Teaching Mathematics with a New Curriculum: Changes to Classroom Organization and Interactions

This report describes a high school mathematics teacher's decisions about classroom organization and interactions during his first two years using a new curriculum intended to support teachers' development of student-centered, contributive classroom discourse. In year one, the teacher conducted class and interacted with students primarily in small groups. In year two, he conducted more whole-class instruction. In both years, teacher-student interactions contained univocal and contributive discourse, but in year two the teacher sustained contributive discourse with students for longer periods. The teacher facilitated the most significant changes to classroom discourse in the instructional format with which he had the greatest experience (whole-class instruction). Over the period of this study, two key factors appeared to affect the teacher's decisions about classroom organization and interactions: his perception of students' expectations about mathematics classroom roles and activity, and his own discomfort associated with using a new curriculum. These areas are important candidates for future research about teachers' use of innovative mathematics curricula.     

Diversifying the Curriculum in a Mathematics Classroom Streamed for High-Ability Learners: A Necessity Unassumed

Gifted learners are considerably more diverse than they are generally believed to be ( Matthews & Keating, 1995 ). Consequently, curricula must provide a wide range of learning opportunities, not simply a lock-step program at an accelerated pace. In the present study, the authors developed an experimental functions curriculum in which everyone learned a core set of concepts, then explored different kinds of functions independently using computer graphing technology. This was tested against a more typical, text-based program. Two groups of high-ability eighth-grade boys participated. Experimental students scored higher on a posttest than control students and showed much more diversity in their answers.     

Classroom Interactions Around Problem Contexts and Task Authenticity in Middle School Mathematics

It has been theorized that contextual tasks support student engagement and sense making. Yet, contradictory ideas exist about the role of these tasks in lessons, and further research is needed to explore how classroom interactions can help achieve their intended purposes. Through video observation of lessons in three eighth-grade classrooms using a problem-based curriculum, I investigated how teachers and students interact around problem contexts in written tasks. I found that they discussed contexts in multiple ways, falling into five general categories: referencing, positioning, elaborating, clarifying, and meta-level commentary. Using this framework, I considered how interactions around contexts related to the authenticity of tasks as written and enacted (Palm, 2006). In several lessons, these interactions led to higher authenticity as enacted than as written. These results offer a framework for interpreting context-related classroom interactions and suggest implications for instruction and research on the role contexts might play in mathematics lessons.     

新课标体系下高中数学对大学工科数学教学产生的问题分析及对策探索

大学工科数学的部分基础内容下移于高中数学,高中数学中原有的基础内容又有所删减,大学工科数学的教材内容并没有因此而调整.所以,新课标体系下的高中数学教学对大学工科数学教学产生了深刻的影响.本文分析了大学工科数学教学面临的问题,在此基础上,结合作者多年的教学实践,探索性的提出了解决问题的对策.     

结合专业特色的理工科数学课程教学探讨

本文以湖南师范大学物理学专业数学物理方程的教学实践为基础,指出了目前理工科数学课程教学中存在的主要问题,探讨了高等院校数学教学与专业特色相结合的教学方法,并从教学内容、师资要求、教学方法和考核方式等方面提出某些具体改革措施,在教学实践中取得了初步成效．     

如何提高高等数学课堂教学的质量

数学的课堂教学过程是在教师的传授和指导下进行学习、掌握数学知识、技能、思想、方法的一种认识过程.影响数学课堂教学质量的因素是多方面的,本文仅就提高高等数学课堂教学质量谈几点个人的认识.     

离散数学的翻转课堂教学法研究

离散数学是计算机专业的重要的基础课程.但是离散数学课程抽象难懂、教学模式单一、理论实际结合能力差,从而影响了这一课程的教学效果.为了提升离散数学的教学效果,面向学生翻转课堂的教学模式被引入.翻转课堂通过视频、示例或者项目、以及拓展等方式充分发挥学生为中心,教师辅助的教学理念,提升学生学习的主动性,提升离散数学的教学效果,为后续计算机专业课程奠定良好的基础.     

