Microcomputer-Assisted Mathematics: Computer-Assisted Polar Graphing

1987 ◽  
Vol 80 (3) ◽  
pp. 246-250
Author(s):  
Karen Doyle Walton ◽  
J. Doyle Walton
Keyword(s):  
Secondary School ◽  
Coordinate System ◽  
Polar Coordinates ◽  
Computer Assisted ◽  
College Level ◽  
Rectangular Coordinates ◽  
The Subject

Faced with the dilemma of how to teach polar coordinates? Whether the subject is being introduced at the secondary school or college level, the problem is the same. At either level, the objectives include the following; (1) introduce a new coordinate system, relating (x, y) rectangular coordinates to (r, Q) polar coordinates; (2) enable the students to plot polar equations; (3) acquaint students with standard types of polar graphs; and (4) find points of intersection of two polar graphs. This article presents a method of using the microcomputer to teach polar coordinates and graphing in an effective, interesting way, avoiding the drudgery of having students plot hundreds of points.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

The characteristics of transforming coordinates from the geocentric system WGS-84 for the Mercator projection under low latitudes conditions

2018 ◽  
Vol 940 (10) ◽  
pp. 2-6
Author(s):  
J.A. Younes ◽  
M.G. Mustafin
Keyword(s):  
Coordinate System ◽  
Satellite System ◽  
Programming Algorithm ◽  
Low Latitude ◽  
Model Calculations ◽  
Mercator Projection ◽  
Low Latitudes ◽  
Rectangular Coordinates ◽  
Global Navigation Satellite ◽  
Coordination Methods

The issue of calculating the plane rectangular coordinates using the data obtained by the satellite observations during the creation of the geodetic networks is discussed in the article. The peculiarity of these works is in conversion of the coordinates into the Mercator projection, while the plane coordinate system on the base of Gauss-Kruger projection is used in Russia. When using the technology of global navigation satellite system, this task is relevant for any point (area) of the Earth due to a fundamentally different approach in determining the coordinates. The fact is that satellite determinations are much more precise than the ground coordination methods (triangulation and others). In addition, the conversion to the zonal coordinate system is associated with errors; the value at present can prove to be completely critical. The expediency of using the Mercator projection in the topographic and geodetic works production at low latitudes is shown numerically on the basis of model calculations. To convert the coordinates from the geocentric system with the Mercator projection, a programming algorithm which is widely used in Russia was chosen. For its application under low-latitude conditions, the modification of known formulas to be used in Saudi Arabia is implemented.

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

scholarly journals Using Cartographies to Map Time and Space in Teacher Learning in and Outside School

2021 ◽  
Vol 20 ◽  
pp. 160940692199290
Author(s):  
Paulo Padilla-Petry ◽  
Fernando Hernández-Hernández ◽  
Joan-Anton Sánchez-Valero
Keyword(s):  
Secondary School ◽  
Teacher Learning ◽  
Secondary School Teachers ◽  
Leisure Activities ◽  
Visual Methods ◽  
School Teachers ◽  
Video Recordings ◽  
The Subject ◽  
Pedagogical Relations ◽  
Over Time

This article explores the relations between teachers’ visual cartographies and oral narratives to better understand the spatial and temporal relations on teacher learning. It builds on a research project whose main questions were: 1) How and where do secondary school teachers learn to teach? 2) What are the consequences of this learning in their pedagogical relations and their students’ learning processes and results? Since narrative research has been a common way of approaching the subject and have led to an emphasis on learning as a journey across contexts and over time, some of its contributions to explore teachers’ learning paths are theoretically discussed, and visual methods, particularly cartographies, are also examined. Furthermore, the article presents the analysis of cartographies and video recordings of 29 secondary school teachers focusing on the interactions in different spaces and moments in time described by them. Findings suggest that learning to be a teacher may happen in interactions with objects, people and spaces beyond the boundaries of school, university and formal places of training and learning. They also show that the rhizomatic character of the cartographies may not prevent teleological thinking or the idea that any kind of learning is purposeful. Finally, this paper concludes that teachers’ learning does not fit the representational frame that distinguishes between formal contents and leisure activities, classrooms and private spaces, lessons and bodies, emotions and knowledge.

scholarly journals Co-occurrence subgroups of child sexual abuse, health risk behaviors and their associations among secondary school students in China

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Yan Zhang ◽  
Xiayun Zuo ◽  
Yanyan Mao ◽  
Qiguo Lian ◽  
Shan Luo ◽  
...  
Keyword(s):  
Sexual Abuse ◽  
Child Sexual Abuse ◽  
Secondary School ◽  
Health Risk ◽  
Risk Behaviors ◽  
Latent Variable ◽  
Secondary School Students ◽  
Latent Class ◽  
Computer Assisted ◽  
School Students

