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…
Occupational Exploration at Ontario Junior High School: 9th Grade.
ERIC Educational Resources Information Center
Bates, Gene; And Others
The document contains 56 activities for Grade 9. The contents include the following areas: questions about the future; job seeking activities and guidelines; career games; a personal interest check list; unit guides for courses in World of Work (55 pages), and Career Educational Planning (40 pages) which include objectives, activities, evaluation,…
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…
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…
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…
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…
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…
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…
ERIC Educational Resources Information Center
Akbas, Yavuz; Gencturk, Ebru
2011-01-01
The aim of this study was to determine the effectiveness of teaching based on conceptual change overcome misconceptions of 9th grade high school students about the subject of air pressure. The sampling of the study was formed with two classes of 9th grade students from a general high school in the city-center of Trabzon. A quasi-experimental…
Problem-Based Learning in 9th Grade Chemistry Class: `Intermolecular Forces'
NASA Astrophysics Data System (ADS)
Tarhan, Leman; Ayar-Kayali, Hulya; Urek, Raziye Ozturk; Acar, Burcin
2008-05-01
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 9th grade students were stratified by cognitive levels and then randomly assigned to experimental (PBL, 40 students) and control (lecture-style teaching, 38 students) groups. Following a preparatory lesson where activation and remediation of existing knowledge occur, a pre-test was given, and no significant difference was found between the two groups of students ( p > .05). After the instruction was completed, a post-test and also a questionnaire related to the quality of the problem, the teacher’s role and group functioning were administered. Results from the post-test of both groups ( p < .05) and questionnaire showed that PBL is affective on students’ achievement, remedying formation of alternate conceptions and also social skills.
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…
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…
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).
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.
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
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…
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
Predicting Turkish Ninth Grade Students' Algebra Performance
ERIC Educational Resources Information Center
Erbas, Ayhan Kursat
2005-01-01
The prediction of students' achievement in algebra in eighth and ninth grades has become a research interest for practical issues of placement. A group of simple, easily accessible variables was used to predict student performance in algebra after completion of eighth grade. The three variables of school type, grade level, and previous year…
Juvenile Delinquency: Crime and Justice. Two 9th Grade Social Studies Units.
ERIC Educational Resources Information Center
Wisconsin State Dept. of Education, Madison.
Two social studies units, one on juvenile delinquency and one on crime and justice, are presented for the ninth grade level. The three-week juvenile delinquency unit focuses on special problems that minors face regarding the law. Students learn the difference between juvenile and adult courts and between status and delinquent offenses. In addition…
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…
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…
Growth: How Much is Too Much? Teacher's Guide. Science Module (9th-10th Grade Biology).
ERIC Educational Resources Information Center
Georgia Univ., Athens. Coll. of Education.
This is a teacher's guide for a learning module 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…
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…
Large - Small or Mini Group Instruction in English, 8th and 9th Grades.
ERIC Educational Resources Information Center
Barber, Herman W.
This curriculum guide describes courses and provides some sample lesson plans for an English program for eighth and ninth grade students. All of the students are required to take a basic writing course for the first nine weeks of the semester. For the next nine weeks some students receive large group instruction in linguistics and the other…
Orange County Academic Decathlon for 9th and 10th Grade Students. Handbook.
ERIC Educational Resources Information Center
Orange County Academic Decathalon Association, CA.
Orange County (California) students in grades 9 and 10 compete in an annually held series of 10 competitive events measuring academic strengths. These events include tests in grammar and literature, fine arts, mathematics, science, social science, study skills, and a super quiz--a team event held before a large audience. In addition, there are…
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
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.
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
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…
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
Mikow, Victoria A.
This survey examined the behaviors associated with the six leading causes of death or disability in one state's high school youth. Participants were 2,439 9th-12th grade students. Results identified alcohol as the drug most frequently used by high school students, with over half of students having used alcohol by their senior year and almost half…
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…
Remedial Math and College Algebra Grades.
ERIC Educational Resources Information Center
Head, L. Quinn
This investigation tried to determine if a statistically significant relationship exists between different sequences of enrollment in remedial mathematics and grades obtained in college algebra classes at Jacksonville State University. Groups consisting of five different enrollment sequences in mathematics were studied. The data collected supports…
Intrinsic and Extrinsic Work Values and Career Maturity of 9th- and 11th-Grade Boys and Girls.
ERIC Educational Resources Information Center
Post-Kammer, Phyllis
1987-01-01
Invesstigated relationships between intrinsic and extrinsic work values and career maturity for ninth- and eleventh-grade boys (N=402) and girls (N=483). Results revealed that sex differences in work values and career maturity were found to a greater extent than were grade differences. Implications for counselors are discussed. (Author/NB)
Remedial Math: Its Effect on the Final Grade in Algebra.
ERIC Educational Resources Information Center
Head, L. Quinn; Lindsey, Jimmy D.
1984-01-01
The effectiveness of one remedial mathematics technique is examined. Results indicated that students who passed remedial math and then took college algebra had significantly higher final algebra grades than did undergraduates who failed remedial math. (MLW)
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
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
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,…
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…
NASA Astrophysics Data System (ADS)
Purdy, Jill E.
This study determined the effects of Readers Theatre when used with ninth grade biology students. The independent variable was the intervention of Readers Theatre and the dependent variables were fluency (reading rate and prosody), composite (vocabulary and content) science scores and student motivation, using both quantitative and qualitative research methods. This study also examined the outcomes by gender, but only in the outcome variable of science composite score. An exploratory analysis examined class type (college preparatory and general) and PSSA reading level (below basic, basic, proficient and advanced) for each dependent variable. Four ninth grade college preparatory biology classrooms and three general biology classes participated. The students involved are from a suburban school district located in the eastern portion of Pennsylvania. Outcomes were analyzed separately by using an ANCOVA. Posttest scores were the dependent variable and pretest scores were the covariate. Using qualitative methodology, participants' questionnaire responses were analyzed to supplement quantitative results and to explore trends in motivation. Significant increases were found in words per minute and prosody in the area of prosody, general classes benefited to a larger extent than college preparatory classes. No significance was found in science composite, vocabulary or content test scores. Indications from students and teachers questionnaires were that Readers Theatre is a motivational technique. In this study, Readers Theater was proven to increase both fluency and prosody, while being motivating to the biology students.
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
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,…
Introduction to Algebra Curriculum Guide, Grade 8, 1987. Bulletin 1802.
ERIC Educational Resources Information Center
Louisiana State Dept. of Education, Baton Rouge. Div. of Academic Programs.
Because of the high incidence of failure in algebra I among ninth-grade students, the Louisiana State Board of Elementary and Secondary Education requested the development of this guide with the intention of providing a good pre-algebra foundation. The purposes of the guide are to recognize standards that involve the application of mathematical…
ERIC Educational Resources Information Center
Dean, Harvey R., Ed.
The document is a guide to a 9th and 10th grade industrial education course investigating the total system of power--how man controls, converts, transmits, and uses energy; the rationale is that if one is to learn of the total system of industry, the subsystem of power must be investigated. The guide provides a "body of knowledge" chart…
q-graded Heisenberg algebras and deformed supersymmetries
Ben Geloun, Joseph; Hounkonnou, Mahouton Norbert
2010-02-15
The notion of q-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for q complex number in the unit disk. Within this formulation, we consider the extension of the notion of supersymmetry in the enveloping algebra. We recover the ordinary Z{sub 2} grading or Grassmann parity for associative superalgebra and a modified version of the usual supersymmetry. As a specific problem, we focus on the interesting limit q{yields}-1 for which the Arik and Coon deformation [J. Math. Phys. 17, 524 (1976)] of the Heisenberg algebra allows one to map fermionic modes to bosonic ones in a modified sense. Different algebraic consequences are discussed.
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
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
Prospective Middle Grade Mathematics Teachers' Knowledge of Algebra for Teaching
ERIC Educational Resources Information Center
Huang, Rongjin; Kulm, Gerald
2012-01-01
This study examined prospective middle grade mathematics teachers' knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It…
Algebra for All: California’s Eighth-Grade Algebra Initiative as Constrained Curricula
Domina, Thurston; Penner, Andrew M.; Penner, Emily K.; Conley, Annemarie
2015-01-01
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 offerings and placing more students into Algebra I. This paper provides a quantitative single-case research study of policy-driven curricular intensification in one California school district. Research Questions (1a) What effect did 8th eighth grade curricular intensification have on mathematics course enrollment patterns in Towering Pines Unified schools? (2b) How did the distribution of prior achievement in Towering Pines math classrooms change as the district constrained the curriculum by universalizing 8th eighth grade Algebra? (3c) Did 8th eighth grade curricular intensification improve students’ mathematics achievement? Setting Towering Pines is an immigrant enclave in the inner-ring suburbs of a major metropolitan area. The district’s 10 middle schools together enroll approximately 4,000 eighth graders each year. The districts’ students are ethnically diverse and largely economically disadvantaged. The study draws upon administrative data describing 8th eighth graders in the district in the 2004–20-05 through 2007–20-08 school years. Intervention/Program/Practice During the study period, Towering Pines dramatically intensified middle school students’ math curricula: In the 2004–20-05 school year 32% of the district’s 8th eighth graders enrolled in Algebra or a higher- level mathematics course; by the 2007–20-08 school year that proportion had increased to 84%. Research Design We use an interrupted time-series design, comparing students’ 8th eighth grade math course enrollments, 10th grade math course enrollments, and 10th grade math test scores across the four cohorts, controlling for demographics and
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…
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
Kirby, Mary C.
Sustained Silent Reading (SSR) has been around in various forms for over 40 years. While this subject has received much study in elementary schools, the influence of SSR on typical, non-at-risk high school students' reading habits appears to be lacking. The purpose of this study is to examine the effect of SSR on ninth grade students' recreational…
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…
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…
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
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…
The 9th INS scientific computational programs
NASA Astrophysics Data System (ADS)
1993-06-01
Twelve groups were accepted as the 9-th INS scientific Computational Programs (ISCP). This ISCP can use full resources of the INS central computer without an operational limitation. The 9-th ISCP started on June/1/92 and ended on March/30/93. Some results were already published in journals or appeared in physical meetings. This is a sum of the used statistics of the 9-th ISCP and reports presented by groups at the 9-th ISCP.
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.
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. …
Underprepared Students' Performance on Algebra in a Double-Period High School Mathematics Program
ERIC Educational Resources Information Center
Martinez, Mara V.; Bragelman, John; Stoelinga, Timothy
2016-01-01
The primary goal of the Intensified Algebra I (IA) program is to enable mathematically underprepared students to successfully complete Algebra I in 9th grade and stay on track to meet increasingly rigorous high school mathematics graduation requirements. The program was designed to bring a range of both cognitive and non-cognitive supports to bear…
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
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…
ERIC Educational Resources Information Center
Spahr, Anthony E.
