Understanding and advancing graduate teaching assistants’ mathematical knowledge for teaching

Graduate student teaching assistants (GTAs) usually teach introductory level courses at the undergraduate level. Since GTAs constitute the majority of future mathematics faculty, their image of effective teaching and preparedness to lead instructional improvements will impact future directions in undergraduate mathematics curriculum and instruction. In this paper, we argue for the need to support GTAs in improving their mathematical meanings of foundational ideas and their ability to support productive student thinking. By investigating GTAs’ meanings for average rate of change, a key content area in precalculus and calculus, we found evidence that even mathematically sophisticated GTAs possess impoverished meanings of this key idea. We argue for the need, and highlight one approach, for supporting GTAs to improve their understanding of foundational mathematical ideas and how these ideas are learned.     

On students’ conceptions of arithmetic average: the case of inference from a fixed total

There is more to understanding the concept of mean than simply knowing and applying the add-them-up and divide algorithm. In the following, we discuss a component of understanding the mean – inference from a fixed total – that has been largely ignored by researchers studying students understanding of mean. We add this component to the list of types of reasoning needed to understand mean and discuss student responses to tasks designed to elicit this component of reasoning. These responses reveal that inference from a fixed total reasoning is rare even in advance high school students.     

Using digital stories to reduce misconceptions and mistakes about fractions: an action study

The aim of this study is to determine the mistakes and misconceptions about fractions of the fourth-grade students in a primary school and to eliminate these mistakes and misconceptions through digital stories. The study has been conducted with a total of 25 students in the fourth-grade of a private primary school in Turkey. An action research method based on qualitative research approach has been used in the study. In the preparation of activities related to digital stories, the mistakes and misconceptions that students have regarding fractions are taken into account. As a data collection tool, the Determination of Misconceptions Form consisting of 30 open ended questions about the fractions prepared by the researchers and the observation notes taken during the implementation process have been used. In addition, semi-structured interviews have been conducted to identify views of teachers and students about activities designed with digital stories. The implementation has been carried out for 5 weeks. Qualitative data analysis techniques have been used in analysing the data. As a result of the research, it has emerged that teaching implementations designed with digital stories have eliminated the mistakes and misconceptions that a large majority of students have about fractions. Most of the students who had a limited perception about the concept of fraction before implementation have fully perceived the definition of fractions after the activities designed with digital stories. Likewise, most of the students who incorrectly modelled the operations with fractions before the implementation, have been able to use the correct model for the operations with fractions after the-implementation fractions. When opinions about the activities designed with digital stories have been examined, it has been found that most students’ express positive opinions on digital story use in lessons and found digital stories fun, instructive and constructive.     

课堂提问在大学数学教学中的意义

课堂提问是一种有效的教学组织形式,它既是重要的教学手段,又是完美的教学艺术.这篇文章以高等代数的教学为例,阐述了大学数学教学中课堂提问的重要意义.希望对年轻的教师能有所启迪和帮助.     

基于经管类学生素质培养视阈探析经管数学基础教改

通过对经济管理类学生所需要的素质和经济管理数学基础所载的特征的分析和比较,得出经济管理数学基础是培养这些素质的最好课程之一,有其独特的和其他课程不可替代的作用．基于此,文章对经济管理数学基础的教学内容与教学方法提出了与素质要求相一致的改进方案．     

模型素养考查之数字实验图像试题的认识与思考*

对模型素养的考查与教学的基本要求是什么、高考中对模型素养的评价主要体现在哪些方面？着重从模型素养之数字实验(图像)试题的视角,对其分类及具体体现形式和上述问题进行了思考和梳理,并结合相关实际教学对学生出现的问题做了分析。     

Convenient Chemical Symbols to Illustrate Electronic Excited States

The problem of poor comprehension of electronic spectra by chemistry students in upper level undergraduate classes is addressed by consistent application of vector addition to both spin and angular momentum. Using the upgraded box‐and‐arrow diagrams, both atomic and molecular electronic states may be described without the use of advanced mathematics. Simple chemical symbols and formulas are suggested for molecular excited states that complement the existing physical/mathematical notation. Elements of a suitable classroom presentation are presented.     

Problematic topics in first-year mathematics: lecturer and student views

In this paper we report on the outcomes of two surveys carried out in higher education institutions of Ireland; one of students attending first-year undergraduate non-specialist mathematics modules and another of their lecturers. The surveys aimed to identify the topics that these students found difficult, whether they had most difficulty with the concepts or procedures involved in the topics, and the resources they used to overcome these difficulties. In this paper we focus on the mathematical concepts and procedures that students found most difficult. While there was agreement between students and lecturers on certain problematic topics, this was not uniform across all topics, and students rated their conceptual understanding higher than their ability to do questions, in contrast to lecturers’ opinions.     

化学师范生教育自传文本的数据挖掘与反思评价*

师范生具有大学生和准教师的双重身份,对于他们教育自传文本的研究无论对于教师教育改革还是对于教师自身发展都具有独特的意义。应用文本挖掘工具和师范生反思水平量表,对90份化学师范生的自传文本进行分析,发现他们成长过程中的关键他人、重要经历、学科认识转变,并对他们教育自传反思水平进行评价。