Effective Teacher Professional Development Programs. A Case Study Focusing on the Development of Mathematical Modeling Skills

A concern in Mathematics Education is the professional development of the teacher and to promote effective training programs. The literature provides principles guiding the design of such programs, which were considered for an instruction intended to strengthen the teacher’s practice in relation to the development of mathematical skills. The objective of this work was to study if the designed program was effective, in relation to the impact on the teacher’s teaching. A case study on a group of in-service teachers focused on the ability of mathematical modeling (MM) and their perspectives of this skill was carried out. This was divided into three moments: before, during, and after the program. The findings show that, before the program, teachers conceived modeling from epistemological, pragmatic and conceptual perspectives; during the program, they focused on the pragmatic and educational perspectives; and at the end of the program, the group was stripped of the pragmatic, epistemological and conceptual perspectives to move towards the educational and socio-critical. They were also able to justify the choice or disassociation of one or more of them. The study advances towards the concretion of more specific and robust professional development programs for mathematics teachers

A Methodology for Automatic Identification of Units with Ecological Significance in Dehesa Ecosystems

The dehesa is an anthropic complex ecosystem typical of some areas of Spain and Portugal, with a key role in soil and biodiversity conservation and in the search for a balance between production, conservation and ecosystem services. For this reason, it is essential to have tools that allow its characterization, as well as to monitor and support decision-making to improve its sustainability. A multipurpose and scalable tool has been developed and validated, which combines several low-cost technologies, computer vision methods and RGB aerial orthophotographs using open data sources and which allows for automated agroforestry inventories, identifying and quantifying units with important ecological significance such as: trees, groups of trees, ecosystem corridors, regenerated areas and sheets of water. The development has been carried out from images of the national aerial photogrammetry plan of Spain belonging to 32 dehesa farms, representative of the existing variability in terms of density of trees, shrub species and the presence of other ecological elements. First, the process of obtaining and identifying areas of interest was automated using WMS services and shapefile metadata. Then, image analysis techniques were used to detect the different ecological units. Finally, a classification was developed according to the OBIA approach, which stores the results in standardized files for Geographic Information Systems. The results show that a stable solution has been achieved for the automatic and accurate identification of ecological units in dehesa territories. The scalability and generalization to all the dehesa territories, as well as the possibility of segmenting the area occupied by trees and other ecological units opens up a great opportunity to improve the construction of models for interpreting satellite images

Methodology for the Automatic Inventory of Olive Groves at the Plot and Polygon Level

The aim of this study was to develop and validate a methodology to carry out olive grove inventories based on open data sources and automatic photogrammetric and satellite image analysis techniques. To do so, tools and protocols have been developed that have made it possible to automate the capture of images of different characteristics and origins, enable the use of open data sources, as well as integrating and metadating them. They can then be used for the development and validation of algorithms that allow for improving the characterization of olive grove surfaces at the plot and cadastral polygon scales. With the proposed system, an inventory of the Andalusian olive grove has been automatically carried out at the level of cadastral polygons and provinces, which has accounted for a total of 1,519,438 hectares and 171,980,593 olive trees. These data have been contrasted with various official statistical sources, thus ensuring their reliability and even identifying some inconsistencies or errors of some sources. Likewise, the capacity of the Sentinel 2 satellite images to estimate the FCC at the cadastral polygon, parcel and 10 × 10 m pixel level has been demonstrated and quantified, as well as the opportunity to carry out inventories with temporal resolutions of approximately up to 5 days

The City as a Tool for STEAM Education: Problem-Posing in the Context of Math Trails

This study presents an experience that combines problem-posing and Math Trails in the context of future teachers’ instruction. Pre-service teachers in the third year of their studies were faced with the design of tasks to be included in Math Trails for primary school students. The study analyzes, from a quantitative approach, 117 tasks contained in 11 Math Trails. The analysis was performed on the basis of classification variables (grade, mathematical content and object or real element involved in every task) and research variables which provide information about the nature of the tasks (procedural vs. problem-solving, level of cognitive demand, degree of contextualization, openness and creativity). Additionally, relationships between the different categories of analysis have been studied. The results reveal certain biases in the tasks in relation to the contents addressed (an abundance of tasks with a geometric component and a scarcity of tasks involving algebra or probability concepts). Most of the tasks are presented in a real context. However, a higher percentage of procedural tasks than problem-solving tasks is observed, with a predominance of low openness, creativity and cognitive demand. These results provide useful lines of work to address difficulties faced by future teachers in the STEAM field

Development of Calibration Models to Predict Mean Fibre Diameter in Llama (Lama glama) Fleeces with Near Infrared Spectroscopy

Llama fibre has the potential to become the most valuable textile resource in the Puna region of Argentina. In this study near infrared reflectance spectroscopy was evaluated to predict the mean fibre diameter in llama fleeces. Analyses between sets of carded and non-carded samples in combination with spectral preprocessing techniques were carried out and a total of 169 spectral signatures of llama samples in Vis and NIR ranges (400–2500 nm) were obtained. Spectral preprocessing consisted in wavelength selection (Vis–NIR, NIR and discrete ranges) and multiplicative and derivative pretreatments; spectra without pretreatments were also included, while modified partial least squares (M-PLS) regression was used to develop prediction models. Predictability was evaluated through R2: standard cross validation error (SECV), external validation error (SEV) and residual predictive value (RPD). A total of 54 calibration models were developed in which the best model (R2 = 0.67; SECV = 1.965; SEV = 2.235 and RPD = 1.91) was obtained in the Vis–NIR range applying the first derivative pretreatment. ANOVA analysis showed differences between carded and non-carded sets and the models obtained could be used in screening programs and contribute to valorisation of llama fibre and sustainable development of textile industry in the Puna territory of Catamarca. The data presented in this paper are a contribution to enhance the scarce information on this subject

Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.University of Cordoba 2020-4-400

How do future teachers model area and perimeter situations? The role of units and formulae

[EN] This study explores those skills associated with modeling that preservice primary and secondary teachers develop when working with measure. The sample was made up of a total of 12 master's degree students and 13 primary school teacher students, who worked in groups to solve a task, which was specically designed to develop skills associated with measure through modeling. The analysis of the models produced by the prospective teachers revealed a great wealth of ideas and evidence of the dependence on formulae for the calculation and estimation of areas. Results also indicate relationship between the model's closeness to the real situation and the tendency of participants to validate it, as well as the importance of the layout of the task on the produced models.[ES] Se presenta una investigación que explora el tipo de modelo que los futuros profesores de educación primaria y secundaria desarrollan cuando trabajan en situaciones de medida. La muestra empleada estuvo compuesta por un total de 12 alumnos de máster de formación de profesorado y 13 estudiantes del grado en educación primaria, que resolvieron en grupos una tarea diseñada específicamente para trabajar la medida a través de la modelización. El análisis de los modelos producidos por los futuros profesores reveló gran riqueza de ideas y evidenció limitaciones al uso de fórmulas para el cálculo y estimación de áreas. Los resultados también indican relación entre la cercanía del modelo con la situación en contexto y la tendencia de los participantes a validarlo, así como la importancia del formato de la tarea empleada sobre los modelos producidos.Montejo-Gámez, J.; Fernández-Ahumada, E.; Adamuz-Povedano, N. (2019). ¿Cómo modelizan los futuros profesores en situaciones de área y perímetro? El papel de las unidades y de las fórmulas. Modelling in Science Education and Learning. 12(1):5-20. https://doi.org/10.4995/msel.2019.11001SWORD520121Ärlebäck, J. B. (2009). 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Mathematics Student Teachers' Modelling Approaches While Solving the Designed Eşme Rug Problem. EURASIA Journal of Mathematics Science and Technology Education, 13 (3), 873-892Huincahue Arcos, J., Borromeo-Ferri, R., y Mena-Lorca, J. (2018). El conocimiento de la modelación matemática desde la reflexión en la formación inicial de profesores de matemática. Enseñanza de las ciencias, 36(1), 99-115.Kaiser, G. (2014). Mathematical modelling and applications in education. En Encyclopedia of mathematics education (pp. 396-404). Springer, Dordrecht.Kaiser, G., Blomhøj, M., y Sriraman, B. (2006). Mathematical modelling and applications: empirical and theoretical perspectives. ZDM - Zentralblatt für Didaktik der Mathematik, 38(2), 82-85.Lesh, R. y Harel, G. (2003). Problem solving, modeling and local conceptual development. Mathematical Thinking and Learning, 5, 157-189.Lesh, R., Hoover, M., Hole, B., Kelly, A., y Post, T. 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Modelización como proceso básico en la resolución de problemas contextualizados: un análisis de necesidades

Este trabajo explora las necesidades formativas del alumnado de primer curso del grado en Educación Primaria en el ámbito de la modelización matemática y la resolución de problemas contextualizados. Se ha puesto el foco en el análisis de las estrategias seguidas por el alumnado para abordar un problema, así como en la detección de los errores cometidos; todo ello con el objeto de diagnosticar las necesidades de formación y elaborar un perfil del alumnado que permita adaptar su instrucción a su conocimiento. Los resultados ponen de manifiesto la necesidad de trabajar estrategias para resolver problemas, el pensamiento visual y el manejo de unidades de medida

Instrumentos para la evaluación del sentido numérico en los primeros años de aprendizaje matemático

En el ámbito de la investigación en educación matemática, la importancia del sentido numérico ha estado presente desde hace décadas. Sin embargo, a pesar de esta larga trayectoria, no se ha llegado a un consenso sobre su definición. En la mayoría de los casos, los autores se limitan a dar un listado de indicadores que evidencian el grado de desarrollo en relación con las competencias numéricas. Por otro lado, recientemente, tanto marcos normativos como referentes universales han puesto de manifiesto la importancia de fomentar el sentido numérico desde los primeros años de aprendizaje. Por ello, se hace necesario disponer de instrumentos que permitan medir y evaluar la adquisición y desarrollo de esta competencia matemática en escolares. En este trabajo, se ofrece una revisión bibliográfica sobre los instrumentos existentes en la literatura con los que medir las diferentes dimensiones que constituyen esta importante componente del conocimiento matemático

Intervención didáctica en azar y probabilidad para la prevención de la ludopatía en jóvenes

El auge de los nuevos medios tecnológicos ha favorecido que la ludopatía afecte cada vez a más personas, de menor edad y con un mayor daño económico y de salud. Algunos expertos avalan la necesidad de apoyar los programas de tratamiento y prevención con propuestas educativas en general, y de educación matemática en particular, que ayuden a entender el funcionamiento de los juegos de azar a las personas afectadas o en riesgo. Partiendo de una revisión exhaustiva de la literatura sobre el tema y del diagnóstico de la situación concreta de un centro de educación secundaria situado en un barrio especialmente afectado por la problemática, se presenta una intervención didáctica experiencial, basada en prácticas contextualizadas relacionadas con el desarrollo de los contenidos propios del bloque de Estadística y Probabilidad. Paralelamente, se realizará una evaluación del impacto de la experiencia en la actitud de los estudiantes en relación con el fenómeno social que nos preocupa. La iniciativa se desarrolla en el marco de una convocatoria de proyectos de transferencia del conocimiento científico con fines sociales y está acompañada de otras acciones educativas, en colaboración con una asociación de jugadores en rehabilitación, asociaciones vecinales y el equipo docente del centro