An investigation of post-primary students' images of mathematics

This research study investigates the image of mathematics held by 5th-year post-primary students in Ireland. For this study, “image of mathematics” is conceptualized as a mental representation or view of mathematics, presumably constructed as a result of past experiences, mediated through school, parents, peers or society. It is also understood to include attitudes, beliefs, emotions, self-concept and motivation in relation to mathematics. This study explores the image of mathematics held by a sample of 356 5th-year students studying ordinary level mathematics. Students were aged between 15 and 18 years. In addition, this study examines the factors influencing students‟ images of mathematics and the possible reasons for students choosing not to study higher level mathematics for the Leaving Certificate. The design for this study is chiefly explorative. A questionnaire survey was created containing both quantitative and qualitative methods to investigate the research interest. The quantitative aspect incorporated eight pre-established scales to examine students‟ attitudes, beliefs, emotions, self-concept and motivation regarding mathematics. The qualitative element explored students‟ past experiences of mathematics, their causal attributions for success or failure in mathematics and their influences in mathematics. The quantitative and qualitative data was analysed for all students and also for students grouped by gender, prior achievement, type of post-primary school attending, co-educational status of the post-primary school and the attendance of a Project Maths pilot school. Students‟ images of mathematics were seen to be strongly indicated by their attitudes (enjoyment and value), beliefs, motivation, self-concept and anxiety, with each of these elements strongly correlated with each other, particularly self-concept and anxiety. Students‟ current images of mathematics were found to be influenced by their past experiences of mathematics, by their mathematics teachers, parents and peers, and by their prior mathematical achievement. Gender differences occur for students in their images of mathematics, with males having more positive images of mathematics than females and this is most noticeable with regards to anxiety about mathematics. Mathematics anxiety was identified as a possible reason for the low number of students continuing with higher level mathematics for the Leaving Certificate. Some students also expressed low mathematical self-concept with regards to higher level mathematics specifically. Students with low prior achievement in mathematics tended to believe that mathematics requires a natural ability which they do not possess. Rote-learning was found to be common among many students in the sample. The most positive image of mathematics held by students was the “problem-solving image”, with resulting implications for the new Project Maths syllabus in post-primary education. Findings from this research study provide important insights into the image of mathematics held by the sample of Irish post-primary students and make an innovative contribution to mathematics education research. In particular, findings contribute to the current national interest in Ireland in post-primary mathematics education, highlighting issues regarding the low uptake of higher level mathematics for the Leaving Certificate and also making a preliminary comparison between students who took part in the piloting of Project Maths and students who were more recently introduced to the new syllabus. This research study also holds implications for mathematics teachers, parents and the mathematics education community in Ireland, with some suggestions made on improving students‟ images of mathematics.

El Conjunt instrumental Orff com a dinamitzador de la motivació en els alumnes de música d’educació secundària

L’estudi que es presenta a continuació aporta una experiència a l’entorn de l’efectivitat del CIO com a material capaç d’incentivar un canvi en l’actitud i en la implicació de l’alumnat d’ESO cap a l’assignatura de música. Aquesta investigació va néixer com a conseqüència de la necessitat d’estimular la motivació personal dels alumnes de dos grups-classe d’ESO cap a la matèria després de detectar la manca d’interès i la facilitat amb què es distreien a l’aula. Aquesta percepció es va poder corroborar mitjançant la realització d’uns qüestionaris informals realitzats a finals del curs 2005-2006 on es demanava a l’alumnat que escrivissin tres aspectes positius i tres de negatius del que havien fet a l’assignatura durant aquell curs. Amb aquesta breu indagació es va confirmar que l’opinió més generalitzada entre l’alumnat era que s’avorrien sovint a les classes perquè eren massa teòriques. Arran d’aquests resultats, es va decidir canviar l’orientació de l’assignatura per tal d’estimular el “fer música” per davant de la “transmissió” de continguts més conceptuals. De les diverses opcions possibles, es va optar per introduir el CIO com a eina per fer possible aquest canvi, ja que algunes experiències educatives prèvies realitzades amb aquest tipus de material demostraven que la intervenció amb els instruments Orff podia contribuir a incrementar l’interès de l’alumnat cap a la matèria i alhora aportar nombrosos beneficis per a la pràctica musical

Simulando catástrofes : recursos para la enseñanza de los riesgos naturales

Los riesgos naturales son abordados por distintas asignaturas de ciencias naturales a lo largo de la ESO y el bachillerato. Su tratamiento en el aula es una evidencia del interés y el carácter aplicado de muchos aspectos de las ciencias de la tierra. Para facilitar su enfoque didáctico se proponen algunas actividades prácticas

Idoneidad didáctica de un protocolo sociocultural de enseñanza y aprendizaje de las matemáticas

