Transition of pupils from Key Stage 2 to 3 deemed gifted and talented in mathematics: an initial study

In this article Geoff Tennant and Dave Harries report on the early stages of a research project looking to examine the transition from Key Stage (KS) 2 to 3 of children deemed Gifted and Talented (G&T) in mathematics. An examination of relevant literature points towards variation in definition of key terms and underlying rationale for activities. Preliminary fieldwork points towards a lack of meaningful communication between schools, with primary school teachers in particular left to themselves to decide how to work with children deemed G&T. Some pointers for action are given, along with ideas for future research and a request for colleagues interested in working with us to get in touch.

Diversity in mathematics assessment equals diversity in opinion?

We undertook a study to investigate the views of both students and staff in our department towards assessment in mathematics, as a precursor to considering increasing the diversity of assessment types. In a survey and focus group there was reasonable agreement amongst the students with regards major themes such as mode of assessment. However, this level of agreement was not seen amongst the staff, where discussions regarding diversity in mathematics assessment definitely revealed a difference of opinion. As a consequence, we feel that the greatest barriers to increasing diversity may be with staff, and so more efforts are needed to communicate to staff the advantages and disadvantages, in order to give them greater confidence in trying a range of assessment types.

Linguistic and cognitive motivations for the typological primacy model of third language (L3) transfer: considering the role of timing of acquisition and proficiency in the previous languages

This article elucidates the Typological Primacy Model (TPM; Rothman, 2010, 2011, 2013) for the initial stages of adult third language (L3) morphosyntactic transfer, addressing questions that stem from the model and its application. The TPM maintains that structural proximity between the L3 and the L1 and/or the L2 determines L3 transfer. In addition to demonstrating empirical support for the TPM, this article articulates a proposal for how the mind unconsciously determines typological (structural) proximity based on linguistic cues from the L3 input stream used by the parser early on to determine holistic transfer of one previous (the L1 or the L2) system. This articulated version of the TPM is motivated by argumentation appealing to cognitive and linguistic factors. Finally, in line with the general tenets of the TPM, I ponder if and why L3 transfer might obtain differently depending on the type of bilingual (e.g. early vs. late) and proficiency level of bilingualism involved in the L3 process.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

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.

Coping with linguistic challenges in UK higher education: the use of strategies by Chinese research students

The present study sets out to examine the strategies used by Chinese learners in a predominantly naturalistic environment and how such learner strategy use relates to their proficiency in the second language. Data were collected from four Chinese research students in the UK using semi-structured interviews. Their proficiency in English was assessed with an oral interview and a listening test. The main findings from this study are that the learners used a wide range of strategies overall, including metacognitive, cognitive, social/affective and compensation strategies. The majority of the commonly reported strategies were metacognitive strategies, suggesting that the learners were self-directed and attempting to manage their own learning in an informal context. They also showed idiosyncrasies in their use of learner strategies. Attempts to explain the learners’ strategy use in relation to their levels of proficiency in English and contextual factors, as well as several other factors, are offered. Implications for target-country institutions in terms of the provision of support to Chinese students are discussed.

Researching task difficulty: towards understanding L2 proficiency

The prime purpose of this article is to put teachers’, learners’ and research perspectives of task difficulty (TD) together and to investigate whether teachers’ and learners’ perceptions of and criteria for TD are in line with the available research on TD. A summary of three interrelated empirical studies on learner and teacher perceptions of TD is presented before the findings are discussed in light of the current models of TD. The chapter concludes by arguing that cognitive demands of a task are a signifcant factor that contributes to TD and should be considered more critically by L2 educators and SLA researchers.

On the typological economy of syntactic transfer: word order and relative clause high/low attachment preference in L3 Brazilian Portuguese

One central question in the formal linguistic study of adult multilingual morphosyntax (i.e., L3/Ln acquisition) involves determining the role(s) the L1 and/or the L2 play(s) at the L3 initial state (e.g., Bardel & Falk, Second Language Research 23: 459–484, 2007; Falk & Bardel, Second Language Research: forthcoming; Flynn et al., The International Journal of Multilingualism 8: 3–16, 2004; Rothman, Second Language Research: forthcoming; Rothman & Cabrelli, On the initial state of L3 (Ln) acquisition: Selective or absolute transfer?: 2007; Rothman & Cabrelli Amaro, Second Language Research 26: 219–289, 2010). The present article adds to this general program, testing Rothman's (Second Language Research: forthcoming) model for L3 initial state transfer, which when relevant in light of specific language pairings, maintains that typological proximity between the languages is the most deterministic variable determining the selection of syntactic transfer. Herein, I present empirical evidence from the later part of the beginning stages of L3 Brazilian Portuguese (BP) by native speakers of English and Spanish, who have attained an advanced level of proficiency in either English or Spanish as an L2. Examining the related domains of syntactic word order and relative clause attachment preference in L3 BP, the data clearly indicate that Spanish is transferred for both experimental groups irrespective of whether it was the L1 or L2. These results are expected by Rothman's (Second Language Research: forthcoming) model, but not necessarily predicted by other current hypotheses of multilingual syntactic transfer; the implications of this are discussed.

“I still can’t question”: issues affecting EFL development in an immersion environment

This study examined the development of EFL proficiency in an immersion environment. Adult Chinese speakers of English were tested at the beginning and end of a ten-month period of immersion in the UK on their acquisition of English question forms using a timed grammaticality judgement task. Participants showed significantly faster response times after ten months, but no significant difference in accuracy of target-like judgements, suggesting that immersion benefits fluency more than accuracy.