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 courses. A…
The Ethnic Context and Attitudes toward 9th Grade Math
ERIC Educational Resources Information Center
Graham, Sandra; Morales-Chicas, Jessica
2015-01-01
The present study examined the relations between ethnic context and attitudes about 9th grade math in youth from different ethnic groups who had recently transitioned to high school. The large sample comprised African American, Latino, White, and Asian youth (n = 2,265, 55% girls, M[subscript age] = 14.6 yrs.) A new questionnaire was developed…
ERIC Educational Resources Information Center
Wurnig, Otto
This paper reports the results of student use of a TI-92 graphing calculator to solve algebra and analytic geometry problems in 9th grade Austrian classes. Students who had been trained in using the TI-92 were asked to compute x, given that a right-angled triangle had sides x, x+3, and x+6 in at least three ways, and to document their solution…
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,…
A Summative Program Evaluation of a Comprehensive 9th Grade Transition Program
ERIC Educational Resources Information Center
Roybal, Victoria M.
2011-01-01
The transition from 8th grade to 9th grade is one that is replete with challenges for students, especially for minority students who live in economically disadvantaged communities. One low-income, high minority comprehensive high school in the western United States implemented five separate strategies to create a freshman transition program to aid…
The Effectiveness of the New 9th Grade Biology Curriculum on Students' Environmental Awareness
ERIC Educational Resources Information Center
Cetin, Gulcan; Nisanci, Seda Hilal
2010-01-01
The aim of this study was to examine the effectiveness of a new 9th grade biology curriculum on students' environmental awareness. Participants included 91 ninth grade students in a high school in Balikesir during the spring semester of the 2008-2009 academic years. Two classrooms, including 22 and 24 students respectively, were randomly assigned…
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
Briede, Liene
2016-01-01
The aim of the study is to investigate the relationship between the teaching approach adopted by mathematics teachers and their 9th grade students' mathematical self. The study searched for the answers on three research questions, namely, about 1) the approaches prevailing in mathematics teachers' beliefs about effective teaching and self-reports…
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…
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…
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…
ERIC Educational Resources Information Center
Al-Hilawani, Yasser A.; And Others
This study explored teachers' behavior as related to effective teaching practices in 8th, 9th, and 10th grade English classrooms in Jordan. The study also examined some variables that could predict teachers' implementation of effective teaching practices and aimed at finding an estimate of the percentage of students in 8th, 9th, and 10th grades…
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.
The Relationship of Grade Span in 9th Grade to Math Achievement in High School
ERIC Educational Resources Information Center
West, John; Miller, Mary Lou; Myers, Jim; Norton, Timothy
2015-01-01
Purpose, Scope, and Method of Study: The purpose of this study was to determine if a correlation exists between grade span for ninth grade and gains in math achievement test scores in 10th grade and 12th grade. A quantitative, longitudinal, correlational research design was employed to investigate the research questions. The population was high…
ERIC Educational Resources Information Center
Corsello, Maryann; Sharma, Anu; Jerabek, Angela
2015-01-01
Ninth grade is a pivotal year for students. Numerous studies find that academic performance in 9th grade often sets the student's trajectory throughout the high school years, as well as the probability of graduation. The Building Assets Reducing Risks (BARR) model is a comprehensive approach that addresses developmental, academic, and school…
The 9th Grade Shock and the High School Dropout Crisis
Pharris-Ciurej, Nikolas; Hirschman, Charles; Willhoft, Joseph
2011-01-01
Retrospective questions on educational attainment in national surveys and censuses tend to over-estimate high school graduation rates by 15 to 20 percentage points relative to administrative records. Administrative data on educational enrollment are, however, only available at the aggregate level (state, school district, and school levels) and the recording of inter-school transfers are generally incomplete. With access to linked individual-level administrative records from a very large “West Coast metropolitan school district” we track patterns of high school attrition and on-time high school graduation of individual students. Even with adjustments for the omission of out-of-district transfers (estimates of omission are presented), the results of this study show that failure in high school, as indexed by retention and attrition, are almost as common as on-time high school graduation. In addition to the usual risk factors of disadvantaged background, we find that the “9th grade shock”—an unpredicted decline in academic performance upon entering high school—is a key mechanism behind the continuing crisis of high school attrition. PMID:23017804
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
Pilav, Salim
2014-01-01
The purpose of this study is to assess the extent to which each of the three types of instruction (authentic, where, differentiated) engages 9th grade high school students in achieving language proficiency. The paper examines the features of these models of instructions and teachers? opinion about them. It includes a descriptive research in survey…
ERIC Educational Resources Information Center
Hill, Grant; Cleven, Brian
2005-01-01
The purposes of this study were to determine the physical education activity preferences of 9th grade students in a southern California school district, to identify which activities students felt should be offered in coeducation or gender separate formats, and to determine whether physical education is one of their favorite classes. Results…
ERIC Educational Resources Information Center
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…
ERIC Educational Resources Information Center
Üstten, Aliye Uslu
2014-01-01
The purpose of this study is to identify the sources of reading difficulties and to evaluate reading fluency of 9th grade students which aims to improve students' reading and their understanding of complex literary texts. The sample is composed of 120 students selected from 9th grade of 10 different high schools in central province of Ankara in…
A Report on the Science Summer Camp for the Gifted 9th Grade Students.
ERIC Educational Resources Information Center
Kyeonggi Province Board of Education, Suweon (Republic of Korea).
A summer science camp was held in Korea for 30 ninth grade students gifted in science. Students were divided into three groups (physics, chemistry, and biology) for activities which included problem solving, brainstorming, and experimental work. The experiments of the physics group addressed the use of solar energy, the chemistry group focused on…
Cal Young Integration of Career Education into 9th Grade Classes: Suggestions for the Subject Areas.
ERIC Educational Resources Information Center
Eugene School District 4J, OR.
The curriculum guide contains suggested learning activities and resource materials designed to integrate career education concepts into subject areas for the ninth grade. The guide provides such things as goals, teacher activities, expected student competencies, vocabulary lists, sample occupations and related information, lists of resource…
ITEM RESPONSE ANALYSES OF THE EDUCATIONAL OPPORTUNITIES SURVEY 9TH GRADE STUDENT QUESTIONNAIRE.
ERIC Educational Resources Information Center
WEINFELD, FREDERIC D.; AND OTHERS
THIS REPORT PRESENTS THE ANALYSIS OF QUESTIONNAIRE ITEM RESPONSES FROM THE NINTH-GRADE STUDENT QUESTIONNAIRE ADMINISTERED AS PART OF THE EDUCATIONAL OPPORTUNITIES SURVEY. THE ANALYSES WERE PERFORMED TO DOCUMENT SOME OF THE BASIC DATA FROM THE SURVEY, TO MAKE THEM AVAILABLE TO INTERESTED EDUCATIONAL RESEARCHERS, AND TO REWORK THE BASIC DATA FOR…
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…
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…
Implementing Interactive Teaching Methods for 9th Grade Organic Chemistry Classes
NASA Astrophysics Data System (ADS)
Traykov, Ivaylo; Galcheva, Petinka
2017-03-01
One of the main challenges facing the current educational system is creating conditions suitable for academic skill development that allow students to navigate and adapt to today's modern society, such as locating relevant information quickly as well as effectively utilizing innovations. We can achieve this objective by using interactive teaching methods. These methods take into account the contemporary issues and changing priorities - from the general content building for the courses to independent, student-centered cognitive activities. The propose of this paper is to present tested and proven interactive methods for Grade 9Organic Chemistry classes. These methods significantly improve the quality of teaching and the students' interest in the subject.
7th to 9th grade obese adolescents' perceptions about obesity in Tamaulipas, Mexico.
de la Luz Martínez-Aguilar, Ma; Flores-Peña, Yolanda; de las Mercedes Rizo-Baeza, Ma; Aguilar-Hernández, Rosa Ma; Vázquez-Galindo, Laura; Gutiérres-Sánchez, Gustavo
2010-01-01
The objective was to explore obese adolescents perceptions about obesity among students in the seventh to ninth grade of a public school in Tamaulipas, Mexico. This is a qualitative study. Participants were 24 adolescents with a body mass index equal to or greater than the 95th percentile. Semistructured interviews were conducted until data saturation was reached and the meaning was understood. The adolescents defined obesity according to standards of measurement. They identified the hereditary factor as the main obesity cause, tended to underestimate obesity and had low self-esteem. They reported problems to do physical exercise and get clothes in order to improve their image, and feel rejected by their peers in school. It was identified that these adolescents have psychological defense mechanisms against obesity and that some of them are making efforts to lose weight. Obesity entails social and psychological health implications for persons suffering from this problem. Interventions should be put in practice.
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.
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
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 "pre-test-post-test…
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…
A Comparison of 9th and 10th Grade Boys' and Girls' Bullying Behaviors in Two States.
ERIC Educational Resources Information Center
Isernhagen, Jody; Harris, Sandy
This study examined the incidences of bullying behaviors among male and female 9th and 10th graders in rural Nebraska and suburban Texas schools. Nebraska students were predominantly Caucasion, and Texas students were African American, Hispanic American, and Caucasion. Student surveys examined such issues as how often bullying occurred, where it…
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)
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…
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 teacher's guide is for an environmental education module to integrate topics of water quality in ninth- and tenth-grade social studies classes. This module was pilot tested in Gwinnett County, Georgia in 1975-76. Included in the guide are overall objectives, the module sequence, an introduction, a suggested teaching sequence, a word review…
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.…
The Use of ICT Tools in Mathematics: A Case-Control Study of Best Practice in 9th Grade Classrooms
ERIC Educational Resources Information Center
Thorvaldsen, Steinar; Vavik, Lars; Salomon, Gavriel
2012-01-01
Results are reported from a study in which teachers' views of highly achieving ninth grade classes in Norway (KappAbel national competition winners) were compared with teachers' views of average achievement classes with regard to the use of information and communication technologies (ICT) and pedagogical practices. The main purpose of the study…
How Middle Grade Teachers Think about Algebraic Reasoning
ERIC Educational Resources Information Center
Glassmeyer, David; Edwards, Belinda
2016-01-01
Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…
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
NASA Astrophysics Data System (ADS)
Dermendzhieva, Stela; Nejdet, Semra
2017-03-01
The purpose of this paper is to follow "Climate change, risks and Natural Resources" in the curriculum of Geography of Bulgaria and the world in 9th and 10th grade and to interpret some didactic aspects. Analysis of key themes, concepts and categories related to the environment, events and approaches to environmental protection and the environmentally sound development of sectors of the economy is didikticheski targeted. Considering the emergence and development of geo-ecological issues, their scope and their importance to the environment, systematize some species and some approaches to solving them. Geography education in grade 9 and 10 involves acquiring knowledge, developing skills and composing behaviors of objective perception and assessment of the reality of globed, regional and local aspect. The emerging consumer and individualistic culture snowballing globalization, are increasingly occurring global warming, declining biodiversity form new realities which education must respond appropriately. The objective, consistency, accessibility and relevance in real terms are meaningful, logical accents. Whether and how reproduced in the study of Geography of Bulgaria and the world is the subject of research study in this report. Geoecological structuring of topics, concepts and categories can be done in different signs. In terms of their scope are local, national or regional, and global. Matter and interdisciplinary approach, which is to reveal the unity of the "man-society-nature" to clarify the complexity of their character with a view to forming a harmonious personality with high Geoecological consciousness and culture, and the activities carried out in their study.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Bureau of Curriculum Development.
The Materials in this bulletin indicate suggested teaching procedures needed to implement the teaching of "mathematics, 9th Year" as outlined in Curriculum Bulletin No. 3, 1958-59 series, Course of Study Mathematics 7-8-9. Whereas the course of study suggests the application of mathematical principles such as commutativity,…
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 teacher developed curriculum guide provides the industrial education teacher with the objectives, equipment lists, material, supplies, references, and activities necessary to teach students of the 9th and/or 10th grade the concepts of interrelationships between material analysis and processing systems. Career information and sociological…
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…
2011-01-01
Background Violence by young people is one of the most visible forms of violence and contributes greatly to the global burden of premature death, injury and disability. Methods The Global School-based Student Health Survey (GSHS), State of Lara, Venezuela (GSHS-Lara) is a school-based surveillance system. It comprises a repeated, cross-sectional, self-administered survey drawn from a representative sample of 7th to 9th grade students, performed in the school years 2003-2004 (GSHS-Lara 2004) and 2007-2008 (GSHS-Lara 2008). It explores, among other things, a general violence indicator such as school absenteeism due to feeling unsafe at school or on the way to or from school for any reason; and more specific indicators of violence such as robbery, bullying, physical fights and use of weapons, as well as exposure to lectures on how to prevent violence. Results are given in terms of prevalence percentage. Results Absenteeism doubled between the two study periods (10.8% to 20.8%). The number of students that were a victim of robbery remained high and without change both outside (14.2% and 14.8%) and inside school (21.7% and 22.0%). The number of victims of bullying was high and increasing (33.4% and 43.6%). Bullying associated with being physically attacked decreased (18.5% to 14.3%). Physical attacks without active participation and not associated with bullying were frequent (21.5%). Physical fighting with active participation prevalence remained high and without change (27.5% and 28.2%). Carrying a weapon almost doubled (4.3% to 7.1%). Less than 65% reported classes for violence prevention. Conclusions The GSHS-Lara shows that violence is an important public health problem that needs to be addressed by the community and its authorities. PMID:22958602
A Cohomology Theory of Grading-Restricted Vertex Algebras
NASA Astrophysics Data System (ADS)
Huang, Yi-Zhi
2014-04-01
We introduce a cohomology theory of grading-restricted vertex algebras. To construct the correct cohomologies, we consider linear maps from tensor powers of a grading-restricted vertex algebra to "rational functions valued in the algebraic completion of a module for the algebra," instead of linear maps from tensor powers of the algebra to a module for the algebra. One subtle complication arising from such functions is that we have to carefully address the issue of convergence when we compose these linear maps with vertex operators. In particular, for each , we have an inverse system of nth cohomologies and an additional nth cohomology of a grading-restricted vertex algebra V with coefficients in a V-module W such that is isomorphic to the inverse limit of the inverse system . In the case of n = 2, there is an additional second cohomology denoted by which will be shown in a sequel to the present paper to correspond to what we call square-zero extensions of V and to first order deformations of V when W = V.
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
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.
Pittsburgh Building "Nation" of 9th Graders
ERIC Educational Resources Information Center
Gewertz, Catherine
2007-01-01
Bitter experience has shown Pittsburgh, Pennsylvania, that if students are going to leave school, they are most likely to do it between the 8th and 9th grades. To combat that problem, the school district has launched a full-on campaign to get its rising freshmen into high school and keep them there. Two weeks before school opened, the district…
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
THE PREDICTION OF GRADES IN COLLEGE ALGEBRA--A CONTINUATION AND EXTENSION.
ERIC Educational Resources Information Center
GELSO, CHARLES J.; WILSON, RAY
HIGH SCHOOL ALGEBRA GRADES OF 157 STUDENTS WERE BETTER PREDICTORS OF THEIR PERFORMANCE IN COLLEGE ALGEBRA (MATH 101) THAN EITHER THEIR SCHOLASTIC APTITUDE TEST-MATHEMATICS PORTION OR THEIR SEQUENTIAL TESTS OF EDUCATION PROGRESS-MATHEMATICS SUBTEST SCORES. THE AVERAGE OF THE STUDENTS' ALGEBRA I AND II GRADES SHOWED A CORRELATION WITH THEIR MATH 101…
ERIC Educational Resources Information Center
Alberta Dept. of Education, Edmonton. Language Services Branch.
Aligned with its 1998 standards for first and second language learning, Alberta Learning has published lesson plans that aim for a closer relationship between learning and evaluation. Each volume in this series presents a specific task for students that involves planning, carrying out and evaluating their work. The task for ninth grade students…
ERIC Educational Resources Information Center
Erickson, Toby
In this interdisciplinary curriculum unit intended for ninth grade students, students explore in groups in a role playing format public policy questions related to rain forests. Examined in the lessons are political, economic, and ecological issues from which students are expected to make recommendations on what policy course should be followed.…
ERIC Educational Resources Information Center
Louisiana State Dept. of Education, Baton Rouge. Div. of Vocational Education.
This curriculum guide, the third volume of the series, outlines the basic program of vocational agriculture for Louisiana students in the ninth and tenth grades. Covered in the five units on plant science are growth processes of plants, cultural practices for plants, insects affecting plants, seed and plant selection, and diseases that affect…
The Impact of New State Accountability Standards on Algebra I Students
ERIC Educational Resources Information Center
Heath, Kyle G.
2013-01-01
The purpose of this quasi-experimental quantitative study was to determine if a new Algebra I curriculum resulted in improved student performance on the state Algebra I exam. The treatment group consisted of 383 9th grade Algebra I students who received the college-ready standards-based (CRSB) curricula. The control group consisted of 338 9th…
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 a written…
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…
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…
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
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. …
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
NASA Astrophysics Data System (ADS)
Schlichenmaier, M.
