A Models and Modeling Approach to Risk and Uncertainty

In this article we describe potential contributions of a Models and Modeling Perspective to research focused on learners’ developing conceptions about uncertainty and variation. In particular, we show how a particular class of realistic problem-solving tasks can illuminate how learners develop models to identify, describe, and predict emergent patterns of regularity in the behavior of various types of systems and in the data these systems generate. We begin by situating current design work in this area within a larger project to investigate idea development in the domain of data modeling over extended (course-length) periods. We give design principles and examples for key components in our research framework, and we provide illustrative examples of these components and their interactions around the themes of distance and measurement that arise centrally in our materials. Next, we show how our approach can support advances in research on risk perception and on the development of ideas around risk assessment and management. Specifically, we identify three key facets of our approach and materials that make them good candidates for contributing to risk-oriented design research in education. Within each of these facets, we suggest research questions that could be addressed, and we provide examples and conjectures based on prior and ongoing work. In particular, we return to the ideas of distance explored in our examples and show connections with important questions in research on learners’ perception and reasoning about risk

A Proposal for a Problem-Driven Mathematics Curriculum Framework

A framework for a problem-driven mathematics curriculum is proposed, grounded in the assumption that students learn mathematics while engaged in complex problem-solving activity. The framework is envisioned as a dynamic technologicallydriven multi-dimensional representation that can highlight the nature of the curriculum (e.g., revealing the relationship among modeling, conceptual, and procedural knowledge), can be used for programmatic, classroom and individual assessment, and can be easily revised to reflect ongoing changes in disciplinary knowledge development and important applications of mathematics. The discussion prompts ideas and questions for future development of the envisioned software needed to enact such a framework

Extracellular free water and glutathione in first-episode psychosis-a multimodal investigation of an inflammatory model for psychosis.

Evidence has been accumulating for an immune-based component to the etiology of psychotic disorders. Advancements in diffusion magnetic resonance imaging (MRI) have enabled estimation of extracellular free water (FW), a putative biomarker of neuroinflammation. Furthermore, inflammatory processes may be associated with altered brain levels of metabolites, such as glutathione (GSH). Consequently, we sought to test the hypotheses that FW is increased and associated with decreased GSH in patients with first-episode schizophrenia (SZ) compared with healthy controls (HC). SZ (n = 36) and HC (n = 40) subjects underwent a multi-shell diffusion MRI scan on a Siemens 3T scanner. 1H-MR spectroscopy data were acquired using a GSH-optimized MEGA-PRESS editing sequence and GSH/creatine ratios were calculated for DLPFC (SZ: n = 33, HC: n = 37) and visual cortex (SZ: n = 29, HC: n = 35) voxels. Symptoms and functioning were measured using the SANS, SAPS, BPRS, and GSF/GRF. SZ demonstrated significantly elevated FW in whole-brain gray (p = .001) but not white matter (p = .060). There was no significant difference between groups in GSH in either voxel. However, there was a significant negative correlation between DLPFC GSH and both whole-brain and DLPFC-specific gray matter FW in SZ (r = -.48 and -.47, respectively; both p < .05), while this relationship was nonsignificant in HC and in both groups in the visual cortex. These data illustrate an important relationship between a metabolite known to be important for immune function-GSH-and the diffusion extracellular FW measure, which provides additional support for these measures as neuroinflammatory biomarkers that could potentially provide tractable treatment targets to guide pharmacological intervention

RF and Optical Communications: A Comparison of High Data Rate Returns From Deep Space in the 2020 Timeframe

As NASA proceeds with plans for increased science data return and higher data transfer capacity for science missions, both RF and optical communications are viable candidates for significantly higher-rate communications from deep space to Earth. With the inherent advantages, smaller apertures and larger bandwidths, of optical communications, it is reasonable to expect that at some point in time and combination of increasing distance and data rate, the rapidly emerging optical capabilities would become more advantageous than the more mature and evolving RF techniques. This paper presents a comparison of the burden to a spacecraft by both RF and optical communications systems for data rates of 10, 100, and 1000 Mbps and large distances. Advanced technology for RF and optical communication systems have been considered for projecting capabilities in the 2020 timeframe. For the comparisons drawn, the optical and RF ground terminals were selected to be similar in cost. The RF system selected is composed of forty-five 12-meter antennas, whereas the selected optical system is equivalent to a 10-meter optical telescope. Potential differences in availability are disregarded since the focus of this study is on spacecraft mass and power burden for high-rate mission data, under the assumption that essential communications will be provided by low-rate, high availability RF. For both the RF and optical systems, the required EIRP, for a given data rate and a given distance, was achieved by a design that realized the lowest possible communications subsystem mass (power + aperture) consistent with achieving the lowest technology risk. A key conclusion of this paper is that optical communications has great potential for high data rates and distances of 2.67 AU and beyond, but requires R&D and flight demonstrations to prove out technologies

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD)

Enseñanza de las ciencias : revista de investigación y experiencias didácticas

Se presenta una reacción al artículo de Luis Rico y otros, acerca de los "Sistemas de representación y aprendizaje de estructuras numéricas" y se centra principalmente en aquellas actividades en las que las capacidades de representación son preponderantes ya que son en las que los resultados que obtienen los estudiantes consisten, en gran parte, en descripciones, interpretaciones, explicaciones, construcciones o predicciones justificadas. Y, puesto que los productos que se espera de los estudiantes incluyen directamente las representaciones, la fluidez en crear representaciones desempeña un papel central en la comprensión y en las capacidades necesarias para el éxito.ES

Acquisition of mathematics concepts and processes

409 p. : il.; 21 cm