Sharing Teaching Ideas: Making Connections between Sequences and Mathematical Models

2000 ◽  
Vol 93 (5) ◽  
pp. 434-436
Author(s):  
Bob Horton
Keyword(s):  
Mathematical Models ◽  
Secondary Mathematics ◽  
Exponential Models ◽  
Mathematics Curricula ◽  
Almost All ◽  
Teaching Ideas

Almost all secondary mathematics curricula include linear and exponential models. More and more programs also include arithmetic and geometric sequences, as well. These topics are linked, but students often do not make the connections.

scholarly journals Fitting mathematical models to lactation curves from holstein cows in the southwestern region of the state of Parana, Brazil

2015 ◽  
Vol 87 (1) ◽  
pp. 503-517 ◽  
Author(s):  
Abílio G.T. Ferreira ◽  
Douglas S. Henrique ◽  
Ricardo A.M. Vieira ◽  
Emilyn M. Maeda ◽  
Altair A. Valotto
Keyword(s):  
Mathematical Models ◽  
Milk Production ◽  
Information Criterion ◽  
The State ◽  
Holstein Cows ◽  
Suitable Model ◽  
Almost All ◽  
Quality Of Fit ◽  
Wood Model

The objective of this study was to evaluate four mathematical models with regards to their fit to lactation curves of Holstein cows from herds raised in the southwestern region of the state of Parana, Brazil. Initially, 42,281 milk production records from 2005 to 2011 were obtained from "Associação Paranaense de Criadores de Bovinos da Raça Holandesa (APCBRH)". Data lacking dates of drying and total milk production at 305 days of lactation were excluded, resulting in a remaining 15,142 records corresponding to 2,441 Holstein cows. Data were sorted according to the parity order (ranging from one to six), and within each parity order the animals were divided into quartiles (Q25%, Q50%, Q75% and Q100%) corresponding to 305-day lactation yield. Within each parity order, for each quartile, four mathematical models were adjusted, two of which were predominantly empirical (Brody and Wood) whereas the other two presented more mechanistic characteristics (models Dijkstra and Pollott). The quality of fit was evaluated by the corrected Akaike information criterion. The Wood model showed the best fit in almost all evaluated situations and, therefore, may be considered as the most suitable model to describe, at least empirically, the lactation curves of Holstein cows raised in Southwestern Parana.

How Reform Secondary Mathematics Texts Stack Up against NCTM's Principles and Standards

2001 ◽  
Vol 94 (7) ◽  
pp. 540-589
Author(s):  
Tami S. Martin ◽  
Cheryl A. Hunt ◽  
John Lannin ◽  
William Leonard ◽  
Gerald L. Marshall ◽  
...  
Keyword(s):  
Secondary Mathematics ◽  
School Mathematics ◽  
Content Standards ◽  
Distinctive Features ◽  
Mathematics Curricula ◽  
Principles And Standards

This analysis of the five NSF–funded secondary mathematics curricula describes their alignment with the Process Standards and Content Standards in Principles and Standards for School Mathematics. Distinctive features and examples are included.

Projects

1997 ◽  
Vol 90 (3) ◽  
pp. 254-255
Author(s):  
Sharon Stenglein
Keyword(s):  
High School ◽  
Middle School ◽  
Mathematics Teachers ◽  
National Science Foundation ◽  
Secondary Mathematics ◽  
School Mathematics ◽  
High School Mathematics ◽  
National Science ◽  
Mathematics Curricula ◽  
High School Mathematics Teachers

ln this National Science Foundation (NFS) Teacher Enhancement Project, fifty Minnesota middle school and high school mathematics teachers are collaborating with three Saint Olaf CoUege mathematics professors to integrate inquiry-based geometry and visualization across their secondary mathematics curricula.

