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Math models of various shapes.

Large Language Models have recently achieved high performance on many writing tasks. In a recent study, math word problems in Carnegie Learning's MATHia adaptive learning software were rewritten by human authors to improve their clarity and specificity. The randomized experiment found that emerging readers who received the rewritten word problems spent less time completing the problems and also achieved higher mastery compared to emerging readers who received the original content. We used GPT-4 to rewrite the same set of math word problems, prompting it to follow the same guidelines that the human authors followed. We lay out our prompt engineering process, comparing several prompting strategies: zero-shot, few-shot, and chain-of-thought prompting. Additionally, we overview how we leveraged GPT's ability to write python code in order to encode mathematical components of word problems. We report text analysis of the original, human-rewritten, and GPT-rewritten problems. GPT rewrites had the most optimal readability, lexical diversity, and cohesion scores but used more low frequency words. We present our plan to test the GPT outputs in upcoming randomized field trials in MATHia.

These were made with Mathmod 9.0, available free online. Its a powerful program with hundreds of examples. You can export in triangle obj format. Models are way big from the program so you need to size them down in the slicer. Its also a bit buggy and in development so be patient and restart program when you get stuck. You can save and modify the model scripts for endless possibilities. There are a few youtube videos. Hope you enjoy the models, I would be interested to see what you do with the program.

Students look at math models called ""Solids in Spring"".

Recently established mathematics and science intervention models, designed to increase participation and achievement of Hispanics, women, minorities, and disadvantaged postsecondary students, are reviewed to identify successful organizational designs and key elements. Organizational designs include collaboration between school district, college, or university and industry; college consortium arrangements to work on special projects; institutional block programs to provide academic and student support services to a cluster of math and science students; and student/faculty mentorship. Twenty-six key elements of models designed for Mexican Americans as a main target group are: high level administrative support, departmental commitment and support, collaborative organizational design featuring early student identification and progressive intervention, active staff participation, use of role models, close faculty and counselor contact with students, contact with parents, strong administrative leadership, use of program advisory committees, staff incentives, early recruitment of high ability students, measurable objectives, long-term goals, high student expectations and use of incentives, practical "hands on" learning experiences, development of communication skills, use of ethno-related math and science concepts, use of student learning communities, parental involvement, visits with practicing scientists and mathematicians, remedial/enrichment activities, long-range multiple-source funding, data collection for program evaluation, formative and summative evaluation, quality-verification and replicability, and documented student outcomes. (NEC)

Recently established mathematics and science intervention models, designed to increase participation and achievement of Hispanics, women, minorities, and disadvantaged postsecondary students, are reviewed to identify successful organizational designs and key elements. Organizational designs include collaboration between school district, college, or university and industry; college consortium arrangements to work on special projects; institutional block programs to provide academic and student support services to a cluster of math and science students; and student/faculty mentorship. Twenty-six key elements of models designed for Mexican Americans as a main target group are: high level administrative support, departmental commitment and support, collaborative organizational design featuring early student identification and progressive intervention, active staff participation, use of role models, close faculty and counselor contact with students, contact with parents, strong administrative leadership, use of program advisory committees, staff incentives, early recruitment of high ability students, measurable objectives, long-term goals, high student expectations and use of incentives, practical "hands on" learning experiences, development of communication skills, use of ethno-related math and science concepts, use of student learning communities, parental involvement, visits with practicing scientists and mathematicians, remedial/enrichment activities, long-range multiple-source funding, data collection for program evaluation, formative and summative evaluation, quality-verification and replicability, and documented student outcomes. (NEC)

Students look at math models called ""Solids in Spring"".

In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose variables are compatible with what is given in the literature on real infestations. We analyze two scenarios: one where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ('superspreader'). For both cases we assess the impact of several collective strategies of treatment.

In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose variables are compatible with what is given in the literature on real infestations. We analyze two scenarios: one where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ('superspreader'). For both cases we assess the impact of several collective strategies of treatment.

The engineering equations and mathematical models developed for use in the space shuttle functional simulator (SSFS) are presented, and include extensive revisions and additions to earlier documentation. Definitions of coordinate systems used by the SSFS models and coordinate tranformations are given, along with documentation of the flexible body mathematical models. The models were incorporated in the SSFS and are in the checkout stage.

The engineering equations and mathematical models developed for use in the space shuttle functional simulator (SSFS) are presented, and include extensive revisions and additions to earlier documentation. Definitions of coordinate systems used by the SSFS models and coordinate tranformations are given, along with documentation of the flexible body mathematical models. The models were incorporated in the SSFS and are in the checkout stage.

