Early Childhood Mathematics Education: Research, Curriculum and Educational Practice

This article reviews data obtained through research into early childhood mathematics education in Spain. It analyses the current curricular directions in mathematics education with early learners. It also provides an overview of mathematical practices in early childhood education classrooms to analyse the commonalities and differences between research, curriculum and educational practice. A review of the research presented at SEIEM symposia from 1997 until 2012 demonstrates: a) very little research has been done, a trend that is repeated in other areas, such as the JCR-Social Sciences Edition or the PME; b) the first steps have been taken to create a more and more cohesive body of research, although until now there has not been enough data to outline the curricular directions; and c) some discrepancies still exist between the mathematical practices in early childhood education classrooms and the official guidelines

Un análisis optimista de la educación matemática en la formación de maestros de educación infantil = An optimistic analysis of mathematics education in training pre-school teachers

This article offers a panorama of mathematics training for future teachers at pre-school level in Spain. With this goal in mind, this article is structured infour sections: where we come from, where we are, where we’re going and where we want to go. It offers, in short, a brief analysis that shows the efforts made to ensure there is sufficient academic and scientific rigour in teachers’ studies at pre-school in general and students’ mathematics education in particular. Together with a description of the progress made in recent years, it also raises some questions for all those involved in training future teachers for this educational stage

A Spanish version of the short Mathematics Anxiety Rating Scale (sMARS)

The aim of this studywas to adapt and assess the psychometric properties of the Spanish version of the sMARS in terms of evidence of validity and reliability of scores. The sMARS was administered to 342 students and, in order to assess convergent and discriminant validity, several subsamples completed a series of related tests. The factorial structure of the sMARSwas analyzed by means of a confirmatory factor analysis and results showed that the three-factor structure reported in the original test fits well with the data. Thus, three dimensions were established in the test: math test, numerical task and math course anxiety. The results of this study provide sound evidence that demonstrates the good psychometric properties of the scores of the Spanish version of the sMARS: strong internal consistency, high 7-week testretest reliability and good convergent/discriminant validity were evident. Overall, this study provides an instrument that allows us to obtain valid and reliable math anxiety measurements. This instrument may be a useful tool for educators and psychologists interested in identifying individuals that may have a low level of math mastery because of their anxiety.

Effects of math anxiety on student success in higher education

This study examines whether math anxiety and negative attitudes toward mathematics have an effect on university students" academic achievement in a methodological course forming part of their degree. A total of 193 students were presented with a math anxiety test and some questions about their enjoyment, self-confidence and motivation regarding mathematics, and their responses were assessed in relation to the grades they had obtained during continuous assessment on a course entitled"Research Design". Results showed that low performance on the course was related to math anxiety and negative attitudes toward mathematics. We suggest that these factors may affect students" performance and should therefore be taken into account in attempts to improve students" learning processes in methodological courses of this kind.

Why Mathematics is essential in Biomedical Sciences degree?

Improvement of mathematical education and motivation of students in the mathematics" area is needed. What can be done? We introduce some ideas to generate the student"s interest for mathematics, because they often present difficulties in appreciating the relevance of mathematics and its role in the health sciences. We consider that a cornerstone in the strategy to attract the students" interest is linking the mathematics with real biomedical situations. We proceed in the following manner: We first present a real biomedical situation to produce interest and to generate curiosity. Second, we ask thought-provoking questions to students as: Which is the biomedical problem presented? Which is my knowledge on this situation? What could I do to solve this biomedical situation? Do I need some new mathematical concepts and procedures? Thereupon, the teacher explains the mathematical concepts necessary to solve the case presented, providing definitions, properties and tools for graphical display and/or mathematical calculations. In this learning methodology, ICTs were cornerstones for reaching the proposed competences. Furthermore, ICTs can also be used in the evaluative task in its two possible aspects: formative and for obtaining a qualification. Comments from students about this new mathematics teaching method indicate that the use of real biomedical case studies kept the lessons in mathematics interesting.

Els llibres de text de matemàtiques en llengua catalana durant el periode 1899-1938

Les investigacions que tracten d'una manera sistematica l'estudi deis llibres de text de matematiques antics són escasses. Hi ha un projecte internacional ambiciós sobre I'analisi comparativa deis manual s més significatius deis diferents pa'isos europeus deis segles XVIII i XIX. Si ens cenyim a l'Estat espanyol, s'estan realitzant investigacions sobre els programes i textos matematics corresponents a l'ensenyament secundari del segle XIX. Tot i així, manquen estudis que facin referencia a I'ensenyament primari i a I'ensenyament professional, i ens trobem que on hi ha més mancana és en la labor de base, és a dir, en la recopilació completa i l'analisi deis textos. Aquesta labor es troba aturada per la dificultat de poder accedir a aquest material.

