Variaciones en el desarrollo, influencias socioculturales, y dificultades en el aprendizaje de las matemáticas

Es sabido que la mayoría de los niños entran en la escuela con conocimientos y recursos fundacionales para su aprendizaje matemático. Sin embargo, esta no es la historia completa. Resultados de investigaciones revelan enormes diferencias en los niveles de competencia matemática de los niños pequeños, y estas diferencias parecen ser más acusadas en los Estados Unidos que en algunos otros países (por ejemplo, China) (Starkey y Klein, 2008). En este artículo se describen los tipos de diferencias que se dan y se ofrece una revisión sobre lo que se sabe acerca de la naturaleza y las fuentes de las variaciones en el desarrollo entre los niños

Fundamentos cognitivos para la iniciación en el aprendizaje de las matemáticas

En este artículo, sobre fundamentos cognitivos para la iniciación en el aprendizaje de las matemáticas, se realiza una revisión de investigaciones sobre el aprendizaje de las matemáticas en educación infantil. Esta revisión está estructurada según los siguientes apartados: Evidencias sobre la comprensión temprana del número, desarrollo del pensamiento espacial y la geometría, desarrollo de la medición, y regulación de la conducta y la atención

Contenido matemático fundacional para el aprendizaje en los primeros años

En este capítulo se describe el contenido matemático fundacional accesible para niñas y niños pequeños. El foco en este capítulo está puesto en las propias ideas matemáticas, más que en la enseñanza y el aprendizaje de las mismas. Estas ideas matemáticas se dan por sentadas por los adultos, pero son sorprendentemente profundas y complejas. Hay dos áreas fundamentales en las matemáticas para la primera infancia: (1) el número y (2) la geometría y la medición, tal como identifican los Focos Currículares del NCTM y subrraya este comité. También hay importantes procesos de razonamiento matemático en que los niños deben implicarse. Este capítulo también describe algunas de las conexiones más importantes de las matemáticas infantiles con las matemáticas posteriores

Fundamentos cognitivos para la iniciación en el aprendizaje de las matemáticas

In this article, about cognitive foundations for early mathematics learning, we make a review of research on the learning of mathematics in the early childhood. We structure this review in the following sections: evidence for early understanding of number, development of spatial thinking and geometry, development of measurement, and regulating behavior and attention.En este artículo, sobre fundamentos cognitivos para la iniciación en el aprendizaje de las matemáticas, se realiza una revisión de investigaciones sobre el aprendizaje de las matemáticas en educación infantil. Esta revisión está estructurada según los siguientes apartados: Evidencias sobre la comprensión temprana del número, desarrollo del pensamiento espacial y la geometría, desarrollo de la medición, y regulación de la conducta y la atención