A study was undertaken at Morton College, in Illinois, to examine the relationship of entering grade point average (GPA) and grades in prerequisite support courses in algebra, biology, and chemistry to graduation in the college's nursing program. A sample was developed of 255 students admitted to the nursing program in 1990, 1991, and 1992 and…
Cooperative learning and algebra performance of eighth grade students in United Arab Emirates.
Alkhateeb, Haitham M; Jumaa, Mustafa
2002-02-01
This study investigated the effect of cooperative learning on eighth grade students' performance in algebra. 54 boys and 57 girls in four middle-school mathematics classes of Grade 8 in the UAE participated. Over a 3-wk. period, two classes (57 students) were taught using a cooperative learning method, and the other two classes (54 students) were taught using the traditional lecture method. Analysis of covariance using pretest scores as a covariant showed no statistically significant increase in the algebra performance for students in the cooperative learning groups compared with the traditional groups. However, boys in the cooperative setting improved significantly on the performance test compared with boys in the traditional setting.
Access to Algebra I: The Effects of Online Mathematics for Grade 8 Students. NCEE 2012-4021
ERIC Educational Resources Information Center
Heppen, Jessica B.; Walters, Kirk; Clements, Margaret; Faria, Ann-Marie; Tobey, Cheryl; Sorensen, Nicholas; Culp, Katherine
2011-01-01
This report presents findings from a randomized control trial designed to inform the decisions of policymakers who are considering using online courses to provide access to Algebra I in grade 8. It focuses on students judged by their schools to be ready to take Algebra I in grade 8 but who attend schools that do not offer the course. The study…
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…
Exploration of the Learning Expectations Related to Grades 1-8 Algebra in Some Countries
ERIC Educational Resources Information Center
Chen, Jung-chih; Cai, Wang-ting
2009-01-01
This study analyzes the learning expectations related to grades 1-8 algebra across several U.S. states and high performing TIMSS Asian countries and regions, including Singapore, Taiwan and Japan. In order to narrow and focus the investigation, only one topic within the strand is carefully reported. Based on the official curriculum documents,…
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…
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
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.…
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…
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
Voloshin, Dmitriy
2009-01-01
This study investigates the effects of Cognitive Tutor Bridge to Algebra (CTBA), a computer-assisted, remedial Algebra I curriculum, on mathematics performance and mathematics attitudes of ninth-grade students (n = 177) including English Learners (n = 78) and Economically Disadvantaged students (n = 93). A total of 95 students participated in CTBA…
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…
Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra
NASA Astrophysics Data System (ADS)
Bergamin, Luzi; Kummer, Wolfgang
2003-05-01
Supergravity extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. On the other hand, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to supergravity algebras (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them - like the one linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint without deformation - we are able not only to remove the ambiguities but, at the same time, the singularities referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.
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 Hopf algebra structure of the h-deformed Z3-graded quantum supergroup GLh,j(1|1)
NASA Astrophysics Data System (ADS)
Yasar, Ergün
2016-07-01
In this work, we define a new proper singular g matrix to construct a Z3-graded calculus on the h-deformed quantum superplane. Using the obtained calculus, we construct a new h-deformed Z3-graded quantum supergroup and give some features of it. Finally, we build up the Hopf algebra structure of this supergroup.
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…
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…
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…
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.
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.
The use of WIKIs in 9^th grade Physics
NASA Astrophysics Data System (ADS)
Lohstreter, Pete; Wyatt, Rachel; Taylor, Richard
2009-04-01
With the introduction of our laptop computer program several years ago, we have been charged with finding more ways to introduce technology into the classroom. It seemed only logical to incorporate the WIKIPEDIA philosophy in our Physics classes. Students are required to make entries to the WIKI on a regular basis. The documents become a storehouse of cumulative knowledge produced by all students and accessible to all students. Example WIKIs will be shown and suggestions on how to incorporate a WIKI into your classroom will be given.
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…
A "Humanities" Approach to 9th Grade Social Studies.
ERIC Educational Resources Information Center
Arnold, William
1979-01-01
Describes an integrated language arts and social studies program designed to consider man as a totality and to promote empathy in students for six different cultural areas in Asia and Africa. Literature, art, music, and writing exercises are listed. Activities include slide shows, cooking a Chinese meal, and a speech by an Indian woman and her…
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…
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.…
Program To Increase Selected 9th and 10th Graders' Career Decision-Making Skills.
ERIC Educational Resources Information Center
Lee, Linda D.
This study addresses some of the career decision challenges facing 9th- and 10th-grade students. The researcher discovered that many students possessed inadequate decision-making strategies, that counselors did not focus on career planning prior to and during registration, and that the school district lacked a comprehensive career guidance…
ERIC Educational Resources Information Center
Ketterlin-Geller, Leanne R.; Chard, David J.
2011-01-01
Developing proficiency in algebra is the focus of instruction in high school mathematics courses and is a minimum expectation for high school completion for all students including those with learning difficulties. However, the foundation for success is laid in grades 4-8 (aged 9-14). In this paper, we assert that students' development of algebraic…
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
Schrecongost, Jonette
This study analyzed the criteria used in Harrison County, WV, to select students to participate in an accelerated mathematics program. The program's main component is an eighth grade Algebra I course that enables the students to complete five years of college preparatory mathematics, ending with calculus. The scores used as selection criteria,…
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…
ERIC Educational Resources Information Center
Ndum, Edwin; Allen, Jeff; Fisher, Teri
2012-01-01
We assessed the relationship of level of QualityCore[R] implementation and student achievement in Algebra I. The study is based on 1,291 9th grade students in three large metropolitan school districts who took EXPLORE in the fall and the QualityCore Algebra I end-of-course assessment (EOC) in the spring. During the same period, the students' 41…
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%…
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…
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…
9th International Conference on Dense Z-Pinches
Bott-Suzuki, Simon
2015-08-31
DOE OFES supported the 9th International Conference on Z-Pinches (DZP 2014) held in Napa, CA in August 2014. Funds were used to support travel for several US students, and to disseminate information through the publication of a proceedings volume.
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…
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.
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
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…
ERIC Educational Resources Information Center
Rickles, Jordan H.
2011-01-01
This study seeks to demonstrate a method for treatment effect estimation in a multisite observational study where the treatment is highly selective and the assignment mechanism varies across sites. The method is demonstrated by addressing three primary research questions about the effect of 8th grade algebra: (1) For students who take algebra in…
Rickles, Jordan H
2011-10-01
Many inquiries regarding the causal effects of policies or programs are based on research designs where the treatment assignment process is unknown, and thus valid inferences depend on tenuous assumptions about the assignment mechanism. This article draws attention to the importance of understanding the assignment mechanism in policy and program evaluation studies, and illustrates how information collected through interviews can develop a richer understanding of the assignment mechanism. Focusing on the issue of student assignment to algebra in 8th grade, I show how a preliminary data collection effort aimed at understanding the assignment mechanism is particularly beneficial in multisite observational studies in education. The findings, based on ten interviews and administrative data from a large school district, draw attention to the often ignored heterogeneity in the assignment mechanism across schools. These findings likely extend beyond the current research project in question to related educational policy issues such as ability grouping, tracking, differential course taking, and curricular intensity, as well as other social programs in which the assignment mechanism can differ across sites.
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.
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
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.
Survey of Oral Health Awareness in Neuchâtel 9th Graders.
Neuhaus, Klaus W; Müller, Magali E; Lussi, Adrian
2016-01-01
The oral health habits of pupils had not yet been analyzed for the canton of Neuchâtel. A questionnaire was provided to 9th grade high school pupils (final year) of the three schools located in the Neuchâtel area to asses both oral health knowledge and habits in this connection. The average age was 15.5±0.8 years, and 78.1% of the questionnaires were returned. The prophylaxis program was conducted for a total of 4.5 h during pupils entire time at school. The results showed that both knowledge and oral health habits could be improved. As a positive outcome, 99% of the pupils brush their teeth before going to bed. Comparisons with similar 10-year-old studies from other cantons (Bern, Vaud) showed major differences in knowledge, for example on the importance of fluoridation. Only 54% of the pupils in Neuchâtel knew that fluoride offers some protection against caries, in spite of the fact that 89% thought that brushing with fluoridated toothpaste protects against caries. Most of the pupils used a fluoridated toothpaste. Furthermore, we found that self-reported sugar consumption was correlated with caries experience, but brushing frequency was not. We recommend introducing a review course for pupils in their last school year, in order to practice interdental cleaning, redefine appropriate, tooth-friendly snacks, and emphasize the importance of regular dental check-ups. PMID:27622326
ERIC Educational Resources Information Center
O'Brien, Judith A.; Tracy, Dyanne M.
In the United States female and male students supposedly have the same educational opportunities. Females continue to score below male students on the mathematics portions of standardized tests and less frequently choose mathematics-oriented careers. In this experimental study (n=95), 47 first-year algebra students participated in a month-long…
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
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
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…
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…
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…
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)…
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…
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
2. Closeup of first floor of 9th Street facade. The ...
2. Close-up of first floor of 9th Street facade. The original first floor arches are visible above the present restaurant front. - Ferree Building, 417 Ninth Street, Northwest, Washington, District of Columbia, DC
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.
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
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…
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.
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...
ERIC Educational Resources Information Center
Lieberman, Gerald A.; Hoody, Linda L.
This document reports on the 9th seminar of the State Education and Environment Roundtable (SEER). It consists of brief overviews of the daily discussions and presentations that were made at the seminar. Topics discussed include connecting service learning and the Environment as an Integrated Context for learning (EIC), and reports from states on…
ERIC Educational Resources Information Center
1997
Astro Algebra is one of six titles in the Mighty Math Series from Edmark, a comprehensive line of math software for students from kindergarten through ninth grade. Many of the activities in Astro Algebra contain a unique technology that uses the computer to help students make the connection between concrete and abstract mathematics. This software…
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…
ERIC Educational Resources Information Center
Pavelle, Richard; And Others
1981-01-01
Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)
37. Mass meeting held July 9th, 1918, in warehouse no.2 ...
37. Mass meeting held July 9th, 1918, in warehouse no.2 on the Fleet Supply Base, Brooklyn, New York col Americo Pio is speaking in Italian. View depicts one of the activities mounted by Turner Construction Company to stimulates labor enthusiasm during its 1918 construction projects for the U.S. Navy and U.s. Army. - U.S. Navy Fleet Supply Base, Storehouse No. 1, 830 Third Avenue, Brooklyn, Kings County, NY
NASA Astrophysics Data System (ADS)
SAME ADDRESS--> Nader Sadeghi,
Summary of the 9th annual meeting of the Italian Society for Virology.
