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1.
Research on teaching primarily adopts the process-product paradigm. Within this paradigm, researchers often speculate about cognitive operations that students engage in during instruction as a means to explain how teacher behaviors (processes) correlate with or cause student achievement (products). This paper argues that the methodology of process-product research is (1) ill-suited to generating theories of teaching effectiveness that use students' cognition to explain process-product relations and (2) invalid for testing such explanations. The cognitive mediational paradigm, which explicitly interposes students' cognition between teaching processes and student products, is proposed as a remedy to these problems. Methodology consistent with the cognitive mediational paradigm is described. 相似文献
2.
Stellan Ohlsson 《Interactive Learning Environments》2013,21(1):205-215
Three computer‐based systems for teaching arithmetic and algebra are discussed. The systems embody several pedagogical tactics: To provide students with augmented repre‐sentations that reveal the structure of problem solutions; to make mathematical symbols meaningful by giving students concrete referents for those symbols; to provide students with enriched feedback about the consequences of their mathematical operations; and to adapt instruction to the cognitive processes of the students. Weaknesses in the three systems are discussed and two general problems, called complexity trade‐off and scaffold removal, are put forward as possible explanations for why the systems are not more effective. The alternative view that mathematics is difficult because it requires abstract thinking is outlined and some of its implications discussed briefly. 相似文献
3.
In this study, we defined and quantified the degree of cognitive conflict induced by a discrepant event from a cognitive perspective. Based on the scheme developed, we investigated the relationship between cognitive conflict and conceptual change, and the influences of students' cognitive characteristics on conflict in learning the concept of density. Subjects were 171 seventh-grade girls from two city middle schools in Korea. Tests regarding logical thinking ability, field dependence/independence, and meaningful learning approach were administered. A preconception test and a test of responses to a discrepant event were also administered. Computer-assisted instruction was then provided to students as a conceptual change intervention. A conception test was administered as a posttest. In analysing students' responses to the discrepant event, seven types of responses were identified: Rejection, reinterpretation, exclusion, uncertainty, peripheral belief change, belief decrease, and belief change. These types were then ordered into four levels. The results indicated that there existed a significant correlation between cognitive conflict and conceptual change. t-test results revealed that there were statistically significant differences in the degree of cognitive conflict by the levels of students' logical thinking ability and field dependence/independence. Meaningful learning approach, however, was found to have no statistically significant effect on cognitive conflict. Educational implications are discussed. 相似文献
4.
This study investigated elements of pedagogical knowledge when students' higher order thinking was an explicit and focused instructional goal. The findings suggest a model that consists of 6 elements. It seems that, for all these elements, the source of differences between teachers' various pedagogies may be tracked to the basic distinction between a traditional transmission-of-knowledge approach to instruction versus a reform oriented constructivist approach. The findings portray how these two pedagogies are played out when higher order thinking is viewed as a distinct educational goal. Appropriate activities are insufficient for students' active thinking. In the absence of adequate pedagogies, teachers adopt algorithmic approaches for teaching thinking that decrease the cognitive demands of tasks. Practical recommendations are discussed. 相似文献
5.
This research examines students’ ability to integrate algebraic variables with arithmetic operations and symbols as a result
of the type of instruction they received, and places their work on scales that illustrate its location on the continuum from
arithmetic to algebraic reasoning. It presents data from pre and post instruction clinical interviews administered to a sample
of middle school students experiencing their first exposure to formal pre-algebra. Roughly half of the sample (n = 15) was taught with a standards-based curriculum emphasizing representation skills, while a comparable group (n = 12) of students received traditional instruction. Analysis of the pre and post interviews indicated that participants receiving
a standards-based curriculum demonstrated more frequent and sophisticated usage of variables when writing equations to model
word problems of varying complexity. This advantage was attenuated on problems that provided more representational support
in which a diagram with a variable was presented with the request that an expression be written to represent the perimeter
and area. Differences in strategies used by the two groups suggest that the traditional curriculum encouraged students to
continue using arithmetic conventions, such as focusing on finding specific values, when asked to model relations with algebraic
notation.
相似文献
| Bryan MoseleyEmail: |
6.
