Teaching algorithmic problem solving or conceptual understanding: Role of developmental level,mental capacity,and cognitive style

It has been shown previously that many students solve chemistry problems using only algorithmic strategies and do not understand the chemical concepts on which the problems are based. It is plausible to suggest that if the information is presented in differing formats, the cognitive demand of a problem changes. The main objective of this study is to investigate the degree to which cognitive variables, such as developmental level, mental capacity, and disembedding ability explain student performance on problems which: (1) could be addressed by algorithms or (2) require conceptual understanding. All conceptual problems used in this study were based on a figurative format. The results obtained show that in all four problems requiring algorithmic strategies, developmental level of the students is the best predictor of success. This could be attributed to the fact that these are basically computational problems, requiring mathematical transformations. Although all three problems requiring conceptual understanding had an important aspect in common (the figurative format), in all three the best predictor of success is a different cognitive variable. It was concluded that: (1) the ability to solve computational problems (based on algorithms) is not the major factor in predicting success in solving problems that require conceptual understanding; (2) solving problems based on algorithmic strategies requires formal operational reasoning to a certain degree; and (3) student difficulty in solving problems that require conceptual understanding could be attributed to different cognitive variables.     

数学理解的三种基本形态及教学启示

数学理解包括三种基本形态,即:记忆性理解、解释性理解和探究性理解,这三种数学理解分别对应着“记得、晓得和明得”三种不同的状态。三种数学理解对数学学习都是有价值的,但仅有记忆性和解释性理解是不够的,探究性理解才是数学教学的最终目标。实践中,不少水平不高的教师常常只能让学生达到记忆性理解,有一定水平的教师能让学生达到解释性理解,真正让学生达到探究性理解的教师并不是很多。教师要不失时机地促进学生数学理解层级的迭代升级,促使学生最终达到探究性理解,吴文俊院士数学学习的经验对把握数学理解的三种基本形态有借鉴和启迪意义。在课堂教学中引导学生从事生动活泼的数学探索性活动常常是一个相当艰难的过程,对教师的数学探究素质提出了较高的要求,教师应努力引导学生去探求数学知识的意义和发现的过程,促使学生数学探究性理解方式的养成。     

Students' Reports of Their Cognitive Processes and Level of Understanding During Regular Classroom Instruction

The study was designed in an attempt to gain greater understanding of the kinds of learning processes engaged in by students during regular classroom instruction, and at investigating the students' level of understanding and problems in understanding parts or all of the lessons. Six school levels of male and female students from 44 secondary and pre-university classes (N=2719) were the subjects of this study. During the lessons, students and teachers were observed and video-taped. Following the lessons, students' reports of their learning processes were obtained using a questionnaire. The questionnaire also served as the basis for a follow-up interview of four randomly selected students from each of the sampled classes. The whole procedure was repeated for each class within a one-month period and for a different curricular area.

Analyses of student responses showed that more of the average ability students as compared to the high or low ability students reported understanding all of the lessons. However, the higher ability students were more likely to report using specific cognitive strategies to monitor their understanding of the lessons and in processing intellectual tasks and lesson content. They were able to provide more elaborate and more specific reasons for not understanding parts of the lessons. The results were interpreted in terms of physical and organizational characteristics of educational classrooms in Singapore. Instructional implications are discussed in relationship to both the findings and previous literature.     

理解远不止于会计算

初中6～8年级学生对与有理数有关知识的掌握情况是:学生并没有真正理解所学知识,在运用数学知识解决实际问题和自己提出问题等方面意识和能力均很薄弱.具体结论为:(1)各年级学生完成有理数计算问题的正确率很高;(2)对不同于教材中给出的有理数相除方法,多数人表现出不接受,且理由为"与书上写的或老师教的不一样";(3)学生在对应用问题给出答案时缺乏联系现实的意识;(4)学生根据算式给出问题的能力远低于计算算式的能力.     

