An unexpected relationship between failure and subsequent mathematics learning

135 high schoolSs were presented with one of three treatment programs: rule (R); rule, then discovery (RD); and discovery, then rule (DR). AllSs were tested on the training rules and on three transfer problems. No significant differences were found on the transfer problems, but the R and RDSs learned the training rules better than the DRSs (p<0.01). It was proposed that failure on the discovery task may have had an inhibiting effect on subsequent learning on the R program.The authors wish to thank the students who participated in the experiment, the members of a teachers' research seminar supported by a government grant to the Montgomery County Instructional Center, and particularly to Mr. Philip Beck and Mr. Philip O'Neil without whose help and cooperation the study could not have been conducted.     

An investigation of the relationship between metacognition and mathematics achievement

The aim of this study is to determine fifth-grade students’ metacognitive knowledge and skills and its relationship with mathematics achievements. A total of 242 primary school students from six different schools were participated in the study. Turkish version of Metacognitive Knowledge and Skills Assessment (MSA-TR) was used to measure metacognitive knowledge and skills. The results demonstrated a significant and positive relationship (r = .648, p < .01) between metacognition and mathematics achievement. Furthermore, research results showed that 42% of total variance of mathematics achievement could be explained with metacognitive knowledge and skills.     

数学学习与学生身心发展的关系

本文探讨了四方面的问题 :数学学习心理研究的发展 ,学生的数学学习特点 ,学生的数学学习过程 ,数学学习心理研究对数学课程设计的启示。     

Relationships between learning environment and mathematics anxiety

We investigated relationships between the learning environment and students’ mathematics anxiety, as well as differences between the sexes in perceptions of learning environment and anxiety. A sample of 745 high-school students in 34 different mathematics classrooms in four high schools in Southern California was used to cross-validate the What Is Happening In this Class? (WIHIC) learning environment instrument, together with an updated Revised Mathematics Anxiety Rating scale. Mathematics anxiety was found to have two factorially-distinct dimensions (namely, learning mathematics anxiety and mathematics evaluation anxiety) which yielded different patterns of results for sex differences and anxiety–environment associations. Relative to males, females perceived a more positive classroom environment and more anxiety about mathematics evaluation, but less anxiety about mathematics learning. Some statistically significant associations were found between anxiety and learning environment scales for learning mathematics anxiety but not for mathematics evaluation anxiety.     

Gender and the relationship between affective beliefs and perceptions of grade 7 mathematics classroom learning environments

This paper examines the relationships between a number of affective variables included in models explaining gender differences in mathematics learning and a range of classroom environment dimensions more likely to be associated with effective mathematics learning. A large sample of 12–13 year old grade 7 students participated in the study. The data were explored at the individual level, for whole class groupings of students, and by gender. For individuals, three of the classroom environment measures were found to be associated with a subset of the affective variables. The patterns of the relationships in classroom learning environments where teacher support emerged as irrelevant were not the same for males and females, however. For class groupings of students, the same three classroom environment measures were related to the affective variables but their salience was different for males and females.     

寻找数学课程中研究性学习的切入点

将一题多解、一题多思作为在数学课程中实施研究性学习的切入点 ,有利于培养学生求异思维和创新思维的发展 ,从而在此基础上进一步提升研究性学习的质量与档次     

初中学生数学自主学习及其与数学成绩的关系研究

全面分析学生自主学习的心理结构,确定包括成就目标定向、学习兴趣、学习价值观、学习效能感和学习策略等五个分量表的自主学习测量问卷,信效度良好,对学生数学学业成绩有良好预测作用．以此作为评价工具实际测查和分析新课程背景下初中学生数学自主学习状况及其与数学成绩的关系．     

大学数学教与学良性互动关系的探讨

数学是一门描述自然法则的语言,是当今科技进步的重要基础.从教学实践出发,总结大学数学教与学的良性互动关系,提出在教学过程中处理好教学关系应注意的几个方面.     

The relationship between perceived learning and satisfaction with college: An alternative view

Student and alumni reports of learning and development during college play an important role in research on educational outcomes. An intriguing finding of this research is the positive relationship between perceived learning and satisfaction with college. While studies have documented an association between perceptions of learning and satisfaction, the nature of the relationship is not clearly defined. This study evaluates two competing models of perceived learning and satisfaction. The first model represents a true relationship between learning and satisfaction, while the second treats the relationship as an artifact of a halo effect. Data came from subjects who completed learning and satisfaction questions as seniors and again two years after graduation. Analyses revealed that treating the learning-satisfaction relationship as an artifact of a halo effect provided the best representation of the data. Although not conclusive, results suggested that educational researchers and assessment practitioners should be careful in interpreting self-reports of learning and development, particularly as they relate to satisfaction with college.Presented at the Annual Forum of the Association for Institutional Research, Atlanta, Georgia, May 10–13, 1992.     

