关于数学自主学习的基本思考

所谓自主学习是指学生在教师的科学指导下,通过能动的创造性的学习活动,实现自主发展的过程。本文试图从相关文献的简述着手,通过分析学生自主学习的现状,在培养学生自主学习的意识和能力的基础上,提出数学自主学习的基本理念,探讨以学生自主学习程度的提高为标志的数学教学策略。     

A self-determination theory approach to predicting school achievement over time: the unique role of intrinsic motivation

Although many studies have examined the relation of academic motivation to school achievement using the Self-Determination Theory perspective, the results have been inconsistent. The present investigation represents the first systematic attempt to use a meta-analysis and controlled, longitudinal studies to examine the relations of specific types of motivation to overall academic achievement. The meta-analysis (Study 1) pointed toward a potentially important role of intrinsic motivation in predicting school achievement. Three empirical studies of high school and college students in Canada (Studies 2 and 3) and in Sweden (Study 4) showed that intrinsic motivation was the only motivation type to be consistently positively associated with academic achievement over a one-year period, controlling for baseline achievement. Amotivation was significantly associated with lower academic achievement in Studies 3 and 4. Interestingly, intrinsic motivation was also associated with reduced amotivation in two of our studies and it was reciprocally associated with higher school achievement in another study. Overall, our findings highlight the unique importance of intrinsic motivation for the future academic success of high school and college students.     

高等数学“双主四环”探究教学模式

有效的探究教学模式必须体现师生“双主”作用．基于高等数学教学改革现状,在新课程理念下,揭示了“双主四环”探究式教学模式的内涵,并构建其模式框架;结合高等数学中微元法的教学案例阐述了“双主四环”探究教学模式的实施策略．     

A latent transition analysis of academic intrinsic motivation from childhood through adolescence

A longitudinal modeling approach was utilized to determine the existence of latent classes with regard to academic intrinsic motivation and the points of stability and transition of individuals between and within classes. A special type of latent Markov Chain model using Mplus was fit to data from the Fullerton Longitudinal Study, with academic intrinsic motivation measured from ages 9 through 17. Model fit using the Bayesian Information Criterion index was examined. The best fit involved a 3-class model, with classes designated as motivationally gifted, intermediate, and at-risk. Transitions between classes occurred mainly during childhood, whereas stability ensued by age 13. Methodological contributions are discussed, as well as theory and applications of the findings with regard to academic intrinsic motivation.     

试析数学建构性教学中教师的作用

建构主义的数学学习观 ,对教师在数学教学中的作用需要作出新的认识 :教师是学生数学学习活动的促进者 ;教师要为学生的数学学习活动创造一个良好的学习环境 ;教师要了解学生的需求信息 ;教师要培养学生的自我调控能力     

Teachers' intrinsic vs. extrinsic instructional goals predict their classroom motivating styles

We introduce the concept of teachers' intrinsic vs. extrinsic instructional goals and demonstrate its contribution to teachers' classroom motivating styles using independent samples across four studies. Based on self-determination theory, we hypothesized that the more teachers adopted intrinsic instructional goals the more they would rely on an autonomy-supportive motivating style, and the more they adopted extrinsic instructional goals the more they would rely on a controlling motivating style. Because no measure existed to assess intrinsic vs. extrinsic instructional goals, we created the new 4-scale, 16-item Teacher Goals Questionnaire (TGQ) in Study 1, using a pool of 72 candidate items and data from 212 fulltime K-12 teachers. In Study 2, we demonstrated the TGQ's construct and factorial validity by sampling 149 fulltime K-12 teachers. In Study 3, we tested our hypothesized model by sampling 147 fulltime K-12 teachers who reported their instructional goals on the TGQ and their motivating styles on two separate measures. Structural equation modeling analyses confirmed the hypothesized model. In Study 4, we replicated the findings from Study 3, using a multilevel sample (92 secondary teachers, 2749 students), a longitudinal research design, and student measures of teachers' motivating styles. The discussion focuses on instructional goals as key antecedents of teachers' classroom motivating styles.     

INSTRUCTIONAL COHERENCE IN CHINESE MATHEMATICS CLASSROOM—A CASE STUDY OF LESSONS ON FRACTION DIVISION

In this study, we examined the instructional coherence in a Chinese mathematics classroom by analyzing a sequence of four videotaped lessons on the topic of fraction division. Our analysis focused on the characteristics of instructional coherence both within and across individual lessons. A framework was developed to focus on lesson instruction in terms of its content and process and the teacher's use of classroom discourse. The analyses of lesson instruction were further supplemented with the analyses of teaching materials and interviews with the teacher. The findings go beyond previous studies that mainly focused on a single lesson to provide further evidence about Chinese teachers' instructional practices and their possible impact on students' learning. In particular, the teacher tried to help students build knowledge connections and coherence through lesson instruction. Results also suggest that coherent curriculum and the teacher's perception of the knowledge coherence facilitated the teacher's construction of coherent classroom instruction.     

