Using a Multi-Dimensional Approach to Understanding to Assess Students' Mathematical Knowledge

2011 ◽  
pp. 17-31 ◽  
Author(s):  
Denisse R. THOMPSON ◽  
Berinderjeet KAUR
Keyword(s):  
Mathematical Knowledge ◽  
Dimensional Approach

Shifting perspectives: method, media and the complex image

1998 ◽  
Vol 10 (1-3) ◽  
pp. 100-108 ◽  
Author(s):  
Alicia Colson ◽  
Ross Parry
Keyword(s):  
Image Processing ◽  
Three Dimensional ◽  
Geographical Location ◽  
Spatial Relationship ◽  
Two Dimensional ◽  
Dimensional Approach ◽  
Complex Image ◽  
Cultural Resonance

This article argues that the analysis of a threedimensional image demanded a three-dimensional approach. The authors realise that discussions of images and image processing inveterately conceptualise representation as being flat, static, and finite. The authors recognise the need for a fresh acuteness to three-dimensionality as a meaningful – although problematic – element of visual sources. Two dramatically different examples are used to expose the shortcomings of an ingrained two-dimensional approach and to facilitate a demonstration of how modern (digital) techniques could sanction new historical/anthropological perspectives on subjects that have become all too familiar. Each example could not be more different in their temporal and geographical location, their cultural resonance, and their historiography. However, in both these visual spectacles meaning is polysemic. It is dependent upon the viewer's spatial relationship to the artifice as well as the spirito-intellectual viewer within the community. The authors postulate that the multi- faceted and multi-layered arrangement of meaning in a complex image could be assessed by working beyond the limitations of the two-dimensional methodological paradigm and by using methods and media that accommodated this type of interconnectivity and representation.

Mathematics Textbook as an Object of Research/Matematički udžbenik kao predmet istraživanja

2014 ◽  
Vol 16 ◽  
Author(s):  
Dubravka Glasnović Gracin
Keyword(s):  
Mathematics Education ◽  
Mathematical Knowledge ◽  
Empirical Studies ◽  
Mathematics Textbooks ◽  
Mathematics Textbook ◽  
Mathematics Book

AbstractA mathematics textbook can be described as an officially authorized and pedagogically designed mathematics book written to provide mathematical knowledge to students. This description suggests the authority of the textbook - because it has been authorized by an administrative source and because it deals with authorized knowledge. This paper provides an overview of research on mathematics textbooks. The emphasis is on questions concerning the extent to which and how textbooks are used in mathematics education in Croatia and in the world.Research results show that mathematics textbooks are widely used in mathematics education worldwide. This finding points to the need for research on the content and structure of textbooks. Such studies are combined with the associated results on how textbooks are used in the classroom and which methods teachers apply in using textbooks in mathematics education. The results of the empirical studies show that teachers use textbooks for lesson preparation and pupils use mathematics textbooks for exercises to a great extent. These results imply that such an important role of textbooks in mathematics education deserves additional attention, with the goal of understanding and improving mathematics education.Key words: mathematics education; overview; research on textbook---SažetakMatematički udžbenik može se opisati kao službeno autorizirana i pedagoki osmiljena matematička knjiga napisana s ciljem da učenicima ponudi matematičke sadržaje. Taj opis sugerira autoritet udžbenika jer ga je autorizirao administrativni izvor i jer sadrži autorizirano znanje. Ovaj članak daje pregled istraživanja matematičkih udžbenika, a naglasak je na pitanjima u kojoj mjeri i kako se udžbenici koriste u nastavi matematike u Hrvatskoj i u svijetu.Rezultati raznih istraživanja pokazuju da se udžbenici u velikoj mjeri koriste u nastavi matematike irom svijeta. Taj nalaz ukazuje na potrebu za istraživanjem sadržaja i strukture matematičkih udžbenika. Uz to, prikazani su rezultati istraživanja o tome na koji se način udžbenici koriste u razredu i koje metode nastavnici prakticiraju prilikom upotrebe udžbenika na nastavi. Rezultati empirijskih studija pokazuju da nastavnici udžbenike većinom koriste za pripremu nastavnog sata, a učenici udžbenike koriste u najvećoj mjeri za vježbanje. Ti rezultati ukazuju na to da tako važna uloga udžbenika u matematičkom obrazovanju zaslužuje dodatnu pažnju s ciljem razumijevanja i poboljanja nastave matematike.Ključne riječi: istraživanje udžbenika; nastava matematike; pregled.

Mathematical Knowledge and the Interplay of Practices

2015 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Philosophy Of Mathematics ◽  
Advanced Mathematics ◽  
New Approach ◽  
Agent Based ◽  
Epistemology Of Mathematics ◽  
Actual Experience ◽  
Elementary Math ◽  
Mathematical Tradition

This book presents a new approach to the epistemology of mathematics by viewing mathematics as a human activity whose knowledge is intimately linked with practice. Charting an exciting new direction in the philosophy of mathematics, the book uses the crucial idea of a continuum to provide an account of the development of mathematical knowledge that reflects the actual experience of doing math and makes sense of the perceived objectivity of mathematical results. Describing a historically oriented, agent-based philosophy of mathematics, the book shows how the mathematical tradition evolved from Euclidean geometry to the real numbers and set-theoretic structures. It argues for the need to take into account a whole web of mathematical and other practices that are learned and linked by agents, and whose interplay acts as a constraint. It demonstrates how advanced mathematics, far from being a priori, is based on hypotheses, in contrast to elementary math, which has strong cognitive and practical roots and therefore enjoys certainty. Offering a wealth of philosophical and historical insights, the book challenges us to rethink some of our most basic assumptions about mathematics, its objectivity, and its relationship to culture and science.

Recommendations for deploying multidimensio

2017 ◽  
Vol 11 (1) ◽  
pp. 68-80
Author(s):  
E. E. Akimkina
Keyword(s):  
Comparative Analysis ◽  
Management System ◽  
Analytical Data ◽  
Enterprise Management ◽  
Multidimensional Data ◽  
Dimensional Approach ◽  
Process Data ◽  
Modeling Systems ◽  
Enterprise Management System ◽  
Practical Recommendations

A comparative analysis of different approaches to analytical data and shows that the most ample opportunities has a multi-dimensional approach, implemented with the help of OLAP technology. Presented multidimensional OLAP-cube model with the measurements for the analysis and processing of process data. Practical recommendations for the deployment of a multidimensional data modeling systems with regard to their integration into existing enterprise management system.

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