关于高等数学课程教学改革的几点措施探析

随着高等数学课程不断进行自我改革和深化,从原来固有的教育思想和观念中解放出来,迎接全新教育模式的变革;改变以往与社会时代脱节的课程教材内容,把刻板式的教学内容和形势改变,进入信息化现代化的教学模式之中。改变脱节的教材内容,让其更加贴入学生专业本身。改变教师的角色,让其正真适应新时期的教育趋势,本文只是抛砖引玉,对于尝试改革中的几点措施做出简述。     

小学数学学习兴趣的培养

记得曾经有一个教育家说过:没有丝毫兴趣的强制性学习,将会扼杀学生探求真理的欲望.所以,作为教师,应该主动地了解当前学生的所思所想,挖掘其内在的兴趣因素,让学生对所学的知识产生浓厚兴趣,从而积极地主动地进行学习.     

Characterising lesson planning: a case study with mathematics teachers

ABSTRACT

The quality of students’ learning experience depends on the learning activities that their teachers plan prior to classroom delivery. This article characterises the lesson planning practices of a group of 27 mathematics teachers. The questionnaire and the associated information coding and analysis procedures designed for that purpose may be applicable to lesson planning characterisation involving larger groups of teachers and of other disciplines. Some of the study group’s needs and difficulties are established. One of the observations discussed is that planning procedures and criteria tend to be generic rather than specific to the lesson at issue. Another is that these teachers’ vision of planning does not necessarily ensure a coordinated approach to all curricular dimensions.     

Linking university mathematics classroom environments to student achievement: The mediation of mathematics beliefs

This study examined the relationships between university mathematics classroom environments, mathematics beliefs, and achievement in the context of mainland China. As a type of affect in mathematics learning, mathematics beliefs including mathematics conceptions and efficacy were examined as mediators. Based on analysis of a sample of 1443 undergraduate students from a university in northern China, the study not only found that the mathematics classroom environment was associated with both affective and cognitive mathematics outcomes, but also confirmed the mediating role of mathematics beliefs. Specifically, a desirable classroom environment was related to students’ cohesive conceptions, enhanced self-efficacy, and higher mathematics achievement. In contrast, students’ perceived difficulty of learning mathematics was connected to their fragmented conceptions, reduced self-efficacy and lower mathematics achievement. Implications of the study are discussed.     

Ethnic and gender differences in mathematics achievement and in dispositions towards the study of mathematics

The study examined the effects of gender and ethnicity on mathematics achievement on a national test and on dispositions (attitudes, perceived parental expectations, effort, and help) towards the study of mathematics of a representative sample of Jewish and Arab eighth graders in Israel. The results indicated a large ethnic gap in achievement in favor of the Jewish students. Significant gender–ethnicity interactions emerged whereby Arab girls, compared to Arab boys, attempted more items on the test. In the Jewish sample, either the reverse held true or there were no significant differences between the sexes. Arab girls also reported receiving less help in doing mathematics homework and perceived their parents' expectations for their success in mathematics as higher than did Arab boys. Jewish girls, on the other hand, perceived their parents' expectations as lower and reported investigating more effort in coping with mathematics tasks and using more supporting tools than did Jewish boys. The results were discussed in light of cultural differences between Jews and Arabs in Israeli society and their respective learning environments.     

Gendered pathways to educational aspirations: The role of academic self-concept,school burnout,achievement and interest in mathematics and reading

The aim of this study was to examine lower secondary school students' (N = 1152) pathways to educational aspirations. The study used multi-group structural equation modelling to investigate the predictions of academic self-concept, school burnout, achievement, and interest in mathematics and reading, in relation to educational aspirations for boys and girls. While certain factors were influential for students' academic aspirations irrespective of gender, some interesting differences also emerged. Academic self-concept and interest in reading predicted educational aspirations for both groups. However, gendered pathways emerged in how achievement and interest in mathematics predicted educational aspirations. Interest in mathematics predicted girls’ educational aspirations, whereas mathematics achievement was a significant predictor for boys. School burnout had negative indirect effects through interest in reading and mathematics in both groups, but for girls, there was also a direct positive effect on educational aspirations.     

