Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

Complex Spacetimes and the Newman-Janis Trick

<p>In this thesis, we explore the subject of complex spacetimes, in which the mathematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions.</p>

Strategies Used by Grade 6 Learners in the Multiplication of Whole Numbers in Five Selected Primary Schools in the Kavango East and West Regions

This research paper reports strategies used by Grade 6 learners in multiplying whole numbers in five selected primary schools in Kavango East and West regions. A total of 200 learners’ mathematics exercise books were analysed in order to identify the commonly used strategies by learners in multiplying whole numbers. A total of ten teachers teaching grade 6 mathematics were also requested to complete a questionnaire which required them to indicate the strategies that they employed in class when teaching multiplication of whole numbers. The teachers indicated that they used a variety of strategies including repeated addition, complete-number (Including doubling), partitioning and compensation to teach multiplication of whole numbers. The results also disclosed that the majority of the learners’ mathematics exercise books reflected the use of the traditional method of repeated addition contrary to the teachers’ claims. It was also found that a few of the learners used other strategies such as long method, short method and learner “invented” strategies. Additionally, the mathematics curriculum for upper primary learners (Grade 4-7 mathematics syllabus) requires learners to use paper and pencil algorithms to carry out multiplication of whole numbers without calculators (Ministry of Education, Arts & Culture [MoEAC], 2015, p. 2). However, at Grade 6, learners were expected to use paper and pencil algorithms to multiply numbers within the range 0-100000. Analysis of the learners’ exercise books indicated that the majority were not able to multiply a two digit by a single digit, a two digit by a two digit and a three digit by a two digit number.

PERBEDAAN MODEL PEMBELAJARAN THINK –TALK –WRITE (TTW) DENGAN TRAFFINGER TERHADAP PENINGKATAN KEMAMPUAN BERPIKIR KRITIS PESERTA DIDIK PADA MATA PELAJARAN SOSIOLOGI

Penelitian bertujuan untuk mengetahui perbedaan model pembelajaran Think –Talk –Write (TTW), model pembelajaran Traffinger dengan model pembelajaran konvensional dalam meningkatkan kemampuan berpikir kritis peserta didik dalam mata pelajaran sosiologi di kelas XI SMAN 10 Bandung. Penelitian ini menggunakan quasi eksperimen, pola penelitian menggunakan Nonequivalent Control Group Design dengan langkah memberi pretest, memberikan perlakuan dengan model pembelajaran yang sudah ditentukan pada dua kelas eksperimen dan satu kelas kontrol dan memberi postets. Short method digunakan dalam pengolahan data. Hasil penelitian menunjukan bahwa tidak ada perbedaan peningkatan kemampuan berpikir kritis antara model pembelajaran Think, Talk and Writen, Traffinger dan metode konvensional pada mata pelajaran sosiologi dengan derajat kebebasan 7 dan taraf signifikan 1% dan t hitung sebesar 3,499.Kata Kunci : Think –Talk –Write (Ttw), Traffinger, Berpikir Kritis