Salata, Cristiano; Calistri, Arianna; Parolin, Cristina; Palù, Giorgio
2011-01-01
The 9th annual meeting of the Italian Society for Virology (SIV) comprised seven plenary sessions focused on: General virology and viral genetics; Virus-Host interaction and pathogenesis; Viral oncology; Emerging viruses and zoonotic, foodborne, and environmental pathways of transmission; Viral immunology and vaccines; Medical virology and antiviral therapy; Viral biotechnologies and gene therapy. Moreover, four hot topics were discussed in special lectures: the Pioneer in human virology lecture regarding the control of viral epidemics with particular emphasis on the human immunodeficiency virus (HIV), the Pioneer in plant virology lecture focused on cell responses to plant virus infection, a Keynote lecture on the epidemiology and genetic diversity of Crimea-Congo Hemorrhagic Fever virus, and the G.B. Rossi lecture on the molecular basis and clinical implications of human cytomegalovirus tropism for endothelial/epithelial cells. The meeting had an attendance of about 160 virologists. A summary of the plenary lectures and oral selected presentations is reported.
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)…
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…
Using Students' Interests as Algebraic Models
ERIC Educational Resources Information Center
Whaley, Kenneth A.
2012-01-01
Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…
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…
How To Prepare Students for Algebra.
ERIC Educational Resources Information Center
Wu, H.
2001-01-01
Suggests that no matter how much algebraic thinking is introduced in the early grades, and no matter how worthwhile this might be, the failure rate in algebra will continue unless the teaching of fractions and decimals is radically revamped. The proper study of fractions provides a ramp that leads students gently from whole number arithmetic up to…
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
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
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…
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 Algebra Initiative Colloquium. Volume 2: Working Group Papers.
ERIC Educational Resources Information Center
Lacampagne, Carole B., Ed.; And Others
This volume presents recommendations from four working groups at a conference on reform in algebra held in Leesburg, Virginia, December 9-12, 1993. Working Group 1: Creating an Appropriate Algebra Experience for All Grades K-12 Students produced the following papers: (1) "Report" (A. H. Schoenfeld); (2) "Five Questions About Algebra Reform (and a…
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
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…
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
Global perspectives on poisonous plants: the 9th international symposium on poisonous plants.
Molyneux, Russell J; Panter, Kip E; Zhao, Mengli
2014-07-30
The 9th International Symposium on Poisonous Plants (ISOPP9) was held July 15-21, 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 Xilinhot Region of the Mongolian Grasslands, encompassing grazing conditions consisting of desert, grassland, and steppes. This was the first time that an ISOPP meeting has been held in Asia and provided an opportunity for visitors from outside China to become aware of livestock poisonings caused by plant species with which they were previously not familiar while at the same time demonstrating that many of the problems experienced around the world have a common etiology. Presentations focused on botany, veterinary science, toxicology, mechanism of action, and chemistry. As is appropriate for the Journal of Agricultural and Food Chemistry, this cluster of papers consists of selected oral and poster presentations in which the chemistry of the toxins played a significant role. The symposium revealed that there is considerable scope for isolation, structural elucidation, and analysis of the toxins from the numerous poisonous plant species that have been identified in China. It became apparent that there are abundant opportunities for chemists both within China and abroad to collaborate with Chinese scientists working on biological aspects of livestock poisonings.
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.
9th Circuit says engaging in sex is a major life activity under ADA.
1999-10-01
The 9th U.S. Circuit Court of Appeals ruled that the ability to engage in sexual relations is a major life activity under the definition of the Americans with Disabilities Act (ADA). The ruling suggests that all adults and adolescents infected with HIV are covered by the ADA because of the risk of transmitting the virus sexually. The U.S. Supreme Court ruled last year in the [name removed] v. [Name removed] case that the ability to procreate is a major life activity, but it left unresolved the issue of whether sexual relations were covered. Several other courts have further defined the issue and ruled that sexual dysfunction should count as a disability. The plaintiff in this case sued after his employer refused to relocate him to a different department, stating he was deprived of a reasonable accommodation. The plaintiff suffered from impotence, and claimed a disability under the ADA. The dissenting judge in the ruling noted that he did not see how one's ability to have sexual relations had any connection to employment. PMID:11367019
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…
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
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…
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…
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
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…
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…
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…
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
NASA Technical Reports Server (NTRS)
Ruge, J. W.; Stueben, K.
1987-01-01
The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.
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.
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.
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…
NASA Astrophysics Data System (ADS)
Vaninsky, Alexander
2011-04-01
This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.
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.
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.
Peer & Parent Encouragement of Early Algebra Enrollment & Mathematics Achievement
ERIC Educational Resources Information Center
Filer, Kimberly L.; Chang, Mido
2008-01-01
Using data from the National Education Longitudinal Study of 1988 (NELS:88), path analytic procedures were performed to test a model of the effects of parent and peer encouragement to take algebra on the mathematics achievement of eighth grade students. The effects of socio-economic status (SES) on middle school algebra course-taking and…
Algebraic Concepts: What's Really New in New Curricula?
ERIC Educational Resources Information Center
Star, Jon R.; Herbel-Eisenmann, Beth A.; Smith, John P., III
2000-01-01
Examines 8th grade units from the Connected Mathematics Project (CMP). Identifies differences in older and newer conceptions, fundamental objects of study, typical problems, and typical solution methods in algebra. Also discusses where the issue of what is new in algebra is relevant to many other innovative middle school curricula. (KHR)
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…
Numerical algebraic geometry and algebraic kinematics
NASA Astrophysics Data System (ADS)
Wampler, Charles W.; Sommese, Andrew J.
In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.
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…
ERIC Educational Resources Information Center
Mowsesian, Richard; Liberty, Paul G., Jr.
A modified version of Super's Work Values Inventory (WVI) was administered to third and fifth grade students in a medium-size industrial community. The original WVI was administered to 9th and 11th grade students in the same community. Internal consistency coefficients, construct validity and ordering of work values are reported by grade and sex.…
Neutron Diffraction Study On Gamma To Alpha Phase Transition In Ce0.9th0.1 Alloy
Lashley, Jason C1; Heffner, Robert H; Llobet, A; Darling, T W; Jeong, I K
2008-01-01
Comprehensive neutron diffraction measurements were performed to study the isostructural {gamma} {leftrightarrow} {alpha} phase transition in Ce{sub 0.9}Th{sub 0.1} alloy. Using Rietveld refinements, we obtained lattice and thermal parameters as a function of temperature. From the temperature slope of the thermal parameters, we determined Debye temperatures {Theta}{sup {gamma}}{sub D} = 133(1) K and {Theta}{sup {alpha}}{sub D} = 140(1) K for the {gamma} phase and the {alpha} phase, respectively. This result implies that the vibrational entropy change is not significant at the {gamma} {leftrightarrow} {alpha} transition, contrary to that from elemental Cerium [Phys. Rev. Lett. 92, 105702, 2004].
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"…
Quantization of Algebraic Reduction
Sniatycki, Jeodrzej
2007-11-14
For a Poisson algebra obtained by algebraic reduction of symmetries of a quantizable system we develop an analogue of geometric quantization based on the quantization structure of the original system.
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…
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.
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…
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…
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…
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.
Discrete Minimal Surface Algebras
NASA Astrophysics Data System (ADS)
Arnlind, Joakim; Hoppe, Jens
2010-05-01
We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
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
Mortasawi, A; Ennker, I C; Albert, A; Rosendahl, U; Dalladaku, F; Alexander, T; Ennker, J
1999-04-01
The rate of the population being 80 years of age and even older, has an increasing tendency in the Federal Republic of Germany. In 1996, a total of 87,372 patients received surgery supported by the heart-lung-machine, 2,383 patients out of these (2.7%) were 80 years of age and older. In view of the limited life expectance, the arterial revascularization in this age category is faced with controverse discussions. We analysed our patients in relation to this aspect. Between January 1, 1995 and June 30, 1997, 4,338 patients underwent surgery supported by the heart-lung-machine. Hundred and fifty-five out of these (3.6%) were in the 9th decade of life. Seventy-seven patients out of the 155 (49.7%, 34 women, 43 men, 80 to 88 years old, mean: 82 years of age) underwent an isolated myocardial revascularization. We performed 55 (71%) elective, 16 (21%) urgent and 6 (8%) emergency surgeries. Twelve patients (15.6%) solely received venous bypasses (Group I), 65 (84.4%) additionally also received unilateral bypasses of the internal mammaria artery (IMA) (Group II). Three patients died at our facility (3.9%), 3 further patients died during the follow-up treatment in outlying hospitals, the in-patient mortality rate in Group I therefore presented a rate of 8.3%, in Group II 7.7% and in total, a rate of 7.8%. In 1996, the in-patient mortality rate could be reduced to 3.6%. The follow-up observation time ranged between 7 and 138 weeks (median 44 weeks). The survival rate for patients with an IMA-bypass after 1 year was 86.3%, after 2 years 77%, and for the entire collective 85.3% and 75%. Whereas 96% of the patients could pre-operatively be related to Class III or IV of the NYHA-classification, 55 of the 63 survivors (87%) belonged to Class I (6%) or II (81%). Two Group I patients (22.2%), 3 Group II patients (5.6%) and 7.9% of the total collective complained about repeated angina symptoms. The myocardial revascularization with the internal mammaria artery performed on patients
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.
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
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
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…
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
Craven, Diane
Proceedings of the Pacific Region Educational Laboratory's (PREL) 9th Annual Pacific Educational Conference, held August 3-5, 1992, in Pago Pago, American Samoa are evaluated in this document. Data were collected from an overall conference evaluation survey, individual workshop surveys, workshop program information, anecdotal information, and…
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
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…
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…
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.
Algebraic Reasoning through Patterns
ERIC Educational Resources Information Center
Rivera, F. D.; Becker, Joanne Rossi
2009-01-01
This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…
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 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
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…
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…
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.
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
NASA Astrophysics Data System (ADS)
Smirnov, Andrey
2010-08-01
New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl( N;?)-case is discussed.
NASA Astrophysics Data System (ADS)
Smirnov, Andrey
2010-08-01
New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.
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)
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.
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.
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.
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…
The Aftermath of Accelerating Algebra: Evidence from a District Policy Initiative. Working Paper 69
ERIC Educational Resources Information Center
Clotfelter, Charles T.; Ladd, Helen F.; Vigdor, Jacob L.
2012-01-01
In 2002/03, the Charlotte-Mecklenburg Schools initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking 8th grade algebra increased from less than half to nearly 90%, then reverted to baseline levels, in the span of just six age cohorts. We use this policy-induced variation to…
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
Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Hamlett, Carol L.; Seethaler, Pamela M.