2014-05-01
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.
Aiming Higher: Is Your 9th Grader on Track for College?
ERIC Educational Resources Information Center
New Visions for Public Schools, 2008
2008-01-01
A teenager's future starts on 9th grade with the safe and welcoming environment, excellent teachers, and challenging instruction provided at this school. Believe it or not, college begins in 9th grade. If parents dream of their son or daughter going to college, they should not put off planning until their junior or senior year in high school--it…
ERIC Educational Resources Information Center
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
Education Development Center, Inc., 2016
2016-01-01
In the domain of "Operations & Algebraic Thinking," Common Core State Standards indicate that in kindergarten, first grade, and second grade, children should demonstrate and expand their ability to understand, represent, and solve problems using the operations of addition and subtraction, laying the foundation for operations using…
The Effects of Online Homework on High School Algebra Students
ERIC Educational Resources Information Center
Schubert, Daniel Joseph
2012-01-01
Technology is changing the way students are able to learn and access mathematics. This study explored the effects that technology can have on 9th grade Integrated Algebra students through computer-assisted instruction. In hopes of raising students' New York State Regents scores, ninety-five high school freshmen from a Title I school in New York…
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, Gateway to Success: The Impact of Eighth-Grade Algebra I
ERIC Educational Resources Information Center
Darling, Emily Jean Skelton
2010-01-01
An understanding of Algebra I and the role that this foundational course plays as an entry to the college preparatory pathway in secondary education and its influence on mathematical achievement is an integral component for the education of American youth in the global world of science and technology. Achievements in high school curricula are…
ERIC Educational Resources Information Center
Raymond, Roger A.
In the second year of a study to compare and evaluate programed and conventional instruction in algebra for the ninth and tenth grades, comparisons of the control and experimental groups in each grade were again based on scores from the Lankton First-Year Algebra Test and the California Study Methods Survey (CSMS). Although there was a…
ERIC Educational Resources Information Center
Liang, Jian-Hua; Heckman, Paul E.; Abedi, Jamal
2012-01-01
In California, an increasing number of 8th graders have taken algebra courses since 2003. This study examines students' California Standards Test (CST) results in grades 7 through 11, aiming to reveal who took the CST for Algebra I in 8th grade and whether the increase has led to a rise in students' taking higher-level mathematics CSTs and an…
ERIC Educational Resources Information Center
Lim, Kok Seng
2010-01-01
Introduction: This study aimed to investigate the errors made by 265 Form 2 male students in simplifying algebraic expressions. Method: A total of 265 Form 2 (Grade 7) male students were selected for this study. 10 high, medium and low ability students in each group were selected for the interviews. 40 items were administered to the respondents to…
ERIC Educational Resources Information Center
Jin, Haiyue; Wong, Khoon Yoong
2015-01-01
Conceptual understanding is a major aim of mathematics education, and concept map has been used in non-mathematics research to uncover the relations among concepts held by students. This article presents the results of using concept map to assess conceptual understanding of basic algebraic concepts held by a group of 48 grade 8 Chinese students.…
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…
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 solve…
ERIC Educational Resources Information Center
Bunrasi, John Bosco Tuptip
2012-01-01
The purpose of this study was to examine constructivist-based algebra lessons and a cooperative construct to address the achievement gap between White (non-Hispanic) and Mexican American 8th grade students at a southern California middle school. The lessons were designed to facilitate social interdependence which promoted peer-to-peer interaction…
Predicting Eighth-Grade Algebra Students with Individualized Education Programs
ERIC Educational Resources Information Center
Faulkner, Valerie N.; Crossland, Cathy L.; Stiff, Lee V.
2013-01-01
This study investigated the extent to which student performance and teacher perception of student performance affect placement in eighth-grade mathematics classes for students with disabilities. Authors used the Early Childhood Longitudinal Study--Kindergarten dataset to investigate how each of the following factors predicted placement in…
Differential graded Lie algebras and singularities of level sets of momentum mappings
NASA Astrophysics Data System (ADS)
Goldman, William M.; Millson, John J.
1990-08-01
The germ of an analytic variety X at a point x∈ X is said to be quadratic if it is bi-analytically isomorphic to the germ of a cone defined by a system of homogeneous quadratic equations at the origin. Arms, Marsden and Moncrief show in [2] that under certain conditions the analytic germ of a level set of a momentum mapping is quadratic. We discuss related ideas in a more algebraic context by associating to an affine Hamiltonian action a differential graded Lie algebra, which in the presence of an invariant positive complex structure, is formal in the sence of [5].
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
Shoecraft, Paul Joseph
Three instructional approaches on translating selected types of algebra word problems were investigated: direct translations, high imagery with materials, and high imagery with drawings. Participating were 366 seventh grade and 336 ninth grade students. Treatment effects by grade used multivariate analysis of covariance for student scores and…
ERIC Educational Resources Information Center
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…
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…
ERIC Educational Resources Information Center
Diaz, Marco Antonio
2013-01-01
This study examines the use of Spanish as the language of instruction with Spanish dominant EL students in a 9th grade Algebra 1 classroom. The study documents conceptions of mathematical symbols at the start and at the end of the academic year of two groups of students; one receiving primary language instruction and another receiving sheltered…
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…
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.
ERIC Educational Resources Information Center
Egodawatte, Gunawardena; Stoilescu, Dorian
2015-01-01
The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…
Teaching Algebra without Algebra
ERIC Educational Resources Information Center
Kalman, Richard S.
2008-01-01
Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…
9th Arnual Great Moonbuggy Race
NASA Technical Reports Server (NTRS)
2002-01-01
Students from across the United States and as far away as Puerto Rico and South America came to Huntsville, Alabama for the 9th annual Great Moonbuggy Race at the U.S. Space Rocket Center. Seventy-seven teams, representing high schools and colleges from 21 states, Puerto Rico, and Columbia, raced human powered vehicles over a lunar-like terrain. 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. 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. In this photograph, the Cornell #1 team, the collegiate first place winner, maneuvers their vehicle through the course. Vehicles powered by two team members, one male and one female, raced one at a time over a half-mile obstacle course of simulated moonscape terrain. The competition is inspired by development, some 30 years ago, of the Lunar Roving Vehicle (LRV), a program managed by the Marshall Space Flight Center. The LRV team had to design a compact, lightweight, all-terrain vehicle that could be transported to the Moon in the small Apollo spacecraft. The Great Moonbuggy Race challenges students to design and build a humanpowered vehicle so they will learn how to deal with real-world engineering problems similar to those faced by the actual NASA LRV team.
9th Arnual Great Moonbuggy Race
NASA Technical Reports Server (NTRS)
2002-01-01
Students from across the United States and as far away as Puerto Rico and South America came to Huntsville, Alabama for the 9th annual Great Moonbuggy Race at the U.S. Space Rocket Center. Seventy-seven teams, representing high schools and colleges from 21 states, Puerto Rico, and Columbia, raced human powered vehicles over a lunar-like terrain. In this photograph, the New Orleans area schools team #2 from New Orleans, Louisiana maneuvers through an obstacle course. The team captured second place in the high school division competition. Vehicles powered by two team members, one male and one female, raced one at a time over a half-mile obstacle course of simulated moonscape terrain. The competition is inspired by the development, some 30 years ago, of the Lunar Roving Vehicle (LRV), a program managed by the Marshall Space Flight Center. The LRV team had to design a compact, lightweight, all-terrain vehicle that could be transported to the Moon in the small Apollo spacecraft. The Great Moonbuggy Race challenges students to design and build a human powered vehicle so they will learn how to deal with real-world engineering problems, similar to those faced by the actual NASA LRV team.
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…
ERIC Educational Resources Information Center
Raymond, Roger A.
Ninth and tenth grade students from two schools were placed in experimental and conventional instruction classes to compare the two methods in teaching algebra by means of achievement test and time needed to complete the course. Pre- and posttests measured aptitude; teachers and students in the experimental groups recorded personal reactions to…
ERIC Educational Resources Information Center
CRAWFORD, ROBERT C.; KEISLAR, EVAN R.
THE MAJOR PROBLEM OF THIS INVESTIGATION WAS TO DETERMINE TO WHAT EXTENT FIRST-GRADE PUPILS ARE CAPABLE OF LEARNING ALGEBRAIC STRUCTURES THROUGH PROGRAMED INSTRUCTION. IN THE EXPERIMENT APPROXIMATELY 130 FIRST-GRADERS WERE INSTRUCTED THROUGH AUDIOVISUAL TEACHING MACHINES FOR APPROXIMATELY 15 WEEKS. AT THE END OF THE PROGRAM, THE CHILDREN WERE…
ERIC Educational Resources Information Center
Kaput, James J.; Blanton, Maria L.
As a part of a long term district-wide study, we report on achievement test results involving students in a third-grade classroom taught by a teacher in a professional development program led by the authors and directed towards the integration of algebraic reasoning with elementary school mathematics. The teacher's practice, reported upon…
ERIC Educational Resources Information Center
Sher, Stephen Korb
2011-01-01
This study looked at 4th grade classrooms to see "how" teachers implement NCTM standards-based or reform-based mathematics instruction and then analyzed it for the capacity to improve students' "algebra readiness." The qualitative study was based on classroom observations, teacher and administrator interviews, and teacher surveys. The study took…
Safety Pharmacology Society: 9th Annual Meeting.
Cavero, Icilio
2010-03-01
The keynote presentation of the Safety Pharmacology (SP) Society 9th Annual Meeting addressed the urgency, for pharmaceutical organizations, to implement strategies for effectively communicating drug risks to all concerned stakeholders and, in particular, the general public. The application of chronobiology to SP investigational protocols can improve the search of drug-induced adverse effects. The Distinguished Service Award Lecture reviewed a life-long journey through trials and tribulations in the quest of the ever-distant scientific truth. The revision process of Directive 86/609/EC for improving animal welfare should be conducted with the purpose of maintaining a fair balance among animal protection, human health and research imperatives in order to prevent the migration of pharmaceutical activities outside Europe. Additional topics of interest were the behavioral, metabolic and cardiovascular problems experienced by small animals housed at the standard laboratory temperature. A technology for the automated collection of blood and urine samples in rats implanted with telemetry sensors was presented. Non-clinical, clinical, regulatory and legal aspects of abuse liability were expertly reviewed. The 'degradability' of pharmaceuticals into environment-friendly chemicals should be an actively searched and optimized feature of future pharmaceuticals in order to prevent drug pollution of ecosystems. Transgenic and diseased animal models should be selected whenever they can facilitate the determination of drug-induced adverse effects. SP strategies to investigate the safety of drug combination products were exemplified and analyzed in depth. The future of SP was proposed to lie not in the performance of regulatory studies of pharmacodynamic nature but in developing and early applying an array of screening assays for clearing clinical candidates against known drug-induced organ function injuries. In conclusion, the 2009 SP Society annual meeting offered a wealth of
"Generalized" algebraic Bethe ansatz, Gaudin-type models and Zp-graded classical r-matrices
NASA Astrophysics Data System (ADS)
Skrypnyk, T.
2016-12-01
We consider quantum integrable systems associated with reductive Lie algebra gl (n) and Cartan-invariant non-skew-symmetric classical r-matrices. We show that under certain restrictions on the form of classical r-matrices "nested" or "hierarchical" Bethe ansatz usually based on a chain of subalgebras gl (n) ⊃ gl (n - 1) ⊃ . . . ⊃ gl (1) is generalized onto the other chains or "hierarchies" of subalgebras. We show that among the r-matrices satisfying such the restrictions there are "twisted" or Zp-graded non-skew-symmetric classical r-matrices. We consider in detail example of the generalized Gaudin models with and without external magnetic field associated with Zp-graded non-skew-symmetric classical r-matrices and find the spectrum of the corresponding Gaudin-type hamiltonians using nested Bethe ansatz scheme and a chain of subalgebras gl (n) ⊃ gl (n -n1) ⊃ gl (n -n1 -n2) ⊃ gl (n - (n1 + . . . +np-1)), where n1 +n2 + . . . +np = n.
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%…
Former 9th and possible future 9th planet in the Solar system
NASA Astrophysics Data System (ADS)
Vidmachenko, A. P.
2016-12-01
4 terrestrial planets and 4 giant planets were formed in the Solar system. The Main asteroid belt is located between them, and the Kuiper belt and Oort cloud are located beyond the giant planets. Therefore, the planetary system is surrounded by a swarm of rocky-icy bodies up to a distance of 105 AU. The former 9th planet in the Solar system, Pluto, is the first known object of the Kuiper Belt. Due to data from the spacecraft "New Horizons" we made significant progress in the study of the physical characteristics of the object and its surface. Numerous observations have shown that the Kuiper belt itself is dynamically stable. And the source of cometary nuclei is a disk scattered by the gravitational perturbation of the giant planets more than 4 billion years ago. Recently, it was reported on indirect evidence of the existence of a new 9th planet in the Solar system with a mass 10 times greater than the mass of the Earth, a distance from the Sun ∼200 AU at perihelion, 600-1200 AU at aphelion, and an orbital period of ∼15000 years. These conclusions are based on the calculation of the orbits of 6 presently known objects of the scattered disc. We pay attention that, in moments close to their discovery, they were located near the perihelion, had a maximum brightness and a maximum orbital velocity. On the basis of probabilistic assumptions, we estimated that the probable number of the same bodies with eccentric orbits should be estimated at many thousands rather than at a few. For the initial evaluation, we used observational data from the Infrared Space Telescope "WISE". They showed that any Saturn's analog has not been registered at distances up to 30 000 AU. Therefore, a super-Earth with a radius of <11000 km (with a mass of ∼10 Earth masses) would have been seen at a distance up to 1000 AU. Thus, either unknown 9th planet is now at a greater distance, or these results cannot be directly scaled to the super-Earth with a disproporti! onately lower internal heat
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 these…
Teacher Quality and Teaching Quality of 7th-Grade Algebra I Honors Teachers
ERIC Educational Resources Information Center
Perez, Barbara
2013-01-01
With more and more focus on accountability, algebra achievement has become a major focus of math curriculum developers. In many states, students are expected to pass standardized Algebra achievement tests in order to satisfy graduation requirements. The purpose of this study was to identify teacher qualities and teaching qualities linked to…
Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target with Bbb Z2n Grading
NASA Astrophysics Data System (ADS)
Ke, San-Min; Li, Xin-Ying; Wang, Chun; Yue, Rui-Hong
2011-10-01
The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target with Bbb Z2n grading is derived using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution. When n = 2, our results coincide with the results given by Magro for the pure spinor description of AdS5 × S5 string theory (when the ghost terms are omitted).
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 Impact of Having 9th Graders "Do History"
ERIC Educational Resources Information Center
Kohlmeier, Jada
2005-01-01
The views of the author's students about history caused her to reflect on her teaching, specifically, what she was lacking in her attempts to teach civic competence through history. This process led her to research historical thinking and design a study in which she exposed her students to the rigors of history. Grant's (2001) study of 9th grade…
Signs and Tools of Algebraic Reasoning: A Study of Models among Fifth Grade Students
ERIC Educational Resources Information Center
Richardson, Kerri
2012-01-01
This study focuses on the types of models created by students during algebraic pattern finding tasks. Attention is also given to the change in models over time. This is an important area of study because a closer look is needed to better understand the models created during mathematical activity, especially in the elementary classroom. It is…
Competence with Fractions in Fifth or Sixth Grade as a Unique Predictor of Algebraic Thinking?
ERIC Educational Resources Information Center
Pearn, Catherine; Stephens, Max
2016-01-01
Researchers have argued that there are strong links between primary school students' competence with fraction concepts and operations and their algebraic readiness. This study involving 162 Years 5/6 students in three primary schools examined the strength of that relationship using a test based on familiar fraction tasks and a test of algebraic…
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…
CCD observations of Phoebe, 9th satellite of Saturn
NASA Astrophysics Data System (ADS)
Fienga, A.; Arlot, J.-E.; Baron, N.; Bec-Borsenberger, A.; Crochot, A.; Emelyanov, N.; Thuillot, W.
2002-08-01
In 1998 and 1999, we started observations of the 9th satellite of Saturn. We made 163 observations using the 120 cm-telescope of Observatoire de Haute-Provence, France. We used the USNO A2 catalogue of stars for the astrometric reduction. With the help of observations of optical counterparts of ICRF sources, a zonal correction to the USNO A2.0 catalogue was computed and applied to the Phoebe positions. A comparison with the most recent theories was made.
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.
Review of the 9th NLTE code comparison workshop
Piron, Robin; Gilleron, Franck; Aglitskiy, Yefim; ...