On the Relationship between Curriculum,Teaching and Assessment of Mathematics

In this paper, a discussion is given of the aims and objectives in teaching mathematics to undergraduates in relation to the development of certain student abilities and skills. Consideration is given to the different methods of assessment which test the acquisition of such skills and abilities.     

论高中数学新课标对大学数学教学内容的影响

随着高中数学新课标的实施,原有的教学内容、教学理念等都发生了很大的变化,但是随之而来的与大学数学教学内容衔接等问题也日益突现,直接对大学数学教学产生一定的影响.因此,大学数学的教材应当适当调整内容,避免出现重合或脱节的现象;同时,教师也应该更新理念,把握好新旧教材之间的差异,采取相应的衔接措施.     

新形势下高等数学分级教学模式的探索

突破以前按照不同专业分层次教学的模式,根据学生不同的学习目的,采用一种新的分级教学模式,针对相同专业学生不同的学习要求,给予不同层次的培养.通过对教育观念的新认识和培养目标的再确定,在高等数学的课程体系,课程内容,教学方法,教学手段等方面进行改革和调整,因材施教,使各层次的学生真正受益,提高整体教学质量,也使基础课教育更有针对性.     

Collaborative Curriculum Investigation as a Vehicle for Teacher Enhancement and Mathematics Curriculum Reform

The Missouri Middle Mathematics (M³) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and field-testing of material facilitates awareness and exploration of alternative instructional and assessment strategies and informed decision making. Early indicators of the model's success are reflected in participants’ enthusiasm and professional growth. Project activities stimulate discussions of critical topics including questioning appropriateness of various teaching practices, research about teaching and learning, tracking policies, appropriate assessment models for gauging student learning and the importance of calculators and manipulatives as teaching and learning tools. These discussions transcend curriculum materials being reviewed and serve as a powerful vehicle for professional growth and development for individual teachers and districts.     

高等数学教学的新问题及对策

随着普通高校由过去的精英教育向大众教育的转化．致使同一学校甚至同一专业学生的数学基础相差较大．本文分析了普通高校的高等数学教学现状。提出了高等数学课分层次教学方法．     

The Role of Interactions Between Student and Classroom Context in Developing Adaptive Self‐Efficacy in One Sixth‐Grade Mathematics Classroom

Research and theory suggest several instructional practices that could enhance student self‐efficacy. However, little is known about the ways these instructional practices interact with individual students to create opportunities or challenges for developing adaptive self‐efficacy. In this study, we focused on two sources of efficacy, mastery experiences, and social persuasion, and examined how these sources were structured for three students with different levels of mathematics achievement and self‐efficacy within a sixth‐grade mathematics classroom. Analyses within each case showed that each student experienced success and received social persuasion differently. On the other hand, analyses across the cases suggest that not only the amount but also the form (i.e., with and without assistance) of successful experiences and the type of performances (e.g., stating definitions, explaining solution procedures, sharing problem‐solving strategies, and making comments on others' ideas) through which the student experienced mastery may have played important role in developing self‐efficacy. Consistently, the amount and form of teacher feedback was different for each focal student. Examining these differences provide insight into each student's self‐efficacy assessed over the course of the study as well as the kind of support each student needed to develop adaptive self‐efficacy.     

The Effects of a Mathematics Infusion Curriculum on Middle School Student Mathematics Achievement

Increasing mathematical competencies of American students has been a focus for educators, researchers, and policy makers alike. One purported approach to increase student learning is through connecting mathematics and science curricula. Yet there is a lack of research examining the impact of making these connections. The Mathematics Infusion into Science Project, funded by the National Science Foundation, developed a middle school mathematics‐infused science curriculum. Twenty teachers utilized this curriculum with over 1,200 students. The current research evaluated the effects of this curriculum on students' mathematics learning and compared effects to students who did not receive the curriculum. Students who were taught the infusion curriculum showed a significant increase in mathematical content scores when compared with the control students.