ERIC Educational Resources Information Center
O'Hanlon, Angela L.
2011-01-01
The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…
ERIC Educational Resources Information Center
Harootunian, Alen
2012-01-01
In this study, relationships were examined between students' perception of their cognition, behavior, environment, and motivation. The purpose of the research study was to explore the extent to which 9th and 10th grade students' perception of environment, cognition, and behavior can predict their motivation in Algebra and Geometry…
ERIC Educational Resources Information Center
Gewertz, Catherine
2009-01-01
For big urban districts, it can be slippery work to catch and hold students who are falling off track at a point that derails too many graduations: the transition from 8th to 9th grade. This article reports that the Chicago school district is putting a suite of new data reports into the hands of those who teach and counsel its 30,000 freshmen this…
Study Probes Enrollment "Bulge" in 9th Grade
ERIC Educational Resources Information Center
Viadero, Debra
2004-01-01
Three decades of mounting academic and testing requirements are snagging growing numbers of students in the 9th grade. "The bulge" is the name education researchers give to the percentage increase in students in the 9th grade over the same period. This article reports on factors that might explain the growing 9th grade bottleneck and sliding…
Help Us Make the 9th Grade Transition
ERIC Educational Resources Information Center
Cushman, Kathleen
2006-01-01
New 9th graders reflect on the worries they had as middle school students about moving into high school. They also suggest ways of easing the transition and providing support in 9th grade. Teens want teachers to connect middle school students regularly with high school students, give them more responsibility in middle school, and focus on…
Indiana's Academic Standards: 9th Grade English/Language Arts.
ERIC Educational Resources Information Center
Indiana State Dept. of Education, Indianapolis.
This booklet of academic standards spells out what students should be able to do in Grade 9 English/Language Arts. The booklet gives examples to help students understand what is required to meet the standards and comes accompanied with a list of 10 things parents can do to help their child get a good education. It outlines the following seven…
A Summative Program Evaluation of a Comprehensive 9th Grade Transition Program
ERIC Educational Resources Information Center
Roybal, Victoria M.
2011-01-01
The transition from 8th grade to 9th grade is one that is replete with challenges for students, especially for minority students who live in economically disadvantaged communities. One low-income, high minority comprehensive high school in the western United States implemented five separate strategies to create a freshman transition program to aid…
The Effectiveness of the New 9th Grade Biology Curriculum on Students' Environmental Awareness
ERIC Educational Resources Information Center
Cetin, Gulcan; Nisanci, Seda Hilal
2010-01-01
The aim of this study was to examine the effectiveness of a new 9th grade biology curriculum on students' environmental awareness. Participants included 91 ninth grade students in a high school in Balikesir during the spring semester of the 2008-2009 academic years. Two classrooms, including 22 and 24 students respectively, were randomly assigned…
Problem-Based Learning in 9th Grade Chemistry Class: "Intermolecular Forces"
ERIC Educational Resources Information Center
Tarhan, Leman; Ayar-Kayali, Hulya; Urek, Raziye Ozturk; Acar, Burcin
2008-01-01
This research study aims to examine the effectiveness of a problem-based learning (PBL) on 9th grade students' understanding of intermolecular forces (dipole-dipole forces, London dispersion forces and hydrogen bonding). The student's alternate conceptions about intermolecular bonding and their beliefs about PBL were also measured. Seventy-eight…
The Effect of Group Work on Misconceptions of 9th Grade Students about Newton's Laws
ERIC Educational Resources Information Center
Ergin, Serap
2016-01-01
In this study, the effect of group work and traditional method on 9th grade students' misconceptions about Newton Laws was investigated. The study was conducted in three classes in an Anatolian Vocational High School in Ankara/Turkey in the second term of the 2014-2015 academic year. Two of these classes were chosen as the experimental group and…
A Comparison of Students' Choices of 9th Grade Physical Education Activities by Ethnicity
ERIC Educational Resources Information Center
Hill, Grant M.; Cleven, Brian
2006-01-01
The purposes of this study were to determine physical education activity preferences of 9th grade students in a southern California school district and to compare preferences by ethnicity. Results indicated that basketball, football, bowling, softball/baseball, swimming, and volleyball were the most preferred activities. These preferences may be…
ERIC Educational Resources Information Center
Al-Hilawani, Yasser A.; And Others
This study explored teachers' behavior as related to effective teaching practices in 8th, 9th, and 10th grade English classrooms in Jordan. The study also examined some variables that could predict teachers' implementation of effective teaching practices and aimed at finding an estimate of the percentage of students in 8th, 9th, and 10th grades…
Analysis of the New Physics Textbook for the 9th Grade of the Greek Schools
NASA Astrophysics Data System (ADS)
Kountouriotis, Georgios
2010-01-01
In the following paper we analyze the new textbook of Physics for the 9th grade (last year of compulsory education) of Greek schools. For this analysis, we use the framework that was developed by Koulaidis, B., Dimopoulos, K., Sklaveniti S., Xristidou B. (2002) The emphasis of this analysis is not in the content of the book, but in the transformation of scientific knowledge to school knowledge, the way the distinction of scientific and everyday knowledge is presented in the book and the pedagogic relations between teachers and students that the book implies. A limited comparison with the previous textbook is also presented.
The Relationship of Grade Span in 9th Grade to Math Achievement in High School
ERIC Educational Resources Information Center
West, John; Miller, Mary Lou; Myers, Jim; Norton, Timothy
2015-01-01
Purpose, Scope, and Method of Study: The purpose of this study was to determine if a correlation exists between grade span for ninth grade and gains in math achievement test scores in 10th grade and 12th grade. A quantitative, longitudinal, correlational research design was employed to investigate the research questions. The population was high…
ERIC Educational Resources Information Center
Corsello, Maryann; Sharma, Anu; Jerabek, Angela
2015-01-01
Ninth grade is a pivotal year for students. Numerous studies find that academic performance in 9th grade often sets the student's trajectory throughout the high school years, as well as the probability of graduation. The Building Assets Reducing Risks (BARR) model is a comprehensive approach that addresses developmental, academic, and school…
NASA Astrophysics Data System (ADS)
Albin, Edward F.
2014-11-01
Fernbank Science Center in Atlanta, GA (USA) offers instruction in planetary science and astronomy to gifted 9th grade students within a program called "Scientific Tools and Techniques" (STT). Although STT provides a semester long overview of all sciences, the planetary science / astronomy section is innovative since students have access to instruction in the Center's Zeiss planetarium and observatory, which includes a 0.9 m cassegrain telescope. The curriculum includes charting the positions of planets in planetarium the sky; telescopic observations of the Moon and planets; hands-on access to meteorites and tektites; and an introduction to planetary spectroscopy utilizing LPI furnished ALTA reflectance spectrometers. In addition, students have the opportunity to watch several full dome planetary themed planetarium presentations, including "Back to the Moon for Good" and "Ring World: Cassini at Saturn." An overview of NASA's planetary exploration efforts is also considered, with special emphasis on the new Orion / Space Launch System for human exploration of the solar system. A primary goal of our STT program is to not only engage but encourage students to pursue careers in the field of science, with the hope of inspiring future scientists / leaders in the field of planetary science.
Project ASTRO: Local Coalitions for Bringing Astronomers to 4th - 9th Grade Classrooms
NASA Astrophysics Data System (ADS)
Fraknoi, Andrew
1998-05-01
We report on Project ASTRO, an NSF and NASA funded program that now links professional and amateur astronomers with local 4th through 9th grade teachers in 10 sites around the country. Each site matches and trains about 20-25 astronomer-teacher partnerships per year, focusing on hands-on, age-appropriate activities, demonstrations of the scientific method, as well as family and community outreach. Over 10,000 copies of the project's 813-page UNIVERSE AT YOUR FINGERTIPS resource and activity notebook (published by the A.S.P) are now in use in educational institututions around the world. The project's HOW-TO-MANUAL is being used as a practical guide to establishing astronomer-teacher partnerships where no formal ASTRO site exists, and a 12-minute video explaining and demonstrating the project is also available. In each of the ten sites, a coalition of educational and scientific institutions is assisting the project with in-kind donations, publicity, personnel, training, materials, etc. We are conducting an experiment (at the behest of NSF) to see to what degree the sites can become self-supporting over time. (One site, in Salt Lake City, has already received full funding from a local foundation.) We will discuss the progress of the project and will have a variety of sample materials available, including our annotated catalog of national astronomy and space science education projects (see associated URL).
ERIC Educational Resources Information Center
Instructional Objectives Exchange, Los Angeles, CA.
A complete set of behavioral objectives for first-year algebra taught in any of grades 8 through 12 is presented. Three to six sample test items and answers are provided for each objective. Objectives were determined by surveying the most used secondary school algebra textbooks. Fourteen major categories are included: (1) whole numbers--operations…
ERIC Educational Resources Information Center
Niemi, Richard G.; Chapman, Chris
This report provides an extensive picture of factors often thought to be associated with promoting good citizenship among youth. In particular, it focuses on the civic development of 9th- through 12th-grade students. Broadly speaking, student characteristics, family influences, the role of schools, media factors, and the possible benefits of…
ERIC Educational Resources Information Center
Pilav, Salim
2014-01-01
The purpose of this study is to assess the extent to which each of the three types of instruction (authentic, where, differentiated) engages 9th grade high school students in achieving language proficiency. The paper examines the features of these models of instructions and teachers? opinion about them. It includes a descriptive research in survey…
ERIC Educational Resources Information Center
Hill, Grant; Cleven, Brian
2005-01-01
The purposes of this study were to determine the physical education activity preferences of 9th grade students in a southern California school district, to identify which activities students felt should be offered in coeducation or gender separate formats, and to determine whether physical education is one of their favorite classes. Results…
ERIC Educational Resources Information Center
Üstten, Aliye Uslu
2014-01-01
The purpose of this study is to identify the sources of reading difficulties and to evaluate reading fluency of 9th grade students which aims to improve students' reading and their understanding of complex literary texts. The sample is composed of 120 students selected from 9th grade of 10 different high schools in central province of Ankara…
ERIC Educational Resources Information Center
Zuhair, Ahmad
2015-01-01
This paper aims at investigating the effect of Arabization of Romanic Alphabets on the development of 9th Grade English as a Foreign Language students' composition writing skills at secondary school level. This experimental study includes 25 secondary school students in their 9th Grade in which English is taught as a foreign language at…
Improving Student Achievement: Can 9th Grade Academies Make a Difference?
ERIC Educational Resources Information Center
Styron, Ronald Anthony; Peasant, Eddie J.
2010-01-01
This study focused on student achievement in ninth grade schools or academies compared to ninth grade students enrolled in traditional high schools. Student achievement was measured by standardized test scores. Other variables tested were gender and ethnicity. All students used in this study were enrolled in the ninth grade during the 2005-2006…
Types of alcoholic beverages usually consumed by students in 9th-12th grades--four states, 2005.
2007-07-27
Excessive alcohol consumption contributes to approximately 4,500 deaths among underage youths in the United States each year (e.g., from homicides, motor-vehicle crashes, and suicides) and an average of 60 years of life lost per death. However, little is known about the specific types of alcoholic beverages consumed by youths. These data are important because numerous evidence-based strategies for reducing underage drinking rates are beverage-specific, including increasing alcohol excise taxes and increasing restrictions on the distribution and sale of alcoholic beverages. To examine types of alcoholic beverages usually consumed by students in 9th-12th grades, CDC analyzed 2005 Youth Risk Behavior Survey (YRBS) data from the four state surveys that included a question on the type of alcohol consumed (Arkansas, Nebraska, New Mexico, and Wyoming). This report describes the results of that analysis, which indicated that liquor (e.g., bourbon, rum, scotch, vodka, or whiskey) was the most prevalent type of alcoholic beverage usually consumed among students in 9th-12th grades who reported current alcohol use or binge drinking. These findings suggest that considering beverage-specific alcohol consumption by youths is important when developing alcohol-control policies, specifically those related to the price and availability of particular types of alcoholic beverages. PMID:17657207
Using Population Data to Create Fun in the 9th-Grade Geography Classroom
ERIC Educational Resources Information Center
Smalley, Elizabeth
2010-01-01
How can teachers encourage their geography students to make sense of big numbers? The key math skills geography students need to apply are ones they learned long ago in fifth grade: estimation and place value. However, in order to recognize the size of a city, or strength of a country's per capita income, or value of a birth rate, they need…
Evaluation of an Energy Conservation Program for 9th Grade Students
ERIC Educational Resources Information Center
Osbaldiston, Richard; Schmitz, Hannah
2011-01-01
The Energy Challenge is an environmental education program that is administered to ninth grade students in the public schools of a small Midwestern city in the United States. The program is sponsored and administered by the two local electric utilities, and it has been going on for seven years. To determine the effectiveness of the program, a…
Water: How Good is Good Enough? Teacher's Guide. Science Module (9th-10th Grade Chemistry).
ERIC Educational Resources Information Center
Georgia Univ., Athens. Coll. of Education.
This is a teacher's guide for a module designed to integrate environmental education into ninth- and tenth-grade chemistry classes. The module, pilot tested in Gwinnett County, Georgia in classes of students, many of whom had learning disabilities, emphasizes activity learning and considerable review. The module is divided into four parts. Part…
Pre-Vocational Curriculum (Career Education) for 9th and 10th Grade Levels. (Teacher Guide).
ERIC Educational Resources Information Center
Arman, Ruby L.; Arman, Mohammad R.
This curriculum guide consists of 17 units of study for use in a prevocational career education course geared toward ninth and tenth grade students. Covered in the individual lessons are the following topics: assessing personal characteristics, completing a personal aptitude inventory, assessing personal interests, using the Dictionary of…
Finite-dimensional simple graded algebras
Bahturin, Yu A; Zaicev, M V; Sehgal, S K
2008-08-31
Let R be a finite-dimensional algebra over an algebraically closed field F graded by an arbitrary group G. In the paper it is proved that if the characteristic of F is zero or does not divide the order of any finite subgroup of G, then R is graded simple if and only if it is isomorphic to a matrix algebra over a finite-dimensional graded skew field. Bibliography: 24 titles.
Lessons for Algebraic Thinking. Grades K-2.
ERIC Educational Resources Information Center
von Rotz, Leyani; Burns, Marilyn
Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help K-2 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…
NASA Astrophysics Data System (ADS)
Da Silva, F. M.; Furtado, W. W.
2012-10-01
The main purpose of this study was to analyze the contribution of using hypertext and pedagogic mediation in search of a Meaningful Learning Process in Sciences. We investigate the usage of hypertext in the teaching and learning methods of Astronomy modules. A survey was conducted with students from the 9th grade of Primary School of a public school in the city of Goiânia, Goiás in Brazil. We have analyzed the possibilities that hypermedia can offer in the teaching and learning process, using as reference David Ausubel's Theory of Meaningful Learning. The study was divided into four phases: application of an initial questionnaire on students, development of didactic material (hypertext), six classes held in a computer lab with the use of hypermedia and a final questionnaire applied in the lab after classes. This research indicated that the use of hypertext linked to pedagogical mediation processes is seen as a motivational tool and has potential to foster to Meaningful Learning.
Demissie, Zewditu; Lowry, Richard; Eaton, Danice K; Nihiser, Allison J
2015-01-01
To examine trends in weight management goals and behaviors among U.S. high school students during 1999-2009. Data from six biennial cycles (1999-2009) of the national Youth Risk Behavior Survey were analyzed. Cross-sectional, nationally representative samples of 9th-12th grade students (approximately 14,000 students/cycle) completed self-administered questionnaires. Logistic regression models adjusted for grade, race/ethnicity, and obesity were used to test for trends in weight management goals and behaviors among subgroups of students. Combined prevalences and trends differed by sex and by race/ethnicity and weight status within sex. During 1999-2009, the prevalence of female students trying to gain weight decreased (7.6-5.7 %). Among female students trying to lose or stay the same weight, prevalences decreased for eating less (69.6-63.2 %); fasting (23.3-17.6 %); using diet pills/powders/liquids (13.7-7.8 %); and vomiting/laxatives (9.5-6.6 %) for weight control. During 1999-2009, the prevalence of male students trying to lose weight increased (26.1-30.5 %). Among male students trying to lose or stay the same weight, the prevalence of exercising to control weight did not change during 1999-2003 and then increased (74.0-79.1 %) while the prevalence of taking diet pills/powders/liquids for weight control decreased (6.9-5.1 %) during 1999-2009. Weight management goals and behaviors changed during 1999-2009 and differed by subgroup. To combat the use of unhealthy weight control behaviors, efforts may be needed to teach adolescents about recommended weight management strategies and avoiding the risks associated with unhealthy methods. PMID:24781877
ERIC Educational Resources Information Center
West, Andrew
2011-01-01
The purpose of this study was to explore and identify the experiences that informed the development of three veteran (15+ years of teaching experience) 9th grade physics teachers' specialized knowledge, or PCK, for using representations to teach the topics of energy transformation and transfer. Through the lens of phenomenography, the study…
ERIC Educational Resources Information Center
Louisiana State Dept. of Education, Baton Rouge. Div. of Vocational Education.
This document is the second volume of a state curriculum guide on vocational agriculture for use in the 9th and 10th grades in Louisiana. Four instructional areas are profiled in this volume: environmental protection, career information, energy conservation, and agricultural mechanics. The environmental protection unit covers safe use of…
ERIC Educational Resources Information Center
Shabatat, Kawthar; Al-Tarawneh, Mohammed
2016-01-01
This study aimed at recognizing the impact of teaching-learning program based on a brain-based learning on the achievement of female students of 9th grade in chemistry, to accomplish the goal of this study the researchers designed instruments of: instructional plans, pre achievement and past achievement exams to use them for the study-validity and…
ERIC Educational Resources Information Center
Louisiana State Dept. of Education, Baton Rouge. Div. of Vocational Education.
This document is the first volume of a state curriculum guide on vocational agriculture for use in the 9th and 10th grades in Louisiana. Three instructional areas are profiled in this volume: orientation to vocational agriculture, agricultural leadership, and soil science. The three units of the orientation area cover introducing beginning…
ERIC Educational Resources Information Center
Kocakaya, F.; Gönen, S.
2014-01-01
Main aim of this study is to examine the influence of computer-assisted roundhouse diagrams on high school 9th grade students' academic achievements in the subjects of "Force and Motion". The study was carried out in a public high school in Diyarbakir the province in the Southeast of Turkey. In the study, the…
A Comparison of 9th and 10th Grade Boys' and Girls' Bullying Behaviors in Two States.
ERIC Educational Resources Information Center
Isernhagen, Jody; Harris, Sandy
This study examined the incidences of bullying behaviors among male and female 9th and 10th graders in rural Nebraska and suburban Texas schools. Nebraska students were predominantly Caucasion, and Texas students were African American, Hispanic American, and Caucasion. Student surveys examined such issues as how often bullying occurred, where it…
The Use of ICT Tools in Mathematics: A Case-Control Study of Best Practice in 9th Grade Classrooms
ERIC Educational Resources Information Center
Thorvaldsen, Steinar; Vavik, Lars; Salomon, Gavriel
2012-01-01
Results are reported from a study in which teachers' views of highly achieving ninth grade classes in Norway (KappAbel national competition winners) were compared with teachers' views of average achievement classes with regard to the use of information and communication technologies (ICT) and pedagogical practices. The main purpose of the study…
ERIC Educational Resources Information Center
Bacza, Gerald L.; And Others
The result of a curriculum development project known as Project Open, this curriculum guide offers a course on communication technology to ninth graders who are participating in the Career Exploration in Technology program and have completed the eighth grade course. Nineteen units form the subject matter of the guide: an introduction, visual…
ERIC Educational Resources Information Center
Georgia Univ., Athens. Coll. of Education.
This learning module is designed to integrate environmental education into ninth- and tenth-grade chemistry classes. This module and a companion social studies module were pilot tested in Gwinnett County, Georgia in classes of students, many of whom had learning disabilities. It emphasizes activity learning. The module is divided into four parts.…
ERIC Educational Resources Information Center
Hinojosa, T.; Bos, J.; O'Brien, B.; Park, S.; Liu, F.; Jerabek, A.
2016-01-01
Students beginning high school commonly experience increased stress and behavior problems alongside declines in grades, attendance, interest in school, and perceptions of academic competence and self-esteem (Alvidrez & Weinstein, 1993; Reyes et al., 2000). Moreover, research indicates that, relative to students who graduate from high school,…
Pre-Vocational Curriculum (Career Education) for 9th and 10th Grade Levels. (Student Study Guide).
ERIC Educational Resources Information Center
Arman, Ruby L.; Arman, Mohammad R.
This student guide consists of 17 units of study for use in a prevocational career education course geared toward ninth and tenth grade students. Covered in the individual lessons are the following topics: assessing personal interests, using the Dictionary of Occupational Titles, identifying occupational choices, identifying vocational and…
ERIC Educational Resources Information Center
Georgia Univ., Athens. Coll. of Education.
This learning module is designed to integrate environmental education into ninth- and tenth-grade social studies courses. The module and a parallel module designed for chemistry classes were pilot tested in Gwinnett County, Georgia in 1975-76. The module is divided into four parts. The first part alerts students to the serious problems that growth…
ERIC Educational Resources Information Center
Georgia Univ., Athens. Coll. of Education.
This learning module is designed to integrate environmental education into ninth- and tenth-grade chemistry classes. This module and a companion social studies module were pilot tested in Gwinnett County, Georgia in 1975-76. The module is divided into four parts. Part one provides a broad overview of unit content and proposes questions to…
Lessons for Algebraic Thinking. Grades 3-5.
ERIC Educational Resources Information Center
Wickett, Maryann; Kharas, Katharine; Burns, Marilyn
Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help 3-5 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…
Lessons for Algebraic Thinking. Grades 6-8.
ERIC Educational Resources Information Center
Lawrence, Ann; Hennessy, Charlie
Algebra is one of the top priorities of mathematics instruction for the elementary and middle grades. This book is designed to help 6-8 teachers meet the challenge of making algebra an integral part of their mathematics instruction and realize both what to teach and how to teach central algebraic concepts. Classroom-tested lessons help teachers…
Infinitesimal deformations of naturally graded filiform Leibniz algebras
NASA Astrophysics Data System (ADS)
Khudoyberdiyev, A. Kh.; Omirov, B. A.
2014-12-01
In the present paper we describe infinitesimal deformations of complex naturally graded filiform Leibniz algebras. It is known that any n-dimensional filiform Lie algebra can be obtained by a linear integrable deformation of the naturally graded algebra Fn3(0) . We establish that in the same way any n-dimensional filiform Leibniz algebra can be obtained by an infinitesimal deformation of the filiform Leibniz algebras Fn1,Fn2and Fn3(α) . Moreover, we describe the linear integrable deformations of the above-mentioned algebras with a fixed basis of HL2 in the set of all n-dimensional Leibniz algebras. Among these deformations one new rigid algebra has been found.
NASA Astrophysics Data System (ADS)
Longo, Palma Joni
2001-12-01
An experimental and interview-based design was used to test the efficacy of visual thinking networking (VTN), a new generation of metacognitive learning strategies. Students constructed network diagrams using semantic and figural elements to represent knowledge relationships. The findings indicated the importance of using color in VTN strategies. The use of color promoted the encoding and reconstruction of earth science knowledge in memory and enhanced higher order thinking skills of problem solving. Fifty-six ninth grade earth science students (13--15 years of age) in a suburban school district outside New York City were randomly assigned to three classes with the same instructor. Five major positive findings emerged in the areas of problem solving achievement, organization of knowledge in memory, problem solving strategy dimensionality, conceptual understanding, and gender differences. A multi-covariate analysis was conducted on the pre-post gain scores of the AGI/NSTA Earth Science Examination (Part 1). Students who used the color VTN strategies had a significantly higher mean gain score on the problem solving criterion test items than students who used the black/white VTN (p = .003) and the writing strategies for learning science (p < .001). During a think-out-loud problem solving interview, students who used the color VTN strategies: (1) significantly recalled more earth science knowledge than students who used the black/white VTN (p = .021) and the writing strategies (p < .001); (2) significantly recalled more interrelated earth science knowledge than students who used black/white VTN strategies (p = .048) and the writing strategy (p < .001); (3) significantly used a greater number of action verbs than students who used the writing strategy (p = .033). Students with low abstract reasoning aptitude who used the color VTNs had a significantly higher mean number of conceptually accurate propositions than students who used the black/white VTN (p = .018) and the
C-Graded vertex algebras and conformal flow
Laber, Rob; Mason, Geoffrey
2014-01-15
We consider C-graded vertex algebras, which are vertex algebras V with a C-grading such that V is an admissible V-module generated by “lowest weight vectors.” We show that such vertex algebras have a “good” representation theory in the sense that there is a Zhu algebra A(V) and a bijection between simple admissible V-modules and simple A(V)-modules. We also consider pseudo vertex operator algebras (PVOAs), which are C-graded vertex algebras with a conformal vector such that the homogeneous subspaces of V are generalized eigenspaces for L(0); essentially, these are VOAs that lack any semisimplicity or integrality assumptions on L(0). As a motivating example, we show that deformation of the conformal structure (conformal flow) of a strongly regular VOA (e.g., a lattice theory, or Wess-Zumino-Witten model) is a path in a space whose points are PVOAs.
Curricular Pathways to Algebra I in Eighth Grade
ERIC Educational Resources Information Center
Griffin, Melinda Rose
2014-01-01
Nationwide, schools are pushing for more students to take Algebra I in eighth grade, prior to formally entering high school. The algebra-for-all movement has been intended to alleviate equity issues which held minority and low-income students back from entering a college-preparatory path in high school. Students with the needed content,…
Some "Big Ideas" of Algebra in the Middle Grades.
ERIC Educational Resources Information Center
Edwards, Thomas G.
2000-01-01
Identifies big ideas for the informal study of algebra-related topics in the middle grades including notation, variable, function, and properties of number. Suggests meaningful ways to accomplish them. (YDS)
2011-01-01
Background Violence by young people is one of the most visible forms of violence and contributes greatly to the global burden of premature death, injury and disability. Methods The Global School-based Student Health Survey (GSHS), State of Lara, Venezuela (GSHS-Lara) is a school-based surveillance system. It comprises a repeated, cross-sectional, self-administered survey drawn from a representative sample of 7th to 9th grade students, performed in the school years 2003-2004 (GSHS-Lara 2004) and 2007-2008 (GSHS-Lara 2008). It explores, among other things, a general violence indicator such as school absenteeism due to feeling unsafe at school or on the way to or from school for any reason; and more specific indicators of violence such as robbery, bullying, physical fights and use of weapons, as well as exposure to lectures on how to prevent violence. Results are given in terms of prevalence percentage. Results Absenteeism doubled between the two study periods (10.8% to 20.8%). The number of students that were a victim of robbery remained high and without change both outside (14.2% and 14.8%) and inside school (21.7% and 22.0%). The number of victims of bullying was high and increasing (33.4% and 43.6%). Bullying associated with being physically attacked decreased (18.5% to 14.3%). Physical attacks without active participation and not associated with bullying were frequent (21.5%). Physical fighting with active participation prevalence remained high and without change (27.5% and 28.2%). Carrying a weapon almost doubled (4.3% to 7.1%). Less than 65% reported classes for violence prevention. Conclusions The GSHS-Lara shows that violence is an important public health problem that needs to be addressed by the community and its authorities. PMID:22958602
A Cohomology Theory of Grading-Restricted Vertex Algebras
NASA Astrophysics Data System (ADS)
Huang, Yi-Zhi
2014-04-01
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the correct cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the algebraic completion of a module for the algebra," instead of linear maps from tensor powers of the algebra to a module for the algebra. One subtle complication arising from such functions is that we have to carefully address the issue of convergence when we compose these linear maps with vertex operators. In particular, for each , we have an inverse system of nth cohomologies and an additional nth cohomology of a grading-restricted vertex algebra V with coefficients in a V-module W such that is isomorphic to the inverse limit of the inverse system . In the case of n = 2, there is an additional second cohomology denoted by which will be shown in a sequel to the present paper to correspond to what we call square-zero extensions of V and to first order deformations of V when W = V.