2011-01-01
The purpose of this study was to explore the utility of a dynamic assessment (DA) of algebraic learning in predicting third graders' development of mathematics word-problem difficulty. In the fall, 122 third-grade students were assessed on a test of math word-problem skill and DA of algebraic learning. In the spring, they were assessed on…
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
Jensen, Jennifer
2014-01-01
This study sought to determine if there is a relationship between students' scores on the eighth-grade Indiana State Test of Education Progress Plus (ISTEP+) exam and success on Indiana's Algebra End-of-Course Assessment (ECA). Additionally, it sought to determine if algebra success could be significantly predicted by the achievement in one or…
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…
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.
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.
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…
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.
On Twisting Real Spectral Triples by Algebra Automorphisms
NASA Astrophysics Data System (ADS)
Landi, Giovanni; Martinetti, Pierre
2016-08-01
We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things, we investigate consequences of the twisting on the fluctuations of the metric and possible applications to the spectral approach to the Standard Model of particle physics.
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…
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…
Structure Sense in High School Algebra: The Effect of Brackets
ERIC Educational Resources Information Center
Hoch, Maureen; Dreyfus, Tommy
2005-01-01
This paper presents an initial attempt to define structure sense for high school algebra and to test part of this definition. A questionnaire was distributed to 92 eleventh grade students in order to identify those who use structure sense. Presence and absence of brackets was examined to see how they affect use of structure sense. The overall use…
On Twisting Real Spectral Triples by Algebra Automorphisms
NASA Astrophysics Data System (ADS)
Landi, Giovanni; Martinetti, Pierre
2016-11-01
We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things, we investigate consequences of the twisting on the fluctuations of the metric and possible applications to the spectral approach to the Standard Model of particle physics.
The Fostering Algebraic Thinking Toolkit: A Guide for Staff Development.
ERIC Educational Resources Information Center
Driscoll, Mark; Zawojeski, Judith; Humez, Andrea; Nikula, Johannah; Goldsmith, Lynn; Hammerman, James
This toolkit contains a set of professional development materials whose goal is to help mathematics teachers in grades 6-10 learn to identify, describe, and foster algebraic thinking in their students. A core belief underlying the Toolkit is that good mathematics teaching begins with understanding how mathematics is learned, so these materials…
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…
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…
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.
Algebra for Gifted Third Graders.
ERIC Educational Resources Information Center
Borenson, Henry
1987-01-01
Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)
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,…
Pseudo Algebraically Closed Extensions
NASA Astrophysics Data System (ADS)
Bary-Soroker, Lior
2009-07-01
This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.
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…
Tütken, Thomas; Langenegger, Elisabeth; Wild, Werner
2008-03-01
At Elsau near Winterthur (CH), a 9th century AD grave with a female skeleton was found in 2003. This grave was reopened one to six years after burial. After manipulating the partially decayed skeleton, the grave was filled with a layer of rocks and a claw of a sea eagle as well as the paw of a fox was placed on top. At least from this time onwards, the grave was situated in the annex of a church. Because of this special burial site for the 42 year old woman, who suffered from different severe illnesses, it is thought that she belonged to the upper class. The postmortal changes at the grave are exceptional and even after thorough research, no equivalent burial procedures are known from this area. To investigate the possibility if the woman migrated to the region of Elsau, the oxygen and strontium isotope composition of several teeth and one long bone of her skeleton was analysed. The results indicate a certain but restricted mobility within the northern Alpine foreland and as a result changes of the isotope composition of the food and drinking water during her childhood. Immigration from regions in which similar burial customs to those used for the woman persisted into the 9th century AD can be largely excluded based on the isotope composition of her skeletal remains. The mobility in the pre-Alpine region supports the interpretation that the woman belonged to the upper class, whose properties where widely distributed.
ERIC Educational Resources Information Center
Benjamin, Carl; And Others
Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra II. Topics covered include: differencing and complements; real numbers; factoring; fractions; linear equations; exponents and radicals; complex numbers,…
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,…
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
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
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…
ERIC Educational Resources Information Center
Renchler, Ron
2000-01-01
This issue reviews grade span, or grade configuration. Catherine Paglin and Jennifer Fager's "Grade Configuration: Who Goes Where?" provides an overview of issues and concerns related to grade spans and supplies profiles of eight Northwest schools with varying grade spans. David F. Wihry, Theodore Coladarci, and Curtis Meadow's "Grade Span and…
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.
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.
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
Shorey, Ryan C; Fite, Paula J; Elkins, Sara R; Frissell, Kevin C; Tortolero, Susan R; Stuart, Gregory L; Temple, Jeff R
2013-12-01
Adolescents of parents who use substances are at an increased risk for substance use themselves. Both parental monitoring and closeness have been shown to mediate the relationship between parents' and their adolescents' substance use. However, we know little about whether these relationships vary across different substances used by adolescents. Using structural equation modeling, we examined these associations within a racially and ethnically diverse sample of 9th and 10th graders (N = 927). Path analyses indicated that maternal closeness partially mediated the association between maternal problematic substance use and adolescent alcohol use. Parental monitoring partially mediated the relationship between paternal problematic substance use and adolescent alcohol, cigarette, marijuana, inhalant, and illicit prescription drug use. These results were consistent across gender and race/ethnicity. These findings suggest that parental interventions designed to increase closeness and monitoring may help to reduce adolescent substance use.
Shorey, Ryan C.; Fite, Paula J.; Elkins, Sara R.; Frissell, Kevin C.; Tortolero, Susan R.; Stuart, Gregory L.; Temple, Jeff R.
2013-01-01
Adolescents of parents who use substances are at an increased risk for substance use themselves. Both parental monitoring and closeness have been shown to mediate the relationship between parents’ and their adolescents’ substance use. However, we know little about whether these relationships vary across different substances used by adolescents. Using structural equation modeling, we examined these associations within a racially and ethnically diverse sample of 9th and 10th graders (N = 927). Path analyses indicated that maternal closeness partially mediated the association between maternal problematic substance use and adolescent alcohol use. Parental monitoring partially mediated the relationship between paternal problematic substance use and adolescent alcohol, cigarette, marijuana, inhalant, and illicit prescription drug use. These results were consistent across gender and race/ethnicity. These findings suggest that parental interventions designed to increase closeness and monitoring may help to reduce adolescent substance use. PMID:24006209
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®,…
Lee, Jaehoon; Wilczek, Frank
2013-11-27
Motivated by the problem of identifying Majorana mode operators at junctions, we analyze a basic algebraic structure leading to a doubled spectrum. For general (nonlinear) interactions the emergent mode creation operator is highly nonlinear in the original effective mode operators, and therefore also in the underlying electron creation and destruction operators. This phenomenon could open up new possibilities for controlled dynamical manipulation of the modes. We briefly compare and contrast related issues in the Pfaffian quantum Hall state.
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.
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.
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…
ERIC Educational Resources Information Center
Hailer-O'Keefe, Laurie
2012-01-01
This paper examines the Algebra II course and California Star Test (CST) proficiency levels in the San Francisco Bay Area and in the State of California. CST proficiency levels are examined by grade level for the State and nine counties of the San Francisco Bay Area region. Algebra II is shown to be one of the more complicated courses in the CSU…
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…
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…
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…
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…
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…
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
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.
Second-Order Algebraic Theories
NASA Astrophysics Data System (ADS)
Fiore, Marcelo; Mahmoud, Ola
Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.
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…
9th Caribbean Geological Conference
NASA Astrophysics Data System (ADS)
Draper, Gren
The ninth in a series of Caribbean Geological Conferences, which are held every 3 or 4 years, took place in Santo Domingo, capital of the Dominican Republic, from the 15th to 26th of August 1980. The conference, which was sponsored by the government of the Dominican Republic and the Universidad Catolica Madre y Maestra, was preceded by 2 days of field trips and was opened by President Antonio Guzman on the evening of the 17th of August. Generous support was provided by Alcoa Exploration Co., Falconbridge Dominicana, and Rosario Dominicana.Geologists and geophysicists from 25 countries presented about 130 papers on a wide variety of topics ranging from geophysics to paleontology. While the whole Caribbean area was discussed, there was special emphasis on the northern Caribbean and Hispaniola, as befitted the site of the conference. The contribution of workers from the Dirección General de Mineriá was particularly notable.
2-Local derivations on matrix algebras over semi-prime Banach algebras and on AW*-algebras
NASA Astrophysics Data System (ADS)
Ayupov, Shavkat; Kudaybergenov, Karimbergen
2016-03-01
The paper is devoted to 2-local derivations on matrix algebras over unital semi-prime Banach algebras. For a unital semi-prime Banach algebra A with the inner derivation property we prove that any 2-local derivation on the algebra M 2n (A), n ≥ 2, is a derivation. We apply this result to AW*-algebras and show that any 2-local derivation on an arbitrary AW*-algebra is a derivation.
Plethystic algebras and vector symmetric functions.
Rota, G C; Stein, J A
1994-01-01
An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]). PMID:11607504
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…
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…
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…
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
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.)
Linear algebra and image processing
NASA Astrophysics Data System (ADS)
Allali, Mohamed
2010-09-01
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.
A Programmed Course in Algebra.
ERIC Educational Resources Information Center
Mewborn, Ancel C.; Hively, Wells II
This programed textbook consists of short sections of text interspersed with questions designed to aid the student in understanding the material. The course is designed to increase the student's understanding of some of the basic ideas of algebra. Some general experience and manipulative skill with respect to high school algebra is assumed.…
Gamow functionals on operator algebras
NASA Astrophysics Data System (ADS)
Castagnino, M.; Gadella, M.; Betán, R. Id; Laura, R.
2001-11-01
We obtain the precise form of two Gamow functionals representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing observables. These functionals do not admit normalization and, with an appropriate choice of the algebra, are time reversal of each other.
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.)
Patterns to Develop Algebraic Reasoning
ERIC Educational Resources Information Center
Stump, Sheryl L.
2011-01-01
What is the role of patterns in developing algebraic reasoning? This important question deserves thoughtful attention. In response, this article examines some differing views of algebraic reasoning, discusses a controversy regarding patterns, and describes how three types of patterns--in contextual problems, in growing geometric figures, and in…
Elementary maps on nest algebras
NASA Astrophysics Data System (ADS)
Li, Pengtong
2006-08-01
Let , be algebras and let , be maps. An elementary map of is an ordered pair (M,M*) such that for all , . In this paper, the general form of surjective elementary maps on standard subalgebras of nest algebras is described. In particular, such maps are automatically additive.
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…
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…
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.
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.
