Cómo estudiantes para profesor interpretan el pensamiento matemático de los estudiantes de Bachillerato: la derivada de una función en un punto

El objetivo de esta investigación es caracterizar grados de desarrollo de la competencia docente “mirar con sentido” el pensamiento matemático de los estudiantes en el ámbito específico de la derivada de una función en un punto. A partir de los resultados de las investigaciones previas sobre la derivada diseñamos un cuestionario formado por tres tareas a partir de las respuestas de estudiantes a 3 problemas sobre el concepto de derivada en un punto. Los resultados han permitido generar descriptores de niveles de desarrollo de la competencia docente “mirar con sentido” el pensamiento matemático de los estudiantes. Estos resultados aportan información para el diseño de intervenciones en la formación de profesores de matemáticas que tengan como uno de sus objetivos el desarrollo de la competencia docente “mirar con sentido” el pensamiento matemático de los estudiantes.

Psychometric properties of the School Anxiety Inventory-Short Version in Spanish secondary education students

Background: The School Anxiety Inventory (SAI) can be applied in different fields of psychology. However, due to the inventory’s administration time, it may not be useful in certain situations. To address this concern, the present study developed a short version of the SAI (the SAI-SV). Method: This study examined the reliability and validity evidence drawn from the scores of the School Anxiety Inventory-Short Version (SAI-SV) using a sample of 2,367 (47.91% boys) Spanish secondary school students, ranging from 12 to 18 years of age. To analyze the dimensional structure of the SAI-SV, exploratory and confirmatory factor analyses were applied. Internal consistency and test-retest reliability were calculated for SAISV scores. Results: A correlated three-factor structure related to school situations (Anxiety about Aggression, Anxiety about Social Evaluation, and Anxiety about Academic Failure) and a three-factor structure related to the response systems of anxiety (Physiological Anxiety, Cognitive Anxiety, and Behavioral Anxiety) were identified and supported. The internal consistency and test-retest reliability were determined to be appropriate. Conclusions: The reliability and validity evidence based on the internal structure of SAI-SV scores was satisfactory.

Competències mediàtiques a l’IES Dr. Balmis d’Alacant

La introducció de les TIC en l’ensenyament (les TAC) planteja molts interrogants entre els membres de la comunitat educativa, especialment entre el professorat. L’atracció del mitjà per als aprenents, la manca de reflexió en l’ús, tant per part del professorat com de l’alumnat, la necessitat d’una formació específica, l’adequació de les infraestructures al concepte i a les possibilitats que ofereix el web 2.0 i la incorporació de les aplicacions TAC en les programacions d’aula són alguns aspectes que mereixen una atenció específica i una anàlisi detinguda. La base de gran part de les respostes rau en una planificació eficaç de la formació del professorat que satisfaça les expectatives de tothom. Els projectes de centre, la utilització de plataformes educatives com Moodle i l’autoformació són sendes que ens acosten envers les solucions. En aquest treball, hi centrem l’atenció en les valoracions, les pràctiques habituals, les actituds i els coneixements relacionats amb la competència mediàtica o digital del professorat de l’IES Dr. Balmis d’Alacant. Ens basem en una enquesta realitzada en línia que aplega aquests continguts en una combinació d’ítems de resposta tancada i d’altres de resposta oberta.

Directory, school officials and teachers, State of Maryland.

Mode of access: Internet.

Mathematics for the elementary school [grades 4-6]

Each grade consists of a set of 3 v. (pt.1, Text [1 v.]--pt.2, Teacher's commentary [2 v.]).

Home, school and community partnerships to support children's numeracy

Presents the findings of a study in Australia which focused on the collaboration between home, school and community that support numeracy development in children. Aims of the project; Framework used in the analysis of various partnerships between the social institutions; Ways in which the partnerships can be initiated; Concerns that are essential in building and sustaining long-term partnerships to support children's numeracy development.

