From Concrete to Abstract: Teaching for Transfer of Learning when Using Manipulatives

One of the most important uses of manipulatives in a classroom is to aid a learner to make connection from tangible concrete object to its abstraction. In this paper we discuss how teacher educators can foster deeper understanding of how manipulatives facilitate student learning of math concepts by emphasizing the connection between concrete objects and math symbolization with, preservice elementary teachers, the future implementers of knowledge. We provide an example and a model, with specific steps of how teacher educators can effectively demonstrate connections between concrete objects and abstract math concepts.

Now You See it, Now You Don't: Why Do Real Estate Agents Withhold Available Houses from Black Customers?

Potential home buyers may initiate contact with a real estate agent by asking to see a particular advertised house. This paper asks whether an agent's response to such a request depends on the race of the potential buyer or on whether the house is located in an integrated neighborhood. We build on previous research about the causes of discrimination in housing by using data from fair housing audits, a matched-pair technique for comparing the treatment of equllay qualified black and white home buyers. However, we shift the focus from differences in the treatment of paired buyers to agent decisions concerning an individual housing unit using a sample of all houses seen during he 1989 Housing Discrimination study. We estimate a random effect, multinomial logit model to explain a real estate agent's joint decisions concerning whether to show each unit to a black auditor and to a white auditor. We find evidence that agents withhold houses in suburban, integrated neighborhoods from all customers (redlining), that agents' decisions to show houses in integrated neighborhoods are not the same for black and white customers (steering), and that the houses agents show are more likely to deviate from the initial request when the customeris black than when the customer is white. These deviations are consistent with the possibility that agents act upon the belief that some types of transactions are relatively unlikely for black customers (statistical discrimination).

Estudio experimental del Sistema de Albañilería Integral en la construcción de viviendas sismorresistentes. Experimental study of the Integral Masonry System in the construction of earthquake resistant houses

This paper presents the application of the Integral Masonry System (IMS) to the construction of earthquake resistant houses and its experimental study. To verify the security of this new type of building in seismic areas of the third world two prototypes have been tested, one with adobe and the other with hollow brick. In both cases it’s a two-story 6x6x6 m3 house built to scale 1/2. The tests are carried out at the Laboratory of Antiseismic Structures of the Department of Engineering, Pontifical Catholic University of Peru in Lima, in collaboration with the UPM (Technical University of Madrid). This article shows the design process of the prototypes to test, including the sizing of the reinforcements, the characteristics of the tests and the results obtained. These results show that the IMS with adobe or brick remains stable with no significant cracks faced with a severe earthquake, with an estimated acceleration of 1.8 g. Este artículo presenta una aplicación del Sistema de Albañilería Integral (SAI) a la construcción de viviendas sismorresistentes y su estudio experimental. Para verificar su seguridad para su construcción en zonas sísmicas del tercer mundo se han ensayado dos prototipos, uno con adobe, y otro con ladrillo hueco. Se trata de una vivienda de 6x6x6 m3 y dos plantas que se construyen a escala 1/2. Los ensayos se realizaron en el Laboratorio de Estructuras Antisísmicas del Departamento de Ingeniería de la Pontificia Católica Universidad del Perú (PUCP) de Lima en colaboración con la UPM (Universidad Politécnica de Madrid). Este artículo muestra el proceso de diseño de los prototipos a ensayar, incluido el dimensionado de los refuerzos, las características de los ensayos y los resultados obtenidos. Estos resultados muestran que el SAI con adobe o ladrillo permanece estable sin grietas significativas ante un sismo severo, con una aceleración estimada de 1,8 g.

Study of the Influence of Fines on a Self-Compacting Concrete

The paper presents the results of the tests of a self-compacting concrete made with fines which include Portland cement and three fillers: hornfels, limestone and metakaolin, in a weight proportion between 23% and 45% of the admixtures. The first mix proportions were designed with a high proportion of Portland cement (720-750kg/m3), and are compared to those having a smaller content of cement and more fillers. The results obtained show that the limestone filler percentage should be higher than the hornfels one, and both of them significantly higher than that of the metakaolin so as to facilitate the fluidity and self-compactability. AIso, the higher proportion of fillers causes a rounded porosity in the mixing which has a bearing on better compressive strength results.