NASA Astrophysics Data System (ADS)
West, Andrew
The purpose of this study was to explore and identify the experiences that informed the development of three veteran (15+ years of teaching experience) 9th grade physics teachers' specialized knowledge, or PCK, for using representations to teach the topics of energy transformation and transfer. Through the lens of phenomenography, the study was guided by the assumption that there are a limited number of experiences in which teachers engage throughout their career that contribute in significant ways to the development of their knowledge. The primary sources of data were observations of an entire unit of instruction on energy and a series of four stimulated-recall interviews throughout the unit of instruction. The stimulated recall interviews focused on the participants' instruction and knowledge regarding the representations used throughout the energy unit. These data sources were supported by interviews focused on the participants' work history and professional development as well interviews focused on their unit/lesson plans. The results of the phenomenographic analysis revealed that nine categories of experiences informed the development of the three participant's PCK for using representations to teach the energy topics. The categories included: 1) teaching experience, 2) Physics First professional development, 3) other school district-supported professional development 4) collaboration with current colleagues, 5) past collaboration with experienced teachers, 6) academic experiences as a learner of science, 7) school district expectations, 8) collaboration with university faculty and other university professional development, and 9) non-academic life experiences. The analysis also revealed that as a result of engaging in the nine experiences, the participants developed more integrated knowledge for using representations in their instruction, which included understandings regarding the essential features of specific representations, knowledge of barriers to
ERIC Educational Resources Information Center
Reents, Jennifer Newton
2002-01-01
Argues that creating separate schools for ninth-grade students improves their academic and social transition to high school. Supports argument with research results and personal anecdotes. Describes school district experiences in developing and operating ninth-grade centers. (PKP)
Eighth Grade Algebra Course Placement and Student Motivation for Mathematics
Simzar, Rahila M.; Domina, Thurston; Tran, Cathy
2016-01-01
This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210
Pittsburgh Building "Nation" of 9th Graders
ERIC Educational Resources Information Center
Gewertz, Catherine
2007-01-01
Bitter experience has shown Pittsburgh, Pennsylvania, that if students are going to leave school, they are most likely to do it between the 8th and 9th grades. To combat that problem, the school district has launched a full-on campaign to get its rising freshmen into high school and keep them there. Two weeks before school opened, the district…
The Differential Graded Odd NilHecke Algebra
NASA Astrophysics Data System (ADS)
Ellis, Alexander P.; Qi, You
2016-05-01
We equip the odd nilHecke algebra and its associated thick calculus category with diagrammatically local differentials. The resulting differential graded Grothendieck groups are isomorphic to two different forms of the positive part of quantum {{{sl}_2}} at a fourth root of unity.
(I,q)-graded Lie algebraic extensions of the Poincaré algebra, constraints on I and q
NASA Astrophysics Data System (ADS)
Wills Toro, Luis Alberto
1995-04-01
The constraints on the index set I and on the function q of the (I,q)-graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single-grading model, particular choices for I and q consistent with the found constraints are determined for K=C. Gradings are then found for which I⊆I=Z2×(Z4N×Z4N)×Gre, with N∈N and Gre an Abelian group. These gradings provide a way for algebraic extensions of the Poincaré Lie algebra beyond the Z2-gradings of supersymmetry and supergravity. In these algebraic extensions, each other commuting space-time parameter can either commute or anticommute with the further parameters of the (I,q)-graded (super) manifold. Different field representations can have—with each other—generalized commutative behavior beyond commutativity and anticommutativity.
Ternary Z3 -graded generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-04-01
We investigate a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, j = e 2πi/3, one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. A cubic analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator. A set of eigenstates in coordinate representation is constructed in terms of functions satisfying linear differential equation of third order.
ERIC Educational Resources Information Center
Erickson, Toby
In this interdisciplinary curriculum unit intended for ninth grade students, students explore in groups in a role playing format public policy questions related to rain forests. Examined in the lessons are political, economic, and ecological issues from which students are expected to make recommendations on what policy course should be followed.…
ERIC Educational Resources Information Center
Louisiana State Dept. of Education, Baton Rouge. Div. of Vocational Education.
This curriculum guide, the third volume of the series, outlines the basic program of vocational agriculture for Louisiana students in the ninth and tenth grades. Covered in the five units on plant science are growth processes of plants, cultural practices for plants, insects affecting plants, seed and plant selection, and diseases that affect…
The Impact of New State Accountability Standards on Algebra I Students
ERIC Educational Resources Information Center
Heath, Kyle G.
2013-01-01
The purpose of this quasi-experimental quantitative study was to determine if a new Algebra I curriculum resulted in improved student performance on the state Algebra I exam. The treatment group consisted of 383 9th grade Algebra I students who received the college-ready standards-based (CRSB) curricula. The control group consisted of 338 9th…
Osgood, D. Wayne; Feinberg, Mark E.; Ragan, Daniel T.
2015-01-01
Seeking to reduce problematic peer influence is a prominent theme of programs to prevent adolescent problem behavior. To support the refinement of this aspect of prevention programming, we examined peer influence and selection processes for three problem behaviors (delinquency, alcohol use, and smoking). We assessed not only the overall strengths of these peer processes, but also their consistency versus variability across settings. We used dynamic stochastic actor-based models to analyze five waves of friendship network data across sixth through ninth grades for a large sample of U.S. adolescents. Our sample included two successive grade cohorts of youth in 26 school districts participating in the PROSPER study, yielding 51 longitudinal social networks based on respondents’ friendship nominations. For all three self-reported antisocial behaviors, we found evidence of both peer influence and selection processes tied to antisocial behavior. There was little reliable variance in these processes across the networks, suggesting that the statistical imprecision of the peer influence and selection estimates in previous studies likely accounts for inconsistencies in results. Adolescent friendship networks play a strong role in shaping problem behavior, but problem behaviors also inform friendship choices. In addition to preferring friends with similar levels of problem behavior, adolescents tend to choose friends who engage in problem behaviors, thus creating broader diffusion. PMID:25943034
ERIC Educational Resources Information Center
Blanton, Maria; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy; Isler, Isil; Kim, Jee-Seon
2015-01-01
This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to…
Early-Algebra Push Seen to Be Flawed
ERIC Educational Resources Information Center
Viadero, Debra
2010-01-01
Spurred by a succession of reports pointing to the importance of algebra as a gateway to college, educators and policymakers embraced "algebra for all" policies in the 1990s and began working to ensure that students take the subject by 9th grade or earlier. A trickle of studies suggests that in practice, though, getting all students past the…
Implications of Eighth Grade Algebra I on High School Mathematics Achievement
ERIC Educational Resources Information Center
Bayard, Robert
2012-01-01
As of 2008, approximately 40% of eighth grade students in the United States enroll in Algebra I (National Council of Teachers of Mathematics, 2008). Although research has shown that students have more opportunities to take advanced mathematics courses by taking eighth grade Algebra I, in the United States, approximately only one-third to one-half…
ERIC Educational Resources Information Center
Clark, Jill P.
2012-01-01
Many students enter large comprehensive high schools without having the necessary social and academic skills or understanding of what will be expected of them as they move through the high school curriculum. To help a higher number of students experience success, schools must help them develop academic, social, and self-management skills.…
Outcomes of Placing Low Performing Eighth Grade Students in Algebra Content Courses
ERIC Educational Resources Information Center
Taylor, Donald Joseph
2011-01-01
In California, Algebra I is the 8th grade math content standard. The United States Department of Education found the annual 8th grade General Math California Standards Test to be out of compliance with the federal No Child Left Behind Act of 2001 since it assesses 6th and 7th grade math standards and not Algebra I math content. In response to the…
ERIC Educational Resources Information Center
Erdogan, Mehmet; Bahar, Mehmet; Usak, Muhammet
2012-01-01
The aim of this study is to analyze 9th-12th grade Biology Course Curricula started to be implemented in 2007 with regard to concepts and attainments addressing to environmental education. In this regard, 9th-12th grade Biology Course Curricula were analyzed using content-analysis technique, one of the qualitative research methods. 9th-12th grade…
ERIC Educational Resources Information Center
Buckner, Barbara Renee
2011-01-01
The purpose of this study was to determine the effect of TI-Nspire graphing calculator use on student achievement and on teacher behavior variables of planning, teaching, and assessing. This study investigated the teaching of functions by teachers using the TI-Nspire graphing calculator versus teachers using a non-graphing scientific calculator. …
Aiming High and Falling Short: California's Eighth-Grade Algebra-for-All Effort
ERIC Educational Resources Information Center
Domina, Thurston; McEachin, Andrew; Penner, Andrew; Penner, Emily
2015-01-01
The United States is in the midst of an effort to intensify middle school mathematics curricula by enrolling more 8th graders in Algebra. California is at the forefront of this effort, and in 2008, the state moved to make Algebra the accountability benchmark test for 8th-grade mathematics. This article takes advantage of this unevenly implemented…
Automorphisms and Derivations of the Insertion-Elimination Algebra and Related Graded Lie Algebras
NASA Astrophysics Data System (ADS)
Ondrus, Matthew; Wiesner, Emilie
2016-07-01
This paper addresses several structural aspects of the insertion-elimination algebra {mathfrak{g}}, a Lie algebra that can be realized in terms of tree-inserting and tree-eliminating operations on the set of rooted trees. In particular, we determine the finite-dimensional subalgebras of {mathfrak{g}}, the automorphism group of {mathfrak{g}}, the derivation Lie algebra of {mathfrak{g}}, and a generating set. Several results are stated in terms of Lie algebras admitting a triangular decomposition and can be used to reproduce results for the generalized Virasoro algebras.
Aiming Higher: Is Your 9th Grader on Track for College?
ERIC Educational Resources Information Center
New Visions for Public Schools, 2008
2008-01-01
A teenager's future starts on 9th grade with the safe and welcoming environment, excellent teachers, and challenging instruction provided at this school. Believe it or not, college begins in 9th grade. If parents dream of their son or daughter going to college, they should not put off planning until their junior or senior year in high school--it…
ERIC Educational Resources Information Center
Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.
2015-01-01
Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…
Multipoint Lax operator algebras: almost-graded structure and central extensions
Schlichenmaier, M
2014-05-31
Recently, Lax operator algebras appeared as a new class of higher genus current-type algebras. Introduced by Krichever and Sheinman, they were based on Krichever's theory of Lax operators on algebraic curves. These algebras are almost-graded Lie algebras of currents on Riemann surfaces with marked points (in-points, out-points and Tyurin points). In a previous joint article with Sheinman, the author classified the local cocycles and associated almost-graded central extensions in the case of one in-point and one out-point. It was shown that the almost-graded extension is essentially unique. In this article the general case of Lax operator algebras corresponding to several in- and out-points is considered. As a first step they are shown to be almost-graded. The grading is given by splitting the marked points which are non-Tyurin points into in- and out-points. Next, classification results both for local and bounded cocycles are proved. The uniqueness theorem for almost-graded central extensions follows. To obtain this generalization additional techniques are needed which are presented in this article. Bibliography: 30 titles.
ERIC Educational Resources Information Center
Atnafu, Mulugeta
2010-01-01
The purpose of this study was to examine the relation between the attitudes and components of attitude of the students towards algebra with their algebra achievements. The population for this study consists of all government tenth grade students and their mathematics teachers in Addis Ababa city administration. Sixteen tenth grade sections were…
The Effects of Online Homework on High School Algebra Students
ERIC Educational Resources Information Center
Schubert, Daniel Joseph
2012-01-01
Technology is changing the way students are able to learn and access mathematics. This study explored the effects that technology can have on 9th grade Integrated Algebra students through computer-assisted instruction. In hopes of raising students' New York State Regents scores, ninety-five high school freshmen from a Title I school in New…
Student Strategy Choices on a Constructed Response Algebra Problem
ERIC Educational Resources Information Center
Ross, Dan; Reys, Robert; Chavez, Oscar; McNaught, Melissa D.; Grouws, Douglas A.
2011-01-01
A central goal of secondary mathematics is for students to learn to use powerful algebraic strategies appropriately. Research has demonstrated student difficulties in the transition to using such strategies. We examined strategies used by several thousand 8th-, 9th-, and 10th-grade students in five different school systems over three consecutive…
Access to Algebra I, Gateway to Success: The Impact of Eighth-Grade Algebra I
ERIC Educational Resources Information Center
Darling, Emily Jean Skelton
2010-01-01
An understanding of Algebra I and the role that this foundational course plays as an entry to the college preparatory pathway in secondary education and its influence on mathematical achievement is an integral component for the education of American youth in the global world of science and technology. Achievements in high school curricula are…
ERIC Educational Resources Information Center
Raymond, Roger A.
In the second year of a study to compare and evaluate programed and conventional instruction in algebra for the ninth and tenth grades, comparisons of the control and experimental groups in each grade were again based on scores from the Lankton First-Year Algebra Test and the California Study Methods Survey (CSMS). Although there was a…
ERIC Educational Resources Information Center
Liang, Jian-Hua; Heckman, Paul E.; Abedi, Jamal
2012-01-01
In California, an increasing number of 8th graders have taken algebra courses since 2003. This study examines students' California Standards Test (CST) results in grades 7 through 11, aiming to reveal who took the CST for Algebra I in 8th grade and whether the increase has led to a rise in students' taking higher-level mathematics CSTs and an…
ERIC Educational Resources Information Center
Lim, Kok Seng
2010-01-01
Introduction: This study aimed to investigate the errors made by 265 Form 2 male students in simplifying algebraic expressions. Method: A total of 265 Form 2 (Grade 7) male students were selected for this study. 10 high, medium and low ability students in each group were selected for the interviews. 40 items were administered to the respondents to…
ERIC Educational Resources Information Center
Jin, Haiyue; Wong, Khoon Yoong
2015-01-01
Conceptual understanding is a major aim of mathematics education, and concept map has been used in non-mathematics research to uncover the relations among concepts held by students. This article presents the results of using concept map to assess conceptual understanding of basic algebraic concepts held by a group of 48 grade 8 Chinese students.…
ERIC Educational Resources Information Center
Kopp, Jaine; Bergman, Lincoln
This teacher guide helps build a solid foundation in algebra for students in grades 3-5 in which students gain essential understanding of properties of numbers, variables, functions, equations, and formulas. Throughout the problem solving activities, students use computational skills and gain a deeper understanding of the number system. Students…
8th Grade Algebra Teachers in Arkansas to Need State Nod
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
Lindsay E. Carlton has taught mathematics to students at different grades, with different ability levels. Now, the young educator's state wants to recognize her ability to work with one group in particular: 8th graders enrolled in introductory algebra. Carlton is one of many math educators across Arkansas who plan to acquire a new, unusual state…
Review of "The Misplaced Math Student: Lost in Eighth-Grade Algebra"
ERIC Educational Resources Information Center
Burris, Carol Corbett
2008-01-01
The Brookings Institution report questions the efficacy of increasing the number of students who take algebra in eighth grade. Although this policy has resulted in more equitable access to advanced math study, the report argues that a subgroup of students enrolled lack the basic mathematical skills needed to succeed. The report further argues that…
Course Placement Series: Spotlight on Eighth Grade Algebra I. Policy Brief
ERIC Educational Resources Information Center
Tennessee Department of Education, 2015
2015-01-01
The Tennessee Department of Education explored course enrollment patterns in an effort to better understand in which courses students are enrolling and whether course enrollment policies and procedures are promoting students' interests. This report focuses on eighth grade Algebra I enrollment, which can propel students to take more rigorous math…
ERIC Educational Resources Information Center
Bunrasi, John Bosco Tuptip
2012-01-01
The purpose of this study was to examine constructivist-based algebra lessons and a cooperative construct to address the achievement gap between White (non-Hispanic) and Mexican American 8th grade students at a southern California middle school. The lessons were designed to facilitate social interdependence which promoted peer-to-peer interaction…
Predicting Eighth-Grade Algebra Students with Individualized Education Programs
ERIC Educational Resources Information Center
Faulkner, Valerie N.; Crossland, Cathy L.; Stiff, Lee V.
2013-01-01
This study investigated the extent to which student performance and teacher perception of student performance affect placement in eighth-grade mathematics classes for students with disabilities. Authors used the Early Childhood Longitudinal Study--Kindergarten dataset to investigate how each of the following factors predicted placement in…
The 9th International Veterinary Immunology Symposium.
Lunney, Joan K; Kai, Chieko; Inumaru, Shigeki; Onodera, Takashi
2012-07-15
This special issue of Veterinary Immunology and Immunopathology summarizes the Proceedings of the 9th International Veterinary Immunology Symposium (9th IVIS) held August 2010, in Tokyo, Japan. Over 340 delegates from 30 countries discussed research progress analyzing the immune systems of numerous food animals and wildlife, probing basic immunity and the influence of stress, genetics, nutrition, endocrinology and reproduction. Major presentations addressed defense against pathogens and alternative control and prevention strategies including vaccines, adjuvants and novel biotherapeutics. A special Organisation for Economic Co-operation and Development (OECD) Co-operative Research Programme Sponsored Conference on "Vaccination and Diagnosis for Food Safety in Agriculture" highlighted the particular issue of "Immunology in Bovine Paratuberculosis". In April 2010 there was an outbreak of foot-and-mouth disease (FMD) in the southern part of Japan. This stimulated a special 9th IVIS session on FMD, sponsored by the World Organization for Animal Health (OIE) and the Ministry of Agriculture, Forestry and Fisheries (MAFF) of Japan, to discuss improvements of FMD vaccines, their use in FMD control, and risk assessment for decision management. The 9th IVIS was supported by the Veterinary Immunology Committee (VIC) of the International Union of Immunological Societies (IUIS) and included workshops for its MHC and Toolkit Committees. Finally VIC IUIS presented its 2010 Distinguished Service Award to Dr. Kazuya Yamanouchi for "outstanding contributions to the veterinary immunology community" and its 2010 Distinguished Veterinary Immunologist Award to Dr. Douglas F. Antczak for "outstanding research on equine immunology". PMID:22766039
Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula
ERIC Educational Resources Information Center
Domina, Thurston; Penner, Andrew M.; Penner, Emily K.; Conley, AnneMarie
2014-01-01
Background/Context: Across the United States, secondary school curricula are intensifying as a growing proportion of students enroll in high-level academic math courses. In many districts, this intensification process occurs as early as eighth grade, where schools are effectively constraining their mathematics curricula by restricting course…
ERIC Educational Resources Information Center
Lopez, Maria I. Hernandez; And Others
In 1962 and again in 1965, a group of sixth and ninth grade students in selected schools in four Puerto Rican communities were interviewed to investigate the factors influencing students' decision to withdraw from school before completing twelfth grade and to identify some characteristics of dropouts. Of 616 students interviewed in 1962, 20.9% of…
ERIC Educational Resources Information Center
Shoecraft, Paul Joseph
Three instructional approaches on translating selected types of algebra word problems were investigated: direct translations, high imagery with materials, and high imagery with drawings. Participating were 366 seventh grade and 336 ninth grade students. Treatment effects by grade used multivariate analysis of covariance for student scores and…
ERIC Educational Resources Information Center
Grandau, Laura
2013-01-01
This study of fourth-grade students and teachers explores mathematics teaching and learning that focuses on discovering and modeling algebraic relationships. The study has two parts: an investigation of how students learn to construct algebraic statements and models for comparisons and measurement situations in the multiplicative domain, and an…
ERIC Educational Resources Information Center
Manitoba Dept. of Education, Winnipeg. Bureau of French Education.
Official instructional materials for the second three years (grades 7-9) of the Manitoba Department of Education's core French language program are presented. These materials, intended for teachers, consist of units of instruction for each year, which contain notes for the teacher, suggestions for class activities, materials for student use, and…
ERIC Educational Resources Information Center
Falcon, Raymond
2009-01-01
Teachers use action research in order to improve their teaching and student learning. This action research will analyze students' algebraic reasoning in finding values of variables in systems of equations pictorially and algebraically. This research will look at students solving linear systems of equations without knowing the algebraic algorithms.…
The Impact of Teachers' Characteristics and Self-Reported Practices on Students' Algebra Achievement
ERIC Educational Resources Information Center
Cope, Liza M.
2013-01-01
This study examined the impact of teachers' characteristics and self-reported practices on students' Algebra achievement while controlling for students' characteristics. This study is based on the secondary analysis of data collected from a nationally representative sample of 9 th grade students and their mathematics teachers during…
Eaton, Danice K; Foti, Kathryn; Brener, Nancy D; Crosby, Alex E; Flores, Glenn; Kann, Laura
2011-01-01
The objective of this study was to identify factors that may account for the disproportionately high prevalence of suicidal behaviors among Hispanic/Latina youth by examining whether associations of health risk behaviors with suicidal ideation and suicide attempts vary by race/ethnicity among female students. Data from the school-based 2007 national Youth Risk Behavior Survey were analyzed. Analyses were conducted among female students in grades 9 through 12 and included 21 risk behaviors related to unintentional injuries and violence; tobacco use; alcohol and other drug use; sexual behaviors that contribute to unintended pregnancy and sexually transmitted infections, including human immunodeficiency virus; physical activity; obesity and weight control; and perceived health status. With the exception of physical activity behaviors and obesity, all risk behaviors examined were associated with suicidal ideation and suicide attempts. Associations of risk behaviors with suicidal ideation varied by race/ethnicity for 5 of 21 behaviors, and for 0 of 21 behaviors for suicide attempts. Stratified analyses provided little insight into factors that may account for the higher prevalence of suicidal behaviors among Hispanic/Latina female students. These results suggest that the increased risk of suicidal behaviors among Hispanic/Latina female students cannot be accounted for by differential associations with these selected risk behaviors. Other factors, such as family characteristics, acculturation, and the socio-cultural environment, should be examined in future research. PMID:21541858
ERIC Educational Resources Information Center
Walston, Jill; McCarroll, Jill Carlivati
2010-01-01
This Brief is intended to provide descriptive statistics about various aspects of algebra enrollment in the eighth grade. The first analyses describe who is taking algebra in the eighth grade; findings compare eighth-grade course enrollment percentages for students with different demographic, family, geographic, and school characteristics (table…
ERIC Educational Resources Information Center
Egodawatte, Gunawardena; Stoilescu, Dorian
2015-01-01
The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
9th Arnual Great Moonbuggy Race
NASA Technical Reports Server (NTRS)
2002-01-01
Students from across the United States and as far away as Puerto Rico and South America came to Huntsville, Alabama for the 9th annual Great Moonbuggy Race at the U.S. Space Rocket Center. Seventy-seven teams, representing high schools and colleges from 21 states, Puerto Rico, and Columbia, raced human powered vehicles over a lunar-like terrain. In this photograph, the team from Lafayette County High school in Higginsville, Missouri, designated Lafayette County team #1, races through the course to cross the finish line to win the high school division. The team beat out 26 other teams representing high schools from 9 states. Vehicles powered by two team members, one male and one female, raced one at a time over a half-mile obstacle course of simulated moonscape terrain. The competition is inspired by the development, some 30 years ago, of the Lunar Roving Vehicle (LRV), a program managed by the Marshall Space Flight Center. The LRV team had to design a compact, lightweight, all-terrain vehicle that could be transported to the Moon in the small Apollo spacecraft. The Great Moonbuggy Race challenges students to design and build a human powered vehicle so they will learn how to deal with real-world engineering problems, similar to those faced by the actual NASA LRV team.
9th Arnual Great Moonbuggy Race
NASA Technical Reports Server (NTRS)
2002-01-01
Students from across the United States and as far away as Puerto Rico and South America came to Huntsville, Alabama for the 9th annual Great Moonbuggy Race at the U.S. Space Rocket Center. Seventy-seven teams, representing high schools and colleges from 21 states, Puerto Rico, and Columbia, raced human powered vehicles over a lunar-like terrain. A team from Cornell University in Ithaca, New York, took the first place honor in the college division. This photograph shows the Cornell #2 team driving their vehicle through the course. The team finished the race in second place in the college division. Vehicles powered by two team members, one male and one female, raced one at a time over a half-mile obstacle course of simulated moonscape terrain. The competition is inspired by development, some 30 years ago, of the Lunar Roving Vehicle (LRV), a program managed by the Marshall Space Flight Center. The LRV team had to design a compact, lightweight, all-terrain vehicle, that could be transported to the Moon in the small Apollo spacecraft. The Great Moonbuggy Race challenges students to design and build a human powered vehicle so they will learn how to deal with real-world engineering problems, similar to those faced by the actual NASA LRV team.
9th Arnual Great Moonbuggy Race
NASA Technical Reports Server (NTRS)
2002-01-01
Students from across the United States and as far away as Puerto Rico and South America came to Huntsville, Alabama for the 9th annual Great Moonbuggy Race at the U.S. Space Rocket Center. Seventy-seven teams, representing high schools and colleges from 21 states, Puerto Rico, and Columbia, raced human powered vehicles over a lunar-like terrain. A team from Cornell University in Ithaca, New York, took the first place honor in the college division. In this photograph, the Cornell #1 team, the collegiate first place winner, maneuvers their vehicle through the course. Vehicles powered by two team members, one male and one female, raced one at a time over a half-mile obstacle course of simulated moonscape terrain. The competition is inspired by development, some 30 years ago, of the Lunar Roving Vehicle (LRV), a program managed by the Marshall Space Flight Center. The LRV team had to design a compact, lightweight, all-terrain vehicle that could be transported to the Moon in the small Apollo spacecraft. The Great Moonbuggy Race challenges students to design and build a humanpowered vehicle so they will learn how to deal with real-world engineering problems similar to those faced by the actual NASA LRV team.
9th Arnual Great Moonbuggy Race
NASA Technical Reports Server (NTRS)
2002-01-01
Students from across the United States and as far away as Puerto Rico and South America came to Huntsville, Alabama for the 9th annual Great Moonbuggy Race at the U.S. Space Rocket Center. Seventy-seven teams, representing high schools and colleges from 21 states, Puerto Rico, and Columbia, raced human powered vehicles over a lunar-like terrain. In this photograph, the New Orleans area schools team #2 from New Orleans, Louisiana maneuvers through an obstacle course. The team captured second place in the high school division competition. Vehicles powered by two team members, one male and one female, raced one at a time over a half-mile obstacle course of simulated moonscape terrain. The competition is inspired by the development, some 30 years ago, of the Lunar Roving Vehicle (LRV), a program managed by the Marshall Space Flight Center. The LRV team had to design a compact, lightweight, all-terrain vehicle that could be transported to the Moon in the small Apollo spacecraft. The Great Moonbuggy Race challenges students to design and build a human powered vehicle so they will learn how to deal with real-world engineering problems, similar to those faced by the actual NASA LRV team.
A Chemistry Course for High Ability 8th, 9th, and 10th Graders.
ERIC Educational Resources Information Center
Kilker, Richard, Jr.
1985-01-01
Describes a chemistry course designed, in cooperation with local public school districts, to intellectually challenge a group of 8th, 9th, and 10th grade students. Organic chemistry and biochemistry are integrated into the course (titled Chemistry and Everyday Life) to emphasize practical applications of chemistry. The course syllabus is included.…
The Illinois 9th Grade Adolescent Health Survey. Full Report.
ERIC Educational Resources Information Center
Illinois State Board of Education, Springfield.
A survey was conducted in Illinois to identify the risk of certain health problems among adolescents; to determine the health status of Illinois youth in relation to the Surgeon General's "Healthy People 2000 Objectives" and monitor progress toward national and state goals; and to help those working at national, state, and local levels develop…
Introduction to Marketing for 9th Grade Students.
ERIC Educational Resources Information Center
Krotosky, Paul; Johnson, Jeannie G.
Designed to enable students to develop knowledge of personal strengths and weaknesses and to be able to understand the relationship of these characteristics to educational and vocational choices, this guide presents an introductory program on vocations using a thematic interdisciplinary approach to career awareness. It is suggested that the…
Safety Pharmacology Society: 9th Annual Meeting.
