Solution of differential equations by application of transformation groups

Report applies transformation groups to the solution of systems of ordinary differential equations and partial differential equations. Lies theorem finds an integrating factor for appropriate invariance group or groups can be found and can be extended to partial differential equations

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report, 17 Jan. 1967 - 16 Jan. 1968

Application of transformation groups to solution of partial differential equation

Application of group and transformation theory to the solution of ordinary and partial differential equations Final report

Lie transformation group for solution of partial differential equation

Prospective Teachers\u27 Use of Representations in Solving Statistical Tasks with Dynamic Statistical Software

This study examined a random stratified sample (n=62) of prospective teachers\u27 work across eight institutions on three tasks that utilized dynamic statistical software. Our work was guided by considering how teachers may utilize their statistical knowledge and technological statistical knowledge to engage in cycles of investigation. Although teachers did not tend to take full advantage of dynamic linking capabilities, they utilized a large variety of graphical representations and often added statistical measures or other augmentations to graphs as part of their analysis

The Quality of Mathematics Education Technology Literature

Background: The present study evaluated the quality of 1,165 scholarly literature papers about mathematics education technology literature.Purpose: The purpose of the present study was to determine the extent to which mathematics education technology literature reports the information needed to support the scientific basis of a study.Setting: N/AIntervention: N/AResearch Design: A systematic review was used to organize the data collection and analysis processes Data Collection and Analysis: A literature search was conducted to identify scholarly papers that addressed the use of technology in mathematics education. A coding process was developed to record descriptive information about each paper. The Quality Framework developed for this process provided a structure to identify key information across research types based on types of analyses conducted, assigning a certain number of possible points based on the type of research conducted.Findings: Dissertations accounted for a surprisingly high portion of the literature and research: 39.7% of the available literature and 57.0% of the research studies. The overall quality of the mathematics education technology literature was lower than we expected, averaging only 48.9% of the points possible. We noted that the quality of research papers, with respect to possible point values averaged 54.6% over four decades. For mathematics education technology researchers, manuscript reviewers, and editors, these results suggest that more attention is needed on the information being included and excluded from scholarly papers, especially with regard to connections to theoretical frameworks and research designs

Research in Mathematics Educational Technology: Current Trends and Future Demands

This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (Research Design, Teacher Knowledge, and TPACK) and three supplementary lenses (Data Sources, Outcomes, and NCTM Principles) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (e.g., knowledge, cognition, affect, and performance) suggest that the effects of incorporating graphing calculator and dynamic geometry technologies have been abundantly studied; however, the usefulness of the results was often limited by missing information regarding measures of validity, reliability, and/or trustworthiness

Inhibition of β-catenin signalling in dermal fibroblasts enhances hair follicle regeneration during wound healing.

New hair follicles (HFs) do not form in adult mammalian skin unless epidermal Wnt signalling is activated genetically or within large wounds. To understand the postnatal loss of hair forming ability we monitored HF formation at small circular (2 mm) wound sites. At P2, new HFs formed in back skin, but HF formation was markedly decreased by P21. Neonatal tail also formed wound-associated HFs, albeit in smaller numbers. Postnatal loss of HF neogenesis did not correlate with wound closure rate but with a reduction in Lrig1-positive papillary fibroblasts in wounds. Comparative gene expression profiling of back and tail dermis at P1 and dorsal fibroblasts at P2 and P50 showed a correlation between loss of HF formation and decreased expression of genes associated with proliferation and Wnt/β-catenin activity. Between P2 and P50, fibroblast density declined throughout the dermis and clones of fibroblasts became more dispersed. This correlated with a decline in fibroblasts expressing a TOPGFP reporter of Wnt activation. Surprisingly, between P2 and P50 there was no difference in fibroblast proliferation at the wound site but Wnt signalling was highly upregulated in healing dermis of P21 compared with P2 mice. Postnatal β-catenin ablation in fibroblasts promoted HF regeneration in neonatal and adult mouse wounds, whereas β-catenin activation reduced HF regeneration in neonatal wounds. Our data support a model whereby postnatal loss of hair forming ability in wounds reflects elevated dermal Wnt/β-catenin activation in the wound bed, increasing the abundance of fibroblasts that are unable to induce HF formation