Similarities and Differences in Barrel Vaults of Traditional and Stately Houses in the Historic Centre of Arequipa, Perú

The traditional architecture of the centre of the city of Arequipa has been analyzed by comparing floor-plans of houses from the eighteenth and nineteenth centuries in order to explain the reasons behind the arrangement of their constructional elements and the evolution of said elements and floor-plans. The historic centre of Arequipa, a city located in the South of Perú, South America (Latitude 16°23' South, Longitude 71 °31' West), is based on a ground plan from 1540 that was set during the city's Spanish foundation. It was declared Patrimony of the Humanity by UNESCO. The manorial architecture is widely known for its decorated fronts and one-of-a-kind designs, but its differences with respect to the popular architecture are not based exclusively on decorative aspects. Peru's colonial period finished around 1825, but the barrel-vault, construction style continued in Arequipa through 1868, when an earthquake destroyed the city. Thereafter, the vaults were replaced by roofs made of rails, with cinders made out of the lava stone. The stately houses belonged to the founding families who settled around the main square on forty nine blocks that formed a square-grid, street layout. Also belonging to this category are the houses of landlords and traders from post-colonial times.

Concrete Swelling in Two Spanish Dams

Several chemical reactions are able to produce swelling of concrete for decades after its initial curing, a problem that affects a considerable number of concrete dams around the world. Principia has had several contracts to study this problem in recent years, which have required reviewing the state-ofthe-art, adopting appropriate mathematical descriptions, programming them into user routines in Abaqus, determining model parameters on the basis of some parts of the dams’ monitored histories, ensuring reliability using some other parts, and finally predicting the future evolution of the dams and their safety margins. The paper describes some of the above experience, including the programming of sophisticated nonisotropic swelling models, that must be compatible with cracking and other nonlinearities involved in concrete behaviour. The applications concentrate on two specific cases, an arch-gravity dam and a double-curvature arch dam, both with a long history of concrete swelling and which, interestingly, entailed different degrees of success in the modelling efforts

Contribution to Theme A of the Benchmark Workshop: Effect of Concrete Swelling on the Equilibrium and Displacements of an Arch Dam

The Kariba dam is undergoing concrete expansion as a result of an alkali-aggregate reaction. The model adopted to simulate the process is explained in the paper; it is based on the model first proposed by Ulm et al, as later modified by Saouma and Perotti. It has been implemented in the commercial finite element code Abaqus and applied to solve the benchmark problem. The parameters of the model were calibrated using the data recorded up to 1995. The calibrated model was then used for predicting the evolution of the dam up to the present date. Apart from this prediction the paper offers a number of conclusions, such as the fact that the stress level appears to have a major influence on the expansion process; and it presents some suggestions to improve the formulation of the benchmark, such as providing temperature data and widening the locations and conditions of the data employed in the calibration

Polypropylene fiber-reinforced self-compacting concrete for the reconstruction of the cathedral of La Laguna, Canary Island, Spain

High performance materials are needed for the reconstruction of such a singular building as a cathedral, since in addition to special mechanical properties, high self compact ability, high durability and high surface quality, are specified. Because of the project’s specifications, the use of polypropylene fiber-reinforced, self-compacting concrete was selected by the engineering office. The low quality of local materials and the lack of experience in applying macro polypropylene fiber for structural reinforcement with these components materials required the development of a pretesting program. To optimize the mix design, performance was evaluated following technical, economical and constructability criteria. Since the addition of fibers reduces concrete self-compactability, many trials were run to determine the optimal mix proportions. The variables introduced were paste volume; the aggregate skeleton of two or three fractions plus limestone filler; fiber type and dosage. Two mix designs were selected from the preliminary results. The first one was used as reference for self-compactability and mechanical properties. The second one was an optimized mix with a reduction in cement content of 20 kg/m3and fiber dosage of 1 kg/m3. For these mix designs, extended testing was carried out to measure the compression and flexural strength, modulus of elasticity, toughness, and water permeability resistance

Effect of the curing conditions of concrete on the behaviour under freeze-thaw cycles*

The aim of this work is to relate the curing conditions of concrete and the addition of an air-entraining admixture with the damage caused by freeze–thaw cycles. In countries with a continental climate, the curing of concrete in summer is performed under climatic conditions of high temperature and low humidity, and during the winter the concrete suffers conditions of freeze–thaw, often accompanied by the use of de-icing salts. This paper shows the experimental results of the behaviour of concrete specimens cured under climatic summer conditions (high temperature and low humidity) and then subjected to freeze–thaw cycles. Curing of the specimens includes conditions of good and bad practice in relation to wetting and protection of the concrete. It also examines the effectiveness of using an air-entraining admixture in both cases. The experimental programme includes an evaluation of the mechanical properties of the concrete, the study of the cement hydration and the measurement of the volume and pore sizes of the concrete. These tests were performed before and after the application of the freeze–thaw cycles. The results obtained showed that the specimens without air-entraining admixture show a deterioration of mechanical properties after the freeze–thaw test. However, the inclusion of air bubbles benefits the behaviour of concrete against freeze–thaw cycles so even better mechanical properties after the test were observed. This anomalous behaviour is because the cement hydration process continues over the freeze–thaw tests, closing the pore structure. This aspect has been confirmed with the DTA and TG tests performed