Contenido matemático fundacional para el aprendizaje en los primeros años

This chapter describes the foundational and achievable mathematics content for young children. The focus of this chapter is on the mathematical ideas themselves rather than on the teaching or learning of these ideas. These mathematical ideas are often taken for granted by adults, but they are surprisingly deep and complex. There are two fundamental areas of mathematics for young children: (1) number and (2) geometry and measurement as identified in NCTM's Curriculum Focal Points and outlined by this committee. There are also important mathematical reasoning processes that children must engage in. This chapter also describes some of the most important connections of the mathematics for young children to later mathematics. In the area of number, a fundamental idea is the connection between the counting numbers as a list and for describing how many objects are in a set. We can represent arbitrarily large counting numbers in an efficient, systematic way by means of the remarkable decimal system (base 10). We can use numbers to compare quantities without matching the quantities directly. The operations of addition and subtraction allow us to describe how amounts are related before and after combining or taking away, how parts and totals are related, and to say precisely how two amounts compare. In the area of geometry and measurement, a fundamental idea is that geometric shapes have different parts and aspects that can be described, and they can be composed and decomposed. To measure the size of something, one first selects a specific measurable attribute of the thing, and then views the thing as composed of some number of units. The shapes of geometry can be viewed as idealized and simplified approximations of objects in the world. Space has structure that derives from movement through space and from relative location within space. An important way to think about the structure of 2-D and 3-D space comes from viewing rectangles as composed of rows and columns of squares and viewing box shapes as composed of layers of rows and columns of cubes.En este capítulo se describe el contenido matemático fundacional accesible para niñas y niños pequeños. El foco en este capítulo está puesto en las propias ideas matemáticas, más que en la enseñanza y el aprendizaje de las mismas. Estas ideas matemáticas se dan por sentadas por los adultos, pero son sorprendentemente profundas y complejas. Hay dos áreas fundamentales en las matemáticas para la primera infancia: (1) el número y (2) la geometría y la medición, tal como identifican los Focos Currículares del NCTM y subrraya este comité. También hay importantes procesos de razonamiento matemático en que los niños deben implicarse. Este capítulo también describe algunas de las conexiones más importantes de las matemáticas infantiles con las matemáticas posteriores.  En el área del número, una idea fundamental es la conexión entre los números de contar como secuencia y en la descripción de cuántos objetos hay en un conjunto. Podemos representar números de contar arbitrariamente grandes de una manera eficiente y sistemática, mediante el notable sistema decimal de numeración (de base 10). Podemos utilizar los números para comparar cantidades sin emparejarlas directamente (sin usar la correspondencia uno a uno). Las operaciones de adición y sustracción nos permiten describir cómo se relacionan las cantidades antes y después de combinarlas o quitar una de otra, cómo se relacionan las partes y el todo, y expresar con precisión la comparación de dos cantidades. En el ámbito de la geometría y la medición, una idea fundamental es que las formas geométricas tienen diferentes partes y aspectos que pueden describirse, y que pueden componerse y descomponerse. Para medir el tamaño de algo, primero se elige un atributo medible específico del objeto, y luego se considera el objeto como composición de un determinado número de unidades. Las formas de la geometría se pueden ver como aproximaciones idealizadas y simplificadas de objetos del mundo. El espacio tiene una estructura que deriva del movimiento a través del espacio y de la posición relativa dentro del espacio. Una forma importante de pensar en la estructura del espacio bidimensional y tridimensional proviene de considerar los rectángulos compuestos de filas y columnas de cuadrados y visualizar la forma de una caja como compuesta de capas formadas por filas y columnas de cubos

Issues for Science and Engineering Researchers in the Digital Age

http://deepblue.lib.umich.edu/bitstream/2027.42/88866/1/2001_Researchers_in_the_Digital_Age.pd

Appropriateness of the probability approach with a nutrient status biomarker to assess population inadequacy: a study using vitamin D

Background: There are questions about the appropriate method for the accurate estimation of the population prevalence of nutrient inadequacy on the basis of a biomarker of nutrient status (BNS). Objective: We determined the applicability of a statistical probability method to a BNS, specifically serum 25-hydroxyvitamin D [25(OH)D]. The ability to meet required statistical assumptions was the central focus. Design: Data on serum 25(OH)D concentrations in adults aged 19–70 y from the 2005–2006 NHANES were used (n = 3871). An Institute of Medicine report provided reference values. We analyzed key assumptions of symmetry, differences in variance, and the independence of distributions. We also corrected observed distributions for within-person variability (WPV). Estimates of vitamin D inadequacy were determined. Results:We showed that the BNS [serum 25(OH)D] met the criteria to use the method for the estimation of the prevalence of inadequacy. The difference between observations corrected compared with uncorrected for WPV was small for serum 25(OH)D but, nonetheless, showed enhanced accuracy because of correction. The method estimated a 19% prevalence of inadequacy in this sample, whereas misclassification inherent in the use of the more traditional 97.5th percentile high-end cutoff inflated the prevalence of inadequacy (36%). Conclusions: When the prevalence of nutrient inadequacy for a population is estimated by using serum 25(OH)D as an example of a BNS, a statistical probability method is appropriate and more accurate in comparison with a high-end cutoff. Contrary to a common misunderstanding, the method does not overlook segments of the population. The accuracy of population estimates of inadequacy is enhanced by the correction of observed measures for WPV

