Advanced mathematics communication beyond modality of sight

This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access to visual fields in an advanced mathematics course does not obstruct a blind student's ability to visualize, but transforms it. The goal of this study is not to compare the visually impaired student with non-visually impaired students to address the ‘differences’ in understanding; instead, I discuss the challenges that a blind student, named Anthony, has encountered and the ways that we tackled those problems. I also demonstrate how the proper and precisely crafted tactile materials empowered Anthony to learn mathematical functions.     

An incentivized early remediation program in Calculus I

Strong prerequisite skills are essential to student success in the calculus sequence; however, many students arrive in Calculus I with weaknesses that are difficult for them to overcome. In this paper, we describe an approach to early incentivized remediation of prerequisite material in a Calculus I course. We present data that supports the idea that a lack of prerequisite knowledge is a significant hurdle for students, but also that participation in the remediation program is correlated with student success. In addition, the program allows for the very early identification of students at high risk of failing. The program is easy to implement, and it would be adaptable to a variety of other courses for which prerequisite knowledge is essential for success including science courses, engineering courses and other mathematics courses.     

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。     

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.     

全新的美国高中生评价体系及其在化学实验评价中的应用

作为一种全新的学生评价体系，A New Model其实质是一份持续更新的全息电子档案，内含学生在高中期间持续追踪记录、评估的8项能力。化学是一门以实验为基础的自然科学，对学生实验的评价直接影响着其实践能力和创新意识的培养，然而当前我国中学阶段对化学实验的评价方式较为单一，最终成绩往往以考试分数来呈现，这严重阻碍着学生的个性化发展。本研究在借鉴A New Model的基础上改进化学实验评价体系，以期对学生实验的评价更加综合、科学、规范。     

The Gibbs' phenomenon from a signal processing point of view

Recently, Fay and Kloppers gave two proofs to show that the well-known Gibbs' phenomenon for Fourier series at a jump discontinuity depends only on the size of the jump and is a multiple of the integral 1/π ∫₀ ^π (sin x / x) dx. We give another proof, based upon low-pass filtering of the Fourier transform, that uses the observation that a truncated Fourier series for a function ? (x) is ‘very nearly’ equal to the convolution integral 1/π ∫ _-∞ ^+∞ ? (x - t)(sin nt / t) dt.     

Student achievement effects of technology-supported remediation of understanding of fractions

Students have difficulty learning fractions, and problems in understanding fractions persist into adulthood, with moderate to severe consequences for everyday and occupational decision-making. Remediation of student misconceptions is hampered by deficiencies in teachers’ knowledge of the discipline and pedagogical content knowledge. We theorized that a technology resource could provide the sequencing and scaffolding that teachers might have difficulty providing. Five sets of learning objects, called CLIPS (Critical Learning Instructional Paths Supports), were developed to provide remediation on fraction concepts. In this article, we describe one stage in a research program to develop, implement and evaluate CLIPS. Two studies were conducted. In Study 1, 14 grade 7–10 classrooms were randomly assigned, within schools, to early and late treatment conditions. A pre-post, delayed treatment design found that CLIPS had no effect on achievement for the Early Treatment group due to unforeseen implementation problems. These hardware and software issues were mitigated in the late treatment in which CLIPS contributed to student achievement (Cohen's d = 0.30). Study 2 was a pre-post, single group replication involving 18 grade 7 classrooms. The independent variable was the number of CLIPS completed. Completion of all five CLIPS contributed to higher student achievement: Cohen's d = 0.53, compared to students who completed none (d = 0.00) or 1–4 CLIPS (d = 0.02). The two studies indicate that a research-based set of learning objects is effective when the full program is implemented. Incomplete sequences deprive students of instruction in one or more constructs linked to other key ideas in the conceptual map and reduce the amount of practice required to remediate student misconceptions.     

多功能恒温保湿芽菜机的研制与实践

通过多功能恒温保湿芽菜机的研制与实践,强化基本技能训练、专业技能训练和创新技能训练,使学生有求新求变的创新思维及对所学知识融会贯通、举一反三的能力,对此进行了有益的尝试,取得了好的实验教学效果.     

The role of symbols in mathematical communication: the case of the limit notation

Symbols play crucial roles in advanced mathematical thinking by providing flexibility and reducing cognitive load but they often have a dual nature since they can signify both processes and objects of mathematics. The limit notation reflects such duality and presents challenges for students. This study uses a discursive approach to explore how one instructor and his students think about the limit notation. The findings indicate that the instructor flexibly differentiated between the process and product aspects of limit when using the limit notation. Yet, the distinction remained implicit for the students, who mainly realised limit as a process when using the limit notation. The results of the study suggest that it is important for teachers to unpack the meanings inherent in symbols to enhance mathematical communication in the classrooms.