The role of scaling up research in designing for and evaluating robustness

One of the great strengths of Jim Kaput’s research program was his relentless drive towards scaling up his innovative approach to teaching the mathematics of change and variation. The SimCalc mission, “democratizing access to the mathematics of change,” was enacted by deliberate efforts to reach an increasing number of teachers and students each year. Further, Kaput asked: What can we learn from research at the next level of scale (e.g., beyond a few classrooms at a time) that we cannot learn from other sources? In this article, we develop an argument that scaling up research can contribute important new knowledge by focusing researchers’ attention on the robustness of an innovation when used by varied students, teachers, classrooms, schools, and regions. The concept of robustness requires additional discipline both in the design process and in the conduct of valid research. By examining a progression of three studies in the Scaling Up SimCalc program, we articulate how scaling up research can contribute to designing for and evaluating robustness.     

Learning to observe: using video to improve preservice mathematics teachers’ ability to notice

Video has assumed an increasingly prominent role in teacher education, particularly in the form of the viewing of videotaped class lessons by preservice teachers. Yet there is little research that confirms whether preservice teachers attend to the aspects of the video(s) that teacher educators anticipate or desire. This article explores this issue and reports on the impact of video viewing as a means to improve teachers’ ability to be observers of classroom practice. We utilized a pre- and post-test design to measure the quantity and type of classroom events that preservice mathematics teachers noticed before and after a teaching methods course where improving observation skills was an explicit goal. The results of the pre-assessment suggest that preservice teachers generally do not enter teaching methods courses with well-developed observation skills. The post-assessment indicates that the course led to significant increases in preservice teachers’ observation skills, particularly in teachers’ ability to notice features of the classroom environment, mathematical content of a lesson, and teacher and student communication during a lesson.

Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.

基于MATLAB的高等数学实验教学

针对高等数学教学现状,讨论了在高等数学教学中开设数学实验的必要性。同时简单地介绍了MATLAB软件,并举例说明利用其进行数学实验教学的优点和作用。     

动画呈现方式对小学四年级学生古诗学习的影响

在语文教学中,多媒体教学是否比传统教学更加有利于学生的学习?教育界对此存在不同看法。对60名小学四年级学生在不同教学条件下的古诗学习效果的实验研究发现:1.相对于文本呈现方式,动画呈现方式可以使低语文阅读能力组的学生更好地体会作者的思想感情;2.无论是高阅读能力组还是低阅读能力组,动画呈现方式都比文本呈现方式更有利于学生对古诗意境的理解,而且这种效应对低阅读能力的学生更为显著;3.不同呈现方式对古诗含义理解和写作方式把握的影响没有显著差异。这一结论为语文教学提供了有益的启示。     

实施凸显数学文化特征的小学数学教育

凸显数学文化特征是小学数学教育应担负的重要责任。应主要从还原数学概念的真实生命、绽放数学法则的严谨之美、彰显数学思想方法的深邃、洋溢数学价值的理性精神四个方面凸显数学的文化特征。     

浅谈数学教学对学生创新能力的培养

素质教育的核心目标 ,在于以课程教学为主渠道 ,培养学生的创新精神和创新能力。按照基础教育课程改革的基本要求 ,在数学教学过程中 ,充分落实学生的主体地位 ,构建和实施以自主学习和探究式学习为主的教学模式 ,对培养学生的创新思维和创新能力 ,夯实终身学习的基础具有重要意义     

试论数学语言的特点及功能

从语言的角度分析数学语言的特点及功能,论述了其在自身发展和其他自然科学的发展中的特殊作用,指出必须重视把数学教育当作一种语言教育来研究.     

用神经网络方法由蛋白质一级序列预测其二级结构含量

基于氨基酸组成和有偏自相关函数的特征参量 ,利用BP神经网络 ,提出了一种预测蛋白质二级结构中α螺旋和 β折叠含量的计算方法 .采用相互独立的非同源蛋白质数据库对该方法的准确性进行检验 ,对蛋白质二级结构α螺旋和 β折叠含量的预测的结果为 :自检验的平均绝对误差分别为 0 .0 70和 0 .0 6 8,相应的标准偏差分别为 0 .0 49和 0 .0 47;他检验的平均绝对误差分别为 0 .0 75和 0 .0 70 ,相应的标准偏差分别为 0 .0 5 0和 0 .0 49.与常用方法相比 ,利用此方法预测蛋白质二级结构含量可有效提高预测精度 .     

数学思想、数学活动与小学数学教学

将"基本(数学)思想"与"基本(数学)活动经验"明确纳入"数学课程目标"之中有一定的合理性。以小学数学教学为背景对此作进一步分析:我们不仅应当针对不同的教学对象对此作出更为具体的界定,从而切实防止简单移植的现象,而且也应很好地处理具体知识内容的学习与基本数学思想的学习以及过程与结果之间的关系,而不应将此绝对地割裂开来。