The purpose of this brief is to synthesize research on coaching and to offer a framework of effective coaching practices. Part 1 provides general information on coaching, including the need for coaching and the goals of coaching. Part 2 describes critical coaching practices that are linked to improvements in teacher practice and learner outcomes. As these practices are most associated with such improvements, they are the recommended practices that should be central to the every-day routine of coaches working in general education or special education settings, as well in environments (e.g., homes, schools, childcare centers) with learners of all ages. Appendix A contains information about various coaching models commonly cited in research and applied in the field (e.g., literacy coaching, behavior coaching, math coaching). This brief is intended to be used in conjunction with the tool entitled "Implementation Guide for Coaching." Research from Implementation Science suggests that how a program, practice, or innovation is put into place impacts the degree to which we can expect that innovation to achieve its intended goals (Fixsen, Naoom, Blase, Friedman, & Wallace, 2005; Greenhalgh, Macfarlane, Bate, Kyriakidou, 2004). Similarly, it is important to attend to how the innovation is implemented. Drawing upon principles of Implementation Science, the guide outlines key areas that should be considered and action steps that should be taken when using coaching as a pathway toward improving teacher practice and learner outcomes.

Our previous study (Thompson et al., under review), tested a brief online intervention focused on teaching adults how to calculate the case fatality rate of COVID-19 vs. the flu. Those in the intervention condition were more likely to answer a transfer problem correctly as compared to the control condition. Further, those in the control condition reported using a strategy aligned with the whole number bias when solving this transfer problem. In the current study, we are investigating whether various visual models (number lines, risk models, or icon arrays) facilitate more accurate COVID-19 problem solving than no visual model at all. Further, we will investigate the relation between COVID-19 problem-solving accuracy, use of whole number bias strategies, perceived COVID-19 likelihood and worry for themselves and other people, and perceived COVID-19 severity. This study was supported in part by U.S. Department of Education Institute of Education Sciences Grants R305A160295 and R305U200004 to C.A. Thompson at Kent State University.

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This collection of abstracts is part of a continuing series providing information on recent doctoral dissertations. The 16 titles deal with a variety of topics, including the following: (1) the effects of rating errors on the speech rating process, (2) the efficiency and accuracy of informal assessment procedures in determining instructional reading levels in the elementary school, (3) reading proficiency discriminators derived from definitions of reading based on a national survey of competency tests for grade 11 from 133 large urban school districts, (4) an administrative model for monitoring the teaching of student assessment standards in communication, (5) the relationship between concept of story and a standardized measure of reading comprehension, (6) differences in student comprehension resulting from the use of a probing technique, (7) the effect of different peer performance discrepancy decision rules on the proportion of elementary school students determined eligible for special education assessment in reading or math, (8) the development and validation of a reading attitude assessment instrument for junior high school students, (9) recalculation of four traditional and two cloze-derived readability formulas, (10) a comparison of two models for individual scoring of National Assessment of Educational Progress's 1979-80 reading/literature data for 17-year olds, and (11) an elementary school program for effective acquisition of basic skills. (HTH)

The report analyzes and compares the various simulation designs and math models of underwater acoustic simulation presently being used in current training devices developed by the Naval Training Device Center. The analysis contains model simplifications and their affects on acoustic propagation loss. The results of these models are compared with the results of the ray trace model developed by the Naval Air Development Center.

The report analyzes and compares the various simulation designs and math models of underwater acoustic simulation presently being used in current training devices developed by the Naval Training Device Center. The analysis contains model simplifications and their affects on acoustic propagation loss. The results of these models are compared with the results of the ray trace model developed by the Naval Air Development Center.

The report analyzes and compares the various simulation designs and math models of underwater acoustic simulation presently being used in current training devices developed by the Naval Training Device Center. The analysis contains model simplifications and their affects on acoustic propagation loss. The results of these models are compared with the results of the ray trace model developed by the Naval Air Development Center.

Mathametic models for VI studens for Math under your fingertips.

Mathametic models for VI studens for Math under your fingertips.