Variation talk: Articulating meaning in statistics

Little is known about the way that teachers articulate notions of variation in their own words. The study reported here was conducted with 17 prospective secondary math and science teachers enrolled in a preservice teacher education course which engaged them in statistical inquiry of testing data. This qualitative study examines how these preservice teachers articulated notions of variation as they compared two distributions. Although the teachers made use of tandard statistical language, they also expressed rich views of variation through nonstandard terminology. This paper details the statistical language used by the rospective teachers, categorizing both standard and nonstandard expressions. Their nonstandard language revealed strong relationships between expressions of variation and expressions of distribution. Implications and the benefits of nonstandard language in statistics are outlined.

'Please Mr Hay, what are my poss(abilities)?': Legitimation of ability through physical education practices

This paper provides two vignettes that draw on data from projects that interrogate how a student can be positioned by practices within physical education (PE) and directed by the PE teacher in relation to their valued or legitimated ability. Through the use of Pierre Bourdieu's conceptual tools of field, habitus and capital we investigate the complex legitimation processes that shape student poss(abilities) and that are situated in the space of the PE class. The first vignette is from the perspective of a student and draws on data from interviews, a journal, questionnaires and photos of her PE experiences in upper primary and lower secondary school. The second vignette focuses on teacher practices and his constitution of the field of a PE class highlighting the significance of teacher perspectives of 'ability' in informing assessment in senior secondary PE. Using these examples we discuss the symbolic violence that works against each student by positioning them as 'less able' or 'unable' despite their participation in a learning context. We argue that by not attending to the possible abilities of students that could have been recognized, developed and legitimated, and through the misuse of capital assignment by teachers, PE may well be counterproductive to students' ongoing engagement with the subject area and the espoused potential upon which such a subject area justifies itself.

PROJETOS EDUCATIVOS COMO FACILITADORES DO ENSINO-APRENDIZAGEM

A experiência tem demonstrado que projetos educativos facilitam o processo de ensino-aprendizagem. Por isso, esta pesquisa teve como objetivo verificar as possibilidades, os limites e os obstáculos enfrentados pelo professor ao trabalhar com projetos educativos. Para tanto, foi feito um estudo de caso em uma escola do município de São Paulo em que os professores possuem como prática o desenvolvimento de projetos. Foram selecionados cinco deles: Ler e Escrever , Xadrez na Escola , Nas Ondas do Rádio pertencentes ao programa da Secretaria Municipal de Educação de São Paulo, e que constam nos projetos político-pedagógicos das escolas da rede desde 2006 e A Caixa de Pandora e Azulejos no Metrô , que aconteceram no ano de 2010. Estes dois últimos não pertencem ao projeto político-pedagógico da escola, mas foram selecionados para este estudo pelo grande número de alunos que envolvem e por terem ultrapassado os muros da instituição. Com base na teoria de vários autores, principalmente Fernando Hernández, que traz a proposta de organização do currículo integrado por meio de projetos de trabalho, e Ulisses F. Araújo, que trata da construção de valores e da influência da afetividade na formação do aluno, e considerando a prática docente e o papel importante do educador, refletiu-se sobre como os projetos educativos contribuem para o aumento do rendimento escolar. De cunho qualitativo, a pesquisa foi desenvolvida tendo como principais técnicas a leitura e a análise de documentos, fotos e vídeos, bem como entrevistas e questionários para professores e alunos. Os resultados apontam para a estratégia de projetos desenvolvida na escola objeto de estudo ela incorpora alguns elementos relativos às teorias utilizadas e para o fato de que a prática docente pode contribuir para a implantação de ações pedagógicas que auxiliam na aquisição do conhecimento e no desenvolvimento de valores, ações que caminham em direção das ideias de interdisciplinaridade e transversalidade.