Bilingual education programs implicitly assume that the acquired knowledge is represented in a language-independent way. This assumption, however, stands in strong contrast to research findings showing that information may be represented in a way closely tied to the specific language of instruction and learning. The present study aims to examine whether and to which extent cognitive costs appear during arithmetic learning when language of instruction and language of retrieving differ. Thirty-nine high school students participating in a bilingual education program underwent a four-day training on multiplication and subtraction problems in one language (German or French), followed by a test session in which they had to solve trained as well as untrained problems in both languages. We found that cognitive costs related to language switching appeared for both arithmetic operations. Implications of our findings are discussed with respect to bilingual education as well as to cognitive mechanisms underlying different arithmetic operations. 相似文献
7.
Aurora Gallardo 《Educational Studies in Mathematics》2002,49(2):171-192
The work described in this article was based on a historical perspective in order to analyze the extension of the natural-number domain to the integers in students' transition from arithmetic to algebra in the context of word problems. The initial historical analysis showed the need to consider mutual interrelationships between the algebraic language and the methods of solving word problems and linear equations, for the understanding of the evolution of negative numbers. Four levels of acceptance of these numbers (subtrahend, relative number, isolated number and formal negative number) were extracted from the historical texts. The empirical analysis showed that the first three levels were observed among 35 students of 12–13 years old as well.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
8.
The article reports aspects of the evolution of a teaching approach over repeated trials for beginning symbolic algebra. The teaching approach emphasized the structural similarity between arithmetic and algebraic expressions and aimed at supporting students in making a transition from arithmetic to beginning algebra. The study was conducted with grade 6 students over 2 years. Thirty-one students were followed for a year, and data were analysed as they participated in the three trials conducted that year. Analysis of students’ written and interview responses as the approach evolved revealed the potential of the approach in creating meaning for symbolic transformations in the context of both arithmetic and algebra as well as making connections between arithmetic and symbolic algebra. Students by the end of the trials learnt to use their understanding of both procedures and a sense of structure of expressions to evaluate/simplify expressions and reason about equality/equivalence of expressions both in the arithmetic and the algebraic contexts. 相似文献
9.
The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic
to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic
interaction between each student and a given problem, (2) the adidactic interaction of each student with the procedures generated
by other students during stage 1. The two kinds of processes – adaptation to a milieu and social interactions – play a critical role in the change of “rationality” required for the move from arithmetic to algebra.
Both the design of the initial mathematical problem given to the students and the organization of the interactions leading
to the debate under study in this article are based on this hypothesis. The research presented in this article is set in a
broader work of didactic engineering that aims at studying didactic conditions for making a connection between arithmetic
practices and algebraic practices. 相似文献
10.
Eddie Gray Marcia Pinto Demetra Pitta David Tall 《Educational Studies in Mathematics》1999,38(1-3):111-133
This paper begins by considering the cognitive mechanisms available to individuals which enable them to operate successfully in different parts of the mathematics curriculum. We base our theoretical development on fundamental cognitive activities, namely, perception of the world, action upon it and reflection on both perception and action. We see an emphasis on one or more of these activities leading not only to different kinds of mathematics, but also to a spectrum of success and failure depending on the nature of the focus in the individual activity. For instance, geometry builds from the fundamental perception of figures and their shape, supported by action and reflection to move from practical measurement to theoretical deduction and euclidean proof. Arithmetic, on the other hand, initially focuses on the action of counting and later changes focus to the use of symbols for both the process of counting and the concept of number. The evidence that we draw together from a number of studies on children's arithmetic shows a divergence in performance. The less successful seem to focus more on perceptions of their physical activities than on the flexible use of symbol as process and concept appropriate for a conceptual development in arithmetic and algebra. Advanced mathematical thinking introduces a new feature in which concept definitions are formulated and formal concepts are constructed by deduction. We show how students cope with the transition to advanced mathematical thinking in different ways leading once more to a diverging spectrum of success.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
11.
