Test item taxonomy based of functional criteria

There are many taxonomies that try to classify and apply some consistency to the very many item types currently in existence. They all have various limitations, however, such as ambiguous classification criteria, little discrimination between format types, and referring almost exclusively to pen-and-paper or screen-based items. This paper aims to overcome these limitations by proposing a new item format taxonomy based on functional criteria. Current classifications are reviewed, the criteria they are based on are examined and their limitations are identified. The proposed alternative classification identifies four essential components of items according to function: the structure of the included content, the device used for transmission of the question to the examinee, the device for receiving the response, and the instructions to the examinee about how to understand and respond to the item. The combination of different facets of these four components allows any format of item to be classified, both existing formats and those that may appear in the future. In addition to systematically and coherently classifying items, this new taxonomy may also be of great utility in the construction and research of new items. The proposed model is illustrated by examples showing how specific items are classified, using a checklist as a guide.Ministerio de Economía y Competitividad de España PSI2014-56114-PMinisterio de Economía y Competitividad de España PSI2017-85724-

El aula virtual de la UAM-A: entre tecnologías, actores y conocimiento

Situándose en el paradigma tecnológico organizado en torno a las TIC, la educación virtual puede entenderse como una experiencia social que se construye en el marco del conocimiento de una nueva tecnología, la cual es utilizada por diferentes actores para reforzar o mejorar sus procesos de enseñanza por un lado y, por el otro, sus experiencias de aprendizaje. Entender la construcción de esta nueva práctica en la universidad, a partir del uso de un instrumento tecnológico, pone de manifiesto las tendencias y el desarrollo futuro de las capacidades de una organización, como lo es la universitaria, donde los actores van generando pautas de permanencia, crecimiento y redefinición, estando de por medio la gestión de los flujos de conocimiento, así como cierto conjunto de actividades o procesos que pueden ser planeados, organizados, dirigidos y medidos, en los cuales participan diversos actores dispuestos a colaborar y a prepararse para ello.Standing in the technological paradigm organized around ICT, virtual education can be understood as a social experience that is built into the framework of knowledge of new technology, which is used by various stakeholders to strengthen or improve their processes education on the one hand and, on the other, their learning experiences. Understanding the construction of this new practice in college, from the use of a technological tool, shows trends and future development of the capabilities of an organization, such as the university, where actors stay patterns are generated, growth and redefinition, being in between the management of knowledge flows as well as a set of activities or processes that can be planned, organized, directed and measured, in which various actors involved are willing to collaborate and prepare for it

On the property (C) of Corson and other sequential properties of Banach spaces

A well-known result of R. Pol states that a Banach space X has property (C) of Corson if and only if every point in the weak*-closure of any convex set C ⊆ BX∗ is actually in the weak*-closure of a countable subset of C. Nevertheless, it is an open problem whether this is in turn equivalent to the countable tightness of BX∗ with respect to the weak*-topology. Frankiewicz, Plebanek and Ryll-Nardzewski provided an affirmative answer under MA + ¬CH for the class of C(K)-spaces. In this article we provide a partial extension of this latter result by showing that under the Proper Forcing Axiom (PFA) the following conditions are equivalent for an arbitrary Banach space X: (1) X has property E′; (2) X has weak*-sequential dual ball; (3) X has property (C) of Corson; (4) (BX∗ , w∗) has countable tightness. This provides a partial extension of a former result of Arhangel’skii. In addition, we show that every Banach space with property E′ has weak*-convex block compact dual ball.The first author was partially supported by Fundación Séneca - ACyT Región de Murcia (grant 21955/PI/22) and by Agencia Estatal de Investigación and EDRF/FEDER “A way of making Europe" (MCIN/AEI/10.13039/501100011033) (grant PID2021-122126NB-C32). The second author is funded by the Center of Mathematical Sciences and Applications at Harvard University

On Weak∗-Extensible Subspaces of Banach Spaces

Let X be a Banach space and Y⊆X be a closed subspace. We prove that if the quotient X/Y is weakly Lindelöf determined or weak Asplund, then for every w∗-convergent sequence (y∗n)n∈N in Y∗ there exist a subsequence (y∗nk)k∈N and a w∗-convergent sequence (x∗k)k∈N in X∗ such that x∗k|Y=y∗nk for all k∈N. As an application, we obtain that Y is Grothendieck whenever X is Grothendieck and X/Y is reflexive, which answers a question raised by González and Kania.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The research is partially supported by Agencia Estatal de Investigación [MTM2017-86182-P, grant cofunded by ERDF, EU] and Fundación Séneca [20797/PI/18]. The research of G. Martínez-Cervantes was also partially supported by the European Social Fund and the Youth European Initiative under Fundación Séneca [21319/PDGI/19]

Experiences of Mexican teenage students when choosing a math degree: a mathematical narrative identity study

There is little qualitative research on mathematics education focused on the experiences of young students when choosing a mathematics degree and how these experiences are assimilated into their mathematics life stories. The objective of this narrative inquiry is to identify the experiences of Mexican students who choose a mathematics degree through their mathematics life story. The conceptualization of a mathematical narrative identity divided into motivations, sources of motivation, and expectations allowed the identification of the following: (1) motivation of Mexican students for choosing a math degree, (2) sources of this motivation, and (3) future expectations related to this choice. This qualitative study was conducted based on a case study to prepare an in-depth analysis of multiple cases and frame them into a general description. Data was gathered from 47 interviews to collect students’ mathematics life stories. The four thematic analyses gave the following results: (1) the three main motivations were “liking mathematics”, self-efficacy belief, and the desire to become a “good teacher”, (2) the two main expectations were “being a good teacher” and “learning more mathematics”, and (3) the four main sources of motivations were self-efficacy belief, having “good teachers”, indirect experiences, and mastering knowledge. Results have similarities with the importance of self-efficacy beliefs and differences between “liking mathematics” and the desire to become a “good teacher” regarding the psychological explanations about the motivational forces to choose a math degree