The Development of Metacognition in Primary School Learning Environments

Constructivist ideas have influenced recent major innovations in Dutch secondary education and new curricula for reading and math in primary education, for example, pay much more attention to metacognition than before. In our study, we compared the growth of student metacognition in varying learning environments, direct instruction, and cognitive apprenticeship in primary school. The study also included a control group of teachers. In order to measure metacognition we developed a questionnaire, with separate parts for metacognitive skills and metacognitive knowledge. In the item selection procedure we made use of item response modeling. It was found that in the direct instruction and the cognitive apprenticeship group the pupils had higher scores on metacognitive skills and metacognitive knowledge compared to the control group pupils. No clear differences were found between direct instruction and cognitive apprenticeship. Interactions of learning environment and student intelligence were non-significant for both output measures.     

数学学习困难学生的元认知特点及教学策略

元认知是个体对自己认识活动的自我意识和自我监控,元认知发展水平是影响学习困难学生的重要因素之一。认真探讨数学学习困难学生的元认知发展特点,提出如何促进数学学习困难学生的元认知发展的教学策略。     

Effects of game-based learning in an OpenSim-supported virtual environment on mathematical performance

This experimental study was intended to examine whether the integration of game characteristics in the OpenSimulator-supported virtual reality (VR) learning environment can improve mathematical achievement for elementary school students. In this pre- and posttest experimental comparison study, data were collected from 132 fourth graders through an achievement test. The same math problem-solving tasks were provided to the experimental and control groups in the VR learning setting. Tasks for the experimental group involved the game characteristics of challenges, a storyline, immediate rewards, and the integration of game-play in the learning content. Analysis of covariance with the achievement test results indicated a significant effect of game-based learning (GBL) in the VR environment, in comparison with non-GBL in the VR environment, in promoting math knowledge test performance.     

The use of a collaborative math tutoring model to improve content knowledge among special education teacher candidates

ABSTRACT

The mathematics achievement gap in special education is a chronic and significant challenge for the field. The need for improved teacher preparation in mathematics is crucial in addressing this gap. This study examines a capstone experience in higher level mathematics tutoring for preservice teachers. Results indicate that the experience was effective at improving preservice teachers’ higher level math content knowledge compared to teachers who did not receive experiential math learning in their teacher preparation. Implications for preservice teacher preparation programs are presented.     

中学数学教学与学生元认知能力的策略培养研究

在数学教学实践中,数学教师应把对学生学习能力的培养、开发学生智力以及使教学更好地适应学生的心理发展作为重要的教学内容。我国当前教育改革的重要目标之一,就是培养学生的独立性和自主性,使学生学会学习。因此,在高中数学教学中培养学生的元认知能力具有十分重要的现实意义。     

Metacognitive skills in Belgian third grade children (age 8 to 9) with and without mathematical learning disabilities

This paper presents a study on mathematical problem solving in third-grade pupils. The relationship between mathematics, metacognition and intelligence was investigated in children with (n = 191) and without mathematical learning disabilities (n = 268). A significant relationship was found between prediction, evaluation, intelligence, procedural and mathematical fact retrieval skills in children without mathematical learning disabilities. In the children with mathematical learning disabilities a relationship was found between metacognitive and procedural skills. No such relationship was found between intelligence and metacognition or between metacognition and mathematical fact retrieval skills. In addition it was investigated if children with mathematical learning disabilities had less adequate metacognitive skills than peers without learning problems. At group level significant differences were found between both groups. However on analyzing these results further, it was found that four out of five children with combined mathematical learning disabilities, half of the children with procedural disabilities and only 5% of the children with a retrieval deficiency had low metacognitive skills. Furthermore, metacognitive problems were found in one out of five children without learning disabilities. Moreover, a majority of the children with mathematical learning disabilities and inadequate metacognitive skills had problems with prediction and evaluation skills. Most third graders with low metacognitive skills only appeared to have problems predicting the level of difficulty of tasks. Inaccurate evaluations were found on a more regular basis in children with mathematical learning disabilities and inadequate metacognitive skills as opposed to the sample of children with inadequate metacognitive skills but without learning difficulties, where their occurrence was rather a one off. The implications of this study for diagnosis and treatment will be discussed later in this paper.     

自我监控策略提高小学数学学习障碍学生解题能力的个案研究

文章以个案研究的方法,对一名小学数学学习障碍学生的数学解题做了自我监控策略的研究,实验分为基线期、介入期、维持期.结果表明,个案的自我监控策略习得分数有增加的趋势并具有维持效果;其数学应用题解题方面的成就分数有显著增加的趋势且具有维持效果.     

Fifth graders metacognitive knowledge: general or domain-specific?

The purpose of the present study was to investigate the structure of metacognitive knowledge in fifth grade pupils and its relation to school achievement. Since the structure of metacognitive knowledge is controversially discussed with little empirical evidence for either its domain specificity or its domain transferability, the debate remains somewhat hypothetical up to date. In theory it is assumed that the development of metacognitive knowledge begins highly domain and situation-specific and becomes more flexible and domain-transcending with practice and experience (Borkowski et al. 2000). As standardized measures to assess metacognitive knowledge of students in the age group under investigation were missing, newly developed instruments were applied to assess the domain-specific metacognitive knowledge in reading and mathematics as well as domain-transcending metacognitive knowledge. The influences of domain-specific and general metacognitive knowledge on school achievement in the two domains were analyzed. While findings on the structure of metacognitive knowledge indicate some degree of domain specificity, they also point out a strong relation between general metacognitive knowledge and domain-specific metacognitive knowledge. The cross-sectional relation between metacognitive knowledge and academic achievement were relatively low. Implications for future research will be discussed.     