Cavero, Icilio
2010-03-01
The keynote presentation of the Safety Pharmacology (SP) Society 9th Annual Meeting addressed the urgency, for pharmaceutical organizations, to implement strategies for effectively communicating drug risks to all concerned stakeholders and, in particular, the general public. The application of chronobiology to SP investigational protocols can improve the search of drug-induced adverse effects. The Distinguished Service Award Lecture reviewed a life-long journey through trials and tribulations in the quest of the ever-distant scientific truth. The revision process of Directive 86/609/EC for improving animal welfare should be conducted with the purpose of maintaining a fair balance among animal protection, human health and research imperatives in order to prevent the migration of pharmaceutical activities outside Europe. Additional topics of interest were the behavioral, metabolic and cardiovascular problems experienced by small animals housed at the standard laboratory temperature. A technology for the automated collection of blood and urine samples in rats implanted with telemetry sensors was presented. Non-clinical, clinical, regulatory and legal aspects of abuse liability were expertly reviewed. The 'degradability' of pharmaceuticals into environment-friendly chemicals should be an actively searched and optimized feature of future pharmaceuticals in order to prevent drug pollution of ecosystems. Transgenic and diseased animal models should be selected whenever they can facilitate the determination of drug-induced adverse effects. SP strategies to investigate the safety of drug combination products were exemplified and analyzed in depth. The future of SP was proposed to lie not in the performance of regulatory studies of pharmacodynamic nature but in developing and early applying an array of screening assays for clearing clinical candidates against known drug-induced organ function injuries. In conclusion, the 2009 SP Society annual meeting offered a wealth of
Different Grade Students' Use and Interpretation of Literal Symbols
ERIC Educational Resources Information Center
Celik, Derya; Gunes, Gonul
2013-01-01
The aim of the study was to determine and compare 7th, 8th, and 9th grades students' level of use and interpret the literal symbols. In addition, students' responses to questions that require use of different roles of literal symbol were examined to identify the errors. For this purpose, Chelsea Diagnostics Algebra test developed by The…
An Intervention Including an Online Game to Improve Grade 6 Students' Performance in Early Algebra
ERIC Educational Resources Information Center
Kolovou, Angeliki; van den Heuvel-Panhuizen, Marja; Koller, Olaf
2013-01-01
This study investigated whether an intervention including an online game contributed to 236 Grade 6 students' performance in early algebra, that is, solving problems with covarying quantities. An exploratory quasi-experimental study was conducted with a pretest-posttest-control-group design. Students in the experimental group were asked to…
ERIC Educational Resources Information Center
Raymond, Roger A.
Ninth and tenth grade students from two schools were placed in experimental and conventional instruction classes to compare the two methods in teaching algebra by means of achievement test and time needed to complete the course. Pre- and posttests measured aptitude; teachers and students in the experimental groups recorded personal reactions to…
ERIC Educational Resources Information Center
Sher, Stephen Korb
2011-01-01
This study looked at 4th grade classrooms to see "how" teachers implement NCTM standards-based or reform-based mathematics instruction and then analyzed it for the capacity to improve students' "algebra readiness." The qualitative study was based on classroom observations, teacher and administrator interviews, and teacher surveys. The study took…
Paradoxes and Paradigms in an Eighth Grade Pre-Algebra Class: A Case Study of a "Good" Math Teacher.
ERIC Educational Resources Information Center
Gregoire, Michele
Evidence is presented from an ethnographic study of an eighth grade pre-algebra teacher's classroom in support of the idea that teachers' beliefs about the ontology and epistemology of math profoundly influence how they teach and thus what students learn. Specifically, beliefs based on a traditional view of mathematics as procedurally-based are…
Delivering the Promise to 9th Graders.
ERIC Educational Resources Information Center
Walsh, Margaret May
2002-01-01
Principal describes experience in establishing and operating the Minne Howard School, a separate school for ninth-grade students in Alexandria, Virginia. Describes keys to success: Create a teacher advisor component, eliminate inschool suspension, teach five classes, and institute a school support team. (PKP)
ERIC Educational Resources Information Center
Kim, Yanghee; Lim, Jae Hoon
2013-01-01
This study examined whether or not embodied-agent-based learning would help middle-grade females have more positive mathematics learning experiences. The study used an explanatory mixed methods research design. First, a classroom-based experiment was conducted with one hundred twenty 9th graders learning introductory algebra (53% male and 47%…
Twisted Quantum Toroidal Algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Liu, Rongjia
2014-09-01
We construct a principally graded quantum loop algebra for the Kac-Moody algebra. As a special case a twisted analog of the quantum toroidal algebra is obtained together with the quantum Serre relations.
A Comparison Study of 9th Graders in the U.S. and Albania
ERIC Educational Resources Information Center
Garo, Sofokli
2008-01-01
The purpose of this research is to compare American and Albanian students' achievement in Algebra 1 and to identify the educational practices that influence students' achievement in each country. The study compared algebraic solving abilities of 242 ninth-grade American students in Grand Forks (U.S.) and 219 students in Durres (Albania). The data…
ERIC Educational Resources Information Center
Senarat, Somprasong; Tayraukham, Sombat; Piyapimonsit, Chatsiri; Tongkhambanjong, Sakesan
2013-01-01
The purpose of this research is to develop a multidimensional computerized adaptive test for diagnosing the cognitive process of grade 7 students in learning algebra by applying multidimensional item response theory. The research is divided into 4 steps: 1) the development of item bank of algebra, 2) the development of the multidimensional…
ERIC Educational Resources Information Center
Rickles, Jordan; Phillips, Meredith; Yamashiro, Kyo
2014-01-01
Between 1990 and 2012, the percentage of 13-year-olds (most of whom are 8th graders) taking algebra more than doubled, from 15% to 34% (National Center for Education Statistics, 2013). Yet recent education policy changes suggest that this movement to encourage algebra-taking in 8th grade has begun to reverse course. Existing research suggests that…
Teacher Quality and Teaching Quality of 7th-Grade Algebra I Honors Teachers
ERIC Educational Resources Information Center
Perez, Barbara
2013-01-01
With more and more focus on accountability, algebra achievement has become a major focus of math curriculum developers. In many states, students are expected to pass standardized Algebra achievement tests in order to satisfy graduation requirements. The purpose of this study was to identify teacher qualities and teaching qualities linked to…
Examining Heterogeneity in the Effect of Taking Algebra in Eighth Grade
ERIC Educational Resources Information Center
Rickles, Jordan H.
2013-01-01
Increased access to algebra was a focal point of the National Mathematics Advisory Panel's 2008 report on improving mathematics learning in the United States. Past research found positive effects for early access to algebra, but the focus on average effects may mask important variation across student subgroups. The author addresses whether…
The Effect of Online Tasks for Algebra on Student Achievement in Grade 8
ERIC Educational Resources Information Center
Drijvers, Paul; Doorman, Michiel; Kirschner, Paul; Hoogveld, Bert; Boon, Peter
2014-01-01
Online resources are widely used for educational purposes, such as the training of skills. For algebra education in particular, online resources are expected to contribute to skill mastery in an efficient and effective way. However, studies that underpin these claims through a randomized experiment are scarce. To experimentally investigate the…
Updating Algebra for All?: Evidence of a Middle-Grades Math Acceleration Policy
ERIC Educational Resources Information Center
Dougherty, Shaun M.; Goodman, Joshua; Hill, Darryl; Litke, Erica; Page, Lindsay
2014-01-01
The Wake County Public School System (WCPSS) in North Carolina recently addressed the issue of advancement in and equitable access to advanced mathematics. Under a recent policy, WCPSS uses a SAS-generated predicted probabilities of students' success in obtaining a passing score on the NC Algebra I End-of-Course (EOC) exam, to determine…
NACA's 9th Annual Aircraft Engineering Research Conference
NASA Technical Reports Server (NTRS)
1934-01-01
Eight of the twelve members of the National Advisory Committee for Aeronautics attending the 9th Annual Aircraft Engineering Research Conference posed for this photograph at Langley Field, Virginia, on May 23, 1934. Those pictured are (left to right): Brig. Gen. Charles A. Lindbergh, USAFR Vice Admiral Arthur B. Cook, USN Charles G. Abbot, Secretary of the Smithsonian Institution Dr. Joseph S. Ames, Committee Chairman Orville Wright Edward P. Warner Fleet Admiral Ernest J. King, USN Eugene L. Vidal, Director, Bureau of Air Commerce.
[Treat Princes in Cordoue (9th-10th centuries)].
Ricordel, Joëlle
2016-03-01
It is proposed, through biographic notes and historical reports, to observe the physicians/power relationships in one hand, and power/medical institutions relationships on the other, in Cordoue, during omeyades' emirate and caliphate, between the 9th and 10th centuries. The gathered information allows to describe the social position of physicians who received marks of favor from princes, but also served the power in place for various responsabilities. These documents are also able to make an evaluation of the role of princes for the development of medico-pharmaceutical subjects and give indications on the health of great figures, on their diseases and the conditions of their death. PMID:27281934
NASA Astrophysics Data System (ADS)
Campbell, D. J.; Barabaschi, P.; Bécoulet, M.; Federici, G.; Hellsten, T.; Loarte, A.; Pautasso, G.; Wilson, H.
2003-04-01
The 9th EFPW took place in December 2001 at Saariselka in Finland, hosted by the Technical Research Centre of Finland (VTT) and the Helsinki University, and sponsored by the European Commission. Within an overall theme of `transient events, their mitigation and their implications for plasma facing components in ITER', four topics of importance to the future development of magnetically confined fusion were discussed in detail. In addition, the key issues for the ITER design which are associated with transient events and a review of the JET scientific and technical programme under EFDA were presented. The main issues discussed and the areas identified as requiring further study are summarized here.
Pre-Algebra. Grade 7A-B. Curriculum Bulletin 82CBM34.
ERIC Educational Resources Information Center
Doucet, Flores J.
This guide for teachers in the Houston schools provides plans for teaching over 80 objectives in the mathematics program for grade 7. For each lesson, the objectives are specified, teaching activities are given, and supplementary materials are listed. Practice exercises, answer keys, and mathematical background comprise the bulk of the guide, and…
General view of underground along 9th street. J street segment ...
General view of underground along 9th street. J street segment intersects at left, 9th street segment intersects alley at right. View to the east. - Coolot Building, 812 J Street, Sacramento, Sacramento County, CA
1. D Street (south) facade (short side) and 9th Street ...
1. D Street (south) facade (short side) and 9th Street (west) facade (long side). North of the D Street facade is the Edward Abner Building (413-415 9th Street) and north of it is the Ferree Building (417 9th Street). - PMI Parking Garage, 403-407 Ninth Street, Northwest, Washington, District of Columbia, DC
ERIC Educational Resources Information Center
Levy, Alissa Beth
2012-01-01
The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…
Introduction to the Proceedings of the 9th ISDH
NASA Astrophysics Data System (ADS)
Bove, V. Michael, Jr.; Riskin, Seth
2013-02-01
The Proceedings As co-chairs of the 9th International Symposium on Display Holography, we welcome readers of this collection of papers and posters presented at the event. We hope that both attendees of the event and others pursuing the art, science, and business of holography and 3D imaging will find the authors' contributions of lasting interest and importance. The Event Since its creation at Lake Forest College in 1982 by Professor Tung H Jeong, ISDH has followed a model that differentiates it from other scientific conferences. The 9th ISDH continued this history, fully occupying a floor of the MIT Media Lab for five days. The single-track conference opened with reports on the state of holography in the various nations represented by the attendees, followed by a series of presentations on Education and Holography. One and one-half days of papers on Art and Holography followed, then sessions on Techniques and Materials, Digital Techniques, and Commercial and Applied Holography. A poster session permitted more in-depth discussion between authors and the audience. Two exhibitions of holographic works opened at ISDH: an informal display area at the symposium, and a 15-month-long MIT Museum exhibition, The Jeweled Net: Views of Contemporary Holography. The success of an event of this sort requires the help of many people and organizations. We wish especially to recognize our Honorary Conference Chairs: Tung H Jeong and Joseph W Goodman; our Technical Program Committee: Hans I Bjelkhagen, Frank Fan, Nasser Peyghambarian, and Hiroshi Yoshikawa; and our Arts and Exhibition Committee: Betsy Connors-Chen, Melissa Crenshaw, John Durant, Dieter Jung, Linda Law, Martin Richardson, Jonathan Ross, and Sally Weber. Betsy also coordinated the on-site exhibition. Kristin Hall at the MIT Media Lab made local arrangements, while registration was handled by MIT Conference Services. We also gratefully acknowledge support from Lake Forest College, holographer.org, and authentibrand
NANOTR9: 9th Nanoscience and Nanotechnology Conference
NASA Astrophysics Data System (ADS)
2014-11-01
The conference series NanoTR is the major conference on nanoscience and nanotechnology in Turkey. It brings together leading scientists and engineers in nanotechnology to exchange information on their latest research progress. An exhibition of the companies working in the related field is also organized as a part of the event. With intensive international participation, NanoTR conference series has spread outside the national border and has become an international event in this field. Among international contributions, a wide interest from the countries around Turkey should be emphasized. 9th in the series was organized by Atatürk University in Erzurum-Turkey on June 24-28, 2013 with more than 900 scientists, researchers, private sector representatives from around the world. Conference program included 6 plenary speakers, 35 invited speakers (18 of them were from outside the country), 116 oral presentations, and 340 poster presentations. In addition to 6 plenary sessions, 17 oral and 4 poster sessions created very lively discussion forums covering a vast range of current and emerging sciences from nano-materials, nanoscience, nanofabrication, nano-engineering, nano-electronics, nano-biotechnology, to ethical and social issues of nanoscience and nanotechnology. Also, panel discussions about industrial applications, tutorial sessions have been organized for students, new-comers and company employees.
ERIC Educational Resources Information Center
Ascher, Carol; Maguire, Cindy
2011-01-01
This report describes a follow-up qualitative study, conducted in 2006 by the Annenberg Institute for School Reform, of a small group of New York City high schools that were "beating the odds" in preparing low-performing 9th-grade students for timely high school graduation and college going. The 13 schools included two long-established…
FOREWORD: 9th International Conference on Compressors and their Systems
NASA Astrophysics Data System (ADS)
Kovacevic, Ahmed, Prof
2015-08-01
The 9th International Conference on Compressors and their Systems will be held in London from 5th - 9th September 2015, and as its Chairman, it is my pleasure to welcome you. This series of conferences started in 1999 organised by the Fluid Machinery Group of the Institution of Mechanical Engineers (IMechE) but since 2009 it has been managed by City University London in conjunction with the IMechE and the Institute of Refrigeration, both of which have been very proactive in promoting it. The Organising committee is grateful for their support and continued encouragement. This year, after rigorous reviewing, we have accepted over 80 technical papers for publication, the highest number in the conference history. On behalf of the organising committee I would like to thank the reviewers for their hard work and assistance. In addition to the main technical sessions, this year we have introduced a third day, specifically for Industry, to consider technology, business and market drivers on compressor developments. The traditional series of the short courses is this year continuing prior to the main event with the second short course/forum on Computational Fluid Dynamics in rotating positive displacement machines. I would like to extend my special thanks to our main sponsors, Holroyd PTG, Howden and Kapp Niels for their continuing support for the conference. With their generous contributions we have managed to keep the conference fees at the same level as in 2013, despite extending it to 3 days and holding it outside the University this year. The welcome reception on Sunday 6th September 2015 is dedicated to the celebration of the 20th anniversary of the Centre for Positive Displacement Compressors Technology which was formed at City University in 1995 with support from the Royal Academy of Engineering and Holroyd; its main aim being to assist British manufacturers of screw compressors. The Centre has since made a significant impact on the screw compressor world, far beyond
ERIC Educational Resources Information Center
Blanton, Maria; Levi, Linda; Crites, Terry; Dougherty, Barbara; Zbiek, Rose Mary
2011-01-01
Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential…
PREFACE: 9th International Symposium on Cavitation (CAV2015)
NASA Astrophysics Data System (ADS)
Farhat, M.; Müller, A.
2015-12-01
It is our pleasure and privilege to welcome all the participants of the 9th International Symposium on Cavitation (CAV2015) to Lausanne. Since its initiation in 1986 in Sendai, Japan, the CAV symposium has grown to become the world's foremost event dedicated to cavitation. Hosted by EPFL (Ecole Polytechnique Fédérale de Lausanne) and staged at the SwissTech Convention Center, CAV2015 is a unique opportunity to exchange with leading scientists and industry experts about the latest advances in theoretical modelling, numerical simulation and experimentation related to cavitation phenomena with a special emphasis on practical applications. The topics covered by CAV2015 include cavitation in ¬fluid machinery and fuel systems, bubble dynamics, cavitation erosion, advanced numerical simulation, sonochemistery, biomedicine and experimental techniques. CAV2015 will also host an exhibition of leading providers of state of the art measurement equipment, including high-speed imaging systems, non-intrusive velocimetry, pressure sensors, as well as numerical solvers. We have accepted over 190 papers, which will be presented in four parallel sessions. The proceedings will appear in the open access Journal of Physics: Conference Series (JPCS), which is part of the IOP Conference Series. All published papers are fully citable and upon publication will be free to download in perpetuity. We would like to thank all the reviewers for their great help during the selection process. We will also propose six plenary speakers to highlight cavitation issues in different fields. Finally, we would like to warmly thank our sponsors for their valuable support and the local Organizing Committee for the efforts in setting up this important event. We look forward to seeing you in Lausanne!
PREFACE: 9th National Symposium on Polymeric Materials (NSPM 2009)
NASA Astrophysics Data System (ADS)
Ali, Aidy; Salit, Sapuan
2010-07-01
NSPM 2009 is the formal proceedings of the 9th National Symposium on Polymeric Materials held in Residence Hotel Uniten Bangi on 14-16 December 2009. It is also organised with The Plastics and Rubber Institute Malaysia PRIM. The symposium proceedings consists of 94 papers covering a large number of issues on experimental and analytical studies of polymeric materials. The objectives of the symposium are to review the state-of-the art, present and latest findings and exchange ideas among engineers, researchers and practitioners involved in this field. We strongly hope the outcomes of this symposium will stimulate and enhanced the progress of experimental and analytical studies on polymeric materials as well as contribute to the fundamental understanding in related fields. After careful refereeing of all manuscripts, 15 papers were selected for publications in this issue. Another 20 papers were selected for publication in Pertanika Journal of Science and Technology (PJST). The content of the material and its rapid dissemination was considered to be more important than its form. We are grateful to all the authors for their papers and presentations in this symposium. They are also the ones who help make this symposium possible through their hard work in the preparation of the manuscripts. We would also like to offer our sincere thanks to all the invited speakers who came to share their knowledge with us. We would also like to acknowledge the untiring efforts of the reviewers, research assistants and students in meeting deadlines and for their patience and perseverance. We are indeed honoured to associate this event with Department of Mechanical and Manufacturing, and Faculty of Engineering, Universiti Putra Malaysia. Finally, we appreciate the sponsor support provided by Faculty of Engineering, The Plastics and Rubber Institute Malaysia (PRIM) and PETRONAS Malaysia. Thank you all. Editors: Aidy Ali and S M Sapuan
Leibniz algebras associated with representations of filiform Lie algebras
NASA Astrophysics Data System (ADS)
Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.
2015-12-01
In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
Teaching Arithmetic and Algebraic Expressions
ERIC Educational Resources Information Center
Subramaniam, K.; Banerjee, Rakhi
2004-01-01
A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students…
ERIC Educational Resources Information Center
Heppen, Jessica; Allensworth, Elaine; Walters, Kirk; Pareja, Amber Stitziel; Kurki, Anja; Nomi, Takako; Sorensen, Nicholas
2012-01-01
This study is an efficacy trial funded by a grant from the Institute of Education Sciences (IES) National Center for Education Research (NCER). Fifteen CPS high schools are receiving funding to implement two Algebra I credit recovery courses during the summer sessions of 2011 and 2012--one online and one face-to-face (f2f). These courses allow…
ERIC Educational Resources Information Center
Malik, Ishan Z.
2011-01-01
Urban African American students lack an abstract understanding of algebra and are below their academic level in comparison to other ethnic groups, and this is a pervasive problem (McKinney, Chappell, Berry, & Hickman, 2009). The purpose of this quantitative study using a quasi-experimental design was to determine whether the use of…
ERIC Educational Resources Information Center
Ralston, Nicole C.
2013-01-01
Elementary school students often exhibit a wide variety of different conceptions associated with algebraic thinking that their teachers fail to recognize or understand (Smith, diSessa, & Roschelle, 1994). It is crucial that elementary school teachers possess knowledge of the variety of different student conceptions and also boast abilities to…
ERIC Educational Resources Information Center
Ilona, Haapasalo; Raili, Valimaa; Lasse, Kannas
2012-01-01
Purpose: The aim of this study was to examine the associations between students' perceptions of the psychosocial school environment, health-compromising behaviours, and selected family factors. The analyses were based on data provided for the Health Behaviour in School-aged Children Study (2006). Design/methodology/approach: The data were obtained…
Mississippi Curriculum Framework for Technology Discovery (9th Grade). CIP: 00.0253.
ERIC Educational Resources Information Center
Mississippi Research and Curriculum Unit for Vocational and Technical Education, State College.
This document, which is intended for technology educators in Mississippi, outlines a technology discovery course in which a modular instruction approach allows ninth graders to experience various workplace technologies within four career cluster areas: agriculture/natural resources technology, business/marketing technology, health/human services…
The 8th and 9th Grades Students' Attitude towards Teaching and Learning Physics
ERIC Educational Resources Information Center
Stefan, Monica; Ciomos, Florentina
2010-01-01
The students' interest and attitude towards Physics have been the object of international testing, the most recent of which is the PISA testing from 2006. The students' attitude towards sciences is considered to be a significant predictor of their school results in science, respectively of pursuing a career in areas related to Science. The present…
ERIC Educational Resources Information Center
Neumann, Susanne; Hopf, Martin
2012-01-01
One basis of good teaching is to know about your students' preconceptions. Studies about typical ideas that students bring to the science classroom have been and continue to be a major field in science education research. This study aims to explore associations and ideas that students have regarding "radiation", a term widely used in various…
NASA Astrophysics Data System (ADS)
Neumann, Susanne; Hopf, Martin
2012-12-01
One basis of good teaching is to know about your students' preconceptions. Studies about typical ideas that students bring to the science classroom have been and continue to be a major field in science education research. This study aims to explore associations and ideas that students have regarding `radiation', a term widely used in various fields and necessary to understand fundamental ideas in science. In an explorative study, the perceptions of 50 high school students were examined using semi-structured interviews. The students were 14-16 years old and were chosen from 7 different high schools in an urban area in Austria. Following an interview guideline, students were asked about their general associations with the term `radiation' as well as about their general understanding of different types of radiation. A qualitative analysis of these interviews following the method of Flick (2009) revealed that the students' associations were, to a great extent, very different from the scientific use of the term. Several conceptions that could inhibit students' learning processes could be identified. Consequences for the teaching of the topic `radiation' in science lessons, which are based on these preconceptions, are presented in the conclusion.
General Shop Competencies in Vocational Agriculture for 9th and 10th Grade Classes.
ERIC Educational Resources Information Center
Novotny, Ronald; And Others
The document presents unit plans which offer list of experiences and competencies to be learned for general shop occupations in vocational agriculture. The units include: (1) arc welding, (2) oxy-acetylene welding, (3) flat concrete, (4) concrete block, (5) lumber patterns and wood building materials, (6) metal fasteners, (7) wood adhesives, (8)…
DG Poisson algebra and its universal enveloping algebra
NASA Astrophysics Data System (ADS)
Lü, JiaFeng; Wang, XingTing; Zhuang, GuangBin
2016-05-01
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let $A$ be any DG Poisson algebra. We construct the universal enveloping algebra of $A$ explicitly, which is denoted by $A^{ue}$. We show that $A^{ue}$ has a natural DG algebra structure and it satisfies certain universal property. As a consequence of the universal property, it is proved that the category of DG Poisson modules over $A$ is isomorphic to the category of DG modules over $A^{ue}$. Furthermore, we prove that the notion of universal enveloping algebra $A^{ue}$ is well-behaved under opposite algebra and tensor product of DG Poisson algebras. Practical examples of DG Poisson algebras are given throughout the paper including those arising from differential geometry and homological algebra.
General view of underground showing the 9th street segment where ...
General view of underground showing the 9th street segment where it intersect with the east end of the J street segment (on the left). View to the east. - Coolot Building, 812 J Street, Sacramento, Sacramento County, CA
NASA Astrophysics Data System (ADS)
Skrypnyk, T.
2016-09-01
We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: {gl}(n)={gl}{(n)}\\bar{0}+{gl}{(n)}\\bar{1}, where {gl}{(n)}\\bar{0}={gl}({n}1)\\oplus {gl}(n-{n}1). Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton–neutron Bardeen–Cooper–Schrieer-type models, n-level many-mode Jaynes–Cummings–Dicke-type models of quantum optics, matrix generalization of Bose–Hubbard dimers, etc. We diagonalize the constructed models by means of the ‘generalized’ nested Bethe ansatz.
ERIC Educational Resources Information Center
Loveless, Tom
2008-01-01
This new study is being released as an advance excerpt of the 2008 Brown Center Report on American Education. This new report finds that the nation's push to challenge more students by placing them in advanced math classes in eighth grade has had unintended and damaging consequences, as some 120,000 middle-schoolers are now struggling in advanced…
ERIC Educational Resources Information Center
Brown, Irving A.; Davis, Trina J.; Kulm, Gerald
2011-01-01
This article presents our plans and initial work to explore how mathematics teacher education programs can prepare teachers for diverse middle grades classrooms. It describes the start-up of a five-year National Science Foundation project to design, develop, and test technology-enriched teacher preparation strategies to address equity in algebra…
The PRIME Partnership: 9th Graders, Graduate Students and Integrated, Inquiry-Based Science
NASA Astrophysics Data System (ADS)
Gaffney, A. M.; Miguelez, S.
2001-12-01
The PRIME program (Partnership for Research in Inquiry-based Math, science and engineering Education) is a collaboration between the UW Colleges of Education and Engineering and several Seattle-area school districts. This project, funded by the NSF GK-12 program, pairs UW graduate students from math, science and engineering disciplines with local middle school teachers. The graduate student spends a year working with the teacher, on projects designed to meet the needs and interests of the specific partnership and classroom. In the partnership, the graduate student spends 15 hours per week in the classroom, interacting with the students, as well as additional planning time outside of the classroom. Goals of the PRIME program are enriched learning by middle school students, professional development for middle school teachers, improved communication and teaching skills for the graduate students, and strengthened partnerships between the University of Washington and local school districts. The goal of our partnership was to develop an inquiry-based, 9th grade unit that integrates the pre-existing Earth Science and Chemistry units, and to assess the effectiveness of teaching Chemistry in the context of Earth Science. We have observed that students often become engaged and excited when they do hands-on activities that utilize the intrinsic understanding that they have of concepts that draw upon experiences in their daily lives. When science is taught and learned in one such context - in the context of the natural world - the students may gain a more solid fundamental understanding of the science that they learn. The day-to-day activities for this unit vary widely. We started each topic with a question designed to get the students thinking independently and to identify the preconceptions that the students brought into the classroom. Discussions of students' preconceptions served as a justification and springboard for the subsequent activities and experiments. Examples of
20. TYPICAL VIEW OF FRONT WINDOWS FROM 4TH TO 9TH ...
20. TYPICAL VIEW OF FRONT WINDOWS FROM 4TH TO 9TH FLOOR WITH WHITE GLAZED TERRA COTTA SILL AND HEADERS. MULLIONS ARE ORANGE BROWN BRICKS LIKE THE WALLS. BRICKS ARE IN FLEMISH BOND PATTERN. - Pacific Telephone & Telegraph Company Building, 1519 Franklin Street, Oakland, Alameda County, CA
Global perspectives on poisonous plants: The 9th International Symposium on Poisonous Plants
Technology Transfer Automated Retrieval System (TEKTRAN)
The 9th International Symposium on Poisonous Plants (ISOPP9) was held from 15th-21st July, 2013, at the Inner Mongolia Agricultural University in Hohhot, Inner Mongolia Autonomous Region of China. The Symposium consisted of three days of oral and poster presentations, followed by a tour of the Xilin...
5. West side of State Steeet looking down 9th Steeet. ...
5. West side of State Steeet looking down 9th Steeet. Immediatly to the west lie the Illinois and Michigan Canal, the Chicago Sanitary and Ship Canal, and the Des Plaines River. - Lockport Historic District, Bounded by Eighth, Hamilton & Eleventh Streets & Illinois & Michigan Canal, Lockport, Will County, IL
Lie algebra of conformal Killing–Yano forms
NASA Astrophysics Data System (ADS)
Ertem, Ümit
2016-06-01
We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing–Yano forms. A new Lie bracket for conformal Killing–Yano forms that corresponds to slightly modified Schouten–Nijenhuis bracket of differential forms is proposed. We show that conformal Killing–Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing–Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing–Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases.