Unit fractions (1/N, for an natural number N) are interesting ideas in mathematics, dating all the way back to the ancient Egyptians. There are numerous ways to write a rational number as the sum of unit fractions. This is an an entry-level design project, allowing students to use their designs to play with basic ideas behind fractions. Among the files, 1 = 1/2 + 1/3 + 1/6, 1= 1/2 + 1/4 + 1/6 + 1/12, (1 = 1/2 + 1/3 + 1/10 + 1/15), (1 = 1/2 + 1/4 + 1/10 + 1/12 + 1/15), and 1 = 1/3 + 1/4 + 1/6 + 1/10 + 1/12 + 1/15. Of course, there are other ways to explore these ideas such as fraction bars and even 3D models (see Liu Hui's cube dissection). Other combinations are possible but are physically less interesting: 1 = 1/2 + 1/3 + 1/8 + 1/24 1 = 1/2 + 1/3 + 1/9 + 1/18 1 = 1/2 + 1/4 + 1/5 + 1/20 1 = 1/2 + 1/5 + 1/6 + 1/8 + 1/120 1 = 1/2 + 1/5 + 1/6 + 1/10 + 1/30 1 = 1/2 + 1/5 + 1/6 + 1/12 + 1/20 1 = 1/3 + 1/4 + 1/5 + 1/6 + 1/20 1 = 1/3 + 1/4 + 1/5 + 1/8 + 1/20 + 1/24 1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/10 + 1/180 1 = 1/3 + 1/4 + 1/5 + 1/9 + 1/18 + 1/20 1 = 1/3 + 1/4 + 1/5 + 1/10 + 1/12 + 1/30 1 = 1/3 + 1/4 + 1/6 + 1/7 + 1/14 + 1/28 1 = 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24 1 = 1/3 + 1/4 + 1/6 + 1/9 + 1/12 + 1/18 References 1. http://mathworld.wolfram.com/EgyptianFraction.html 2. http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html

Snap Linkage Bars I have always liked linkage structures, simple to construct but fascinating to play with in math or mechanics. All children should have some experience with some linkages before entering the world of abstract geometry, I think. They provide numerous opportunities for children to wonder about the mathematics of geometry and movements. With 3D design, it is getting easier and more flexible. I have designed these pieces with K-12 teachers and students in mind. They are fairly easy to assemble or disassemble for open-ended explorations. The center-to-center distance is 40mm. There are two types of links or bars and four types of pins, allowing for a variety of construction. Whenever you need to fix a point (e.g., with a nail of diameter about 3.5mm), you should use a hollow pin. If you need to connect three bars (layers), you need use a three-layer pin. Sometimes you may need a spacer to align the bars in space, too. There are numerous possibilities. Please print a bunch and give them to your kids. Yes, you could insert a regular pencil in the handle ring or a ballpoint pen (diameter < 3.5 mm) in a hollow pin and play with drawing! Warning: As always, please take some time to educate young children not to put small parts in their mouth. Have fun making connections. References: 1. https://en.wikipedia.org/wiki/Linkage_(mechanical) 2. Cundy, H. M., & Rollett, A. P. (1961). Mathematical models (2nd ed.). London, UK: Oxford University Press.

Snap Linkage Bars I have always liked linkage structures, simple to construct but fascinating to play with in math or mechanics. All children should have some experience with some linkages before entering the world of abstract geometry, I think. They provide numerous opportunities for children to wonder about the mathematics of geometry and movements. With 3D design, it is getting easier and more flexible. I have designed these pieces with K-12 teachers and students in mind. They are fairly easy to assemble or disassemble for open-ended explorations. The center-to-center distance is 40mm. There are two types of links or bars and four types of pins, allowing for a variety of construction. Whenever you need to fix a point (e.g., with a nail of diameter about 3.5mm), you should use a hollow pin. If you need to connect three bars (layers), you need use a three-layer pin. Sometimes you may need a spacer to align the bars in space, too. There are numerous possibilities. Please print a bunch and give them to your kids. Yes, you could insert a regular pencil in the handle ring or a ballpoint pen (diameter < 3.5 mm) in a hollow pin and play with drawing! Warning: As always, please take some time to educate young children not to put small parts in their mouth. Have fun making connections. References: 1. https://en.wikipedia.org/wiki/Linkage_(mechanical) 2. Cundy, H. M., & Rollett, A. P. (1961). Mathematical models (2nd ed.). London, UK: Oxford University Press.

The goal of this effort was to explore ways of characterizing the complexity, performance, vulnerability, and dynamic properties of networks and complex systems. Techniques investigated included information theory measures and stochastic resonance, together with graphical and statistical assessments. Network persistance was characterized by the Hurst parameter in a network model based on fractional brownian motion, generalized by fast Fourier transform and studied with wavelet analysis. Network uncertainty was characterized with approximate entropy. General applicability to other complex systems were studied in the areas of sunspot cycles, chatbot detection, genetic data, and image processing.

