Multipurpose Professional Growth Sequence: The catwalk problem as a paradigmatic example

An important concern in mathematics teacher education is how to create learning opportunities for prospective and practicing teachers that make a difference in their professional growth as educators. The first purpose of this article is to describe one way of working with prospective and practicing teachers in a graduate mathematics education course that holds promise for positively influencing the way teachers think about mathematics, about student learning, and about mathematics teaching. Specifically, I use the “catwalk” task as an example of how a single problem can serve as the basis for a coherent sequence of professional learning experiences. A second purpose of this article is to provide background information that contextualizes the subsequent two articles, each of which details the positive influence of the catwalk task sequence on the authors’ professional growth.     

Using TODIM to evaluate green supply chain practices under uncertainty

This study approaches the problem of exploring the importance and performance levels in green supply chain practices (GSCP) under conditions of uncertainty. This contribution creates a mechanism that assists in the process of analyzing and selecting the alternatives aligned with the proposed criteria on both the qualitative and quantitative scales. This analysis uses the acronym from the interactive and multi-criteria decision-making method (known as TODIM in Portuguese), a discrete multi-criteria method based on prospect theory. However, the criteria weights and alternatives are described as linguistic preferences and involve quantitative data. The qualitative preferences transformed into crisp values and the quantitative data converts into comparable scale. The results indicate the discrepancies between the importance and performance levels of the GSCP. This study identified set of principal criteria that can influence the recommendations for strategic direction in the most systematic and wide-ranging manner.     

Transforming the mathematical practices of learners and teachers through digital technology*

ABSTRACT

This article argues that mathematical knowledge, and its related pedagogy, is inextricably linked to the tools in which the knowledge is expressed. The focus is on digital tools and the different roles they play in shaping mathematical meanings and in transforming the mathematical practices of learners and teachers. Six categories of digital tool-use that distinguish their differing potential are presented: (1) dynamic and graphical tools; (2) tools that outsource processing power; (3) tools that offer new representational infrastructures for mathematics; (4) tools that help to bridge the gap between school mathematics and the students’ world; (5) tools that exploit high-bandwidth connectivity to support mathematics learning; and (6) tools that offer intelligent support for the teacher when their students engage in exploratory learning with digital technologies. Following exemplification of each category, the article ends with some reflections on the progress of research in this area and identifies some remaining challenges.     

Isotopic characterization as a screening tool in authentication of organic produce commercially available in western North America

The use of nitrogen stable isotopes to discriminate between conventionally and organically grown crops has been further developed in this study. Soil and irrigation water from different regions, as well as nitrogen fertilizers used, have been examined in detail to determine their effects on nitrogen isotope composition of spinach, lettuce, broccoli and tomatoes. Over 1000 samples of various types of organically and conventionally grown produce of known origin, along with the samples of nitrogen fertilizers used for their growth, have been analysed in order to assemble the datasets of crop/fertilizer correlations. The results demonstrate that the developed approach can be used as a valuable component in the verification of agricultural practices for more than 25 different types of commercially grown green produce, either organic or conventional. Over a period of two years, various organic and non-organic greens, from different stores in Seattle (WA, USA) and Victoria (BC, Canada), were collected and analysed using this methodology with the objective of determining any pattern of misrepresentation.     

Should proof be minimal? Ms T's evaluation of secondary school students’ proofs

Calls for reform in mathematics education around the world state that proofs should be part of school mathematics at all levels. Turning these calls into a reality falls on teachers’ shoulders. This paper focuses on one secondary school teacher's reactions to students’ suggested proofs and justifications in elementary number theory. To determine whether the justifications are acceptable, the teacher used not only her SMK regarding mathematical aspects, but also her PCK about what a student giving this justification might know or not know. A discussion of the findings is followed by some questions that arise.     

The many facets of a definition: The case of periodicity

This paper was triggered by an authentic conversation between two mathematics teacher educators who debated whether a constant function is a periodic function, within the framework of a professional development program for secondary mathematics teachers. Their initial conversation led to deep mathematical and pedagogical musing surrounding mathematical definitions. In this paper, we present various aspects of a mathematical definition, including the role and nature of definitions in school mathematics, critical versus preferable features of a definition, and the arbitrariness underlying the choice of definition. We discuss the interplay between logical and pedagogical considerations with respect to definitions, drawing on the definition of a periodic function as an example.     

浅谈高等数学教学实践

培养学生分析解决问外的能力和培养学生自学能力,是高等数学教学的基本任务之一.本文结合从事高等数学教学的实践,阐述如何培养提高大学生的分析问题、解决问题的能力及自学能力,以及如何用科学家的坚忍不拔的精神激励鞭策大学生学习.     

Built-in quality systems in regulated contract research organizations (CRO) conducting bioequivalence studies: a regulatory science perspective

As contract research organizations are now familiar with GXPs and have become more popular for conducting bioequivalence studies, it is very important that the sponsor has the assurance that the study has been conducted not only to the highest standard of science but also in compliance with regulatory requirements. The dynamic role of quality personnel requires alert knowledgeable people to recognise all the issues which arise and take the proper actions—experienced persons can detect and rectify these. On the basis of equality, for quality system personnel and scientists a firm grasp of regulatory science is needed to succeed. It must be remembered that compliance is monitored by adherence to regulatory standards, whereas the regulatory bodies review the appropriately implemented regulatory science principles. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

药学类专业基础课程有机化学教学现状的调查分析与对策

为了确保有机化学课程的教学改革具有科学性和针对性,本课程组对西安交通大学药学和制药专业85名学生进行了问卷调查。通过对调查结果的统计和分析,课程组认为:有机化学的教学改革应从教师、学生和课程3个方面统一进行有针对性的调整和变化,才能实现学生从"被动"到"主动"学习方式的转变。     

Teacher listening: The role of knowledge of content and students

In this research report we consider the kinds of knowledge needed by a mathematician as she implemented an inquiry-oriented abstract algebra curriculum. Specifically, we will explore instances in which the teacher was unable to make sense of students’ mathematical struggles in the moment. After describing each episode we will examine the instructor's efforts to listen to the students and the way that these efforts were supported or constrained by her mathematical knowledge for teaching. In particular, we will argue that in each case the instructor was ultimately constrained by her knowledge of how students were thinking about the mathematics.