Opportunities to learn: Mathematics textbooks and students’ achievements

This study explores how textbooks function in education. It asked whether opportunities provided in math textbooks to engage in tasks demanding different levels of understanding correlate with students’ achievements on tasks demanding equivalent levels of understanding on a standardized exam. The textbooks evaluated were two 8^th grade mathematics textbooks used by students in the Arab community in Israel, showing that Textbook A makes more cognitive demands than Textbook B. The study correlated textbooks’ cognitive demand with the scores of all 8^th grade students in the Arab community who completed the national math test in 2015 and studied in schools using either Textbook A or B (N = 4040), while attending to mediating variables. The findings show that if a textbook provides the opportunity to engage in tasks demanding higher levels of understanding, students using this book will have higher scores. The study shows that gender and SES play an important role in how opportunities provided in textbooks interact with students’ scores. Many factors influence variations in mathematics achievements within and between nations. The findings illuminate textbooks’ ability to provide opportunities to learn mathematics. As a result, they raise new questions about how teachers use textbooks and about the role of textbooks in promoting access and equity in mathematics education. Although the work explored specific textbooks, its findings shed light on how learning opportunities relate to achievements more generally.     

数学教育的异化

数学能力被分为“‘学校式’的数学能力”和“创造性的数学能力”是数学教育长期背离正确方向所造成的。传统的数学教育只让学生去理解和记忆已完成的数学理论，而忽略了经验材料的数学组织化和数学理论的运用。数学教学应该是学生从事全面的数学活动的过程，数学教材应该是由系统的数学活动组成的体系。     

突出核心 重视“思想”

分析了大连市2013年中考数学试题特点以及学生作答存在的主要问题,指出初中数学教学应抓住教材重点,把握内容核心,重视过程教学,丰富学生数学活动经验,提高学生分析问题、解决问题能力。     

基于核心素养的小学数学教材资源整合探讨

新课改要求教师摒弃以教材为本的旧观念,树立以学生发展为本的新观念。整合教材资源,培养学生的数学核心素养,成了教师首先要解决的问题。本文从数学教材与信息技术整合、数学教材与游戏整合、从生活中挖掘数学教材资源三个方面,探讨基于核心素养的小学数学教材资源整合问题。     

Mainstream university pedagogy in feminist perspective

This article analyses university pedagogy by contrasting mainstream pedagogy and feminist pedagogical thought. The data consist of two textbooks, and we investigate what kinds of teaching, learning and knowledge the textbooks construct and what kinds of student and teacher positions they suggest. The inquiry shows that learning in the textbooks is seen as a strictly defined, hierarchical process and that ideal teaching stresses methods over content. The power of knowledge is not discussed, nor are gender, sexuality and other differences. Academics are seen as professional teachers who master teaching methods, and students are framed as customers. An assumed human sameness, marketisation of education, emphasis on vocational benefit and ‘pathos of the new’ were found to be themes guiding mainstream pedagogy. We suggest that feminist pedagogy can offer an alternative approach, one enabling a critical analysis of the power of knowledge and an awareness of differences among students.     

Optimizing Early Mathematics Experiences for Children from Low-Income Families: A Study on Opportunity to Learn Mathematics

Both the National Council of Teachers of Mathematics and the National Association for the Education of Young Children recognize that well-designed opportunity to learn mathematics can help improve mathematics achievement of students from low-income families and from minority backgrounds. Using data from a nationally representative sample, the Early Childhood Longitudinal Study-Kindergarten cohort, this study empirically examined a subset of children from low-income families to determine whether African American and Caucasian students have differential opportunity to learn mathematics and the extent to which opportunities to learn predict gains in mathematics achievement at kindergarten. Results indicated African American kindergartners have differential opportunity to learn mathematics than their Caucasian peers from low-income families. African American students were found to have received, on average, more reported instructional time spent on mathematics, higher use of math manipulatives, worksheets, textbooks and chalkboard work than their Caucasian peers. Moreover, greater opportunity to learn mathematics predicted higher mathematics achievement for both African American and Caucasian students from low-income families, specifically, opportunity to learn skills such as telling time, using measurement tools accurately, estimating quantities, and knowing the value of coins and cash.     

数字时代中的数学教材研究与开发及使用——第三届国际数学教材研究和发展会议综述

数学教材往往是数学课程发展、研究过程及整个数学教育史中最为可靠和重要的历史见证,对于"定义"作为学校科目的数学、为学生创设学习机会、为教师提供工作及专业发展上的支持,数学教材都发挥着举足轻重的作用。数学教材中的内容、开发及其使用已然成为数学教育研究的重要主题之一。通过对第三届国际数学教材研究和发展会议(ICMT3)的大会报告及主题研讨的介绍,对数字时代下的数学教材在设计、内容、使用及评价等提出新的思考,也进一步揭示出对理解教材在数学的教与学的作用存在更大更高的需求。     

法国中学数学教材的特色及启示

法国中学数学教材具有鲜明的特色.如:以现代数学内容及方法为统领;注意与多学科联系,突出数学的文化价值和应用意识;以实验、探究等活动方式展示“活生生的数学”,等.这对我国中学数学教材编写具有一定的启示作用:中学几何内容应融入现代数学内容及其方法;应注意数学与其他学科的联系;妥善处理信息技术与数学教育的关系.     

A comparison of Korean and American secondary school textbooks: the case of quadratic equations

This study compares quadratic equations sections of Korean and American textbooks. The number of topics, contents and mathematics items were analyzed. The results show Korean students learn some topics relatively earlier than American students. American textbooks include more problems requiring explanations and various representations and problems requiring higher level cognitive demand. This result could indicate that textbooks might not be the reason for American and Korean students’ performances in international comparative studies. More studies analyzing other standards based textbooks and teaching practice might be needed to have further understanding of mathematics education in two countries.     