2017-02-24
Here, we review the 9th NLTE code comparison workshop, which was held in the Jussieu campus, Paris, from November 30th to December 4th, 2015. This time, the workshop was mainly focused on a systematic investigation of iron NLTE steady-state kinetics and emissivity, over a broad range of temperature and density. Through these comparisons, topics such as modeling of the dielectronic processes, density effects or the effect of an external radiation field were addressed. The K-shell spectroscopy of iron plasmas was also addressed, notably through the interpretation of tokamak and laser experimental spectra.
On a possible origin of the 9th planet
NASA Astrophysics Data System (ADS)
Doultsinou, V.; Varvoglis, H.
2017-03-01
In order to interpret some observational evidence in the bodies of the external Solar System (Kuiper Belt Objects - KBOs), it has been recently hypothesized that there exists a so-called 9th planet in the outskirts of our Solar System. Based on this assumption, we have decided to study a new scenario on the possible origin of this body. Instead of assuming that it originates from the Solar System, we will attempt to show that there can be a non-trivial possibility that the 9th planet was originally a free-floating planet (FFP) which, after a close encounter with the Solar System, was either gravitationally captured or flew by, affecting certain orbital elements, ω, Ω and π, as well as the position and orientation in physical space of certain KBOs. We have used a rather simple toy-model based on gravitational scattering in the general 3-dimensional 3-body problem, with the KBOs initially on a circular orbit around the Sun. Promising results serve as indications on this being a plausible scenario, and so this effort could be used as a springboard for a more involved study, based on a more realistic model.
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.
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 dissertation,…
ERIC Educational Resources Information Center
Sabers, Darrell Lee
There were three objectives of a revision and validation of the Iowa Algebra Aptitude Test (IAAT): (1) to reduce the importance of speed; (2) to improve the quality of the existing items; and (3) to replace a subtest with one of potentially greater predictive validity. The last of these goals involved the development of a new subtest composed of a…
Introduction to the Proceedings of the 9th ISDH
NASA Astrophysics Data System (ADS)
Bove, V. Michael, Jr.; Riskin, Seth
2013-02-01
The Proceedings As co-chairs of the 9th International Symposium on Display Holography, we welcome readers of this collection of papers and posters presented at the event. We hope that both attendees of the event and others pursuing the art, science, and business of holography and 3D imaging will find the authors' contributions of lasting interest and importance. The Event Since its creation at Lake Forest College in 1982 by Professor Tung H Jeong, ISDH has followed a model that differentiates it from other scientific conferences. The 9th ISDH continued this history, fully occupying a floor of the MIT Media Lab for five days. The single-track conference opened with reports on the state of holography in the various nations represented by the attendees, followed by a series of presentations on Education and Holography. One and one-half days of papers on Art and Holography followed, then sessions on Techniques and Materials, Digital Techniques, and Commercial and Applied Holography. A poster session permitted more in-depth discussion between authors and the audience. Two exhibitions of holographic works opened at ISDH: an informal display area at the symposium, and a 15-month-long MIT Museum exhibition, The Jeweled Net: Views of Contemporary Holography. The success of an event of this sort requires the help of many people and organizations. We wish especially to recognize our Honorary Conference Chairs: Tung H Jeong and Joseph W Goodman; our Technical Program Committee: Hans I Bjelkhagen, Frank Fan, Nasser Peyghambarian, and Hiroshi Yoshikawa; and our Arts and Exhibition Committee: Betsy Connors-Chen, Melissa Crenshaw, John Durant, Dieter Jung, Linda Law, Martin Richardson, Jonathan Ross, and Sally Weber. Betsy also coordinated the on-site exhibition. Kristin Hall at the MIT Media Lab made local arrangements, while registration was handled by MIT Conference Services. We also gratefully acknowledge support from Lake Forest College, holographer.org, and authentibrand
NANOTR9: 9th Nanoscience and Nanotechnology Conference
NASA Astrophysics Data System (ADS)
2014-11-01
The conference series NanoTR is the major conference on nanoscience and nanotechnology in Turkey. It brings together leading scientists and engineers in nanotechnology to exchange information on their latest research progress. An exhibition of the companies working in the related field is also organized as a part of the event. With intensive international participation, NanoTR conference series has spread outside the national border and has become an international event in this field. Among international contributions, a wide interest from the countries around Turkey should be emphasized. 9th in the series was organized by Atatürk University in Erzurum-Turkey on June 24-28, 2013 with more than 900 scientists, researchers, private sector representatives from around the world. Conference program included 6 plenary speakers, 35 invited speakers (18 of them were from outside the country), 116 oral presentations, and 340 poster presentations. In addition to 6 plenary sessions, 17 oral and 4 poster sessions created very lively discussion forums covering a vast range of current and emerging sciences from nano-materials, nanoscience, nanofabrication, nano-engineering, nano-electronics, nano-biotechnology, to ethical and social issues of nanoscience and nanotechnology. Also, panel discussions about industrial applications, tutorial sessions have been organized for students, new-comers and company employees.
ERIC Educational Resources Information Center
Blanton, Maria; Levi, Linda; Crites, Terry; Dougherty, Barbara; Zbiek, Rose Mary
2011-01-01
Like algebra at any level, early algebra is a way to explore, analyze, represent, and generalize mathematical ideas and relationships. This book shows that children can and do engage in generalizing about numbers and operations as their mathematical experiences expand. The authors identify and examine five big ideas and associated essential…
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
ERIC Educational Resources Information Center
Cavanagh, Sean
2008-01-01
A popular humorist and avowed mathphobe once declared that in real life, there's no such thing as algebra. Kathie Wilson knows better. Most of the students in her 8th grade class will be thrust into algebra, the definitive course that heralds the beginning of high school mathematics, next school year. The problem: Many of them are about three…
Survey of Oral Health Awareness in Neuchâtel 9th Graders.
Neuhaus, Klaus W; Müller, Magali E; Lussi, Adrian
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.
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
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…
Central extensions of Lax operator algebras
NASA Astrophysics Data System (ADS)
Schlichenmaier, M.; Sheinman, O. K.
2008-08-01
Lax operator algebras were introduced by Krichever and Sheinman as a further development of Krichever's theory of Lax operators on algebraic curves. These are almost-graded Lie algebras of current type. In this paper local cocycles and associated almost-graded central extensions of Lax operator algebras are classified. It is shown that in the case when the corresponding finite-dimensional Lie algebra is simple the two-cohomology space is one-dimensional. An important role is played by the action of the Lie algebra of meromorphic vector fields on the Lax operator algebra via suitable covariant derivatives.
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…
The Use of Communicative Approach in 9th Grade EFL Classes
ERIC Educational Resources Information Center
Denkci Akkas, Ferdane; Coker, Berna
2016-01-01
Problem Statement: Having appeared in the 60s, the Communicative Approach still keeps its popularity in language teaching contexts. There is almost no doubt that its application varies depending on the teacher's understanding of the methodology. Likewise, some studies on the application of the Communicative Approach in Turkey have revealed that…
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…
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…
College Knowledge of 9th and 11th Grade Students: Variation by School and State Context
ERIC Educational Resources Information Center
Bell, Angela D.; Rowan-Kenyon, Heather T.; Perna, Laura W.
2009-01-01
While college enrollment rates have increased over the last 40 years, gaps still exist across groups. College enrollment rates are lower for high school graduates whose parents have not attended college, those with low-incomes, as well as Black and Latino/a students than for other high school graduates. One source of differences across groups in…
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)
Roytenberg, Dmitry
2007-11-01
A Lie 2-algebra is a linear category equipped with a functorial bilinear operation satisfying skew-symmetry and Jacobi identity up to natural transformations which themselves obey coherence laws of their own. Functors and natural transformations between Lie 2-algebras can also be defined, yielding a 2-category. Passing to the normalized chain complex gives an equivalence of 2-categories between Lie 2-algebras and certain "up to homotopy" structures on the complex; for strictly skew-symmetric Lie 2-algebras these are L∞-algebras, by a result of Baez and Crans. Lie 2-algebras appear naturally as infinitesimal symmetries of solutions of the Maurer-Cartan equation in some differential graded Lie algebras and L∞-algebras. In particular, (quasi-) Poisson manifolds, (quasi-) Lie bialgebroids and Courant algebroids provide large classes of examples.
ERIC Educational Resources Information Center
Brown, Irving A.; Davis, Trina J.; Kulm, Gerald
2011-01-01
This article presents our plans and initial work to explore how mathematics teacher education programs can prepare teachers for diverse middle grades classrooms. It describes the start-up of a five-year National Science Foundation project to design, develop, and test technology-enriched teacher preparation strategies to address equity in algebra…
The PRIME Partnership: 9th Graders, Graduate Students and Integrated, Inquiry-Based Science
NASA Astrophysics Data System (ADS)
Gaffney, A. M.; Miguelez, S.
2001-12-01
The PRIME program (Partnership for Research in Inquiry-based Math, science and engineering Education) is a collaboration between the UW Colleges of Education and Engineering and several Seattle-area school districts. This project, funded by the NSF GK-12 program, pairs UW graduate students from math, science and engineering disciplines with local middle school teachers. The graduate student spends a year working with the teacher, on projects designed to meet the needs and interests of the specific partnership and classroom. In the partnership, the graduate student spends 15 hours per week in the classroom, interacting with the students, as well as additional planning time outside of the classroom. Goals of the PRIME program are enriched learning by middle school students, professional development for middle school teachers, improved communication and teaching skills for the graduate students, and strengthened partnerships between the University of Washington and local school districts. The goal of our partnership was to develop an inquiry-based, 9th grade unit that integrates the pre-existing Earth Science and Chemistry units, and to assess the effectiveness of teaching Chemistry in the context of Earth Science. We have observed that students often become engaged and excited when they do hands-on activities that utilize the intrinsic understanding that they have of concepts that draw upon experiences in their daily lives. When science is taught and learned in one such context - in the context of the natural world - the students may gain a more solid fundamental understanding of the science that they learn. The day-to-day activities for this unit vary widely. We started each topic with a question designed to get the students thinking independently and to identify the preconceptions that the students brought into the classroom. Discussions of students' preconceptions served as a justification and springboard for the subsequent activities and experiments. Examples of
Global perspectives on poisonous plants: The 9th International Symposium on Poisonous Plants
Technology Transfer Automated Retrieval System (TEKTRAN)
The 9th International Symposium on Poisonous Plants (ISOPP9) was held from 15th-21st July, 2013, at the Inner Mongolia Agricultural University in Hohhot, Inner Mongolia Autonomous Region of China. The Symposium consisted of three days of oral and poster presentations, followed by a tour of the Xilin...
5. West side of State Steeet looking down 9th Steeet. ...
5. West side of State Steeet looking down 9th Steeet. Immediatly to the west lie the Illinois and Michigan Canal, the Chicago Sanitary and Ship Canal, and the Des Plaines River. - Lockport Historic District, Bounded by Eighth, Hamilton & Eleventh Streets & Illinois & Michigan Canal, Lockport, Will County, IL
The Evaluation of Health Education Program (HEP) of 9th Graders
ERIC Educational Resources Information Center
Erdogan, Polat; Gürol, Mehmet
2016-01-01
The main purpose of evaluation is to improve the quality of program. So, the purpose of this study was to evaluate the Health Education Program of 9th graders (HEP) with Educational Criticism Model of Eisner. The study was conducted with the qualitative research method. A holistic single case design was employed in this study. The typical case…
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…
UCSMP Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2007
2007-01-01
"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…
Embedding Algebraic Thinking throughout the Mathematics Curriculum
ERIC Educational Resources Information Center
Vennebush, G. Patrick; Marquez, Elizabeth; Larsen, Joseph
2005-01-01
This article explores the algebra that can be uncovered in many middle-grades mathematics tasks that, on first inspection, do not appear to be algebraic. It shows connections to the other four Standards that occur in traditional algebra problems, and it offers strategies for modifying activities so that they can be used to foster algebraic…
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…
NASA Astrophysics Data System (ADS)
Chieng Chen, Vincent Lee
2015-04-01
A very warm welcome to all participants of the 9th Curtin University Technology, Science and Engineering (CUTSE) Conference 2014. This annual conference dates back to 2006 when the first Curtin University of Technology Science and Engineering (CUTSE) Conference was held in Curtin University, Miri Sarawak. CUTSE Conference was initially intended for Curtin's undergraduates such that they are able to experience the presentation of their work in a conference environment. As time passes and following the urge of knowledge dissemination, CUTSE Conference is hence open to public. This year the Department of Mechanical Engineering has been given the honour to organize the 9th CUTSE Conference. It has been a pleasure to watch CUTSE grow from strength to strength over the years. This year, our theme is "Discovering, Innovating and Engineering". We hope that it is in this spirit that CUTSE participants may align their respective work, such that we all aim for a greater and better implementation of "Discovering, Innovating and Engineering". The 9th CUTSE Conference 2014 is an excellent avenue for researchers, engineers, scientists, academicians, professionals from industry and students to share their research findings and initiate further collaborations in their respective fields. Parallel sessions in Mechanical, Electrical, Computer, Civil and Chemical engineering as well as the sciences will be hosted over a period of two days. Each year, the conference attracts participation from a number of countries in addition to Malaysia and Australia. In addition, student participants will get the opportunity to present their research projects and gain valuable feedback from industry professionals. This year the Conference will be organised by the Department of Mechanical Engineering of Curtin Sarawak's School of Engineering and Science in collaboration with The Institute of Engineers Malaysia, Miri Branch. On behalf of the organizing committee, I would like to thank this year
9th Circuit to reconsider earlier ruling in religious rights case.
1999-11-26
The 9th U.S. Circuit Court of Appeals will re-examine a ruling that allows landlords with strongly held religious beliefs to refuse to rent to unmarried persons. In [name removed] v. Anchorage Equal Rights Commission, the court ruled that landlords did not have to comply with local and State statutes forbidding discrimination on the basis of marital status. An appeals panel had ruled that landlords had a valid claim to First Amendment and Fifth Amendment protection. The court is expected either to reverse on the issue of standing or to find that the hybrid rights doctrine was misused in the case.
Multidisciplinary molecular diagnostics: the 9th European meeting on molecular diagnostics.
Loonen, Anne J M; Schuurman, Rob; van den Brule, Adriaan J C
2016-01-01
This report presents a summary of the 9th European Meeting on Molecular Diagnostics held in Noordwijk, The Netherlands, 14-16 October 2015. This 3-day conference covered many relevant topics in the field of molecular diagnostics in humans, including infectious disease, oncology, outbreak management, population-based cancer screening, standardization and quality control, chronic diseases and pharmacogenetics. Beyond these different areas, shared values are new technologies and novel technical and clinical applications. Approximately 450 participants, the majority coming from European countries, attended the meeting. Besides high quality scientific presentations, more than 35 diagnostic companies presented their latest innovations, altogether in an informal and inspiring scientific ambience.
Geometric frustration on a 1/9th site depleted triangular lattice
NASA Astrophysics Data System (ADS)
Hopkinson, John; Beck, Jarrett
2013-03-01
In the searches both for new spin liquid and spin ice (artificial and macroscopic) candidates, geometrically frustrated two-dimensional spin systems have played a prominent role. Here we present a study of the classical antiferromagnetic Ising (AFI) model on the sorrel net, a 1/9th site depleted and 1/7th bond depleted triangular lattice. The AFI model on this corner-shared triangle net is found to have a large residual entropy per spin S/N = 0 . 48185 +/- 0 . 00008 , indicating the sorrel net is highly geometrically frustrated. Anticipating that it may be difficult to achieve perfect bond depletion, we investigate the physics resulting from turning back on the depleted bonds (J2). We present the phase diagram, analytic expressions for the long range partially ordered ground state spin structure for antiferromagnetic J2 and the short range ordered ground state spin structure for ferromagnetic J2, the magnetic susceptibility and the static structure factor. We briefly comment on the possibility that artificial spin ice on the sorrel lattice could by made, and on a recent report [T. D. Keene et al., Dalton Trans. 40 2983 (2011)] of the creation of a 1/9th depleted cobalt hydroxide oxalate. This work was supported by NSERC (JMH) and NSERC USRA (JJB)
Classification of central extensions of Lax operator algebras
Schlichenmaier, Martin
2008-11-18
Lax operator algebras were introduced by Krichever and Sheinman as further developments of Krichever's theory of Lax operators on algebraic curves. They are infinite dimensional Lie algebras of current type with meromorphic objects on compact Riemann surfaces (resp. algebraic curves) as elements. Here we report on joint work with Oleg Sheinman on the classification of their almost-graded central extensions. It turns out that in case that the finite-dimensional Lie algebra on which the Lax operator algebra is based on is simple there is a unique almost-graded central extension up to equivalence and rescaling of the central element.