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
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
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
NASA Astrophysics Data System (ADS)
The 9th INTEGRAL workshop "An INTEGRAL view of the high-energy sky (the first 10 years)" took place from 15 to 19 October 2012 in Paris, Bibliothèque Nationale de France (Bibliothèque François Mitterrand). The workshop was sponsored by ESA, CNES and other French and European Institutions. During this week, and in particular on 17 October 2012, we celebrated the 10th anniversary of the launch of the INTEGRAL mission. The main goal of this workshop was to present and to discuss (via invited and contributed talks and posters) latest results obtained in the field of high-energy astrophysics using the International Gamma-Ray Astrophysics Laboratory INTEGRAL, as well as results from observations from other ground- and space-based high-energy observatories and from associated multi-wavelength campaigns. Contributions to the workshop covered the following scientific topics: - X-ray binaries (IGR sources, black holes, neutron stars, white dwarfs) - Isolated neutron stars (gamma-ray pulsars, magnetars) - Nucleo-synthesis (SNe, Novae, SNRs, ISM) and gamma-ray lines (511 keV) - Galactic diffuse continuum emission (including Galactic Ridge) - Massive black holes in AGNs, elliptical galaxies, nucleus of the Galaxy - Sky surveys, source populations and unidentified gamma-ray sources - Cosmic background radiation - Gamma-ray bursts - Coordinated observations with other ground- and space-based observatories - Science data processing and analysis (posters only) - Future instruments and missions (posters only)
Infinite rank Schrödinger-Virasoro type Lie conformal algebras
NASA Astrophysics Data System (ADS)
Fan, Guangzhe; Su, Yucai; Xia, Chunguang
2016-08-01
Motivated by the structure of certain modules over the loop Virasoro Lie conformal algebra and the Lie structures of Schrödinger-Virasoro algebras, we construct a class of infinite rank Lie conformal algebras CSV(a, b), where a, b are complex numbers. The conformal derivations of CSV(a, b) are uniformly determined. The rank one conformal modules and ℤ-graded free intermediate series modules over CSV(a, b) are classified. Corresponding results of the conformal subalgebra CHV(a, b) of CSV(a, b) are also presented.
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)
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.
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.
Constraint algebra in bigravity
NASA Astrophysics Data System (ADS)
Soloviev, V. O.
2015-07-01
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.
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.
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.
Readiness and Preparation for Beginning Algebra.
ERIC Educational Resources Information Center
Rotman, Jack W.
Drawing from experience at Lansing Community College (LCC), this paper discusses how to best prepare students for success in a beginning algebra course. First, an overview is presented of LCC's developmental math sequence, which includes Basic Arithmetic (MTH 008), Pre-Algebra (MTH 009), Beginning Algebra (MTH 012), and Intermediate Algebra (MTH…
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.
Two-parameter twisted quantum affine algebras
NASA Astrophysics Data System (ADS)
Jing, Naihuan; Zhang, Honglian
2016-09-01
We establish Drinfeld realization for the two-parameter twisted quantum affine algebras using a new method. The Hopf algebra structure for Drinfeld generators is given for both untwisted and twisted two-parameter quantum affine algebras, which include the quantum affine algebras as special cases.
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…
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…
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
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
Foltz, Ross
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…
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.
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)
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).
Sjaardema, G.; Gilkey, A.; Smith, M.; Forsythe, C.
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.
Algebraic Systems and Pushdown Automata
NASA Astrophysics Data System (ADS)
Petre, Ion; Salomaa, Arto
We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.
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.…
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.
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
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.
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
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…
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…
BRST charges for finite nonlinear algebras
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Krivonos, S. O.; Ogievetsky, O. V.
2010-07-01
Some ingredients of the BRST construction for quantum Lie algebras are applied to a wider class of quadratic algebras of constraints. We build the BRST charge for a quantum Lie algebra with three generators and ghost-anti-ghosts commuting with constraints. We consider a one-parametric family of quadratic algebras with three generators and show that the BRST charge acquires the conventional form after a redefinition of ghosts. The modified ghosts form a quadratic algebra. The family possesses a nonlinear involution, which implies the existence of two independent BRST charges for each algebra in the family. These BRST charges anticommute and form a double BRST complex.
Some Remarks on Kite Pseudo Effect Algebras
NASA Astrophysics Data System (ADS)
Dvurečenskij, Anatolij; Holland, W. Charles
2014-05-01
Recently a new family of pseudo effect algebras, called kite pseudo effect algebras, was introduced. Such an algebra starts with a po-group G, a set I and with two bijections λ, ρ: I→ I. Using a clever construction on the ordinal sum of ( G +) I and ( G -) I , we can define a pseudo effect algebra which can be non-commutative even if G is an Abelian po-group. In the paper we give a characterization of subdirect product of subdirectly irreducible kite pseudo effect algebras, and we show that every kite pseudo effect algebra is an interval in a unital po-loop.
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…
Operator product expansion algebra
Holland, Jan; Hollands, Stefan
2013-07-15
We establish conceptually important properties of the operator product expansion (OPE) in the context of perturbative, Euclidean φ{sup 4}-quantum field theory. First, we demonstrate, generalizing earlier results and techniques of hep-th/1105.3375, that the 3-point OPE,
Constructing a parasupersymmetric Virasoro algebra
NASA Astrophysics Data System (ADS)
Kuwata, S.
2011-03-01
We construct a para SUSY Virasoro algebra by generalizing the ordinary fermion in SUSY Virasoro algebra (Ramond or Neveu-Schwarz algebra) to the parafermion. First, we obtain a polynomial relation (PR) between different-mode parafermion fi's by generalizing the corresponding single-mode PR to such that is invariant under the unitary transformation of fi (Green's condition). Differently from a usual context, where the Green's condition is imposed only on the defining relation of fi (degree three with respect to fi and fi†), we impose it on any degree of PR. For the case of order-two parafermion (the simplest case of para SUSY), we calculate a PR between the parasupercharge G0, the bosonic hamiltonian LB0 and parafermionic one LF0, although it is difficult to obtain a PR between G0 and the total hamiltonian L0 (= LB0 + LF0). Finally, we construct a para SUSY Virasoro algebra by generalizing L0 to the Ln's such that form a Virasoro algebra.
ERIC Educational Resources Information Center
Williamson, Ronald
2012-01-01
Where to locate the 7th and 8th grade is a perennial question. While there are many variations, three approaches are most often used---include them in a 7-12 secondary campus, maintain a separate middle grades campus, or include them as part of a K-8 program. Research says that grade configuration is inconclusive at best and there is no research…
A Metric Conceptual Space Algebra
NASA Astrophysics Data System (ADS)
Adams, Benjamin; Raubal, Martin
The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.
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.
ERIC Educational Resources Information Center
Ramirez, Sonia; Siadat, M. Vali
2008-01-01
The purpose of this study is to identify factors that influence students' performance in the intermediate algebra classes at the college by analyzing parameters such as test scores, grades, attitude towards mathematics, time lapse between subsequent courses, placement, and teaching practices. This study will investigate the correlation of several…
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…
ERIC Educational Resources Information Center
Daher, Wajeeh M.; Anabousi, Anlam A.
2015-01-01
The topic of function transformations is a difficult mathematical topic for school and college students. This article examines how students conceive function transformations after working with GeoGebra, when this conceiving relates to the algebraic representation. The research participants were 19 ninth grade high achieving students who learned,…
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…
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…
ERIC Educational Resources Information Center
Walkington, Candace; Sherman, Milan; Petrosino, Anthony
2012-01-01
This study critically examines a key justification used by educational stakeholders for placing mathematics in context--the idea that contextualization provides students with access to mathematical ideas. We present interviews of 24 ninth grade students from a low-performing urban school solving algebra story problems, some of which were…
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…
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…
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…
Colored Quantum Algebra and Its Bethe State
NASA Astrophysics Data System (ADS)
Wang, Jin-Zheng; Jia, Xiao-Yu; Wang, Shi-Kun
2014-12-01
We investigate the colored Yang—Baxter equation. Based on a trigonometric solution of colored Yang—Baxter equation, we construct a colored quantum algebra. Moreover we discuss its algebraic Bethe ansatz state and highest wight representation.
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.
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.
Discrimination in a General Algebraic Setting.
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.
Discrimination in a General Algebraic Setting
Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis
2015-01-01
Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras. PMID:26171421
Characteristic Numbers of Matrix Lie Algebras
NASA Astrophysics Data System (ADS)
Zhang, Yu-Feng; Fan, En-Gui
2008-04-01
A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.
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.
Twining characters and orbit Lie algebras
Fuchs, Jurgen; Ray, Urmie; Schellekens, Bert; Schweigert, Christoph
1996-12-05
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary characters of some other generalized Kac-Moody algebra, the so-called orbit Lie algebra. Some applications to problems in conformal field theory, algebraic geometry and the theory of sporadic simple groups are sketched.
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.
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…
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…
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…
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…
Computer Algebra Systems, Pedagogy, and Epistemology
ERIC Educational Resources Information Center
Bosse, Michael J.; Nandakumar, N. R.
2004-01-01
The advent of powerful Computer Algebra Systems (CAS) continues to dramatically affect curricula, pedagogy, and epistemology in secondary and college algebra classrooms. However, epistemological and pedagogical research regarding the role and effectiveness of CAS in the learning of algebra lags behind. This paper investigates concerns regarding…
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"…
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
National Science Teachers Association, Washington, DC.
This instructional unit contains six classroom lessons in which 9th, 10th, or 11th grade social studies students examine the effects of competition among nations and world regions as demand for oil outstrips supply. The overall objective is to help students understand the concept that energy is a commodity to be bought and sold like any other…
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…
ERIC Educational Resources Information Center
Modin, Bitte; Ostberg, Viveca; Toivanen, Susanna; Sundell, Knut
2011-01-01
This study explores the psychosocial working conditions of 7930 Swedish 9th grade students, distributed over 475 classes and 130 schools, in relation to their subjective health using multilevel modeling. At the individual level, students with "strained" working conditions in school (i.e. those experiencing a high level of demands in combination…
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
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…
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.
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…
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…
Dimension independence in exterior algebra.
Hawrylycz, M
1995-01-01
The identities between homogeneous expressions in rank 1 vectors and rank n - 1 covectors in a Grassmann-Cayley algebra of rank n, in which one set occurs multilinearly, are shown to represent a set of dimension-independent identities. The theorem yields an infinite set of nontrivial geometric identities from a given identity. PMID:11607520
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…
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…
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.
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.
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…
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…
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…
ERIC Educational Resources Information Center
Deakin, Michael A. B.
1974-01-01
Euler's famous formula, e to the (i, pi) power equals -1, is developed by a purely algebraic method that avoids the use of both trigonometry and calculus. A heuristic outline is given followed by the rigorous theory. Pedagogical considerations for classroom presentation are suggested. (LS)
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…
Math for All Learners: Algebra.
ERIC Educational Resources Information Center
Meader, Pam; Storer, Judy
This book consists of a series of activities aimed at providing a problem solving, hands-on approach so that students can experience concepts in algebra. Topics include ratio and proportion, patterns and formulas, integers, polynomials, linear equations, graphs, and probability. The activities come in the form of reproducible blackline masters…
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…
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…
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
NASA Astrophysics Data System (ADS)
Kuipers, J.