Teachers' conceptions of their role

An analysis is made of the conceptions which serving teachers have of their role, though no attempt is made to relate this to their practice of teaching. A series of role items was collected to afford a description of the teacher's role in terms of school and society expectations as well as classroom behaviours. These were taken from the literature and from interviews with teachers, and confirmed in a preliminary survey. Presented as a questionnaire, replies to the main investigation were made by 881 teachers, working in a variety of schools from nurseries to comprehensives. Two attempts have been made to construct a role model. The first, depending on the judgement of items fitting theoretically derived roles, failed, due to diffuseness in the role of teacher. The second used factor analysis; six factors were extracted which represent meaningful and distinct areas of role. The analysis has depended largely on examination of scores taken from these factors. Teachers in all types of school have similar conceptions of discipline. Nursery-infant and junior staff generally agree on the other areas investigated, but the concepts of secondary teachers are distinct. They are more conservative and less child-centered. When the class being taught is held constant, few differences in role conception are found to be related to sex, being a parent, graduate status, or personality, as measured in terms of the extrovert and neurotic dimensions. The first few years of teaching bring considerable changes in role conception, and further changes occur with prolonged experience. Deputy heads in junior schools and nursery nurses have quite distinct role conceptions; those of all other teachers, including those holding senior posts in secondary schools, are similar. The perception of school climate influences the role conception of primary teachers directly, but it does not influence that of secondary teachers. The greatest variation in role conception is related to scores on the radical scale of Oliver and Butcher. Primary school teachers experience little constraint, but that reported by secondary school teachers is considerable, especially that coming from the head. Despite difficulties caused by the wide division between primary and secondary education, teachers have an accurate perception of the roles their colleagues adopt. A few misunderstandings may be due to a feeling of idealism amongst nursery and infant teachers. There is evidence in their conception of role that would enhance the professional standing of teachers, but this is not in a form which is likely to be recognised by the public.

School children's attitudes towards computers as a fucntion of gender, course subjects and availability of home computers

The attitudes of 328 British Secondary School children towards computers were examined in a cross-sectional survey. Measures of both general attitudes towards computers and affective reactions towards working with computers were examined in relation to the sex of the subject, courses studied (computer related/noncomputer related) and availability of a home computer. A differential pattern of results was observed. With respect to general attitudes towards computers, main effects were found for all three independent variables indicating that more favourable attitudes increased as a function of being male, doing computer courses and having a home computer. In contrast to this, affective reactions to working with computers was primarily related to doing computer courses, such that those doing computer courses reported more positive and less negative reactions. The practical and theoretical implications of these results are discussed.

Percent in a Nutshell …

Ironically, the “learning of percent” is one of the most problematic aspects of school mathematics. In our view, these difficulties are not associated with the arithmetic aspects of the “percent problems”, but mostly with two methodological issues: firstly, providing students with a simple and accurate understanding of the rationale behind the use of percent, and secondly - overcoming the psychological complexities of the fluent and comprehensive understanding by the students of the sometimes specific wordings of “percent problems”. Before we talk about percent, it is necessary to acquaint students with a much more fundamental and important (regrettably, not covered by the school syllabus) classical concepts of quantitative and qualitative comparison of values, to give students the opportunity to learn the relevant standard terminology and become accustomed to conventional turns of speech. Further, it makes sense to briefly touch on the issue (important in its own right) of different representations of numbers. Percent is just one of the technical, but common forms of data representation: p% = p × % = p × 0.01 = p × 1/100 = p/100 = p × 10-2 "Percent problems” are involved in just two cases: I. The ratio of a variation m to the standard M II. The relative deviation of a variation m from the standard M The hardest and most essential in each specific "percent problem” is not the routine arithmetic actions involved, but the ability to figure out, to clearly understand which of the variables involved in the problem instructions is the standard and which is the variation. And in the first place, this is what teachers need to patiently and persistently teach their students. As a matter of fact, most primary school pupils are not yet quite ready for the lexical specificity of “percent problems”. ....Math teachers should closely, hand in hand with their students, carry out a linguistic analysis of the wording of each problem ... Schoolchildren must firmly understand that a comparison of objects is only meaningful when we speak about properties which can be objectively expressed in terms of actual numerical characteristics. In our opinion, an adequate acquisition of the teaching unit on percent cannot be achieved in primary school due to objective psychological specificities related to this age and because of the level of general training of students. Yet, if we want to make this topic truly accessible and practically useful, it should be taught in high school. A final question to the reader (quickly, please): What is greater: % of e or e% of Pi