Mathematics turned inside out: the intensive faculty versus the extensive faculty

Research universities in the United States have larger mathematics faculties outside their mathematics departments than inside. Members of this “extensive” faculty conduct most mathematics research, their interests are the most heavily published areas of mathematics, and they teach this mathematics in upper division courses independent of mathematics departments. The existence of this de facto faculty challenges the pertinence of institutional and national policies for higher education in mathematics, and of philosophical and sociological studies of mathematics that are limited to mathematics departments alone.     

初中数优生、数困生的数学学习投入研究

通过对208名初中数优生、数困生的问卷调查,考察两类初中生数学学习投入的特点及其影响因素。结果表明：（1）数困生的数学学习投入显著低于数优生;数优生与数困生的数学学习投入有不同的变化趋势：数优生的学习投入一直维持在较高水平,而数困生的学习投入随年级的升高在逐渐下降;数困生的情感投入水平比认知投入、行为投入更低;数学学习投入的性别差异不显著。（2）社会支持、数学观和数学自我效能感对数优生、数困生的数学学习投入均具有显著影响;社会支持对数学学习投入既具有直接影响,同时也具有间接影响;数学观和数学自我效能感在社会支持和数学学习投入之间起着中介作用。     

数学方法论对提高数学课堂教学效率的指导作用——从几个低效教学实例引发的思考

运用数学方法论指导中小学数学课堂教学是提高教学效率的一个有效途径,恰当运用数学方法论有利于加深学生对知识的理解和记忆,有利于发展学生的数学能力特别是创新能力和应用数学的能力,有利于节省讲授时间,有利于提高学生探究问题的效率。     

中学生数学焦虑的调查与分析

数学焦虑作为一种消极的数学学习体验已成为数学教育中的一个热点问题.对数学焦虑与数学成绩、数学兴趣、自我效能、性别差异和年级差异的关系进行调查,结果发现:数学成绩与数学焦虑显著相关;数学兴趣、自我效能均与数学焦虑呈显著负相关;男、女生在数学焦虑上存在显著差异,女生焦虑水平比男生高;中学各个年级的数学焦虑水平没有显著差异,初三学生的焦虑水平在中学阶段是最高的.     

Mathematics for teaching: A form of applied mathematics

In this article we elaborate a conceptualisation of mathematics for teaching as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design and implementation of a special kind of mathematics tasks whose use in mathematics teacher education can support the development of knowledge of mathematics for teaching. Also, we discuss broader implications of the article for mathematics teacher education, including implications for mathematics teacher educators' knowledge for promoting mathematics for teaching.     

美国《中学数学教与学》教材的特点及其对中国数学教师教育的启示

美国《中学数学教与学》是初中年级数学教师教育"数学教学法"课程的教材,其特点表现为:单元主题以数学教学理论为线索呈现,单元内容以具体数学知识为载体展开并且以参与式活动的形式组织教学活动.该教材对我国的数学教师教育有如下启示:数学教师教育课程应以数学知识为载体学习数学教育理论;数学教师教育教材应突出教学方式的示范性,体现做中学,在数学教学活动中学习数学教学方法;数学教师教育应注重教师学科专业素质的提升.     

“Doing the Math”: Maternal Beliefs About Early Mathematics Versus Language Learning

Research Findings: Little is known about how parents approach preschoolers' mathematics learning and how this aligns with early mathematics education research and policy. This study examined these questions by contrasting parents' approaches to early mathematics and language and by exploring key themes in parents' talk about mathematics learning and education. Consistent with current research and policy, parents reported helping preschoolers learn mathematics and attempting to connect this learning to children's interests and everyday experiences. However, parents admitted to lacking goals for and knowledge about early mathematics. In addition, compared to language, parents reported that mathematics was taught less often at home, should be emphasized less in preschools, was less interesting to preschoolers, required more direct instruction, and was less of a personal interest and strength. Practice or Policy: Parent interventions could capitalize on parents' beliefs and practices by providing parents with concrete examples of what mathematics preschoolers learn through daily activities, how to maximize children's mathematics interests, and what the similarities are between early mathematics and language. These efforts will also need to help parents overcome their mathematics anxieties and show parents why early mathematics education is important. Similar strategies could be used to help early childhood teachers improve their mathematics practice.     