Tracy Goodson-Espy 《Educational Studies in Mathematics》1998,36(3):219-245
This study utilized a psychological constructivist perspective to examine the transitions that students make from arithmetic to algebra in the context of problems, that from the expert's perspective, involve the concept of linear inequality. Unstructured interviews were used to gather data that were used to develop an explanation concerning student understanding. Thirteen college students were interviewed individually and asked to solve nine related tasks. The interviews were videotaped and the protocols were analyzed to document student conceptions. Five case studies were used to develop and substantiate an explanation regarding students' transitions from arithmetic to algebra. Cifarelli's (1988) levels of reflective abstraction and Sfard and Linchevski's (1994) theory of reification provided a framework for this explanation. This paper discusses an integration of Cifarelli and Sfard's constructs. Students who completed a transition to algebra operated at higher levels of reflective abstraction than students who were unable to complete such a transition. Operating at higher levels of reflective abstraction enabled these students to consider concepts as both processes and abstract objects. Developing this ability was found to be critical in achieving a transition to using algebraic methods. 相似文献
12.
在数学教学中,小学与中学(主要是初中)的衔接问题,仅仅依赖体制上的变革根本无法解决。而在新课程标准的推进当中,由于更加强调整体性和一贯性,所以,衔接问题的解决已刻不容缓。算术中的准变量(表达式)正是解决这一问题的强有力思想。准变量表达式既动摇了算术与代数之间的传统割裂,又在算术思维与代数思维之间起到了桥梁作用。而且,它还体现了新课程标准所倡导的算法多样化之精神。准变量(表达式)思想对改进义务教育阶段数学教学有着诸多切实的现实意义。 相似文献
13.
Hsin-Yih Cindy Shyu 《British journal of educational technology : journal of the Council for Educational Technology》2000,31(1):57-69
The purpose of this study is to investigate the effects of computer-assisted videodisc-based anchored instruction on attitudes toward mathematics and instruction as well as problem-solving skills among Taiwanese elementary students. Results from a t-test indicate a significant main effect on student attitudes toward mathematics. Results from a two-way Repeated Measures ANOVA show that students' problem-solving skills improve significantly with anchored instruction. Results also indicate that all the students benefit from the effects of anchored instruction on their problem-solving performance regardless of their mathematics and science abilities. The findings suggest that video-based anchored instruction provide a more motivating environment that enhanced students' problem-solving skills. This study is significant because it establishes an example of video-based anchored instruction for Taiwanese students and also provides empirical evidence of its effects on affective and cognitive responses among fifth graders in learning mathematics. This study is helpful to educators who want to help students learn to think and learn throughout technology. 相似文献
14.
Katya A. Karathanos 《International Journal of Inclusive Education》2013,17(1):49-65
This study explored to what extent two groups of mainstream teachers in the Midwestern region of the USA with differing degrees of English language learner‐specific university preparation reportedly engaged in practices that incorporated the native languages of English language learner students in instruction. The study further examined specific strategies reported by mainstream teachers in promoting native language use in instruction as well as challenges identified in implementing this practice. The study used a mixed‐method design that included analyses of survey data from a quantitative study (n = 227) and qualitative analyses of teacher discourse from course documents and open‐ended survey questions. Findings indicated that while both groups of teachers reportedly engaged in practices that promoted native language use in instruction to some extent, teachers with at least three courses of English language learner‐specific university preparation appeared to engage in these practices to a much greater extent than those without such preparation. This paper explores the implications of results from this study for teacher education programmes in the USA with the responsibility of preparing teachers effectively to serve growing numbers of culturally and linguistically diverse student populations. 相似文献
15.
LOU EDWARD MATTHEWS 《Educational Studies in Mathematics》2003,53(1):61-82
A collective case study guided by reconceptualized critical theory explored the teaching of four elementary teachers as they
incorporated a model of culturally relevant teaching into their mathematics instruction at four predominantly Black schools
in Bermuda. The study examined how teachers sought to (a) foster critical mathematical thinking and critical consciousness,
(b) build on informal mathematical and cultural knowledge; and (c) utilize empowerment orientations toward students' culture
and experience. The teachers embraced culturally relevant teaching but varied in their efforts to incorporate these perspectives
into instruction. Four facets of their teaching are illuminated. These complexities included situations were teaching focused
on sustaining empowered relationships;building on or to students' cultural knowledge; and fostering critical thinking as framed in the model, or personal definitions.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
16.
