Metaphor Clusters: Characterizing Instructor Metaphorical Reasoning on Limit Concepts in College Calculus

Novice students have difficulty with the topic of limits in calculus. We believe this is in part because of the multiple perspectives and shifting metaphors available to solve items correctly. We investigated college calculus instructors' personal concepts of limits. Based upon previous research investigating introductory calculus student metaphorical reasoning, we examined 11 college instructors' metaphorical reasoning on limit concepts. This paper focused on previous research of metaphor clusters observed among students to answer the following: (a) Do college instructors use metaphorical reasoning to conceptualize the meaning of a limit? (b) Can we characterize instructor metaphorical reasoning similar to those observed among students? (c) Will an instructor's self‐identification of metaphor clusters be consistent with our metaphor coding? We found that college instructors' perspectives vary, either graphical or algebraic, in their explanations of limit items. All the instructors used metaphors, and instructor metaphorical reasoning aligned with student metaphor clusters. Instructors tended to change their metaphors with respect to the limit item. Instructors were not aware of their use of metaphors, nor were they aware of their inconsistency in their choice of metaphor. We believe that instructor awareness of their own distinct perspectives and metaphors would assist students' understanding of limit concepts.     

Synthesis and Chemical Transformation of 2 -Acetoxyimino-3,4, 6-tri-O-acetyl-2-deoxy-β-D-arabino-hexopyranosyl Azide

Abstract

The title compound 3 has been synthesized from 3,4,6-tri-O-acetyl-2-deoxy-2-nitroso-α-D-glucopyranosyl chloride (1) via compound 2. Azide reduction of 3 is accompanied by O→N-acetyl migration to afford N-acetyl-N-(3,4,6-tri-O-acetyl-2-deoxy-2-hydroxyimino-β-D-arabino-hexopyranosyl) amine (4), also characterized as its Z and E peracetates. On the basis of IR, ¹H NMR and X-ray structural data from compound 4, its β-NHAc configuration, (Z) 2-hydroxyimino, and °S₂ conformation, were established.     

A Homological Approach to Two Problems on Finite Sets

We propose a homological approach to two conjectures descended from the Erdös-Ko-Rado Theorem, one due to Chvátal and the other to Frankl and Füredi. We apply the method to reprove, and in one case improve, results of these authors related to their conjectures.     

Certification of reference materials for ochratoxin A analysis in coffee and wine

Mycotoxins are important non-anthropogenic food and feed contaminants, which can be present on almost every agricultural commodity. Effective consumer protection therefore essentially depends on food surveillance by reliable quantitative analysis enabled by appropriate quality control. Certified (matrix) reference materials (CRMs) are versatile tools to support quality assurance. However, in the case of ochratoxin A (OTA), a hepato- and nephrotoxic mycotoxin, which is regulated in various foods, there is a lack of suitable CRMs. This lack has now been overcome by the development of two European Reference Materials (ERM^?) for the determination of OTA in roasted coffee (ERM^?-BD475) and red wine (ERM^?-BD476). This article discusses the material preparation process as well as the results of homogeneity and stability testing. Furthermore, the results of the in-house certification studies carried out at BAM Federal Institute for Materials Research and Testing are presented and discussed. Interlaboratory comparison studies involving selected expert laboratories with documented expertise in the field of mycotoxin analysis were conducted to confirm the certified values determined by BAM. The certified ochratoxin A values and their corresponding expanded uncertainties (k?=?2) were assigned in full compliance with the requirements of ISO Guide 35 and are as follows: (6.0?±?0.6)???g?kg^?1 for roasted coffee, ERM^?-BD475, and (0.52?±?0.11)???g?L^?1 for red wine, ERM^?-BD476.     

Determination of 1,4-Dichlorobenzene in Environmental Matrices

1,4-Dichlorobenzene is a frequently used lavatory deodorant although it has strong endocrine disrupting and potential carcinogenic effects. A large amount (approximately 15,000 tonnes annually worldwide) of this compound is released into the environment. This paper deals with the determination of 1,4-dichlorobenzene in a variety of environmental matrices. Various extraction and concentration methods such as charcoal absorbtion tubes and headspace sampling were applied. Sensitive and selective ion monitoring GC-MS measurements were used for determination. Significant concentrations of the compound have been identified in lavatory air, waste water, waste water sludge and human breast milk.

     

On the determination and construction of optimal row-column designs having unequal row and column sizes

In this paper we consider experimental situations requiring usage of a row-column design where v treatments are to be applied to experimental units arranged in b ₁ rows and b ₂ columns where row i has size k _1i , i=1,..., b ₁ and column j has size k _2j , j=1,..., b ₂. Conditions analogous to those given in Kunert (1983, Ann. Statis., 11, 247–257) and Cheng (1978, Ann. Statist., 6, 1262–1272) are given which can often be used to establish the optimality of a given row-column design from the optimality of an associated block design. In addition, sufficient conditions are derived which guarantee the existence of an optimal row-column design which can be constructed by appropriately arranging treatments within blocks of an optimal block design.Visiting from the Indian Statistical Institute.     

The experience of accreditation of an analytical laboratory at the Argentine Atomic Energy Commission

The implementation of a quality system based on the ISO/IEC 17025:1999 standard is a growing necessity for analytical laboratories to demonstrate their technical competence. In 2001, the Nuclear Analytical Techniques Group of the Argentine Atomic Energy Commission obtained the recognition of the International Atomic Energy Agency in the application of neutron activation analysis and the accreditation by the national accreditation body. The importance of the participation of the group in the Agency's Regional Programme for Latin America, ARCAL XXVI on Quality Assurance in Analytical laboratories is discussed, as well as the activities performed to attain these objectives. Some improvements worth mentioning resulted from the implementation of the quality system and, following the premise of continuous improvement, changes were introduced aiming at the laboratory re-accreditation.