UCSMP Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2007
2007-01-01
"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…
Build an Early Foundation for Algebra Success
ERIC Educational Resources Information Center
Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela
2016-01-01
Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…
The Importance of the Ninth Grade on High School Graduation Rates and Student Success
ERIC Educational Resources Information Center
McCallumore, Kyle Megan; Sparapani, Ervin F.
2010-01-01
Researchers target 9th grade as the make or break year for completing high school. During the 9th-grade year, many students for the first time have to earn passing grades in core courses, and these core courses are typically some of the toughest and most rigorous academic classes a student must take in high school. Furthermore, the rising use of…
Higher level twisted Zhu algebras
Ekeren, Jethro van
2011-05-15
The study of twisted representations of graded vertex algebras is important for understanding orbifold models in conformal field theory. In this paper, we consider the general setup of a vertex algebra V, graded by {Gamma}/Z for some subgroup {Gamma} of R containing Z, and with a Hamiltonian operator H having real (but not necessarily integer) eigenvalues. We construct the directed system of twisted level p Zhu algebras Zhu{sub p,{Gamma}}(V), and we prove the following theorems: For each p, there is a bijection between the irreducible Zhu{sub p,{Gamma}}(V)-modules and the irreducible {Gamma}-twisted positive energy V-modules, and V is ({Gamma}, H)-rational if and only if all its Zhu algebras Zhu{sub p,{Gamma}}(V) are finite dimensional and semisimple. The main novelty is the removal of the assumption of integer eigenvalues for H. We provide an explicit description of the level p Zhu algebras of a universal enveloping vertex algebra, in particular of the Virasoro vertex algebra Vir{sup c} and the universal affine Kac-Moody vertex algebra V{sup k}(g) at non-critical level. We also compute the inverse limits of these directed systems of algebras.
Low Performers Found Unready to Take Algebra
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
As state and school leaders across the country push to have more students take algebra in 8th grade, a new study argues that middle schoolers struggling the most in math are being enrolled in that course despite being woefully unprepared. "The Misplaced Math Student: Lost in Eighth Grade Algebra," scheduled for release by the Brookings Institution…
NASA Astrophysics Data System (ADS)
SAME ADDRESS--> Nader Sadeghi,
The Use of Ninth-Grade Early Warning Indicators to Improve Chicago Schools
ERIC Educational Resources Information Center
Allensworth, Elaine
2013-01-01
Chicago has been in the forefront of the country in its use of 9th-grade indicators of dropout. Catalyzed by the development of the freshman on-track indicator and research around it, Chicago school administrators, central office personnel, and external partners have developed a number of mechanisms using 9th-grade indicators to stimulate school…
Loop Virasoro Lie conformal algebra
Wu, Henan Chen, Qiufan; Yue, Xiaoqing
2014-01-15
The Lie conformal algebra of loop Virasoro algebra, denoted by CW, is introduced in this paper. Explicitly, CW is a Lie conformal algebra with C[∂]-basis (L{sub i} | i∈Z) and λ-brackets [L{sub i} {sub λ} L{sub j}] = (−∂−2λ)L{sub i+j}. Then conformal derivations of CW are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CW are classified.
Ternary generalization of Heisenberg's algebra
NASA Astrophysics Data System (ADS)
Kerner, Richard
2015-06-01
A concise study of ternary and cubic algebras with Z3 grading is presented. We discuss some underlying ideas leading to the conclusion that the discrete symmetry group of permutations of three objects, S3, and its abelian subgroup Z3 may play an important role in quantum physics. We show then how most of important algebras with Z2 grading can be generalized with ternary composition laws combined with a Z3 grading. We investigate in particular a ternary, Z3-graded generalization of the Heisenberg algebra. It turns out that introducing a non-trivial cubic root of unity, , one can define two types of creation operators instead of one, accompanying the usual annihilation operator. The two creation operators are non-hermitian, but they are mutually conjugate. Together, the three operators form a ternary algebra, and some of their cubic combinations generate the usual Heisenberg algebra. An analogue of Hamiltonian operator is constructed by analogy with the usual harmonic oscillator, and some properties of its eigenfunctions are briefly discussed.
ERIC Educational Resources Information Center
Cavalluzzo, Linda; Lowther, Deborah L.; Mokher, Christine; Fan, Xitao
2012-01-01
The 2006-11 Regional Educational Laboratory Appalachia at CNA conducted a rigorous evaluation of the Kentucky Virtual Schools hybrid algebra I curriculum. The curriculum combines traditional face-to-face instruction with an online program. This study used a two-cohort sample with 25 high schools in year 1 (SY 07/08: 13 treatment and 12 control)…
ERIC Educational Resources Information Center
Newbold, Anthony J.
2014-01-01
An achievement gap exists in mathematics between low-income African American male students and their European American counterparts. Although this problem has been approached using different interventions with minimal results, the impact of homogenous grouping is not well understood in spite of its use. As a result, this study was conducted to…
ERIC Educational Resources Information Center
Arkansas State Univ., State University.
This curriculum package contains materials for teaching the career orientation course in the junior high schools of Arkansas. Following the introduction, which describes the course and provides a rationale for it, along with instructions to teachers for conducting the course, the package is divided into 35 units organized under five major…
ERIC Educational Resources Information Center
Sears, Bill
This curriculum unit requires students to use science, geography, and language arts skills in studying the weather. Students are asked to report on weather anomalies and are provided with background information, detailed instructions, online resources, and reflection questions. The teacher's guide describes the unit's purpose, correlation to…
ERIC Educational Resources Information Center
Johnson-Moore, Brenda
This paper discusses a practicum designed to address young teen mothers' lack of knowledge, experience, and skills needed to appropriately care for their infants. It documents that increased knowledge, enhanced interpersonal relationships, and augmented parenting skills made a difference in the teen mothers' approach to parenting. Parenting…
ERIC Educational Resources Information Center
Fried, Lise E.; Williams, Sandra; Cabral, Howard; Hacker, Karen
2013-01-01
The purpose of the study is to assess the relationship between timing of adolescent development and risk factors for suicide. Nationally representative data from the Add Health survey were used. The relationship of sociodemographic characteristics, known risk factors, and physical developmental timing and cognitive developmental style to suicide…
The Impact of the Early College High School Model on Core 9th and 10th Grade Student Outcomes
ERIC Educational Resources Information Center
Edmunds, Julie A.; Bernstein, Lawrence; Unlu, Fatih; Glennie, Elizabeth; Arshavsky, Nina
2011-01-01
To address concerns about low graduation rates and a lack of workforce readiness, states and districts have been experimenting with different models of high school reform. One of the most popular models has been the Early College High School (ECHS) model, small schools that blur the line between high school and college. Since 2002, over 200 ECHSs…
A Better 9th Grade: Early Results from an Experimental Study of the Early College High School Model
ERIC Educational Resources Information Center
SERVE Center at University of North Carolina at Greensboro, 2010
2010-01-01
To increase the number of students graduating from high school prepared for college, North Carolina has established the largest number of Early College High Schools (ECHS) in the United States. Early results from a rigorous, independent study of North Carolina's initiative have shown that these schools have substantial positive impacts on student…
ERIC Educational Resources Information Center
Degner, Kate M.
2013-01-01
This study uses data from the National Center of Education Statistics (NCES) High School Longitudinal Study of 2009 (HLS:09). Parent responses to the Parent Involvement survey, given as part of the NCES study were considered, along with their child's socio-economic status (SES) and self-reported level of mathematics course enrollment during…
ERIC Educational Resources Information Center
Hayden, Harvey; And Others
To some educators, infusing environmental education into different subject areas at different levels may seem like an insurmountable task. This handbook was developed to take the guesswork out of this process and alleviate the fear and confusion that may result. It was designed to assist with infusing knowledge, skill and attitude activities into…
Does Grading Affect Educational Attainment? A Longitudinal Study
ERIC Educational Resources Information Center
Klapp, Alli
2015-01-01
The purpose of the study was to investigate how grading in primary school affected students' achievement measured by grades in 7th, 8th and 9th Grade and educational attainment in upper secondary school (12th Grade), and how the effect varied as a function of students' cognitive ability, gender and socio-economic status. The data derived from the…
Calif. Laws Shift Gears on Algebra, Textbooks
ERIC Educational Resources Information Center
Robelen, Erik W.
2012-01-01
New laws in California have set the state on a course for some potentially significant changes to the curriculum, including a measure that revisits the matter of teaching Algebra 1 in 8th grade and another that revamps the state's textbook-adoption process and hands districts greater leeway in choosing instructional materials. The algebra-related…
ERIC Educational Resources Information Center
Hemphill, David C.
2011-01-01
The first pretest-posttest hypothesis was tested using the dependent t test. Null hypotheses for test score improvement over time were rejected for the end of fifth-grade pretest compared to ending sixth-grade posttest math Essential Learner Outcome scores converted to standard scores for randomly selected sixth-grade girls meeting measured test…
A case of unilateral coronal synostosis from Medieval Hungary (9th century A.D.).
Évinger, Sándor; Hajdu, Tamás; Biró, Gergely; Zádori, Péter; Marcsik, Antónia; Molnár, Erika; Wolff, Katalin
2016-01-01
A unique single suture craniosynostosis case from the 9(th) century is presented in this paper. Although craniosynostosis is a fairly common pediatric anomaly nowadays, its occurrence in archaeological collections is an uncommon precedent. Since the diagnosis and treatment of premature cranial suture closure usually happens at an early age, evaluation of the whole developmental process is a rare opportunity. The right-sided coronal suture synostosis of this 30-35 years old woman gives an interesting opportunity to observe the effect of this phenomenon in adulthood. Only slight distortion of the viscerocranium and no bony signs of elevated intracranial pressure can be seen on the skull. The women suffered remarkable bending of the whole face and cranial base of the midsagittal plane. Besides the aesthetic disorder, the condition might have contributed to a chronic headache and visual disturbances. The lack of any other typical symptom suggests the diagnosis of isolated craniosynostosis or a milder type of syndromic craniosynostosis, the possibility of an underlying causative mutation cannot be ruled out. PMID:26555924
F/A-18 1/9th scale model tail buffet measurements
NASA Technical Reports Server (NTRS)
Martin, C. A.; Glaister, M. K.; Maclaren, L. D.; Meyn, L. A.; Ross, J.
1991-01-01
Wind tunnel tests were carried out on a 1/9th scale model of the F/A-18 at high angles of attack to investigate the characteristics of tail buffet due to bursting of the wing leading edge extension (LEX) vortices. The tests were carried out at the Aeronautical Research Laboratory low-speed wind tunnel facility and form part of a collaborative activity with NASA Ames Research Center, organized by The Technical Cooperative Program (TTCP). Information from the program will be used in the planning of similar collaborative tests, to be carried out at NASA Ames, on a full-scale aircraft. The program covered the measurement of unsteady pressures and fin vibration for cases with and without the wing LEX fences fitted. Fourier transform methods were used to analyze the unsteady data, and information on the spatial and temporal content of the vortex burst pressure field was obtained. Flow visualization of the vortex behavior was carried out using smoke and a laser light sheet technique.
Fish from Head to Tail: The 9th European Zebrafish Meeting in Oslo.
Griffiths, Gareth; Müller, Ferenc; Ledin, Johan; Patton, E Elizabeth; Gjøen, Tor; Lobert, Viola Hélène; Winther-Larsen, Hanne Cecilie; Mullins, Mary; Joly, Jean-Stephane; Weltzien, Finn-Arne; Press, Charles McLean; Aleström, Peter
2016-04-01
The 9th European Zebrafish Meeting took place recently in Oslo (June 28-July 2, 2015). A total of 650 participants came to hear the latest research news focused on the zebrafish, Danio rerio, and to its distant evolutionary relative medaka, Oryzias latipes. The packed program included keynote and plenary talks, short oral presentations and poster sessions, workshops, and strategic discussions. The meeting was a great success and revealed dramatically how important the zebrafish in particular has become as a model system for topics, such as developmental biology, functional genomics, biomedicine, toxicology, and drug development. A new emphasis was given to its potential as a model for aquaculture, a topic of great economic interest to the host country Norway and for the future global food supply in general. Zebrafish husbandry as well as its use in teaching were also covered in separate workshops. As has become a tradition in these meetings, there was a well-attended Wellcome Trust Sanger Institute and ZFIN workshop focused on Zebrafish Genome Resources on the first day. The full EZM 2015 program with abstracts can be read and downloaded from the EZM 2015 Web site zebrafish2015.org . PMID:26859625
Report on the 9th EONS Congress, Istanbul, Turkey, 18–19 September 2014: nursing highlights
Lichosik, D; Caruso, R
2014-01-01
The European Oncology Nursing Society (EONS), in partnership with the Oncology Nursing Association of Turkey (TONA), organised the 9th EONS Congress in Istanbul, Turkey, 18–19 September 2014. The Congress venue was in Harbiye Cultural Centre and Istanbul Military Museum and offered two days of unprecedented scientific, educational, and networking opportunities for all stakeholders active in the field of oncology nursing around the world. EONS is a pan-European organisation dedicated to the support and development of cancer nurses. Through individual members and national societies EONS engages in projects to help nurses develop their skills, network with each other, and raise the profile of cancer nursing across Europe. This biennial Congress brings together cancer nurses across the globe from many fields of expertise to ‘Celebrate Excellence in Cancer Nursing’ through interactive sessions, lectures, and collegial networking. The format was specifically designed to meet the needs of nurses working in the field of cancer care, education, and research. PMID:25435909
Should College Algebra be a Prerequisite for Taking Psychology Statistics?
ERIC Educational Resources Information Center
Sibulkin, Amy E.; Butler, J. S.
2008-01-01
In order to consider whether a course in college algebra should be a prerequisite for taking psychology statistics, we recorded students' grades in elementary psychology statistics and in college algebra at a 4-year university. Students who earned credit in algebra prior to enrolling in statistics for the first time had a significantly higher mean…
ERIC Educational Resources Information Center
Nomi, Takako; Raudenbush, Stephen W.
2014-01-01
Algebra is often considered as a gateway for later achievement. A recent report by the Mathematics Advisory Panel (2008) underscores the importance of improving algebra learning in secondary school. Today, a growing number of states and districts require algebra for all students in ninth grade or earlier. Chicago is at the forefront of this…
ERIC Educational Resources Information Center
Browne, Jeffrey C.; Schmidt, Jeffrey K.; Lemke, Melissa
2007-01-01
This is the 9th annual report on conditions affecting the Racine Unified School District RUSD). Over the past decade, the conditions affecting the district as well as the school outcomes have changed in some ways and remained stable in others. This analysis compares RUSD to nine peer school districts and the state of Wisconsin. RUSD peer…
9th International Conference on Damage Assessment of Structures (DAMAS 2011)
NASA Astrophysics Data System (ADS)
Ouyang, Huajiang
2011-07-01
Dear Delegates We would like to welcome you to the 9th International Conference on Damage Assessment of Structures. This series of conferences has been held as a biannual event since 1995. The previous venues were Pescara (Italy, 1995), Sheffield (UK, 1997), Dublin (Ireland, 1999), Cardiff (UK, 2001), Southampton (UK, 2003), Gdansk (Poland, 2005), Torino (Italy, 2007) and Beijing (China, 2009). The conference will cover all research topics relevant to damage assessment of engineering structures and systems including signal processing of sensor measurements and theoretical techniques as well as experimental case studies, and numerical simulations. It has established itself as a major international forum for the above research areas. Typically over 100 papers are presented at each conference. It is thought appropriate to keep the conference at this size to facilitate knowledge exchange. DAMAS Conferences have had support from other learned societies and industry. These include the Technical Division of Vibration and Acoustics of the American Society of Mechanical Engineers, the British Society for Strain Measurement, to name a few. There are exhibitors at some conferences. The venue of DAMAS2011, Oxford, is a world-renowned university town. Oxford is also located in the Cotswolds, an area of outstanding natural beauty. And July is arguably the best month of the year in UK. It is hoped that all delegates will enjoy the conference and continue to support DAMAS conferences in the future. Huajiang Ouyang On behalf of the Organising Committee: Professor Huajiang Ouyang, University of Liverpool, UK (Conference Chair) Professor Vadim Silberschmidt, University of Loughborough, UK Professor Fulei Chu, Tsinghua University, China Professor Wieslaw Ostachowicz, Polish Academy of Science, Poland Professor Cecilia Surace, Politecnico di Torino, Italy
ERIC Educational Resources Information Center
Oishi, Lindsay
2011-01-01
"Solve for x." While many people first encountered this enigmatic instruction in high school, the last 20 years have seen a strong push to get students to take algebra in eighth grade or even before. Today, concerns about the economy highlight a familiar worry: American eighth-graders trailed their peers in five Asian countries on the 2007 TIMSS…
Contractions of affine Kac-Moody algebras
NASA Astrophysics Data System (ADS)
Daboul, J.; Daboul, C.; de Montigny, M.
2008-08-01
I review our recent work on contractions of affine Kac-Moody algebras (KMA) and present new results. We study generalized contractions of KMA with respect to their twisted and untwisted KM subalgebras. As a concrete example, we discuss contraction of D(1)4 and D(3)4, based on Z3-grading. We also describe examples of 'level-dependent' contractions, which are based on Z-gradings of KMA. Our work generalizes the Inönü-Wigner contraction of P. Majumdar in several directions. We also give an algorithm for constructing Kac-Moody-like algebras hat g for any Lie algebra g.
Algebraic Apect of Helicities in Hadron Physics
NASA Astrophysics Data System (ADS)
An, Murat; Ji, Chueng
2015-04-01
We examined the relation of polarization vectors and spinors of (1 , 0) ⊕(0 , 1) representation of Lorentz group in Clifford algebra Cl1 , 3 , their relation with standard algebra, and properties of these spinors. Cl1 , 3 consists of different grades:e.g. the first and the second grades represent (1 / 2 , 1 / 2) and (1 , 0) ⊕(0 , 1) representation of spin groups respectively with 4 and 6 components. However, these Clifford numbers are not the helicity eigenstates and thus we transform them into combinations of helicity eigenstates by expressing them as spherical harmonics. We relate the spin-one polarization vectors and (1 , 0) ⊕(0 , 1) spinors under one simple transformation with the spin operators. We also link our work with Winnberg's work of a superfield of a spinors of Clifford algebra by giving a physical meaning to Grassmann variables and discuss how Grassman algebra is linked with Clifford algebra.
I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2009
2009-01-01
The I CAN Learn[R] Education System is an interactive, self-paced, mastery-based software system that includes the I CAN Learn[R] Fundamentals of Math (5th-6th grade math) curriculum, the I CAN Learn[R] Pre-Algebra curriculum, and the I CAN Learn[R] Algebra curriculum. College algebra credit is also available to students in participating schools…
Pay-Offs from Expanding Summer Credit Recovery in Algebra
ERIC Educational Resources Information Center
Allensworth, Elaine; Nomi, Takako; Heppen, Jessica
2013-01-01
The consequences of failing core academic courses during the first year are dire. In Chicago, over a quarter of students fail at least one semester of algebra in their ninth grade year, and only 13% of students who fail both semesters of Algebra I in ninth grade graduate in 4 years. Offering credit recovery options is one strategy to deal with…
Effects of Expanding Summer Credit Recovery in Algebra
ERIC Educational Resources Information Center
Allensworth, Elaine; Michelman, Valerie; Nomi, Takako; Heppen, Jessica
2014-01-01
In Chicago, over a quarter of students fail at least one semester of algebra in their ninth grade year, and only 13% of students who fail both semesters of Algebra I in ninth grade graduate in 4 years. Offering credit recovery options is one strategy to deal with high failure rates. The primary goal of credit recovery programs is to give students…
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
ERIC Educational Resources Information Center
Napaphun, Vishnu
2012-01-01
Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…
Lax operator algebras and integrable systems
NASA Astrophysics Data System (ADS)
Sheinman, O. K.
2016-02-01
A new class of infinite-dimensional Lie algebras, called Lax operator algebras, is presented, along with a related unifying approach to finite-dimensional integrable systems with a spectral parameter on a Riemann surface such as the Calogero-Moser and Hitchin systems. In particular, the approach includes (non-twisted) Kac-Moody algebras and integrable systems with a rational spectral parameter. The presentation is based on quite simple ideas about the use of gradings of semisimple Lie algebras and their interaction with the Riemann-Roch theorem. The basic properties of Lax operator algebras and the basic facts about the theory of the integrable systems in question are treated (and proved) from this general point of view. In particular, the existence of commutative hierarchies and their Hamiltonian properties are considered. The paper concludes with an application of Lax operator algebras to prequantization of finite-dimensional integrable systems. Bibliography: 51 titles.
The Great Debate: Should All 8th Graders Take Algebra?
ERIC Educational Resources Information Center
McKibben, Sarah
2009-01-01
While 8th grade algebra was once reserved as a course for the gifted, today, more U.S. 8th graders take algebra than any other math course. This article discusses a report from the Brookings Institution which chronicles the history of the 8th-grade algebra surge and its impact on today's low-performing students. The report indicates that many of…
Special Issue for the 9th International Conference on Carbonaceous Particles in the Atmosphere
Strawa, A.W.; Kirchstetter, T.W.; Puxbaum, H.
2009-12-11
Carbonaceous particles are a minor constituent of the atmosphere but have a profound effect on air quality, human health, visibility and climate. The importance of carbonaceous particles has been increasingly recognized and become a mainstream topic at numerous conferences. Such was not the case in 1978, when the 1st International Conference on Carbonaceous Particles in the Atmosphere (ICCPA), or ''Carbon Conference'' as it is widely known, was introduced as a new forum to bring together scientists who were just beginning to reveal the importance and complexity of carbonaceous particles in the environment. Table 1 lists the conference dates, venues in the series as well as the proceedings, and special issues resulting form the meetings. Penner and Novakov (Penner and Novakov, 1996) provide an excellent historical perspective to the early ICCPA Conferences. Thirty years later, the ninth in this conference series was held at its inception site, Berkeley, California, attended by 160 scientists from 31 countries, and featuring both new and old themes in 49 oral and 83 poster presentations. Topics covered such areas as historical trends in black carbon aerosol, ambient concentrations, analytic techniques, secondary aerosol formation, biogenic, biomass, and HULIS1 characterization, optical properties, and regional and global climate effects. The conference website, http://iccpa.lbl.gov/, holds the agenda, as well as many presentations, for the 9th ICCPA. The 10th ICCPA is tentatively scheduled for 2011 in Vienna, Austria. The papers in this issue are representative of several of the themes discussed in the conference. Ban-Weiss et al., (Ban-Weiss et al., accepted) measured the abundance of ultrafine particles in a traffic tunnel and found that heavy duty diesel trucks emit at least an order of magnitude more ultrafine particles than light duty gas-powered vehicles per unit of fuel burned. Understanding of this issue is important as ultrafine particles have been shown to
Spontaneous Meta-Arithmetic as a First Step toward School Algebra
ERIC Educational Resources Information Center
Caspi, Shai; Sfard, Anna
2012-01-01
Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…
Al-Habib, Amro
2015-01-01
The 9th Saudi Association of Neurological Surgery (9th SANS) Annual Meeting was held in the Sheraton Dammam Hotel and Towers, Dammam, Saudi Arabia on March 3-5, 2015, organized by the Department of Neurosurgery, University of Dammam with a theme of “Research is the Bridge to the Future.” The meeting was preceded by a Public Awareness Campaign on March 2, 2015 held at King Fahd Hospital of the University, Al-Khobar, Saudi Arabia, and several pre-conference workshops that were highly beneficial for neurosurgery today. The scientific program was loaded with innovative and interactive presentations from respected and reputable speakers from different parts of the world. Abstracts were carefully selected and reviewed based on their scientific value and relevance to the clinical, surgical, academic, and research aspects of neurosurgery in the Kingdom, and the world.
Ninth Grade Repeaters--Why They Did Better in Summer School.
ERIC Educational Resources Information Center
Jones, Helen
A widely held perception is that public schools are failing American children and society. Some research indicates that 9th-graders are more at risk for school failure than are students in other grades. This paper presents findings of a study that examined 9th-graders in the Durham Public School System (North Carolina) who were enrolled in a Basic…
2002-05-01
Antiretroviral research presented recently at the 9th Conference on Retroviruses and Opportunistic Infections demonstrates that investigators and pharmaceutical companies continue to strive for the next highly potent and easily tolerated anti-HIV drug. Among the new approaches are entry inhibitor drug and second-generation non-nucleoside reverse transcriptase inhibitors. New studies also looked into potency against multidrug-resistant virus and medication regimens that are simpler to take and have fewer side effects. PMID:12030213
ERIC Educational Resources Information Center
Eissa, Mourad Ali
2015-01-01
The purpose of this study was to explore the effect of a self regulated learning intervention program on cognitive and metacognitive EFL reading comprehension of 9th graders with reading disabilities. The participants in this study were 40 9th Graders with reading disabilities, selected from two schools located in Baltim Educational Edara. A…
Determining Faculty Grading Variation.
ERIC Educational Resources Information Center
Demerjian, Marlene D.
A study was undertaken at the College of the Canyons, in California, to assess the variation of grades given by mathematics instructors teaching intermediate algebra. A sample was drawn from all instructors who taught Math 070 repeatedly from fall 1990 to fall 1994, resulting in the examination of the grades of at least 200 students from classes…
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-04-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Difficulties in initial algebra learning in Indonesia
NASA Astrophysics Data System (ADS)
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-12-01
Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.
Experimental Course Report/Grade Nine.
ERIC Educational Resources Information Center
Davis, Robert B.
Described is the development of an approach to the algebra of real numbers which includes three areas of mathematics not commonly found in grade 9--the theory of limits of infinite sequences, a frequent use of Cartesian co-ordinates, and algebra of matrices. Seventy per cent of the course is abstract axiomatic algebra and the remaining portion…
Algebraic vs physical N = 6 3-algebras
Cantarini, Nicoletta; Kac, Victor G.
2014-01-15
In our previous paper, we classified linearly compact algebraic simple N = 6 3-algebras. In the present paper, we classify their “physical” counterparts, which actually appear in the N = 6 supersymmetric 3-dimensional Chern-Simons theories.
Computer animation in teaching science: Effectiveness in teaching retrograde motion to 9th graders
NASA Astrophysics Data System (ADS)
Klenk, Kristin Elmstrom
The purpose of this study is to determine whether an instructional approach which includes computer animations is more effective than a traditional textbook-only approach in helping ninth grade students learn an abstract concept, in this case planetary retrograde motion. This investigation uses a quasi-experimental design with convenient sampling. The independent variable is the type of instruction provided to students; traditional text-based instruction (control group) compared to traditional instruction which also includes the viewing of 4 computer animations (treatment). Two conditions of the treatment examine the relative advantage of the order of the presentation of the animations and text-based instruction, as well as the quality of understanding and the retention of the learning over time. The dependent variable is student achievement which is measured using an instrument designed specifically for this study. Comparison of the independent variable to the dependent variable based upon the results from a Repeated Measure Factorial Design in ANOVA indicates that the treatment is an effective instructional technique. The posttest1 mean score of the treatment groups was significantly greater than the posttest1 mean score of the control group. Further posthoc tests indicate that there was no significant difference between the two treatments (1 and 2); read/animation versus animation/read. However, there was a significant difference in the mean score depending on the pathway, students enrolled in the A pathway achieved a significantly higher mean score after the treatment than students in the B pathway. The A pathway (n = 185) represent the larger heterogeneous population of students as compared to the B pathway (n=16) which includes students with lower cognitive abilities and special needs. When all of the students are included in the analysis the results indicate that students do not retain their understanding of the concept. However, when the students in the B
Awaad, Rania; Ali, Sara
2016-01-01
Morbid fears and phobias have been mentioned in religious, philosophical and medical manuscripts since ancient times. Despite early insights by the Greeks, phobias did not appear as a separate clinical phenomenon in Western medicine until the 17th century and has evolved substantially since. However, robust investigations attempting to decipher the clinical nature of phobias emerged in pre-modern times during the oft-overlooked Islamic Golden Era (9th-12th centuries); which overlapped with Europe's medieval period. An innovative attempt was made by the 9th century Muslim scholar, Abu Zayd al-Balkhi, in his medical manuscript "Sustenance of the Body and Soul," to define phobias as a separate diagnostic entity. Al-Balkhi was one of the earliest to cluster psychological and physical symptoms of phobias under one category, "al-Fazaá", and outline a specific management plan. We analyze al-Balkhi's description of phobias, according to the modern understanding of psychiatric classifications and symptomatology as described in the DSM-5. PMID:26741063
Three centuries of geomagnetic field intensity changes in Spain (from the 9th to the 12th centuries)
NASA Astrophysics Data System (ADS)
Gomez-Paccard, M.; Osete, M. L.; Chauvin, A.; Jimenez-Castillo, P.; Perez-Asensio, M.
