to Implement Curriculum Goals

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The Missing Curriculum in Physics Problem-Solving Education

Physics is often seen as an excellent introduction to science because it allows students to learn not only the laws governing the world around them, but also, through the problems students solve, a way of thinking which is conducive to solving problems outside of physics and even outside of science. In this article, we contest this latter idea and argue that in physics classes, students do not learn widely applicable problem-solving skills because physics education almost exclusively requires students to solve well-defined problems rather than the less-defined problems which better model problem solving outside of a formal class. Using personal, constructed, and the historical accounts of Schrödinger’s development of the wave equation and Feynman’s development of path integrals, we argue that what is missing in problem-solving education is practice in identifying gaps in knowledge and in framing these knowledge gaps as questions of the kind answerable using techniques students have learned. We discuss why these elements are typically not taught as part of the problem-solving curriculum and end with suggestions on how to incorporate these missing elements into physics classes.     

论数学应用问题解决的认知过程模式

数学应用问题是一个完整的知识结构系统,是用一定的情节描述的数量关系问题。情节和数量关系是它的两个基本构成要素,两者密不可分。数学应用问题解决的认知过程模式是主体在数学元认知监控下,摆脱情节结构、建立并处理数量关系结构的一种数学认知活动,由情境理解与问题表征、问题归类与模式识别、建模解模与解题迁移、验模用模与自我评价等4个相互关联的子系统组成的一个动态过程模式。认知结构在数学应用问题解决中具有极其重要的作用。影响数学应用问题解决认知过程的主要因素有认知因素、非认知因素、问题情境结构因素和外部环境因素。     

Self-Efficacy Beliefs and Mathematical Problem-Solving of Gifted Students

Path analysis was used to test the predictive and mediational role that self-efficacy beliefs play in the mathematical problem-solving of middle school gifted students (n= 66) mainstreamed with regular education students (n= 232) in algebra classes. Self-efficacy of gifted students made an independent contribution to the prediction of problem-solving in a model that controlled for the effects of math anxiety, cognitive ability, mathematics GPA, self-efficacy for self-regulated learning, and sex. Gifted girls surpassed gifted boys in performance but did not differ in self-efficacy. Gifted students reported higher math self-efficacy and self-efficacy for self-regulated learning as well as lower math anxiety than did regular education students. Although most students were overconfident about their capabilities, gifted students had more accurate self-perceptions and gifted girls were biased toward underconfidence. Results support the hypothesized role of self-efficacy in A. Bandura's (1986) social cognitive theory.     

论数学课程实施中的数学课程资源

目前制约我国课程实施的主要问题之一就是课程资源严重缺乏.对数学课程资源的研究应注意两个重要问题:一是,凡是有利于数学课程实施与生成的各种物质的和非物质的条件与因素,都应属于数学课程资源;二是,研究数学课程资源的有效开发和利用的相关途径.     

问题解决视野下的信息技术课程与教学

信息技术课程的总目标是提升学生的信息素养,从认知心理学角度看,信息素养应定位在基于信息技术的问题解决。本文在阐述问题解决概念、过程与策略的基础上,从问题解决的视野对普通高中信息技术课程的目标、模块设置、知识建构与教学策略进行分析。     

螺旋课程思想的滥觞——《从小学到大学课程研究报告》述评

美国全国教育协会于1876年发布《从小学到大学课程研究报告》,其主要内容包括:学生应该在多大年龄进入学校学习;幼儿园应先开展关于阅读、写作和算术的课程;如何让学校开设工业类的课程数量占多数;公立学校和私立学校的争论问题;如何考虑古典文化课程的问题;为什么一般的语言课程占据了学校课程的大部分时间;课程学习的自然秩序和合适的次序是什么。《从小学到大学课程研究报告》与1828年《耶鲁报告》的相同之处是:都认为古典教育非常重要。相异之处是:《耶鲁报告》在肯定古代文学、古代语言的价值的同时,并没有提倡要在大学中加强科学课程、实用课程;而《从小学到大学课程研究报告》在肯定需要学习古代语言的同时,也认识到要增加一些实用的课程,例如科学课程。《从小学到大学课程研究报告》发布后,对美国教育产生了较大的影响,也获得了比较高的评价。该报告是布鲁纳的螺旋课程思想的滥觞,在推动美国教育发展方面发挥了承上启下的作用,但是其摇摆于理想主义和传统主义的指导思想导致了其失败。     

用施瓦布实践课程观设计培养教师问题解决能力的课程

在教师教育中,以施瓦布实践课程开发理论为指导,设计培养教师问题解决能力的课程旨在从新的角度认识学科结构,使教师学科问题解决过程中的思维更加清晰。课程以师生为双主体,以学科问题为内容中心,以教师为课程的行动研究者,强调在学科情境之中践行理论与实践的结合。从课程本身出发,对各种实际需要和问题进行综合的建设性探讨,是施瓦布实践课程观的根本思想。     

