This paper focuses on algorithms for an efficient scalar multiplication. It proposes two algorithms for computing points of the form 2kP in affine coordinates. One works for k = 2, and the other works for an arbitrary natural number k. The efficiency of these algorithms is based on a trade-off between a field inversion and several field multiplications. Montgomery trick is used to implement thi...

Readers The challenge of understanding reading comprehension derives, in part, from the difficulty of defining its borders. Comprehension was defined by the Research and Development (RAND) Reading Study Group (RRSG, 2002) as ‘‘the process of simultaneously constructing and extracting meaning through interaction and engagement with print.’’ This definition was intended to signal the importance o...

Publishing graded readers is big business, but there is evidence that the texts themselves are not being read in sufficient quantity to improve language proficiency. This article reports on a study of graded readers, focusing on interviews with some major publishers of graded readers, to investigate their production rationales. The findings suggest that the opinions of the ultimate consumers, t...

In recent years, the Education for All movement has focused more intensely on the quality of education, rather than simply provision. Many recent and current education quality interventions focus on literacy, which is the core skill required for further academic success. Despite this focus on the quality of literacy instruction in developing countries, little rigorous research has been conducte...

Reading is an important skill for gaining knowledge and discovering new information in a global society. Reading competence also strongly influences a person’s learning ability. However, in building better reading skills, one of the major difficulties is an absence of background knowledge to help learners read and understand material. Background knowledge helps learners make connections to cons...

Found in the collected works of Eisenstein are twenty continued fraction expansions. The expansions have since emerged in the literature in various forms, although a complete historical account and self-contained treatment has not been given. We provide one here, motivated by the fact that these expansions give continued fraction expansions for modular forms. Eisenstein himself did not record p...

Background A significant body of research supports the notion that best practice in the teaching and learning of language incorporates complementary use of technology with the development of foundational knowledge and use of language (Hoopingarner 2009; Goh et al. 2004). Sometimes referred to as e-language learning, myriad opportunities exist for the exploration of the innovative ways technolog...