Classification of central extensions of Lax operator algebras
NASA Astrophysics Data System (ADS)
Schlichenmaier, Martin
2008-11-01
Lax operator algebras were introduced by Krichever and Sheinman as further developments of Krichever's theory of Lax operators on algebraic curves. They are infinite dimensional Lie algebras of current type with meromorphic objects on compact Riemann surfaces (resp. algebraic curves) as elements. Here we report on joint work with Oleg Sheinman on the classification of their almost-graded central extensions. It turns out that in case that the finite-dimensional Lie algebra on which the Lax operator algebra is based on is simple there is a unique almost-graded central extension up to equivalence and rescaling of the central element.
ERIC Educational Resources Information Center
Cavanagh, Sean
2009-01-01
As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…
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…
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.
Proceedings of the 9th International Workshop on Accelerator Alignment (IWAA06)
Fuss, B.,; /SLAC
2006-12-18
The 9th International Workshop on Accelerator Alignment (IWAA06) took place at SLAC from September 25th to 29th of 2006. On Monday many participants registered for the event and took part in an ice-breaker reception sponsored by FARO Technologies. Following this, four days of talks and discussion began with status reports and presentations from various accelerators or similar laboratories around the world. Subsequent talks ranged from large-scale metrology, integrating and adjusting survey data, survey instrumentation and presentations on monitoring systems. This event included ongoing poster displays and a vendor exhibition. In these proceedings the presentations, papers and posters of the IWAA06 participants are available for online review.
NASA Astrophysics Data System (ADS)
Sungging Mumpuni, Emanuel; Zamzam Nurzaman, Muhamad; Suryana, Nana
2016-11-01
Spectroscopy observation of solar corona has been carried out from 9th March 2016 Total Solar Eclipse expedition in Maba, East Halmahera. Due to limitation by the weather condition during the observation, the obtained data were not favorable. Because of the low signal to noise ratio, the wavelength calibration was not straightforward. To obtain the optimum results, steps for data reduction were performed as the following: selecting the finest data, extracting the 1D spectrum from 2D spectrum, and calibrating spectrum wavelength (including careful interpolation). In this preliminary result, we discuss the instrumentation, the data under investigation, the extraction process of spectrum, and the polynomial interpolation that has been used for extracting information from our data.
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
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…
ERIC Educational Resources Information Center
Sears, Bill
This curriculum unit requires students to use science, geography, and language arts skills in studying the weather. Students are asked to report on weather anomalies and are provided with background information, detailed instructions, online resources, and reflection questions. The teacher's guide describes the unit's purpose, correlation to…
ERIC Educational Resources Information Center
Johnson-Moore, Brenda
This paper discusses a practicum designed to address young teen mothers' lack of knowledge, experience, and skills needed to appropriately care for their infants. It documents that increased knowledge, enhanced interpersonal relationships, and augmented parenting skills made a difference in the teen mothers' approach to parenting. Parenting…
ERIC Educational Resources Information Center
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
Grillo, Stacy A.
2012-01-01
The transition into high school is a traumatic event in an adolescent's life. Students face several emotional challenges during their high school years as they struggle to gain a sense of self, develop the tools needed to advocate for their own needs, and navigate the demands of a new school. A successful transition into high school has a…
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
Arkansas State Univ., State University.
This curriculum package contains materials for teaching the career orientation course in the junior high schools of Arkansas. Following the introduction, which describes the course and provides a rationale for it, along with instructions to teachers for conducting the course, the package is divided into 35 units organized under five major…
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…
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…
Gary M. Klingler Algebra Teacher Assistance Packages
ERIC Educational Resources Information Center
Klingler, Gary
2005-01-01
Several packages designed by Elizabeth Marquez for mathematics teachers of grades 6-12, officially entitled the Teacher Assistance Package in Support of Better Algebra Assessment, is a series of resources developed to accompany ET's End-of-Course Algebra Assessment. It is designed to enhance teachers classroom assessment by providing examples of…
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…
The Impact of Early Algebra: Results from a Longitudinal Intervention
ERIC Educational Resources Information Center
Brizuela, Bárbara M.; Martinez, Mara V.; Cayton-Hodges, Gabrielle A.
2013-01-01
In this paper, we provide evidence of the impact of early algebra (EA) over time. We document this impact in the following ways: (a) by showing the performance over time of an experimental group of 15 children on an algebra assessment, from 3rd to 5th grade; and (b) by showing how the performance on an algebra assessment of children from an…
Changing Pre-Service Elementary Teachers' Attitudes to Algebra.
ERIC Educational Resources Information Center
McGowen, Mercedes A.; Davis, Gary E.
This article addresses the question: "What are the implications for the preparation of prospective elementary teachers of 'early algebra' in the elementary grades curriculum?" Part of the answer involves language aspects of algebra: in particular, how a change in pre-service teachers' attitudes to algebra, from instrumental to relational, is…
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…
Identification of moon craters and solar corona during total solar eclipse on 9th March 2016
NASA Astrophysics Data System (ADS)
Luthfiandari; Ekawanti, N.; Purwati, F. G.; Herdiwijaya, D.
2016-11-01
Total Solar Eclipse (TSE) is a rare natural event in which the positions of Sun, Moon, and Earth are perfectly aligned. In the past by using this phenomenon, many researches have been done to understand characteristic of the corona. In this paper we carried out the study of TSE which crossed over Indonesia from West to East on 9th March 2016. We observed TSE which occured in Palembang (2.9883° S 104.7513° E), Indonesia. The aim of this research is to understand the effect of moon craters on the appearance of solar corona and identification of solar active regions during TSE. This research was done using Canon SX170 IS camera with ND 5 sun-filter. Although the sky was cloudy during the totality of the phase, coronal video was still taken. Camera also took solar images of partial eclipse phase. Coronal images for every frame were then extracted from the video. Image processing of coronal images was done using RegiStax and PhotoScape freewares. To study solar corona, images from Virtual Moon Atlas, Hinode XRT, and SOHO-LASCO were compared with the result of oriented coronal image. Wider and many more moon craters were found having positive correlation with the brighter effect on solar corona as shown at westward coronal streamer. Those craters are represented by Bel'kovich crater, the biggest one. We also found that only the eastward coronal streamer was correlated with active region, sunspot number 12519, from behind solar limb.
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.
Obsessional Disorders in al-Balkhi's 9th century treatise: Sustenance of the Body and Soul.
Awaad, Rania; Ali, Sara
2015-07-15
Some argue that the earliest case of Obsessive-Compulsive Disorder (OCD) was reported by Robert Burton in his compendium The Anatomy of Melancholy (1621) and that only in the 19th century did modern concepts of OCD evolve, differentiating it from other types of mental illness. In this paper, we aim to reveal an even earlier presentation of the malady we now call OCD based on the 9th century work, Sustenance of the Body and Soul, written by Abu Zayd al-Balkhi during the Islamic Golden Era. Discovery of this manuscript reveals that Abu Zayd al-Balkhi should be credited with differentiating OCD from other forms of mental illnesses nearly a millennium earlier than is currently claimed by anthologies documenting the history of mental illness. Particular attention is paid to al-Balkhi's classifications, symptom descriptions, predisposing factors, and the treatment modalities for obsessional disorders. Analysis of this manuscript in light of the DSM-5 and modern scientific discoveries reveals transcultural diagnostic consistency of OCD across many centuries. Theoretical and clinical implications of these findings are also discussed.
Stellar background observation during Total Solar Eclipse March 9th 2016
NASA Astrophysics Data System (ADS)
Mumtahana, Farahhati; Timur Jaelani, Anton; Muhamad, Johan; Sutastio, Heri
2016-11-01
We report observation and an early analysis of stellar background from total solar eclipse in Ternate, Indonesia. The eclipse phenomena which occurred on March, 9th 2016 was observed with certain portable instruments in order to obtain the stars behind the Sun in particular field of view and resolution. From our observation site in Ternate city, solar eclipse occurred in the late morning when the weather was unfortunately cloudy. However, during the darkness of totality, we obtained several point source objects between the gaps of the moving clouds and we suspected them as very faint stars due to their appearance in several frames. Those so called stars have been identified and measured with respect to their positions toward the center of the Sun. The main purpose of this research is to revisit strong lensing calculation of the Sun during total solar eclipse by measuring the deflection angle of the background stars as it had been calculated by Einstein and proved by Eddington at a total solar eclipse in 1919. To accomplish this aim, we need to conduct another observation to measure position of the same stars in the next period when those stars appear in the night sky.
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…
NASA Technical Reports Server (NTRS)
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
NASA Astrophysics Data System (ADS)
Mikhalev, A. V.; Pinchuk, I. A.
2005-06-01
The structure of Steinberg conformal algebras is studied; these are analogues of Steinberg groups (algebras, superalgebras).A Steinberg conformal algebra is defined as an abstract algebra by a system of generators and relations between the generators. It is proved that a Steinberg conformal algebra is the universal central extension of the corresponding conformal Lie algebra; the kernel of this extension is calculated.
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
Pay-Offs from Expanding Summer Credit Recovery in Algebra
ERIC Educational Resources Information Center
Allensworth, Elaine; Nomi, Takako; Heppen, Jessica
2013-01-01
The consequences of failing core academic courses during the first year are dire. In Chicago, over a quarter of students fail at least one semester of algebra in their ninth grade year, and only 13% of students who fail both semesters of Algebra I in ninth grade graduate in 4 years. Offering credit recovery options is one strategy to deal with…
Effects of Expanding Summer Credit Recovery in Algebra
ERIC Educational Resources Information Center
Allensworth, Elaine; Michelman, Valerie; Nomi, Takako; Heppen, Jessica
2014-01-01
In Chicago, over a quarter of students fail at least one semester of algebra in their ninth grade year, and only 13% of students who fail both semesters of Algebra I in ninth grade graduate in 4 years. Offering credit recovery options is one strategy to deal with high failure rates. The primary goal of credit recovery programs is to give students…
Relational Thinking: Learning Arithmetic in Order to Promote Algebraic Thinking
ERIC Educational Resources Information Center
Napaphun, Vishnu
2012-01-01
Trends in the curriculum reform propose that algebra should be taught throughout the grades, starting in elementary school. The aim should be to decrease the discontinuity between the arithmetic in elementary school and the algebra in upper grades. This study was conducted to investigate and characterise upper elementary school students…
ERIC Educational Resources Information Center
Capani, Antonio; De Dominicis, Gabriel
This paper proposes a model for a general interface between people and Computer Algebra Systems (CAS). The main features in the CAS interface are data navigation and the possibility of accessing powerful remote machines. This model is based on the idea of session management, in which the main engine of the tool enables interactions with the…
I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report
ERIC Educational Resources Information Center
What Works Clearinghouse, 2007
2007-01-01
The "I CAN Learn[R] Pre-Algebra" and "Algebra" computerized curricula are designed to cover mathematics and problem-solving skills for ethnically diverse, inner-city students in grades 6-12. The curricula are designed to equip students with the skills they need to meet district, state, and national math objectives through an…
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
Effects of Career Education on 9th Graders in Rural Mississippi.
ERIC Educational Resources Information Center
Sprabery, Carol A.; King, Jo Carol
This study evaluated a career education program for 141 ninth grade students at Kemper County High School in rural Mississippi in an effort to reduce the dropout rate and increase career awareness. A mental health counselor gave students monthly instruction on career issues necessary for vocational life after high school graduation. A local…
Ninth Grade Repeaters--Why They Did Better in Summer School.
ERIC Educational Resources Information Center
Jones, Helen
A widely held perception is that public schools are failing American children and society. Some research indicates that 9th-graders are more at risk for school failure than are students in other grades. This paper presents findings of a study that examined 9th-graders in the Durham Public School System (North Carolina) who were enrolled in a Basic…
Herold, Hajnalka
2012-11-01
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.
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.
PREFACE: 9th IAEA Technical Meeting on H-mode Physics and Transport Barriers
NASA Astrophysics Data System (ADS)
Groebner, Richard
2004-05-01
This special issue of Plasma Physics and Controlled Fusion contains invited and contributed papers presented at the 9th IAEA Technical Meeting on H-mode Physics and Transport Barriers. This meeting was held at the Catamaran Hotel in San Diego, California, on 24-26 September, 2003, and it was organized by General Atomics. As has been the tradition at the last four meetings of this series, the programme was sub-divided into six topics. For each topic there was an invited talk whose purpose was to give an overview of the topic, based on contributed papers presented at the meeting and on external results. These talks were followed by discussion periods, which were used for extended question and answer sessions for the invited speakers or for additional short presentations by contributing speakers. For each topic there was an associated poster session for contributed papers, of which there were about 70. The topics were: Structure and dynamics of internal transport barriers Structure and dynamics of the H-mode pedestal Understanding transport barriers through modelling Control of transport barriers Transport within transport barriers: theorist's view of the future Diagnostic and analysis issues for transport barriers The topics were focused on the physics of edge and core transport barriers. Similar to the previous meeting, held in Toki, Japan, the universality of this physics in axisymmetric and non-axisymmetric machines was featured. In addition, the physics of transport barriers in relation to burning plasma experiments was emphasized. In particular, one of the hopes and goals of the participants is that the physics of transport barriers can be used to enhance the prospects for burning plasmas. Because this meeting occurred approximately 21 years after the discovery of the H-mode in 1982, a special session was held to commemorate more than 20 years of research on transport barriers. In this session, Dr R Stambaugh and Professor K Itoh presented personal views on the
Gradings on the real form 𝔢6,-26
NASA Astrophysics Data System (ADS)
Draper, Cristina; Guido, Valerio
2016-10-01
We describe four fine gradings on the real form 𝔢6,-26 of the complex Lie algebra 𝔢6. They are precisely the gradings whose complexifications are fine gradings on the complex algebra. The universal grading groups are Z2 6 , Z × Z2 4 , Z 2 × Z2 3 , and Z 4 × Z2 4 .
Algebraic Lattices in QFT Renormalization
NASA Astrophysics Data System (ADS)
Borinsky, Michael
2016-07-01
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.
Difficulties in initial algebra learning in Indonesia
NASA Astrophysics Data System (ADS)
Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja
2014-12-01
Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.
Experimental Course Report/Grade Nine.
ERIC Educational Resources Information Center
Davis, Robert B.
Described is the development of an approach to the algebra of real numbers which includes three areas of mathematics not commonly found in grade 9--the theory of limits of infinite sequences, a frequent use of Cartesian co-ordinates, and algebra of matrices. Seventy per cent of the course is abstract axiomatic algebra and the remaining portion…
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.
Derive Workshop Matrix Algebra and Linear Algebra.
ERIC Educational Resources Information Center
Townsley Kulich, Lisa; Victor, Barbara
This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…
ERIC Educational Resources Information Center
Kaput, James J.
This paper asserts that the key to algebra reform is to integrate algebraic reasoning across all grades and all topics, to "algebrafy" school mathematics. The distinction is made between algebra "the institution" and algebra "the web of knowledge and skill," which is also clarified. Finally, suggestions are made as to how the educational community…
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
NASA Astrophysics Data System (ADS)
Arlot, J.-E.; Bec-Borsenberger, A.; Fienga, A.; Baron, N.
2003-11-01
In order to improve the model used for the ephemerides of Phoebe, the 9th satellite of Saturn, we started observations in 1998. We made 135 observations in 1998 and 39 observations in 1999 using the 120 cm-telescope of Observatoire de Haute-Provence, France. We used a numerical integration in order to calculate new initial conditions and to be able to build new ephemerides. We also used some precise observations made from 1995 to 2000 together with old observations for that purpose. The result is a decrease in the uncertainties on Phoebe's orbit. Based in part on observations made at observatoire de Haute Provence (CNRS), France.
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.
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.
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…
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…
Quantum cluster algebras and quantum nilpotent algebras
Goodearl, Kenneth R.; Yakimov, Milen T.
2014-01-01
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197
Supersymmetry in physics: an algebraic overview
Ramond, P.
1983-01-01
In 1970, while attempting to generalize the Veneziano model (string model) to include fermions, I introduced a new algebraic structure which turned out to be a graded Lie algebra; it was used as a spectrum-generating algebra. This approach was soon after generalized to include interactions, yielding a complete model of fermions and boson (RNS model). In an unrelated work in the Soviet Union, it was shown how to generalize the Poincare group to include fermionic charges. However it was not until 1974 that an interacting field theory invariant under the Graded Poincare group in 3 + 1 dimensions was built (WZ model). Supersymmetric field theories turned out to have less divergent ultraviolet behavior than non-supersymmetric field theories. Gravity was generalized to include supersymmetry, to a theory called supergravity. By now many interacting local field theories exhibiting supersymmetry have been built and studied from 1 + 1 to 10 + 1 dimensions. Supersymmetric local field theories in less than 9 + 1 dimensions, can be understood as limits of multilocal (string) supersymmetric theories, in 9 + 1 dimensions. On the other hand, graded Lie algebras have been used in non-relativistic physics as approximate symmetries of Hamiltonians. The most striking such use so far helps comparing even and odd nuclei energy levels. It is believed that graded Lie algebras can be used whenever paired and unpaired fermions excitations can coexist. In this overview of a tremendously large field, I will only survey finite graded Lie algebras and their representations. For non-relativistic applications, all of GLA are potentially useful, while for relativistic applications, only these which include the Poincare group are to be considered.
