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.

Computing Fresnel integrals via modified trapezium rules

In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J Math Phys 34:298–307, 1956) and Hunter and Regan (Math Comp 26:539–541, 1972). We construct approximations which we prove are exponentially convergent as a function of N , the number of quadrature points, obtaining explicit error bounds which show that accuracies of 10−15 uniformly on the real line are achieved with N=12 , this confirmed by computations. The approximations we obtain are attractive, additionally, in that they maintain small relative errors for small and large argument, are analytic on the real axis (echoing the analyticity of the Fresnel integrals), and are straightforward to implement.

Optimal steady motions for oriented vehicles

Motivated by the motion planning problem for oriented vehicles travelling in a 3-Dimensional space; Euclidean space E3, the sphere S3 and Hyperboloid H3. For such problems the orientation of the vehicle is naturally represented by an orthonormal frame over a point in the underlying manifold. The orthonormal frame bundles of the space forms R3,S3 and H3 correspond with their isometry groups and are the Euclidean group of motion SE(3), the rotation group SO(4) and the Lorentzian group SO(1; 3) respectively. Orthonormal frame bundles of space forms coincide with their isometry groups and therefore the focus shifts to left-invariant control systems defined on Lie groups. In this paper a method for integrating these systems is given where the controls are time-independent. For constant twist motions or helical motions, the corresponding curves g(t) 2 SE(3) are given in closed form by using the well known Rodrigues’ formula. However, this formula is only applicable to the Euclidean case. This paper gives a method for computing the non-Euclidean screw/helical motions in closed form. This involves decoupling the system into two lower dimensional systems using the double cover properties of Lie groups, then the lower dimensional systems are solved explicitly in closed form.

Computing journey start times with recurrent traffic conditions

n this study, the authors discuss the effective usage of technology to solve the problem of deciding on journey start times for recurrent traffic conditions. The developed algorithm guides the vehicles to travel on more reliable routes that are not easily prone to congestion or travel delays, ensures that the start time is as late as possible to avoid the traveller waiting too long at their destination and attempts to minimise the travel time. Experiments show that in order to be more certain of reaching their destination on time, a traveller has to leave early and correspondingly arrive early, resulting in a large waiting time. The application developed here asks the user to set this certainty factor as per the task in hand, and computes the best start time and route.

Cloud computing in e-science: research challenges and opportunities

SOA (Service Oriented Architecture), workflow, the Semantic Web, and Grid computing are key enabling information technologies in the development of increasingly sophisticated e-Science infrastructures and application platforms. While the emergence of Cloud computing as a new computing paradigm has provided new directions and opportunities for e-Science infrastructure development, it also presents some challenges. Scientific research is increasingly finding that it is difficult to handle “big data” using traditional data processing techniques. Such challenges demonstrate the need for a comprehensive analysis on using the above mentioned informatics techniques to develop appropriate e-Science infrastructure and platforms in the context of Cloud computing. This survey paper describes recent research advances in applying informatics techniques to facilitate scientific research particularly from the Cloud computing perspective. Our particular contributions include identifying associated research challenges and opportunities, presenting lessons learned, and describing our future vision for applying Cloud computing to e-Science. We believe our research findings can help indicate the future trend of e-Science, and can inform funding and research directions in how to more appropriately employ computing technologies in scientific research. We point out the open research issues hoping to spark new development and innovation in the e-Science field.

The MELODIES project: integrating diverse data using Linked Data and cloud computing

We present an overview of the MELODIES project, which is developing new data-intensive environmental services based on data from Earth Observation satellites, government databases, national and European agencies and more. We focus here on the capabilities and benefits of the project’s “technical platform”, which applies cloud computing and Linked Data technologies to enable the development of these services, providing flexibility and scalability.

Major differences of cloud computing adoption in universities: Europe vs. Middle East

The extensive use of cloud computing in educational institutes around the world brings unique challenges for universities. Some of these challenges are due to clear differences between Europe and Middle East universities. These differences stem from the natural variation between people. Cloud computing has created a new concept to deal with software services and hardware infrastructure. Some benefits are immediately gained, for instance, to allow students to share their information easily and to discover new experiences of the education system. However, this introduces more challenges, such as security and configuration of resources in shared environments. Educational institutes cannot escape from these challenges. Yet some differences occur between universities which use cloud computing as an educational tool or a form of social connection. This paper discusses some benefits and limitations of using cloud computing and major differences in using cloud computing at universities in Europe and the Middle East, based on the social perspective, security and economics concepts, and personal responsibility.

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.