En este estudio se evalúa la adecuación de un protocolo para la enseñanza del concepto de poliedro regular, destinado a alumnos de 14 y 15 años. Este protocolo se ha diseñado desde una perspectiva sociocultural y su evaluación se basa en la aplicación de los criterios de idoneidad didáctica que ofrece el enfoque ontosemiótico. La idoneidad se estudia con la revisión de sus diferentes dimensiones: matemática, cognitiva, interaccional, mediacional, emocional y ecológica. El análisis ha permitido detectar algunos factores que favorecen la validez del protocolo y la adecuación para su empleo en el aula, como el tipo de discurso, el uso de material manipulable o el trabajo cooperativo

Los Riesgos geológicos: algunas consideraciones didácticas

From the development of concepts related with Natural and Geological Hazards different exercises and activities are proposed. All of them can be used as didactic recourses in order to study such a subject for the most appropriate educative levels

Essentialism i religionsundervisningen : Ett religionsdidaktiskt problem

Essentialist concepts of religion are common in the teaching of religion in schools and to a certain extent also in the academic discipline of religious studies. In this article, a number of problems with essentialist perceptions of religion are discussed. In the first part of the article a thesis is maintained, according to which essentialist conceptions of religion or specific religions are too limited to be of value in the teaching of religion. This is done through examples of essentialist expressions about religion. The examples are grouped according to a typology of different kinds of essentialism. Two main categories, each with two sub-categories are identified. Thus, the category of essentialism regarding the substance of religion is divided into transcendental or theological essentialism (which presupposes the existence of a sacred power of some kind, the experience of which is the basis for religion), and core essentialism (where it is presupposed that certain ideas or concepts constitute religion as a general category or specific religions). Likewise, the category of essentialism regarding the function of religion has two sub-categories: positive and negative essentialism. These kinds of essentialism presuppose that religion or specific religions are inherently good or harmful respectively to human beings. Examples from each of these categories are given and discussed. In the second part of the article, Benson Saler’s open concept of religion is presented as an alternative to essentialist or bounded perceptions. It is based on Ludwig Wittgenstein’s idea of family resemblances and on prototype theory. In connection with this, it is argued that a certain kind of conscious ethnocentrism is needed as a point of departure in the study and teaching of religion. The metaphor of education as a journey from the familiar out into the unfamiliar and back again is suggested as a possible pattern for such teaching. Finally,some examples of non-essentialist ways to introduce religions are offered.

Determination of the optimal quantity of crop residues for energy in sugarcane crop management using linear programming in variety selection and planting strategy

The aim of this work was to present organizational models for optimizing the reduction of crop residue generated by the sugarcane culture. The first model consisted of the selection of varieties of sugarcane to be planted meeting the mill requirements and, at the same time, to minimize the quantity of residue produced. The second model discussed the use of residue to produce energy. This is related to the selection of variety and quantity to be planted, in order to meet the requirements of the mill, to reduce the quantity of residue, and to maximize as much as possible the energy production. The use of linear programming was proposed. The two models presented similar results in this study, and both may be used to define the varieties and areas to be cultivated. (C) 2001 Published by Elsevier B.V. Ltd.

Metabolite profiles of essential oils in citrus peels and their taxonomic implications

China is an important center of origin for the genus Citrus L. of the family Rutaceae and is rich in wild Citrus species. The taxonomy of Citrus has been a subject of controversy for more than a half century. We propose that the metabolite profiles of Chinese native Citrus species can be used for classification and understanding of the taxonomic relationships within the Citrus germplasm. In this study, triplicate gas chromatography-mass spectrometry (GC-MS) metabolite profiles of 20 Citrus species/varieties were acquired, including 10 native varieties originating in China. R-(+)-limonene, alpha-pinene, sabinene and alpha-terpinene were found to be major characteristic components of the essential oils analyzed in this study, and these compounds contributed greatly to the metabolic classification. The three basic species of the subgenus Eucitrus (Swingle's system), i.e., C. reticulata Blanco, C. medica L. and C. grandis Osb., were clearly differentiated based upon their metabolite profiles using hierarchical cluster analysis (HCA) and partial least square-discriminant analysis (PLS-DA). All the presumed hybrid genotypes, including sweet orange (C. sinensis Osb.), sour orange (C. aurantium L.), lemon (C. limon Burm.f.), rough lemon (C. jambhiri Lush.), rangpur lime (C. limonia Osb.) and grapefruit (C. paradisi Macf.), were grouped closely together with one of their suggested parent species in the HCA-dendrogram and the PLS-DA score plot. These results clearly demonstrated that the metabolite profiles of Citrus species could be utilized for the taxonomic classification of the genus and are complementary to the existing taxonomic evidence, especially for the identification and differentiation of hybrid species.