NASA Astrophysics Data System (ADS)
Marion, F.; Mours, B.
2005-09-01
The yearly Gravitational Wave Data Analysis Workshop (GWDAW) is now a well established meeting. As usual, the scope of the meeting covered the status of ground-based and space-based detectors, sources and population modelling, detector characterization, event searches, multi-detector analysis and new analysis methods. The 9th GWDAW followed the trend observed in previous years: more presentations that included real data and more sophisticated analysis techniques. However, the biggest change observed was a significant increase in the number of presentations dealing with the analysis of data coming from multiple detectors. Our field needs to combine these data to best extract the astrophysical information. This yearly meeting, bringing together all the worldwide players in the field, is a chance for us to make progress in this direction, and we will certainly see more results in future GWDAW meetings. The importance of the 9th GWDAW meeting can be assessed not only by the record attendance and number of submitted contributions, but also by looking at the work schedules of the various groups. People are now using the GWDAW dates to set deadlines for their activities in order to present their results at the next GWDAW. This special issue of Classical and Quantum Gravity contains the most up-to-date papers on the topics covered by the meeting. Besides being a good reference that will fit proudly into the series of previous GWDAW proceedings, it provides valuable details about current work. As organizers of this workshop, we would like to thank not only the sponsors that made this meeting possible, but also all the participants for coming, sharing their results and enjoying the event with us. The following institutions have sponsored the 9th GWDAW: Laboratoire d'Annecy-le-Vieux de Physique des Particules (LAPP) European Gravitational Observatory (EGO) Université de Savoie Groupement de Recherche: Phénomènes cosmiques de haute énergie (GDR-PCHE) Institut National de
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].
Gadher, Suresh Jivan; Marczak, Łukasz; Łuczak, Magdalena; Stobiecki, Maciej; Widlak, Piotr; Kovarova, Hana
2016-01-01
Every year since 2007, the Central and Eastern European Proteomic Conference (CEEPC) has excelled in representing state-of-the-art proteomics in and around Central and Eastern Europe, and linking it to international institutions worldwide. Its mission remains to contribute to all approaches of proteomics including traditional and often-revisited methodologies as well as the latest technological achievements in clinical, quantitative and structural proteomics with a view to systems biology of a variety of processes. The 9th CEEPC was held from June 15th to 18th, 2015, at the Institute of Bioorganic Chemistry, Polish Academy of Sciences in Poznań, Poland. The scientific program stimulated exchange of proteomic knowledge whilst the spectacular venue of the conference allowed participants to enjoy the cobblestoned historical city of Poznań.
Programed Instruction in Elementary Algebra: An Experiment
ERIC Educational Resources Information Center
Lial, Margaret L.
1970-01-01
Report of an experiment which investigated the use of a programed elementary algebra text as a teaching method. The method was evaluated on the basis of student evaluation of the course and the percentage of students achieving a grade of C or better. Results indicated that the use of programed texts was superior to the traditional approach using…
Using Technology to Balance Algebraic Explorations
ERIC Educational Resources Information Center
Kurz, Terri L.
2013-01-01
In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…
Graded geometry and Poisson reduction
Cattaneo, A. S.; Zambon, M.
2009-02-02
The main result extends the Marsden-Ratiu reduction theorem in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof for the main result.
Teachers' Understanding of Algebraic Generalization
NASA Astrophysics Data System (ADS)
Hawthorne, Casey Wayne
Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby teachers respond to and build upon the ideas that arise from students' explorations of these activities. Although more and more teachers are engaging their students in such generalizing tasks, little is known about teachers' understanding of generalization and their understanding of students' mathematical thinking in this domain. In this work, I addressed this gap, exploring the understanding of algebraic generalization of 4 exemplary 8th-grade teachers from multiple perspectives. A significant feature of this investigation is an examination of teachers' understanding of the generalization process, including the use of algebraic symbols. The research consisted of two phases. Phase I was an examination of the teachers' understandings of the underlying quantities and quantitative relationships represented by algebraic notation. In Phase II, I observed the instruction of 2 of these teachers. Using the lens of professional noticing of students' mathematical thinking, I explored the teachers' enacted knowledge of algebraic generalization, characterizing how it supported them to effectively respond to the needs and queries of their students. Results indicated that teachers predominantly see these figural patterns as enrichment activities, disconnected from course content. Furthermore, in my analysis, I identified conceptual difficulties teachers experienced when solving generalization tasks, in particular, connecting multiple symbolic representations with the quantities in the figures. Moreover, while the teachers strived to overcome the challenges of connecting different representations, they invoked both productive and unproductive
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…
ERIC Educational Resources Information Center
Miller, L. Diane; England, David A.
1989-01-01
Describes a study in a large metropolitan high school to ascertain what influence the use of regular writing in algebra classes would have on students' attitudes towards algebra and their skills in algebra. Reports the simpler and more direct the writing topics the better. (MVL)
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.
Applied Algebra Curriculum Modules.
ERIC Educational Resources Information Center
Texas State Technical Coll., Marshall.
This collection of 11 applied algebra curriculum modules can be used independently as supplemental modules for an existing algebra curriculum. They represent diverse curriculum styles that should stimulate the teacher's creativity to adapt them to other algebra concepts. The selected topics have been determined to be those most needed by students…
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…
Ternary Virasoro - Witt algebra.
Zachos, C.; Curtright, T.; Fairlie, D.; High Energy Physics; Univ. of Miami; Univ. of Durham
2008-01-01
A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations.
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.
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
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.
NASA Astrophysics Data System (ADS)
Silvestro, F.; Rebora, N.; Giannoni, F.; Cavallo, A.; Ferraris, L.
2016-10-01
On the 9th October, 2014 a strong event hit the central part of Liguria Region producing disastrous consequences to the city of Genoa where the Bisagno Creek flooded causing one death and lots of damage. The precipitation pattern responsible for the event had peculiar spatial and temporal characteristics that led to an unexpected flash flood. The temporal sequence of rainfall intensities and the particular severity of rainfall showers at small temporal scale, together with the size of the sub-basin hit by the most intense part of the rainfall were the unfortunate concurrent ingredients that led to an "almost perfect" flash flood. The peak flow was estimated to be a 100-200 years order return period. The effects of the spatial and temporal scales of the precipitation pattern were investigated by coupling a rainfall downscaling model with a hydrological model setting up an experiment that follows a probabilistic approach. Supposing that the correct volume of precipitation at different spatial and temporal scales is known, the experiment provided the probability of generating events with similar effects in terms of streamflow. Furthermore, the study gives indications regarding the goodness and reliability of the forecasted rainfall field needed, not only in terms of total rainfall volume, but even in spatial and temporal pattern, to produce the observed ground effects in terms of streamflow.
Post-seismic deformation of the Mw 6.4 Shonbeh earthquake (south western Iran) of April 9th, 2013
NASA Astrophysics Data System (ADS)
Fathian Baneh, Aram; Tolomei, Cristiano; Lugari, Alessandro; Trasatti, Elisa; Salvi, Stefano
2016-04-01
The study of post-seismic deformation within a region is of high significance to have a better understanding of the kinematic behavior of a seismogenic fault. We perform the Small Baseline Subset (SBAS) method to process a large number of X-Band, COSMO-SkyMed images to measure the post-seismic deformation due to the Shonbeh earthquake (Iran) of 9th April 2013 (Mw 6.4). The meizoseismal zone of the earthquake and following aftershocks' epicenters cover an area in the frontal edge of the Zagros Simply Folded Zone, in the southwest of Iran, between Kaki and Kangan anticlines. Exploiting the available dataset of images from the beginning of 2013 to mid 2014, we observe the concentration of the deformation along at least two NW- striking, southwest-dipping fault segments arranged in right-step pattern and parallel to the trend of the folds. The preliminary InSAR results illustrate the migration of the post-seismic deformation and stress relaxation from the southeastern toward the northwestern fault segments.
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…
STUDY OF VARIABLES ASSOCIATED WITH FINAL GRADES IN MATHEMATICS COURSES.
ERIC Educational Resources Information Center
DAVIS, ELTON C.; RISSER, JOHN J.
THIS STUDY WAS CONDUCTED IN ORDER TO DETERMINE THE RELATIVE VALUE OF PREVIOUS GRADES IN MATHEMATICS COURSES, THE OVERALL HIGH SCHOOL GRADE POINT AVERAGE, AND THE PLACEMENT TEST IN MATHEMATICS DEVELOPED AT THE COLLEGE AS PREDICTORS OF ACHIEVEMENT IN INTRODUCTORY AND INTERMEDIATE ALGEBRA, IN COLLEGE ALGEBRA, IN TRIGONOMETRY, AND IN ANALYTIC GEOMETRY…
NASA Astrophysics Data System (ADS)
Schultz, Ludwig; Holzapfel, Bernhard
2010-04-01
During the 9th European Conference on Applied Superconductivity 6 plenary, 22 invited, 206 oral and 429 poster contributions were presented on recent developments in the field of applied superconductivity. This issue of Journal of Physics: Conference Series contains all contributed papers that were accepted for the Conference Proceedings. The Dresden EUCAS conference with 712 participants from 43 countries continued the tradition of preceding EUCAS conferences of combining basic superconductivity research contributions with the discussion of recent material advances and new developments in large scale and electronic applications. In Dresden, contributions on the recently discovered Fe based superconductors were presented for the first time during a EUCAS conference and their potential for applications was intensively discussed. Finally we want to acknowledge the help of the International Advisory and National Committees in setting up the scientific program and especially we would like to express our gratitude to all members of the Local Organization Committee. Their enthusiastic and well organized work made this Dresden EUCAS conference a memorable event for all participants. Last but not least we are very grateful to W. Goldacker , S. Haindl, J. Hänisch, R. Hühne, M. Noe, P. Seidel and M. Siegel for their extraordinary help during the proceedings review process. Bernhard Holzapfel Ludwig Schultz Conference Chairmen The IW-SMI 2010 Organizing Committee: Masato Okada (University of Tokyo) Yoshiyuki Kabashima, General Chair (Tokyo Institute of Technology) Shin Ishii (Kyoto University) Jun-ichi Inoue, Publications Chair (Hokkaido University) Kazuyuki Tanaka (Tohoku University) Toshiyuki Tanaka, Vice-General Chair (Kyoto University)
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
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.…
Prediction of Algebraic Instabilities
NASA Astrophysics Data System (ADS)
Zaretzky, Paula; King, Kristina; Hill, Nicole; Keithley, Kimberlee; Barlow, Nathaniel; Weinstein, Steven; Cromer, Michael
2016-11-01
A widely unexplored type of hydrodynamic instability is examined - large-time algebraic growth. Such growth occurs on the threshold of (exponentially) neutral stability. A new methodology is provided for predicting the algebraic growth rate of an initial disturbance, when applied to the governing differential equation (or dispersion relation) describing wave propagation in dispersive media. Several types of algebraic instabilities are explored in the context of both linear and nonlinear waves.
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
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
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…
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
Bicovariant quantum algebras and quantum Lie algebras
NASA Astrophysics Data System (ADS)
Schupp, Peter; Watts, Paul; Zumino, Bruno
1993-10-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(mathfrak{G}_q ) to U q g, given by elements of the pure braid group. These operators—the “reflection matrix” Y≡L + SL - being a special case—generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N).
Parastatistics Algebras and Combinatorics
NASA Astrophysics Data System (ADS)
Popov, T.
2005-03-01
We consider the algebras spanned by the creation parafermionic and parabosonic operators which give rise to generalized parastatistics Fock spaces. The basis of such a generalized Fock space can be labelled by Young tableaux which are combinatorial objects. By means of quantum deformations a nice combinatorial structure of the algebra of the plactic monoid that lies behind the parastatistics is revealed.
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…
Learning Activity Package, Algebra.
ERIC Educational Resources Information Center
Evans, Diane
A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…
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.
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…
ERIC Educational Resources Information Center
Carson, Cristi L.; Day, Judith
This paper argues that operations with negative numbers should be taught using a curriculum that is grounded in algebraic geometry. This position is supported by the results from a study that compared the conceptual understanding of grade 9 students who received the Algebra Project transition curriculum to a control group of grade 6 gifted…
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…
Minimum deformations of commutative algebra and linear group GL(n)
NASA Astrophysics Data System (ADS)
Zupnik, B. M.
1993-06-01
In the algebra of formal series M q ( x i ), the relations of generalized commutativity that preserve the tensor I q grading and depend on parameters q(i, k) are considered. A norm of the differential calculus on M q consistent with the I q grading is chosen. A new construction of a symmetrized tensor product of algebras of the type M q ( x i ) and a corresponding definition of the minimally deformed linear group QGL(n) and Lie algebra qgl(n) are proposed. A study is made of the connection of QGL(n) and qgl(n) with the special matrix algebra Mat( n, Q), which consists of matrices with noncommuting elements. The deformed determinant in the algebra Mat( n, Q) is defined. The exponential mapping in the algebra Mat( n, Q) is considered on the basis of the Campbell-Hausdorff formula.
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
Algebraic Nonlinear Collective Motion
NASA Astrophysics Data System (ADS)
Troupe, J.; Rosensteel, G.
1998-11-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real numberΛ. TheΛ=0 solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear group action on Euclidean space transforms a certain family of deformed droplets among themselves. For positiveΛ, the droplets have a neck that becomes more pronounced asΛincreases; for negativeΛ, the droplets contain a spherical bubble of radius |Λ|1/3. The nonlinear vector field algebra is extended to the nonlinear general collective motion algebra gcm(3) which includes the inertia tensor. The quantum algebraic models of nonlinear nuclear collective motion are given by irreducible unitary representations of the nonlinear gcm(3) Lie algebra. These representations model fissioning isotopes (Λ>0) and bubble and two-fluid nuclei (Λ<0).
Algebraic invariants for homotopy types
NASA Astrophysics Data System (ADS)
Blanc, David
1999-11-01
We define a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the [Pi]-algebra [pi][low asterisk]X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract [Pi]-algebra can be realized as the homotopy [Pi]-algebra of a space.
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,…
Superalgebra realization of the 3-algebras in N=6, 8 Chern-Simons-matter theories
NASA Astrophysics Data System (ADS)
Chen, Fa-Min
2012-01-01
We use superalgebras to realize the 3-algebras used to construct N=6, 8 Chern-Simons-matter (CSM) theories. We demonstrate that the superalgebra realization of the 3-algebras provides a unified framework for classifying the gauge groups of the Nge 5 theories based on 3-algebras. Using this realization, we rederive the ordinary Lie algebra construction of the general N=6 CSM theory from its 3-algebra counterpart and reproduce all known examples as well. In particular, we explicitly construct the Nambu 3-bracket in terms of a double graded commutator of PSU(2|2). The N=8 theory of Bagger, Lambert and Gustavsson (BLG) with SO(4) gauge group is constructed by using several different ways. A quantization scheme for the 3-brackets is proposed by promoting the double graded commutators as quantum mechanical double graded commutators.
Geary, David C.; Hoard, Mary K.; Nugent, Lara; Rouder, Jeffrey N.
2015-01-01
The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 (92 girls) 9th graders, controlling parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation, but not schema memory. Frequency of fact-retrieval errors was related to schema memory but not coordinate plane or expression evaluation accuracy. The results suggest the ANS may contribute to or is influenced by spatial-numerical and numerical only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest different brain and cognitive systems are engaged during the learning of different components of algebraic competence, controlling demographic and domain general abilities. PMID:26255604
Mathematics Curriculum Guide. First and Second Course in Algebra. Supplement No. 2.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 9 and 10 (first and second courses). SUBJECT MATTER: Algebra. ORGANIZATION AND PHYSICAL APPEARANCE: The material for each grade is presented in four columns: major areas, significant anticipated outcomes, observations and suggestion, and references and films. The topics covered in the first course include reviews of set…
Pseudo-Riemannian Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2008-08-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.
NASA Astrophysics Data System (ADS)
Markarian, Nikita
2017-03-01
We introduce Weyl n-algebras and show how their factorization complex may be used to define invariants of manifolds. In the appendix, we heuristically explain why these invariants must be perturbative Chern-Simons invariants.
Developing Algebraic Thinking.
ERIC Educational Resources Information Center
Alejandre, Suzanne
2002-01-01
Presents a teaching experience that resulted in students getting to a point of full understanding of the kinesthetic activity and the algebra behind it. Includes a lesson plan for a traffic jam activity. (KHR)
Jordan Algebraic Quantum Categories
NASA Astrophysics Data System (ADS)
Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander
2015-03-01
State cones in orthodox quantum theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox quantum theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized quantum theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal tensor products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic quantum theory. More generally, we explicitly derive the structure of hybrid quantum composites with subsystems of arbitrary Jordan algebraic type.