内隐学习研究对大学英语教学的启示 总被引：4，自引：0，他引：4
内隐学习理论对我国大学英语教学有重要的启示意义，主要表现在：大学英语教学应充分注意和发挥学生无意识的内隐认知活动；外显的指导和已有知识经验的积累是学生英语语言素质提高的关键；大学英语对人文精神的培养不应忽视学生的内隐社会认知过程；内隐学习的研究思路对我国大学英语教学进行科学化的研究是很好的借鉴。 相似文献
17.
Bradley S. Witzel Cecil D. Mercer M. David Miller 《Learning disabilities research & practice》2003,18(2):121-131
Abstract. Thirty‐four matched pairs of sixth‐ and seventh‐grade students were selected from 358 participants in a comparison of an explicit concrete‐to‐representational‐to‐abstract (CRA) sequence of instruction with traditional instruction for teaching algebraic transformation equations. Each pair of students had been previously labeled with a specific learning disability or as at risk for difficulties in algebra. Students were matched according to achievement score, age, pretest score, and class performance. The same math teacher taught both members of each matched pair, but in different classes. All students were taught in inclusive settings under the instruction of a middle school mathematics teacher. Results indicated that students who learned how to solve algebra transformation equations through CRA outperformed peers receiving traditional instruction on both postinstruction and follow‐up tests. Additionally, error pattern analysis indicated that students who used the CRA sequence of instruction performed fewer procedural errors when solving for variables. 相似文献
18.
This paper presents the results of a study of the development of early mathematical competence among young poor arithmetic achievers in the 4–7 year age group. Research has shown that arithmetic difficulties later in life can be explained by an insufficient development of early mathematical competence: i.e. different aspects of early mathematical competence. The different aspects of early mathematical competence are derived from cognitive psychology and from a didactical point of view with an emphasis on (the various phases of) counting. The Piagetian operations (seriation, correspondence and classification) are used, however, as much as possible embedded in a counting context.After selection by way of an early mathematical competence test, children with a score below a criterium are presented with an additional program. This program consists of activities, embedded in real (daily) life themes, in which attention is paid to the different aspects of early mathematical competence. The program is given to the children with a guiding or a structuring instruction form. The results of the study show that it is possible to stimulate the development of early mathematical competence among young poor arithmetic achievers. The way in which instruction is offered has no influence on achievement. 相似文献
19.
Dr. Johannes E.H. van Luit 《欧洲特需教育杂志》2013,28(4):237-246
Abstract Impulsivity is an important and co‐determining factor in the arising of learning difficulties. Impulsive children make many mistakes in arithmetic because of inattention and because they don't use the selfcontrol necessary to correct possible mistakes. In this investigation we examine whether a self‐instructional training program, applied in the teaching of arithmetic, has influences on the impulsivity (measured with help of the MFFT) of pupils who have a quick reaction time and who make many errors. The study involved 52 pupils selected from schools providing special education to children with learning disabilities and educable mentally retarded children. Sixteen of them could be categorized as impulsive children. The effectiveness of the training program is statistically investigated by means of t‐tests for correlated samples. The results show that training with a self‐instruction strategy can be effectively employed in teaching addition and substraction to educable mentally retarded and learning disabled children with arithmetic deficits. Besides, the impulsive children show after the training a more reflective cognitive style when compared to their cognitive style before the training was started. 相似文献
20.
英语学习策略及在课堂中的训练 总被引：11，自引：0，他引：11
李俏 《课程.教材.教法》2004,(3)
根据学习和信息加工的一般认知模式,中学阶段学生英语学习过程中要培养的学习策略应为认知策略、元认知策略和资源管理策略。学生学习策略能力的提高,需要进行必要的训练,为此教师应做好以下准备:1.建立一个以学习者为主体的课堂;2.培养学生反思的意识;3.学生对语言学习的自我评估;4.帮助学生识别正在使用的学习策略;5.教学生学写学习日记。学生学习策略的课堂训练主要包括:介绍、讲授、练习、评价、扩展五个步骤。 相似文献