We contribute to research on visualization as an epistemic learning tool by inquiring into the didactical potential of having students visualize one phenomenon in accord with two different partial meanings of the same concept. 22 Grade 4-6 students participated in a design study that investigated the emergence of proportionalequivalence notions from mediated perceptuomotor schemas. Working as individuals or pairs in tutorial clinical interviews, students solved non-symbolic interaction problems that utilized remote-sensing technology. Next, they used symbolic artifacts interpolated into the problem space as semiotic means to objectify in mathematical register a variety of both additive and multiplicative solution strategies. Finally, they reflected on tensions between these competing visualizations of the space. Micro-ethnographic analyses of episodes from three paradigmatic case studies suggest that students reconciled semiotic conflicts by generating heuristic logico-mathematical inferences that integrated competing meanings into cohesive conceptual networks. These inferences hinged on revisualizing additive elements multiplicatively. Implications are drawn for rethinking didactical design for proportions. I didn't pay enough attention to change of perspective. …. The subject deserves a more systematic treatment, which I do not dare undertake. …. Learning processes are marked by a succession of changes in perspective which should be provoked and reinforced by those who are expected to guide them. (Freudenthal, 1991, as cited in Streefland, 1993 This article builds on a paper presented to the Special Interest Group on Research in Mathematics Education (SIG RME) at the 2012 annual meeting of the American Educational Research Association (AERA).

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An efficient method, based on the Ritz concept, for dynamic analysis of response of multistorey buildings including foundation interaction to earthquake ground motion is presented. The system considered is a shear building on a rigid circular disc footing attached to the surface of a linearly elastic halfspace. In this method, the structural displacements are transformed to normal modes of vibration of the building on a rigid foundation. The analysis procedure is developed and numerical results are presented to demonstrate that excellent results can be obtained by considering only the first few modes of vibration. As the number of unknowns are reduced by transforming to generalized co‐ordinates, the method presented is much more efficient than direct methods.

Radical constructivists advocate discovery-based pedagogical regimes that enable students to incrementally and continuously adapt their cognitive structures to the instrumented cultural environment. Some sociocultural theorists, however, maintain that learning implies discontinuity in conceptual development, because novices must appropriate expert analyses that are schematically incommensurate with their naive views. Adopting a conciliatory, dialectical perspective, we concur that naive and analytic schemes are operationally distinct and that cultural-historical artifacts are instrumental in schematic reconfiguration yet argue that students can be steered to bootstrap this reconfiguration in situ; moreover, students can do so without any direct modeling from persons fluent in the situated use of the artifacts. To support the plausibility of this mediated-discovery hypothesis, we present and analyze vignettes selected from empirical data gathered in a conjecture-driven design-based research study investigating the microgenesis of proportional reasoning through guided engagement in technology-based embodied interaction. 22 Grade 4-6 students participated in individual or paired semi-structured tutorial clinical Abrahamson's coauthors are all members of the Embodied Design Research Laboratory in the Graduate School of Education at the University of California, Berkeley. The construct of ''hook and shift'' first emerged during a debriefing interaction between Abrahamson and Trninic. Thanks to Mark Howison for his technological development work on the MIT, Daniel Reinholz for earlier contributions to the project and the art in the figures, and Brian Waismeyer and Lucie Vosicka for thinking with us and reviewing earlier drafts.interviews, in which they were tasked to remote-control the location of virtual objects on a computer display monitor so as to elicit a target feedback of making the screen green. The screen would be green only when the objects were manipulated on the screen in accord with a ''mystery'' rule. Once the participants had developed and articulated a successful manipulation strategy, we interpolated various symbolic artifacts onto the problem space, such as a Cartesian grid. Participants appropriated the artifacts as strategic or discursive means of accomplishing their goals. Yet, so doing, they found themselves attending to and engaging certain other embedded affordances in these artifacts that they had not initially noticed yet were supporting performance subgoals. Consequently, their operation schemas were surreptitiously modulated or reconfigured-they saw the situation anew and, moreover, acknowledged their emergent strategies as enabling advantageous interaction. We propose to characterize this two-step guided re-invention process as: (a) hookingengaging an artifact as an enabling, enactive, enhancing, evaluative, or explanatory means of effecting and elaborating a current strategy; and (b) shifting-tacitly reconfiguring current strategy in response to the hooked artifact's emergent affordances t...