Teacher self-efficacy is the belief a teacher holds that he or she can make a difference in student achievement, even when the student is difficult or unmotivated (Guskey & Passaro, 1994). It has been linked to positive teacher practices and student outcomes. This mixed methods study of preservice elementary and early childhood math teachers explored how having students engage in hands-on activities and view video teaching models in a graduate mathematics methods course influenced their teacher self-efficacy for math. The study took place in two phases, with course modifications made between the two. Statistical analyses of pre- and post-test scores on the Mathematics Teaching Efficacy Beliefs Instrument showed positive outcomes in Phase 1 but not Phase 2. Qualitative data in both phases suggested working with hands-on materials and viewing video models was beneficial to building student self-efficacy and in improving mathematical content knowledge.

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An analysis technique was developed for expanding the aerothermodynamic envelope of the Space Shuttle without subjecting the vehicle to sustained flight at more stressing heating conditions. A transient analysis program was developed to take advantage of the transient maneuvers that were flown as part of this analysis technique. Heat rates were derived from flight test data for various locations on the orbiter. The flight derived heat rates were used to update heating models based on predicted data. Future missions were then analyzed based on these flight adjusted models. A technique for comparing flight and predicted heating rate data and the extrapolation of the data to predict the aerothermodynamic environment of future missions is presented.

Math models called ""Solids in Spring"".

This report presents the method, bases and results of the final reliability prediction performed on the URC-78 equipment design. The predicted MTBF for the three system configurations is 9,515 hours for the Manpack, 1,925 hours for the Vehicular and 1,925 hours for the Airborne. This report updates the 17 July 1973 submittal. It reflects the anticipated design changes needed for the production model.

The results of the first phase of Research on an Expert System for Database Operation of Simulation/Emulation Math Models, is described. Techniques from artificial intelligence (AI) were to bear on task domains of interest to NASA Marshall Space Flight Center. One such domain is simulation of spacecraft attitude control systems. Two related software systems were developed to and delivered to NASA. One was a generic simulation model for spacecraft attitude control, written in FORTRAN. The second was an expert system which understands the usage of a class of spacecraft attitude control simulation software and can assist the user in running the software. This NASA Expert Simulation System (NESS), written in LISP, contains general knowledge about digital simulation, specific knowledge about the simulation software, and self knowledge.

A reference manual is provided for NESS, a simulation expert system. This manual gives user information regarding starting and operating NASA expert simulation system (NESS). This expert system provides an intelligent interface to a generic simulation program for spacecraft attitude control problems. A menu of the functions the system can perform is provided. Control repeated returns to this menu after executing each user request.

Spectral analyses of angle-modulated communication systems is studied by: (1) performing a literature survey of candidate power spectrum computational techniques, determining the computational requirements, and formulating a mathematical model satisfying these requirements; (2) implementing the model on UNIVAC 1230 digital computer as the Spectral Analysis Program (SAP); and (3) developing the hardware specifications for a data acquisition system which will acquire an input modulating signal for SAP. The SAP computational technique uses extended fast Fourier transform and represents a generalized approach for simple and complex modulating signals.

Spectral analyses of angle-modulated communication systems is studied by: (1) performing a literature survey of candidate power spectrum computational techniques, determining the computational requirements, and formulating a mathematical model satisfying these requirements; (2) implementing the model on UNIVAC 1230 digital computer as the Spectral Analysis Program (SAP); and (3) developing the hardware specifications for a data acquisition system which will acquire an input modulating signal for SAP. The SAP computational technique uses extended fast Fourier transform and represents a generalized approach for simple and complex modulating signals.

The Integrated Math Model for Cryogenic Systems is a flexible, broadly applicable systems parametric analysis tool. The program will effectively accommodate systems of considerable complexity involving large numbers of performance dependent variables such as are found in the individual and integrated cryogen systems. Basically, the program logic structure pursues an orderly progression path through any given system in much the same fashion as is employed for manual systems analysis. The system configuration schematic is converted to an alpha-numeric formatted configuration data table input starting with the cryogen consumer and identifying all components, such as lines, fittings, and valves, each in its proper order and ending with the cryogen supply source assembly. Then, for each of the constituent component assemblies, such as gas generators, turbo machinery, heat exchangers, and accumulators, the performance requirements are assembled in input data tabulations. Systems operating constraints and duty cycle definitions are further added as input data coded to the configuration operating sequence.