History of Mathematics in Korean Mathematics Textbooks: Implication for Using Ethnomathematics in Culturally Diverse School

From a multicultural perspective, this research investigated to what extent Korean mathematics textbooks use history of mathematics. The results show even though educational use of history presented in Korean mathematics textbooks may provide a rich outlook, it does not encourage a fundamental change in the educational practice of school mathematics that has traditionally been entrenched in the Eurocentric narrative of mathematics. This suggests that the mathematics textbooks were not organized effectively to promote students’ understanding of diversity. Based on the results, we discuss the implications for the development of mathematics textbook from multicultural perspectives.     

数学文化在小学数学新教材中的实践研究——以西师版为例

数学教育本质上就是数学文化的教育.基础教育课程改革以来,各版本小学数学新教材已经将数学文化作为一个新的教学要求渗透于其中,这是《标准》的要求,也是教学的需求.国内已有多套教材在这方面做了有益的探索,以西师版小学数学教材为例说明:小学数学教材中数学文化的题材选取要体现多样化,数学文化的呈现形式可以图文并茂,数学文化有必要并且能够从低年级多维度渗透到小学数学教材中.     

试论小学数学几何图形概念教学的策略

在小学数学几何图形教学中,几何图形作为小学数学教材中重要的学习内容之一,对学生来说是有一定的学习难度的。教师要在实际教学中,针对小学生的个性化发展以及性格特征,合理地制定教学方案,并促使学生掌握正确的学习方式,使学生对几何图形有所认知。因此,本文对试论小学数学几何图形概念教学的策略进行分析研究,以期能够提升教师的教学质量,帮助小学生掌握更多的几何图形知识。     

Middle and high school math teaching for students with mild intellectual disability

The author briefly reviews studies on the math teaching of secondary school students with mild intellectual disabilities. Then, the author demonstrates ways to teach secondary-level mathematics to students with mild intellectual disabilities. In this article, readers will learn about how to use manipulatives, diagrams, and gestures to support students' thinking. Readers will also learn how to make connections between new and challenging math content to students' experiences inside and outside of school to support them as they think through mathematics.     

小学数学课堂合作学习的有效性策略研究

合作学习能有效锻炼学生综合能力,在数学课堂上抓住合作学习契机可以给学生营造良好的学习氛围,激发学生的积极性、主动性,有助于培养数学学习的兴趣。为提高合作学习质量,应对当前教学中的不足展开分析,做出有效的改进。本文首先分析当前课上小组合作学习中的问题,进而提出三点教学策略,以打造高效数学课堂。     

Understanding mathematics textbooks through reader-oriented theory

Textbooks have the potential to be powerful tools to help students develop an understanding of mathematics. However, many students are unable to use their textbooks effectively as learning tools. This paper presents a framework that can be used to analyze factors that impact the ways students read textbooks. It adapts ideas from reader-oriented theory and applies them to the domain of mathematics textbooks. In reader-oriented theory, the reader is viewed as actively constructing meaning from a text through the reading process; this endeavor is shaped and constrained by the intentions of the author, the beliefs of the reader, and the qualities the text requires the reader to possess. This paper also discusses how reading mathematics textbooks is further constrained by the authority and closed structure of these textbooks. After describing the framework, the paper discusses recommendations for future avenues of research and pedagogy, highlighting the importance of teachers' roles in mediating their students' use of textbooks.     

浅论数学教师应具备的素养

从广博精深的专业知识、堪称一绝的数学艺术及树立正确的现代数学观念三个方面论述了新时期面临新课改的数学教师应具备怎样的教学素质，才能拓展学生的视野，使学生学习方法更灵活、兴趣更浓厚、目标更明确，才能顺应时代的要求把学生培养成新世纪新型的中学生。     

发掘数学教材的评价功能——对美国加州小学数学教材的分析与启示

对比美国加州小学数学教材可以发现,中国小学数学教材较为忽视教材对学生的评价载体功能,评价方式单一,还没有形成完整的评价结构,教材缺乏学生自评与互评的工具作用.而美国的小学数学教材却有着评价内容较为丰富,评价结构相对完整,评价方式多样,评价标准明确,评价目的鲜明等诸多特点.5点启示是:应树立评价意识;构建中国教材中的评价结构;创新评价方式;重视《数学课程标准》的指导作用;正确认识教材中评价的功能.     

立足教材 突出核心 引导教学——大连市2012年中考数学试题特点及教学启示

通过分析大连市2012年中考数学试题的特点,说明初中数学教学应关注教材、用好教材,把握核心,重视思想。     

Establishing an Explanatory Model for Mathematics Identity

This article empirically tests a previously developed theoretical framework for mathematics identity based on students’ beliefs. The study employs data from more than 9,000 college calculus students across the United States to build a robust structural equation model. While it is generally thought that students’ beliefs about their own competence in mathematics directly impact their identity as a “math person,” findings indicate that students’ self‐perceptions related to competence and performance have an indirect effect on their mathematics identity, primarily by association with students’ interest and external recognition in mathematics. Thus, the model indicates that students’ competence and performance beliefs are not sufficient for their mathematics identity development, and it highlights the roles of interest and recognition.     

提高小学数学课堂教学趣味化的策略研究

随着课程改革不断深入,趣味化教学走进了小学数学课堂。教师给学生营造轻松愉快的学习氛围,激发学生数学学习兴趣,鼓励学生对教师提出的数学问题进行思考,鼓励学生之间相互探讨,培养学生数学逻辑思维能力,提高学生解题能力,进而提高课堂教学有效性,提高教学质量和效率。鉴于此,本文将对如何提高小学数学课堂趣味化教学展开论述,并提出行之有效的策略,以供参考。