免费师范生数学专业素质的调查研究

数学知识、数学能力和数学情意是影响数学免费师范生数学专业素质的主要因素.数学免费师范生的数学情意素质具备程度较高,数学能力素质具备程度较低;数学专业素质在性别和年级之间存在差异;数学专业素质与数学知识、数学能力和数学情意均存在显著的正相关;数学知识、数学能力和数学情意对数学免费师范生的数学专业素质的形成和发展有不同程度的影响。     

我国西部少数民族地区数学教育的理性思考

分析当前数学教育的国际背景,结合我国西部少数民族地区数学教育的现状,提出了有针对性的民族地区数学教育的理性思考：一是改革教学方法,实现真正意义上的素质教育;二是注重用数学思想方法考察和处理问题的能力;三是充分发挥信息技术的作用和影响,使之融入数学课程和教学中;四是客观地看待当前进行的数学课程改革;五是理性地分析数学教育的改革与发展。     

Perceived autonomy support and autonomous motivation toward mathematics activities in educational and out-of-school contexts is related to mathematics homework behavior and attainment

We adopted a trans-contextual model of motivation to examine the processes by which school students' perceived autonomy support (defined as students' perceptions that their teachers' support their autonomous or self-determined motivation) and autonomous forms of motivation (defined as motivation to act out of a sense of choice, ownership, and personal agency) toward mathematics activities in an educational context predict autonomous motivation and intentions toward mathematics homework, and actual mathematics homework behavior and attainment, as measured by homework grades, in an out-of-school context. A three-wave prospective study design was adopted. High-school students (N = 216) completed self-report measures of perceived autonomy support and autonomous forms of motivation toward mathematics activities in school in the first wave of data collection. One-week later, participants completed measures of autonomous forms of motivation, attitudes, subjective norms, perceived behavioral control, and intentions with respect to mathematics homework outside school. Students' self-reported homework behavior and homework grades from students' class teachers were collected 5-weeks later. A structural equation model supported model hypotheses. Perceived autonomy support and autonomous forms of motivation toward mathematics activities in school were related to autonomous forms of motivation toward mathematics homework outside of school. Autonomous forms of motivation toward mathematics homework predicted intentions to do mathematics homework mediated by attitudes, subjective norms and perceived behavioral control. Intentions predicted self-reported mathematics homework behavior and mathematics homework grades. Perceived autonomy support and autonomous forms of motivation toward mathematics in school had statistically significant indirect effects on mathematics homework intentions mediated by the motivational sequence of the model. Results provide preliminary support for the model and evidence that autonomous motivation toward mathematics activities in the classroom is linked with autonomous motivation, intention, behavior and actual attainment in mathematics homework outside of school.     

Computer Programming

Summary

Computers can be powerful aids to mathematics teaching and learning. Changes brought about by the availability of these tools and the demands of an increasingly technological society impact curricular content and pedagogy in mathematics education as well as the very nature of mathematical thinking and understanding. This article presents ways in which technology is changing mathematics education, guidelines for appropriate technology use in the mathematics classroom, the impact of computers on mathematics learning, common uses of computers in mathematics education, and issues and concerns related to technology use in mathematics.     

数学教育:在哲学思想牵引下自由呼吸简

当下数学教育最显性的问题是教师“数学观”、“数学教育观”的遮蔽、遗忘或缺席。作为教育主导者,教师必须自觉反思、追问数学本体和数学教育的价值,即“数学是什么”和“数学教育为了什么”,并在好的“数学观”和“数学教育观”的牵引下去捕捉数学文本中的“哲学基因”和数学教学的“哲学气质”!     

新课程观下数学概念教学的层次分析

学生学习数学概念要经历操作活动,理解过程,形成数学对象,最后建立数学概念的综合心理图式。初中学生正处于思维发展的关键期,教师在教学中应注意树立建构主义教学观并精心设计学习活动;体现数学知识形成中的数学思想方法;创设学生主动建构数学对象的课堂教学氛围;重视数学概念学习中的错误分析,加强"反思教学"。     

初中生数学逆商的调查与分析——基于数学考试成绩和数学考试焦虑维度

基于数学考试成绩和数学考试焦虑的维度探讨影响数学逆商的因素有利于揭示初中生数学学习过程中的真实状态,探寻大面积提高学生数学学习水平的方略.采用自编的数学逆商调查量表、数学考试焦虑量表以及学生期中数学考试成绩等对初中生进行调查.发现:初中生的数学逆商和数学考试成绩呈显著正相关(P<0.01),数学考试成绩对数学逆商具有显著影响作用.初中生的数学逆商和数学考试焦虑呈显著负相关(P<0.01),数学考试焦虑的缓解有利于数学逆商的提升.     