论初任教师的教学理解

初任教师的教学问题常常根源于初任教师的教学理解,尤其是他们在教学中对知识、学生和教师三者相互作用关系的理解。其中,体验是教学理解的本质要求和本性所在。初任教师主要通过对知识理解的建构性体验、对学生理解的责任感体验、对自我理解的探究性体验三条基本途径形成自己的教学理解。     

论理解教学的实现形式

作为一种新的教学形态,理解教学已引起国内外教育学者、一线教师的关注, 并开始进入课堂教学领域。理解教学主要有反思型理解和对话型理解两种实现形式。反思型理解是以反思为主要手段的教学理解,主要表现是师生的理解自我;对话型理解是以对话为主要手段的教学理解,表现为师生对话式理解、生生对话式理解和生本对话式理解。     

University students’ understanding of the concepts empirical,theoretical, qualitative and quantitative research

University research education in many disciplines is frequently confronted by problems with students’ weak level of understanding of research concepts. A mind map technique was used to investigate how students understand central methodological concepts of empirical, theoretical, qualitative and quantitative. The main hypothesis was that some students have a confused conception of empirical. The mind maps revealed that in the beginning of the course, 75% of the students hold a problematic conception of research, and after the half year course, still half of the participated students had problems with expressing a scientifically sound conception of research. In addition to general undevelopedness of the maps, a severe confused conception of drawing a link from empirical to qualitative or quantitative, but not to both, was found. This finding indicates that some students have problems with understanding the very basic and central concept of empirical.     

东中西部中学生国际理解观比较

通过对东中西部中学生国际理解观的调查比较发现:东部地区学生的国际理解观水平要高于中西部地区;东中西部地区学生国际理解观的性别差异相似,女生的开放意识均强于男生,男生的国际理解能力意识强于女生;东中西部地区中学生国际理解观的年级差异相似,初中生的国际理解观高于高中生;东中西部地区学生使用计算机的时间与其国际理解观之间均存在正相关关系。东中西部地区学生国际理解观的成熟度及学校国际理解教育的开展方面还存在一些问题,中国需加强学校国际理解教育活动。     

培养推理判断技能 提高阅读理解能力

理解能力是英语阅读能力的核心，是学生阅读能力的重要标志，而推理判断技能作为英语阅读的重要技能之一，直接影响到人们的阅读能力的强与弱，如何培养外语学习者的这种技能和如何提高理解能力是英语阅读课所面临的一个重要课题。     

梧凤之鸣:大学师生关系的诉求与应然

梧凤之鸣是大学师生关系的本真写照。但是,目前大学存在科技理性使师生陷于教化、制度控制使师生缺失自我、孤独对话使师生走向疏离等症结,让梧凤相离,师生渐行渐远。回顾大学师生融融的片段,师生关系实质是一种师生之间的关联与互动、民主与平等、关心与理解。因而,诉求大学师生关系有赖于感性的维护、自由的发展、理解的对话的确立。     

信息技术支持的促进理解的教学模式构建

学生不理解知识一直是教学过程中存在的普遍又亟待解决的问题。通过对理解过程和数学理解障碍的探讨,以及对影响促进理解的教学开展的主要因素的研究,进而构建一种信息技术支持的促进理解的教学模式,帮助解决学生不理解的问题,从而促进他们更好地学习。     

Epistemological understanding in science learning: the consistency of representations across contexts

This article addresses the extent to which written diagnostic questions can be used to assess science students' representations of the nature of science. The responses of 731 European science students in upper secondary school and undergraduate programmes to two written diagnostic questions are analysed for consistency. The written questions yielded some insights into students' views. There is evidence that the majority of students in this sample draw upon different epistemological representations in different contexts. The paper concludes with a discussion of the use of data from such questions in science education, and the significance of models of students' epistemological knowledge.     

Hearing Students: The Complexity of Understanding What they are Saying,Showing, and Doing

Teachers are expected today to assess student understanding as an integral part of instruction, using a combination of various assessment methods and tools, among which are observing students solve problems in class and listening to their mathematical discussions. The aim of our study is to explore what it might mean for a teacher to hear students and to interpret their talk and actions. Analysis of an interview with Ruth – an experienced elementary school teacher – after she observed two of her students solve a mathematics problem, suggests four types of her interpretation: describing, explaining, assessing and justifying. This analysis illustrates the complexity of the way Ruth hears her students, as is indicated even in the relatively simple case of describing. Using various sources of data we also analyze different characteristics of Ruth’s hearing for the describing and explaining types of interpretation and examine possible resources for her over-hearing, compatible-hearing, under-hearing, non-hearing and biased-hearing.     

Students' Understandings of Gravity in an Orbiting Space-Ship

We report on an investigation of students' ideas about gravity after a semester of instruction in physics at university. There are two aspects to the study which was concerned with students' answers to a carefully designed qualitative examination question on gravity. The first aspect is a classification of the answers and a comparative study of the ways the problem was tackled by two large groups of students who had different backgrounds in physics and were exposed to different teaching styles. The second aspect is to investigate how students link concepts to solve the problem. We used a phenomenographic analysis of student responses to extract patterns of reasoning and alternative conceptions behind the solutions. We found no differences between the classes of answers given by students in the two courses. Our analysis also identifies a hierarchy in the complexity of the hypothetical reasoning pathways, which we interpret as reflecting the ways in which students may link concepts and resolve conflicts as they solve the problem. The hypothetical reasoning pathways may help educators to develop instructional material or lecture room dialogue in order to tease out key issues. An unexpected finding is that there is a discrepancy between our conclusion that the two groups of answers are similar and the distribution of marks awarded by the examiner – which implies that the quality of the answers is different for the two groups.     

