Educaçãdo matemática na realidade do ciberespaço - Que aspectos ontológicos e científicos se apresentam?

The question that leads this article is What is this virtual space in the on-line mathematics education process? We focus on the question of the real and virtual as issues taken as components of cyberspace. We investigate these notions in the history of philosophy, looking to Granger to find their meaning, to enable us to understand them and fit them into the sphere of Mathematics Education. This theoretical-philosophical article, then, claims that the virtuality of cyberspace is supported by the computer screen, built by the unification of the sciences (mathematics), technology and its applications. Software and the actions taken by Internet users update the capability of these programs in a variety of characteristics and possibilities such as space-time flow interconnections as well as during the mathematics education process.

Aula Web "Pensamiento Matemático". Un complemento a la enseñanza de las matemáticas

Al igual que otras asignaturas pero quizás de manera más pronunciada las matemáticas, están viendo reducidos en gran medida sus créditos en los nuevos planes de estudios. Por ello, ofertar acciones que posibiliten alcanzar competencias relacionadas con esta y otras ciencias básicas resulta de gran utilidad. Con este propósito, desde el Grupo de Innovación Educativa de la Universidad Politécnica de Madrid “Pensamiento Matemático”, se ofrece a los alumnos un “Aula de Pensamiento Matemático”. En ella se presentan una serie de actividades on-line que permiten la capacitación de los alumnos en diversas competencias transversales, la mayoría relacionadas con el pensamiento matemático.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

ICT driven pedagogies and its impact on learning outcomes in high school mathematics

ICT (Information and Communication Technology) creates numerous opportunities for teachers to re-think their pedagogies. In subjects like mathematics which draws upon abstract concepts, ICT creates such an opportunity. Instead of a mimetic pedagogical approach, suitably designed activities with ICT can enable learners to engage more proactively with their learning. In this quasi-experimental designed study, ICT was used in teaching mathematics to a group of first year high school students (N=25) in Australia. The control group was taught predominantly through traditional pedagogies (N=22). Most of the variables that had previously impacted on the design of such studies were suitably controlled in this yearlong investigation. Quantitative and qualitative results showed that students who were taught by ICT driven pedagogies benefitted from the experience. Pre and post-test means showed that there was a difference between the treatment and control groups. Of greater significance was that the students (in the treatment group) believed that the technology enabled them to engage more with their learning.

Low achieving mathematics students' attitudinal and achievement changes as a result of using an integrated learning system

This paper reports on a study to measure the effectiveness of an integrated learning system (ILS) in improving mathematics achievement for low achieving Year 5 to 9 students. The study found that statistically significant gains on the integrated learning system were not supported by scores on standardised mathematics achievement tests. It also found that although student attitudes to computers decreased (significantly for some items), the students still liked the integrated learning system and felt that it had helped them to learn.

Tutoring with higher mathematics and the use of technology

We discuss three approaches to the use of technology as a teaching and learning tool that we are currently implementing for a target group of about one hundred second level engineering mathematics students. Central to these approaches is the underlying theme of motivating relatively poorly motivated students to learn, with the aim of improving learning outcomes. The approaches to be discussed have been used to replace, in part, more traditional mathematics tutorial sessions and lecture presentations. In brief, the first approach involves the application of constructivist thinking in the tertiary education arena, using technology as a computational and visual tool to create motivational knowledge conflicts or crises. The central idea is to model a realistic process of how scientific theory is actually developed, as proposed by Kuhn (1962), in contrast to more standard lecture and tutorial presentations. The second approach involves replacing procedural or algorithmic pencil-and-paper skills-consolidation exercises by software based tasks. Finally, the third approach aims at creating opportunities for higher order thinking via "on-line" exploratory or discovery mode tasks. The latter incorporates the incubation period method, as originally discussed by Rubinstein (1975) and others.

The use of explicit algorithms and episodic context to teach subtraction to students with learning problems in mathematics /

This research attempted to address the question of the role of explicit algorithms and episodic contexts in the acquisition of computational procedures for regrouping in subtraction. Three groups of students having difficulty learning to subtract with regrouping were taught procedures for doing so through either an explicit algorithm, an episodic content or an examples approach. It was hypothesized that the use of an explicit algorithm represented in a flow chart format would facilitate the acquisition and retention of specific procedural steps relative to the other two conditions. On the other hand, the use of paragraph stories to create episodic content was expected to facilitate the retrieval of algorithms, particularly in a mixed presentation format. The subjects were tested on similar, near, and far transfer questions over a four-day period. Near and far transfer algorithms were also introduced on Day Two. The results suggested that both explicit and episodic context facilitate performance on questions requiring subtraction with regrouping. However, the differential effects of these two approaches on near and far transfer questions were not as easy to identify. Explicit algorithms may facilitate the acquisition of specific procedural steps while at the same time inhibiting the application of such steps to transfer questions. Similarly, the value of episodic context in cuing the retrieval of an algorithm may be limited by the ability of a subject to identify and classify a new question as an exemplar of a particular episodically deflned problem type or category. The implications of these findings in relation to the procedures employed in the teaching of Mathematics to students with learning problems are discussed in detail.