Abstract Background Little is known on the co-occurrence and heterogeneity of child sexual abuse (CSA) or health risk behavior (HRB) prevalence nor the associations among the victims. Objectives To detect the prevalence and subgroups of adolescents reporting CSAs or HRBs, and to examine the association between the subgroups. Methods Participants were secondary school students in a national survey in China (N = 8746). Self-reported CSA and HRB experiences were collected through a computer assisted questionnaire. Prevalence and confidence intervals were calculated. Multigroup latent class analysis (LCA) was used to examine latent subgroups of CSA and HRB. Dual latent class regression analysis was used to examine the association between CSA and HRB classes. Results A total of 8746 students participated in our study. The prevalence of having ever experienced any of the reported seven CSA items was 12.9%. The preferred LCA model consisted of a three-class CSA latent variable, i.e. “Low CSAs”(95.7% of the total respondents), “Verbal or exhibitionism CSAs”(3.3%), and “high multiple CSAs” (1.1%); and a three-class HRB latent variable, i.e. “Low HRBs”(70.5%), “externalizing HRBs” (20.7%), and “internalizing HRBs” (8.7%). Students in the “Verbal or exhibitionism CSAs” or “high multiple CSAs” classes had higher probabilities of being in “externalizing HRBs” or “internalizing HRBs” classes. The probabilities were higher in “high multiple CSAs” class(male externalizing OR 4.05, 95%CI 1.71–9.57; internalizing OR 11.77, 95%CI 4.76–29.13; female externalizing OR 4.97, 95%CI 1.99–12.44; internalizing OR 9.87, 95%CI 3.71–26.25) than those in “Verbal or exhibitionism CSA”(male externalizing OR 2.51, 95%CI 1.50–4.20; internalizing OR 3.08, 95%CI 1.48–6.40; female externalizing OR 2.53, 95%CI 1.63–3.95; internalizing OR 6.05, 95%CI 3.73–9.80). Conclusions Prevalence of CSA items varies. Non-contact CSAs are the most common forms of child sexual abuse among Chinese school students. There are different latent class co-occurrence patterns of CSA items or HRB items among the respondents. CSA experiences are in association with HRB experiences and the associations between latent classes are dose-responded. Multi-victimization has more significantly negative effects. The results could help identify high-risk subgroups and promote more nuanced interventions addressing adverse experiences and risk behaviors among at-risk adolescents.

Science education: too much of too little.

1990 ◽  
Vol 258 (6) ◽  
pp. S3 ◽  
Author(s):  
R L Malvin
Keyword(s):  
Science Education ◽  
Secondary School ◽  
Science Teachers ◽  
School Children ◽  
Scientific Literacy ◽  
Scientific Productivity ◽  
College And University ◽  
The Subject ◽  
University Scientists ◽  
Read Number

By all measures attempted, scientific literacy of the American public is sadly wanting. The vast majority of our secondary school children and adults have no knowledge of most of the basic terms or concepts of science. The reasons for this shortcoming are many but prominent among them are sadly deficient texts, teachers untrained in the subject matter they teach, and college and university scientists who divorce themselves from the problem, although probably deploring it. Our institutions are no aid. They reward scientific productivity (read: number of papers published per year and research dollars), not teaching. Some suggested cures are production of better texts, training of science teachers in the field in which they teach, and, most importantly, involvement of scientists in the process. We must be willing to spend some of our time with secondary school pupils and their teachers. All will gain from the experience.

scholarly journals Psycho-administrative determinants for choice of physical education among senior secondary school students at external examination bodies

2021 ◽  
Vol 8 (2) ◽  
pp. 109-118
Author(s):  
Olusola Samson
Keyword(s):  
Physical Education ◽  
Secondary School ◽  
Secondary School Students ◽  
School Students ◽  
Chi Square ◽  
Senior Secondary School ◽  
External Examination ◽  
Validated Questionnaire ◽  
The Subject ◽  
Senior Secondary

Empirical observations reveal low enrolment of senior secondary school students for physical education at external examination bodies. The poor rate of students' choice of the subject at this level is a matter of concern to professionals, given the fact of monumental benefits of physical education as a science subject to humanity. The study was conducted to examine how psycho-administrative factors influence the choice of physical education by senior secondary school students at external examination bodies (in Nigeria) to come up with modalities to increase enrolment of the subject at external examination bodies. Descriptive method was applied for the study due to large respondents involved. Self-developed validated questionnaire tagged psycho-administrative determinants for choice of physical education among senior secondary school students at external examination bodies (PADGPEAS) was applied for the research. Out of three thousand and twenty-four (3024) questionnaire forms administered, only two thousand and fifty (2950) copies completed and returned were coded for analysis, with the use of descriptive statistics of percentages and nonparametric statistics of Chi-square (x 2) at 0.05 level of significant. Results unraveled a remarkable influence of psycho-administrative variables on the choice at physical education among senior secondary school students at external examination bodies. Based on this outcome, it is suggested that utilization of variety of methods by physical education teachers will go a long way to kindle the interest of the students for the subject. Enlightenment of students and parents on the values of physical education will facilitate remarkable positive attitude of both parts that relocate their position in favor of the subject.

scholarly journals Students learning with interactive virtual math: an exploratory study in the classroom

2017 ◽  
Vol 1 (1) ◽  
pp. 80 ◽  
Author(s):  
Sônia Palha
Keyword(s):  
Secondary School ◽  
Secondary School Students ◽  
Tertiary Education ◽  
Learning Experience ◽  
Small Scale ◽  
School Students ◽  
Dynamic Events ◽  
The Subject ◽  
Scale Experiment ◽  
Further Development

Interactive Virtual Math (IVM) is a visualization tool to support secondary school students’ learning of graphs by dynamic events. In the prototype version students construct a graph and try to improve it themselves and with the feedback of the tool. In a small-scale experiment, which involved four classes at secondary and tertiary education and their mathematics teachers we investigated how the students used the tool in the classroom. In this study we focus on the students learning experience and the results are expected to provide knowledge and directions for further development of the tool. The corpus data consists of self-reported questionnaires and lessons observations. One main finding is that students, at different school levels, find the tool useful to construct or improve graphical representations and it can help to get a better understanding of the subject. The tool features that helped students most were the self-construction of the graphs and to get feedback about their own graph at the end. Other findings are that the students can work independently with the tool and we know more about the tool features that are attractive or need to be improved.

A college-level, computer-assisted course in nutrition

1984 ◽  
Vol 16 (2) ◽  
pp. 46-50 ◽  
Author(s):  
Lyndon B. Carew ◽  
David W. Elvin ◽  
Bethany A. Yon ◽  
Frances A. Alster
Keyword(s):  
Computer Assisted ◽  
College Level
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