培养应用意识:数学教育改革的新视界

发展数学应用意识,是数学课程改革极力倡导的新理念。数学应用意识的内涵主要表现于对数学应用的广泛性、策略性、情境性的理解与感悟。教师要根据数学本质的沿革与数学教育现状的反思等方面深层次地探讨培养学生应用意识的诱因。通过创设问题情境、拓展学习资源、丰富数学实践活动等有效策略进行培养。     

浅谈中学生数学焦虑的成因和对策

引起中学生数学焦虑的因素主要有知识、观念技能与能力等认知体验因素及家庭、教师学习者等情感体验因素。改善学生数学学习的途径有帮助学生剖析焦虑根源,使用技术暗示及鼓励合作等。     

从专业需求看高职应用数学课的作用和地位

高职教育是一种全新的教育模式,对数学知识的需求也较普通高等教育不同。高职教育的应用数学为学生的后续学习提供必备基础知识,教学中要以“必需、够用、有用、实用”为准则,培养学生必备的能力。     

数学教学改革与高职学生成绩评定

本文分析了高等职业教育的现状，阐述了高职数学教育的意义和任务。针对目前高职学生数学基础普遍较差的实际情况，提出了转变观念，根据高职教育的培养目标，改革教学方法和教学手段，建立以能力为主的学生成绩多元评价体系。     

中小学数学教育与性别差异调查初报及其思考

对韩山师范学院数学专业的大学生在数学知识的发展过程的调研结果表明：小学数学教育与性别无明显差异；中学数学教育与性别存在不同程度的差异．     

The effects of self-regulated learning training on community college students’ metacognition and achievement in developmental math courses

The effects of training in self-regulation on metacognition and math achievement were investigated. The participants were 116 community college students enrolled in developmental math courses. Students enrolled in 16 classrooms were randomly assigned to the treatment and control groups. Participants in the treatment group completed four self-regulated learning (SRL) exercises based on Zimmerman’s (2002) cyclical model. The exercises were completed weekly and repeated for a total of 3 weeks. During the last week of class, participants completed a final exam to measure math achievement as well as the metacognitive self-regulation and time/study environment management scales on the Motivated Strategies for Learning Questionnaire ([MSLQ], Pintrich, Smith, Garcia, & McKeachie, 1991). There were significant differences between the two groups, indicating that training in SRL improved math achievement and metacognitive skills assessed on both MSLQ scales. The findings suggested that training in SRL improves math achievement, metacognitive self-regulation and time/study environmental management skills of students enrolled in developmental math courses.     

Longitudinal Pathways From Math Intrinsic Motivation and Achievement to Math Course Accomplishments and Educational Attainment

Abstract

Across 20 years, pathways from math intrinsic motivation and achievement (ages 9–17) to high school math course accomplishments and educational attainment (age 29) were analyzed. Academic intrinsic motivation was the theoretical foundation. To determine how initial status and change in motivation and achievement related to course accomplishments and educational attainment, a latent curve model was fit to data from the Fullerton Longitudinal Study. Levels of motivation and achievement at 9 had positive, direct, and mutually indirect paths to course accomplishments. Dual declines in motivation and achievement related to course accomplishments, directly for achievement, and indirectly for motivation via achievement. Greater decline corresponded to fewer course accomplishments which in turn predicted, and served as a mediator to educational attainment. Implications are discussed.     

论数学焦虑对学生数学认知和社会化的影响

数学焦虑是学生学习数学过程中产生的负面情感体验。过度焦虑会影响学生的数学认知构建、数学学习策略的选择和数学能力的发展．导致状态性焦虑的形成。若焦虑症状未能得到减轻．长期以往会固化下来。形成特质性焦虑，严重影响学生的心理健康．阻碍个体社会性的发展．     

谈高职数学教学中学生数学素质的培养

数学教育不仅要传授数学知识、技能,更重要的是要提高学生数学素质和培养学生数学创新思维能力。在高等数学教学中,要激发学生学习高等数学的兴趣,因材施教,培养学生的创新能力;同时要用严谨的教学态度感染学生,这样才能提高学生数学素质。     

信息技术与高职教育数学课程整合的思考

信息技术与高职教育数学课程整合,就是通过高职教育数学课把信息技术与高职教育数学教学有机地结合起来,将信息技术与高职教育数学课的教与学融为一体,将技术作为一种工具,提高教与学的效率,使数学教学融入了现代的教育思想观念与教育艺术,使数学教学真正实现改革。     

高师院校应重视数学语言表达与数学交流能力的培养——谈高师数学教学如何配合基础教育课程改革

数学的语言表达与交流能力是数学教师的基本功,基础教育课程改革提出"以数学方式表达和交流"、"学会与人合作,并能与他人交流思维的过程和结果",也就是数学语言的掌握和运用。中小学数学教师由于数学语言使用不当而表达不清甚至导致教学失误是常见的,这就需要承担基础教育师资培养任务的高师院校重视培养学生数学语言表达和交流能力,作者对此进行了探讨。     

Integrating written metacognitive awareness guidance as a ‘psychological tool’ to improve student performance

A study was designed to test the effect of using MetaCognitive Awareness Guidance (MCAG) as a vehicle for activating and engaging learners’ existing prior knowledge before they begin a reading assessment task. A total of 300 pupils (aged 9–10) studying in ten 4th grade classes in four different schools in Israel participated in the research. The major assumption of the study was confirmed: increasing learners’ metacognitive awareness by means of well-planned guidance, built on prior knowledge, facilitates their learning and improves outcomes on a reading assessment task. This paper focuses on the linkage between three components of learner performance, what we refer to as the ‘Assessment Triangle’: (1) achievement on reading assessment tasks; (2) performance on metacognitive awareness guidance; and (3) awareness of metacognitive reading strategies. The implications and the function of this revealed linkage will be discussed.