La promoción del pensamiento algebraico en alumnos de primaria requiere implementar acciones formativas específicas para los profesores, lo que a su vez implica elaborar instrumentos de evaluación del estado de sus conocimientos didáctico - matemáticos sobre el tema. En este trabajo presentamos resultados del estudio realizado para la construcción de un cuestionario de evaluación de los conocimientos didáctico - matemáticos de estudiantes de magisterio sobre razonamiento algebraico elemental. Describimos las categorías de conocimientos algebraicos tenidas en cuenta (estructuras, funciones y modelización) y las categorías de conocimientos didácticos (facetas epistémica, cognitiva, instruccional y ecológica). Así mismo se describen y analizan las tareas incluidas en el cuestionario informando de la validez de contenido del mismo.

The properties of hexose transport across the apical and basolateral membranes of chicken enterocytes have been studied in the small and large intestine. Results show that (a) isolated epithelial cells from all segments except the coprodeum can accumulate 3-O-methylglucose (Glc3Me) against a concentration gradient, by a Na(+)-dependent and phloridizin-sensitive mechanism. (b) The cell cumulative capacity for Glc3Me (control/phloridizin-incubated cells) is lower in the small intestine than in the large intestine (rectum = proximal caecum = ileum > jejunum > duodenum). (c) Theophylline enhances the cell Glc3Me cumulative capacity 2.9-fold in the duodenum and 2.4-fold in the jejunum but has no effect in the other segments studied. (d) Analysis of sugar uptake indicates that net hexose influx rates decrease from proximal to distal regions: jejunum > duodenum > ileum = proximal caecum = rectum for the apical transport system (alpha-methyl glucoside as substrate and phloridizin as inhibitor) and duodenum > jejunum > ileum = proximal caecum = rectum for the basolateral system (2-deoxyglucose; theophylline). (e) The duodenum and the jejunum show high apical and basolateral hexose transport rates, which confer a significant capacity for sugar absorption on the proximal intestine. More distal regions, including the ileum, the proximal caecum and the rectum, have transport systems analogous to those of the proximal intestine that keep a considerable potential capability to recover hexoses from the lumen.

It is widely known that mathematics and science are among the subjects that present the most learning difficulties for students. Another well-supported finding is that playing is one of the most important ways in which small children learn. In this context, a subject matter was newly developed in the final year of a Bachelor's Degree in Early Childhood Education, at the University of Granada (Spain), with the aim of applying play to the teaching of science and mathematics to children. The idea is to take advantage of the beneficial aspects of playing for the learning process, in order to improve science and mathematics education from early childhood. A study using both quantitative and qualitative methods was conducted to examine the pre-service teachers' conceptions of play, science, mathematics, and education. An open-ended questionnaire with four parts was used. The first and second parts were related to play and its social and educational implications, while the third part dealt with scientific and mathematical thinking. The last part concerned the relationships among play, science, mathematics, and education. After a qualitative analysis, on average, 17 emerging categories were found in each query and 18% of them was provided by each student teacher. The quantitative analysis of the data reveals that 79% of pre-service teachers referred to learning when asked about play, and also 71% alluded to social interactions among the children and the learning opportunities, concerning the social and educational implications of playing. For the student teachers, to interpret reality through abstractions (35%) and to experiment (29%) are the main characteristics of mathematics and science, respectively, and 29% emphasized daily-life aspects, too. The most relevant aspect (56%) regarding the relationships among play, science, mathematics, and education was that playing could develop scientific and mathematical thinking.

Background: Despite its social importance, the learning associated with STEAM thinking (science, technology, engineering, arts, and mathematics) we consider is not fully developed in classrooms. Objectives: This research proposes to promote STEAM skills through game-based learning.. Design: These were used to design an integrated educational proposal, called the Micro Play Project (MPL), following the principles of game-based learning and an intercultural approach focused on Ethnomathematics. Setting and Participants: This MPL was implemented in a Spanish school with small groups of students from Preschool and Primary Education, dedicating three sessions to each of the four games, which were recorded on video. Data collection and analysis: Studying the Jamaican culture, we discovered that the game is a relevant cultural sign in Jamaica, we compiled and analyzed its traditional games, generating a catalog, from which we selected four games, for their potential to develop STEAM learning at school .Qualitative-interpretive research was carried out through a case study and content analysis, using a proprietary tool. Results: they are diverse skills, artistic, scientific and mathematical manifested when playing, such as: musical sense, detection of similarities, ability to turn, identification of shapes, estimation of distances, formulation of hypotheses and establishment of relationships by criteria, which have confirmed the didactic potential of these games, in an environment of ethnomathematical intercultural education. Conclusions: The validity of the MPL as a didactic method to develop STEAM learning is deduced from the results. We hope to strengthen and spread this method by making new elaborations and applications of MPL.

According to previous research, we consider it necessary to extend the use of games, as mediating elements, in the learning of STEAM (Science, Technology, Engineering, Arts and Mathematics) contents rejected by many students. For this, we have carried out an educational research project on games, with an ethnomathematical approach, since games are an important cultural sign with mathematical and scientific potentialities. We have prepared an anthropological study and an analytical one, generating a catalogue of games from different cultures. Thus, we have verified that, starting with culture, we can get to the game, but we posed the query as to whether, starting from certain games, we could achieve enculturation, by activating mathematical and scientific content in the players. To answer this query, we have created a curricular design called “playful microproject” with three traditional games from different cultures and geographical contexts. The microproject was implemented with 32 participants, from 8 to 12 years old. To analyse the results of the microproject, a case study was carried out using qualitative methodology. As part of the playful microproject, the necessary materials for each game were made by hand, and the games were then played. Both the realization of the games and the act of playing showed evidence of mathematical and scientific content, although more in the act of playing. The results revealed that: (1) the three games mobilized 21 categories of analysis, made up of scientific-mathematical content; (2) the three games proved to be equivalent in strong didactic potential; (3) that the microproject provides a valuable intercultural educational approach. The contents evidenced constitute a fundamental part of the Primary Education curriculum: classify, organize, measure, and quantify items, as well as formulate hypotheses, draw conclusions, place oneself in space, and design strategies, among others. It is concluded that these games can promote scientific-mathematical enculturation in a contextualized way.