Matemàtiques a distància: anàlisi de dues experiències

Els invents del teléfon i la televisió i la feina deis carters van popularitzar un treball de formació anomenat usualment ensenyament per correspondencia. Amb aixb es tractava d'eixamplar I'educació per a tothom qui no pogués seguir el ritme de I'escola oficial. Ara, I'ús de la informatica ens permet anar més Iluny i parlem d'educació a distancia i telematica educativa (vegeu el monografic TE, 16). En particular, fer matematiques a distancia té com a objectiu facilitar I'accés a processos formatius a una part de la població que, d'altra forma, tindria dificultats per fer-ho: malalts, persones grans, interns a les presons, etc.

Crònica d'una reforma: Curricula de matemàtiques

L'any 2000 -Any Internacional de les Matematiques- ha provocat i provocara multitud d'actes, publicacions, jornades i congressos promoguts pels qui les valoren i les estimen, amb la intenció d'apropar-Ies a la major quantitat de gent possible. Per aquest col·lectiu, les matematiques són una manifestació cultural i, com a tal, patrimoni de la humanitat. Si qualsevol moment és bo per meditar sobre el passat, el present i el futur, ara és un moment ideal per fer-ho sobre I'educació matematica en el nostre país, amb una reforma educativa en marxa. El present de I'ensenyament de les matematiques és extremadament divers, cosa que fa impossible una descripció acurada d'on som i cap a on anem. Pero tot present té un passat proper que ajuda a entendre'l i que dóna eines per prendre decisions de cara al futuro La meva implicació en el procés de la reforma educativa que s'esta duent a terme m'impossibilita de fer-ne una descripció plenament objectiva, així que donaré la meva visió personal d'aquest projecte tan complex amb la intenció de proporcionar, d'una banda, informació sobre alguns fets rellevants i, de I'altra, elements de reflexió sobre el que pot representar per a l'estament educatiu el camí cap a la renovació professional. En aquest itinerari m'aturaré en les causes de la reforma, les intencions i les condicions per a I'éxit. Les consideracions sobre el passat que no es vol que torni i I'analisi que farem del present portara de manera natural a les propostes per al futuro.

L'error com a forma de coneixement

" Has comes un error" . " Estas en un error" . " És un error votar aquest parti!" . " És un error votar" . " És un error afirmar que 2 + 3 = 9" . " És un error afirmar que és un error afirmar que 2 + 3 = 5" . " És un error afirmar que, quan dividim, sempre obtenim un nombre més petit" . " És un error que l'existencia precedeixi l'essencia" . " És un error que vulguis enganyar-me" . " És un error afirmar que a = a" ... i així fins a acomplir les il'limitades possibilitats del llenguatge. Qualsevol judici, en la mesura que té un significat, en la mesura que és assertori, és susceptible de ser erroni, de ser fals. Peró, l'error té sempre la mateixa qualitat? Us hem proposat un reguitzell d'exemples. És obvi (si excloem la mentida, que no és error, sinó mentida) que el significat d'" error" (o el seu valor) no és identic en tots els casos.

Un estudio comparado de las actitudes hacia la estadística en profesores en formación y en ejercicio

En este trabajo presentamos los resultados de una escala de actitudes en una muestra de 66 profesores en ejercicio y 74 profesores en educación infantil y primaria. No encontramos diferencias por géneros, aunque sí una mejoría en aquellos alumnos que estudiaron estadística previamente. La actitud es algo mejor en los profesores en ejercicio, aunque tiende a empeorar con el uso o la enseñanza de la estadística. Pensamos que estos resultados sugieren la dificultad que tiene dicha materia para los profesores y la necesidad de apoyo que éstos deberían recibir desde los departamentos de didáctica y tas facultades de educación.