A general substructure method for analysis of response of structures to earthquake ground motion, including the effects of structure‐soil interaction, is presented. The method is applicable to complex structures idealized as finite element systems and the soil region treated as either a continuum, for example as a viscoelastic halfspace, or idealized as a finite element system. The halfspace idealization permits reliable analysis for sites where essentially similar soils extend to large depths and there is no rigid boundary such as soil‐rock interface. For sites where layers of soft soil are underlain by rock at shallow depth, finite element idealization of the soil region is appropriate; in this case, the direct and substructure methods would lead to equivalent results but the latter provides the better alternative. Treating the free field motion directly as the earthquake input in the substructure method eliminates the deconvolution calculations and the related assumption—regarding type and direction of earthquake waves—required in the direct method. Spatial variations in the input motion along the structure‐soil interface of embedded structures or along the base of long surface supported structures are included in the formulation. The substructure method is computationally efficient because the two substructures—the structure and the soil region—are analysed separately; and, more important, it permits taking advantage of the important feature that response to earthquake ground motion is essentially contained in the lower few natural modes of vibration of the structure on fixed base.

What are the nature, forms, and roles of metaphors in mathematics instruction ? We present and closely analyze three examples of idiosyncratic metaphors produced during one-to-one tutorial clinical interviews with 11-year-old participants as they attempted to use unfamiliar artifacts and procedures to reason about realistic probability problems. Our interpretations of these episodes suggest that metaphor is both spurred by and transformative of joint engagement in situated activities: metaphor serves individuals as semiotic means of objectifying and communicating their own evolving understanding of disciplinary representations and procedures, and its multimodal instantiation immediately modifies interlocutors' attention to and interaction with the artifacts. Instructors steer this process toward normative mathematical views by initiating, modifying, or elaborating metaphorical constructions. We speculate on situation parameters affecting students' utilization of idiosyncratic resources as well as how socio-mathematical license for metaphor may contribute to effective instructional discourse.

In many Latin American countries, people have traditionally built and still build their houses with 'bamboo bahareque' walls (these walls have a timber frame with split bamboo in the middle, covered with cement plaster on both sides). However, this constructive technique has not been technically studied, which is necessary to validate or, if necessary, improve it as a previous step to a much needed dissemination effort. The objective of the research reported in this paper is (a) to experimentally evaluate the strength and deformation capacities of prefabricated 'bamboo bahareque' shear walls developed in Costa Rica by the Bamboo Foundation (FUNBAMBU), under horizontal cyclic loads simulating earthquake effects, and (b) to propose testing procedures and provide reliable design recommendations for 'bamboo bahareque' house design and construction. For this purpose, 7 full-scale 'bamboo bahareque' walls were built and tested at the Materials and Structural Models National Laboratory (LANAMME), School of Civil Engineering, University of Costa Rica. The dimensions of the walls are 2.4 m in height and 2.7 m in length with a thickness varying from 40 to 60 mm. The results showed that the tested 'bamboo bahareque' walls have enough capacity to withstand earthquake induced loads of considerable magnitude. They also presented some ductile behaviour under cyclic loading.

Quality control of products is everyday more and more demanding. Machine vision is becoming one of the most efficient technologies for the reliable and fast control of different types of products. The more classical techniques in machine vision 2D are valuables in lots of applications, but insufficient when it is necessary a three-dimensional data of the object to study. Classical linear 3D laser detection scanners are not optimized for revolution elements, since the features extraction algorithm needs to be different in each inspection zone and there are shadow zones where the inspection is not possible. In this paper, a novel 3D laser based rotating scanner is described (Patent Pending request nº ES-P200600068). This approach enables inspecting revolution elements avoiding the problems mentioned before. This rotating scanner implementation in a 3D Steel tube Quality Control Application is also described.