2012-06-01
New features of the symbolic algebra package Form 4 are discussed. Most importantly, these features include polynomial factorization and polynomial gcd computation. Examples of their use are shown. One of them is an exact version of Mincer which gives answers in terms of rational polynomials and 5 master integrals.
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
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.
Formal scattering theory by an algebraic approach
NASA Astrophysics Data System (ADS)
Alhassid, Y.; Levine, R. D.
1985-02-01
Formal scattering theory is recast in a Lie-algebraic form. The central result is an algebraic Lippmann-Schwinger equation for the wave operator from which an algebraic form of the Born series (containing only linked terms) is obtained. When a finite Lie algebra is sufficient, The Mo/ller wave operator, on the energy shell, can be solved for explicitly as an element of the corresponding group. The method is illustrated for the separable potential whose relevant algebra is found to be U(1,1).
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
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.
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.
Linear algebra algorithms for divisors on an algebraic curve
NASA Astrophysics Data System (ADS)
Khuri-Makdisi, Kamal
We use an embedding of the symmetric $d$th power of any algebraic curve $C$ of genus $g$ into a Grassmannian space to give algorithms for working with divisors on $C$, using only linear algebra in vector spaces of dimension $O(g)$, and matrices of size $O(g^2)\\times O(g)$. When the base field $k$ is finite, or if $C$ has a rational point over $k$, these give algorithms for working on the Jacobian of $C$ that require $O(g^4)$ field operations, arising from the Gaussian elimination. Our point of view is strongly geometric, and our representation of points on the Jacobian is fairly simple to work with; in particular, none of our algorithms involves arithmetic with polynomials. We note that our algorithms have the same asymptotic complexity for general curves as the more algebraic algorithms in Hess' 1999 Ph.D. thesis, which works with function fields as extensions of $k[x]$. However, for special classes of curves, Hess' algorithms are asymptotically more efficient than ours, generalizing other known efficient algorithms for special classes of curves, such as hyperelliptic curves (Cantor), superelliptic curves (Galbraith, Paulus, and Smart), and $C_{ab}$ curves (Harasawa and Suzuki); in all those cases, one can attain a complexity of $O(g^2)$.
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
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.
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.
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.
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 code 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.
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
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.
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.
Introduction to Image Algebra Ada
NASA Astrophysics Data System (ADS)
Wilson, Joseph N.
1991-07-01
Image Algebra Ada (IAA) is a superset of the Ada programming language designed to support use of the Air Force Armament Laboratory's image algebra in the development of computer vision application programs. The IAA language differs from other computer vision languages is several respects. It is machine independent, and an IAA translator has been implemented in the military standard Ada language. Its image operands and operations can be used to program a range of both low- and high-level vision algorithms. This paper provides an overview of the image algebra constructs supported in IAA and describes the embodiment of these constructs in the IAA extension of Ada. Examples showing the use of IAA for a range of computer vision tasks are given. The design of IAA as a superset of Ada and the implementation of the initial translator in Ada represent critical choices. The authors discuss the reasoning behind these choices as well as the benefits and drawbacks associated with them. Implementation strategies associated with the use of Ada as an implementation language for IAA are also discussed. While one can look on IAA as a program design language (PDL) for specifying Ada programs, it is useful to consider IAA as a separate language superset of Ada. This admits the possibility of directly translating IAA for implementation on special purpose architectures. This paper explores strategies for porting IAA to various architectures and notes the critical language and implementation features for porting to different architectures.
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.…
Secondary Schools Curriculum Guide, Mathematics, Grades 7-9. Revised.
ERIC Educational Resources Information Center
Cranston School Dept., RI.
Behavioral objectives are specified for 82 topics in mathematics to be covered in grades 7 through 9. A general objective is given for each, followed by specific behavioral objectives with suggested activities. Topics include number properties and operations, geometry, number theory, algebra, set theory, ratio, proportion and percent, the metric…
Advanced Placement Mathematics Calculus, Grade 12 Curriculum Guide.
ERIC Educational Resources Information Center
Scharf, John; And Others
This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…
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
Kumjian-Pask algebras of desourcification
NASA Astrophysics Data System (ADS)
Rosjanuardi, Rizky; Yusnitha, Isnie
2016-02-01
Kumjian-Pask algebra which was introduced by Pino, Clark, an Huef and Raeburn [1] in 2013, gives a purely algebraic version of a k-graph algebra. Rosjanuardi [2] gave necessary and sufficient condition of finitely dimensional complex Kumjian-Pask algebra of row-finite k-graph without sources. We will improve the previous results which allows us to deal with sources. We will consider Kumjian-Pask algebra for locally convex row-finite k-graph which was introduced by Clark, Flynn and an Huef [3], and use the desourcification of the graph to get conditions which characterise when the complex Kumjian-Pask algebra of locally convex row-finite k-graph is finite dimensional.
Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras
NASA Astrophysics Data System (ADS)
Zhang, Tianjie; Gao, Xing; Guo, Li
2016-10-01
The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.
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.
Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Powell, Sarah R.; Schumacher, Robin F.; Hamlett, Carol L.; Vernier, Emily; Namkung, Jessica M.; Vukovic, Rose K.
2012-01-01
The purpose of this study was to investigate the contributions of domain-general cognitive resources and different forms of arithmetic development to individual differences in pre-algebraic knowledge. Children (n=279; mean age=7.59 yrs) were assessed on 7 domain-general cognitive resources as well as arithmetic calculations and word problems at start of 2nd grade and on calculations, word problems, and pre-algebraic knowledge at end of 3rd grade. Multilevel path analysis, controlling for instructional effects associated with the sequence of classrooms in which students were nested across grades 2–3, indicated arithmetic calculations and word problems are foundational to pre-algebraic knowledge. Also, results revealed direct contributions of nonverbal reasoning and oral language to pre-algebraic knowledge, beyond indirect effects that are mediated via arithmetic calculations and word problems. By contrast, attentive behavior, phonological processing, and processing speed contributed to pre-algebraic knowledge only indirectly via arithmetic calculations and word problems. PMID:22409764
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].
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.
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.
On Realization of Generalized Effect Algebras
NASA Astrophysics Data System (ADS)
Paseka, Jan
2012-12-01
A well-known fact is that there is a finite orthomodular lattice with an order determining set of states which is not representable in the standard quantum logic, the lattice L(H) of all closed subspaces of a separable complex Hilbert space. We show that a generalized effect algebra is representable in the operator generalized effect algebra G(H) of effects of a complex Hilbert space H iff it has an order determining set of generalized states. This extends the corresponding results for effect algebras of Riečanová and Zajac. Further, any operator generalized effect algebra G(H) possesses an order determining set of generalized states.
NASA Astrophysics Data System (ADS)
Chajda, Ivan
2014-10-01
Commutative BCI-algebras can be considered as semilattices whose sections are equipped with certain involutions. A similar view can be applied to commutative BCK-algebras. However, for general BCK-algebras a certain construction was settled by the author and J. Kühr (Miskolc Math. Notes 8:11-21, 2007) showing that they can be considered as structures essentially weaker than semilattices but still with certain involutions in sections. The aim of this paper is to involve a similar approach for BCI-algebras.
Literal algebra for satellite dynamics. [perturbation analysis
NASA Technical Reports Server (NTRS)
Gaposchkin, E. M.
1975-01-01
A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.
Entanglement and algebraic independence in fermion systems
NASA Astrophysics Data System (ADS)
Benatti, Fabio; Floreanini, Roberto
2014-04-01
In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between operators from subalgebras localized in spatially disjoint regions. While this algebraic approach is straightforward for bosons, in the case of fermions it is subtler since one has to distinguish between micro-causality, that is the anti-commutativity of the basic creation and annihilation operators, and algebraic independence that is the commutativity of local observables. We argue that a consistent algebraic formulation of separability and entanglement should be compatible with micro-causality rather than with algebraic independence.
Some C∗-algebras which are coronas of non-C∗-Banach algebras
NASA Astrophysics Data System (ADS)
Voiculescu, Dan-Virgil
2016-07-01
We present results and motivating problems in the study of commutants of hermitian n-tuples of Hilbert space operators modulo normed ideals. In particular, the C∗-algebras which arise in this context as coronas of non-C∗-Banach algebras, the connections with normed ideal perturbations of operators, the hyponormal operators and the bidual Banach algebras one encounters are discussed.
ERIC Educational Resources Information Center
Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos
2016-01-01
This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…
Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra
NASA Astrophysics Data System (ADS)
Camacho, Luisa M.; Ladra, Manuel; Karimjanov, Iqboljon A.; Omirov, Bakhrom A.
2016-03-01
In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.
ERIC Educational Resources Information Center
Ozgun-Koca, S. Ash
2010-01-01
Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…
Cluster automorphism groups of cluster algebras with coefficients
NASA Astrophysics Data System (ADS)
Chang, Wen; Zhu, Bin
2016-10-01
We study the cluster automorphism group of a skew-symmetric cluster algebra with geometric coefficients. For this, we introduce the notion of gluing free cluster algebra, and show that under a weak condition the cluster automorphism group of a gluing free cluster algebra is a subgroup of the cluster automorphism group of its principal part cluster algebra (i.e. the corresponding cluster algebra without coefficients). We show that several classes of cluster algebras with coefficients are gluing free, for example, cluster algebras with principal coefficients, cluster algebras with universal geometric coefficients, and cluster algebras from surfaces (except a 4-gon) with coefficients from boundaries. Moreover, except four kinds of surfaces, the cluster automorphism group of a cluster algebra from a surface with coefficients from boundaries is isomorphic to the cluster automorphism group of its principal part cluster algebra; for a cluster algebra with principal coefficients, its cluster automorphism group is isomorphic to the automorphism group of its initial quiver.
The Structure of Parafermion Vertex Operator Algebras: General Case
NASA Astrophysics Data System (ADS)
Dong, Chongying; Wang, Qing
2010-11-01
The structure of the parafermion vertex operator algebra associated to an integrable highest weight module for any affine Kac-Moody algebra is studied. In particular, a set of generators for this algebra has been determined.
ERIC Educational Resources Information Center
Osler, James Edward; Waden, Carl
2013-01-01
This paper discusses the implementation of the Tri-Squared Test as one of many advanced statistical measures used to verify and validate the outcomes of an initial study on academic professional's perspectives on the use, success, and viability of 9th Grade Freshman Academies, Centers, and Center Models. The initial research investigation…
Gene algebra from a genetic code algebraic structure.
