Space wars and the new urban imperialism

The dissertation analyzes recent urban transformations through the lens of space wars. The main focus is on investment flows in the commercial property market, changes in urban governance and changes in social geography, and how these three aspects are related. Drawing on cross border investment data, archive studies, interviews with key actors and street walking experiences in Copenhagen, Lisbon and New York, the book offers insight into the ?glocal? logic of urban imperialism and its tendency towards uneven development ? fundamental forces that shape our cities in the 21st century. In Chapter One, I introduce the concepts of space wars and the new urban imperialism and present the research questions and methodological considerations. Chapter Two analyzes processes of globalization in property markets through an empirical investigation into the commercial property market of Copenhagen. Globalization of property markets is defined, a framework for analysis is presented and methodological problems are reported. The chapter aims to improve our understanding of globalization in the sphere of immobile property, and to show to what extent globalization (in this limited sense) has occurred in Copenhagen. In Chapter Three I analyze linkages between rescaling of commercial property markets and changes in urban governance in Lisbon. The chapter aims to further advance understanding of globalization in the sphere of immobile property, and its relation with shifts in urban governance. Cautious comparisons with Copenhagen are made. Chapter Four expands the analysis of Copenhagen as a globalizing city. Through the optic of the imagineering of Copenhagen as ?creative city? ? part of Copenhagen's competition with other cities ? relations between globalization, urban governance and social geography are analyzed. The chapter problematizes what on the surface seems to be an unequivocally positive quality (?creative?) and goal (?creativity?). Chapter Five employs the concept of the global-local nexus of space wars, forging links between highly localized processes of urban transformation, competition between cities and global movements of capital and people. It shows how mental and material boundaries as well as ethnicity and class are central elements in space wars. Through the example of Sydhavn, a rapidly changing part of Copenhagen, the chapter aims to illustrate how processes of material and social construction and transformation of urban space constitute urban space wars, engaging actors at all scales. The Epilogue serves as a supplement to my short film ?Space wars: a street level odyssey through the centre of the American empire ? New York City?. The film offers a street level voyage through the urban topography of New York, centre of the American empire, showing how the rhythms of vagabond capitalism manifest themselves as space wars. At first glance, every day in the city seems an original performance, but underneath the surface, we find a myriad of rhythms that reveal traces of millennia of human cultures and histories. In urban centers throughout the globe we can observe contemporary modern society and the materialized topographies of different modes of time-space production. The film seeks to direct attention to, and stimulate discussion on issues of space wars at different scales and in different contexts

A systematic analysis of the generalisation concept in early algebra for young learners – some ideas for the classroom