Accounting Equals Applied Algebra.
ERIC Educational Resources Information Center
Roberts, Sondra
1997-01-01
Argues that students should be given mathematics credits for completing accounting classes. Demonstrates that, although the terminology is different, the mathematical concepts are the same as those used in an introductory algebra class. (JOW)
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.
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
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…
An Investigation of Selected Variables Related to Student Algebra I Performance in Mississippi
ERIC Educational Resources Information Center
Scott, Undray
2016-01-01
This research study attempted to determine if specific variables were related to student performance on the Algebra I subject-area test. This study also sought to determine in which of grades 8, 9, or 10 students performed better on the Algebra I Subject Area Test. This study also investigated the different criteria that are used to schedule…
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…
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…
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…
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
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,…
Grading for Understanding - Standards-Based Grading
NASA Astrophysics Data System (ADS)
Zimmerman, Todd
2017-01-01
Standards-based grading (SBG), sometimes called learning objectives-based assessment (LOBA), is an assessment model that relies on students demonstrating mastery of learning objectives (sometimes referred to as standards). The goal of this grading system is to focus students on mastering learning objectives rather than on accumulating points. I have used SBG in an introductory physics course for the past five years and worked with several physics faculty members to implement SBG in the first and second semester of algebra-based and calculus-based introductory physics courses at a primarily undergraduate comprehensive public university with class sizes of 48 students. In this article I will discuss methods for implementing SBG in a physics class.
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.
Algebraic mesh quality metrics
KNUPP,PATRICK
2000-04-24
Quality metrics for structured and unstructured mesh generation are placed within an algebraic framework to form a mathematical theory of mesh quality metrics. The theory, based on the Jacobian and related matrices, provides a means of constructing, classifying, and evaluating mesh quality metrics. The Jacobian matrix is factored into geometrically meaningful parts. A nodally-invariant Jacobian matrix can be defined for simplicial elements using a weight matrix derived from the Jacobian matrix of an ideal reference element. Scale and orientation-invariant algebraic mesh quality metrics are defined. the singular value decomposition is used to study relationships between metrics. Equivalence of the element condition number and mean ratio metrics is proved. Condition number is shown to measure the distance of an element to the set of degenerate elements. Algebraic measures for skew, length ratio, shape, volume, and orientation are defined abstractly, with specific examples given. Combined metrics for shape and volume, shape-volume-orientation are algebraically defined and examples of such metrics are given. Algebraic mesh quality metrics are extended to non-simplical elements. A series of numerical tests verify the theoretical properties of the metrics defined.
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…
The Algebra Solution to Mathematics Reform: Completing the Equation
ERIC Educational Resources Information Center
Spielhagen, Frances R.
2011-01-01
How can we increase mathematics achievement among all students? This book provides a straightforward explanation of how changing mathematics tracking policies to provide algebra instruction to all students by at least eighth grade can bring about changes in both student achievement and teacher performance. Spielhagen chronicles the success of a…
Computer Algebra System Calculators: Gender Issues and Teachers' Expectations
ERIC Educational Resources Information Center
Forgasz, Helen J.; Griffith, Shirly
2006-01-01
In this paper we present findings from two studies focusing on computer algebra system (CAS) calculators. In Victoria, Australia, it is currently mandatory for students to use graphics calculators in some grade 12 mathematics examinations. Since 2001, a pilot study has been conducted involving Victorian Certificate of Education (VCE) students…
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
ERIC Educational Resources Information Center
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
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.
NASA Astrophysics Data System (ADS)
Durka, R.
2017-04-01
The S-expansion framework is analyzed in the context of a freedom in closing the multiplication tables for the abelian semigroups. Including the possibility of the zero element in the resonant decomposition, and associating the Lorentz generator with the semigroup identity element, leads to a wide class of the expanded Lie algebras introducing interesting modifications to the gauge gravity theories. Among the results, we find all the Maxwell algebras of type {{B}m} , {{C}m} , and the recently introduced {{D}m} . The additional new examples complete the resulting generalization of the bosonic enlargements for an arbitrary number of the Lorentz-like and translational-like generators. Some further prospects concerning enlarging the algebras are discussed, along with providing all the necessary constituents for constructing the gravity actions based on the obtained results.
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)
A Holistic Approach to Algebra.
ERIC Educational Resources Information Center
Barbeau, Edward J.
1991-01-01
Described are two examples involving recursive mathematical sequences designed to integrate a holistic approach to learning algebra. These examples promote pattern recognition with algebraic justification, full class participation, and mathematical values that can be transferred to other situations. (MDH)
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.
The Dixmier Map for Nilpotent Super Lie Algebras
NASA Astrophysics Data System (ADS)
Herscovich, Estanislao
2012-07-01
In this article we prove that there exists a Dixmier map for nilpotent super Lie algebras. In other words, if we denote by {Prim({U}({g}))} the set of (graded) primitive ideals of the enveloping algebra {{U}({g})} of a nilpotent Lie superalgebra {{g}} and {{A}d0} the adjoint group of {{g}0}, we prove that the usual Dixmier map for nilpotent Lie algebras can be naturally extended to the context of nilpotent super Lie algebras, i.e. there exists a bijective map I : {g}0^{*}/{A}d0 rightarrow Prim({U}({g})) defined by sending the equivalence class [ λ] of a functional λ to a primitive ideal I( λ) of {{U}({g})}, and which coincides with the Dixmier map in the case of nilpotent Lie algebras. Moreover, the construction of the previous map is explicit, and more or less parallel to the one for Lie algebras, a major difference with a previous approach ( cf. [18]). One key fact in the construction is the existence of polarizations for super Lie algebras, generalizing the concept defined for Lie algebras. As a corollary of the previous description, we obtain the isomorphism {{U}({g})/I(λ) ˜eq Cliffq(k) ⊗ Ap(k)}, where {(p,q) = (dim({g}0/{g}0^{λ})/2,dim({g}1/{g}1^{λ}))}, we get a direct construction of the maximal ideals of the underlying algebra of {{U}({g})} and also some properties of the stabilizers of the primitive ideals of {{U}({g})}.
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.
An algebra of reversible computation.
Wang, Yong
2016-01-01
We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.
ERIC Educational Resources Information Center
Ketterlin-Geller, Leanne R.; Jungjohann, Kathleen; Chard, David J.; Baker, Scott
2007-01-01
Much of the difficulty that students encounter in the transition from arithmetic to algebra stems from their early learning and understanding of arithmetic. Too often, students learn about the whole number system and the operations that govern that system as a set of procedures to solve addition, subtraction, multiplication, and division problems.…
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…
Algebraic Thinking through Origami.
ERIC Educational Resources Information Center
Higginson, William; Colgan, Lynda
2001-01-01
Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)
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…
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.
On Dunkl angular momenta algebra
NASA Astrophysics Data System (ADS)
Feigin, Misha; Hakobyan, Tigran
2015-11-01
We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl( N ) version of the subalge-bra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.
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…
Potential for Significant Reductions in Dropout Rates: Analysis of an Entire 3rd Grade State Cohort
ERIC Educational Resources Information Center
Cratty, Dorothyjean
2012-01-01
Nineteen percent of 1997-98 North Carolina 3rd graders were observed to drop out of high school. A series of logits predict probabilities of dropping out on determinants such as math and reading test scores, absenteeism, suspension, and retention, at the following grade levels: 3rd, 5th, 8th, and 9th. The same cohort and variables are used to…
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…
Project TALENT's Nonrespondent Follow-up Survey: The 10th Grade Special Sample. Interim Report.
ERIC Educational Resources Information Center
Carrel, Kathleen S.; And Others
Described are procedures used in the location of a sample of individuals not responding to follow-up questionnaires, eleven years after they were originally interviewed in 1960 as 10th graders. The individuals in question were a subset of more than 400,000 9th, 10th, 11th and 12th grade students used in Project TALENT's longitudinal study of the…
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…
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…
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…
An Experiment in Teaching Punctuation in the Ninth Grade by Means of Intonation Cues.
ERIC Educational Resources Information Center
Held, Jeanette R.
In answer to the need for more effective punctuation instruction, a project, based on the theory that an essential relationship exists between intonation and punctuation, was designed for and executed with two 9th-grade student groups--one experimental, the other control. The experimental group received punctuation instruction through the use of…
2014-01-01
A one-day workshop on Burkitt lymphoma (BL) was held at the 9th African Organization for Research and Training in Cancer (AORTIC) conference in 2013 in Durban, South Africa. The workshop featured 15 plenary talks by delegates representing 13 institutions that either fund or implement research on BL targeting AORTIC delegates primarily interested in pediatric oncology. The main outcomes of the meeting were improved sharing of knowledge and experience about ongoing epidemiologic BL research, BL treatment in different settings, the role of cancer registries in cancer research, and opportunities for African scientists to publish in scientific journals. The idea of forming a consortium of BL to improve coordination, information sharing, accelerate discovery, dissemination, and translation of knowledge and to build capacity, while reducing redundant efforts was discussed. Here, we summarize the presentations and discussions from the workshop. PMID:25686906
Giersing, Birgitte K; Modjarrad, Kayvon; Kaslow, David C; Moorthy, Vasee S
2016-06-03
There are more vaccines in development, against a greater number of pathogens, than ever before. A challenge with this exceptional level of activity and investment is how to select and resource the most promising approaches to have the most significant impact on public health. The WHO Product Development for Vaccines Advisory Committee (PDVAC) was established in 2014 to provide strategic advice and recommendations to WHO for vaccines in clinical development that could have a significant impact on public health in low and middle income countries. On 7-9th September 2015, PDVAC was convened for the second time, when the committee reviewed vaccine developments in 24 disease areas. This report summarises the key recommendations from that consultation.
Balaji, Chinnasamy; Kevinkumar, Vijayakumar; Aravindhan, Vivekanandhan
2017-03-01
Vaccine induced serum cytokines not only serves as a biomarker of immunity but also serves as a reliable measure of inflammation. Long term persistence of inflammation can lead to metabolic derangement. Towards this end, in the present study, we measured levels of cytokines along with hormones (insulin, leptin and adiponectin) in children who have been vaccinated with Salmonella typhi Vi conjugate vaccine, 30months after vaccination. Vaccinated children showed a unique cytokine profile with suppressed Th1-Th2 and increased Th9-Th17 cytokines indicating immune polarization which was associated with decreased serum adiponectin (but not insulin or leptin) levels. The study gains major importance since it is a longitudinal study which reports vaccine induced long term persistence of inflammation for the first time in the high risk ethnic population.
Hamacher, Michael; Eisenacher, Martin; Tribl, Florian; Stephan, Christian; Marcus, Katrin; Hardt, Tanja; Wiltfang, Jens; Martens, Lennart; Desiderio, Dominic; Gutstein, Howard; Park, Young Mok; Meyer, Helmut E
2008-06-01
The Human Brain Proteome Project (HUPO BPP) aims at advancing knowledge and the understanding of neurodiseases and aging with the purpose of identifying prognostic and diagnostic biomarkers, as well as to push new diagnostic approaches and medications. The participating groups meet in semi-annual workshops to discuss the progress, as well as the needs, within the field of proteomics. The 9(th) HUPO BPP workshop took place in Barbados from 9-10 January, 2008. Discussing the future HUPO BPP Roadmap, the attendees drafted the so called HUPO BPP wish list containing timelines, suggestions and missions. This wish list will be updated regularly and will serve as a guideline for the next phase.
Marquette, Ian
2013-07-15
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently.
ERIC Educational Resources Information Center
Weiss, Christopher C.; Baker-Smith, E. Christine
2010-01-01
We examine a set of academic and social outcomes in 9th grade, comparing middle school attendees with those who attended K-8 schools. Previous research with these data has shown that there are few differences in 8th-grade outcomes by school type. Here we extend these findings to determine whether school form influences student outcomes in the…
ERIC Educational Resources Information Center
Kaput, James J.; Blanton, Maria L.
This paper describes an intensive 3-year classroom- and district-based study of the process of integrating the development of algebraic reasoning into elementary school mathematics in an educationally underachieving school district based on a year-long pilot effort in 1997-98 with two 5th grade teachers and one 6th grade teacher. In 1998-99, the…
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…
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.
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.
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®,…
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
Linchevski, Liora; Herscovics, Nicolas
1996-01-01
Reports the results of a teaching experiment involving like terms and equations in algebra. Seventh-grade students (n=6) experienced difficulties in decomposing an additive term into a difference. (Author/MKR)
Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras
NASA Astrophysics Data System (ADS)
Catto, Sultan; Gürcan, Yasemin; Khalfan, Amish; Kurt, Levent; Kato La, V.
2016-10-01
We discuss a construction scheme for Clifford numbers of arbitrary dimension. The scheme is based upon performing direct products of the Pauli spin and identity matrices. Conjugate fermionic algebras can then be formed by considering linear combinations of the Clifford numbers and the Hermitian conjugates of such combinations. Fermionic algebras are important in investigating systems that follow Fermi-Dirac statistics. We will further comment on the applications of Clifford algebras to Fueter analyticity, twistors, color algebras, M-theory and Leech lattice as well as unification of ancient and modern geometries through them.
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.
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
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…
Applications of algebraic grid generation
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Smith, Robert E.
1990-01-01
Techniques and applications of algebraic grid generation are described. The techniques are univariate interpolations and transfinite assemblies of univariate interpolations. Because algebraic grid generation is computationally efficient, the use of interactive graphics in conjunction with the techniques is advocated. A flexible approach, which works extremely well in an interactive environment, called the control point form of algebraic grid generation is described. The applications discussed are three-dimensional grids constructed about airplane and submarine configurations.
2012-07-01
residents, medical students, nursing, pharmacy, and undergraduate trainees. Each trainee presentation was judged by an august group of faculty and a total...Environmental Enrichment-Mediated Functional Improvement After Experimental Traumatic Brain Injury." 62 Megan Miller, BS - " COMT Gene Variant
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.
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…
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
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…
Viterbi/algebraic hybrid decoder
NASA Technical Reports Server (NTRS)
Boyd, R. W.; Ingels, F. M.; Mo, C.
1980-01-01
Decoder computer program is hybrid between optimal Viterbi and optimal algebraic decoders. Tests have shown that hybrid decoder outperforms any strictly Viterbi or strictly algebraic decoder and effectively handles compound channels. Algorithm developed uses syndrome-detecting logic to direct two decoders to assume decoding load alternately, depending on real-time channel characteristics.
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.)
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.
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.
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.)
Learning Algebra from Worked Examples
ERIC Educational Resources Information Center
Lange, Karin E.; Booth, Julie L.; Newton, Kristie J.
2014-01-01
For students to be successful in algebra, they must have a truly conceptual understanding of key algebraic features as well as the procedural skills to complete a problem. One strategy to correct students' misconceptions combines the use of worked example problems in the classroom with student self-explanation. "Self-explanation" is the…
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…
The Algebra of Complex Numbers.
ERIC Educational Resources Information Center
LePage, Wilbur R.
This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…
Peñarrocha-Diago, María; Blaya-Tárraga, Juan-Antonio
2017-01-01
This manuscript summarizes the statements and clinical recommendations in periapical implant lesions, as per the state of the art and expert opinion agreement among the participants in the 9th Mozo-Grau Conference 2016 held in Quintanilla (Valladolid, Spain). The current status of the concept, frequency, etiology, diagnosis, clinical classification, surgical procedure and prognosis are described. If following implant placement localized pain develops in the periapical area, with or without radiographic changes, the diagnosis of periapical implant lesion should be suspected. It is important to monitor the condition in order to identify any change in its evolution. Radiological changes in the periapical radiographs are not always manifest in the early stages, and in this regard small-volume cone beam computed tomography can help us visualize such peri-implant changes. The early diagnosis of periapical implant lesions during the osseointegration phase and the provision of early treatment result in increased implant survival rates, thereby avoiding the need for implant extraction. Key words:Apical peri-implantitis, retrograde peri-implantitis, inflammatory peri-implantitis lesion. PMID:28298994
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.
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
2016-08-24
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.
Cattaruzzi, C; Troncon, M G; Agostinis, L; García Rodríguez, L A
1999-06-01
We identified patients whose records in the Sistema Informativo Sanitario Regionale database in the Italian region of Friuli-Venezia Giulia showed a code of upper gastrointestinal bleeding (UGIB) and perforation according to codes of the International Classification of Diseases (ICD)-9th revision. The validity of site- and lesion-specific codes (531 to 534) and nonspecific codes (5780, 5781, and 5789) was ascertained through manual review of hospital clinical records. The initial group was made of 1779 potential cases of UGIB identified with one of these codes recorded. First, the positive predictive values (PPV) were calculated in a random sample. As a result of the observed high PPV of 531 and 532 codes, additional hospital charts were solely requested for all remaining potential cases with 533, 534, and 578 ICD-9 codes. The overall PPV reached a high of 97% for 531 and 532 site-specific codes, 84% for 534 site-specific codes, and 80% for 533 lesion-specific codes, and a low of 59% for nonspecific codes. These data suggest a considerable research potential for this new computerized health care database in Southern Europe.
