A classification scheme for radar target recognition based on natural-resonances and principal-component analysis named as NRPCA is described and tested. It uses a multilayer perceptron (MLP) neural network as classifier and complex natural resonances (CNRs) as inputs to the net. The benefit of using natural resonances is that they are aspect-angle independent. Nevertheless, the extraction process of natural resonances is an ill-conditioned problem and noise affects the estimation of the parameters. To reduce this noise sensitivity the NRPCA algorithm extracts the resonances from a reconstructed response generated by a principal-component analysis (PCA) stage over a set of reference targets prior to the MLP neural network classifier. Furthermore, NRPCA uses the step time response instead of impulse time response to minimize any error in CNR extraction process (matrix pencil method). To test the NRPCA algorithm several geometrical conducting bodies are used as reference targets of a radar system.

Understanding statistical tables is a main component of statistical literacy, although related research dealing with secondary school students is scarce. The purpose of this study was to investigate secondary school students’ performance when translating graphs to tables and then interpreting the resulting table. Using content analysis of the responses to a questionnaire given to a sample of Spanish students, we analysed the correctness of the constructed table, the semiotic conflicts that appeared in their construction, the interpretation of the table elements, the ability to argue on the basis of the information in the table, and the reading level exhibited by the student in this task. Most students correctly translated a pictogram to a frequency table, and a half of them a double bar graph to a two-way table. The main semiotic conflicts were misinterpretation of the icon in the pictogram and incorrect computation of marginal frequencies. About 40% of the sample correctly justified a statement using the data in the graph and then reached the upper reading level of the graph and table, but only a minority achieved that level when the question required knowledge of the context. The findings of the study suggested points to reinforce the teaching of statistical graphs and tables.

[Objective] The aim of this study is to evaluate the didactic-mathematical knowledge of prospective Spanish teachers about the sampling distribution of the mean – specifically, basic knowledge about content, as well as epistemic and cognitive aspects of didactic knowledge. [Methodology] A sample of prospective teachers were asked to solve a problem presented to students in the university’s entrance exams, to identify the concepts, properties and procedures required for its solution, and to describe the foreseeable errors of the students in this process. [Results] The results obtained showed very good levels of common mathematical knowledge, although some errors were observed, such as confusing population distributions with sampling distributions. The participants were reasonably competent in analyzing the mathematical objects (concepts, procedures and properties) required to solve the proposed task, but the level of competence in identifying possible student errors in solving the task was lower. [Conclusions] The study identifies areas for improvement in the training of prospective teachers about the sampling distribution of the mean, which should be well understood when making inferences. Such training should emphasize the difference between the three probability sampling distributions and the difference between statistics and parameters, since prospective teachers do not recognize the possibility of this type of error by their students.

En este trabajo partimos de la idea de sentido estadístico, como unión de la cultura y el razonamiento estadístico, particularizándola para el caso de los gráficos estadísticos y describiendo sus componentes. Argumentamos la especial importancia del sentido gráfico en la actual etapa marcada por la pandemia del COVID-19, debido a la necesidad de interpretar información estadística presentada en gráficos de diverso tipo en los medios de comunicación y actualizada a diario, para comprender y colaborar con las decisiones de las autoridades sanitarias y políticas. Se analizan algunos ejemplos de gráficos asociados a la COVID presentados en los medios de comunicación, para clarificar las componentes del sentido gráfico, resaltando sus características dinámicas y multivariantes, no tenidas en cuenta en los gráficos incluidos en las directrices curriculares. Se concluye la necesidad de una mejor enseñanza de los gráficos y la utilidad de los gráficos estadísticos tomados de los medios de comunicación para motivar a los estudiantes y reforzar su sentido gráfico.

Resumen Actualmente, la inferencia estadística es un tema enseñado en el Bachillerato español y evaluado en los exámenes de acceso a la universidad, pero la preparación didáctica específica no es suficiente para los profesores encargados de la enseñanza del tema. El objetivo del trabajo es evaluar el conocimiento matemático común de este contenido y las facetas epistémica y cognitiva del conocimiento didáctico en una muestra de futuros profesores españoles. Con esta finalidad se les plantea la resolución de una tarea tomada de las pruebas de acceso a la universidad para estudiantes de Bachillerato y se les pide resolverla, identificar los objetos matemáticos requeridos en su solución y los posibles errores de los estudiantes en este proceso. Los resultados muestran un buen conocimiento matemático de los futuros profesores y un inicio de conocimiento en las facetas epistémica y cognitiva. No obstante, su identificación de objetos matemáticos y errores es escasa y prácticamente se restringe al aspecto procedimental. Concluimos la necesidad de reforzar la preparación en la didáctica de la inferencia de los futuros profesores.

In this communication, we present a new contribution to radar-target identification via the extinction-pulse (E-pulse) method. New E-pulses are built using exponential β-splines, which include in their construction free parameters that are adjusted to obtain more robust identification systems. The adjusting process is done by searching for the free parameters that maximize the discrimination capability of the system in the absence of noise. Simulation results justify the approach and show that the E-pulses obtained by maximization of the discrimination capability improve the results obtained with the classical scheme.