Teachers' professional learning within communities of mathematics-for-teaching practice

Ontario bansho is an emergent mathematics instructional strategy used by teachers working within communities of practice that has been deemed to have a transformational effect on teachers' professional learning of mathematics. This study sought to answer the following question: How does teachers' implementation of Ontario bansho within their communities of practice inform their professional learning process concerning mathematics-for-teaching? Two other key questions also guided the study: What processes support teachers' professional learning of content-for-teaching? What conditions support teachers' professional learning of content-for-teaching? The study followed an interpretive phenomenological approach to collect data using a purposive sampling of teachers as participants. The researcher conducted interviews and followed an interpretive approach to data analysis to investigate how teachers construct meaning and create interpretations through their social interactions. The study developed a model of professional learning made up of 3 processes, informing with resources, engaging with students, and visualizing and schematizing in which the participants engaged and 2 conditions, ownership and community that supported the 3 processes. The 3 processes occur in ways that are complex, recursive, nonpredictable, and contextual. This model provides a framework for facilitators and leaders to plan for effective, content-relevant professional learning by placing teachers, students, and their learning at the heart of professional learning.

Disambiguating the Effects of Social Instability Stress in Adolescence on Learning and Memory Tasks that Involve the Medial Prefrontal Cortex and Hippocampus

Exposure to chronic stress can alter the structure and function of brain regions involved in learning and memory, and these effects are typically long-lasting if the stress occurs during sensitive periods of development. Until recently, adolescence has received relatively little attention as a sensitive period of development, despite marked changes in behaviour, heightened reactivity to stressors, and cognitive and neural maturation. Therefore, the purpose of the present study was to investigate the long-term effects of chronic stress in adolescence on two spatial learning and memory tasks (Morris water maze and Spatial Object Location test) and on a working memory task (Delayed Alternation task). Male rats were randomly assigned to chronic social instability stress (SS; daily 1 hour isolation and subsequent change of cage partner between postnatal days 30 and 45) or to a no-stress control group (CTL). During acquisition learning in the Morris water maze task, SS rats demonstrated impaired long-term memory for the location of the hidden escape platform compared to CTL rats, although the impairment was only seen after the first day of training. Similarly, SS rats had impaired long-term memory in the Spatial Object Location test after a long delay (240 minutes), but not after shorter delays (15 or 60 minutes) compared to CTL rats. On the Delayed Alternation task, which assessed working memory across delays ranging from 5 to 90 seconds, no group differences were observed. These results are partially in line with previous research that revealed adult impairment on spatial learning and memory tasks after exposure to chronic social instability stress in adolescence. The observed deficits, however, appear to be limited to long-term memory as no group differences were observed during brief periods of retention.

Windows into Elementary Mathematics:Alternate public images of mathematics and mathematicians

Research on students’ (and teachers’) images of mathematics and mathematicians reveals a number of stereotypical images, most of which are negative. In this paper we present an overview of some these images and stereotypes and consider the questions: (1) how might the image of mathematics and mathematicians be a problem in mathematics education, and (2) what can be done to remedy the situation? Also, we consider an outreach project called Windows into Elementary Mathematics. In this project mathematicians are interviewed about their perspectives on elementary mathematics topics and their interviews are videotaped and are posted online, along with supporting images and interactive content. In this context we consider the questions: (3) what is the Windows project about, and (4) how might it offer an alternate (and perhaps better) image of mathematics and mathematicians? Lastly, we share an example where activities from the project were used in a math-for-teachers course.

Características del desarrollo de una mirada profesional en estudiantes para profesor de matemáticas en un contexto b-learning

Esta investigación presenta un estudio cuyo objetivo es identificar aspectos que apoyan el desarrollo de la mirada profesional en estudiantes para profesores de matemáticas en un contexto b-learning. Analizamos las producciones de un grupo de estudiantes para profesores de matemáticas de educación secundaria (documentos escritos y participaciones en un debate on-line) cuando analizaban el razonamiento proporcional de estudiantes de educación secundaria. Los resultados indican que la interacción en el debate en línea permitió a algunos estudiantes para profesor mejorar su capacidad de identificar e interpretar aspectos relevantes del pensamiento matemático de los estudiantes de educación secundaria. Estos resultados indican que el desarrollo de “una mirada profesional” del profesor es un proceso complicado pero que la posibilidad de construir un discurso progresivo en línea es un factor importante para su desarrollo.

Development of prospective mathematics teachers’ professional noticing in a specific domain: proportional reasoning

The aim of this research is to identify aspects that support the development of prospective mathematics teachers’ professional noticing in a b-learning context. The study presented here investigates the extent to which prospective secondary mathematics teachers attend and interpret secondary school students’ proportional reasoning and decide how to respond. Results show that interactions in an on-line discussion improve prospective mathematics teachers’ ability to identify and interpret important aspects of secondary school students’ mathematical thinking.

A funny thing happened on the way to the forum: Electronic discussion and foreign language learning

Amongst the opportunities for cross-cultural contact created by the burgeoning use of the Internet are those provided by electronic discussion lists. This study looks at what happens when language students venture out of the classroom (virtual or otherwise) to participate in on-line discussion groups with native speakers. Responses to messages and commentary by moderators and other participants on the (in) appropriateness of contributions allow us to determine what constitutes successful participation and to make suggestions regarding effective teaching strategies for this medium. A case study examines the threads started by four anglophone students of French when they post messages to a forum on the Web site of the French newspaper Le Monde. Investigation of these examples points to the ways in which electronic discussion inflects and is inflected by cultural and generic expectations. We suggest that successful participation on Internet fora depends on awareness of such cultural and generic mores and an ability to work within and/or with them. Teachers therefore need to find ways in which students can be sensitized to such issues so that their participation in such electronic discussion is no longer seen as linguistic training, but as engagement with a cultural practice.