Manipulative Use and Elementary School Students’ Mathematics Learning

Using data from the Early Childhood Longitudinal Study (ECLS) 1998/1999, we examine the relationship between elementary students’ (K–5) manipulative use and mathematics learning. Using a cross-sectional correlational analysis, we found no relationship between manipulative use and student mathematics achievement. However, using a longitudinal analysis, we documented a positive relationship between manipulative use and student mathematics learning during their elementary school years (K–5). From a teaching and learning perspective, these findings provide important evidence of the influence of long-term manipulative use on students’ overall learning. From policy and methodological perspectives, these findings provide evidence for the importance of modeling student learning (as opposed to achievement) when studying the effectiveness of instructional strategies.     

Language factors associated with achievement grouping in math classrooms: a cross-sectional and longitudinal study

The study examines the effects of classroom achievement grouping (AG) practices on the early mathematics performance of language-minority students and compares their mathematics achievement to that of English-speaking majority students. Using a nationally representative database of the USA, both cross-sectional and longitudinal analyses were done. In the cross-sectional analyses we explored the direct effect of grouping practice on students performance, while in the longitudinal analysis we looked at the growth trajectory in mathematics learning. The results of cross-sectional analyses indicated that the effect of AG was negative on the math achievement in 1st and 5th graders. The longitudinal analysis showed a significant negative effect of AG for English Language Learners (ELL). The paper provides the basis for practical guidelines for the grouping practices in mathematics.     

高师学生＂双主四环＂探究试教模式的思考

有效的探究教学必须体现师生“双主”作用;基于高师学生课堂试教现状,在新课程理念下,揭示了“双主四环”探究式试教模式的内涵,并构建其模式框架;结合高中数学中“椭圆及其标准方程”的教学案例阐述了“双主四环”探究试教模式的实施模式。     

Effort on homework in grades 5-9: development, motivational antecedents, and the association with effort on classwork

In 2 studies, an expectancy-value framework was applied to investigate effort expended on mathematics homework. In Study 1 (2,712 students in grades 5, 7, and 9; mean age=13.37 years), lower homework effort was found in higher grades. The effects of intrinsic value on homework effort were higher in the older cohorts, whereas the effects of the expectancy component were lower. In Study 2 (571 students in grades 8 and 9; mean age=14.72), an expanded expectancy-value framework was found to explain both homework and classwork variables. The means for effort and value were lower for homework than for classwork; these differences were partly moderated by students' conscientiousness. The implications of homework behavior and motivation for developmental research are highlighted.     

教师教学行为转变的文化学思考

教师教学行为转变是教学文化变革最直接的表现形式。课程改革的深切呼唤、有效教学的内在需求和学生发展的时代诉求是教师教学行为转变的文化境遇。从控制型向民主型转变、从隔离型向合作型转变、从守成型向创生型转变是当下教师教学行为转变的主要文化路向。     

Student/teacher relations and attitudes toward mathematics before and after the transition to junior high school

In a longitudinal study of 1,301 students and the teachers they had for mathematics before and after the transition to junior high school, we assessed whether changes across the transition in students' perceptions of their teachers' supportiveness were related to changes in their valuing of mathematics. Using repeated-measures multivariate analysis of variance, we found that when students moved from elementary teachers they perceived to be low in support to junior high teachers they perceived to be high in support, the intrinsic value of math was enhanced, while students who moved from teachers they perceived to be high in support to teachers they perceived to be low in support experienced a sharp decline in both the intrinsic value and perceived usefulness and importance of math. For students' perceptions of the usefulness and importance of math there was an interaction with achievement level. Math values decreased more sharply during the first year of junior high for low-achieving students who moved from more supportive to less supportive teachers than for high-achieving students who experienced the same change.     

Effective classroom management and the development of subject-related interest

This article examines the effect of classroom management strategies on students' interest development in secondary school mathematics classes. Two studies using student questionnaire data (one cross-sectional, with data from 400 students; the other longitudinal, with 1900 students) are reported. Results show that students' perceptions of rule clarity and teacher monitoring are positively related to their interest. Hierarchical linear modeling was used to examine the effect of classroom management on interest development over one school year, revealing that only individually perceived classroom management strategies and none of the class-level teaching characteristics (aggregated student data) affected interest development.     

