Working in the Mathematics Frame: Maximizing the Potential to Learn From Students' Mathematics Classroom Discussions

The quality of students' mathematics classroom discussions is an important factor in determining mathematics classroom learning outcomes. Good mathematics classroom discussions provide an opportunity for ideas to be shared and developed, but not all mathematics classroom discussions produce these learning opportunities. In this paper I discuss three constructs (subject, purpose, and frame) and how they can be used to analyze and characterize the quality of students' mathematics classroom discussions in terms of the mathematics learning potential that those discussions provide. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Effect of Cooperative Learning Approach Based on Conceptual Change Condition on Students' Understanding of Chemical Equilibrium Concepts

The purpose of this study is to investigate the effects of the cooperative learning approach based on conceptual change conditions over traditional instruction on 10th grade students' conceptual understanding and achievement of computational problems related to chemical equilibrium concepts. The subjects of this study consisted of 87 tenth grade students from two intact classes of a Chemistry Course instructed by the same teacher. One of the classes was randomly assigned as the experimental group, which was instructed with cooperative learning approach based on conceptual change conditions and the other class was assigned as the control group, which was instructed with traditional instruction. Chemical Equilibrium Concept Test (CECT) was administered to the experimental and the control groups as pre- and post-tests to measure the students' conceptual understanding, and Chemical Equilibrium Achievement Test (CEAT) was administered to the experimental and the control groups as a post-test to measure the students' achievements related to computational problems. Science Process Skills Test was used at the beginning of the study to determine the students' science process skills. Multivariate Analysis of Covariate (MANCOVA) was used to analyze the data. The results showed that students in the experimental group had better conceptual understanding, and achievement of computational problems related to the chemical equilibrium concepts. Furthermore, students' science process skills were accounted for a significant portion of variations in conceptual understanding and achievements related to the computational problems.     

化学平衡若干典型问题的辨析

分析了化学平衡中若干容易造成理解错误的问题，对大学无机化学的教学和中学教学中对该类问题的理解有很大帮助。     

浅析无机化学中的化学平衡及其应用

化学平衡内容在无机化学课程中,涉及诸多章节,占较大篇幅。正确理解平衡概念和掌握相关计算技巧,在无机化学教学中至关重要,它会影响到本课程及后续课程的学习。由于学习的阶段性,大多数无机化学教材对这部分内容分章节介绍,学生难以将有关内容进行联系融合,学习有难度。本文将无机化学中有关化学平衡问题进行浅析、综合,目的是使看似复杂的问题简单化,使学生对该内容更易理解、学习和掌握。     

无机化学中化学平衡常数的推导

在现行的无机化学教课书中,化学平衡常数有三种完全不同的推导方式．对于化学工作者,弄清究竟哪一种推导最为合情合理尽管相当重要,但是,更有意义的是研究这些推导过程中所引出的新的问题．     

Some Student Misconceptions in Chemistry: A Literature Review of Chemical Bonding

Students' misconceptions before or after formal instruction have become a major concern among researchers in science education because they influence how students learn new scientific knowledge, play an essential role in subsequent learning and become a hindrance in acquiring the correct body of knowledge. In this paper some students' misconceptions on chemical bonding reported in the literature were investigated and presented. With this aim, a detailed literature review of chemical bonding was carried out and the collected data was presented from past to day historically. On the basis of the results some suggestions for teaching were made.     

大学生中的小群体分析

客观要求、亲合动机和时代氛围是大学生小群体存在的原因;大学生中存有正式、地缘、志缘和异性朋友四种小群体;小群体能促进学生社会化、培养学生对学校的归属感,并作为社会控制手段。     

Design and Development of a Computer Learning Environment on the Basis of Students' Initial Conceptions and Learning Difficulties About Chemical Equilibrium

This paper describes the design and development of an interactive learning environment inspired from the constructivist view of learning and aiming at helping students improve their conceptions about chemical equilibrium. The design of the software was based on data that emerged from research we undertook with 175 Greek students (aged 17–18), in order to detect their conceptions and learning difficulties about chemical equilibrium. The students' answers to a written questionnaire showed that they had inadequate representations of systems of substances at chemical equilibrium related to the empirical and the atomic level, manifested serious difficulties in conceiving the initial situation of a system at chemical equilibrium and the equilibrium shift, made overextended use of the Le Chatelier principle and applied intuitive personal rules instead of the equilibrium constant law. The aim of this computer application is to help students to create and/or improve their own representations about substances at chemical equilibrium in the empirical, atomic and symbolic level, to establish appropriate links among thes multiple representations, and to construct appropriate conceptions about the Le Chatelier principle and the equilibrium constant law. The software contains simulations and visualizations of experiments representing systems at chemical equilibrium, simulations of chemical reactions related to the atomic level, symbolic representations and dynamic graphs, and a step-by-step derivation of the equilibrium constant law.     