高中数学中公理化方法改革的构想

欧几里得《几何原本》自诞生之日起，就肩负着渗透公理化思想的重任．但由于几何内容的改变，公理化方法在中学课本中的地位有所削弱．应该从作为学校课程构成法的公理化方法和作为学习对象的公理化方法2个方面加强其在中学课本中的地位，以加深学生对公理化方法的理解．     

运用数学软件开展高校数学基础课程改革初探

作为理工科专业基础课的高校数学基础课程,在教学效果和学习体验上差强人意。本文阐述了在数学基础课程中运用数学软件的模式与意义,论述了运用数学软件开展数学基础课程在知识掌握衡量标准、学科专业背景融入、课外拓展活动需求和今后工作学习需求的四大立足点,并为这一数学教学模式提出了加强学科支撑、实施分层教学、更新学分认定、加大资源统筹的推进措施和建议。     

Using Films as a Learning Tool

<正>Most people would agree that watching movies is one of their favorite free-time activities. We often think of movies as fun entertainment, but have you ever considered that movies can also be used to help us     

新课程数学概念"螺旋式"上升编排的认知审视

数学新课程充分体现了皮亚杰的认知发展论及其建构主义课程观和布鲁纳的表征发展论及其结构主义课程观.儿童的表象系统并非一开始就是成熟的,而是缓慢而有规则地发展起来的.对一些重要的数学概念采取逐步渗透、深化、"螺旋式"上升的编排方式,使学生在感知简单结构的表征基础上,逐渐理解复杂结构的表征模式,不断提高数学认知水平,进而掌握概念,达到促进学生智慧或认知成长的目的.     

《数学课程标准》对数学教学的改革

《数学课程标准》对传统数学教学作出了改革，主要体现在“关注目标，呈现多元”、“关注现实．贴近生活”、“关注合作，促进交流”、“关注实践，突出应用”等15个方面．     

中国课程学术话语自主建构的困境及路径

学术话语是一个学科的内在架构。学术话语生成和建构的自主性直接影响到学科的自主性。在建构中国学术话语体系的时代要求下,中国课程学术话语却陷入本土失语、学科失语和实践失语的困境。本文尝试透过历史分析的视角,从实践理性、学术依附和权威主义性格等方面分析影响中国课程学术话语自主建构的因素,并以坚守课程学科的基本立场、明确学术话语的言说规范、掌握课程研究的主动权作为破解失语困境的可能路径。     

将数学文化融入独立学院数学课堂的教学实践

随着人们对数学文化认识的不断深入,数学文化的教育价值越来越受到广大数学教育工作者的关注和重视,近年来数学文化课程的教学在各高校开展得如火如荼,也有了较为成熟的教学模式和教学方法。综合考虑独立学院的实际情况,对数学文化的课程融入进行研究：（1）更新教育观念,明确数学文化的地位;（2）优化数学课程内容,注重教学策略;（3）以人为本,改变学生的学习方式。     

螺旋式综合实践活动课程开发研究

螺旋式课程开发是指在不同学段对同一主题内容进行螺旋式进阶设计、实施与评价,它可以解决普通综合实践活动课程低水平重复、缺乏必要深度的问题。皮亚杰认知发展理论,布鲁纳、塔巴的螺旋式设计理论为螺旋式综合实践活动课程开发提供了重要的理论依据。螺旋式综合实践活动课程开发包括活动目标、活动内容、活动方法、活动评价的设计与实施。其发展路径为:由点到面,由单项活动走向多项活动;持续跟踪,学段打通,螺旋式递进;加强实证研究,先试验,再推广。     

Information Processing Taxonomy (IPT): An Alternative Technique for Assessing Mathematical Problem-Solving

This paper describes the development of the Information Processing Taxonomy (IPT) Model which models children's thinking at different hierarchical levels. The main features of the Model consist of retrieving information from external memory and primary and secondary productions of Type A and B information. These features constitute the components of different levels of thinking which could be used to confirm and describe the children's cognitive processes. Examples are shown to illustrate how the Model could be used to construct test items at different levels on the basis of these features. The Guttman procedure was applied to test the consistency of the hierarchical nature of the Model. Results show that the items constructed using the Model were scalable.     

浅谈金刚石薄膜刀具课程的开发

金刚石薄膜刀具课程的开发,应该紧紧围绕金刚石薄膜的制备等典型工作任务来进行。从课程地位、课程目标和课程标准等因素入手,将课程内容融入教学情境中,教学效果很好。     

MultiMap: An Interactive Tool for Mathematical Experimentation

Abstract

This article describes a computer program, “Multi‐Map,” designed to introduce experimentation and exploration in the precollege mathematics curriculum. The central activity in MultiMap involves the creation of planar maps which may be applied interactively to graphical objects. The maps may be affine or nonlinear; and (among other activities) they can easily be edited, composed, or applied iteratively. We outline MultiMap's interface and basic functionality, describe a wide variety of exploratory mathematical activities that can be undertaken with the program, and present some observations on the use of MultiMap in the classroom.