The therapeutic potential of stem cells

In recent years, there has been an explosion of interest in stem cells, not just within the scientific and medical communities but also among politicians, religious groups and ethicists. Here, we summarize the different types of stem cells that have been described: their origins in embryonic and adult tissues and their differentiation potential in vivo and in culture. We review some current clinical applications of stem cells, highlighting the problems encountered when going from proof-of-principle in the laboratory to widespread clinical practice. While some of the key genetic and epigenetic factors that determine stem cell properties have been identified, there is still much to be learned about how these factors interact. There is a growing realization of the importance of environmental factors in regulating stem cell behaviour and this is being explored by imaging stem cells in vivo and recreating artificial niches in vitro. New therapies, based on stem cell transplantation or endogenous stem cells, are emerging areas, as is drug discovery based on patient-specific pluripotent cells and cancer stem cells. What makes stem cell research so exciting is its tremendous potential to benefit human health and the opportunities for interdisciplinary research that it presents

Endogenous fantasy and learning in digital games.

Many people believe that educational games are effective because they motivate children to actively engage in a learning activity as part of playing the game. However, seminal work by Malone (1981), exploring the motivational aspects of digital games, concluded that the educational effectiveness of a digital game depends on the way in which learning content is integrated into the fantasy context of the game. In particular, he claimed that content which is intrinsically related to the fantasy will produce better learning than that which is merely extrinsically related. However, this distinction between intrinsic and extrinsic (or endogenous and exogenous) fantasy is a concept that has developed a confused standing over the following years. This paper will address this confusion by providing a review and critique of the empirical and theoretical foundations of endogenous fantasy, and its relevance to creating educational digital games. Substantial concerns are raised about the empirical basis of this work and a theoretical critique of endogenous fantasy is offered, concluding that endogenous fantasy is a misnomer, in so far as the "integral and continuing relationship" of fantasy cannot be justified as a critical means of improving the effectiveness of educational digital games. An alternative perspective on the intrinsic integration of learning content is described, incorporating game mechanics, flow and representations

SMARTER Teamwork: System for Management, Assessment, Research, Training, Education, and Remediation for Teamwork

SMARTER Teamwork: System for Management, Assessment, Research, Training, Education, and Remediation for TeamworkThe rapid adoption of Team-Maker and the Comprehensive Assessment of Team MemberEffectiveness (CATME) tools for team formation and peer evaluation make it possible to extendtheir success to have a significant impact on the development of team skills in higher education.The web-based systems have been used by more than 110,000 students of more than 2400faculty at more than 500 institutions internationally—the figure below shows the growth of theuser base. 2400 The system has had 113,373 unique student users. 2200 Fitted curves are third order. 2000 1800 Faculty and staff 1600 1400 1200 Number of 1000 users 800 Institutions 600 400 Aug Oct. 2005 2012 200 0 0 1 2 3 4 5 6 7 Years since software was releasedThis paper and its accompanying poster will describe strategies for broadening the scope of thosetools into a complete system for the management of teamwork in undergraduate education. TheSystem for the Management, Assessment, Research, Training, Education, and Remediation ofTeamwork (SMARTER Teamwork) has three specific goals: 1) to equip students to work inteams by providing them with training and feedback, 2) to equip faculty to manage student teamsby providing them with information and tools to facilitate best practices, and 3) to equipresearchers to understand teams by broadening the system’s capabilities to collect additionaltypes of data so that a wider range of research questions can be studied through a secureresearcher interface. The three goals of the project support each other in hierarchical fashion:research informs faculty practice, faculty determine the students’ experience, which, if wellmanaged based on research findings, equips students to work in teams. Our strategies forachieving these goals are based on a well-accepted training model that has five elements:information, demonstration, practice, feedback, and remediation.The paper that will be submitted and the poster presented at the conference will focus on newfeatures of the system, the development of training materials, and the deployment of a partnerwebsite that shares information about the SMARTER tools for teamwork and provides basicinformation about teamwork and team management