Using the van Hiele theory to analyse geometrical conceptualisation in grade 12 students: a Namibian perspective

The study reported here utilised a theory of levels of geometric thinking. This theory was proposed and developed by two Dutch mathematics educators, Pierre van Hiele and his wife, Dina van Hiele-Geldof. The van Hiele theory enables investigations into why many students experience difficulties in learning geometry. In many nations, such as the UK, the USA, Netherlands, the USSR and to a certain extent, Nigeria and South Africa, research evidence has indicated that the overall students’ mathematical competencies are linked to their geometric thinking levels. This study is the first of its kind to apply the van Hiele theory of geometric thinking in the Namibian context to analyse geometrical conceptualisation in Grade 12 mathematics students. In all, 50 Grade 12 students (20 from School A and 30 from School B) were involved in this study. These students wrote a van Hiele Geometry Test adapted from the Cognitive Development and Achievement in Secondary School Geometry test items. Thereafter, a clinical interview with the aid of manipulatives was conducted. The results from this study indicated that many of the School A and School B students who participated in the research have a weak conceptual understanding of geometric concepts: 35% of the School A and 40% of the School B subsamples were at the prerecognition level. 25% and 30% of the School A, and 20% and 23.3% of the School B students were at van Hiele levels 1 and 2 respectively. An equal number of students but different in percentages, 2 (10%) in School A and 2 (6.7%) in School B, were at van Hiele level 3. Only one student from School B attained van Hiele level 4. These results were found to be consistent with those of previous similar studies in UK, USA, Nigeria and South Africa. The findings of this study also highlight issues of how the Namibian Grade 12 geometry syllabus should be aligned with the van Hiele levels of geometric thinking as well as the use of appropriate and correct language in geometrical thinking and problem solving

Empréstimos de Origem Angolana em Voz de Angola - clamando no deserto

Foi a 23 de outubro de 1575 que, com o decreto do Rei D. Sebastião, o panorama geopolílico angolano se metamorfoseou. Dos primeiros contactos entre portugueses e angolanos resultou a colonização do segundo povo, com início no século XV e que se prolongou até ao século XX. A colonização teve duas fases, a saber: a fase da penetração territorial que implicou os primeiros contactos (1482 a …) e a fase da ocupação territorial. Na escola, o colonizado tinha de, obrigatoriamente, falar o idioma do colonizador. Houve, efetivamente, influências linguísticas. As unidades lexicais confirmam, sobretudo, a história deste contacto, pois cada palavra pode implicar uma realidade de um povo. Este estudo visa recolher, organizar, analisar e descrever os empréstimos de origem angolana encontrados no periódico Voz de Angola – Clamando no Deserto (1901). Deve também contribuir para a criação de um Vocabulário Ortográfico Nacional para Angola. Em virtude do surgimento da imprensa em Angola no século XIX, começaram a publicar-se alguns periódicos. De entre estes, os jornais e as revistas refletem obviamente a produtividade de empréstimos. O primeiro periódico de que há registo é o Boletim Oficial (1845), cuja responsabilidade cabe ao Governador Pedro Alexandrino da Cunha. Por outro lado, o último periódico da época colonial de que se tem conhecimento é Mensagem – A Voz dos Naturais de Angola (1951), revista sob a alçada da Associação dos Novos Intelectuais de Angola. Visto que os jornalistas e os escritores são nitidamente criadores de palavras, reconhecemos que há unidades lexicais de origem angolana registadas nos jornais daquela época que se tornaram laivos perenes da realidade sociopolítica dos dois povos. As línguas de Angola, de facto, têm processos muito peculiares que descaracterizam as unidades lexicais de outras línguas, particularmente as do português. Alguns processos de formação de palavras das línguas de Angola convergem e outros divergem com os do português, pois as línguas de Angola apresentam processos de formação de palavras muito diferentes. Por desconhecimento destes processos, muitos articulistas recorriam ao decalque, tendo como base a estrutura do português.It was on 23 October 1575, with the decree of Portuguese King Sebastian, that the Angolan geopolitical panorama changed. The first contacts between Portuguese and Angolans resulted in the colonisation of the Angolans, beginning in the 15th century and continuing until the 20th century. The colonisation had two phases, namely: the phase of territorial penetration which implied the first contacts (1482 to ...) and the phase of territorial occupation. At school, the colonised had to speak the language of the coloniser. There were, indeed, linguistic influences. The lexical units confirm above all the history of this contact, for each word may imply a reality of a people. This study aims to collect, organise, analyse and describe loans of Angolan origin found in the periodical Voz de Angola – Clamando no Deserto (1901). It should also contribute to the creation of a National Orthographic Vocabulary for Angola. Due to the emergence of the press in Angola in the 19th century, some periodicals started being published. Newspapers and magazines obviously reflected the productivity of lexical loans. The first periodical of which there is a record is the Boletim Oficial (1845), under the responsibility of the Governor Pedro Alexandrino da Cunha. On the other hand, the last periodical of the colonial period known and dated is Mensagem – A Voz dos Naturais de Angola (1951), a magazine under the responsibility of the Association of New Intellectuals of Angola. Since journalists and writers are clearly creators of words, we recognise that there are lexical units of Angolan origin registered in the newspapers of that time that became perennial marks of the social-political reality of the two peoples. The languages of Angola, in fact, have very peculiar processes that deprive the lexical units of other languages, particularly those of the Portuguese language. Some processes of word formation of the Angolan languages converge and others diverge with those of the Portuguese, because the languages of Angola present very different processes of formation of words. Due to a lack of knowledge of these processes, many writers used the decal based on the Portuguese structure