2013-12-01
Available European data indicate that during the past 2500 years there have been periods of rapid intensity geomagnetic fluctuations (at least of ~20 μT/century) interspersed with periods of little change. The challenge now is to precisely describe these rapid changes by the acquisition of well-dated high-quality archeomagnetic data. In this study we report the archeomagnetic study of Spanish ceramic fragments. The collected fragments belong to 14 superposed stratigraphic levels corresponding to a surface no bigger than 3 m by 7 m. The pottery fragments dates back to the 9th and 11th centuries. The dating was established by 4 radiocarbon dates and by archeological/historical constraints including typological comparisons and well-controlled stratigraphic constrains between the different stratigraphic units. From classical Thellier experiments including TRM anisotropy and cooling rate corrections upon archeointensity estimates and conducted on 79 fragments, twelve new high-quality mean intensities have been obtained. Together with previously published high-quality data from Western Europe, the new data provide an improved description of the intensity changes that took place in Spain between the 9th and the 12th centuries. The results confirm that rapid intensity changes took place in Western Europe during the recent history of the Earth.
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, Inc., Reston, VA.
This is a reprint of the historical capsules dealing with algebra from the 31st Yearbook of NCTM,"Historical Topics for the Mathematics Classroom." Included are such themes as the change from a geometric to an algebraic solution of problems, the development of algebraic symbolism, the algebraic contributions of different countries, the origin and…
Figueroa-O'Farrill, Jose Miguel
2009-11-15
We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern-Simons theories with matter.
Ninth Grade Students' Understanding of The Nature of Scientific Knowledge
ERIC Educational Resources Information Center
Kilic, Kerem; Sungur, Semra; Cakiroglu, Jale; Tekkaya, Ceren
2005-01-01
The purpose of this study was to investigate the 9th-grade students' understandings of the nature of scientific knowledge. The study also aimed to investigate the differences in students' understanding of the nature of scientific knowledge by gender, and school types. A total of 575 ninth grade students from four different school types (General…
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
NASA Astrophysics Data System (ADS)
Marion, F.; Mours, B.
2005-09-01
The yearly Gravitational Wave Data Analysis Workshop (GWDAW) is now a well established meeting. As usual, the scope of the meeting covered the status of ground-based and space-based detectors, sources and population modelling, detector characterization, event searches, multi-detector analysis and new analysis methods. The 9th GWDAW followed the trend observed in previous years: more presentations that included real data and more sophisticated analysis techniques. However, the biggest change observed was a significant increase in the number of presentations dealing with the analysis of data coming from multiple detectors. Our field needs to combine these data to best extract the astrophysical information. This yearly meeting, bringing together all the worldwide players in the field, is a chance for us to make progress in this direction, and we will certainly see more results in future GWDAW meetings. The importance of the 9th GWDAW meeting can be assessed not only by the record attendance and number of submitted contributions, but also by looking at the work schedules of the various groups. People are now using the GWDAW dates to set deadlines for their activities in order to present their results at the next GWDAW. This special issue of Classical and Quantum Gravity contains the most up-to-date papers on the topics covered by the meeting. Besides being a good reference that will fit proudly into the series of previous GWDAW proceedings, it provides valuable details about current work. As organizers of this workshop, we would like to thank not only the sponsors that made this meeting possible, but also all the participants for coming, sharing their results and enjoying the event with us. The following institutions have sponsored the 9th GWDAW: Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP) European Gravitational Observatory (EGO) Université de Savoie Groupement de Recherche: Phénomènes cosmiques de haute énergie (GDR-PCHE) Institut National de
High School Algebra Readiness Program: A Quasi-Experimental Study
ERIC Educational Resources Information Center
Birnbohm, Carol L.
2010-01-01
This quasi-experimental study measured the effectiveness of a locally created summer Algebra readiness program in a large suburban high school district in New Jersey. Incoming ninth grade students who were not ready for high school algebra were invited to participate in the summer program. The program was designed to provide access to more…
The Aftermath of Accelerating Algebra: Evidence from District Policy Initiatives
ERIC Educational Resources Information Center
Clotfelter, Charles T.; Ladd, Helen F.; Vigdor, Jacob L.
2014-01-01
In 2008, the California State Board of Education voted to require all students to enroll in algebra by 8th grade. This policy initiative, yet to be actually implemented, represents the culmination of a decades-long movement toward offering algebra instruction before the traditional high school years. Nationally, the proportion of 8th grade…
Learning Beginning Algebra with Spreadsheets in a Computer Intensive Environment
ERIC Educational Resources Information Center
Tabach, Michal; Hershkowitz, Rina; Arcavi, Abraham
2008-01-01
This study is part of a large research and development project aimed at observing, describing and analyzing the learning processes of two seventh grade classes during a yearlong beginning algebra course in a computer intensive environment (CIE). The environment includes carefully designed algebra learning materials with a functional approach, and…
Gadher, Suresh Jivan; Marczak, Łukasz; Łuczak, Magdalena; Stobiecki, Maciej; Widlak, Piotr; Kovarova, Hana
2016-01-01
Every year since 2007, the Central and Eastern European Proteomic Conference (CEEPC) has excelled in representing state-of-the-art proteomics in and around Central and Eastern Europe, and linking it to international institutions worldwide. Its mission remains to contribute to all approaches of proteomics including traditional and often-revisited methodologies as well as the latest technological achievements in clinical, quantitative and structural proteomics with a view to systems biology of a variety of processes. The 9th CEEPC was held from June 15th to 18th, 2015, at the Institute of Bioorganic Chemistry, Polish Academy of Sciences in Poznań, Poland. The scientific program stimulated exchange of proteomic knowledge whilst the spectacular venue of the conference allowed participants to enjoy the cobblestoned historical city of Poznań. PMID:26558656
ERIC Educational Resources Information Center
Capraro, Mary Margaret; Joffrion, Heather
2006-01-01
Using symbolic algebra to represent and solve linear equations is one of the expectations within the "Algebra" content standard for the 6-8-grade band in the National Council of Teachers of Mathematics (NCTM) "Principles and Standards for School Mathematics" (2000). Students' understanding of these concepts, even before a formal algebra course,…
The Development of Writing Proficiency as a Function of Grade Level: A Linguistic Analysis
ERIC Educational Resources Information Center
Crossley, Scott A.; Weston, Jennifer L.; McLain Sullivan, Susan T.; McNamara, Danielle S.
2011-01-01
In this study, a corpus of essays stratified by level (9th grade, 11th grade, and college freshman) are analyzed computationally to discriminate differences between the linguistic features produced in essays by adolescents and young adults. The automated tool Coh-Metrix is used to examine to what degree essays written at various grade levels can…
Programed Instruction in Elementary Algebra: An Experiment
ERIC Educational Resources Information Center
Lial, Margaret L.
1970-01-01
Report of an experiment which investigated the use of a programed elementary algebra text as a teaching method. The method was evaluated on the basis of student evaluation of the course and the percentage of students achieving a grade of C or better. Results indicated that the use of programed texts was superior to the traditional approach using…
Using Technology to Balance Algebraic Explorations
ERIC Educational Resources Information Center
Kurz, Terri L.
2013-01-01
In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…
Introduction to Algebra (Part 2). Preliminary Edition.
ERIC Educational Resources Information Center
Haag, V. H.; And Others
This is part two of a two-part SMSG algebra text for ninth-grade students. The text was written for those students whose mathematical talent is underdeveloped. Chapter topics include the real numbers, addition of real numbers, multiplication of real numbers, properties of order, and subtraction and division for real numbers. (MP)
Learning Algebra in a Computer Algebra Environment
ERIC Educational Resources Information Center
Drijvers, Paul
2004-01-01
This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…
Realizations of Galilei algebras
NASA Astrophysics Data System (ADS)
Nesterenko, Maryna; Pošta, Severin; Vaneeva, Olena
2016-03-01
All inequivalent realizations of the Galilei algebras of dimensions not greater than five are constructed using the algebraic approach proposed by Shirokov. The varieties of the deformed Galilei algebras are discussed and families of one-parametric deformations are presented in explicit form. It is also shown that a number of well-known and physically interesting equations and systems are invariant with respect to the considered Galilei algebras or their deformations.
NASA Technical Reports Server (NTRS)
Iachello, Franco
1995-01-01
An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.
Orientation in operator algebras
Alfsen, Erik M.; Shultz, Frederic W.
1998-01-01
A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457
Developing Thinking in Algebra
ERIC Educational Resources Information Center
Mason, John; Graham, Alan; Johnson-Wilder, Sue
2005-01-01
This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…
Connecting Arithmetic to Algebra
ERIC Educational Resources Information Center
Darley, Joy W.; Leapard, Barbara B.
2010-01-01
Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
Profiles of Algebraic Competence
ERIC Educational Resources Information Center
Humberstone, J.; Reeve, R.A.
2008-01-01
The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
NASA Astrophysics Data System (ADS)
Kosian, Menne; Weerts, Henk; Steur, Roeland; Abrahamse, Jaap-Evert
2013-04-01
Why was the Early-medieval trade-port of Dorestad located at a relatively inland position in the Rhine delta and not at the coast, as one would expect? We combined palaeogeographical, environmental-archaeological, geomorphological/geological and laser-altimetry data to propose an answer to this question. Local Dorestad data had to be combined with a regional paleogeographical reconstruction of active river branches in the 9th-century Rhine delta to come to a satisfactory answer. The location of Dorestad on a high natural levee along a relatively stable navigable branch of the Rhine in the central Rhine delta was perfect for trade. The high levee gave protection from the annual river floods. Although this branch of the Rhine was fairly stable in the heydays of Dorestad, the meanders near Dorestad slowly migrated. Excavations at Dorestad show that the harbour works of Dorestad were constantly adapted to this migration, thereby following the meander on which they were located. Ships could reach the port from the sea through at least three navigable Rhine branches: the Lek, the Old Rhine and the Vecht rivers. Dorestad was thus easily accessible and yet far enough from the coast to be safe from storm floods - but was it located at its specific location for these reasons alone? We combined existing geomorphological and geological maps with recent nation-wide laser-altimetry (AHN, General Elevation model of the Netherlands') for a regional palaeogeographical reconstruction of 9th-century active Rhine branches in a GIS. This reconstruction revealed that river connections with the Flemish, French and German hinterland were perfect. Other delta branches ensured safe connections to the Zeeland delta and the open Flemish coast, all the way to Dover Straight to the south and to the open Frisian coast all the way to present Southern Denmark in the North. The dangerously closed coast of Holland without any safe shelter places for storms could thus be avoided by ships coming in
What Your 9th, 10th, and 11th Grader Should Know about Reading, Writing, and Math [and] Science.
ERIC Educational Resources Information Center
Colorado State Dept. of Education, Denver.
Three guides provide sample problems like the ones students would solve on the Colorado Student Assessment Program tests. For each question, the pertinent Colorado state standard is identified. The ninth grade guide contains questions in reading, writing and mathematics; the guide to the 10th grade examination also contains questions related to…
Graded geometry and Poisson reduction
Cattaneo, A. S.; Zambon, M.
2009-02-02
The main result extends the Marsden-Ratiu reduction theorem in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof for the main result.
Computer algebra and operators
NASA Technical Reports Server (NTRS)
Fateman, Richard; Grossman, Robert
1989-01-01
The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.
Peters, Cole; Nigim, Fares; Chiocca, E Antonio; Rabkin, Samuel D
2016-01-01
Boston, Massachusetts, was the site of the 9th International Conference on Oncolytic Virus Therapeutics held 13–16 June 2015. An overarching theme of the meeting was the continued development of combinatorial treatment regimens to bolster the therapeutic potential of oncolytic viruses (OVs). Several talks focused on combining OVs with immune checkpoint inhibitors in a wide array of tumors, signaling an experimental and thematic shift toward driving immune activation to clear a tumor versus relying on direct viral oncolysis. An important aspect of the meeting was the variety of ongoing OV clinical trials. Topics ranged from basic virology to clinical trials and from academic research to intellectual property and biotechnology. There was much excitement due to the US Food and Drug Administration’s recent consideration of talimogene laherparepvec (T-VEC) for the treatment of advanced melanoma (T-VEC was approved in October, following the conference). Here, we summarize the meeting’s primary themes, which reflect the current state of the field.
Krestin, G P; Grenier, P A; Hricak, H; Jackson, V P; Khong, P L; Miller, J C; Muellner, A; Schwaiger, M; Thrall, J H
2012-11-01
The International Society for Strategic Studies in Radiology held its 9th biennial meeting in August 2011. The focus of the programme was integrated diagnostics and massive computing. Participants discussed the opportunities, challenges, and consequences for the discipline of radiology that will likely arise from the integration of diagnostic technologies. Diagnostic technologies are increasing in scope, including advanced imaging techniques, new molecular imaging agents, and sophisticated point-of-use devices. Advanced information technology (IT), which is increasingly influencing the practice of medicine, will aid clinical communication and the development of "population images" that represent the phenotype of particular diseases, which will aid the development of diagnostic algorithms. Integrated diagnostics offer increased operational efficiency and benefits to patients through quicker and more accurate diagnoses. As physicians with the most expertise in IT, radiologists are well placed to take the lead in introducing IT solutions and cloud computing to promote integrated diagnostics. To achieve this, radiologists must adapt to include quantitative data on biomarkers in their reports. Radiologists must also increase their role as participating physicians, collaborating with other medical specialties, not only to avoid being sidelined by other specialties but also to better prepare as leaders in the selection and sequence of diagnostic procedures. Key Points • New diagnostic technologies are yielding unprecedented amounts of diagnostic information.• Advanced IT/cloud computing will aid integration and analysis of diagnostic data.• Better diagnostic algorithms will lead to faster diagnosis and more rapid treatment. PMID:22699871
Herold, Hajnalka
2012-01-01
THE STRUCTURE, FUNCTION(S) and symbolism of early medieval (9th–10th centuries ad) fortified settlements from central Europe, in particular today’s Austria, Hungary, Czech Republic and Slovakia, are examined in this paper. It offers an overview of the current state of research together with new insights based on analysis of the site of Gars-Thunau in Lower Austria. Special emphasis is given to the position of the fortified sites in the landscape, to the elements of the built environment and their spatial organisation, as well as to graves within the fortified area. The region under study was situated on the SE border of the Carolingian (and later the Ottonian) Empire, with some of the discussed sites lying in the territory of the ‘Great Moravian Empire’ in the 9th and 10th centuries. These sites can therefore provide important comparative data for researchers working in other parts of the Carolingian Empire and neighbouring regions. PMID:23564981
Post-seismic deformation of the Mw 6.4 Shonbeh earthquake (south western Iran) of April 9th, 2013
NASA Astrophysics Data System (ADS)
Fathian Baneh, Aram; Tolomei, Cristiano; Lugari, Alessandro; Trasatti, Elisa; Salvi, Stefano
2016-04-01
The study of post-seismic deformation within a region is of high significance to have a better understanding of the kinematic behavior of a seismogenic fault. We perform the Small Baseline Subset (SBAS) method to process a large number of X-Band, COSMO-SkyMed images to measure the post-seismic deformation due to the Shonbeh earthquake (Iran) of 9th April 2013 (Mw 6.4). The meizoseismal zone of the earthquake and following aftershocks' epicenters cover an area in the frontal edge of the Zagros Simply Folded Zone, in the southwest of Iran, between Kaki and Kangan anticlines. Exploiting the available dataset of images from the beginning of 2013 to mid 2014, we observe the concentration of the deformation along at least two NW- striking, southwest-dipping fault segments arranged in right-step pattern and parallel to the trend of the folds. The preliminary InSAR results illustrate the migration of the post-seismic deformation and stress relaxation from the southeastern toward the northwestern fault segments.
NASA Astrophysics Data System (ADS)
Holzapfel, Bernhard; Schultz, Ludwig; Schlörb, Heike
2010-03-01
During the 9th European Conference on Applied Superconductivity, 6 plenary, 22 invited, 206 oral and 429 poster contributions were presented on recent developments in the field of applied superconductivity. This issue of Superconductor Science and Technology contains plenary, invited and a selection of contributed oral papers of the four main EUCAS areas: materials, wires and tapes, large scale applications and electronics. The remaining contributed papers that were selected for the conference proceedings will be published in the Journal of Physics: Conference Series. The Dresden EUCAS conference, with 712 participants from 43 countries, continued the tradition of preceding EUCAS conferences of combining basic superconductivity research contributions with the discussion of recent material advances and new developments in large scale and electronic applications. In Dresden, contributions on the recently discovered Fe-based superconductors were presented for the first time during a EUCAS conference and their potential for applications was intensively discussed. Among all the high level papers of this issue we particularly want to highlight the plenary contribution of Praveen Chaudhari on grain boundaries in cuprate superconductors. In his paper Praveen discusses the Jc limitation in HTSC tapes and tunnelling spectroscopy in LSCO thin film bicrystals. Just a few weeks ago we received the sad news that Praveen had passed away on 13 January 2010. Already fighting with his serious illness, Praveen spent all his efforts last fall finishing his plenary talk and paper. This paper will remind us always of his contributions to basic and applied aspects of superconductivity in general and especially his important work on HTSC grain boundaries. Finally we want to acknowledge the help of the International Advisory and National Committees in setting up the scientific program and we would especially like to express our gratitude to all the members of the Local Organization
Race and Teacher Evaluations as Predictors of Algebra Placement
ERIC Educational Resources Information Center
Faulkner, Valerie N.; Stiff, Lee V.; Marshall, Patricia L.; Nietfeld, John; Crossland, Cathy L.
2014-01-01
This study is a longitudinal look at the different mathematics placement profiles of Black students and White students from late elementary school through 8th grade. Results revealed that Black students had reduced odds of being placed in algebra by the time they entered 8th grade even after controlling for performance in mathematics. An important…
NASA Astrophysics Data System (ADS)
Schultz, Ludwig; Holzapfel, Bernhard
2010-04-01
During the 9th European Conference on Applied Superconductivity 6 plenary, 22 invited, 206 oral and 429 poster contributions were presented on recent developments in the field of applied superconductivity. This issue of Journal of Physics: Conference Series contains all contributed papers that were accepted for the Conference Proceedings. The Dresden EUCAS conference with 712 participants from 43 countries continued the tradition of preceding EUCAS conferences of combining basic superconductivity research contributions with the discussion of recent material advances and new developments in large scale and electronic applications. In Dresden, contributions on the recently discovered Fe based superconductors were presented for the first time during a EUCAS conference and their potential for applications was intensively discussed. Finally we want to acknowledge the help of the International Advisory and National Committees in setting up the scientific program and especially we would like to express our gratitude to all members of the Local Organization Committee. Their enthusiastic and well organized work made this Dresden EUCAS conference a memorable event for all participants. Last but not least we are very grateful to W. Goldacker , S. Haindl, J. Hänisch, R. Hühne, M. Noe, P. Seidel and M. Siegel for their extraordinary help during the proceedings review process. Bernhard Holzapfel Ludwig Schultz Conference Chairmen The IW-SMI 2010 Organizing Committee: Masato Okada (University of Tokyo) Yoshiyuki Kabashima, General Chair (Tokyo Institute of Technology) Shin Ishii (Kyoto University) Jun-ichi Inoue, Publications Chair (Hokkaido University) Kazuyuki Tanaka (Tohoku University) Toshiyuki Tanaka, Vice-General Chair (Kyoto University)
A Richer Understanding of Algebra
ERIC Educational Resources Information Center
Foy, Michelle
2008-01-01
Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…
Connecting Algebra and Chemistry.
ERIC Educational Resources Information Center
O'Connor, Sean
2003-01-01
Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)
ERIC Educational Resources Information Center
Chang, Yu-Liang; Huang, Yu-I
2014-01-01
The intention of this study was to improve the learning deficiency in algebraic learning and to enhance Taiwanese middle students' learning achievement and interest in algebra. By using a grade skipping experimental design, the research team intended to find out an effective way to benefit these students' leaning in abstract algebraic concepts.…
ERIC Educational Resources Information Center
Mikow, Victoria A.
A survey of 2,439 high school students (the 1993 Youth Risk Behavior Survey) in North Carolina found that students present a mixed picture of healthy and risky physical, nutritional, and weight management practices. The survey examined perception of body weight; weight control by gender; method of weight control; consumption of fruit or fruit…
ERIC Educational Resources Information Center
Parra, Gilbert R.; Jobe-Shields, Lisa; Kitzmann, Katherine M.; Luebbe, Aaron M.; Olsen, James P.; Davis, Genevieve L.
2011-01-01
The purpose of the present study was to examine whether adolescent perceptions of mothers' and fathers' contributions to interparental discord changed from early to middle adolescence and if the changes were related to adolescent negative mood. Data were drawn from the National Longitudinal Survey of Youth 1997. Adolescents who were in 7th grade…
ERIC Educational Resources Information Center
Quarles, Donald
2011-01-01
As schools try to meet state and federal requirements of No Child Left Behind, student academic achievement becomes a crucial part of that standard. However, schools are faced with challenges that may hinder overall student success. Some secondary schools are struggling with student tardiness and absenteeism. Tardies and absenteeism have an impact…
ERIC Educational Resources Information Center
George, Gail, Ed.
These resource materials are a part of a larger plan for groundwater education, as detailed in the Iowa Groundwater Education Strategy. The six units are arranged in priority order. The first unit covers the basics of groundwater and hydrogeology in Iowa. The other five units cover Iowa's groundwater issues in priority order, as outlined in the…
NASA Astrophysics Data System (ADS)
Dias, N. A.; Matias, L.; Tellez, J.; Senos, L.; Gaspar, J. L.
2003-04-01
The Azores Islands, located at a tectonic triple Junction, geodynamically are a highly active place. The seismicity in this region occurs mainly in the form of two types of seismic swarms with tectonic and/or volcanic origins, lasting from hours to years. In some cases the swarm follows a main stronger shock, while in others the more energetic event occurs sometime after the beginning of the swarm. In order to understand the complex phenomena of this region, a multidisciplinary approach is needed, involving geophysical, geological and geochemical studies such as the one being carried under the MASHA project (POCTI/CTA/39158/2001), On July 9th 1998 an Mw=6.2 earthquake stroked the island of Faial, in the central group of the Azores archipelago, followed by a seismic swarm still active today. We will present some preliminary results of the shear-wave polarization analysis of a selected dataset of events of this swarm. These correspond to the 112 best- constrained events, record during the first 2 weeks by the seismic network deployed on the 3 islands surrounding the area of the main shock. The objective was to analyse the behaviour of the S wave polarization and the eventual relationship with the presence of seismic anisotropy under the seismic stations, and to correlate this with the regional structure and origin of the Azores plateau. Two main tectonic features are observable on the islands, one primarily orientated SE-NW and the other crossing it roughly with the WNW-ESE direction. The polarization direction observed in the majority of the seismic stations is not stable, varying from SE-NW to WSW-ENE, and showing also the presence in same cases of shear-wave splitting, indicating the presence of anisotropy. Part of the polarization seems to be coherent with the direction of the local tectonic features, but its instability suggest a more complex seismic anisotropy than that proposed by the model EDA of Crampin. Furthermore, the dataset revealed some limitations to
NASA Astrophysics Data System (ADS)
Khalili, N.; Valliappan, S.; Li, Q.; Russell, A.
2010-07-01
The use for mathematical models of natural phenomena has underpinned science and engineering for centuries, but until the advent of modern computers and computational methods, the full utility of most of these models remained outside the reach of the engineering communities. Since World War II, advances in computational methods have transformed the way engineering and science is undertaken throughout the world. Today, theories of mechanics of solids and fluids, electromagnetism, heat transfer, plasma physics, and other scientific disciplines are implemented through computational methods in engineering analysis, design, manufacturing, and in studying broad classes of physical phenomena. The discipline concerned with the application of computational methods is now a key area of research, education, and application throughout the world. In the early 1980's, the International Association for Computational Mechanics (IACM) was founded to promote activities related to computational mechanics and has made impressive progress. The most important scientific event of IACM is the World Congress on Computational Mechanics. The first was held in Austin (USA) in 1986 and then in Stuttgart (Germany) in 1990, Chiba (Japan) in 1994, Buenos Aires (Argentina) in 1998, Vienna (Austria) in 2002, Beijing (China) in 2004, Los Angeles (USA) in 2006 and Venice, Italy; in 2008. The 9th World Congress on Computational Mechanics is held in conjunction with the 4th Asian Pacific Congress on Computational Mechanics under the auspices of Australian Association for Computational Mechanics (AACM), Asian Pacific Association for Computational Mechanics (APACM) and International Association for Computational Mechanics (IACM). The 1st Asian Pacific Congress was in Sydney (Australia) in 2001, then in Beijing (China) in 2004 and Kyoto (Japan) in 2007. The WCCM/APCOM 2010 publications consist of a printed book of abstracts given to delegates, along with 247 full length peer reviewed papers published with
Social Studies: Grade 9: Asian and African Culture Studies.
ERIC Educational Resources Information Center
New York State Education Dept., Albany. Bureau of Secondary Curriculum Development.
A framework of non-western culture, specifically Asia and Africa, is provided in this 9th grade teaching guide. It is hoped that students will understand the heritage, situations, and problems of those emerging nations. Cross-cultural comparisons help students identify likenesses, differences, and effects of internal and external events on a…
Coinvariant algebras and fake degrees for spin Weyl groups of classical type
NASA Astrophysics Data System (ADS)
Baltera, Constance; Wang, Weiqiang
2014-01-01
The coinvariant algebra of a Weyl group plays a fundamental role in several areas of mathematics. The fake degrees are the graded multiplicities of the irreducible modules of a Weyl group in its coinvariant algebra, and they were computed by Steinberg, Lusztig and Beynon-Lusztig. In this paper we formulate a notion of spin coinvariant algebra for every Weyl group. Then we compute all the spin fake degrees for each classical Weyl group, which are by definition the graded multiplicities of the simple modules of a spin Weyl group in the spin coinvariant algebra. The spin fake degrees for the exceptional Weyl groups are given in a sequel.
ERIC Educational Resources Information Center
Merlin, Ethan M.
2013-01-01
This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…
NASA Technical Reports Server (NTRS)
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
NASA Astrophysics Data System (ADS)
Tomitori, Masahiko; Onishi, Hiroshi
2007-02-01
The advent of scanning probe microscopy (SPM) in the 1980s has significantly promoted nanoscience and nanotechnology. In particular, non-contact atomic force microscopy (NC-AFM), one of the SPM family, has unique capabilities with high spatial resolution for nanoscale measurements in vacuum, air and liquids. In the last decade we have witnessed the rapid progress of NC-AFM with improved performance and increasing applications. A series of NC-AFM international conferences have greatly contributed to this field. Initiated in Osaka in 1998, the NC-AFM meeting has been followed by annual conferences at Pontresina, Hamburg, Kyoto, Montreal, Dingle, Seattle and Bad Essen. The 9th conference was held in Kobe, Japan, 16-20 July 2006. This special issue of Nanotechnology contains the outstanding contributions of the conference. During the meeting delegates learnt about a number of significant advances. Topics covered atomic resolution imaging of metals, semiconductors, insulators, ionic crystals, oxides, molecular systems, imaging of biological materials in various environments and novel instrumentation. Work also included the characterization of electronic and magnetic properties, tip and cantilever fabrication and characterization, atomic distinction based on analysis of tip-sample interaction, atomic scale manipulation, fabrication of nanostructures using NC-AFM, and related theories and simulations. We are greatly impressed by the increasing number of applications, and convinced that NC-AFM and related techniques are building a bridge to a future nano world, where quantum phenomena will dominate and nano devices will be realized. In addition, a special session on SPM road maps was held as a first trial in the field, where the future prospects of SPM were discussed enthusiastically. The overall success of the NC-AFM 2006 conference was due to the efforts of many individuals and groups with respect to scientific and technological progress, as well as the international
Semigroups and computer algebra in algebraic structures
NASA Astrophysics Data System (ADS)
Bijev, G.