Sanchez, R; Morgado, E; Grau, R
2005-10-01
By considering two important factors involved in the codon-anticodon interactions, the hydrogen bond number and the chemical type of bases, a codon array of the genetic code table as an increasing code scale of interaction energies of amino acids in proteins was obtained. Next, in order to consecutively obtain all codons from the codon AAC, a sum operation has been introduced in the set of codons. The group obtained over the set of codons is isomorphic to the group (Z(64), +) of the integer module 64. On the Z(64)-algebra of the set of 64(N) codon sequences of length N, gene mutations are described by means of endomorphisms f:(Z(64))(N)-->(Z(64))(N). Endomorphisms and automorphisms helped us describe the gene mutation pathways. For instance, 77.7% mutations in 749 HIV protease gene sequences correspond to unique diagonal endomorphisms of the wild type strain HXB2. In particular, most of the reported mutations that confer drug resistance to the HIV protease gene correspond to diagonal automorphisms of the wild type. What is more, in the human beta-globin gene a similar situation appears where most of the single codon mutations correspond to automorphisms. Hence, in the analyses of molecular evolution process on the DNA sequence set of length N, the Z(64)-algebra will help us explain the quantitative relationships between genes.
Dirac matrices as elements of a superalgebraic matrix algebra
NASA Astrophysics Data System (ADS)
Monakhov, V. V.
2016-08-01
The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix algebra exists in this algebra, the Clifford exten-sion of the Grassmann algebra is a generalization of the matrix algebra and contains superalgebraic operators expanding matrix algebra and produces supersymmetric transformations.
Automated Angular Momentum Recoupling Algebra
NASA Astrophysics Data System (ADS)
Williams, H. T.; Silbar, Richard R.
1992-04-01
We present a set of heuristic rules for algebraic solution of angular momentum recoupling problems. The general problem reduces to that of finding an optimal path from one binary tree (representing the angular momentum coupling scheme for the reduced matrix element) to another (representing the sub-integrals and spin sums to be done). The method lends itself to implementation on a microcomputer, and we have developed such an implementation using a dialect of LISP. We describe both how our code, called RACAH, works and how it appears to the user. We illustrate the use of RACAH for several transition and scattering amplitude matrix elements occurring in atomic, nuclear, and particle physics.
Does Calculation or Word-Problem Instruction Provide A Stronger Route to Pre-Algebraic Knowledge?
Fuchs, Lynn S.; Powell, Sarah R.; Cirino, Paul T.; Schumacher, Robin F.; Marrin, Sarah; Hamlett, Carol L.; Fuchs, Douglas; Compton, Donald L.; Changas, Paul C.
2014-01-01
The focus of this study was connections among 3 aspects of mathematical cognition at 2nd grade: calculations, word problems, and pre-algebraic knowledge. We extended the literature, which is dominated by correlational work, by examining whether intervention conducted on calculations or word problems contributes to improved performance in the other domain and whether intervention in either or both domains contributes to pre-algebraic knowledge. Participants were 1102 children in 127 2nd-grade classrooms in 25 schools. Teachers were randomly assigned to 3 conditions: calculation intervention, word-problem intervention, and business-as-usual control. Intervention, which lasted 17 weeks, was designed to provide research-based linkages between arithmetic calculations or arithmetic word problems (depending on condition) to pre-algebraic knowledge. Multilevel modeling suggested calculation intervention improved calculation but not word-problem outcomes; word-problem intervention enhanced word-problem but not calculation outcomes; and word-problem intervention provided a stronger route than calculation intervention to pre-algebraic knowledge. PMID:25541565
ERIC Educational Resources Information Center
Richardson, Sandra
2009-01-01
This article describes experiences from a professional development project designed to prepare in-service eighth-grade mathematics teachers to develop, explore, and advance technological pedagogical content knowledge (TPCK) in the teaching and learning of Algebra I. This article describes the process of the participating teachers' mathematical…
ERIC Educational Resources Information Center
Izsak, Andrew
2003-01-01
Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…
ERIC Educational Resources Information Center
Chiu, Ming Ming
2008-01-01
The micro-time context of group processes (such as argumentation) can affect a group's micro-creativity (new ideas). Eighty high school students worked in groups of four on an algebra problem. Groups with higher mathematics grades showed greater micro-creativity, and both were linked to better problem solving outcomes. Dynamic multilevel analyses…
Geometry and Algebra: Glow with the Flow. NASA Connect: Program 2 in the 2000-2001 Series.
ERIC Educational Resources Information Center
National Aeronautics and Space Administration, Hampton, VA. Langley Research Center.
This teaching unit is designed to help students in grades 5 to 8 explore the concepts of geometry and algebra in the context of the force of drag. The units in the series have been developed to enhance and enrich mathematics, science, and technology education and to accommodate different teaching and learning styles. Each unit consists of…
Sorting and Supporting: Why Double-Dose Algebra Led to Better Test Scores but More Course Failures
ERIC Educational Resources Information Center
Nomi, Takako; Allensworth, Elaine M.
2013-01-01
In 2003, Chicago schools required students entering ninth grade with below-average math scores to take two periods of algebra. This led to higher test scores for students with both above- and below-average skills, yet failure rates increased for above-average students. We examine the mechanisms behind these surprising results. Sorting by incoming…
ERIC Educational Resources Information Center
Zahner, William
2015-01-01
This paper uses a multilevel analysis of mathematical reasoning rooted in Cultural Historical Activity Theory to examine how mathematical discourse and student reasoning about linear functions developed across 3 weeks in a ninth grade bilingual algebra class. Despite the teacher's expertise teaching with a conceptual focus, and her stated…
Patterns, Functions, and Algebra: Wired for Space. NASA Connect: Program 3 in the 2000-2001 Series.
ERIC Educational Resources Information Center
National Aeronautics and Space Administration, Hampton, VA. Langley Research Center.
This teaching unit is designed to help students in grades 5 to 8 explore the concepts of patterns, functions, and algebra in the context of propelling spacecraft. The units in the series have been developed to enhance and enrich mathematics, science, and technology education and to accommodate different teaching and learning styles. Each unit…
Using PROC GLIMMIX to Analyze the Animal Watch, a Web-Based Tutoring System for Algebra Readiness
ERIC Educational Resources Information Center
Barbu, Otilia C.
2012-01-01
In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch…
The Relative Lie Algebra Cohomology of the Weil Representation
NASA Astrophysics Data System (ADS)
Ralston, Jacob
We study the relative Lie algebra cohomology of so(p,q) with values in the Weil representation piof the dual pair Sp(2k, R) x O(p,q ). Using the Fock model defined in Chapter 2, we filter this complex and construct the associated spectral sequence. We then prove that the resulting spectral sequence converges to the relative Lie algebra cohomology and has E0 term, the associated graded complex, isomorphic to a Koszul complex, see Section 3.4. It is immediate that the construction of the spectral sequence of Chapter 3 can be applied to any reductive subalgebra g ⊂ sp(2k(p + q), R). By the Weil representation of O( p,|q), we mean the twist of the Weil representation of the two-fold cover O(pq)[special character omitted] by a suitable character. We do this to make the center of O(pq)[special character omitted] act trivially. Otherwise, all relative Lie algebra cohomology groups would vanish, see Proposition 4.10.2. In case the symplectic group is large relative to the orthogonal group (k ≥ pq), the E 0 term is isomorphic to a Koszul complex defined by a regular sequence, see 3.4. Thus, the cohomology vanishes except in top degree. This result is obtained without calculating the space of cochains and hence without using any representation theory. On the other hand, in case k < p, we know the Koszul complex is not that of a regular sequence from the existence of the class ϕkq of Kudla and Millson, see te{KM2}, a nonzero element of the relative Lie algebra cohomology of degree kq. For the case of SO0(p, 1) we compute the cohomology groups in these remaining cases, namely k < p. We do this by first computing a basis for the relative Lie algebra cochains and then splitting the complex into a sum of two complexes, each of whose E0 term is then isomorphic to a Koszul complex defined by a regular sequence. This thesis is adapted from the paper, [BMR], this author wrote with his advisor John Millson and Nicolas Bergeron of the University of Paris.
Algebraic Thinking through Koch Snowflake Constructions
ERIC Educational Resources Information Center
Ghosh, Jonaki B.
2016-01-01
Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both…
Investigating Algebraic Procedures Using Discussion and Writing
ERIC Educational Resources Information Center
Harper, Jonathan; Ford, Jeffrey
2012-01-01
This study reports on the implementation of an intermediate algebra curriculum centered on a framework of student-centered questions designed to investigate algebraic procedures. Instructional activities were designed to build discourse in the small-group discussion meetings of the course. Students were assigned writing prompts to emphasize the…
Practicing Algebraic Skills: A Conceptual Approach
ERIC Educational Resources Information Center
Friedlander, Alex; Arcavi, Abraham
2012-01-01
Traditionally, a considerable part of teaching and learning algebra has focused on routine practice and the application of rules, procedures, and techniques. Although today's computerized environments may have decreased the need to master algebraic skills, procedural competence is still a central component in any mathematical activity. However,…
THE RADICAL OF A JORDAN ALGEBRA
McCrimmon, Kevin
1969-01-01
In this paper we define a Jacobson radical for Jordan algebras analogous to that for associative algebras and show that it enjoys many of the properties of the associative radical. We then relate the corresponding notion of “semisimplicity” to the previously defined notion of “nondegeneracy” (Jacobson, N., these Proceedings, 55, 243-251 (1966)). PMID:16591736
The operator algebra approach to quantum groups
Kustermans, Johan; Vaes, Stefaan
2000-01-01
A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory. PMID:10639116
Situated Learning in an Abstract Algebra Classroom
ERIC Educational Resources Information Center
Ticknor, Cindy S.
2012-01-01
Advisory committees of mathematics consider abstract algebra as an essential component of the mathematical preparation of secondary teachers, yet preservice teachers find it challenging to connect the topics addressed in this advanced course with the high school algebra they must someday teach. This study analyzed the mathematical content…
Solving Absolute Value Equations Algebraically and Geometrically
ERIC Educational Resources Information Center
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Success in Algebra among Community College Students
ERIC Educational Resources Information Center
Reyes, Czarina
2010-01-01
College algebra is a required course for most majors, but is viewed by many as a gatekeeper course for degree completion by students. With almost half a million students taking college algebra each year, faculty are experimenting with new course lengths of time that might result in higher success, completion, and retention rates for college…
Using the Internet To Investigate Algebra.
ERIC Educational Resources Information Center
Sherwood, Walter
The lesson plans in this book engage students by using a tool they enjoy--the Internet--to explore key concepts in algebra. Working either individually or in groups, students learn to approach algebra from a problem solving perspective. Each lesson shows learners how to use the Internet as a resource for gathering facts, data, and other…
New directions in algebraic dynamical systems
NASA Astrophysics Data System (ADS)
Schmidt, Klaus; Verbitskiy, Evgeny
2011-02-01
The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.
