Calculus Students' Use and Interpretation of Variables: Algebraic vs. Arithmetic Thinking

Abstract

The ability to use and interpret algebraic variables as generalized numbers and changing quantities is fundamental to the learning of calculus. This study considers the use of variables in these advanced ways as a component of algebraic thinking. College introductory calculus students' (n = 174) written responses to algebra problems requiring the use and interpretation of variables as changing quantities were examined for evidence of algebraic and arithmetic thinking. A framework was developed to describe and categorize examples of algebraic, transitional, and arithmetic thinking reflected in these students' uses of variables. The extent to which students' responses showed evidence of algebraic or arithmetic thinking was quantified and related to their course grades. Only one third of the responses of these entering calculus students were identified as representative of algebraic thinking. This study extends previous research by showing that evidence of algebraic thinking in students' work was positively related to successful performance in calculus.     

Fatigue life assessment of nodular cast iron containing casting defects

The fatigue behaviour of a nodular cast iron containing casting defects has been investigated in the high-cycle fatigue regime. In this paper, we propose a fatigue life assessment model for flawed materials based on a fracture mechanics approach which takes into account the position and size of the defect, short crack behaviour and the notch effect introduced by the defect. The fatigue behaviour of smooth samples, and long and short crack behaviour have been experimentally determined in order to identify the relevant mechanical parameters; these being introduced into the model. An experimental study has been made both in air and in vacuum in order to account for the position of the defect, noting that internal defects are supposed to be under vacuum conditions. Experimental results, which are based on a two-crack front-marking technique specially developed for this study, show that the propagation of natural cracks is controlled by the effective stress intensity factor in air as well as in vacuum. The K calculation for a short crack in the stress field of a notch is analysed using numerical elastic–plastic results. Comparison between experimental results and the computation of fatigue life for fatigue lives less than 10⁶ cycles shows that the fatigue behaviour of nodular cast iron is controlled by a propagation process. The model proposed is thus relevant for fatigue lives less than 10⁶ cycles so that the defect can be considered as a crack and the initiation stage neglected. Closer to the fatigue limit, this study shows that the initiation stage should be considered in the assessment of fatigue life of nodular cast iron, because a single macroscopic propagation assessment is not enough to describe the whole fatigue life. The defect cannot be considered as a pre-existent crack in the high-cycle fatigue range (>10⁶ cycles), and the initiation stage that contains microcrack propagation around the defect should be evaluated when assessing the high-cycle fatigue life of nodular cast iron.     

A software tool for research in linguistics and lexicography: Application to Somali

General-purpose database management systems, whose structure is built in, are not an appropriate solution to situations where problems of translation or areas of research cannot be bounded in advance, for example, when lexicography and linguistic research are closely related. Consequently, an original system has been developed, and is being applied to linguistic and lexicographical data on the Somali language.Jacqueline Lecarme has a master's degree in Lettres Classiques (University of Grenoble, 1969) and a Ph.D. in linguistics (University of Montreal, 1978). Carole Maury has a master's degree and a doctorate in computer science (University of Nice, 1986).     

Comparison of glycemic index of spelt and wheat bread in human volunteers

The assessment of the glycemic index (GI) seems to be an important parameter to take into account in order to better understand the physiologic effects of foods with high carbohydrate levels. Among cereals, which are major sources of carbohydrates, spelt (Triticum spelta L.) has been considered as particularly interesting from a nutritional point of view. The aim of this study was to evaluate in vivo the GI of white spelt bread in healthy subjects. The wheat (Triticum aestivum L.) white bread was used as reference food. To avoid differences in the production of both breads, spelt and wheat breads were baked under the same controlled conditions. Results showed that the glycemic profile of spelt white bread was not different from that of wheat white bread (GI of 93 ± 9). The area under the glycemic curve significantly and negatively correlated to fasting glycemia and carbohydrate intake during evening meals preceding the test. In conclusion, the glycemic response to spelt bread was similar to that of wheat bread. However, in order to avoid more inter-individual variability, our data supports the importance to propose standardised carbohydrate content for the last meal before evaluating the GI of food.     

New procedure for the study of odour representativeness of aromatic extracts from smoked salmon

The representativeness of an aromatic extract of smoked salmon obtained from simultaneous steam distillation and extraction with diethyl ether is discussed. After extraction, the extract is diluted in ethanol with an evaporation of diethyl ether, which allows the extract to be redeposited on matrices physically similar to those of the original product. When the shift of the matrix effect is taken into account, the sensorial results are closer to reality and more representative of the real interaction conditions between the matrix and the extract. Several sensory methods are used to describe the representativeness of the smoked salmon extracts, such as triangular and notation tests. Preliminary work is carried out on standards known both to contribute to the aroma of many seafood products and to have a high volatility in comparison with those expected in smoked salmon in order to test the method in difficult conditions of recovery. This enables the recovery yield of the extraction (from 62% for limonene to 97% for 2-methylphenol) to be assessed leading to a better characterization of the representativeness taking into account the odour dilutions. The final aromatic extract is found to be about 70% representative of the original product.     

