The Importance of Writing in Mathematics: Why Writing Allows for a Deeper understanding of the Mathematical Content

When learning a new subject or course material, writing can be an essential tool for a deeper understanding of content. The importance of writing in mathematics is no different—yet in mathematics, writing seems to be the odd-ball out (exception). However, in classrooms where students have little depth of understanding mathematics, writing can be a vital instrument in the learning process. A common misconception when learning mathematics is that it is all numbers and memorizing equations—when in fact writing is a main component and first step to developing a deeper understanding of the mathematical content. As students continue to grow and mature mentally, their traditional reading and writing literacy increases

An Alternative for Alternatives: Designing a Teacher Licensure Program for Teacher-led Schools

The research question addressed in this project was, what are the essential components of an alternative licensure program designed to best prepare teachers for success in a teacher-led school? It documents the creation of a teacher preparation program designed specifically for the unique skills and knowledge sets required for a teacher to be successful in a teacher-led school setting. The research question was influenced by the researcher’s own experience, both as a product of a traditional teacher preparation program and as a teacher in a teacher-led school. To determine the essential components for the teacher preparation program, the capstone first reviews the relevant literature, encompassing the history of teacher preparation in the United States as well as defining teacher-led schools. To determine the necessary elements, the researcher conducted interviews with many currently working in the field in various capacities: teachers, researchers, education writers, administrators, higher education faculty, and education policy advocates. These interviews were used to create a draft of a teacher preparation program. This draft was then reviewed and critiqued by a series of small focus groups. This final feedback was used to refine the draft into the capstone’s final result: a teacher-preparation program designed specifically for a teacher-led school setting

Getting the best from tractor tyres

The amount of pull a tractor develops depends largely on tyre efficiency and so with so many tyre size options for the one tractor model it is very easy to make the wrong decision on tyre fitment. Tyre efficiency varies with tractor weight, soil conditions, inflation pressure and tyre size. Hers we look at some of these factors and how changing them may affect efficiency

Hypercluster parallel processing library user's manual

This User's Manual describes the Hypercluster Parallel Processing Library, composed of FORTRAN-callable subroutines which enable a FORTRAN programmer to manipulate and transfer information throughout the Hypercluster at NASA Lewis Research Center. Each subroutine and its parameters are described in detail. A simple heat flow application using Laplace's equation is included to demonstrate the use of some of the library's subroutines. The manual can be used initially as an introduction to the parallel features provided by the library. Thereafter it can be used as a reference when programming an application

Initial operating capability for the hypercluster parallel-processing test bed

The NASA Lewis Research Center is investigating the benefits of parallel processing to applications in computational fluid and structural mechanics. To aid this investigation, NASA Lewis is developing the Hypercluster, a multi-architecture, parallel-processing test bed. The initial operating capability (IOC) being developed for the Hypercluster is described. The IOC will provide a user with a programming/operating environment that is interactive, responsive, and easy to use. The IOC effort includes the development of the Hypercluster Operating System (HYCLOPS). HYCLOPS runs in conjunction with a vendor-supplied disk operating system on a Front-End Processor (FEP) to provide interactive, run-time operations such as program loading, execution, memory editing, and data retrieval. Run-time libraries, that augment the FEP FORTRAN libraries, are being developed to support parallel and vector processing on the Hypercluster. Special utilities are being provided to enable passage of information about application programs and their mapping to the operating system. Communications between the FEP and the Hypercluster are being handled by dedicated processors, each running a Message-Passing Kernel, (MPK). A shared-memory interface allows rapid data exchange between HYCLOPS and the communications processors. Input/output handlers are built into the HYCLOPS-MPK interface, eliminating the need for the user to supply separate I/O support programs on the FEP

A message passing kernel for the hypercluster parallel processing test bed

A Message-Passing Kernel (MPK) for the Hypercluster parallel-processing test bed is described. The Hypercluster is being developed at the NASA Lewis Research Center to support investigations of parallel algorithms and architectures for computational fluid and structural mechanics applications. The Hypercluster resembles the hypercube architecture except that each node consists of multiple processors communicating through shared memory. The MPK efficiently routes information through the Hypercluster, using a message-passing protocol when necessary and faster shared-memory communication whenever possible. The MPK also interfaces all of the processors with the Hypercluster operating system (HYCLOPS), which runs on a Front-End Processor (FEP). This approach distributes many of the I/O tasks to the Hypercluster processors and eliminates the need for a separate I/O support program on the FEP

Turbomachinery CFD on parallel computers

The role of multistage turbomachinery simulation in the development of propulsion system models is discussed. Particularly, the need for simulations with higher fidelity and faster turnaround time is highlighted. It is shown how such fast simulations can be used in engineering-oriented environments. The use of parallel processing to achieve the required turnaround times is discussed. Current work by several researchers in this area is summarized. Parallel turbomachinery CFD research at the NASA Lewis Research Center is then highlighted. These efforts are focused on implementing the average-passage turbomachinery model on MIMD, distributed memory parallel computers. Performance results are given for inviscid, single blade row and viscous, multistage applications on several parallel computers, including networked workstations