Classical and quantum Kummer shape algebras
NASA Astrophysics Data System (ADS)
Odzijewicz, A.; Wawreniuk, E.
2016-07-01
We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.
Fourier theory and C∗-algebras
NASA Astrophysics Data System (ADS)
Bédos, Erik; Conti, Roberto
2016-07-01
We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.
Teaching Algebra to Students with Learning Disabilities
ERIC Educational Resources Information Center
Impecoven-Lind, Linda S.; Foegen, Anne
2010-01-01
Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…
Arithmetic and Cognitive Contributions to Algebra
ERIC Educational Resources Information Center
Cirino, Paul T.; Tolar, Tammy D.; Fuchs, Lynn S.
2013-01-01
Algebra is a prerequisite for access to STEM careers and occupational success (NMAP, 2008a), yet algebra is difficult for students through high school (US DOE, 2008). Growth in children's conceptual and procedural arithmetical knowledge is reciprocal, although conceptual knowledge has more impact on procedural knowledge than the reverse…
Just Say Yes to Early Algebra!
ERIC Educational Resources Information Center
Stephens, Ana; Blanton, Maria; Knuth, Eric; Isler, Isil; Gardiner, Angela Murphy
2015-01-01
Mathematics educators have argued for some time that elementary school students are capable of engaging in algebraic thinking and should be provided with rich opportunities to do so. Recent initiatives like the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) have taken up this call by reiterating the place of early algebra in…
An Inquiry-Based Linear Algebra Class
ERIC Educational Resources Information Center
Wang, Haohao; Posey, Lisa
2011-01-01
Linear algebra is a standard undergraduate mathematics course. This paper presents an overview of the design and implementation of an inquiry-based teaching material for the linear algebra course which emphasizes discovery learning, analytical thinking and individual creativity. The inquiry-based teaching material is designed to fit the needs of a…
Parabolas: Connection between Algebraic and Geometrical Representations
ERIC Educational Resources Information Center
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Algebraic Geodesics on Three-Dimensional Quadrics
NASA Astrophysics Data System (ADS)
Kai, Yue
2015-12-01
By Hamilton-Jacobi method, we study the problem of algebraic geodesics on the third-order surface. By the implicit function theorem, we proved the existences of the real geodesics which are the intersections of two algebraic surfaces, and we also give some numerical examples.
ERIC Educational Resources Information Center
Rickard, Caroline
2008-01-01
Shortly after starting work for the University of Chichester in the School of Teacher Education, the author was planning a session relating to algebra and found herself inspired by an article in MT182: "Algebraic Infants" by Andrews and Sayers (2003). Based on the making of families of "Multilink" animals, Andrews and Sayers (2003) claim that…
Focus on Fractions to Scaffold Algebra
ERIC Educational Resources Information Center
Ooten, Cheryl Thomas
2013-01-01
Beginning algebra is a gatekeeper course into the pipeline to higher mathematics courses required for respected professions in engineering, science, statistics, mathematics, education, and technology. Beginning algebra can also be a perfect storm if the necessary foundational skills are not within a student's grasp. What skills ensure beginning…
Some Applications of Algebraic System Solving
ERIC Educational Resources Information Center
Roanes-Lozano, Eugenio
2011-01-01
Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…
A Technology-Intensive Approach to Algebra.
ERIC Educational Resources Information Center
Heid, M. Kathleen; Zbiek, Rose Mary
1995-01-01
Computer-Intensive Algebra (CIA) focuses on the use of technology to help develop a rich understanding of fundamental algebraic concepts in real-world settings using computing tools for easy access to numerical, graphical, and symbolic representations of mathematical ideas. (MKR)
Modern Algebra, Mathematics: 5293.36.
ERIC Educational Resources Information Center
Edwards, Raymond J.
This guidebook covers Boolean algebra, matrices, linear transformations of the plane, characteristic values, vectors, and algebraic structures. Overall course goals and performance objectives for each unit are specified; sequencing of units and various time schedules are suggested. A sample pretest and posttest are given, and an annotated list of…
Teaching Modeling and Axiomatization with Boolean Algebra.
ERIC Educational Resources Information Center
De Villiers, Michael D.
1987-01-01
Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)
Hypersymmetry: A Z{sub 3}-graded generalization of supersymmetry
Abramov, V.; Kerner, R.; Le Roy, B.
1997-03-01
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z{sub 3}-graded structures. In the new algebraic structures we define, all products of two entities are left free, the only constraining relations being imposed on ternary products. These relations reflect the action of the Z{sub 3}-group, which may be either trivial, i.e., abc=bca=cab, generalizing the usual commutativity, or non-trivial, i.e., abc=jbca, with j=e{sup (2{pi}i)/3}. The usual Z{sub 2}-graded structures such as Grassmann, Lie, and Clifford algebras are generalized to the Z{sub 3}-graded case. Certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed. {copyright} {ital 1997 American Institute of Physics.}
MODEL IDENTIFICATION AND COMPUTER ALGEBRA
Bollen, Kenneth A.; Bauldry, Shawn
2011-01-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.
Topological membranes, current algebras and H-flux-R-flux duality based on Courant algebroids
NASA Astrophysics Data System (ADS)
Bessho, Taiki; Heller, Marc A.; Ikeda, Noriaki; Watamura, Satoshi
2016-04-01
We construct a topological sigma model and a current algebra based on a Courant algebroid structure on a Poisson manifold. In order to construct models, we reformulate the Poisson Courant algebroid by supergeometric construction on a QP-manifold. A new duality of Courant algebroids which transforms H-flux and R-flux is proposed, where the transformation is interpreted as a canonical transformation of a graded symplectic manifold.
Generalization of n-ary Nambu algebras and beyond
Ataguema, H.; Makhlouf, A.; Silvestrov, S.
2009-08-15
The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.
Working memory, worry, and algebraic ability.
Trezise, Kelly; Reeve, Robert A
2014-05-01
Math anxiety (MA)-working memory (WM) relationships have typically been examined in the context of arithmetic problem solving, and little research has examined the relationship in other math domains (e.g., algebra). Moreover, researchers have tended to examine MA/worry separate from math problem solving activities and have used general WM tasks rather than domain-relevant WM measures. Furthermore, it seems to have been assumed that MA affects all areas of math. It is possible, however, that MA is restricted to particular math domains. To examine these issues, the current research assessed claims about the impact on algebraic problem solving of differences in WM and algebraic worry. A sample of 80 14-year-old female students completed algebraic worry, algebraic WM, algebraic problem solving, nonverbal IQ, and general math ability tasks. Latent profile analysis of worry and WM measures identified four performance profiles (subgroups) that differed in worry level and WM capacity. Consistent with expectations, subgroup membership was associated with algebraic problem solving performance: high WM/low worry>moderate WM/low worry=moderate WM/high worry>low WM/high worry. Findings are discussed in terms of the conceptual relationship between emotion and cognition in mathematics and implications for the MA-WM-performance relationship.
Weak homological dimensions and biflat Koethe algebras
Pirkovskii, A Yu
2008-06-30
The homological properties of metrizable Koethe algebras {lambda}(P) are studied. A criterion for an algebra A={lambda}(P) to be biflat in terms of the Koethe set P is obtained, which implies, in particular, that for such algebras the properties of being biprojective, biflat, and flat on the left are equivalent to the surjectivity of the multiplication operator A otimes-hat A{yields}A. The weak homological dimensions (the weak global dimension w.dg and the weak bidimension w.db) of biflat Koethe algebras are calculated. Namely, it is shown that the conditions w.db {lambda}(P)<=1 and w.dg {lambda}(P)<=1 are equivalent to the nuclearity of {lambda}(P); and if {lambda}(P) is non-nuclear, then w.dg {lambda}(P)=w.db {lambda}(P)=2. It is established that the nuclearity of a biflat Koethe algebra {lambda}(P), under certain additional conditions on the Koethe set P, implies the stronger estimate db {lambda}(P), where db is the (projective) bidimension. On the other hand, an example is constructed of a nuclear biflat Koethe algebra {lambda}(P) such that db {lambda}(P)=2 (while w.db {lambda}(P)=1). Finally, it is shown that many biflat Koethe algebras, while not being amenable, have trivial Hochschild homology groups in positive degrees (with arbitrary coefficients). Bibliography: 37 titles.
Algebraic curves of maximal cyclicity
NASA Astrophysics Data System (ADS)
Caubergh, Magdalena; Dumortier, Freddy
2006-01-01
The paper deals with analytic families of planar vector fields, studying methods to detect the cyclicity of a non-isolated closed orbit, i.e. the maximum number of limit cycles that can locally bifurcate from it. It is known that this multi-parameter problem can be reduced to a single-parameter one, in the sense that there exist analytic curves in parameter space along which the maximal cyclicity can be attained. In that case one speaks about a maximal cyclicity curve (mcc) in case only the number is considered and of a maximal multiplicity curve (mmc) in case the multiplicity is also taken into account. In view of obtaining efficient algorithms for detecting the cyclicity, we investigate whether such mcc or mmc can be algebraic or even linear depending on certain general properties of the families or of their associated Bautin ideal. In any case by well chosen examples we show that prudence is appropriate.
Inequalities, assessment and computer algebra
NASA Astrophysics Data System (ADS)
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 contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students' answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.
Local Algebras of Differential Operators
NASA Astrophysics Data System (ADS)
Church, P. T.; Timourian, J. G.
2002-05-01
There is an increasing literature devoted to the study of boundary value problems using singularity theory. The resulting differential operators are typically Fredholm with index 0, defined on infinite-dimensional spaces, and they have often led to folds, cusps, and even higher-order Morin singularities. In this paper we develop some of the local algebras of germs of such differential Fredholm operators, extending the theory of the finite-dimensional case. We apply this work to nonlinear elliptic boundary value problems: in particular, we make further progress on a question proposed and initially studied by Ruf [1999, J. Differential Equations 151, 111-133]. We also make comments on several problems raised by others.
PC Basic Linear Algebra Subroutines
1992-03-09
PC-BLAS is a highly optimized version of the Basic Linear Algebra Subprograms (BLAS), a standardized set of thirty-eight routines that perform low-level operations on vectors of numbers in single and double-precision real and complex arithmetic. Routines are included to find the index of the largest component of a vector, apply a Givens or modified Givens rotation, multiply a vector by a constant, determine the Euclidean length, perform a dot product, swap and copy vectors, andmore » find the norm of a vector. The BLAS have been carefully written to minimize numerical problems such as loss of precision and underflow and are designed so that the computation is independent of the interface with the calling program. This independence is achieved through judicious use of Assembly language macros. Interfaces are provided for Lahey Fortran 77, Microsoft Fortran 77, and Ryan-McFarland IBM Professional Fortran.« less