2012-11-01
Some concepts in semigroup theory can be interpreted in several algebraic structures. A generalization fA,B,fA,B(X) = A(X')B of the complement operator (') on Boolean matrices is made, where A and B denote any rectangular Boolean matrices. While (') is an isomorphism between Boolean semilattices, the generalized complement operator is homomorphism in the general case. The map fA,B and its general inverse (fA,B)+ have quite similar properties to those in the linear algebra and are useful for solving linear equations in Boolean matrix algebras. For binary relations on a finite set, necessary and sufficient conditions for the equation αξβ = γ to have a solution ξ are proved. A generalization of Green's equivalence relations in semigroups for rectangular matrices is proposed. Relationships between them and the Moore-Penrose inverses are investigated. It is shown how any generalized Green's H-class could be constructed by given its corresponding linear subspaces and converted into a group isomorphic to a linear group. Some information about using computer algebra methods concerning this paper is given.
ERIC Educational Resources Information Center
Powell, Sarah R.; Fuchs, Lynn S.
2014-01-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…
Lie algebra extensions of current algebras on S3
NASA Astrophysics Data System (ADS)
Kori, Tosiaki; Imai, Yuto
2015-06-01
An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
The relationship between adolescent academic capability beliefs, parenting and school grades.
Juang, Linda P; Silbereisen, Rainer K
2002-02-01
The purpose of this study was to examine the interplay between parenting, adolescent academic capability beliefs and school grades. First, we examined how aspects of parenting and adolescent's cognitive ability predicted adolescent academic capability beliefs and school grades at 6th grade, which, in turn, predicted adolescent school outcomes at 9th grade. Second, we examined how configurations of adolescents (based on cognitive ability, parental involvement, and capability beliefs) at 6th grade, related to their school grades at 9th grade. The sample included 641 German adolescents. The first set of analyses suggest that parents who demonstrated more warmth, engaged in more discussions concerning academic and intellectual matters with their adolescents, had higher school aspirations for their adolescents, and reported more interest/involvement in their adolescent's schooling, had adolescents with higher capability beliefs at 6th grade, and this, in turn, related to better school grades for adolescents at 9th grade. In the second set of analyses, results show that adolescents who were characterized by the configuration of having above average ability, parental school involvement and capability beliefs, received the best school grades. In contrast, adolescents who were characterized by below average ability, parental school involvement and capability beliefs, demonstrated the worst school performance. PMID:12009746
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
Algebraic integrability: a survey.
Vanhaecke, Pol
2008-03-28
We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863
Algebraic Semantics for Narrative
ERIC Educational Resources Information Center
Kahn, E.
1974-01-01
This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)
Aprepro - Algebraic Preprocessor
2005-08-01
Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Covariant deformed oscillator algebras
NASA Technical Reports Server (NTRS)
Quesne, Christiane
1995-01-01
The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.
NASA Astrophysics Data System (ADS)
Hiley, B. J.
In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.
Application of Algebra Curriculum-Based Measurements for Decision Making in Middle and High School
ERIC Educational Resources Information Center
Johnson, Evelyn S.; Galow, Patricia A.; Allenger, Robert
2013-01-01
This article reports the results of a study examining the utility of curriculum-based measurement (CBM) in algebra for predicting performance on a state math assessment and informing instructional placement decisions for students in seventh, eighth, and tenth grades. Students completed six Basic Skills algebra probes across different time…
Primary School Students' Strategies in Early Algebra Problem Solving Supported by an Online Game
ERIC Educational Resources Information Center
van den Heuvel-Panhuizen, Marja; Kolovou, Angeliki; Robitzsch, Alexander
2013-01-01
In this study we investigated the role of a dynamic online game on students' early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10-12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the…
ERIC Educational Resources Information Center
Checkley, Kathy
2001-01-01
Robert P. Moses, teacher and Civil Rights activist, discusses contributions of his Algebra Project for predominantly minority youngsters in Cambridge, Massachusetts. Taking and passing algebra in the eighth grade qualifies students for high-school honors math courses and improves their chances to enter college. Transforming neighborhood schools is…
A Schematic-Theoretic View of Problem Solving and Development of Algebraic Thinking
ERIC Educational Resources Information Center
Steele, Diana F.; Johanning, Debra I.
2004-01-01
This study explored the problem-solving schemas developed by 7th-grade pre-algebra students as they participated in a teaching experiment that was designed to help students develop effective schemas for solving algebraic problem situations involving contexts of (1) growth and change and (2) size and shape. This article describes the qualities and…
ERIC Educational Resources Information Center
Howard, Keith A.; Scott, Allison; Romero, Martin; Saddler, Derrick
2015-01-01
In this article, the authors use the High School Longitudinal Study 2009 (HSLS:09) national database to analyze the relationships between algebra failure, subsequent performance, motivation, and college readiness. Students who failed eighth-grade Algebra I did not differ significantly in mathematics proficiency from those who passed lower-level…
ERIC Educational Resources Information Center
Clotfelter, Charles T.; Ladd, Helen F.; Vigdor, Jacob L.
2012-01-01
In 2002/03, the Charlotte-Mecklenburg Schools in North Carolina initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking algebra in 8th grade increased from half to 85%, then reverted to baseline levels, in the span of just five years. We use this policy-induced variation to…
Enhancing Engagement in Algebra: Didactical Strategies Implemented and Discussed by Teachers
ERIC Educational Resources Information Center
Nyman, Rimma; Kilhamn, Cecilia
2015-01-01
The aim of this study is to investigate student engagement from the point of view of the teacher, by focusing on teacher's didactical strategies used to engage students during algebra introduction. Eight teachers in grade 6 and 7 participated in a focus-group interview study. The findings are based on episodes of student engagement in algebra and…
Spontaneous Meta-Arithmetic as the First Step toward School Algebra
ERIC Educational Resources Information Center
Caspi, Shai; Sfard, Anna
2012-01-01
Taking as a point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following six pairs of 7th-grade students (12-13 years old) as they gradually modify their spontaneous meta-arithmetic toward the "official" algebraic form of talk. In this paper we take a look at the very beginning of…
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY.
This curriculum bulletin is designed to help teachers meet the diverse needs in mathematics of the children in fifth grade classes. In addition to the emphasis that is placed on arithmetic computational skills, the bulletin shows how to include other areas considered important, such as concepts, skills, and ideas from algebra and geometry. The 80…
ERIC Educational Resources Information Center
Jamison, Sandra; Campbell, Bruce
The ninth grade unit of the FICSS series (Focus on Inner City Social Studies -- see SO 008 271) studies the economic and political realities of the inner city. This document, the first unit of the 9th grade section, deals with the ecological crises involving pollution and its causes. Specific problems include air pollution, pesticides, herbicides,…
Hayes, Roger; LeLacheur, Richard; Dumont, Isabelle; Couerbe, Philippe; Safavi, Afshin; Islam, Rafiq; Pattison, Colin; Cape, Stephanie; Rocci, Mario; Briscoe, Chad; Cojocaru, Laura; Groeber, Elizabeth; Silvestro, Luigi; Bravo, Jennifer; Shoup, Ron; Verville, Manon; Zimmer, Jennifer; Caturla, Maria Cruz; Khadang, Ardeshir; Bourdage, James; Hughes, Nicola; Fatmi, Saadya; Di Donato, Lorella; Sheldon, Curtis; Keyhani, Anahita; Satterwhite, Christina; Yu, Mathilde; Fiscella, Michele; Hulse, James; Lin, Zhongping John; Garofolo, Wei; Savoie, Natasha; Xiao, Yi Qun; Kurylak, Kai; Harris, Sarah; Saxena, Manju; Buonarati, Mike; Lévesque, Ann; Boudreau, Nadine; Lin, Jenny; Khan, Masood U; Ray, Gene; Liu, Yansheng; Xu, Allan; Soni, Gunjan; Ward, Ian; Kingsley, Clare; Ritzén, Hanna; Tabler, Edward; Nicholson, Bob; Bennett, Patrick; van de Merbel, Nico; Karnik, Shane; Bouhajib, Mohammed; Wieling, Jaap; Mulvana, Daniel; Ingelse, Benno; Allen, Mike; Malone, Michele; Fang, Xinping
2016-03-01
The 9th GCCClosed Forum was held just prior to the 2015 Workshop on Recent Issues in Bioanalysis (WRIB) in Miami, FL, USA on 13 April 2015. In attendance were 58 senior-level participants, from eight countries, representing 38 CRO companies offering bioanalytical services. The objective of this meeting was for CRO bioanalytical representatives to meet and discuss scientific and regulatory issues specific to bioanalysis. The issues selected at this year's closed forum include CAPA, biosimilars, preclinical method validation, endogenous biomarkers, whole blood stability, and ELNs. A summary of the industry's best practices and the conclusions from the discussion of these topics is included in this meeting report. PMID:26916197
ERIC Educational Resources Information Center
Hong, Guanglei; Nomi, Takako
2011-01-01
A recent report by the Mathematics Advisory Panel referred to algebra as a "gateway" to later achievement (National Mathematics Advisory Panel, 2008). To address the problem of low academic performance in algebra, an increasing number of states and districts have started to implement a policy of requiring algebra for all students in ninth-grade or…
Zeta functional equation on Jordan algebras of type II
NASA Astrophysics Data System (ADS)
Kayoya, J. B.
2005-02-01
Using the Jordan algebras methods, specially the properties of Peirce decomposition and the Frobenius transformation, we compute the coefficients of the zeta functional equation, in the case of Jordan algebras of type II. As particular cases of our result, we can cite the case of studied by Gelbart [Mem. Amer. Math. Soc. 108 (1971)] and Godement and Jacquet [Zeta functions of simple algebras, Lecture Notes in Math., vol. 260, Springer-Verlag, Berlin, 1972], and the case of studied by Muro [Adv. Stud. Pure Math. 15 (1989) 429]. Let us also mention, that recently, Bopp and Rubenthaler have obtained a more general result on the zeta functional equation by using methods based on the algebraic properties of regular graded algebras which are in one-to-one correspondence with simple Jordan algebras [Local Zeta Functions Attached to the Minimal Spherical Series for a Class of Symmetric Spaces, IRMA, Strasbourg, 2003]. The method used in this paper is a direct application of specific properties of Jordan algebras of type II.
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
Using Cognitive Tutor Software in Learning Linear Algebra Word Concept
ERIC Educational Resources Information Center
Yang, Kai-Ju
2015-01-01
This paper reports on a study of twelve 10th grade students using Cognitive Tutor, a math software program, to learn linear algebra word concept. The study's purpose was to examine whether students' mathematics performance as it is related to using Cognitive Tutor provided evidence to support Koedlinger's (2002) four instructional principles used…
Getting from Arithmetic to Algebra: Balanced Assessments for the Transition
ERIC Educational Resources Information Center
Schwartz, Judah L.; Kenney, Joan M.
2012-01-01
In this innovative book, two experienced educators present a fresh and engaging approach to mathematics learning in the middle grades with the transition from arithmetic to algebra. The authors provide a collection of balanced, multi-dimensional assessment tasks designed to evaluate students' ability to work with mathematical objects and perform…
Algebra 33: Introduction through Unit V-B.
ERIC Educational Resources Information Center
Nederland Independent School District, TX.
GRADES OR AGES: No mention. SUBJECT MATTER: Algebra. ORGANIZATION AND PHYSICAL APPEARANCE: The guide is divided into seven separately bound units. Unit headings are introduction, sets of numbers and axioms, open sentences in one variable, systems of linear open sentences, polynomials and factoring, rational numbers and expressions (A), and…
Geometric and Algebraic Approaches in the Concept of Complex Numbers
ERIC Educational Resources Information Center
Panaoura, A.; Elia, I.; Gagatsis, A.; Giatilis, G.-P.
2006-01-01
This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…
Early Algebra to Reach the Range of Learners
ERIC Educational Resources Information Center
Schifter, Deborah; Russell, Susan Jo; Bastable, Virginia
2009-01-01
Since 2001, the authors have been working with groups of teachers to investigate students' early algebraic thinking--learning representations, connections, and generalizations in the elementary school grades. They began paying attention to students' explicit remarks about regularities in the number system or what students imply by their…
Studies in Mathematics, Volume VIII. Concepts of Algebra. Preliminary Edition.
ERIC Educational Resources Information Center
Clarkson, Donald R., Ed.; And Others
This volume is designed to provide information for teachers and prospective teachers who will teach the basic concepts of algebra normally taught in grade 9. Each section of the book contains background information, suggestions for instruction, and problems. Sections in the book include: (1) Numerals and Variables; (2) Open Sentences and English…
The Algebra Solution to Mathematics Reform: Completing the Equation
ERIC Educational Resources Information Center
Spielhagen, Frances R.
2011-01-01
How can we increase mathematics achievement among all students? This book provides a straightforward explanation of how changing mathematics tracking policies to provide algebra instruction to all students by at least eighth grade can bring about changes in both student achievement and teacher performance. Spielhagen chronicles the success of a…
Computer Algebra System Calculators: Gender Issues and Teachers' Expectations
ERIC Educational Resources Information Center
Forgasz, Helen J.; Griffith, Shirly
2006-01-01
In this paper we present findings from two studies focusing on computer algebra system (CAS) calculators. In Victoria, Australia, it is currently mandatory for students to use graphics calculators in some grade 12 mathematics examinations. Since 2001, a pilot study has been conducted involving Victorian Certificate of Education (VCE) students…
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Computer Program For Linear Algebra
NASA Technical Reports Server (NTRS)
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
NASA Technical Reports Server (NTRS)
Shahshahani, M.
1991-01-01
The performance characteristics are discussed of certain algebraic geometric codes. Algebraic geometric codes have good minimum distance properties. On many channels they outperform other comparable block codes; therefore, one would expect them eventually to replace some of the block codes used in communications systems. It is suggested that it is unlikely that they will become useful substitutes for the Reed-Solomon codes used by the Deep Space Network in the near future. However, they may be applicable to systems where the signal to noise ratio is sufficiently high so that block codes would be more suitable than convolutional or concatenated codes.
NASA Astrophysics Data System (ADS)
Bouwknegt, Peter
1988-06-01
We investigate extensions of the Virasoro algebra by a single primary field of integer or halfinteger conformal dimension Δ. We argue that for vanishing structure constant CΔΔΔ, the extended conformal algebra can only be associative for a generic c-value if Δ=1/2, 1, 3/2, 2 or 3. For the other Δ<=5 we compute the finite set of allowed c-values and identify the rational solutions. The case CΔΔΔ≠0 is also briefly discussed. I would like to thank Kareljan Schoutens for discussions and Sander Bais for a careful reading of the manuscript.
Assessing Elementary Algebra with STACK
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2007-01-01
This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…
Spinors in the hyperbolic algebra
NASA Astrophysics Data System (ADS)
Ulrych, S.
2006-01-01
The three-dimensional universal complex Clifford algebra Cbar3,0 is used to represent relativistic vectors in terms of paravectors. In analogy to the Hestenes spacetime approach spinors are introduced in an algebraic form. This removes the dependance on an explicit matrix representation of the algebra.
ERIC Educational Resources Information Center
Glick, David
1995-01-01
Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)
ERIC Educational Resources Information Center
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott
2007-01-01
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
Computer Algebra versus Manipulation
ERIC Educational Resources Information Center
Zand, Hossein; Crowe, David
2004-01-01
In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…
ERIC Educational Resources Information Center
Boiteau, Denise; Stansfield, David
This document describes mathematical programs on the basic concepts of algebra produced by Louisiana Public Broadcasting. Programs included are: (1) "Inverse Operations"; (2) "The Order of Operations"; (3) "Basic Properties" (addition and multiplication of numbers and variables); (4) "The Positive and Negative Numbers"; and (5) "Using Positive…
Thinking Visually about Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
ERIC Educational Resources Information Center
Kennedy, John
This text provides information and exercises on arithmetic topics which should be mastered before a student enrolls in an Elementary Algebra course. Section I describes the fundamental properties and relationships of whole numbers, focusing on basic operations, divisibility tests, exponents, order of operations, prime numbers, greatest common…
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
NASA Astrophysics Data System (ADS)
Zhang, Ming; Yao, JingTao
2004-04-01
The XML is a new standard for data representation and exchange on the Internet. There are studies on XML query languages as well as XML algebras in literature. However, attention has not been paid to research on XML algebras for data mining due to partially the fact that there is no widely accepted definition of XML mining tasks. This paper tries to examine the XML mining tasks and provide guidelines to design XML algebras for data mining. Some summarization and comparison have been done to existing XML algebras. We argue that by adding additional operators for mining tasks, XML algebras may work well for data mining with XML documents.
2014-01-01
A one-day workshop on Burkitt lymphoma (BL) was held at the 9th African Organization for Research and Training in Cancer (AORTIC) conference in 2013 in Durban, South Africa. The workshop featured 15 plenary talks by delegates representing 13 institutions that either fund or implement research on BL targeting AORTIC delegates primarily interested in pediatric oncology. The main outcomes of the meeting were improved sharing of knowledge and experience about ongoing epidemiologic BL research, BL treatment in different settings, the role of cancer registries in cancer research, and opportunities for African scientists to publish in scientific journals. The idea of forming a consortium of BL to improve coordination, information sharing, accelerate discovery, dissemination, and translation of knowledge and to build capacity, while reducing redundant efforts was discussed. Here, we summarize the presentations and discussions from the workshop. PMID:25686906
Giersing, Birgitte K; Modjarrad, Kayvon; Kaslow, David C; Moorthy, Vasee S
2016-06-01
There are more vaccines in development, against a greater number of pathogens, than ever before. A challenge with this exceptional level of activity and investment is how to select and resource the most promising approaches to have the most significant impact on public health. The WHO Product Development for Vaccines Advisory Committee (PDVAC) was established in 2014 to provide strategic advice and recommendations to WHO for vaccines in clinical development that could have a significant impact on public health in low and middle income countries. On 7-9th September 2015, PDVAC was convened for the second time, when the committee reviewed vaccine developments in 24 disease areas. This report summarises the key recommendations from that consultation. PMID:26993336
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
Algebraic connectivity and graph robustness.
Feddema, John Todd; Byrne, Raymond Harry; Abdallah, Chaouki T.
2009-07-01
Recent papers have used Fiedler's definition of algebraic connectivity to show that network robustness, as measured by node-connectivity and edge-connectivity, can be increased by increasing the algebraic connectivity of the network. By the definition of algebraic connectivity, the second smallest eigenvalue of the graph Laplacian is a lower bound on the node-connectivity. In this paper we show that for circular random lattice graphs and mesh graphs algebraic connectivity is a conservative lower bound, and that increases in algebraic connectivity actually correspond to a decrease in node-connectivity. This means that the networks are actually less robust with respect to node-connectivity as the algebraic connectivity increases. However, an increase in algebraic connectivity seems to correlate well with a decrease in the characteristic path length of these networks - which would result in quicker communication through the network. Applications of these results are then discussed for perimeter security.
Concerns About Ninth-Grade Students' Poor Academic Performance: One School's Action Plan.
ERIC Educational Resources Information Center
Fulk, Barbara M.
2003-01-01
Survey of high school teachers' and students' concerns about the academic performance of incoming 9th grade students. Finds teachers' major areas of concerns are time management, motivation, and homework. Students' greatest concerns are study habits, self-regulation, and test anxiety. Used survey results to develop strategies to improve student…
The Impact of Homework and Homework Preferences in Ninth Grade Geography
ERIC Educational Resources Information Center
Schuster, Nicholas C.
2009-01-01
This study measured the impact of homework and student homework preferences on the learning of 9th grade geography students of average and below average reading levels. Quiz averages were compared between two student groups that had alternating periods of exogenous manipulation, where one group was assigned homework while the alternate group was…
Energy Systems - Present, Future: Extra Terrestrials, Grades 7, 8, 9,/Science.
ERIC Educational Resources Information Center
National Science Teachers Association, Washington, DC.
The 12 lessons presented in this guide are structured so that they may be integrated into science lessons in 7th-, 8th-, or 9th-grades. Suggestions are made for extension of study. Lessons are approached through classroom role-playing of outer space visitors who seek to understand energy conversion principles used on Earth. Major emphasis is…
Parent Engagement in Science with Ninth Graders and with Students in Higher Grades
ERIC Educational Resources Information Center
Shumow, Lee; Schmidt, Jennifer A.
2014-01-01
By high school, parent engagement is likely to differ not only by grade, but by subject. This study surveyed students enrolled in high school science classes and found that parents of freshmen (9th graders) are more involved at home, less involved at school, and equally involved in educational planning compared to parents of high school students…
Effects of Grade Retention on Achievement and Self-Concept in Science and Mathematics
ERIC Educational Resources Information Center
Ehmke, Timo; Drechsel, Barbara; Carstensen, Claus H.
2010-01-01
The study analyzes the effects of grade repetition on science and mathematics achievement and on self-concept in mathematics using longitudinal data from a representative sample of 9th graders in Germany. Same-age comparisons were applied between three groups: (a) the retained students, (b) a matched group of promoted students, and (c) the entire…
Developmental Trajectories of Proactive and Reactive Aggression from Fifth to Ninth Grade
ERIC Educational Resources Information Center
Fite, Paula J.; Colder, Craig R.; Lochman, John E.; Wells, Karen C.
2008-01-01
This study examined the developmental trajectories of proactive and reactive aggression from 5th to 9th grade in a sample of 126 children (66% male) screened to be in the top 31% on a measure of aggression. Prospective relations between proactive and reactive aggression and delinquency were also examined. Findings suggested that levels of both…
Minimal dynamics and the classification of C*-algebras.
Toms, Andrew S; Winter, Wilhelm
2009-10-01
Let X be an infinite, compact, metrizable space of finite covering dimension and alpha: X --> X a minimal homeomorphism. We prove that the crossed product C(X) times sign, right closed(alpha) Z absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a consequence, these algebras are determined up to isomorphism by their graded ordered K-theory under the necessary condition that their projections separate traces. This result applies, in particular, to those crossed products arising from uniquely ergodic homeomorphisms. PMID:19805164
Minimal dynamics and the classification of C*-algebras
Toms, Andrew S.; Winter, Wilhelm
2009-01-01
Let X be an infinite, compact, metrizable space of finite covering dimension and α: X → X a minimal homeomorphism. We prove that the crossed product C(X) ⋊α ℤ absorbs the Jiang-Su algebra tensorially and has finite nuclear dimension. As a consequence, these algebras are determined up to isomorphism by their graded ordered K-theory under the necessary condition that their projections separate traces. This result applies, in particular, to those crossed products arising from uniquely ergodic homeomorphisms. PMID:19805164
A Flexible Variable Truncated Power Series Algebra in Zlib
Yan, Y.T.; /SLAC
2011-08-25
Zlib is a numerical library for Truncated Power Series Algebra (TPSA) and Lie Algebra for application to nonlinear analysis of single particle dynamics. The first version was developed in 1990 with the use of the One-Step Index Pointers (OSIP's). The OSIP's form the Zlib nerve that offers optimal computation and alloworder grading as well as flexible initialization of the global number of variables for the TPSA. While the OSIP's are still kept for minimum index passing to achieve efficient computation, Zlib has been being upgraded to allow flexible and gradable local number of variables in each C++ object of the Truncated Power Series (Tps) class. Possible applications using Zlib are discussed.
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
NASA Astrophysics Data System (ADS)
Dankova, T. S.; Rosensteel, G.
1998-10-01
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.
ERIC Educational Resources Information Center
Beigie, Darin
2014-01-01
Most people who are attracted to STEM-related fields are drawn not by a desire to take mathematics tests but to create things. The opportunity to create an algebra drawing gives students a sense of ownership and adventure that taps into the same sort of energy that leads a young person to get lost in reading a good book, building with Legos®,…
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.
Vertex Algebras, Kac-Moody Algebras, and the Monster
NASA Astrophysics Data System (ADS)
Borcherds, Richard E.
1986-05-01
It is known that the adjoint representation of any Kac-Moody algebra A can be identified with a subquotient of a certain Fock space representation constructed from the root lattice of A. I define a product on the whole of the Fock space that restricts to the Lie algebra product on this subquotient. This product (together with a infinite number of other products) is constructed using a generalization of vertex operators. I also construct an integral form for the universal enveloping algebra of any Kac-Moody algebra that can be used to define Kac-Moody groups over finite fields, some new irreducible integrable representations, and a sort of affinization of any Kac-Moody algebra. The ``Moonshine'' representation of the Monster constructed by Frenkel and others also has products like the ones constructed for Kac-Moody algebras, one of which extends the Griess product on the 196884-dimensional piece to the whole representation.
ERIC Educational Resources Information Center
Mack, Roy James
2011-01-01
The central purpose of this research was to assess student learning outcomes in the Algebra I credit recovery course offered at traditional schools in Louisiana and the Algebra I credit recovery course offered online by the Louisiana Virtual School (LVS). It was also conducted to assess the associations of gender, grade level, and socio-economic…
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2014-01-01
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
Palmkvist, Jakob
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
ERIC Educational Resources Information Center
Snipes, Jason; Huang, Chun-Wei; Jaquet, Karina; Finkelstein, Neal
2015-01-01
The Effects of the Elevate Math summer program on math achievement and algebra readiness: This randomized trial examined the effects of the Elevate Math summer program on math achievement and algebra readiness, as well as math interest and self-efficacy, among rising 8th grade students in California's Silicon Valley. The Elevate Math summer math…
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Locally finite dimensional Lie algebras
NASA Astrophysics Data System (ADS)
Hennig, Johanna
We prove that in a locally finite dimensional Lie algebra L, any maximal, locally solvable subalgebra is the stabilizer of a maximal, generalized flag in an integrable, faithful module over L. Then we prove two structure theorems for simple, locally finite dimensional Lie algebras over an algebraically closed field of characteristic p which give sufficient conditions for the algebras to be of the form [K(R, *), K( R, *)] / (Z(R) ∩ [ K(R, *), K(R, *)]) for a simple, locally finite dimensional associative algebra R with involution *. Lastly, we explore the noncommutative geometry of locally simple representations of the diagonal locally finite Lie algebras sl(ninfinity), o( ninfinity), and sp(n infinity).
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Verburgt, Lukas M
2016-01-01
This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s. PMID:26806075
On the cohomology of Leibniz conformal algebras
NASA Astrophysics Data System (ADS)
Zhang, Jiao
2015-04-01
We construct a new cohomology complex of Leibniz conformal algebras with coefficients in a representation instead of a module. The low-dimensional cohomology groups of this complex are computed. Meanwhile, we construct a Leibniz algebra from a Leibniz conformal algebra and prove that the category of Leibniz conformal algebras is equivalent to the category of equivalence classes of formal distribution Leibniz algebras.
Assessing Algebraic Solving Ability: A Theoretical Framework
ERIC Educational Resources Information Center
Lian, Lim Hooi; Yew, Wun Thiam
2012-01-01
Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…
ERIC Educational Resources Information Center
Linchevski, Liora; Herscovics, Nicolas
1996-01-01
Reports the results of a teaching experiment involving like terms and equations in algebra. Seventh-grade students (n=6) experienced difficulties in decomposing an additive term into a difference. (Author/MKR)
NASA Astrophysics Data System (ADS)
Sheinman, O. K.
2015-12-01
Based on ℤ-gradings of semisimple Lie algebras and invariant polynomials on them, we construct hierarchies of Lax equations with a spectral parameter on a Riemann surface and prove the commutativity of the corresponding flows.