Kinematic Analysis of Swiss Lever Escapement

2014 ◽  
Vol 945-949 ◽  
pp. 684-689
Author(s):  
Jie Pan ◽  
Yu Fu ◽  
Ru Xu Du
Keyword(s):  
Mathematical Models ◽  
Kinematic Analysis ◽  
Critical Role ◽  
Half Cycle ◽  
Depth Study ◽  
Almost All ◽  
Escapement Mechanism

The escapement mechanism in a mechanical watch movement plays a critical role. Its purpose is to maintain and count the oscillations of the balance wheel. The timekeeping accuracy is therefore regulated. The motion of the escapement mechanism is highly complicated and no in-depth study on its kinematics has been done by now. This paper investigates the kinematics of the Swiss lever escapement which is used in almost all mechanical watches. One half cycle of the motion is described in different phases. Mathematical models for each key component are developed. Simulation result shows that the model is precise in describing and predicting the motion of the escapement. This method is essential for improving and optimizing the design.

SULLE RACCOLTE MUSEALI ITALIANE DI MODELLI PER LE MATEMATICHE SUPERIORI

Nuncius ◽  
2001 ◽  
Vol 16 (2) ◽  
pp. 781-790 ◽  
Author(s):  
FRANCO PALLADINO ◽  
NICLA PALLADINO
Keyword(s):  
Mathematical Models ◽  
Web Sites ◽  
General Catalogue ◽  
The 1950S ◽  
Almost All

Abstracttitle SUMMARY /title We present here the general catalogue and the website of the mathematical models found in the Italian universities of Catania, Messina, Bari, Naples, Rome, Florence, Bologna, Modena, Ferrara, Parma, Pavia, Milan, Padua, Turin and Genoa. For the most part they consist of old models published by the firms Ludwig Brill in Darmstadt, Martin Schilling in Halle an der Saale (later Leipzig), by H. Wiener for G. B. Teubner in Leipzig or belonging to the Collections Charles Muret published by Charles Delagrave in Paris. Other models were produced by different firms. A small number were even produced in Italy at the laboratories annexed to universities and, among these we also include the reproduction created in Florence by Luigi Campedelli in the 1950s with the support of the Unione Matematica Italiana. The research on the models (almost all of which are accompanied by the relevant images) can be carried out principally on the basis of the following criteria: Name of model - Catalogue - Material - Year of publication - Designer - Builder - Publisher - Location. The address of the mirrored web sites are: www.dmi.unisa.it/people/palladino/modelli and www.dma.unina. it/~nicla.palladino/catalogo.

scholarly journals UnderstandingThe Problem of Social Cost

2014 ◽  
Vol 11 (2) ◽  
pp. 329-352 ◽  
Author(s):  
BRETT M. FRISCHMANN ◽  
ALAIN MARCIANO
Keyword(s):  
Mathematical Models ◽  
Real World ◽  
Social Cost ◽  
Legal Cases ◽  
New Approach ◽  
Classical Economics ◽  
Sustained Use ◽  
History Of ◽  
Seminal Article ◽  
Almost All

AbstractCoase always expressed dissatisfaction with neo-classical economics and advocated for a new approach. Rather than using toy mathematical models built from unrealistic, idealized assumptions, Coase preferred to study real-world contexts, including actual legal cases. He demonstrated the utility of his approach in ‘The Problem of Social Cost’. Yet almost all of Coase's contemporaries completely ignored, Coase's call for a new approach and his sustained use of legal cases to illustrate his arguments and to situate his analysis in reality. In this paper, we show that the profession interpreted Coase's seminal article exactly the opposite of what he had intended, and reduced his analytical contributions to a toy model of the exact sort he was criticizing. This ironic history of the most cited article both in law and in economics helps us understand the development of ideas within both fields and how disciplinary blinders shape intellectual progress.

scholarly journals Mathematical models of unshadowing the wages

2018 ◽  
pp. 19-26
Author(s):  
Olesia Martyniuk ◽  
Stepan Popina
Keyword(s):  
Mathematical Models ◽  
Shadow Economy ◽  
Economic Security ◽  
Sustainable Growth ◽  
Tax Rates ◽  
State Budget ◽  
Scientific Methods ◽  
High Level ◽  
Almost All ◽  
The Impact

