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.

Band gap control via tuning of inversion degree in CdIn2S4 spinel

Based on theoretical arguments we propose a possible route for controlling the band-gap in the promising photovoltaic material CdIn2S4. Our ab initio calculations show that the experimental degree of inversion in this spinel (fraction of tetrahedral sites occupied by In) corresponds approximately to the equilibrium value given by the minimum of the theoretical inversion free energy at a typical synthesis temperature. Modification of this temperature, or of the cooling rate after synthesis, is then expected to change the inversion degree, which in turn sensitively tunes the electronic band-gap of the solid, as shown here by Heyd-Scuseria-Ernzerhof screened hybrid functional calculations.

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.

Speech-like and non-speech lip kinematics and coordination in aphasia

Background and aims: In addition to the well-known linguistic processing impairments in aphasia, oro-motor skills and articulatory implementation of speech segments are reported to be compromised to some degree in most types of aphasia. This study aimed to identify differences in the characteristics and coordination of lip movements in the production of a bilabial closure gesture between speech-like and nonspeech tasks in individuals with aphasia and healthy control subjects. Method and procedure: Upper and lower lip movement data were collected for a speech-like and a nonspeech task using an AG 100 EMMA system from five individuals with aphasia and five age and gender matched control subjects. Each task was produced at two rate conditions (normal and fast), and in a familiar and a less-familiar manner. Single articulator kinematic parameters (peak velocity, amplitude, duration, and cyclic spatio-temporal index) and multi-articulator coordination indices (average relative phase and variability of relative phase) were measured to characterize lip movements. Outcome and results: The results showed that when the two lips had similar task goals (bilabial closure) in speech-like versus nonspeech task, kinematic and coordination characteristics were not found to be different. However, when changes in rate were imposed on the bilabial gesture, only speech-like task showed functional adaptations, indicated by a greater decrease in amplitude and duration at fast rates. In terms of group differences, individuals with aphasia showed smaller amplitudes and longer movement durations for upper lip, higher spatio-temporal variability for both lips, and higher variability in lip coordination than the control speakers. Rate was an important factor in distinguishing the two groups, and individuals with aphasia were limited in implementing the rate changes. Conclusion and implications: The findings support the notion of subtle but robust differences in motor control characteristics between individuals with aphasia and the control participants, even in the context of producing bilabial closing gestures for a relatively simple speech-like task. The findings also highlight the functional differences between speech-like and nonspeech tasks, despite a common movement coordination goal for bilabial closure.

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.