Clifford algebras and Hestenes spinors
NASA Astrophysics Data System (ADS)
Lounesto, Pertti
1993-09-01
This article reviews Hestenes' work on the Dirac theory, where his main achievement is a real formulation of the theory within the real Clifford algebra Cl 1,3 ≃ M2 (H). Hestenes invented first in 1966 his ideal spinorsφ in Cl_{1,3 _2}^1 (1 - γ _{03} ) and later 1967/75 he recognized the importance of his operator spinors ψ ∈ Cl{/1,3 + } ≃ M2 (C). This article starts from the conventional Dirac equation as presented with matrices by Bjorken-Drell. Explicit mappings are given for a passage between Hestenes' operator spinors and Dirac's column spinors. Hestenes' operator spinors are seen to be multiples of even parts of real parts of Dirac spinors (real part in the decomposition C ⊗ Cl 1,3 and not in C ⊗ M4 (R)=M4 (C)). It will become apparent that the standard matrix formulation contains superfluous parts, which ought to be cut out by Occam's razor. Fierz identities of bilinear covariants are known to be sufficient to study the non-null case but are seen to be insufficient for the null case ψ†γ0ψ=0, ψ†γ0γ0123ψ=0. The null case is thoroughly scrutinized for the first time with a new concept called boomerang. This permits a new intrinsically geometric classification of spinors. This in turn reveals a new class of spinors which has not been discussed before. This class supplements the spinors of Dirac, Weyl, and Majorana; it describes neither the electron nor the neutron; it is awaiting a physical interpretation and a possible observation. Projection operators P±, Σ± are resettled among their new relatives in End(Cl 1,3 ). Finally, a new mapping, called tilt, is introduced to enable a transition from Cl 1,3 to the (graded) opposite algebra Cl 3,1 without resorting to complex numbers, that is, not using a replacement γμ → iγμ.
ERIC Educational Resources Information Center
Novotna, Jarmila; Hoch, Maureen
2008-01-01
Many students have difficulties with basic algebraic concepts at high school and at university. In this paper two levels of algebraic structure sense are defined: for high school algebra and for university algebra. We suggest that high school algebra structure sense components are sub-components of some university algebra structure sense…
Handheld Computer Algebra Systems in the Pre-Algebra Classroom
ERIC Educational Resources Information Center
Gantz, Linda Ann Galofaro
2010-01-01
This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…
Abstract Algebra to Secondary School Algebra: Building Bridges
ERIC Educational Resources Information Center
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
Algebra and Algebraic Thinking in School Math: 70th YB
ERIC Educational Resources Information Center
National Council of Teachers of Mathematics, 2008
2008-01-01
Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…
Philip, Bobby; Chartier, Dr Timothy
2012-01-01
methods based on Local Sensitivity Analysis (LSA). The method can be used in the context of geometric and algebraic multigrid methods for constructing smoothers, and in the context of Krylov methods for constructing block preconditioners. It is suitable for both constant and variable coecient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems that do not arise from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid and Krylov solvers while providing a powerful tool for adaptively constructing methods tuned to a problem.
Statecharts Via Process Algebra
NASA Technical Reports Server (NTRS)
Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance
1999-01-01
Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics
2013-05-06
AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less
Kaupová, Sylva; Herrscher, Estelle; Velemínský, Petr; Cabut, Sandrine; Poláček, Lumír; Brůžek, Jaroslav
2014-12-01
In the Central European context, the 9th and 10th centuries are well known for rapid cultural and societal changes concerning the development of the economic and political structures of states as well as the adoption of Christianity. A bioarchaeological study based on a subadult skeletal series was conducted to tackle the impact of these changes on infant and young child feeding practices and, consequently, their health in both urban and rural populations. Data on growth and frequency of nonspecific stress indicators of a subadult group aged 0-6 years were analyzed. A subsample of 41 individuals was selected for nitrogen and carbon isotope analyses, applying an intra-individual sampling strategy (bone vs. tooth). The isotopic results attest to a mosaic of food behaviors. In the urban sample, some children may have been weaned during their second year of life, while some others may have still been consuming breast milk substantially up to 4-5 years of age. By contrast, data from the rural sample show more homogeneity, with a gradual cessation of breastfeeding starting after the age of 2 years. Several factors are suggested which may have been responsible for applied weaning strategies. There is no evidence that observed weaning strategies affected the level of biological stress which the urban subadult population had to face compared with the rural subadult population. PMID:25256815
Sargent, Charli; Roberts, Paul; Dawson, Drew; Ferguson, Sally; Meuleners, Lynn; Brook, Libby; Roach, Gregory D
2016-01-01
The 9th International Conference on Managing Fatigue in Transportation, Resources and Health was held in Fremantle, Western Australia in March 2015. The purpose of the conferences in this series is to provide a forum for industry representatives, regulators, and scientists to discuss recent advances in the field of fatigue research. We have produced a Special Issue of the International Journal of Environmental Research and Public Health based on papers from the conference that were focused on various aspects of public health. First, the Special Issue highlights the fact that working long shifts and/or night shifts can affect not only cognitive functioning, but also physical health. In particular, three papers examined the potential relationships between shiftwork and different aspects of health, including the cardiovascular system, sleep disordered breathing, and eating behaviour. Second, the Special Issue highlights the move away from controlling fatigue through prescriptive hours of service rules and toward the application of risk management principles. In particular, three papers indicated that best-practice fatigue risk management systems should contain multiple redundant layers of defense against fatigue-related errors and accidents. PMID:27563919
Gorenec, Lana; Zidovec Lepej, Snjezana; Grgic, Ivana; Planinic, Ana; Iscic Bes, Janja; Vince, Adriana; Begovac, Josip
2016-08-01
The aim of this study was to compare cytokine expression on both gene and protein levels in acute and chronic phase of HIV type 1 (HIV-1) infection. Thirty four patients were enrolled for cytokine expression analysis on protein level in acute and chronic stage of HIV-1 infection. Using PCR array technology, expression of 84 cytokine genes was measured in 3 patients in acute and 3 patients in chronic stage of HIV-1 infection. Bead-based cytometry was used to quantify levels of Th1/Th2/Th9/Th17/Th22 cytokines. The results showed statistically significant increase of 13 cytokine gene expression (cd40lg, csf2, ifna5, il12b, il1b, il20, lta, osm, spp1, tgfa, tnfsf 11, 14 and 8) and downregulation of the il12a expression in chronic HIV type 1 infection. Concentrations of IL-10, IL-4 and TNF-α were increased in the acute HIV type 1 infection when compared to control group. During chronic HIV type 1 infection there was an increase of IL-10, TNF-α, IL-2, IL-6, IL-13 and IL-22 levels when compared to control group. Comparison of cytokine expression between two stages of infection showed a significant decrease in IL-9 concentration. This study showed changes in cytokine profiles on both gene and protein levels in different stages of HIV-infection. PMID:27268396
NASA Astrophysics Data System (ADS)
Isaac, Phillip S.; Marquette, Ian
2016-03-01
We generalize the construction of integrals of motion for quantum superintegrable models and the deformed oscillator algebra approach. This is presented in the context of 1D systems admitting ladder operators satisfying a parabosonic algebra involving reflection operators and more generally {c}λ extended oscillator algebras with grading. We apply the construction on two-dimensional {c}λ oscillators. We also introduce two new superintegrable Hamiltonians that are the anisotropic Dunkl and the singular Dunkl oscillators. Integrals are constructed by extending the approach of Daskaloyannis to include grading. An algebraic derivation of the energy spectra of the two models is presented, making use of finite dimensional unitary representations. We show how the spectra divide into sectors, and make comparisons with the physical case.
Deformations of Poisson brackets and extensions of Lie algebras of contact vector fields
NASA Astrophysics Data System (ADS)
Ovsienko, V.; Roger, C.
1992-12-01
CONTENTSIntroduction § 1. Main theoremsChapter I. Algebra § 2. Moyal deformations of the Poisson bracket and *-product on \\mathbb R^{2n} § 3. Algebraic construction § 4. Central extensions § 5. ExamplesChapter II. Deformations of the Poisson bracket and *-product on an arbitrary symplectic manifold § 6. Formal deformations: definitions § 7. Graded Lie algebras as a means of describing deformations § 8. Cohomology computations and their consequences § 9. Existence of a *-productChapter III. Extensions of the Lie algebra of contact vector fields on an arbitrary contact manifold §10. Lagrange bracket §11. Extensions and modules of tensor fieldsAppendix 1. Extensions of the Lie algebra of differential operatorsAppendix 2. Examples of equations of Korteweg-de Vries typeReferences
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Algebraic Squares: Complete and Incomplete.
ERIC Educational Resources Information Center
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
ERIC Educational Resources Information Center
Buerman, Margaret
2007-01-01
Finding real-world examples for middle school algebra classes can be difficult but not impossible. As we strive to accomplish teaching our students how to solve and graph equations, we neglect to teach the big ideas of algebra. One of those big ideas is functions. This article gives three examples of functions that are found in Arches National…
Online Algebraic Tools for Teaching
ERIC Educational Resources Information Center
Kurz, Terri L.
2011-01-01
Many free online tools exist to complement algebraic instruction at the middle school level. This article presents findings that analyzed the features of algebraic tools to support learning. The findings can help teachers select appropriate tools to facilitate specific topics. (Contains 1 table and 4 figures.)
Condensing Algebra for Technical Mathematics.
ERIC Educational Resources Information Center
Greenfield, Donald R.
Twenty Algebra-Packets (A-PAKS) were developed by the investigator for technical education students at the community college level. Each packet contained a statement of rationale, learning objectives, performance activities, performance test, and performance test answer key. The A-PAKS condensed the usual sixteen weeks of algebra into a six-week…
Algebraic Thinking in Adult Education
ERIC Educational Resources Information Center
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
Linear Algebra and Image Processing
ERIC Educational Resources Information Center
Allali, Mohamed
2010-01-01
We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)
Exploring Algebraic Patterns through Literature.
ERIC Educational Resources Information Center
Austin, Richard A.; Thompson, Denisse R.
1997-01-01
Presents methods for using literature to develop algebraic thinking in an environment that connects algebra to various situations. Activities are based on the book "Anno's Magic Seeds" with additional resources listed. Students express a constant function, exponential function, and a recursive function in their own words as well as writing about…
Learning Algebra from Worked Examples
ERIC Educational Resources Information Center
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is…
Thermodynamics. [algebraic structure
NASA Technical Reports Server (NTRS)
Zeleznik, F. J.
1976-01-01
The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.
Invariants of triangular Lie algebras
NASA Astrophysics Data System (ADS)
Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman
2007-07-01
Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated.
ERIC Educational Resources Information Center
Fradiska, John
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
Ford, Nelson S.
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
Best, Terrence
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
Darnell, Janice Marie
2012-01-01
The purpose of this correlational study was to examine Georgia's Criterion-Referenced Competency Test (CRCT) scores of 8th grade students and End of Course Test (EOCT) scores of the same students as 9th graders in the areas of language arts and mathematics to test the theory that a relationship exists between the two tests. The study also…
ERIC Educational Resources Information Center
Myrick, Gloria H.
A self-esteem building program was developed and implemented to reduce the failure and potential dropout rate of limited English proficient 9th-grade Haitian students (N=15) who were enrolled in bilingual classes and were selected based on recommendations from their bilingual teachers, referrals for behavior problems, and failure in two or more…
ERIC Educational Resources Information Center
Todd, John J., Ed.
This document contains the proceedings of the 9th Biennial National Conference of the Australian Association for Environmental Education and the Marine Society of Australasia. The contents provide a valuable snapshot of the state of environmental education in Australia while moving towards the end of the 20th century. Papers include: (1) "Stand…
Nowak, Anna K; Armato, Samuel G; Ceresoli, Giovanni Luca; Yildirim, Huseyin; Francis, Roslyn J
2010-10-01
Imaging of malignant pleural mesothelioma (MPM) poses many challenges for imaging specialists and clinicians due to the anatomic location and unique growth pattern of this tumor. Nevertheless, imaging in MPM plays a critical role in diagnosis, prognostication, prediction or measurement of response to therapy, and monitoring of disease recurrence after aggressive surgical management. Imaging-based studies presented at the 9th International Conference of the International Mesothelioma Interest Group (IMIG) in October 2008 sought to further define the current practice and future potential of imaging for the mesothelioma patient. The Imaging Session was dominated by presentations that addressed the use of fluorodeoxyglucose positron emission tomography (FDG-PET), a clear indication of the expanding role of this modality. These uses included FDG-PET imaging at the point of diagnosis, in prognostication, and in the assessment of response to chemotherapy. Often FDG-PET studies were combined with computed tomography (CT) scans in an attempt to overcome limitations associated with either imaging modality alone. At diagnosis, FDG-PET parameters had a high sensitivity and specificity for differentiation of benign from malignant pleural disease. The use of FDG-PET to extract quantitative features from metabolically active tumor volume was shown to be a significant factor in the prediction of patient survival. The prognostic value of FDG-PET was not confounded by prior talc pleurodesis, despite the inflammatory response associated with the procedure. Metabolic response based on FDG-PET was found to be significantly correlated with progression-free survival. CT-based assessment of mesothelioma was determined to be inconsistent with spherical-model-based criteria so that changes in tumor area, a presumably more complete assessment of tumor burden, exhibited a 46% concordance rate with changes in linear measurements. PMID:20541834
ERIC Educational Resources Information Center
Gonzalez-Vega, Laureano
1999-01-01
Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)
Chen, J.; Safro, I.
2011-01-01
Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.
Constraint algebra in bigravity
Soloviev, V. O.
2015-07-15
The number of degrees of freedom in bigravity theory is found for a potential of general form and also for the potential proposed by de Rham, Gabadadze, and Tolley (dRGT). This aim is pursued via constructing a Hamiltonian formalismand studying the Poisson algebra of constraints. A general potential leads to a theory featuring four first-class constraints generated by general covariance. The vanishing of the respective Hessian is a crucial property of the dRGT potential, and this leads to the appearance of two additional second-class constraints and, hence, to the exclusion of a superfluous degree of freedom—that is, the Boulware—Deser ghost. The use of a method that permits avoiding an explicit expression for the dRGT potential is a distinctive feature of the present study.
Quantum algebra of N superspace
Hatcher, Nicolas; Restuccia, A.; Stephany, J.
2007-08-15
We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.
A Z{sub 3} generalization of Pauli's principle, quark algebra and the Lorentz invariance
Kerner, Richard
2012-09-24
The fundamental difference between bosons and fermions is that they obey two alternative representations of the Z{sub 2} group, resulting in symmetric or anti-symmetric binary commutation relations. Our aim is to explore possibilities offered by ternary Z{sub 3} generalization commutation relations. This leads to cubic and ternary algebras which are a direct generalization of usual commutation relations, with Z{sub 3}-grading replacing the usual Z{sub 2}-grading. Properties and structure of such algebras are discussed, with special interest in a low-dimensional one, with two generators. Invariant cubic forms on such algebras are introduced, and it is shown how the SL(2,C) group arises naturally as the symmetry group preserving these forms. In the case of lowest dimension, with only two generators, it is shown how the cubic combinations of elements of the same Z{sub 3} grade behave like Lorentz spinors, while binary products of elements of this algebra with an element of the conjugate algebra behave like Lorentz vectors. The wave equation generalizing the Dirac operator to the Z{sub 3}-graded case is introduced, whose diagonalization leads to a third-order equation. The solutions of this equation cannot propagate because their exponents always contain non-oscillating real damping factor. We show how certain cubic products can propagate nevertheless. The model suggests the origin of the color SU(3) symmetry obeyed by quark states.
Taiwanese Arithmetic and Algebra
ERIC Educational Resources Information Center
Lo, Jane-Jane; Tsai, Feng-Chiu
2011-01-01
Taiwanese students consistently rank near the top on international exams on mathematics and science. In 2007, Taiwan recorded the highest TIMSS math score for eighth grade. The central education agency in Taiwan publishes detailed mathematics curriculum guidelines, which textbooks and national exams follow closely. In May each year, all ninth…
Personalized Learning in Algebra
ERIC Educational Resources Information Center
Walkington, Candace; Sherman, Milan; Howell, Elizabeth
2014-01-01
Mathematical "funds of knowledge" (Civil 2007) that students bring from their community and home lives can offer entry points for concepts such as functions and rate of change, which are important "big ideas" across all grade levels (NCTM 2000). The Common Core State Standards (CCSSI 2010) ask high school students to…
Using Homemade Algebra Tiles To Develop Algebra and Prealgebra Concepts.
ERIC Educational Resources Information Center
Leitze, Annette Ricks; Kitt, Nancy A.
2000-01-01
Describes how to use homemade tiles, sketches, and the box method to reach a broader group of students for successful algebra learning. Provides a list of concepts appropriate for such an approach. (KHR)
Distance geometry and geometric algebra
NASA Astrophysics Data System (ADS)
Dress, Andreas W. M.; Havel, Timothy F.
1993-10-01
As part of his program to unify linear algebra and geometry using the language of Clifford algebra, David Hestenes has constructed a (well-known) isomorphism between the conformal group and the orthogonal group of a space two dimensions higher, thus obtaining homogeneous coordinates for conformal geometry.(1) In this paper we show that this construction is the Clifford algebra analogue of a hyperbolic model of Euclidean geometry that has actually been known since Bolyai, Lobachevsky, and Gauss, and we explore its wider invariant theoretic implications. In particular, we show that the Euclidean distance function has a very simple representation in this model, as demonstrated by J. J. Seidel.(18)
Hopf algebras and Dyson-Schwinger equations
NASA Astrophysics Data System (ADS)
Weinzierl, Stefan
2016-06-01
In this paper I discuss Hopf algebras and Dyson-Schwinger equations. This paper starts with an introduction to Hopf algebras, followed by a review of the contribution and application of Hopf algebras to particle physics. The final part of the paper is devoted to the relation between Hopf algebras and Dyson-Schwinger equations.
ERIC Educational Resources Information Center
Fletcher, Richard Kenard, Jr.
This study was designed to determine experimentally the relationship between achievement and grade level for 64 tenth-grade students, 48 eleventh-grade students, and 95 twelfth-grade physics students. All students were enrolled in the Project Physics course in their respective schools. The Physics Achievement Test (PAT) and the algebra I and II…
Sequential products on effect algebras
NASA Astrophysics Data System (ADS)
Gudder, Stan; Greechie, Richard
2002-02-01
A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEA's. For example, there are no finite nonboolean SEA's, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEA's is characterized and examples of horizontal sums and tensor products are presented.
Curvature calculations with spacetime algebra
Hestenes, D.
1986-06-01
A new method for calculating the curvature tensor is developed and applied to the Scharzschild case. The method employs Clifford algebra and has definite advantages over conventional methods using differential forms or tensor analysis.
GCD, LCM, and Boolean Algebra?
ERIC Educational Resources Information Center
Cohen, Martin P.; Juraschek, William A.
1976-01-01
This article investigates the algebraic structure formed when the process of finding the greatest common divisor and the least common multiple are considered as binary operations on selected subsets of positive integers. (DT)
Cartooning in Algebra and Calculus
ERIC Educational Resources Information Center
Moseley, L. Jeneva
2014-01-01
This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.
NASA Technical Reports Server (NTRS)
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
Semiclassical states on Lie algebras
Tsobanjan, Artur
2015-03-15
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following the methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.
NASA Astrophysics Data System (ADS)
Lannes, A.; Teunissen, P. J. G.
2011-05-01
The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called `phase closure imaging.' In both cases, the analysis of the related structures appeals to the algebraic graph theory and the algebraic number theory. For example, the estimable functions of carrier-phase ambiguities, which were introduced in GNSS to correct some rank defects of the undifferenced equations, prove to be `closure-phase ambiguities:' the so-called `closure-delay' (CD) ambiguities. The notion of closure delay thus generalizes that of double difference (DD). The other estimable functional variables involved in the phase and code undifferenced equations are the receiver and satellite pseudo-clock biases. A related application, which corresponds to the second objective of this paper, concerns the definition of the clock information to be broadcasted to the network users for their precise point positioning (PPP). It is shown that this positioning can be achieved by simply having access to the satellite pseudo-clock biases. For simplicity, the study is restricted to relatively small networks. Concerning the phase for example, these biases then include five components: a frequency-dependent satellite-clock error, a tropospheric satellite delay, an ionospheric satellite delay, an initial satellite phase, and an integer satellite ambiguity. The form of the PPP equations to be solved by the network user is then similar to that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, an operation which can be performed in real time via appropriate decorrelation techniques, estimates of these float biases can be immediately obtained. No other ambiguity is to be fixed. The satellite pseudo-clock biases can thus be obtained in real time. This is
NASA Astrophysics Data System (ADS)
Sternberg, Andris; Grinberga, Liga; Sarakovskis, Anatolijs; Rutkis, Martins
2015-03-01
The joint International Symposium RCBJSF-2014-FM&NT successfully has united two international events - 12th Russia/CIS/Baltic/Japan Symposium on Ferroelectricity (RCBJSF-12) and 9th International Conference Functional Materials and Nanotechnologies (FM&NT-2014). The RCBJSF symposium is a continuation of series of meetings on ferroelectricity, the first of which took place in Novosibirsk (USSR) in 1976. FM&NT conferences started in 2006 and have been organized by Institute of Solid State Physics, University of Latvia in Riga. In 2012 the International program committee decided to transform this conference into a traveling Baltic State conference and the FM&NT-2013 was organized by the Institute of Physics, University of Tartu, Estonia. In 2014 the joint international symposium RCBJSF-2014-FM&NT was organized by the Institute of Solid State Physics, University of Latvia and was part of Riga - 2014, the European Capital of Culture event. The purpose of the joint Symposium was to bring together scientists, students and high-level experts in solid state physics, materials science, engineering and related disciplines. The number of the registered participants from 26 countries was over 350. During the Symposium 128 high quality scientific talks (5 plenary, 42 invited, 81 oral) and over 215 posters were presented. All presentations were divided into 4 parallel sessions according to 4 main topics of the Symposium: Ferroelectricity, including ferroelectrics and multiferroics, pyroelectrics, piezoelectrics and actuators, integrated ferroelectrics, relaxors, phase transitions and critical phenomena. Multifunctional Materials, including theory, multiscale and multiphenomenal material modeling and simulation, advanced inorganic, organic and hybrid materials. Nanotechnologies, including progressive methods, technologies and design for production, investigation of nano- particles, composites, structures, thin films and coatings. Energy, including perspective materials and
Hopf algebras and topological recursion
NASA Astrophysics Data System (ADS)
Esteves, João N.
2015-11-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).
2005-04-11
The ALGEBRA program allows the user to manipulate data from a finite element analysis before it is plotted. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database. The ALGEBRA program evaluates user-supplied functions of the data and writes the results to an output EXODUS II database that can be read by plot programs.
ERIC Educational Resources Information Center
Wood, Bonnie S.; Brown, Lorrie A.
1997-01-01
Details a study in which grade 9 females were assigned to either an all-female or mixed-sex algebra class. Findings indicate that the all-female intervention group demonstrated a greater gain in math scores between grades 8-11 than the nonintervention group. Contains 41 references. (DDR)
NASA Astrophysics Data System (ADS)
Kuzmin, Dmitri; Möller, Matthias; Gurris, Marcel
Flux limiting for hyperbolic systems requires a careful generalization of the design principles and algorithms introduced in the context of scalar conservation laws. In this chapter, we develop FCT-like algebraic flux correction schemes for the Euler equations of gas dynamics. In particular, we discuss the construction of artificial viscosity operators, the choice of variables to be limited, and the transformation of antidiffusive fluxes. An a posteriori control mechanism is implemented to make the limiter failsafe. The numerical treatment of initial and boundary conditions is discussed in some detail. The initialization is performed using an FCT-constrained L 2 projection. The characteristic boundary conditions are imposed in a weak sense, and an approximate Riemann solver is used to evaluate the fluxes on the boundary. We also present an unconditionally stable semi-implicit time-stepping scheme and an iterative solver for the fully discrete problem. The results of a numerical study indicate that the nonlinearity and non-differentiability of the flux limiter do not inhibit steady state convergence even in the case of strongly varying Mach numbers. Moreover, the convergence rates improve as the pseudo-time step is increased.
ERIC Educational Resources Information Center
Fong, Anthony B.; Jaquet, Karina; Finkelstein, Neal
2014-01-01
This REL West study explores the prevalence of students repeating Algebra I, who is most likely to repeat the course, and the level of improvement for students who repeat. Using six years of data from a cohort of 3,400 first-time seventh grade students in a California school district, authors found that 44 percent of students repeated algebra I.…
Building a Foundation for Learning Algebra in the Elementary Grades.
ERIC Educational Resources Information Center
Carpenter, Thomas P.; Levi, Linda; Farnsworth, Valerie
2000-01-01
"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…
Middle Grades Students' Algebraic Understanding in a Reform Curriculum
ERIC Educational Resources Information Center
Krebs, Angela S.
2003-01-01
The National Council of Teachers of Mathematics' "Curriculum and Evaluation Standards" in 1989 was pivotal in mathematics reform. The National Science Foundation funded several curriculum projects to address the vision described in the "Standards." This study investigates students' learning in one of these "Standards"-based curricula, the…
Bilinear covariants and spinor fields duality in quantum Clifford algebras
Abłamowicz, Rafał; Gonçalves, Icaro; Rocha, Roldão da
2014-10-15
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying Z-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, “The unpredictability of quantum gravity,” Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Bilinear covariants and spinor fields duality in quantum Clifford algebras
NASA Astrophysics Data System (ADS)
Abłamowicz, Rafał; Gonçalves, Icaro; da Rocha, Roldão
2014-10-01
Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields, the duality between spinor and quantum spinor fields can be discussed. Thus, by endowing the underlying spacetime with an arbitrary bilinear form with an antisymmetric part in addition to a symmetric spacetime metric, quantum algebraic spinor fields and deformed bilinear covariants can be constructed. They are thus compared to the classical (non quantum) ones. Classes of quantum spinor fields classes are introduced and compared with Lounesto's spinor field classification. A physical interpretation of the deformed parts and the underlying {Z}-grading is proposed. The existence of an arbitrary bilinear form endowing the spacetime already has been explored in the literature in the context of quantum gravity [S. W. Hawking, "The unpredictability of quantum gravity," Commun. Math. Phys. 87, 395 (1982)]. Here, it is shown further to play a prominent role in the structure of Dirac, Weyl, and Majorana spinor fields, besides the most general flagpoles and flag-dipoles. We introduce a new duality between the standard and the quantum spinor fields, by showing that when Clifford algebras over vector spaces endowed with an arbitrary bilinear form are taken into account, a mixture among the classes does occur. Consequently, novel features regarding the spinor fields can be derived.
Nonnumeric Computer Applications to Algebra, Trigonometry and Calculus.
ERIC Educational Resources Information Center
Stoutemyer, David R.
1983-01-01
Described are computer program packages requiring little or no knowledge of computer programing for college algebra, calculus, and abstract algebra. Widely available computer algebra systems are listed. (MNS)
Powell, Sarah R; Fuchs, Lynn S
2014-08-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2(nd)- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044
Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces
Koibuchi, H. )
1991-10-10
In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.
Invertible linear transformations and the Lie algebras
NASA Astrophysics Data System (ADS)
Zhang, Yufeng; Tam, Honwah; Guo, Fukui
2008-07-01
With the help of invertible linear transformations and the known Lie algebras, a way to generate new Lie algebras is given. These Lie algebras obtained have a common feature, i.e. integrable couplings of solitary hierarchies could be obtained by using them, specially, the Hamiltonian structures of them could be worked out. Some ways to construct the loop algebras of the Lie algebras are presented. It follows that some various loop algebras are given. In addition, a few new Lie algebras are explicitly constructed in terms of the classification of Lie algebras proposed by Ma Wen-Xiu, which are bases for obtaining new Lie algebras by using invertible linear transformations. Finally, some solutions of a (2 + 1)-dimensional partial-differential equation hierarchy are obtained, whose Hamiltonian form-expressions are manifested by using the quadratic-form identity.