What they notice in video: a study of prospective secondary mathematics teachers learning to teach

Most teacher preparation programs have embraced the use of video as an effective methodology for developing teachers’ noticing skills. This study focused on learning about what secondary mathematics prospective teachers (PSTs) were able to notice when viewing video of their own co-teaching, particularly in a microteaching setting that consisted of peers. PSTs documented their observations on an observation tool while re-watching their video and then identified and ranked their top three observations. The ranked noticing statements were analyzed based on a grounded theory approach. Overall, PSTs’ ranked observations were more likely to attend to students and had a strong focus on mathematics and student learning. Ranked observations equally demonstrated both broad and specific understanding of video moments and often made suggestions that something they noticed could be improved in the implementation stage, versus improvements in planning or changes in themselves. Results support PSTs’ use of video for developing noticing skills in teacher education programs.     

Issues relating to curriculum,policy and gender raised by national and international surveys of achievement in mathematics

Scottish schools have provided performance data for five international surveys of attainment in mathematics since 1990. Performance measured against national targets and progression over time and between age‐stages have been monitored nationally, on a regular basis, for 20 years, within the Assessment of Achievement Programme (AAP) (Scotland). The 1994 AAP mathematics survey findings facilitated interpretation of the age 9 and 13 TIMSS results for Scotland. Both studies were influential in formulation of national policies to improve learning and teaching of mathematics, at ages 5–14. Research available to support policies recommended in 1997 is examined. Concerns about validity and reliability of findings from international studies are discussed in the context of a collaboration undertaken between Scotland and France in 1994. It is concluded that simplistic comparisons ignore important cultural and curricular differences. Outcomes of more recent national and international surveys are reported and performance findings from 1988–2000 that relate to gender are reviewed.     

创设情境,激发学生学习数学的兴趣

论文从不同角度探讨了如何激发学生主动学习、探究数学的兴趣,给出了一些激发学生学习兴趣的方法。可以使学生发现数学"很好玩",并非想象中的艰涩难懂。数学是我们良好思维的体操,与我们的生活密不可分,数学无处不在。     

The supply of mathematics teachers in England and Wales

This paper reports the findings of an ethnographic study of student teaching experiences in a preparation program that emphasizes field‐based practicums. It explores what students do in these practicum sites; what forces influence their behavior, ideas, and/or attitudes; and the different ways students respond to the constraints found in their field placements. Finally, it discusses the implications of the study's findings towards the theoretical constructs of reproduction and resistance as they apply to the professional socialization of future teachers.     

The importance of number sense to mathematics achievement in first and third grades

Children's symbolic number sense was examined at the beginning of first grade with a short screen of competencies related to counting, number knowledge, and arithmetic operations. Conventional mathematics achievement was then assessed at the end of both first and third grades. Controlling for age and cognitive abilities (i.e., language, spatial, and memory), number sense made a unique and meaningful contribution to the variance in mathematics achievement at both first and third grades. Furthermore, the strength of the predictions did not weaken over time. Number sense was most strongly related to the ability to solve applied mathematics problems presented in various contexts. The number sense screen taps important intermediate skills that should be considered in the development of early mathematics assessments and interventions.     

Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers

Although video cases are increasingly being used in teacher education as a means of situating learning and developing habits of reflection, there has been little evidence of the outcomes of such use. This study investigates the effects of using a coherent video-case curriculum in a university mathematics methods course by addressing two issues: (1) how the use of a video-case curriculum affects the reflective stance of prospective teachers (PTs); and (2) the extent to which a reflective stance developed while reflecting on other teachers’ practice transfers for reflecting on one’s own practice. Data sources include videotapes of course sessions and PTs’ written work from a middle school mathematics methods course that used a video-case curriculum as a major instructional tool. Both qualitative and quantitative analytical methods were used, including comparative and chi-square contingency table analyses. The PTs in this study showed changes in their level of reflection, their tendency to ground their analyses in evidence, and their focus on student thinking. In particular, they began to analyze teaching in terms of how it affects student thinking, to consider multiple interpretations of student thinking, and to develop a more tentative stance of inquiry. More significantly, the reflective stance developed via the video curriculum transferred to the PTs’ self-reflection in a course field experience. The results of this study speak to the power of using a video-case curriculum as a means of developing a reflective stance in prospective mathematics teachers.