例谈合作学习形式与学习任务的关系

合作学习的模式化日益凸显,教学效果令人质疑。如何使合作更加有效?我们认为,应视不同层级的学习任务而运用不同的合作学习形式。本文以《开辟文明交往的航线》一课的教学,从实践层面来观察合作学习形式与学习任务的关系。     

经历学习过程 体验数学学习

文章主要阐述了怎样在学生学习过程中凸现“经历学习过程”、“在体验中获得经验”这一“课标》中的新理念。从经历主动建构的过程、体验丰富多彩的数学活动和形成富有个性．体现多样化学习需求的数学学习过程三个方面进行了陈述，并且通过一些具体事例的描述论证了以上的观点．表述了“让学生经历学习过程，充分体验数学学习，感受成功的喜悦，增强信心，从而达到学会学习的目的”的观点，以期推动课改的进程。     

The relationship between student-generated learning issues and self-study in problem-based learning

A major assumption of problem-based learning (PBL) is that learning issues, generated by students while discussing a problem, are used as guides for self-directed learning activities. This assumption, though basic to PBL, has never been tested. At the University of Limburg, the Netherlands, two procedures have been developed that reflect the extent to which students are able to identify important learning issues given a particular problem, and whether subsequent, independent, learning corresponds with these learning issues. The focus of the present article will be on the relationship between the two. We have explored to what extent student-generated learning issues are a major factor influencing the nature of students' self-study, or whether other factors may be involved in decisions on what to study and how much time to spend on topics selected. First, the production of learning issues was studied and represented as the percentage of overlap between learning issues raised by students and pre-set faculty objectives for each problem. The second procedure consisted of the administration of a Topic Checklist (TOC) which purports to measure students' actual self-directed learning activities. The TOC consists of a list of topics specifying the intended course content. Students were asked to indicate on a five-point Likert scale how much time they had spent studying each topic and to what degree they had mastered that topic. Third, learning issues and TOC topics were compared directly in a qualitative sense. Comparisons between the procedures revealed that a low proportion of variance of TOC scores could be predicted from the percentage of faculty objectives identified for each problem and the direct match between learning issues and TOC scores. It is concluded that scrutinizing student-generated learning issues and topics covered during self-study may provide information about what content is covered by students in tutorial groups. The discrepancy between the results of the measurements suggests, however, that learning issues produced during group discussion are not the sole source on which students base self-study decisions. Several other factors may be involved, such as tutor guidance, content already covered in previous units, issues raised during sessions with resource persons, and the nature of the learning resources available. Therefore, the relationship between learning issues and content covered during self-study is not as straightforward as is suggested.     

体验式教学对高师生数学学习效果的实验研究

目前五年制高等师范学校的数学教学现状是:教师教的辛苦,学生学的痛苦。为了改变这一现状,我们实施了体验式教学,加强对学生学情的了解,把话语权、主动权交给学生;从学生的角度出发,追求适合学生的教学难度;课后作业增加了数学写作,不仅提高了学生的反思能力,还促进了师生的交流,改善了师生的关系。     

ICT,learning and primary mathematics

A report of a decline in the extra-curricular activities available to the children in a West London junior school is presented. Using interviews with the school staff as evidence, reasons for the decline and its wider implications are discussed.     

Pre-service teachers learning mathematics using calculators: a failure to connect current and future practice

This study brings to the forefront pre-service teachers’ contrasting views between their own use of calculators and their views of appropriate use of calculators in the elementary school classroom. Using a Heideggerian perspective, this paper describes a course in which pre-service teachers study mathematics in a reform setting but may fail to connect their use of calculators and their views of how their future students could utilize technology in a similar manner. This study also demonstrates that, in contrast to commonly held beliefs about students’ overuse of calculators, most of the pre-service teachers did not rely exclusively on their calculators.     

Information processing and mathematics learning difficulties

Abstract

Successful mathematics learning requires the efficient processing of the information that defines the arithmetic tasks. Information processing relates to the ways in which individuals make sense of, or interpret, the information to which they are exposed.

The present study examines four aspects of information processing and their relationship for whole number computation for third and fifth grade students. The aspects included students’ ability to (1) manipulate numerals, (2) encode number sentences , (3) recognise order among numbers and (4) perform an arithmetic procedure.

Information processing in each area correlated with computational skill. At risk students were less efficient in their information processing. As well, the complexity of the numerical information affected how well the students could use it. The more complex the numerical information was, the greater the load it placed on the learner. The implications for diagnosing low mathematics achievement are discussed.