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.

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.

Educação matemática encena

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Towards improving public understanding of judgement practice in standards-referenced assessment : an Australian perspective

Internationally there has been a move towards standards-referenced assessment with countries such as Australia developing a National Curriculum and Achievement Standards, New Zealand adopting National Standards for literacy and numeracy that involve schools making and reporting judgements about the reading, writing and mathematics achievement of children up to Year 8 (the end of primary school) and in Canada, classroom assessment standards aimed at the improvement of assessment practice of K-12 education are being formulated. Standards-driven reform has major implications for teachers’ work. The consequences of adopting a standards-driven approach to educational change by systems are often under-estimated with the unintended effects not fully understood by either the policy writers, and the public, including parents. It is for these reasons that the contention developed in this article relates to the teacher’s role, which it is argued remains central to policy focused on the improvement of the quality of education and educational standards.

When sex doesn't sell: Using sexualized images of women reduces support for ethical campaigns

Images of scantily clad women are used by advertisers to make products more attractive to men. This ‘‘sex sells’’ approach is increasingly employed to promote ethical causes, most prominently by the animal-rights organization PETA. Yet sexualized images can dehumanize women, leaving an unresolved paradox – is it effective to advertise an ethical cause using unethical means? In Study 1, a sample of Australian male undergraduates (N = 82) viewed PETA advertisements containing either sexualized or non-sexualized images of women. Intentions to support the ethical organization were reduced for those exposed to the sexualized advertising, and this was explained by their dehumanization of the sexualized women, and not by increased arousal. Study 2 used a mixed-gender community sample from the United States (N = 280), replicating this finding and extending it by showing that behaviors helpful to the ethical cause diminished after viewing the sexualized advertisements, which was again mediated by the dehumanization of the women depicted. Alternative explanations relating to the reduced credibility of the sexualized women and their objectification were not supported. When promoting ethical causes, organizations may benefit from using advertising strategies that do not dehumanize women.

Preparing engineering graduates for the knowledge economy through blended delivery of mathematics

Contemporary higher education institutions are making significant efforts to develop cohesive, meaningful and effective learning experiences for Science, Technology, Engineering and Mathematics (STEM) curricula to prepare graduates for challenges in the modern knowledge economy, thus enhancing their employability (Carnevale et al, 2011). This can inspire innovative redesign of learning experiences embedded in technology-enhanced educational environments and the development of research-informed, pedagogically reliable strategies fostering interactions between various agents of the learning-teaching process. This paper reports on the results of a project aimed at enhancing students’ learning experiences by redesigning a large, first year mathematics unit for Engineering students at a large metropolitan public university. Within the project, the current study investigates the effectiveness of selected, technology-mediated pedagogical approaches used over three semesters. Grounded in user-centred instructional design, the pedagogical approaches explored the opportunities for learning created by designing an environment containing technological, social and educational affordances. A qualitative analysis of mixed-type questionnaires distributed to students indicated important inter-relations between participants’ frames of references of the learning-teaching process and stressed the importance (and difficulty) of creating appropriate functional context. Conclusions drawn from this study may inform instructional design for blended delivery of STEM-focused programs that endeavor to enhance students’ employability by educating work-ready graduates.

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order H-m (H-n), m is an element of N-n, under the heat kernel transform on H-n, using direct sum and direct integral of Bergmann spaces and certain unitary representations of H-n which can be realized on the Hilbert space of Hilbert-Schmidt operators on L-2 (R-n). We also show that the image of Sobolev space of negative order H-s (H-n), s(> 0) is an element of R is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on H-n under the heat kernel transform. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Morphological routine proposal to extraction of highways in digital images of high resolution

This research proposes to apply techniques of Mathematics Morphology to extract highways in digital images of high resolution, targeting the upgrade of cartographic products. Remote Sensing data and Mathematical Morphological techniques were integrated in the process of extraction. Mathematical Morphology's objective is to improve and extract the relevant information of the visual image. In order to test the proposed approach some morphological operators related to preprocess, were applied to the original images. Routines were implemented in the MATLAB environment. Results indicated good performances by the implemented operators. The integration of the technologies aimed to implement the semiautomatic extraction of highways with the purpose to use them in processes of cartographic updating.

Parallel sets and morphological measurements of CT images of soil pore structure in a vineyard

Important physical and biological processes in soil-plant-microbial systems are dominated by the geometry of soil pore space, and a correct model of this geometry is critical for understanding them. We analyze the geometry of soil pore space with the X-ray computed tomography (CT) of intact soil columns. We present here some preliminary results of our investigation on Minkowski functionals of parallel sets to characterize soil structure. We also show how the evolution of Minkowski morphological measurements of parallel sets may help to characterize the influence of conventional tillage and permanent cover crop of resident vegetation on soil structure in a Spanish Mediterranean vineyard.

The basic concepts of mathematics; a companion to current textbooks on algebra and analytic geometry.

pt.1. Algebra.

A concise history of mathematics.

Includes bibliographies.

New images of man. With statements by the artists.

Errata slip inserted.

A concise history of mathematics.

"In this reprint we have corrected several misprints and errors which had slipped into the first printing."

On the study and difficulties of mathematics /

First edition, 1831.

Enriched teaching of mathematics in the junior and senior high school; a source book for teachers of mathematics, listing chiefly free and low cost illustrative and supplementary materials,

Blank pages are provided at the end of each section for listing additional sources.