La Superación de la Adversidad en el Aprendizaje Matemático

Superar la adversidad en el ámbito de la formación matemática tiene una traducción inmediata: la resolución de problemas. Un problema es un obstáculo a superar sin conocer una estrategia de antemano. Su resolución requiere de la creatividad una combinación adecuada de propiedades, relaciones y datos. A pesar de que la argumentación se rija por la lógica, ésta no sirve para llegar a la solución, no es suficiente. Para mejorar esta capacidad de superar adversidades, sería necesario programar una serie de actividades pero siempre respetando los diferentes ritmos de aprendizaje, en función del conocimiento, actitud e implicación. Si se consigue motivar al alumnado, se conseguirá una mayor implicación por parte de éste. Consecuentemente, aumentará el aprendizaje en estrategias de resolución. Estas estrategias solucionarán problemas particulares, pero aportarán un importante bagaje de cara a nuevos problemas.

Abnormal Error Monitoring in Math-Anxious Individuals: Evidence from Error-Related Brain Potentials.

This study used event-related brain potentials to investigate whether math anxiety is related to abnormal error monitoring processing. Seventeen high math-anxious (HMA) and seventeen low math-anxious (LMA) individuals were presented with a numerical and a classical Stroop task. Groups did not differ in terms of trait or state anxiety. We found enhanced error-related negativity (ERN) in the HMA group when subjects committed an error on the numerical Stroop task, but not on the classical Stroop task. Groups did not differ in terms of the correct-related negativity component (CRN), the error positivity component (Pe), classical behavioral measures or post-error measures. The amplitude of the ERN was negatively related to participants" math anxiety scores, showing a more negative amplitude as the score increased. Moreover, using standardized low resolution electromagnetic tomography (sLORETA) we found greater activation of the insula in errors on a numerical task as compared to errors in a nonnumerical task only for the HMA group. The results were interpreted according to the motivational significance theory of the ERN.

Reactive Recruitment of Attentional Control in Math Anxiety: An ERP Study of Numeric Conflict Monitoring and Adaptation

This study uses event-related brain potentials (ERPs) to investigate the electrophysiological correlates of numeric conflict monitoring in math-anxious individuals, by analyzing whether math anxiety is related to abnormal processing in early conflict detection (as shown by the N450 component) and/or in a later, response-related stage of processing (as shown by the conflict sustained potential; Conflict-SP). Conflict adaptation effects were also studied by analyzing the effect of the previous trial"s congruence in current interference. To this end, 17 low math-anxious (LMA)and 17 high math-anxious (HMA) individuals were presented with a numerical Stroop task. Groups were extreme in math anxiety but did not differ in trait or state anxiety or in simple math ability. The interference effect of the current trial (incongruent-congruent) and the interference effect preceded by congruence and by incongruity were analyzed both for behavioral measures and for ERPs. A greater interference effect was found for response times in the HMA group than in the LMA one. Regarding ERPs, the LMA group showed a greater N450 component for the interference effect preceded by congruence than when preceded by incongruity, while the HMA group showed greater Conflict-SP amplitude for the interference effect preceded by congruence than when preceded by incongruity. Our study showed that the electrophysiological correlates of numeric interference in HMA individuals comprise the absence of a conflict adaptation effect in the first stage of conflict processing (N450) and an abnormal subsequent up-regulation of cognitive control in order to overcome the conflict (Conflict-SP). More concretely, our study shows that math anxiety is related to a reactive and compensatory recruitment of control resources that is implemented only when previously exposed to a stimuli presenting conflicting information

Pere Puig i Adam: ahir, avui i sempre

El tema central d'aquesta Lliçó serà doncs la figura emblemàtica del gran professor i matemàtic català Pere Puig i Adam (1900-1960). Si bé el centenari del seu naixement ja justifica per si mateix l'oportunitat de l'homenatge, hi ha un valor afegit al fet de parlar d'en Pere Puig i Adam : tots nosaltres com a catalans i com a gent de Matemàtiques podem unir a l'orgull de rememorar una figura senyera del nostre passat científic, el goig de conservar avui el seu patrimoni i el deure de projectar el seu exemple vers el nostre futur. Així doncs parlarem de qui va ser i qué va fer en Pere Puig i Adam, per després analitzar, amb ulls d'avui, la vigència i possible projecció del seu llegat.

El deporte como instrumento de desarrollo de la capacidad crítica de los adolescentes. Experiencias realizadas en cuatro centros de secundaria = Sport as a tool in the development of critical capacity of teenagers. Experiments carried out in four centres of Secondary education

In the article we resume four experiments of an interdisciplinary nature carried out in four different secondary education centres. The nexus of the union of these didactic proposals is that of looking at values in sport and the critical capacity of the students from distinct perspectives: violence, mass media, politics and gender and the treatment of body in our society