Factors in the current adjustment of young adult daughters of alcoholic and problem drinking fathers.

The adjustment status of women whose fathers were alcoholic, psychiatrically disturbed, or normal was compared to determine the extent of daughters' vulnerability and whether family climate and social support variables moderated the development of symptomatology. The 240 respondents, who were either university staff members or students, comprised four groups: women with normal fathers (n?=?81), women with alcoholic and problem drinking fathers (n?=?114), women with psychiatrically disturbed fathers (n?=?30), and women with both parents who were alcoholic or problem drinkers (n?=?15). Daughters of alcoholic and problem drinking fathers reported more neurotic and acting-out symptoms than did daughters of normal fathers. However, a similar elevation of neurotic and acting-out symptoms was found among the daughters of psychiatrically disturbed fathers, who in addition had significantly higher depression scores than did the daughters of alcoholic and problem drinking fathers. Daughters' rates of alcohol use did not distinguish the groups. Family climate and social support variables were found to be related to daughters' current adjustment. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Two-wave-plate compensator method for full-field retardation measurements

The two-wave-plate compensator (TWC) method is expanded for full-field retardation measurements by use of a polarization microscope. The sample image is projected onto a CCD camera connected to a computer, allowing the retardation to be measured at all pixels. The retardation accuracy of this implementation of the TWC is evaluated to be 0.06 nm. The method is applied to polarization-maintaining fibers and long-period fiber gratings. The measured retardation is in good agreement with the crossed-polarizer images of the fibers. The method achieves a spatial resolution of 0.45 microm and a retardation resolution of 0.07 nm. The full-field TWC method can thus be a useful tool for characterizing and monitoring the fabrication of optical devices.     

Helping families move: Relocation counseling for housing-voucher recipients

As the U.S. Department of Housing and Urban Development (HUD) shifts its emphasis from project-based subsidies to housing vouchers, a key question is the amount of relocation help that should be provided to voucher recipients. To address these and related issues, this article examines the use of and influence of relocation counseling at four distressed federally subsidized housing developments (in Baltimore, Maryland; Newport News, Virginia; Kansas City, Missouri; and San Francisco, California) where families were provided with vouchers and relocation counseling in order to expedite moves into the private housing market. Both qualitative and quantitative analysis techniques were used to examine the different approaches to relocation counseling provided by four types of providers: 1) community-based non-profit housing agencies; 2) a private company and its subcontractor, an out-of-town consultant specializing in relocation counseling; 3) a state housing agency; and 4) the on-site housing management company. Underutilization of relocation counseling was a problem: only two-fifths of the sample reported using relocation services. Middle-aged tenants and those at the Baltimore site were most likely to take advantage of the services; those living in overcrowded units were least likely. Programs need to be developed to increase participation rates while recognizing that tenant involvement must remain voluntary in nature at such sites. Although there was some evidence that the more intensive relocation counseling provided in Newport News opened up more housing options for residents, in general the counseling had limited impact. Those who used relocation counseling did not consider more housing options than others, nor were they more likely to focus their housing search on distant neighborhoods. Furthermore, residents depended on friends and relatives, rather than relocation counselors, to learn about their new home. Even though many respondents made short-distance moves (especially in Baltimore and Kansas City), they usually were able to improve their housing and neighborhood conditions. These findings suggest that it may be unreasonable to expect families-particularly those relying on public transportation—to relocate to new and unfamiliar neighborhoods without support, or without intensive counseling, encouraging them to do so. Spatial deconcentration may not always be an appropriate goal for all voucher recipients. David P. Varady co-principal investigator, Professor of Planning is Professor of Planning at the University of Cincinnati. Professor Varady has written widely about community conservation and housing policy, both in the United States and the United Kingdom. His most recent book, co-edited with Wolfgang F.E. Preiser and Francis P. Russell,New Directions in Urban Public Housing, was published by the Center for Urban Policy Research, Fall, 1988. Carole C. Walker co-principal investigator, is Assistant Director of the Center for Urban Policy Research at Rutgers University. In her years at the Center, she has studied a broad range of public policy issues, including program evaluation, affordable housing,subdivision regulations, and land use development. She is the author of numerous research studies and co-author with David Listokin ofThe Subdivision and Site Plan Handbook. Kirk McClure investigator, is an Associate Professor with the Graduate Program in Urban Planning at the University of Kansas. His teaching and research interests are in the areas of housing and community development. He has recently completed research evaluating the ten-year performance of the Low-Income Housing Tax Credit program and is now engaged in an examination of the secondary mortgage market as an aid to affordable housing. Janet Smith-Heimer, investigator, is the founding principal of Bay Area Economics (BAE), a national consulting firm specializing in urban and real estate economics. She has been actively engaged in urban development since 1978 and has developed expertise in affordable housing, economic development, and military base closure. Sherry Larkins research assistant, is a Ph.D. candidate in sociology at Rutgers University. Her areas of interest are race relations, urban sociology, and substance abuse.