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.

Evoked prior learning experience and approach to learning as predictors of academic achievement

Background. In separate studies and research from different perspectives, five factors are found to be among those related to higher quality outcomes of student learning (academic achievement). Those factors are higher self-efficacy, deeper approaches to learning, higher quality teaching, students’ perceptions that their workload is appropriate, and greater learning motivation. University learning improvement strategies have been built on these research results. Aim. To investigate how students’ evoked prior experience, perceptions of their learning environment, and their approaches to learning collectively contribute to academic achievement. This is the first study to investigate motivation and self-efficacy in the same educational context as conceptions of learning, approaches to learning and perceptions of the learning environment. Sample. Undergraduate students (773) from the full range of disciplines were part of a group of over 2,300 students who volunteered to complete a survey of their learning experience. On completing their degrees 6 and 18 months later, their academic achievement was matched with their learning experience survey data. Method. A 77-item questionnaire was used to gather students’ self-report of their evoked prior experience (self-efficacy, learning motivation, and conceptions of learning), perceptions of learning context (teaching quality and appropriate workload), and approaches to learning (deep and surface). Academic achievement was measured using the English honours degree classification system. Analyses were conducted using correlational and multi-variable (structural equation modelling) methods. Results. The results from the correlation methods confirmed those found in numerous earlier studies. The results from the multi-variable analyses indicated that surface approach to learning was the strongest predictor of academic achievement, with self-efficacy and motivation also found to be directly related. In contrast to the correlation results, a deep approach to learning was not related to academic achievement, and teaching quality and conceptions of learning were only indirectly related to achievement. Conclusions. Research aimed at understanding how students experience their learning environment and how that experience relates to the quality of their learning needs to be conducted using a wider range of variables and more sophisticated analytical methods. In this study of one context, some of the relations found in earlier bivariate studies, and on which learning intervention strategies have been built, are not confirmed when more holistic teaching–learning contexts are analysed using multi-variable methods.

The Mathematics of Control Theory

This text contains papers presented at the Institute of Mathematics and its Applications Conference on Control Theory, held at the University of Strathclyde in Glasgow. The contributions cover a wide range of topics of current interest to theoreticians and practitioners including algebraic systems theory, nonlinear control systems, adaptive control, robustness issues, infinite dimensional systems, applications studies and connections to mathematical aspects of information theory and data-fusion.

Mathematics as a tool in the Life Sciences

Teaching mathematics to students in the biological sciences is often fraught with difficulty. Students often discover mathematics to be a very 'dry' subject in which it is difficult to see the motivation of learning it given its often abstract application. In this paper I advocate the use of mathematical modelling as a method for engaging students in understanding the use of mathematics in helping to solve problems in the Biological Sciences. The concept of mathematics as a laboratory tool is introduced and the importance of presenting students with relevant, real-world examples of applying mathematics in the Biological Sciences is discussed.

Vocabulary size revisited: the link between vocabulary size and academic achievement

Many researchers have tried to assess the number of words adults know. A general conclusion which emerges from such studies is that vocabularies of English monolingual adults are very large with considerable variation. This variation is important given that the vocabulary size of schoolchildren in the early years of school is thought to materially affect subsequent educational attainment. The data is difficult to interpret, however, because of the different methodologies which researchers use. The study in this paper uses the frequency-based vocabulary size test from Goulden et al (1990) and investigates the vocabulary knowledge of undergraduates in three British universities. The results suggest that monolingual speaker vocabulary sizes may be much smaller than is generally thought with far less variation than is usually reported. An average figure of about 10,000 English words families emerges for entrants to university. This figure suggests that many students must struggle with the comprehension of university level texts.

The effect of class size on student achievement: evidence from Bangladesh

This study examines the effect of class size on student achievement in Bangladesh using national secondary school survey data. A Ministry of Education rule regarding allocation of teachers to secondary grades is exploited to construct an instrument for class size. This rule causes a discontinuity between grade enrolment and class size thereby generating exogenous variation in the latter. It is found that OLS and IV estimates of class size effects have perverse signs: both yield a positive coefficient on the class size variable. The results suggest that reduction in class size in secondary grades is not efficient in a developing country like Bangladesh. Last, as by-product, some evidence is found suggesting that greater competition among schools improve student achievement.