An investigation of mathematics anxiety among sixth through eighth grade students in Turkey

The purpose of the present study is to investigate mathematics anxiety among 220 sixth through eighth grade Turkish students in terms of mathematics achievement levels, perceived enjoyment of the mathematics teaching method, perceived enjoyment of mathematics, and perceived help with mathematics from parents. The Mathematics Anxiety Scale for Primary School Students (Bindak, 2005) was used to assess the levels of mathematics anxiety. A 3 × 2 factorial analysis of variance results showed that there was not a significant interaction effect or main effect of gender; however, there was a significant main effect of grade level. Standard multiple regression analyses show that independent variables accounted for 63% to 70% of variability in the dependent variable. The results also indicate that not only the perceived enjoyment of mathematics, but also the enjoyment of the mathematics teaching method and help with mathematics from parents had a significant effect on mathematics anxiety.     

THE ROLE OF TEACHER CHARACTERISTICS AND PRACTICES ON UPPER SECONDARY SCHOOL STUDENTS�� MATHEMATICS SELF-EFFICACY IN NYANZA PROVINCE OF KENYA: A MULTILEVEL ANALYSIS

The study identified two dimensions of teacher self-efficacy and practices and five dimensions of students’ mathematics self-efficacy and sought to determine the extent to which teacher characteristics and practices can enhance secondary school students’ self-efficacy. Data were collected from 13,173 students in 193 teachers’ classrooms from 141 schools in the 10 districts of Lake Victoria Region of Kenya. Two-level hierarchical linear model revealed that teachers’ frequent use of mathematics homework, their level of interest and enjoyment of mathematics, as well as their ability and competence in teaching mathematics were found to play a key role in promoting students’ mathematics self-efficacy. Teachers’ ability and competence in teaching were also found to be effective in narrowing the gender gap in students’ self-confidence and competence in mathematics. The study recommends that teacher training colleges emphasize such teacher practices and values in order to enhance students’ mathematics self-efficacy, reduce their level of anxiety and fear of mathematics, and consequently, enhance their achievement in mathematics. Professional development opportunities should also be made available to in-service teachers to continually update their knowledge and skills and develop new strategies for teacher effectiveness.     

数学教育改革中的几个问题

课程、教师、学生作为数学教育的核心要素,反映到数学教育改革中,既是一项复杂的社会现象,又是一项复杂的系统工程．认为数学教育研究和改革应落实学术规范与行为规范;数学课程建设应突出数学化的基础知识和基本技能,加强数学能力和数学理性精神的培养; 数学教学过程应促使学生对数学问题或实际问题产生质疑、兴趣和好奇心．改革的关键是:既要解决好教师的数学修养,又要发挥教师在数学教学过程中的教学艺术创造性．     

An Experiment with the Otis Group Intelligence Scale in the Needham,Massachusetts, High School

ABSTRACT

This study used Early Childhood Longitudinal Study–Kindergarten Cohort data to examine influences of the home and classroom learning environments on kindergarten mathematics achievement of Black, Latino, and White children. Regardless of race/ethnicity, children who started kindergarten proficient in mathematics earned spring scores about 7–8 points higher. There was significant variability in the home and classroom learning environments of Black, Latino, and White children and associations with these children's mathematics scores. Nevertheless, reading at home was a significant predictor for spring mathematics scores for all groups. If children started kindergarten proficient in mathematics, the Latino-White mathematics gap, after controlling for home and classroom factors and other covariates, was no longer significant. However, the Black–White mathematics gap remained significant. If children did not start kindergarten proficient in mathematics, both the Latino–White and Black–White mathematics gaps remained significant.     

Deweyan Democratic Agency and School Math: Beyond Constructivism and Critique

In this article, Kurt Stemhagen reconstructs mathematics education in light of Dewey's democratic theory and his ideas about mathematics and mathematics education. The resulting democratic philosophy and pedagogy of mathematics education emphasizes agency and the connections between mathematics and students' social experiences. Stemhagen considers questions about the disconnect between constructivist reformers and critical mathematics educators, and he positions Dewey's ideas as a way to draw on the best of both to create an active and more democratic school math experience.     

重建高师数学教学论课程体系的基本构想

重建数学教学论课程体系是高师数学教育适应时代发展、应对改革挑战的客观需要,我们必须以高度的历史责任感从事建构工作。依据“成功之树”模式,数学教学论课程体系的建构围绕树根——数学教学信念、树干——数学教学理论、树枝——数学课堂教学、树叶——数学教学行为4个维度进行,以切实有效地帮助师范大学数学教育专业学生奠基从事数学教学工作的基本素养。