Information-theoretical assessment of the performance of likelihood ratio computation methods

This is the accepted version of the following article: Ramos, D., Gonzalez-Rodriguez, J., Zadora, G. and Aitken, C. (2013), Information-Theoretical Assessment of the Performance of Likelihood Ratio Computation Methods. Journal of Forensic Sciences, 58: 1503–1518. doi: 10.1111/1556-4029.12233, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1111/1556-4029.12233/Performance of likelihood ratio (LR) methods for evidence evaluation has been represented in the past using, for example, Tippett plots. We propose empirical cross-entropy (ECE) plots as a metric of accuracy based on the statistical theory of proper scoring rules, interpretable as information given by the evidence according to information theory, which quantify calibration of LR values. We present results with a case example using a glass database from real casework, comparing performance with both Tippett and ECE plots. We conclude that ECE plots allow clearer comparisons of LR methods than previous metrics, allowing a theoretical criterion to determine whether a given method should be used for evidence evaluation or not, which is an improvement over Tippett plots. A set of recommendations for the use of the proposed methodology by practitioners is also given.Supported by the Spanish Ministry of Science and Innovation under project TEC2009-14719-C02-01 and co-funded by the Universidad Autonoma de Madrid and the Comunidad Autonoma de Madrid under project CCG10-UAM/TIC-5792

Using Schema Training to Facilitate Students\u27 Understanding of Challenging Engineering Concepts in Heat Transfer and Thermodynamics

Background: Chi and colleagues have argued that some of the most challenging engineering concepts exhibit properties of emergent systems. However, students often lack a mental framework, or schema, for understanding emergence. Slotta and Chi posited that helping students develop a schema for emergent systems, referred to as schema training, would increase the understanding of challenging concepts exhibiting emergent properties. Purpose: We tested the effectiveness of schema training and explored the nature of challenging concepts from thermodynamics and heat transfer. We investigated if schema training could (a) repair misconceptions in advanced engineering students and (b) prevent them in beginning engineering students. Method: We adapted Slotta and Chi\u27s schema training modules and tested their impact in two studies that employed an experimental design. Items from the Thermal and Transport Concept Inventory and expert-developed multiple-choice questions were used to evaluate conceptual understanding of the participants. The language used by students in their open-ended explanations of multiple-choice questions was also coded. Results: In both studies, students in the experimental groups showed larger gains in their understanding of some concepts—specifically in dye diffusion and microfluidics in Study One, and in the final test for thermodynamics in Study Two. But in neither study did students exhibit any gain in conceptual questions about heat transfer. Conclusion: Our studies suggest the importance of examining the nature of the phenomena underlying the concepts being taught because the language used in instruction has implications for how students understand them. Therefore, we suggest that instructors reflect on their own understanding of the concepts

Harm–benefit analysis – what is the added value?:A review of alternative strategies for weighing harms and benefits as part of the assessment of animal research

Animal experiments are widely required to comply with the 3Rs, to minimise harm to the animals and to serve certain purposes in order to be ethically acceptable. Recently, however, there has been a drift towards adding a so-called harm-benefit analysis as an additional requirement in assessing experiments. According to this, an experiment should only be allowed if there is a positive balance when the expected harm is weighed against the expected benefits. This paper aims to assess the added value of this requirement. Two models, the discourse model and the metric model, are presented. According to the former, the weighing of harms and benefits must be conducted by a committee in which different stakeholders engage in a dialogue. Research into how this works in practice, however, shows that in the absence of an explicit and clearly defined methodology, there are issues about transparency, consistency and fairness. According to the metric model, on the other hand, several dimensions of harms and benefits are defined beforehand and integrated in an explicit weighing scheme. This model, however, has the problem that it makes no real room for ethical deliberation of the sort committees undertake, and it has therefore been criticised for being too technocratic. Also, it is unclear who is to be held accountable for built-in ethical assumptions. Ultimately, we argue that the two models are not mutually exclusive and may be combined to make the most of their advantages while reducing the disadvantages of how harm-benefit analysis in typically undertaken