The National School-to-Work Office in collaboration with the National Association for Gifted Children, the Council for Exceptional Children, the Association for the Gifted, and the Council of State Directors of Programs for the Gifted have identified 11 gifted education/school-to-work (GT/STW) models that are either best practices or unique approaches. This information packet provides an overview of one of the best practices models: the Mott Hall School for Advanced Studies in Math, Science, and Technology in New York. This innovative Harlem middle school stresses community-based partnerships and mentoring to develop leaders in mathematics, science, and technology. The Mott Hall School services 450 gifted students (grades 4-8) who are 80 percent Latino, 17 percent African American, and over 60 percent female. The STARS (student apprenticeships in research) model for 7th and 8th graders exposes underrepresented minorities and girls to careers in mathematics and science. In 7th grade, students have scientists as mentors, become proficient in the scientific method of inquiry, and learn about science and technology careers. In 8th grade, 50 students have intensive, 8-month internships with science mentors and college students. The information packet includes a description of the different activities at the Mott Hall School and relevant articles. (CR)

New designs for mainshaft thrust bearings for gas turbine engines are derived from mathematical and experimental analyses. The predictions of two bearing computer models, DREB and SHABERTH, being used by the Aero Propulsion Laboratory, were compared to experimental data generated by this study. This test bearing was a 100 mm bore, angular contact, ball bearing which was designed for R&D. Overall, the SHABERTH model was found to be a more practical tool for preliminary bearing design. However, DREB showed promise of being a valuable tool for diagnosing the dynamics of the bearing cage. This study also presents a new method for measuring three-dimensional kinematics of the bearing cage. A bibliography of the pertinent literature is included. (Author)

A computer program for rapid parametric evaluation of various types of cryogenics spacecraft systems is presented. The mathematical techniques of the program provide the capability for in-depth analysis combined with rapid problem solution for the production of a large quantity of soundly based trade-study data. The program requires a large data bank capable of providing characteristics performance data for a wide variety of component assemblies used in cryogenic systems. The program data requirements are divided into: (1) the semipermanent data tables and source data for performance characteristics and (2) the variable input data which contains input parameters which may be perturbated for parametric system studies.

A computer program for rapid parametric evaluation of various types of cryogenics spacecraft systems is presented. The mathematical techniques of the program provide the capability for in-depth analysis combined with rapid problem solution for the production of a large quantity of soundly based trade-study data. The program requires a large data bank capable of providing characteristics performance data for a wide variety of component assemblies used in cryogenic systems. The program data requirements are divided into: (1) the semipermanent data tables and source data for performance characteristics and (2) the variable input data which contains input parameters which may be perturbated for parametric system studies.

The Integrated Math Model for Cryogenic Systems is a flexible, broadly applicable systems parametric analysis tool. The program will effectively accommodate systems of considerable complexity involving large numbers of performance dependent variables such as are found in the individual and integrated cryogen systems. Basically, the program logic structure pursues an orderly progression path through any given system in much the same fashion as is employed for manual systems analysis. The system configuration schematic is converted to an alpha-numeric formatted configuration data table input starting with the cryogen consumer and identifying all components, such as lines, fittings, and valves, each in its proper order and ending with the cryogen supply source assembly. Then, for each of the constituent component assemblies, such as gas generators, turbo machinery, heat exchangers, and accumulators, the performance requirements are assembled in input data tabulations. Systems operating constraints and duty cycle definitions are further added as input data coded to the configuration operating sequence.

A computer program for rapid parametric evaluation of various types of cryogenics spacecraft systems is presented. The mathematical techniques of the program provide the capability for in-depth analysis combined with rapid problem solution for the production of a large quantity of soundly based trade-study data. The program requires a large data bank capable of providing characteristics performance data for a wide variety of component assemblies used in cryogenic systems. The program data requirements are divided into: (1) the semipermanent data tables and source data for performance characteristics and (2) the variable input data which contains input parameters which may be perturbated for parametric system studies.

Over the next decade or more, the Space Shuttle will continue to be the primary transportation system for delivering payloads to Earth orbit. Although a number of payloads have already been successfully carried by the Space Shuttle in the payload bay of the Orbiter vehicle, there continues to be a need for evaluation of the procedures used for verifying and updating the math models of the payloads. The verified payload math models is combined with an Orbiter math model for the coupled-loads analysis, which is required before any payload can fly. Several test procedures were employed for obtaining data for use in verifying payload math models and for carrying out the updating of the payload math models. Research was directed at the evaluation of test/update procedures for use in the verification of Space Shuttle payload math models. The following research tasks are summarized: (1) a study of free-interface test procedures; (2) a literature survey and evaluation of model update procedures; and (3) the design and construction of a laboratory payload simulator.