Contributos para a caracterização do português em Angola: clíticos em contraste com o PE e o PB

A presente dissertação tem como principal objetivo estudar os clíticos do Português de Angola em comparação com os do Português Europeu e do Português Brasileiro, com vista à caracterização da Variedade do Português de Angola. O estudo baseou-se num conjunto de textos de opinião retirados dos Jornais de Angola, Público e Globo, textos esses produzidos por redatores cuja linguagem é mais formal do que a linguagem de informantes de textos orais que tem servido para descrever o vernáculo angolano. Em Angola, verificam-se tendências particulares nos padrões de colocação de clíticos: a modalidade oral apresenta critérios de colocação que se aproximam dos critérios do Português Brasileiro, ao passo que a modalidade escrita formal segue as tendências consolidadas no Português Europeu. Nesta dissertação procurou-se verificar este último aspeto a partir de um corpus constituído para o efeito; Abstract: Contributions to the Characterization of Angolan Portuguese (AP): Use of Clitics in AP as They Compare to Usage in European Portuguese (EP) and Brazilian Portuguese (BP) The main goal of this dissertation is to study Portuguese clitics in Angolan Portuguese versus those in European and Brazilian Portuguese as a way to contribute to the characterization of the Angolan variant of Portuguese. This study was based on the analysis of a set of editorial articles gathered from local Angolan newspapers—i.e., Público and Globo—written by journalists whose language is more formal than the vernacular of the individuals whose speech samples were used to analyze the spoken, more relaxed Angolan Portuguese. In Angola, particular trends are observed in clitics placement patterns: in spoken, more relaxed Angolan Portuguese, the criteria for placing clitics are closer to those of Brazilian Portuguese, whereas in formal, written Angolan Portuguese the criteria follow the patterns of European Portuguese. In this dissertation, I sought to verify this last aspect from a corpus generated specifically for this purpose

The evolution of a Gondwanan collisional orogen: A structural and geochronological appraisal from the Southern Granulite Terrane, South India

Gondwana amalgamated along a suite of Himalayan-scale collisional orogens, the roots of which lace the continents of Africa, South America, and Antarctica. The Southern Granulite Terrane of India is a generally well-exposed, exhumed, Gondwana-forming orogen that preserves a record of the tectonic evolution of the eastern margin of the East African Orogen during the Ediacaran-Cambrian (circa 600–500 Ma) as central Gondwana formed. The deformation associated with the closure of the Mozambique Ocean and collision of the Indian and East African/Madagascan cratonic domains is believed to have taken place along the southern margin of the Salem Block (the Palghat-Cauvery Shear System, PCSS) in the Southern Granulite Terrane. Investigation of the structural fabrics and the geochronology of the high-grade shear zones within the PCSS system shows that the Moyar-Salem-Attur shear zone to the north of the PCSS system is early Paleoproterozoic in age and associated with dextral strike-slip motion, while the Cauvery shear zone (CSZ) to the south of the PCSS system can be loosely constrained to circa 740–550 Ma and is associated with dip-slip dextral transpression and north side-up motion.To the south of the proposed suture zone (the Cauvery shear zone), the structural fabrics of the Northern Madurai Block suggest four deformational events (D1–D4), some of which are likely to be contemporaneous. The timing of high pressure-ultrahigh temperature metamorphism and deformation (D1–D3) in the Madurai Block (here interpreted as the southern extension of Azania) is constrained to circa 550–500 Ma and interpreted as representing collisional orogeny and subsequent orogenic collapse of the eastern margin of the East African Orogen. The disparity in the nature of the structural fabrics and the timing of the deformation in the Salem and the Madurai Blocks suggest that the two experienced distinct tectonothermal events prior to their amalgamation along the Cauvery shear zone during the Ediacaran/Cambrian