Mathematics applied to the climate system: outstanding challenges and recent progress

The societal need for reliable climate predictions and a proper assessment of their uncertainties is pressing. Uncertainties arise not only from initial conditions and forcing scenarios, but also from model formulation. Here, we identify and document three broad classes of problems, each representing what we regard to be an outstanding challenge in the area of mathematics applied to the climate system. First, there is the problem of the development and evaluation of simple physically based models of the global climate. Second, there is the problem of the development and evaluation of the components of complex models such as general circulation models. Third, there is the problem of the development and evaluation of appropriate statistical frameworks. We discuss these problems in turn, emphasizing the recent progress made by the papers presented in this Theme Issue. Many pressing challenges in climate science require closer collaboration between climate scientists, mathematicians and statisticians. We hope the papers contained in this Theme Issue will act as inspiration for such collaborations and for setting future research directions.

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.

Relationship between classroom authority and epistemological beliefs as espoused by primary school mathematics teachers from the very high and very low socio-economic regions in Thailand

This article presents findings of a larger single-country comparative study which set out to better understand primary school teachers’ mathematics education-related beliefs in Thailand. By combining the interview and observation data collected in the initial stage of this study with data gathered from the relevant literature, the 8-belief / 22-item ‘Thai Teachers’ Mathematics Education-related Beliefs’ (TTMEB) Scale was developed. The results of the Mann-Whitney U Test showed that Thai teachers in the two examined socio-economic regions espouse statistically different beliefs concerning the source and stability of mathematical knowledge, as well as classroom authority. Further, these three beliefs are found to be significantly and positively correlated.

Achievement motives and goals: a developmental analysis

Achievement motivation represents the energization and direction of competence-based behavior. Despite the ubiquity and importance of achievement motivation across the life span, developmental research in this area is quite sparse. In this chapter, we discuss developmental considerations and provide an overview of the developmentally relevant research that has been conducted on achievement motivation. Our review focuses specifically on the two most prominent constructs that have emerged in the achievement motivation literature in the past century: Motive dispositions (the need for achievement and fear of failure) and goals (mastery-approach, performance-approach, mastery-avoidance, and performance-avoidance achievement goals). (PsycINFO Database Record (c) 2012 APA, all rights reserved)(chapter)

On the measurement of achievement goals: critique, illustration, and application

The authors identified several specific problems with the measurement of achievement goals in the current literature and illustrated these problems, focusing primarily on A. J. Elliot and H. A. McGregor's (2001) Achievement Goal Questionnaire (AGQ). They attended to these problems by creating the AGQ-Revised and conducting a study that examined the measure's structural validity and predictive utility with 229 (76 male, 150 female, 3 unspecified) undergraduates. The hypothesized factor and dimensional structures of the measure were confirmed and shown to be superior to a host of alternatives. The predictions were nearly uniformly supported with regard to both the antecedents (need for achievement and fear of failure) and consequences (intrinsic motivation and exam performance) of the 4 achievement goals. In discussing their work, the authors highlight the importance and value of additional precision in the area of achievement goal measurement. (PsycINFO Database Record (c) 2012 APA, all rights reserved)(journal abstract)

A 3 × 2 achievement goal model

In the present research, a 3 × 2 model of achievement goals is proposed and tested. The model is rooted in the definition and valence components of competence, and encompasses 6 goal constructs: task-approach, task-avoidance, self-approach, self-avoidance, other-approach, and other-avoidance. The results from 2 studies provided strong support for the proposed model, most notably the need to separate task-based and self-based goals. Studies 1 and 2 yielded data establishing the 3 × 2 structure of achievement goals, and Study 2 documented the antecedents and consequences of each of the goals in the 3 × 2 model. Terminological, conceptual, and applied issues pertaining to the 3 × 2 model are discussed. (PsycINFO Database Record (c) 2012 APA, all rights reserved)(journal abstract)