Music, mathematics and Bach

In the earlier part of this article, an introduction to musical scales, counterpoint and harmony was given. In this part these themes are developed further with reference to Bach’s music and the emergence of the equally tempered scale.     

试论巴赫钢琴复调音乐

钢琴作品充满复调结构,复调音乐是每位钢琴学习者的必修课.复调大师巴赫的钢琴作品《巴赫初级钢琴曲集》和《巴赫创意曲集》是学习复调音乐的最佳教材,学习过程中不仅需要在音乐理论上掌握复调音乐的创作特点,还应着重训练大脑多层次思维能力、多声部听辨能力及手指控制能力,如均衡、力度、色彩、声音等的准确表现和音乐性质的统一.     

Constructivism,mathematics and mathematics education

Learning theories such as behaviourism, Piagetian theories and cognitive psychology, have been dominant influences in education this century. This article discusses and supports the recent claim that Constructivism is an alternative paradigm, that has rich and significant consequences for mathematics education. In the United States there is a growing body of published research that claims to demonstrate the distinct nature of the implications of this view. There are, however, many critics who maintain that this is not the case, and that the research is within the current paradigm of cognitive psychology. The nature and tone of the dispute certainly at times appears to describe a paradigm shift in the Kuhnian model. In an attempt to analyse the meaning of Constructivism as a learning theory, and its implications for mathematics education, the use of the term by the intuitionist philosophers of mathematics is compared and contrasted. In particular, it is proposed that Constructivism in learning theory does not bring with it the same ontological commitment as the Intuitionists' use of the term, and that it is in fact a relativist thesis. Some of the potential consequences for the teaching of mathematics of a relativist view of mathematical knowledge are discussed here.     

研究性数学、教育数学与数学教育

数学可分为研究性数学和教育性数学。研究性数学主要注重科学逻辑的序,而教育性数学则注重科学逻辑的序与认知心理的序之间的完美结合,后者即“教育数学”。教育数学是在研究性数学基础上的再创造、再提高,教育数学对数学教育改革具有深远的意义。     

Learning environment,self-efficacy for teaching mathematics,and beliefs about mathematics

Learning environment research has a long history of significant relationships between the learning environment and student outcomes. This study investigated relationships between the learning environments of mathematics courses in a teacher education program and two outcomes, mathematics teaching self-efficacy and beliefs about mathematics. These two outcomes have been repeatedly shown to influence the future teaching practices of preservice teachers but, to date, their relationships with learning environment have been investigated neither with preservice teachers nor at all in the United Arab Emirates or wider Gulf region. The learning environment was found to be significantly related to preservice teachers’ mathematics teaching self-efficacy and beliefs about mathematics. Learning environments perceived more favourably by preservice teachers were associated with higher self-efficacy for teaching mathematics, but also with more-traditional beliefs, making these findings important for higher education institutes and teacher educators.

     

生命系统·音乐·音乐教育

人之称其为人 ,即在于其有情欲 ,有理智。因此 ,异于一般动物的人的生命存在 ,本质上可划分为两大系统 :情感欲望系统和精神理性系统。此亦可视为人的两大生命需要。情感欲望方面的需要 ,主要表现为人对生物欲望或说物质欲望的满足的孜孜追求 ,它具有一定的动物性 ,但也不失为     

Positive biases in self-assessment of mathematics competence, achievement goals, and mathematics performance

The study examined how biases in self-evaluations of math competence relate to achievement goals and progress in math achievement. It was expected that performance goals would be related to overestimation and mastery goals to accurate self-assessments. A sample of French high-school students completed a questionnaire measuring their math achievement goals and their perceived competence in math. Students’ math grades for the three trimesters of the school year were collected from school records. Bias in self-evaluations was computed by comparing students’ rating on the ‘perceived competence in math’ scale with their actual math achievement as measured by their second trimester math grades. Students were classified into one of three groups (over-raters, accurate raters, or under-raters) depending on whether their self-perceptions of competence in math were higher than, similar to, or lower than their relative math achievement in their class. As expected, overrating of one's performance was related to performance goals. Furthermore, the over-raters were the only group who progressed in their math achievement from Trimester 2 to 3. No relation was found between mastery goals and accurate self-assessment.     

关于数学与数学教育——科学家关于数学的论述及其对我们的启示

在学习、理解科学家关于数学论述的基础上 ,进一步阐述了对数学与数学教育等问题的新认识     

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.     

Examining fourth-grade mathematics writing: features of organization,mathematics vocabulary,and mathematical representations

Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and use writing features to convey mathematics knowledge. We collected mathematics-writing samples from 155 4th-grade students in 2 states. Each student wrote about a computation word problem and fraction representations. We compared mathematics-writing samples to a norm-referenced measure of essay writing to examine similarities in how students use writing features such as introductions, conclusions, paragraphs, and transition words. We also analyzed the mathematics vocabulary terms that students incorporated within their writing and whether mathematics computation skills were related to the mathematics vocabulary students used in writing. Finally, we coded and described how students used mathematics representations in their writing. Findings indicate that students use organizational features of writing differently across the norm-referenced measure of essay writing and their mathematics writing. Students also use mathematics vocabulary and representations with different levels of success. Implications for assessment, practice, and intervention development are discussed.     

狗为何喜欢古典乐?

Are dogs as discerning as humans?Dogs become sweet-tempered and relaxed when they listen to classical music(古典乐) but put up a howl(嚎叫) when they listen to heavy metal(重金属摇滚乐), according to researchers.     

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.