Inclusive approaches to teaching and learning mathematics

This chapter explores the role of mentors in supporting pre-service teachers to include all children in mathematics teaching, no matter what their individual needs.

Promoting mother–infant book sharing and infant attention and language development in an impoverished South African population: a pilot study

The low rates of child literacy in South Africa are cause for considerable concern. Research from the developed world shows that parental sharing of picture books with infants and young children is beneficial for child language and cognitive development, as well as literacy skills. We conducted a pilot study to examine whether such benefits might extend to an impoverished community in South Africa, by evaluating the impact of training mothers in book sharing with their 14–18 month old infants. Seventeen mothers received book sharing training; and 13 mothers did not, but instead received a comparison training in toy play. We assessed the mothers’ behavior during both book sharing and toy play before and after training, and we also assessed infant attention and language. Mothers receiving book sharing training engaged well with it, and they also benefited from it; thus, compared to the comparison group mothers, they became more sensitive, more facilitating, and more elaborative with their infants during book sharing, and they also became more sensitive to their infants during toy play. In addition, infants whose mothers received the book sharing training showed greater benefits than the comparison group infants in both their attention and language. Training in book sharing for families living in conditions of marked socio-economic adversity in South Africa has the potential to be of considerable benefit to child developmental progress. A large scale controlled trial is required to confirm this.

Competing priorities: Singapore teachers’ perspectives on critical literacy

This paper explores a group of Singaporean English language teachers’ knowledge and beliefs about critical literacy as well as their perspectives on how best to teach literacy and critical literacy in Singapore schools. A face-to-face survey was conducted among 58 English language teachers by using open-ended questions. The survey covered various topics related to literacy instruction including text decoding, meaning construction, and critical analysis of texts. The participating teachers believed strongly that reading and writing are transactional and interactional practices. However, they were less certain in their beliefs about teaching critical literacy including the critical, analytical and evaluative aspects of text reading. Some teachers saw a conflict between using time on teaching critical literacy and preparing students to pass their exams. As critical literacy is not a requirement at exams, they found it difficult to justify using time teaching it. The results suggest that the teachers’ belief systems are strongly influenced by the broad macrostructure of the educational system in Singapore and their own educational experiences.

Disambiguating with Bourdieu: unravelling policy from practice in the teaching of children with English as an additional language

This article explores the use of Bourdieusian analysis for examining how policy and practice interact in the teaching of English and therefore in the development of children’s language and literacy; in particular how Bourdieusian analysis uncovers the ways in which teachers’ practice has been influenced unconsciously by centralised shaping of the curriculum for English in England while the pupil demographic in schools has become more linguistically diverse. Data were collected from interviews with both newly qualified and very experienced primary school (pupil ages 5 – 11) teachers, whose pedagogical norms for the teaching of English were challenged by the arrival of non-English speakers in their classrooms. The discussion highlights how the use of Bourdieusian constructs of field, habitus and capital can disambiguate teachers’ practical classroom decisions from the influences of policy expectations.

Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

Spacelike Surfaces in L(4) with Degenerate Gauss Map

In this paper we study and present a complete classification of spacelike surfaces with degenerate Gauss map in the Lorentz-Minkowski space L(4).

Curvature Estimates for Submanifolds in Warped Products

We give estimates of the intrinsic and the extrinsic curvature of manifolds that are isometrically immersed as cylindrically bounded submanifolds of warped products. We also address extensions of the results in the case of submanifolds of the total space of a Riemannian submersion.

Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space

We describe several families of Lagrangian submanifolds in complex Euclidean space which are H-minimal, i.e. critical points of the volume functional restricted to Hamiltonian variations. We make use of various constructions involving planar, spherical and hyperbolic curves, as well as Legendrian submanifolds of the odd-dimensional unit sphere.

Associated Family of G-Structure Preserving Minimal Immersions in Semi-Riemannian Manifolds

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details minimal embeddings into product of space forms.

NAVET's Boxes - an Evaluation of the Post-Visit Loan Service at a Science Centre in Borås

Many pedagogues believe science centres to be a good complement to the more formal school teaching. For a visit to a science centre to be as educational as possible, there is a need for pre-visit information of some sort, a guided visit, and post-visit work. Many science centres offer loan services of different kinds. At Navet, a science centre in Borås, teachers can borrow boxes with experiments connected to the different themes they provide. The experiments are supposed to be a continuation of the visit and help settle the knowledge gained during the visit. This thesis is an evaluation of how the boxes function in the schools, and what the teachers think of them. The study was conducted through questionnaires and interviews with both teachers and the staff at Navet. The results of the study are very positive. Many teachers have been involved with Navet from the very beginning and they see a visit to Navet as an integrated part of their teaching. Some boxes work better than others and some might need clearer information, but overall the teachers see the boxes as timesavers, as a way to vary their teaching more easily, and as a help for teachers not specialized in mathematics and science.

Upper secondary school students' gendered conceptions about mathematics

This study explores Swedish Natural Science students' conceptions about gender and mathematics. I conducted and compared the results from two questionnaires. The first questionnaire revealed a view of rather traditional feminities and masulinities, a result that did not repeat itself in the second questionnaire. There was a discrepancy between the traits the students ascribed as gender different and the traits they ascribed to themselves.