Strengthening Grade 3-5 Students' Foundational Knowledge of Rational Numbers
ERIC Educational Resources Information Center
Good, Thomas L.; Wood, Marcy B.; Sabers, Darrell; Olson, Amy M.; Lavigne, Alyson Leah; Sun, Huaping; Kalinec-Craig, Crystal
2013-01-01
Background: American students have done poorly in algebra and that has generated policy concerns about preparing students for STEM careers. There has been growing recognition that the algebra problem may begin in earlier grades when students do not adequately master rational numbers. Purpose: The study provided a series of workshops organized…
ERIC Educational Resources Information Center
Curry, Steven James
2012-01-01
This quantitative study investigated relationships between higher level mathematics learning and multiplication fact fluency, multiplication fact speed-recall, and reading grade equivalency of eighth grade students in Algebra I and Pre-Algebra. Higher level mathematics learning was indicated by an average score of 80% or higher on first and second…
NASA Astrophysics Data System (ADS)
Cifra, Michal; Pokorný, Jirí; Kucera, Ondrej
2011-12-01
This volume contains papers presented at the International Fröhlich's Symposium entitled 'Electrodynamic Activity of Living Cells' (1-3 July 2011, Prague, Czech Republic). The Symposium was the 9th meeting devoted to physical processes in living matter organized in Prague since 1987. The hypothesis of oscillation systems in living cells featured by non-linear interaction between elastic and electrical polarization fields, non-linear interactions between the system and the heat bath leading to energy downconversion along the frequency scale, energy condensation in the lowest frequency mode and creation of a coherent state was formulated by H Fröhlich, founder of the theory of dielectric materials. He assumed that biological activity is based not only on biochemical but also on biophysical mechanisms and that their disturbances form basic links along the cancer transformation pathway. Fröhlich outlined general ideas of non-linear physical processes in biological systems. The downconversion and the elastic-polarization interactions should be connected in a unified theory and the solution based on comprehensive non-linear characteristics. Biochemical and genetic research of biological systems are highly developed and have disclosed a variety of cellular and subcellular structures, chemical reactions, molecular information transfer, and genetic code sequences - including their pathological development. Nevertheless, the cancer problem is still a big challenge. Warburg's discovery of suppressed oxidative metabolism in mitochondria in cancer cells suggested the essential role of physical mechanisms (but his discovery has remained without impact on cancer research and on the study of physical properties of biological systems for a long time). Mitochondria, the power plants of the cell, have several areas of activity-oxidative energy production is connected with the formation of a strong static electric field around them, water ordering, and liberation of non
ERIC Educational Resources Information Center
Cook, Paul
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
Fradiska, John
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
One Feather, Vivian
To enable the student to better his self-image, this project endeavors to give the student opportunity to acquire factual knowledge as well as new experience and skills. Through an integrated program of instructional materials, the 9th grade Oglala Sioux student studies the history and culture of the Oglala people on the Pine Ridge Indian…
ERIC Educational Resources Information Center
Whitfield, Melvin
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
Skager, Rodney; And Others
This second survey of drug and alcohol use among 7th, 9th, and 11th grade students enrolled in California's public secondary schools was conducted from December 1987 to February 1988. The purpose of this survey was to provide information on levels of substance use and related attitudes and experiences among young people who are enrolled in public…
ERIC Educational Resources Information Center
New York State Education Dept., Albany. Bureau of Secondary Curriculum Development.
This guide, part 2 of a two-part publication, contains resource units on life today in China which can be used with 9th-grade students. The materials and activities, gathered by American secondary-school teachers who visited China in 1973, are intended to provide a pattern for an elective course or supplementary material for regular social studies…
Beyond Dirac - a Unified Algebra
NASA Astrophysics Data System (ADS)
Lundberg, Wayne R.
2001-10-01
A introductory insight will be shared regarding a 'separation of variables' approach to understanding the relationship between QCD and the origins of cosmological and particle mass. The discussion will then build upon work presented at DFP 2000, focussing on the formal basis for using 3x3x3 matrix algebra as it underlies and extends Dirac notation. A set of restrictions are established which break the multiple symmetries of the 3x3x3 matrix algebra, yielding Standard Model QCD objects and interactions. It will be shown that the 3x3x3 matrix representation unifies the algebra of strong and weak (and by extension, electromagnetic) interactions. A direct correspondence to string theoretic objects is established by considering the string to be partitioned in thirds. Rubik's cube is used as a graphical means of handling algebraic manipulation of 3x3x3 algebra. Further, its potential utility for advancing pedagogical methods through active engagement is discussed. A simulated classroom exercize will be conducted.
Moving frames and prolongation algebras
NASA Technical Reports Server (NTRS)
Estabrook, F. B.
1982-01-01
Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.
Early Algebra with Graphics Software as a Type II Application of Technology
ERIC Educational Resources Information Center
Abramovich, Sergei
2006-01-01
This paper describes the use of Kid Pix-graphics software for creative activities of young children--in the context of early algebra as determined by the mathematics core curriculum of New York state. It shows how grade-two appropriate pedagogy makes it possible to bring about a qualitative change in the learning process of those commonly…
Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations
ERIC Educational Resources Information Center
Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie
2015-01-01
The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…
Step-by-Step Solution Possibilities in Different Computer Algebra Systems.
ERIC Educational Resources Information Center
Tonisson, Eno
This paper compares a number of different Computer Algebra Systems (CAS) in their solution of one-step and multi-step problems. The CAS programs considered include DERIVE, Maple, Mathematica, and MuPAD while the problems are taken from the final examinations of grades 9 and 12 in Estonian schools. The different outputs to one-step problems with…
Indicators of Student Engagement: What Teachers Notice during Introductory Algebra Lessons
ERIC Educational Resources Information Center
Nyman, Rimma
2015-01-01
This article presents results from an empirical study of how student engagement is visible during introductory algebra. Previously, the notion of engagement in mathematics has been studied from students' and researchers' perspectives. This study is instead focused on teachers' perspectives on student engagement. Eight teachers in grade 6-7 have…
Introducing a Computer Algebra System in Mathematics Education--Empirical Evidence from Germany
ERIC Educational Resources Information Center
Schmidt, Karsten; Kohler, Anke; Moldenhauer, Wolfgang
2009-01-01
This paper reports on the effects the use of a pocket calculator-based computer algebra system (CAS) has on the performance in mathematics of grade 11 students in Germany. A project started at 8 of about one hundred upper secondary schools in the federal state of Thuringia in 1999; 3 years later the former restrictions on the use of technology in…
ERIC Educational Resources Information Center
Fong, Anthony; Jaquet, Karina; Finkelstein, Neal
2016-01-01
The information provided in this report shows how students perform when they repeat algebra I and how the level of improvement varies depending on initial course performance and the academic measure (course grades or CST scores). This information can help inform decisions and policies regarding whether and under what circumstances students should…
Proposing and Testing a Model to Explain Traits of Algebra Preparedness
ERIC Educational Resources Information Center
Venenciano, Linda; Heck, Ronald
2016-01-01
Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…
The Effects of the Elevate Math Summer Program on Math Achievement and Algebra Readiness
ERIC Educational Resources Information Center
Snipes, Jason; Huang, Chun-Wei; Jaquet, Karina; Finkelstein, Neal
2016-01-01
To raise math success rates in middle school, many schools and districts have implemented summer math programs designed to improve student preparation for algebra content in grade 8. However, little is known about the effectiveness of these programs. While students who participate typically experience learning gains, there is little rigorous…
Algebra I, Package 03-03, Addition and Multiplication of Real Numbers.
ERIC Educational Resources Information Center
Thompson, Russ; Fuller, Albert
This teacher guide is part of the materials prepared for an individualized program for ninth-grade algebra and basic mathematics students. Materials written for the program are to be used with audiovisual lessons recorded on tape cassettes. For an evaluation of the program, see ED 086 545. In this guide, the teacher is provided with objectives for…
Generalized Galilean algebras and Newtonian gravity
NASA Astrophysics Data System (ADS)
González, N.; Rubio, G.; Salgado, P.; Salgado, S.
2016-04-01
The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.
Computer Algebra Systems in Undergraduate Instruction.
ERIC Educational Resources Information Center
Small, Don; And Others
1986-01-01
Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)
Motivating Activities that Lead to Algebra
ERIC Educational Resources Information Center
Menon, Ramakrishnan
2004-01-01
Four activities consisting of puzzles are introduced, which help students to recognize the strength of algebraic generalizations. They also assist them to comprehend algebraic concepts, and enable them to develop their individual puzzles and games.
Scalable Parallel Algebraic Multigrid Solvers
Bank, R; Lu, S; Tong, C; Vassilevski, P
2005-03-23
The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.
Computational triadic algebras of signs
Zadrozny, W.
1996-12-31
We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.
ERIC Educational Resources Information Center
Star, Jon R.; Rittle-Johnson, Bethany
2009-01-01
Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…
Spatial-Operator Algebra For Robotic Manipulators
NASA Technical Reports Server (NTRS)
Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.
1991-01-01
Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.
The weak Hopf algebras related to generalized Kac-Moody algebra
Wu Zhixiang
2006-06-15
We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying J{sup m}=J{sup m-1} for some integer m. We denote this algebra by wU{sub q}{sup {tau}}(G). This algebra is a weak Hopf algebra if and only if m=2. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usually quantum envelope algebra U{sub q}(G) of a generalized Kac-Moody algebra G.
NASA Astrophysics Data System (ADS)
Ghodssi, Reza; Livermore, Carol; Arnold, David
2010-10-01
This special section of the Journal of Micromechanics and Microengineering presents papers selected from the 9th International Workshop on Micro and Nanotechnology for Power Generation and Energy Conversion Applications (PowerMEMS 2009), which was held in Washington DC, USA from 1-4 December 2009. Since it was first held in Sendai, Japan in 2000, the PowerMEMS workshop has focused on small-scale systems that process, convert, or generate macroscopically significant amounts of power, typically with high power density or high energy density. In the workshop's early years, much of the research presented was on small-scale fueled systems, such as micro heat engines and micro fuel cells. The past nine years have seen a dramatic expansion in the range of technologies that are brought to bear on the challenge of high-power, small-scale systems, as well as an increase in the applications for such technologies. At this year's workshop, 158 contributed papers were presented, along with invited and plenary presentations. The papers focused on applications from micro heat engines and fuel cells, to energy harvesting and its enabling electronics, to thermal management and propulsion. Also presented were the technologies that enable these applications, such as the structuring of microscale, nanoscale and biological systems for power applications, as well as combustion and catalysis at small scales. This special section includes a selection of 12 expanded papers representing energy harvesting, chemical and fueled systems, and elastic energy storage at small scales. We would like to express our appreciation to the members of the International Steering Committee, the Technical Program Committee, the Local Organizing Committee, and to the workshop's financial supporters. We are grateful to the referees for their contributions to the review process. Finally, we would like to thank Dr Ian Forbes, the editorial staff of the Journal of Micromechanics and Microengineering, and the staff
Algebra? A Gate! A Barrier! A Mystery!
ERIC Educational Resources Information Center
Mathematics Educatio Dialogues, 2000
2000-01-01
This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…
Graphing Calculator Use in Algebra Teaching
ERIC Educational Resources Information Center
Dewey, Brenda L.; Singletary, Ted J.; Kinzel, Margaret T.
2009-01-01
This study examines graphing calculator technology availability, characteristics of teachers who use it, teacher attitudes, and how use reflects changes to algebra curriculum and instructional practices. Algebra I and Algebra II teachers in 75 high school and junior high/middle schools in a diverse region of a northwestern state were surveyed.…
New family of Maxwell like algebras
NASA Astrophysics Data System (ADS)
Concha, P. K.; Durka, R.; Merino, N.; Rodríguez, E. K.
2016-08-01
We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.
A Balancing Act: Making Sense of Algebra
ERIC Educational Resources Information Center
Gavin, M. Katherine; Sheffield, Linda Jensen
2015-01-01
For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…
Difficulties in Initial Algebra Learning in Indonesia
ERIC Educational Resources Information Center
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-01-01
Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…
Teaching Strategies to Improve Algebra Learning
ERIC Educational Resources Information Center
Zbiek, Rose Mary; Larson, Matthew R.
2015-01-01
Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…
Unifying the Algebra for All Movement
ERIC Educational Resources Information Center
Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.
2015-01-01
There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…
Weaving Geometry and Algebra Together
ERIC Educational Resources Information Center
Cetner, Michelle
2015-01-01
When thinking about student reasoning and sense making, teachers must consider the nature of tasks given to students along with how to plan to use the tasks in the classroom. Students should be presented with tasks in a way that encourages them to draw connections between algebraic and geometric concepts. This article focuses on the idea that it…
Inequalities, Assessment and Computer Algebra
ERIC Educational Resources Information Center
Sangwin, Christopher J.
2015-01-01
The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in…
ERIC Educational Resources Information Center
Bosse, Michael J.; Ries, Heather; Chandler, Kayla
2012-01-01
Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…
Implementing Change in College Algebra
ERIC Educational Resources Information Center
Haver, William E.
2007-01-01
In this paper, departments are urged to consider implementing the type of changes proposed in Beyond Crossroads in College Algebra. The author of this paper is chair of the Curriculum Renewal Across the First Two Years (CRAFTY) Committee of the Mathematical Association of America. The committee has members from two-year colleges, four-year…
Algebraic Activities Aid Discovery Lessons
ERIC Educational Resources Information Center
Wallace-Gomez, Patricia
2013-01-01
After a unit on the rules for positive and negative numbers and the order of operations for evaluating algebraic expressions, many students believe that they understand these principles well enough, but they really do not. They clearly need more practice, but not more of the same kind of drill. Wallace-Gomez provides three graphing activities that…
Fuzzy-algebra uncertainty assessment
Cooper, J.A.; Cooper, D.K.
1994-12-01
A significant number of analytical problems (for example, abnormal-environment safety analysis) depend on data that are partly or mostly subjective. Since fuzzy algebra depends on subjective operands, we have been investigating its applicability to these forms of assessment, particularly for portraying uncertainty in the results of PRA (probabilistic risk analysis) and in risk-analysis-aided decision-making. Since analysis results can be a major contributor to a safety-measure decision process, risk management depends on relating uncertainty to only known (not assumed) information. The uncertainties due to abnormal environments are even more challenging than those in normal-environment safety assessments; and therefore require an even more judicious approach. Fuzzy algebra matches these requirements well. One of the most useful aspects of this work is that we have shown the potential for significant differences (especially in perceived margin relative to a decision threshold) between fuzzy assessment and probabilistic assessment based on subtle factors inherent in the choice of probability distribution models. We have also shown the relation of fuzzy algebra assessment to ``bounds`` analysis, as well as a description of how analyses can migrate from bounds analysis to fuzzy-algebra analysis, and to probabilistic analysis as information about the process to be analyzed is obtained. Instructive examples are used to illustrate the points.
Entropy algebras and Birkhoff factorization
NASA Astrophysics Data System (ADS)
Marcolli, Matilde; Tedeschi, Nicolas
2015-11-01
We develop notions of Rota-Baxter structures and associated Birkhoff factorizations, in the context of min-plus semirings and their thermodynamic deformations, including deformations arising from quantum information measures such as the von Neumann entropy. We consider examples related to Manin's renormalization and computation program, to Markov random fields and to counting functions and zeta functions of algebraic varieties.
Algebra for All. Research Brief
ERIC Educational Resources Information Center
Bleyaert, Barbara
2009-01-01
The call for "algebra for all" is not a recent phenomenon. Concerns about the inadequacy of math (and science) preparation in America's high schools have been a steady drumbeat since the 1957 launch of Sputnik; a call for raising standards and the number of math (and science) courses required for graduation has been a part of countless national…
Exploring Algebraic Misconceptions with Technology
ERIC Educational Resources Information Center
Sakow, Matthew; Karaman, Ruveyda
2015-01-01
Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…
An Introduction to Algebraic Multigrid
Falgout, R D
2006-04-25
Algebraic multigrid (AMG) solves linear systems based on multigrid principles, but in a way that only depends on the coefficients in the underlying matrix. The author begins with a basic introduction to AMG methods, and then describes some more recent advances and theoretical developments
Elementary Algebra Connections to Precalculus
ERIC Educational Resources Information Center
Lopez-Boada, Roberto; Daire, Sandra Arguelles
2013-01-01
This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…
Adventures in Flipping College Algebra
ERIC Educational Resources Information Center
Van Sickle, Jenna
2015-01-01
This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…
Kinds of Knowledge in Algebra.
ERIC Educational Resources Information Center
Lewis, Clayton
Solving equations in elementary algebra requires knowledge of the permitted operations, and knowledge of what operation to use at a given point in the solution process. While just these kinds of knowledge would be adequate for an ideal solver, human solvers appear to need and use other kinds of knowledge. First, many errors seem to indicate that…
Algebra, Home Mortgages, and Recessions
ERIC Educational Resources Information Center
Mariner, Jean A. Miller; Miller, Richard A.
2009-01-01
The current financial crisis and recession in the United States present an opportunity to discuss relevant applications of some topics in typical first-and second-year algebra and precalculus courses. Real-world applications of percent change, exponential functions, and sums of finite geometric sequences can help students understand the problems…
Algebra from Chips and Chopsticks
ERIC Educational Resources Information Center
Yun, Jeong Oak; Flores, Alfinio
2012-01-01
Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
Algebraic methods in system theory
NASA Technical Reports Server (NTRS)
Brockett, R. W.; Willems, J. C.; Willsky, A. S.
1975-01-01
Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
Principals + Algebra (- Fear) = Instructional Leadership
ERIC Educational Resources Information Center
Carver, Cynthia L.
2010-01-01
Recent state legislation in Michigan mandates that all graduating seniors successfully pass algebra I and II. Numerous initiatives have been enacted to help mathematics teachers meet this challenge, yet school principals have had little preparation for the necessary curricular and instructional changes. To address this unmet need, university-based…
Experts Question California's Algebra Edict
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
Business leaders from important sectors of the American economy have been urging schools to set higher standards in math and science--and California officials, in mandating that 8th graders be tested in introductory algebra, have responded with one of the highest such standards in the land. Still, many California educators and school…
The Exocenter of a Generalized Effect Algebra
NASA Astrophysics Data System (ADS)
Foulis, David J.; Pulmannová, Sylvia
2011-12-01
Elements of the exocenter of a generalized effect algebra (GEA) correspond to decompositions of the GEA as a direct sum and thus the exocenter is a generalization to GEAs of the center of an effect algebra. The exocenter of a GEA is shown to be a boolean algebra, and the notion of a hull mapping for an effect algebra is generalized to a hull system for a GEA. We study Dedekind orthocompleteness of GEAs and extend to GEAs the notion of a centrally orthocomplete effect algebra.
Array algebra estimation in signal processing
NASA Astrophysics Data System (ADS)
Rauhala, U. A.
A general theory of linear estimators called array algebra estimation is interpreted in some terms of multidimensional digital signal processing, mathematical statistics, and numerical analysis. The theory has emerged during the past decade from the new field of a unified vector, matrix and tensor algebra called array algebra. The broad concepts of array algebra and its estimation theory cover several modern computerized sciences and technologies converting their established notations and terminology into one common language. Some concepts of digital signal processing are adopted into this language after a review of the principles of array algebra estimation and its predecessors in mathematical surveying sciences.
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-15
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.
Atomic effect algebras with compression bases
Caragheorgheopol, Dan; Tkadlec, Josef
2011-01-15
Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
Atomic effect algebras with compression bases
NASA Astrophysics Data System (ADS)
Caragheorgheopol, Dan; Tkadlec, Josef
2011-01-01
Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.
NASA CONNECT: Algebra: Mirror, Mirror on the Universe
NASA Technical Reports Server (NTRS)
2000-01-01
'Algebra: Mirror, Mirror on the Universe' is the last of seven programs in the 1999-2000 NASA CONNECT series. Produced by NASA Langley Research Center's Office of Education, NASA CONNECT is an award-winning series of instructional programs designed to enhance the teaching of math, science and technology concepts in grades 5-8. NASA CONNECT establishes the 'connection' between the mathematics, science, and technology concepts taught in the classroom and NASA research. Each program in the series supports the national mathematics, science, and technology standards; includes a resource-rich teacher guide; and uses a classroom experiment and web-based activity to complement and enhance the math, science, and technology concepts presented in the program. NASA CONNECT is FREE and the programs in the series are in the public domain. Visit our web site and register. http://connect.larc.nasa.gov In 'Algebra: Mirror, Mirror on the Universe', students will learn how algebra is used to explore the universe.
Universal effective hadron dynamics from superconformal algebra
NASA Astrophysics Data System (ADS)
Brodsky, Stanley J.; de Téramond, Guy F.; Dosch, Hans Günter; Lorcé, Cédric
2016-08-01
An effective supersymmetric QCD light-front Hamiltonian for hadrons composed of light quarks, which includes a spin-spin interaction between the hadronic constituents, is constructed by embedding superconformal quantum mechanics into AdS space. A specific breaking of conformal symmetry inside the graded algebra determines a unique effective quark-confining potential for light hadrons, as well as remarkable connections between the meson and baryon spectra. The results are consistent with the empirical features of the light-quark hadron spectra, including a universal mass scale for the slopes of the meson and baryon Regge trajectories and a zero-mass pion in the limit of massless quarks. Our analysis is consistently applied to the excitation spectra of the π, ρ, K, K* and ϕ meson families as well as to the N, Δ, Λ, Σ, Σ*, Ξ and Ξ* in the baryon sector. We also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. The mass of light hadrons is expressed in a universal and frame-independent decomposition in the semiclassical approximation described here.
Universal effective hadron dynamics from superconformal algebra
Brodsky, Stanley J.; de Teramond, Guy F.; Dosch, Hans Gunter; Lorce, Cedric
2016-05-25
An effective supersymmetric QCD light-front Hamiltonian for hadrons composed of light quarks, which includes a spin–spin interaction between the hadronic constituents, is constructed by embedding superconformal quantum mechanics into AdS space. A specific breaking of conformal symmetry inside the graded algebra determines a unique effective quark-confining potential for light hadrons, as well as remarkable connections between the meson and baryon spectra. The results are consistent with the empirical features of the light-quark hadron spectra, including a universal mass scale for the slopes of the meson and baryon Regge trajectories and a zero-mass pion in the limit of massless quarks. Ourmore » analysis is consistently applied to the excitation spectra of the π , ρ , K , K* and Φ meson families as well as to the N , Δ, Λ, Σ, Σ* , Ξ and Ξ* in the baryon sector. Here, we also predict the existence of tetraquarks which are degenerate in mass with baryons with the same angular momentum. The mass of light hadrons is expressed in a universal and frame-independent decomposition in the semiclassical approximation described here.« less
Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type
NASA Astrophysics Data System (ADS)
Khongsap, Ta; Wang, Weiqiang
2009-01-01
We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group W and two skew-polynomial subalgebras of anticommuting generators. This algebra is shown to be Morita equivalent to another new DaHa which are generated by W and two polynomial-Clifford subalgebras. There is yet a third algebra containing a spin Weyl group algebra which is Morita (super)equivalent to the above two algebras. We establish the PBW properties and construct Verma-type representations via Dunkl operators for these algebras.
2003-06-03
The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran codemore » is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.« less
Single axioms for Boolean algebra.
McCune, W.
2000-06-30
Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.
The algebras of large N matrix mechanics
Halpern, M.B.; Schwartz, C.
1999-09-16
Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
Alternative algebraic approaches in quantum chemistry
Mezey, Paul G.
2015-01-22
Various algebraic approaches of quantum chemistry all follow a common principle: the fundamental properties and interrelations providing the most essential features of a quantum chemical representation of a molecule or a chemical process, such as a reaction, can always be described by algebraic methods. Whereas such algebraic methods often provide precise, even numerical answers, nevertheless their main role is to give a framework that can be elaborated and converted into computational methods by involving alternative mathematical techniques, subject to the constraints and directions provided by algebra. In general, algebra describes sets of interrelations, often phrased in terms of algebraic operations, without much concern with the actual entities exhibiting these interrelations. However, in many instances, the very realizations of two, seemingly unrelated algebraic structures by actual quantum chemical entities or properties play additional roles, and unexpected connections between different algebraic structures are often giving new insight. Here we shall be concerned with two alternative algebraic structures: the fundamental group of reaction mechanisms, based on the energy-dependent topology of potential energy surfaces, and the interrelations among point symmetry groups for various distorted nuclear arrangements of molecules. These two, distinct algebraic structures provide interesting interrelations, which can be exploited in actual studies of molecular conformational and reaction processes. Two relevant theorems will be discussed.
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
NASA Technical Reports Server (NTRS)
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
ERIC Educational Resources Information Center
Nevada State Dept. of Education, Carson City.
These standards offer a vision of excellence for K-12 foreign language education in Nevada. They are designed to provide guidance for school districts as they develop high quality foreign language programs through Nevada schools. The standards are benchmarked for the following grades: kindergarten, 3rd, 5th, 8th, 9th, 10th, and 12th. For each…
Secondary Schools Curriculum Guide, Mathematics, Grades 10-12. Revised.
ERIC Educational Resources Information Center
Cranston School Dept., RI.
Behavioral objectives for grades 10 through 12 are specified for plane geometry, algebra, general mathematics, computer mathematics, slide rule mathematics, basic college mathematics, trigonometry, analytic geometry, calculus and probability. Most sections present material in terms of portions of a school year. At least one major objective is…
Walendziak, Andrzej
2015-01-01
The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050
Algebra: A Challenge at the Crossroads of Policy and Practice
ERIC Educational Resources Information Center
Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.
2011-01-01
The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…
Coverings of topological semi-abelian algebras
NASA Astrophysics Data System (ADS)
Mucuk, Osman; Demir, Serap
2016-08-01
In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.
Stability of algebraically unstable dispersive flows
NASA Astrophysics Data System (ADS)
King, Kristina; Zaretzky, Paula; Weinstein, Steven; Cromer, Michael; Barlow, Nathaniel
2015-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to a class of partial differential equations describing wave propagation in dispersive media. There are several morphological differences between algebraically growing disturbances and the exponentially growing wave packets inherent to classical linear stability analysis, and these are elucidated in this study.
Explicit travelling waves and invariant algebraic curves
NASA Astrophysics Data System (ADS)
Gasull, Armengol; Giacomini, Hector
2015-06-01
We introduce a precise definition of algebraic travelling wave solution of n-th order partial differential equations and prove that the only algebraic travelling waves solutions for the celebrated Fisher-Kolmogorov equation are the ones found in 1979 by Ablowitz and Zeppetella. This question is equivalent to study when an associated one-parameter family of planar ordinary differential systems has invariant algebraic curves.
NASA Astrophysics Data System (ADS)
Manerowska, Anna; Nieznański, Edward; Mulawka, Jan
2013-10-01
Our aim is to present the algebra of concepts in two formal languages. First, after introducing a primary relation between concepts, which is subsumption, we shall specify in a language that uses quantifiers, the Boolean algebra of general concepts. Next, we shall note down the same algebra in simplified non-quantifying language, in order to use it as basis for two specific implementations, i.e. to create the Boolean algebras of deontic concepts and axiological concepts.
Factors associated with middle-school mathematics achievement in Greece: the case of algebra
NASA Astrophysics Data System (ADS)
Skouras, A. S.
2014-01-01
This study presents a subset of factors and their association with students' achievement in school algebra. The participants were students who had enrolled in 2007 at the ninth year of Greek public education (third year of middle school). A total of 735 students participated (aged 14-15 years) from 37 public secondary schools. The sample consisted of 378 girls (51.4%) and 357 boys (48.6%). A written algebra test and a questionnaire including demographic survey items were used to collect data. The results show that attitude towards mathematics (ATM) and the current teacher rating of mathematics performance were identified as the more significant predictors of algebra achievement, contributing by 18.1% and 24.7%, respectively, in total variance of mean at the end of ninth grade.
Higher gauge theories from Lie n-algebras and off-shell covariantization
NASA Astrophysics Data System (ADS)
Carow-Watamura, Ursula; Heller, Marc Andre; Ikeda, Noriaki; Kaneko, Yukio; Watamura, Satoshi
2016-07-01
We analyze higher gauge theories in various dimensions using a supergeometric method based on a differential graded symplectic manifold, called a QP-manifold, which is closely related to the BRST-BV formalism in gauge theories. Extensions of the Lie 2-algebra gauge structure are formulated within the Lie n-algebra induced by the QP-structure. We find that in 5 and 6 dimensions there are special extensions of the gauge algebra. In these cases, a restriction of the gauge symmetry by imposing constraints on the auxiliary gauge fields leads to a covariantized theory. As an example we show that we can obtain an off-shell covariantized higher gauge theory in 5 dimensions, which is similar to the one proposed in [1].
Representations of Super Yang-Mills Algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2013-06-01
We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149-158, 2002), and in fact they appear as a "background independent" formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras {{Cliff}q(k) ⊗ Ap(k)}, for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.
Multicloning and Multibroadcasting in Operator Algebras
NASA Astrophysics Data System (ADS)
Kaniowski, Krzysztof; Lubnauer, Katarzyna; Łuczak, Andrzej
2015-12-01
We investigate multicloning and multibroadcasting in the general operator algebra framework in arbitrary dimension, generalizing thus results obtained in this framework for simple cloning and broadcasting.