Effect of Cooperative Learning Strategies on Students' Understanding of Concepts in Electrochemistry

The present study was conducted to investigate the degree of effectiveness of cooperative learning instruction over a traditional approach on 11th grade students' understanding of electrochemistry. The study involved forty-one 11th grade students from two science classes with the same teacher. To determine students' misconceptions concerning electrochemistry, the Electrochemistry Concept Test consisting of 8 open-ended and 12 multiple-choice questions was used as a pre-test and some students were interviewed. According to the results, twenty-four misconceptions (six of them initially identified) about electrochemistry were identified. The classrooms were randomly assigned to a control group (traditional instruction, 21 students) and an experimental group (cooperative learning based on a constructivist approach, 20 students). After instruction, the same test was administered to both groups as a post-test. The results from the t-test indicated that the students who were trained using cooperative learning instruction had significantly higher scores in terms of achievement than those taught by the traditional approach. According to the post-test and interviews, it was also found that instruction for the cooperative group was more successful in remediation of the predetermined misconceptions.     

Response to Contradiction: Conflict Resolution Strategies Used by Students in Solving Problems of Chemical Equilibrium

The main objective of this investigation was to show that a novel problem of chemical equilibrium based on a closely related sequence of items can facilitate students' conceptual understanding. Students were presented a chemical reaction in equilibrium to which a reactant was added as an external effect. A series of three studies were designed. In Study 1, the sequence of items started with a major alternative conception, namely, After the reaction has started, the rate of the forward reaction increases with time and that of the reverse reaction decreases, until equilibrium is reached. In Study 2, the major alternative conception was presented the last. In Study 3, instead of the sequence, only the following statement was presented: Rate of the reverse reaction increases gradually. In all three studies students had to agree/disagree with the statements and provide justifications. Results obtained show that at least one group of students, in Study 1 used a contradictory response pattern based on the generation and resolution of a cognitive conflict, which facilitated conceptual understanding. In Studies 2 and 3 students did not experience a similar cognitive conflict. Given the complexity of conceptual change and students' resistance to alter their alternative conceptions (cf. hard core, Lakatos )1970) Criticism and the Growth of Knowledge, Cambridge University Press, Cambridge, UK, pp. 91–106), it is suggested that changes in students' responses may have undergone a Peripheral Theory Change (Chinn and Brewer (1993) Review of Educational Research 63: 1–49).     

外物干扰平衡移动中的自变量选择

详细阐述了议题中选择ni（或惰）为自变量之后,各微积分表达式更简洁、整齐和实用,且不影响所用浓度（i）的内涵特点。     

催化剂与反应速率及化学平衡关系的论证

文章论证了可逆反应中正逆反应Arrhenius公式内指前因子的比值为一常数,催化剂的存在可降低正逆反应的表观活化能和改变指前因子,但不能改变正逆反应指前因子的比值,进而从化学动力学角度推证了催化剂不影响化学平衡的热力学论断,指明催化剂的催化作用是通过降低表观活化能和改变表观指前因子的协同效应而实现的.     

Enhancement of Quality in Chemical Inquiry by Pre-University Students

Our pre-university chemistry students face problems achieving sufficient quality in chemical inquiry. To try to enhance the quality of student performance in chemical inquiry, Dutch pre-university chemistry students (age 17) carried out an authentic research project on Diffusion of ions in distilled water. The learning materials for this student inquiry project, the teaching scenario and the website were designed in cooperation with five chemistry teachers. Three teachers from this network and two other teachers also implemented the project with 80 students to find out whether the emphasis on relevant concepts of evidence (CoE) improves the quality of student inquiry outcomes. This part – with its emphasis on the CoE – in the student inquiry task is based on four key features: the students feel motivated to explore, focus their attention on, give meaning to and reflect upon CoE. In teams students conducted a guide experiment, analysed a scientific article, did an inquiry and wrote a report, discussed CoE with peers on the Internet and rewrote their reports. All lessons were observed, field notes were made and analysed on whether the intended student activities had been realised. The Internet discussion was recorded in a database and analysed. The first and final reports of all teams were coded and analysed. Also the students appreciation of the activities was assessed. The teaching and learning activities were realized to a very large extent as planned in the design. The emphasis on CoE resulted in 65% of the students achieving a sufficient level of quality in their final reports.     