Yasuda, H; Komiyama, T; Fujitaka, K
1999-09-01
Organ/Tissue absorbed doses were measured with a life-size human phantom torso in the 9th Shuttle/Mir Mission (STS-91) from June 2 to 12, 1998. This is the first attempt to measure directly organ/tissue doses over a whole human body in space. The absorbed dose was measured by combination of two integrating detectors: thermo- luminescent dosemeter of Mg2SiO4: Tb (TDMS) and plastic nuclear track detector (PNTD). Both detectors were calibrated on ground using high-energy charged-particle beams. The detectors were packed in 59 cases of tissue-equivalent resin; and put into the positions of radiologically important organs and tissues in the phantom. Efficiency reductions of TDMS for high-LET particles were corrected based on the LET-differential particle fluence of space radiation measured with PNTDs. The accumulated absorbed doses during this 9.8-days mission at low-earth orbit (400 km x 51.6 degrees) ranged from 1.6 mGy at colon to 2.6 mGy at bone surface (shoulder) with a variation factor of 1.6. The absorbed doses at some internal organs were higher than the skin dose. This fact is important from the viewpoint of radiological protection for astronauts.
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.
Symplectic Clifford Algebraic Field Theory.
NASA Astrophysics Data System (ADS)
Dixon, Geoffrey Moore
We develop a mathematical framework on which is built a theory of fermion, scalar, and gauge vector fields. This field theory is shown to be equivalent to the original Weinberg-Salam model of weak and electromagnetic interactions, but since the new framework is more rigid than that on which the original Weinberg-Salam model was built, a concomitant reduction in the number of assumptions lying outside of the framework has resulted. In particular, parity violation is actually hiding within our framework, and with little difficulty we are able to manifest it. The mathematical framework upon which we build our field theory is arrived at along two separate paths. The first is by the marriage of a Clifford algebra and a Lie superalgebra, the result being called a super Clifford algebra. The second is by providing a new characterization for a Clifford algebra employing its generators and a symmetric array of metric coefficients. Subsequently we generalize this characterization to the case of an antisymmetric array of metric coefficients, and we call the algebra which results a symplectic Clifford algebra. It is upon one of these that we build our field theory, and it is shown that this symplectic Clifford algebra is a particular subalgebra of a super Clifford algebra. The final ingredient is the operation of bracketing which involves treating the elements of our algebra as endomorphisms of a particular inner product space, and employing this space and its inner product to provide us with maps from our algebra to the reals. It is this operation which enables us to manifest the parity violation hiding in our algebra.
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…
Self-Reported Health-Related Behaviors of Grade 9 Students: A Pre and Post Project Study
ERIC Educational Resources Information Center
Miller-Whitehead, Marie
2005-01-01
The purpose of this research was threefold. The first purpose was to conduct a needs assessment for a local school district to obtain additional funding for the nutrition and healthy eating habits unit of the 9th grade Wellness curriculum. The Wellness program consisted of one semester of physical education and one semester of classroom…
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
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.
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.
ERIC Educational Resources Information Center
Fletcher, Richard Kenard, Jr.
This study was designed to determine experimentally the relationship between achievement and grade level for 64 tenth-grade students, 48 eleventh-grade students, and 95 twelfth-grade physics students. All students were enrolled in the Project Physics course in their respective schools. The Physics Achievement Test (PAT) and the algebra I and II…
2009-01-01
Most mammalian cells must adhere to the extracellular matrix (ECM) to maintain proper growth and development. Fibronectin is a predominant ECM protein that engages integrin cell receptors through its Arg-Gly-Asp (RGD) and Pro-His-Ser-Arg-Asn (PHSRN) peptide binding sites. To study the roles these motifs play in cell adhesion, proteins derived from the 9th (containing PHSRN) and 10th (containing RGD) type III fibronectin domains were engineered to be in frame with cutinase, a serine esterase that forms a site-specific, covalent adduct with phosphonate ligands. Self-assembled monolayers (SAMs) that present phosphonate ligands against an inert background of tri(ethylene glycol) groups were used as model substrates to immobilize the cutinase-fibronectin fusion proteins. Baby hamster kidney cells attached efficiently to all protein surfaces, but only spread efficiently on protein monolayers containing the RGD peptide. Cells on RGD-containing protein surfaces also displayed defined focal adhesions and organized cytoskeletal structures compared to cells on PHSRN-presenting surfaces. Cell attachment and spreading were shown to be unaffected by the presence of PHSRN when compared to RGD alone on SAMs presenting higher densities of protein, but PHSRN supported an increased efficiency in cell attachment when presented at low protein densities with RGD. Treatment of suspended cells with soluble RGD or PHSRN peptides revealed that both peptides were able to inhibit the attachment of FN10 surfaces. These results support a model wherein PHSRN and RGD bind competitively to integrins―rather than a two-point synergistic interaction―and the presence of PHSRN serves to increase the density of ligand on the substrate and therefore enhance the sticking probability of cells during attachment. PMID:20560553
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)…
Investigating Teacher Noticing of Student Algebraic Thinking
ERIC Educational Resources Information Center
Walkoe, Janet Dawn Kim
2013-01-01
Learning algebra is critical for students in the U.S. today. Algebra concepts provide the foundation for much advanced mathematical content. In addition, algebra serves as a gatekeeper to opportunities such as admission to college. Yet many students in the U.S. struggle in algebra classes. Researchers claim that one reason for these difficulties…
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…
Asymptotic aspect of derivations in Banach algebras.
Roh, Jaiok; Chang, Ick-Soon
2017-01-01
We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.
Computing Matrix Representations of Filiform Lie Algebras
NASA Astrophysics Data System (ADS)
Ceballos, Manuel; Núñez, Juan; Tenorio, Ángel F.
In this paper, we compute minimal faithful unitriangular matrix representations of filiform Lie algebras. To do it, we use the nilpotent Lie algebra, g_n, formed of n ×n strictly upper-triangular matrices. More concretely, we search the lowest natural number n such that the Lie algebra g_n contains a given filiform Lie algebra, also computing a representative of this algebra. All the computations in this paper have been done using MAPLE 9.5.
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.
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)
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.
Coherent States for Hopf Algebras
NASA Astrophysics Data System (ADS)
Škoda, Zoran
2007-07-01
Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. If, in addition, the Hopf algebra has a left Haar integral, then a formula for noncommutative resolution of identity in terms of the family of coherent states holds. Examples come from quantum groups.
Multiplier operator algebras and applications
Blecher, David P.; Zarikian, Vrej
2004-01-01
The one-sided multipliers of an operator space X are a key to “latent operator algebraic structure” in X. We begin with a survey of these multipliers, together with several of the applications that they have had to operator algebras. We then describe several new results on one-sided multipliers, and new applications, mostly to one-sided M-ideals. PMID:14711990
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).
ERIC Educational Resources Information Center
Nomi, Takako
2012-01-01
In 1997, Chicago implemented a policy that required algebra for all ninth-grade students, eliminating all remedial coursework. This policy increased opportunities to take algebra for low-skill students who had previously enrolled in remedial math. However, little is known about how schools respond to the policy in terms of organizing math…
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…
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.
2014-01-01
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 2nd- 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
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.
Building a Foundation for Learning Algebra in the Elementary Grades.
ERIC Educational Resources Information Center
Carpenter, Thomas P.; Levi, Linda; Farnsworth, Valerie
2000-01-01
"In Brief" focuses on K-12 mathematics and science research and implications for policymakers, educators, and researchers seeking to improve student learning and achievement This brief highlights the learning gains of 240 elementary students involved in a long-term study in Madison, Wisconsin and their remarkable ability to reason with arithmetic…
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…
Novikov algebras with associative bilinear forms
NASA Astrophysics Data System (ADS)
Zhu, Fuhai; Chen, Zhiqi
2007-11-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.
Quantum Q systems: from cluster algebras to quantum current algebras
NASA Astrophysics Data System (ADS)
Di Francesco, Philippe; Kedem, Rinat
2017-02-01
This paper gives a new algebraic interpretation for the algebra generated by the quantum cluster variables of the A_r quantum Q-system (Di Francesco and Kedem in Int Math Res Not IMRN 10:2593-2642, 2014). We show that the algebra can be described as a quotient of the localization of the quantum algebra U_{√{q}}({n}[u,u^{-1}])subset U_{√{q}}(widehat{{sl}}_2), in the Drinfeld presentation. The generating current is made up of a subset of the cluster variables which satisfy the Q-system, which we call fundamental. The other cluster variables are given by a quantum determinant-type formula, and are polynomials in the fundamental generators. The conserved quantities of the discrete evolution (Di Francesco and Kedem in Adv Math 228(1):97-152, 2011) described by quantum Q-system generate the Cartan currents at level 0, in a non-standard polarization. The rest of the quantum affine algebra is also described in terms of cluster variables.
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…
ERIC Educational Resources Information Center
Geist, John E.
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
Fradiska, John
This booklet, one of a series developed by the Frederick County Board of Education, Frederick, Maryland, provides an instruction module for an individualized or flexible approach to 7th, 8th, and 9th grade science teaching. Subjects and activities in this series of booklets are designed to supplement a basic curriculum or to form a total…
ERIC Educational Resources Information Center
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
Geist, John E.
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…
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
Algebra: Mirror, Mirror on the Universe. NASA Connect: Program 7 in the 1999-2000 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 4-8 explore the concepts of algebra in the context of exploring the universe. The units in this 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 a storyline…
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…
Visual, Algebraic and Mixed Strategies in Visually Presented Linear Programming Problems.
ERIC Educational Resources Information Center
Shama, Gilli; Dreyfus, Tommy
1994-01-01
Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…
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…
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
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…
ERIC Educational Resources Information Center
Essien, Anthony A.
2011-01-01
This study investigated how a teacher in a multilingual classroom attempted to support learners who are struggling to translate written/verbal mathematics into a symbolic form. Thirty-six Grade ten learners in one multilingual classroom in South Africa were given a written test involving one algebraic question and then a discussion on the solution…
ERIC Educational Resources Information Center
Fuchs, Lynn S.; Compton, Donald L.; Fuchs, Douglas; Hollenbeck, Kurstin N.; Craddock, Caitlin F.; Hamlett, Carol L.
2008-01-01
Dynamic assessment (DA) involves helping students learn a task and indexing responsiveness to that instruction as a measure of learning potential. The purpose of this study was to explore the utility of a DA of algebraic learning in predicting third graders' development of mathematics problem solving. In the fall, 122 third-grade students were…
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,…
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.
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.
Using Number Theory to Reinforce Elementary Algebra.
ERIC Educational Resources Information Center
Covillion, Jane D.
1995-01-01
Demonstrates that using the elementary number theory in algebra classes helps students to use acquired algebraic skills as well as helping them to more clearly understand concepts that are presented. Discusses factoring, divisibility rules, and number patterns. (AIM)
Algebraic orbifold conformal field theories
Xu, Feng
2000-01-01
The unitary rational orbifold conformal field theories in the algebraic quantum field theory and subfactor theory framework are formulated. Under general conditions, it is shown that the orbifold of a given unitary rational conformal field theory generates a unitary modular category. Many new unitary modular categories are obtained. It is also shown that the irreducible representations of orbifolds of rank one lattice vertex operator algebras give rise to unitary modular categories and determine the corresponding modular matrices, which has been conjectured for some time. PMID:11106383
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.
Symmetry algebras of linear differential equations
NASA Astrophysics Data System (ADS)
Shapovalov, A. V.; Shirokov, I. V.
1992-07-01
The local symmetries of linear differential equations are investigated by means of proven theorems on the structure of the algebra of local symmetries of translationally and dilatationally invariant differential equations. For a nonparabolic second-order equation, the absence of nontrivial nonlinear local symmetries is proved. This means that the local symmetries reduce to the Lie algebra of linear differential symmetry operators. For the Laplace—Beltrami equation, all local symmetries reduce to the enveloping algebra of the algebra of the conformal group.
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.
... Other Funding Find NCI funding for small business innovation, technology transfer, and contracts Training Cancer Training at ... much of the tumor tissue has normal breast (milk) duct structures Nuclear grade : an evaluation of the ...
Applications of Algebraic Logic and Universal Algebra to Computer Science
1989-06-21
conference, with roughly equal representation from Mathematics and Computer Science . The conference consisted of eight invited lectures (60 minutes...each) and 26 contributed talks (20-40 minutes each). There was also a round-table discussion on the role of algebra and logic in computer science . Keywords
Toro, L.A.
1996-02-01
Consistent algebraic extensions of the Poincar{acute e} algebra are obtained in which the novel generators can act with commutators or {ital anticommutators} on the Poincar{acute e} generators. {copyright} {ital 1996 American Institute of Physics.}
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…
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…
Constraint-Referenced Analytics of Algebra Learning
ERIC Educational Resources Information Center
Sutherland, Scot M.; White, Tobin F.
2016-01-01
The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…
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"…
Teacher Actions to Facilitate Early Algebraic Reasoning
ERIC Educational Resources Information Center
Hunter, Jodie
2015-01-01
In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…
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…
Cyclic homology for Hom-associative algebras
NASA Astrophysics Data System (ADS)
Hassanzadeh, Mohammad; Shapiro, Ilya; Sütlü, Serkan
2015-12-01
In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology and cohomology for this class of algebras generalizing these theories from the associative to the Hom-associative setting.
Carry Groups: Abstract Algebra Projects
ERIC Educational Resources Information Center
Miller, Cheryl Chute; Madore, Blair F.
2004-01-01
Carry Groups are a wonderful collection of groups to introduce in an undergraduate Abstract Algebra course. These groups are straightforward to define but have interesting structures for students to discover. We describe these groups and give examples of in-class group projects that were developed and used by Miller.
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…
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…
Easing Students' Transition to Algebra
ERIC Educational Resources Information Center
Baroudi, Ziad
2006-01-01
Traditionally, students learn arithmetic throughout their primary schooling, and this is seen as the ideal preparation for the learning of algebra in the junior secondary school. The four operations are taught and rehearsed in the early years and from this, it is assumed, "children will induce the fundamental structure of arithmetic" (Warren &…
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…
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.
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 contemporary…
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…
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…
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.
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…
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 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
Alberta Dept. of Education, Edmonton. Language Services Branch.
Aligned with its 1998 standards for first- and second-language learning, Alberta Learning has published lesson plans that aim for a closer relationship between learning and evaluation. Each volume in this series presents a specific task for students that involves planning, carrying out, and evaluating their work. Three separate lesson plans in the…
Explicit field realizations of W algebras
NASA Astrophysics Data System (ADS)
Wei, Shao-Wen; Liu, Yu-Xiao; Zhang, Li-Jie; Ren, Ji-Rong
2009-06-01
The fact that certain nonlinear W2,s algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize W2,s algebras from linear W1,2,s algebras. In this paper, we first construct the explicit field realizations of linear W1,2,s algebras with double scalar and double spinor, respectively. Then, after a change of basis, the realizations of W2,s algebras are presented. The results show that all these realizations are Romans-type realizations.
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.
On special classes of n-algebras
NASA Astrophysics Data System (ADS)
Vainerman, L.; Kerner, R.
1996-05-01
We define n-algebras as linear spaces on which the internal composition law involves n elements: m:V⊗n■V. It is known that such algebraic structures are interesting for their applications to problems of modern mathematical physics. Using the notion of a commutant of two subalgebras of an n-algebra, we distinguish certain classes of n-algebras with reasonable properties: semisimple, Abelian, nilpotent, solvable. We also consider a few examples of n-algebras of different types, and show their properties.
On the Structure of Graded Lie Superalgebras
NASA Astrophysics Data System (ADS)
Calderón Martín, Antonio J.; Sánchez Delgado, José M.
2012-08-01
We study the structure of graded Lie superalgebras with arbitrary dimension and over an arbitrary field 𝕂. We show that any of such algebras 𝔏 with a symmetric G-support is of the form 𝔏 = U + ∑jIj with U a subspace of 𝔏1 and any Ij a well-described graded ideal of 𝔏, satisfying [Ij, Ik] = 0 if j≠k. Under certain conditions, it is shown that 𝔏 = (⨁k∈K Ik) ⊕ (⨁q ∈Q Iq), where any Ik is a gr-simple graded ideal of 𝔏 and any Iq is a completely determined low-dimensional non-gr-simple graded ideal of 𝔏, satisfying [Iq, Iq'] = 0 for any q'∈Q with q ≠q'.
Recursion and feedback in image algebra
NASA Astrophysics Data System (ADS)
Ritter, Gerhard X.; Davidson, Jennifer L.