Classroom instructional quality,exposure to mathematics instruction and mathematics achievement in fifth grade

This study examined the quality of teacher–child interactions and exposure to mathematics instruction as predictors of 5th grade student’s mathematics achievement. The sample was a subset of the children involved in the NICHD–SECC longitudinal study (N = 657). Results indicate that, even after controlling for student demographic characteristics, more exposure to mathematics instruction was related to increased fifth grade mathematics achievement for both calculations and applied problems assessments, but there was no main effect for improved instructional quality. Findings also indicate that, in classrooms where lower instructional quality was observed, greater exposure to mathematics instruction predicted improved mathematics achievement. Findings are discussed in terms of differing aspects of mathematics instruction and the possible compensatory role of exposure to instruction in classrooms of lower quality.     

数学课堂教学应如何激发学生的兴趣

兴趣是最好的老师。如何激发学生学习的兴趣是每一位老师面临的一个重要课题。数学,因其学科的特点,让很多学生对数学没有兴趣,觉得数学枯燥乏味。那么,激发学生学习数学的兴趣则对每一位数学教师提出一个更高、更难的要求,是每个数学教师教学工作中的关键,是数学教学中的永恒话题。有兴趣才有动力,有兴趣才会有良好的学习效果,才会使学生的逻辑思维能力不断发展提高。     

The training of teachers in special education

ABSTRACT

The aims and content of training in special education have been extended in recent years as a result of the practice of integrated education and also the recognition of a larger group of children with special educational needs. Provision in ordinary schools is being seen as the development of whole‐school policies for curricula and organization, including the development of systems of support within and sometimes, across schools. These developments have implications for the training of special education teachers and also for the pre‐service and in‐service education and training of all teachers and for the variety of strategies to be employed.     

The special needs of teachers of special needs children

More and more, special needs children are entering early childhood education programs. But the integration of special needs children into the regular classroom — and their acceptance by their nonhandicapped peers — continues to be a concern of both parents and teachers. Many of the proposed benefits of mainstreaming are based upon opportunities for interactions between special needs children and their nonhandicapped peers. What we know about enhancing the quality of these interactions has definite implications for teachers. After examining the research on social relations and social skills training programs for special needs children, we will discuss these implications.Cary A. Buzzelli is an assistant professor in the Department of Curriculum and Instruction at the University of Alabama at Birmingham in Birmingham, Alabama. Nancy File is a doctoral student in the Department of Child Development and Family Studies at Purdue University in West Lafayette, Indiana.     

The role of goal orientations for adolescent mathematics achievement

This study examines the association between personal goal orientations and mathematics achievement within the trichotomous goal framework. Participants comprised approximately 2000 seventh and eighth grade White, Hispanic, and Vietnamese students in a low-income urban school district in California. Regression analysis with classroom fixed effects minimized biases arising from non-random assignment of teachers and students to schools and classrooms. While all three achievement goal orientations were correlated with mathematics achievement, only a mastery goal orientation consistently predicted achievement when a full set of prior achievement and demographic controls were included. Performance-approach and performance-avoidance goal orientations did not predict achievement in the full model.     

An international perspective of early number sense: Identifying components predictive of difficulties in early mathematics achievement

Abstract

From preschool to high school, number sense is included as an important outcome in mathematics syllabi. It is a term associated with the development of concepts and skills in mathematics and as such appears frequently in the teaching literature. However number sense is a term yet to be operationally defined. The present study used a modified Delphi procedure to determine the level of agreement amongst six early mathematics experts from Britain, Europe and the United States, with respect to a variety of components of early number sense. The results of this study are discussed in relation to a similar Australasian study and the emerging literature on early number sense assessment. This study revealed some components of number sense worthy of further investigation in relation to early mathematical achievement but also confirmed a lack of consensus on what exactly constitutes early number sense.