The Emerging Pracitces of a Novice Teacher: The Roles of His School Mathematics Images

The relationship between teachers' beliefs about mathematics and its teaching and learning, and their classroom practices, has been investigated in many studies. The results of these studies are by no means unanimous, and the purpose of the present report is to contribute to a further understanding of the significance of one teacher's beliefs and images of school mathematics on his teaching practices. The article presents a novice teacher whose images of school mathematics were strongly influenced by the current reform of mathematics education. The study focuses on how the teacher coped with the complexities of the classroom. On the basis of the teacher's role within the classroom interactions, the construct of critical incidents of practice is developed, and some of the results of previous research in the field are re-examined. This revised version was published online in August 2006 with corrections to the Cover Date.     

Materialism does not pay: Materialistic students have lower motivation,engagement, and achievement

The aim of this study was to examine how materialism, or the focus on acquiring money and material possessions, is associated with students’ academic engagement and achievement via their motivational regulation (amotivation, controlled motivation, and autonomous motivation). Study 1 (n = 606 secondary students) was a cross-sectional study which found that materialism was negatively associated with engagement. This association was partially mediated by amotivation. Study 2 (n = 404 secondary students) was a longitudinal study which found that Time 1 materialism was negatively associated with Time 2 engagement and Time 3 academic achievement via amotivation. Results of the two studies provide converging lines of evidence that materialism is negatively associated with key indicators of learning. Students with high levels of materialism have lower levels of engagement and achievement, and these associations are partially mediated by amotivation. Theoretical and practical implications are discussed.     

Self-regulatory teaching in mathematics: relations to teachers' motivation,affect and professional commitment

The purpose of this study was to examine the relationships between teachers' reports on self-regulatory strategy use in mathematics instruction and individual motivational and affective factors. Two hundred and ninety-two Greek primary school teachers responded to two questionnaires assessing (a) the strategies they use themselves to plan, monitor and evaluate mathematics instruction and (b) the strategies they use to activate and enhance students' self-regulated learning in mathematics. Path analysis showed that teachers' self-regulation strategies both for their own teaching and for enhancing students' self-regulation in mathematics were predicted by their self-efficacy beliefs in teaching mathematics, the value they attribute to mathematics and their emotional commitment to their profession. Teachers' enjoyment of mathematics teaching did not directly predict their reported use of self-regulatory instructional strategies. The implications of the study are related to the development of teachers' training programmes in self-regulated instruction.     

Understanding Teacher Educators and Their Pre-Service Teachers through Multi-Media Case Studies of Practice

The challenges facing those who seek to prepare mathematics teachers are well established in the literature. Most of the research to date has focused on the perceptions and understandings of pre-service teachers, but not on the perceptions and understandings of teacher educators. In this study, we explore how four teacher educators understand their pre-service secondary teachers as the pre-service teachers attempt to make sense of teaching through the investigation of a multimedia case study of practice. We found that the teacher educators adopted two different implementation strategies: one strategy tended to be open-ended and exploratory; the other was more focused on the teacher educators' goals of anticipating student understanding and developing mathematical content knowledge for teaching. We also found that, in using the case study, teacher educators elicited pre-service teachers' thinking about the complexities of the teacher's role in small group work, about the value of explicitly revealing the teacher's reflections on the lessons, about the role of planning and preparation, and about the limits of pre-service teachers' abilities to understand and appreciate students' thinking and to extend lesson ideas. Both teacher educators and their pre-service teachers gained perspectives on the role of a teacher's mathematical content knowledge. These results imply that multimedia case studies of practice can serve as vehicles for revealing the knowledge and practice of teacher educators, as they engage in supporting the professional development of pre-service teachers.     

The effect of block scheduling high school mathematics courses on student achievement and teachers' use of time: implications for educational productivity

Block scheduling involves the reallocation of instructional time into longer class sessions to encourage more active teaching strategies, reduce fragmentation inherent in single-period schedules, and improve student performance. To the degree that such policies reallocate existing resources to realize higher levels of desired educational outcomes, the goal of productivity can be served. Despite widespread experimentation with various forms of block scheduling, there is conflicting evidence on the impact of these innovations on student achievement, and little evidence of their effect on classroom practice. This study explores these relationships. More specifically, the study draws on data from the National Education Longitudinal Study: 1988 to estimate the impact of block-scheduled mathematics courses on tenth-grade student achievement and teachers' use of class time. Findings suggest that while block scheduling is positively associated with teachers' use of multiple instructional methods and more individualized instruction, this scheduling reform has a negative impact on students' tenth-grade mathematics scores, controlling for other factors. Implications for educational productivity are discussed.