The Effect of Integrating Aesthetic Understanding in Reflective Inquiry Activities

The purpose of this study was to explore the effectiveness of integrating aesthetic understanding in reflective inquiry activities. Three typical classes of Taiwanese eighth graders (n = 106) and nine additional low‐achieving students in the same school participated in the study. The treatment for experimental students emphasized scaffolding aesthetic understanding and reflections on inquiry strategies. It was found that the experimental group students consistently outperformed their counterparts on the post‐test and the delayed post‐test in conceptual understanding and application of science knowledge. In addition, the low‐achieving students were motivated by the treatment and made significant progress on the two tests. The results of interview and classroom observation also revealed that the intervention made a difference in students’ affective perceptions.     

论阅读教学中影响文本有效理解的因素

文本是阅读教学中师生间展开对话的中介,学生对文本的理解直接关系到阅读教学的成败和效率。在具体的阅读教学实践中,作为教学活动构成要素的学生、文本、教师都会影响到对文本的理解。语文阅读教学中的文本理解是一个复杂的过程,只有坚持从学生从自身的实际经验出发,结合文本的不同特点、对阅读活动的不同要求,并且适时合理地发挥教师的辅助和引导作用,才能最终实现对文本的有效理解。     

论理解取向的信息技术课程教学设计

“理解”一直以来被认为是教育的重要价值,当前信息技术课程教学中出现的种种问题均是以忽略学生理解而导致的.该文针对课程的核心价值和教学问题,提出了理解取向的教学策略,包括：确定核心问题、制定理解的目标、设计理解性活动、促进理解的表现和持续性的多元评价等五个环节.着重理解的信息技术课程设计,强调围绕衍生性问题,让学生理解信息技术背后所蕴含的科学原理;理解信息技术所涉及的情感态度价值观等社会议题;理解信息技术操作背后的方法、规则和规律.     

论孔子的对话德育模式

孔子的对话德育模式是在春秋时期官学没落、私学兴起、儒家思想体系尚未成为主流意识形态的背景中产生的。孔子的对话德育模式与早期儒家解决社会问题的人文路线、主体思维方式和孔子的德治思想有内在的联系。孔子与学生展开了立足于现实生活的、真诚的道德对话 ,使师生形成对道德现象相似的理解 ,彼此受到启迪 ,道德观念得到升华。孔子的对话德育模式是建立在师生平等关系、教师高超的对话艺术和人格魅力的基础上的。     

Students’ understanding of a groundwater system and attitudes towards groundwater use and conservation

The purpose of this study was to investigate students’ understanding of groundwater as a system, and to further examine whether and how their understanding is related to attitudes towards groundwater use and conservation. A total of 676 junior high school students completed a groundwater survey including a drawing activity and a questionnaire. An additional group of university students with environmental science majors were recruited for the survey for the purpose of determining reasonable expectations and validating interpretations of the results. Analysis of student drawings indicated that students generally held an incomplete and unconnected understanding of the groundwater system. Correlation analysis showed that student levels of understanding were associated with their perceptions of environmental impacts as well as environmental concern regarding groundwater problems. These findings re-emphasised the importance of promoting students’ understanding of environmental systems, as well as their ability to think systemically.     

Conceptualizing climate change in the context of a climate system: implications for climate and environmental education

Today there is much interest in teaching secondary students about climate change. Much of this effort has focused directly on students’ understanding of climate change. We hypothesize, however, that in order for students to understand climate change they must first understand climate as a system and how changes to this system due to both natural and human influences result in climatic and environmental changes and feedbacks. The purpose of this article is to articulate a climate system framework for teaching about climate change and to stimulate discussion about what secondary students should know and understand about a climate system. We first provide an overview of the research on secondary students’ conceptions of climate and climate change. We then present a climate system framework for teaching about climate and climate change that builds on students’ conceptions and scientific perspectives. We conclude by articulating a draft conceptual progression based on students’ conceptions and our climate system framework as a means to inform curriculum development, instructional design, and future research in climate and environmental education.