Don’t aim too high for your kids: parental over-aspiration undermines students’ learning in mathematics

Previous research has suggested that parents’ aspirations for their children’s academic attainment can have a positive influence on children’s actual academic performance. Possible negative effects of parental over-aspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German schoolchildren and their parents (N = 3,530; grades 5 to 10), we showed that parental aspiration and children’s mathematical achievement were linked by positive reciprocal relations over time. Importantly, we also found that parental aspiration that exceeded their expectation (i.e., over-aspiration) had negative reciprocal relations with children’s mathematical achievement. These results were fairly robust after controlling for a variety of demographic and cognitive variables such as children’s gender, age, intelligence, school type, and family SES. The results were also replicated with an independent sample of US parents and their children. These findings suggest that unrealistically high parental aspiration can be detrimental for children’s achievement.

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.