Thesis (MEd)--Stellenbosch University, 2022.ENGLISH ABSTRACT: The importance of introducing algebra concepts and skills in the early years of mathematics education, has become increasingly acknowledged as imperative for algebra success in the secondary grades of mathematics teaching and learning. Research has shown that learners at a young age are able to reason algebraically. Generalisation is described as one of the core aspects of early algebra and should be embedded throughout the mathematics curriculum to form a deep understanding of the underlying structure of mathematics. In South Africa, the field of early algebra remains largely unexplored in the mathematics education research context. The content area, ‘Patterns, functions and algebra’ which aims to provide guidelines for the teaching of early algebra in South African early years classrooms, seems to be inadequate for the implementation of early algebra in early years classrooms. A lack of a relational approach in the sequencing of curriculum documents and learning and teaching materials, are provided for the teaching of patterns, functions, and algebra in the foundation phase. The purpose of this study was to determine how the generalisation concept can be implemented in early years classrooms to develop early algebra skills and concepts. A systematic literature review was conducted with the aim of extending on current research by designing a higher-order construct from existing literature. A thematic analysis of the literature led to the synthesis of an instructional sequence for the implementation of generalisation in early years classrooms. The instructional sequence was based on the principles of Realistic Mathematics Education from the Netherlands which included guided reinvention and emergent modelling as foundational principles. A historical overview of the development of algebra through the ages indicated three historical stages: the rhetorical stage, the syncopated stage, and the symbolic stage, as well as four conceptual stages: the geometric stage, the static-equation stage, the dynamic function stage, and the abstract stage. The emergence of the main components and big ideas of algebra from these stages provided a valuable insight as to how algebraic thinking developed naturally and informed an instructional sequence for the implementation of generalisation. An in-depth systematic review of the concepts which emerged from history was further conducted to understand the current state of algebra in schools, how algebraic thinking develops, the levels of algebraic thinking and what the main components of early algebra are, with a specific focus on generalisation. The study further explored an appropriate learning approach, namely the problem-centred approach, which ensures that mathematics is learned for understanding. The historical overview and the systematic review of early algebra, generalisation, and structure were used to construct the instructional sequence for the implementation of generalisation in early years classrooms.AFRIKAANSE OPSOMMMING: Dit word algemeen aanvaar dat daar ‘n behoefte bestaan om algebra op ‘n vroeër fase deel te maak van die wiskunde kurrikulum. Vroee algebra word beskou as noodsaaklik om die sukses van die verstaan van formele algebra in later grade te verseker. Navorsing dui aan dat leerders daartoe in staat is om van ‘n vroee ouderdom algebraïes te redeneer. Veralgemening word beskryf as een van die kern aspekte van vroee algebra. Veralgemening moet dwarsdeur die wiskunde kurrikulum integreer word sodat leerders die struktuur van wiskunde gouer en beter kan verstaan. In Suid- Afrika, is die veld van vroee algebra meestal onontgin in die konteks van vroee wiskundeonderwys. Die inhoud area ‘Patrone, funksies en algebra’ het die doel om riglyne voor te skryf vir die onderrig en leer van algebra in Suid-Afrikaanse grondslagfase klaskamers, maar blyk onvoldoende te wees vir die effektiewe onderrig en leer van vroee algebra. ‘n Gebrek aan ‘n verhouding en samehang in die volgorde van kurrikulumdokumente, en onderrig en leer materiaal kan waargeneem word. Die oogmerk van hierdie studie was om te bepaal hoe die veralgemeningskonsep in grondslagfase klaskamers geimplementeer kan word met die doel om vroee algebra vaardighede en konsepte in jong leerders te ontwikkel. ‘n Sistematiese literatuurstudie was uitgevoer met die hoop om op huidige literatuur uit te brei deur ‘n hoer-orde konstruksie te ontwerp op grond van bestaande literatuur. ‘n Tematiese analise van die literatuur het gelei tot die sintese van ‘n geordende onderrig patroon of leer- teoretiese model wat die implementering van veralgemening in die grondslagfase klas verduidelik. Die model is gebaseer op die beginsels van die Realistiese Wiskundeonderwysbenadering van Nederland (‘Realistic Mathematics Education’) wat onder andere insluit, gerigte herontdekking (‘guided reinvetion’) en ontluikende modellering (‘emergent modelling’). ‘n Historiese oorsig van die ontwikkeling van algebra deur die eeue het drie ontwikkelingsfases blootgele: die retoriese fase, die sinkopering fase, en die simboliese fase. Ook is daar vier konseptuele fases aangedui: die geometriese fase, die fase van die oplos van statiese vergelykings, die dinamiese funksie fase, en die abstrakte fase. Die opkoms van die sleutelkonsepte en groot idees van vroee algebra vanuit hierdie fases, het waardevolle insigte gelewer ten opsigte van die natuurlike ontwikkeling van algebra. Hierdie insigte is gebruik in die ontwerp van die onderrig-volgorde van die implementering van veralgemening. ‘n Verdere in- diepte sistematiese studie van die konsepte wat uit die geskiedenis verskyn het, was uitgevoer om vas te stel wat die huidige situasie van vroee algebra in skole is, hoe algebraïese denke ontwikkel word, hoe die vlakke van algebraïese denke ontwikkel en wat die kernaspekte van algebra is, met ‘n sterk fokus op veralgemening. Die studie het ook die probleem-gesentreerde benadering gekies as ‘n leerbenadering wat die doel het om die leer van wiskunde-met-begrip te verseker. Die oorsig van die geskiedenis van die ontwikkeling van algebra, sowel as die sistematiese analise van vroee algebra gefokus op veralgemening en struktuur, het ‘n onderrig-volgorde of leer- teoretiese model vir die implementering van veralgemening in die grondslagfase gelewer.Master