1991-04-01
Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure developed for use in image processing and image analysis, provides a common mathematical environment for expressing image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1]. Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These examples show that image algebra can express these important feedback concepts in a succinct way.
Deformed Kac Moody and Virasoro algebras
NASA Astrophysics Data System (ADS)
Balachandran, A. P.; Queiroz, A. R.; Marques, A. M.; Teotonio-Sobrinho, P.
2007-07-01
Whenever the group {\\bb R}^n acts on an algebra {\\cal A} , there is a method to twist \\cal A to a new algebra {\\cal A}_\\theta which depends on an antisymmetric matrix θ (θμν = -θνμ = constant). The Groenewold-Moyal plane {\\cal A}_\\theta({\\bb R}^{d+1}) is an example of such a twisted algebra. We give a general construction to realize this twist in terms of {\\cal A} itself and certain 'charge' operators Qμ. For {\\cal A}_\\theta({\\bb R}^{d+1}), Q_\\mu are translation generators. This construction is then applied to twist the oscillators realizing the Kac-Moody (KM) algebra as well as the KM currents. They give different deformations of the KM algebra. From one of the deformations of the KM algebra, we construct, via the Sugawara construction, the Virasoro algebra. These deformations have an implication for statistics as well.
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.
Algebraic complexities and algebraic curves over finite fields
Chudnovsky, D. V.; Chudnovsky, G. V.
1987-01-01
We consider the problem of minimal (multiplicative) complexity of polynomial multiplication and multiplication in finite extensions of fields. For infinite fields minimal complexities are known [Winograd, S. (1977) Math. Syst. Theory 10, 169-180]. We prove lower and upper bounds on minimal complexities over finite fields, both linear in the number of inputs, using the relationship with linear coding theory and algebraic curves over finite fields. PMID:16593816
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…
Universal effective hadron dynamics from superconformal algebra
Brodsky, Stanley J.; de Teramond, Guy F.; Dosch, Hans Gunter; ...
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
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. 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. 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.
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.
Algebraic Methods to Design Signals
2015-08-27
group theory are employed to investigate the theory of their construction methods leading to new families of these arrays and some generalizations...sequences and arrays with desirable correlation properties. The methods used are very algebraic and number theoretic. Many new families of sequences...context of optical quantum computing, we prove that infinite families of anticirculant block weighing matrices can be obtained from generic weighing
Computer algebra and transport theory.
Warsa, J. S.
2004-01-01
Modern symbolic algebra computer software augments and complements more traditional approaches to transport theory applications in several ways. The first area is in the development and enhancement of numerical solution methods for solving the Boltzmann transport equation. Typically, special purpose computer codes are designed and written to solve specific transport problems in particular ways. Different aspects of the code are often written from scratch and the pitfalls of developing complex computer codes are numerous and well known. Software such as MAPLE and MATLAB can be used to prototype, analyze, verify and determine the suitability of numerical solution methods before a full-scale transport application is written. Once it is written, the relevant pieces of the full-scale code can be verified using the same tools I that were developed for prototyping. Another area is in the analysis of numerical solution methods or the calculation of theoretical results that might otherwise be difficult or intractable. Algebraic manipulations are done easily and without error and the software also provides a framework for any additional numerical calculations that might be needed to complete the analysis. We will discuss several applications in which we have extensively used MAPLE and MATLAB in our work. All of them involve numerical solutions of the S{sub N} transport equation. These applications encompass both of the two main areas in which we have found computer algebra software essential.
BLAS- BASIC LINEAR ALGEBRA SUBPROGRAMS
NASA Technical Reports Server (NTRS)
Krogh, F. T.
1994-01-01
The Basic Linear Algebra Subprogram (BLAS) library is a collection of FORTRAN callable routines for employing standard techniques in performing the basic operations of numerical linear algebra. The BLAS library was developed to provide a portable and efficient source of basic operations for designers of programs involving linear algebraic computations. The subprograms available in the library cover the operations of dot product, multiplication of a scalar and a vector, vector plus a scalar times a vector, Givens transformation, modified Givens transformation, copy, swap, Euclidean norm, sum of magnitudes, and location of the largest magnitude element. Since these subprograms are to be used in an ANSI FORTRAN context, the cases of single precision, double precision, and complex data are provided for. All of the subprograms have been thoroughly tested and produce consistent results even when transported from machine to machine. BLAS contains Assembler versions and FORTRAN test code for any of the following compilers: Lahey F77L, Microsoft FORTRAN, or IBM Professional FORTRAN. It requires the Microsoft Macro Assembler and a math co-processor. The PC implementation allows individual arrays of over 64K. The BLAS library was developed in 1979. The PC version was made available in 1986 and updated in 1988.
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.
ERIC Educational Resources Information Center
Osler, James Edward; Waden, Carl
2012-01-01
This paper provides an active discourse on the use of innovative solutions to conduct an in-depth investigation on the success and viability of 9th Grade Freshman Academies, Centers, and Center Models to aid in the retention of at risk students. These types of academic programs provide an active solution for the retention and projected completion…
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.…
Bilinear forms on fermionic Novikov algebras
NASA Astrophysics Data System (ADS)
Chen, Zhiqi; Zhu, Fuhai
2007-05-01
Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic type and Hamiltonian operators in formal variational calculus. Fermionic Novikov algebras correspond to a certain Hamiltonian super-operator in a super-variable. In this paper, we show that there is a remarkable geometry on fermionic Novikov algebras with non-degenerate invariant symmetric bilinear forms, which we call pseudo-Riemannian fermionic Novikov algebras. They are related to pseudo-Riemannian Lie algebras. Furthermore, we obtain a procedure to classify pseudo-Riemannian fermionic Novikov algebras. As an application, we give the classification in dimension <=4. Motivated by the one in dimension 4, we construct some examples in high dimensions.
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.
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.
Numerical linear algebra algorithms and software
NASA Astrophysics Data System (ADS)
Dongarra, Jack J.; Eijkhout, Victor
2000-11-01
The increasing availability of advanced-architecture computers has a significant effect on all spheres of scientific computation, including algorithm research and software development in numerical linear algebra. Linear algebra - in particular, the solution of linear systems of equations - lies at the heart of most calculations in scientific computing. This paper discusses some of the recent developments in linear algebra designed to exploit these advanced-architecture computers. We discuss two broad classes of algorithms: those for dense, and those for sparse matrices.
Symbolic Lie algebras manipulations using COMMON LISP
NASA Astrophysics Data System (ADS)
Cecchini, R.; Tarlini, M.
1989-01-01
We present a description and an implementation of a program in COMMON LISP to perform symbolic computations in a given Lie algebra. Using the general definitions of vector space Lie algebra and enveloping algebra, the program is able to compute commutators, to evaluate similarity transformations and the general Baker-Campbell-Hausdorff formula. All the computations are exact, including numerical coefficients. For the interactive user an optional menu facility and online help are available. LISP knowledge is unnecessary.
Lie algebras of classical and stochastic electrodynamics
NASA Astrophysics Data System (ADS)
Neto, J. J. Soares; Vianna, J. D. M.
1994-03-01
The Lie algebras associated with infinitesimal symmetry transformations of third-order differential equations of interest to classical electrodynamics and stochastic electrodynamics have been obtained. The structure constants for a general case are presented and the Lie algebra for each particular application is easily achieved. By the method used here it is not necessary to know the explicit expressions of the infinitesimal generators in order to determine the structure constants of the Lie algebra.
NASA Astrophysics Data System (ADS)
Manerowska, Anna; Nieznański, Edward; Mulawka, Jan
2013-10-01
Our aim is to present the algebra of concepts in two formal languages. First, after introducing a primary relation between concepts, which is subsumption, we shall specify in a language that uses quantifiers, the Boolean algebra of general concepts. Next, we shall note down the same algebra in simplified non-quantifying language, in order to use it as basis for two specific implementations, i.e. to create the Boolean algebras of deontic concepts and axiological concepts.
Dispersion Operators Algebra and Linear Canonical Transformations
NASA Astrophysics Data System (ADS)
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-04-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
Dispersion Operators Algebra and Linear Canonical Transformations
NASA Astrophysics Data System (ADS)
Andriambololona, Raoelina; Ranaivoson, Ravo Tokiniaina; Hasimbola Damo Emile, Randriamisy; Rakotoson, Hanitriarivo
2017-02-01
This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.
Banach Algebras Associated to Lax Pairs
NASA Astrophysics Data System (ADS)
Glazebrook, James F.
2015-04-01
Lax pairs featuring in the theory of integrable systems are known to be constructed from a commutative algebra of formal pseudodifferential operators known as the Burchnall- Chaundy algebra. Such pairs induce the well known KP flows on a restricted infinite-dimensional Grassmannian. The latter can be exhibited as a Banach homogeneous space constructed from a Banach *-algebra. It is shown that this commutative algebra of operators generating Lax pairs can be associated with a commutative C*-subalgebra in the C*-norm completion of the *-algebra. In relationship to the Bose-Fermi correspondence and the theory of vertex operators, this C*-algebra has an association with the CAR algebra of operators as represented on Fermionic Fock space by the Gelfand-Naimark-Segal construction. Instrumental is the Plücker embedding of the restricted Grassmannian into the projective space of the associated Hilbert space. The related Baker and tau-functions provide a connection between these two C*-algebras, following which their respective state spaces and Jordan-Lie-Banach algebras structures can be compared.
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.
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…
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…
Hypersymmetry: A openface3-graded generalization of supersymmetry
NASA Astrophysics Data System (ADS)
Abramov, Viktor; Kerner, Richard; Le Roy, Bertrand
1997-03-01
We propose a generalization of non-commutative geometry and gauge theories based on ternary Z3-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 Z3-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(2πi)/3. The usual Z2-graded structures such as Grassmann, Lie, and Clifford algebras are generalized to the Z3-graded case. Certain suggestions concerning the eventual use of these new structures in physics of elementary particles and fields are exposed.
Classification of filiform Lie algebras of order 3
NASA Astrophysics Data System (ADS)
Navarro, Rosa María
2016-12-01
Lie algebras of order 3 constitute a generalization of Lie algebras and superalgebras. Throughout this paper the classification problem of filiform Lie algebras of order 3 is considered and therefore this work is a continuation papers seen in the literature. We approach this classification by extending Vergne's result for filiform Lie algebras and by considering algebras of order 3 of high nilindex. We find the expression of the law to which any elementary filiform Lie algebra of order 3 is isomorphic.
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
2014-11-01
The focus of this study was connections among 3 aspects of mathematical cognition at 2(nd) 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 2(nd)-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.
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…
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…
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…
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…
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…
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
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…
The Algebra of Lexical Semantics
NASA Astrophysics Data System (ADS)
Kornai, András
The current generative theory of the lexicon relies primarily on tools from formal language theory and mathematical logic. Here we describe how a different formal apparatus, taken from algebra and automata theory, resolves many of the known problems with the generative lexicon. We develop a finite state theory of word meaning based on machines in the sense of Eilenberg [11], a formalism capable of describing discrepancies between syntactic type (lexical category) and semantic type (number of arguments). This mechanism is compared both to the standard linguistic approaches and to the formalisms developed in AI/KR.
Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras
NASA Astrophysics Data System (ADS)
Konig, Martinvaldo
2014-10-01
Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both Łukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical implications are defined as primitive operators. We prove this logic to be decidable, to be strongly complete and to have the deduction-detachment theorem.
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: A Problem Solving Approach
ERIC Educational Resources Information Center
Windsor, Will
2010-01-01
Algebraic thinking is a crucial and fundamental element of mathematical thinking and reasoning. It initially involves recognising patterns and general mathematical relationships among numbers, objects and geometric shapes. This paper will highlight how the ability to think algebraically might support a deeper and more useful knowledge, not only of…
Learning from Student Approaches to Algebraic Proofs
ERIC Educational Resources Information Center
D'Ambrosio, Beatriz S.; Kastberg, Signe E.; Viola dos Santos, Joao Ricardo
2010-01-01
Many mathematics teachers struggle to support their students' developing understanding of proof as an essential element in investigations of mathematics. The area of mathematics where the development of an understanding of proof is most challenging is algebra. In the case of algebraic proof, analysis of student written work on tasks that demand…
From operator algebras to superconformal field theory
Kawahigashi, Yasuyuki
2010-01-15
We survey operator algebraic approach to (super)conformal field theory. We discuss representation theory, classification results, full and boundary conformal field theories, relations to supervertex operator algebras and Moonshine, connections to subfactor theory of Jones, and certain aspects of noncommutative geometry of Connes.
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)
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…
Post-Lie Algebras and Isospectral Flows
NASA Astrophysics Data System (ADS)
Ebrahimi-Fard, Kurusch; Lundervold, Alexander; Mencattini, Igor; Munthe-Kaas, Hans Z.
2015-11-01
In this paper we explore the Lie enveloping algebra of a post-Lie algebra derived from a classical R-matrix. An explicit exponential solution of the corresponding Lie bracket flow is presented. It is based on the solution of a post-Lie Magnus-type differential equation.
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)
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…
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…
An algebraic approach to the scattering equations
NASA Astrophysics Data System (ADS)
Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui
2015-12-01
We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.
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
Cartan calculus on quantum Lie algebras
Schupp, P.; Watts, P.; Zumino, B.
1993-12-09
A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions au into one big algebra, the ``Cartan Calculus.``
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
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…
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…
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…
Symbolic Notations and Students' Achievements in Algebra
ERIC Educational Resources Information Center
Peter, Ebiendele E.; Olaoye, Adetunji A.
2013-01-01
This study focuses on symbolic notations and its impact on students' achievement in Algebra. The main reason for this study rests on the observation from personal and professional experiences on students' increasing hatred for Algebra. One hundred and fifty (150) Senior Secondary School Students (SSS) from Ojo Local Education District, Ojo, Lagos,…
SAYD Modules over Lie-Hopf Algebras
NASA Astrophysics Data System (ADS)
Rangipour, Bahram; Sütlü, Serkan
2012-11-01
In this paper a general van Est type isomorphism is proved. The isomorphism is between the Lie algebra cohomology of a bicrossed sum Lie algebra and the Hopf cyclic cohomology of its Hopf algebra. We first prove a one to one correspondence between stable-anti-Yetter-Drinfeld (SAYD) modules over the total Lie algebra and those modules over the associated Hopf algebra. In contrast to the non-general case done in our previous work, here the van Est isomorphism is proved at the first level of a natural spectral sequence, rather than at the level of complexes. It is proved that the Connes-Moscovici Hopf algebras do not admit any finite dimensional SAYD modules except the unique one-dimensional one found by Connes-Moscovici in 1998. This is done by extending our techniques to work with the infinite dimensional Lie algebra of formal vector fields. At the end, the one to one correspondence is applied to construct a highly nontrivial four dimensional SAYD module over the Schwarzian Hopf algebra. We then illustrate the whole theory on this example. Finally explicit representative cocycles of the cohomology classes for this example are calculated.
Algebraic Formulas for Areas between Curves.
ERIC Educational Resources Information Center
Gabai, Hyman
1982-01-01
Korean secondary school students preparing for college learn about a simple algebraic formula for area bounded by a parabola and line. The approach does not seem well-known among American students. It is noted that, while the formula derivations rely on integration, algebra students could use the formulas without proofs. (MP)
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…
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…
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,…
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…
Is Algebra Really Difficult for All Students?
ERIC Educational Resources Information Center
Egodawatte, Gunawardena
2009-01-01
Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-07
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.
LINPACK. Simultaneous Linear Algebraic Equations
Miller, M.A.
1990-05-01
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
LINPACK. Simultaneous Linear Algebraic Equations
Dongarra, J.J.
1982-05-02
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
Hexagonal tessellations in image algebra
NASA Astrophysics Data System (ADS)
Eberly, David H.; Wenzel, Dennis J.; Longbotham, Harold G.
1990-11-01
In image algebra '' the concept of a coordinate set X is general in that such a set is simply a subset of ndimensional Euclidean space . The standard applications in 2-dimensional image processing use coordinate sets which are rectangular arrays X 72 x ZZm. However some applications may require other geometries for the coordinate set. We look at three such related applications in the context of image algebra. The first application is the modeling of photoreceptors in primate retinas. These receptors are inhomogeneously distributed on the retina. The largest receptor density occurs in the center of the fovea and decreases radially outwards. One can construct a hexagonal tessellation of the retina such that each hexagon contains approximately the same number of receptors. The resulting tessellation called a sunflower heart2 consists of concentric rings of hexagons whose sizes increase as the radius of the ring increases. The second application is the modeling of the primary visual . The neurons are assumed to be uniformly distributed as a regular hexagonal lattice. Cortical neural image coding is modeled by a recursive convolution of the retinal neural image using a special set of filters. The third application involves analysis of a hexagonally-tessellated image where the pixel resolution is variable .