小城镇化工企业环境因素模糊综合评价体系的构建与实践

利用模糊综合评价研究我国小城镇化工企业环境因素的问题,提出符合我国国情的小城镇化工企业环境因素评价方法和评价指标体系．为促进我国城镇化的快速、健康、高效发展以及为制定我国小城镇化工企业环境因素的相关政策提供理论依据．     

Qualitative Differences Between Learning Environments Using Videos in Small Groups and Whole Class Discussions: A Preliminary Study in Physics

Interactivity, group learning and student engagement are accepted as key features of social constructivist learning theories. The challenge is to understand the interplay between such features in different learning environments. This study focused on the qualitative differences between two interventions—small-groups and whole-class discussions. In both interventions, three short video slices on the abstract topic ‘the physics of superconductivity’ were interspersed with the different discussion styles. The video slices are based on the Bruner stages. Twenty-nine first year university physics students completed a pre-test, underwent the intervention and completed a post-test. The remainder of the data were collected from student drawings, video recordings, observer notes and facilitator feedback. Results indicate that the use of the video slices in both interventions were successful in changing students’ understandings of superconductivity. However, the small groups treatment tended to facilitate questioning, meaning-making and subsequent changes of ideas more so than the whole class discussions. Implications for research and practice are discussed.     

Individual to collaborative: guided group work and the role of teachers in junior secondary science classrooms

This paper, through discussion of a teaching intervention at two secondary schools in Hong Kong, demonstrates the learning advancement brought about by group work and dissects the facilitating role of teachers in collaborative discussions. One-hundred and fifty-two Secondary Two (Grade 8) students were divided into three pedagogical groups, namely ‘whole-class teaching’, ‘self-directed group work’ and ‘teacher-supported group work’ groups, and engaged in peer-review, team debate, group presentation and reflection tasks related to a junior secondary science topic (i.e. current electricity). Pre- and post-tests were performed to evaluate students’ scientific conceptions, alongside collected written responses and audio-recorded discussions. The results indicate that students achieved greater cognitive growth when they engaged in cooperative learning activities, the interactive and multi-sided argumentative nature of which is considered to apply particularly well to science education and Vygotsky’s zone of proximal development framework. Group work learning is also found to be most effective when teachers play a role in navigating students during the joint construction of conceptual knowledge.     

职业学校学生非正式群体的问题分析

职业学校学生非正式群体的形成是多种因素综合作用的结果,其存在具有一定的合理性和不可替代性。但其在发挥积极作用的同时,也不可避免地产生一些负面影响。本文在分析职业学校学生非正式群体问题的基础上,结合其成因,从道德教育、强化非正式群体的服务功能、营造良好的校园文化氛围等方面提出教育对策。     

由单组分浓度的测定求连串反应平衡常数的极限值

介绍了利用求极值的方法 ,通过对反应体系中单组分平衡浓度的测定 ,求连串反应的平衡常数。     

交互式语言教学环境下的英语课堂分组讨论问题

分组讨论是一种广泛运用于英语课堂教学的组织形式，在交互式教学法中尤其重要，对学习者交互能力和交际能力的培养均有重大意义。分组讨论分三个阶段：准备阶段；监控阶段；反馈阶段。提高分组讨论效果的对策有：提问技巧的培训；说话者自我功能的定位；说话者对讨论进程的及时评估。     

大一无机化学教学中引入化学热力学的一点浅见

ΔG变化值反映体系变化自发趋向的可能性、程度;当体系处于平衡时,应用化学等温式就可求算平衡常数K。将这一思路应用于溶液中的化学平衡,能很简结地得出与实验相当吻合的数据。为拓宽热力学在无机化学教学中的产用,必须在教学中增加ΔG°变化在溶液平衡中的产用,而这增加不作精密处理,采取直接引入的方法。