The article addresses a social and economic phenomenon of shadow economy, which is typical for many countries and may result in a macroeconomic imbalance. The latter hinders the sustainable growth of the economy and leads to state budget losses. Shadow economy is penetrating into almost all sectors of the national economy. As shown in the paper, a high level of shadow economy is a threat to the national economic security of the country and a cause of declining its competitiveness. The findings confirm that measuring the impact of some factors of shadow economy on the economic security of the country is quite difficult. However, there are some factors for which mathematical models can be built to describe a correlation between economic indicators and a certain factor of shadow economy. Since salary expenses constitute a significant portion of enterprise’s basic expenses, it is important to build mathematical models for calculating the correlation between shadow salaries and tax rates. Thus, the purpose of the article is to examine mathematical models of the correlation between official and shadow salaries and tax rates. The developed mathematical models demonstrate that a reduction of tax rates is followed by changes in a shadow part of salaries. The article describes a number of cases when there are no changes in salaries and tax revenues, as well as cases of pay increase. The analysis finally suggests ways to increase salaries and techniques to de-shadow salaries. The authors use general scientific methods of generalization, comparison, analysis, and the method of mathematical modeling.

scholarly journals Reassessment of Thin-Layer Drying Models for Foods: A Critical Short Communication

Processes ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 118
Author(s):  
Sencer Buzrul
Keyword(s):  
Mathematical Model ◽  
Thin Layer ◽  
Mathematical Models ◽  
Short Communication ◽  
Time Data ◽  
Thin Layer Drying ◽  
Drying Models ◽  
Thin Layer Drying Models ◽  
Almost All ◽  
Ratio Versus

Modeling the thin-layer drying of foods is based on describing the moisture ratio versus time data by using a suitable mathematical model or models. Several models were proposed for this purpose and almost all studies were related to the application of these models to the data, a comparison and selecting the best-fitted model. A careful inspection of the existing drying data in literature revealed that there are only a limited number of curves and, therefore, the use of some models, especially the complex ones and the ones that require a transformation of the data, should be avoided. These were listed based on evidence with the use of both synthetic and published drying data. Moreover, the use of some models were encouraged, again based on evidence. Eventually, some suggestions were given to the researchers who plan to use mathematical models for their drying studies. These will help to reduce the time of the analyses and will also avoid the arbitrary usage of the models.

scholarly journals Mathematical models are a powerful method to understand and control the spread of Huanglongbing

2016 ◽  
Author(s):  
Rachel A Taylor ◽  
Erin Mordecai ◽  
Christopher A Gilligan ◽  
Jason R Rohr ◽  
Leah R Johnson
Keyword(s):  
Data Collection ◽  
Mathematical Models ◽  
Management Strategies ◽  
Intervention Strategy ◽  
Cost Effective ◽  
Plant Diseases ◽  
Disease Spread ◽  
Vector Borne ◽  
Almost All ◽  
And Control

Huanglongbing, or citrus greening, is a global citrus disease occurring in almost all citrus growing regions and causing substantial economic burdens to individual growers, citrus industries and governments. Successful management strategies to reduce disease burden are desperately needed but with so many possible interventions and combinations thereof, it is difficult to know which are worthwhile or cost-effective. We review how mathematical models have yielded useful insights into controlling disease spread for other vector-borne plant diseases, and the small number of mathematical models of Huanglongbing. We adapt a malaria model to Huanglongbing, by including temperature-dependent psyllid traits and economic costs, to show how models can be used to highlight which parameters require more data collection or which should be targeted for intervention. We analyze the most common intervention strategy, insecticide spraying, to determine the most cost-effective spraying strategy. We found that fecundity and feeding rate of the vector require more experimental data collection, for wider temperatures ranges. The best strategy for insecticide intervention was to spray for more days rather than pay extra for a more efficient spray. We conclude that mathematical models are able to provide useful recommendations for managing Huanglongbing spread.

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