Analysis of Newton's Third Law Questions on the Force Concepts Inventory at Georgia State University

NASA Astrophysics Data System (ADS)

Oakley, Christopher; Thoms, Brian

2012-03-01

A major emphasis of the Physics Education Research program at Georgia State University is an effort to assess and improve students' understanding of Newton's Laws concepts. As part of these efforts the Force Concepts Inventory (FCI) has been given to students in both the algebra-based and calculus-based introductory physics sequences. In addition, the algebra-based introductory physics sequence is taught in both a SCALE-UP and a traditional lecture format. The results of the FCI have been analyzed by individual question and also as categorized by content. The analysis indicates that students in both algebra and calculus-based courses are successful at overcoming Aristotelian misconceptions regarding Newton's Third Law (N3) in the context of a stationary system. However, students are less successful on N3 questions involving objects in constant motion or accelerating. Interference between understanding of Newton's Second and Third Laws as well as other possible explanations for lower student performance on N3 questions involving non-stationary objects will be discussed.

Modeling the Water Balloon Slingshot

NASA Astrophysics Data System (ADS)

Bousquet, Benjamin D.; Figura, Charles C.

2013-01-01

In the introductory physics courses at Wartburg College, we have been working to create a lab experience focused on the scientific process itself rather than verification of physical laws presented in the classroom or textbook. To this end, we have developed a number of open-ended modeling exercises suitable for a variety of learning environments, from non-science major classes to algebra-based and calculus-based introductory physics classes.

Linking Science Fiction and Physics Courses

NASA Astrophysics Data System (ADS)

McBride, Krista K.

2016-05-01

Generally, cohorts or learning communities enrich higher learning in students. Learning communities consist of conventionally separate groups of students that meet together with common academic purposes and goals. Types of learning communities include paired courses with concurrent student enrollment, living-learning communities, and faculty learning communities. This article discusses a learning community of 21 students that I created with a colleague in the English department. The community encompasses two general education courses: an algebra-based physics course entitled "Intro to Physics" and a literature course entitled "Science Fiction, Science Fact." Students must enroll in both of these courses during the same semester. Additionally, I highlight advantages to linking these courses through surveying the assignments and course materials that we used in our learning community. Figure 1 shows the topics that are covered in both physics and literature courses.

The Elements of Teaching Nonscientists: Make it Conceptual, Social, Modern, and Interactive

NASA Astrophysics Data System (ADS)

Hobson, Art

2001-03-01

Physics literacy for all students should be a top priority for every physics department. Reasons include each department's self-interest, and the health of our profession. But most importantly, as the American Association for the Adancement of Science puts it, "Without a scientifically literate population, the outlook for a better world is not promising." Because nonscientists have little need and less desire for algebra-based physics problems, these courses should be conceptual (non-algebraic) although they should certainly be numerate. Since 1976, I have developed and taught a course of this type that includes most of the major principles of physics. Its success has stemmed from (1) a conceptual approach, (2) inclusion of relevant societal topics such as energy resources, scientific methodology, pseudoscience, global warming, and technological risk, (3) modern physics topics that occupy 50instruction techniques even in (especially in!) classes of over 200. I will describe this course and present interactive teaching ideas for one socially relevant topic: transportation and energy efficiency. A textbook is available: Physics: Concepts and Connections, by Art Hobson (Prentice Hall, 2nd Edition 1999). Further info: http://www.uark.edu/depts/physics/about/hobson.html

The Elements of Teaching Nonscientists: Make it Conceptual, Social, Modern, and Interactive

NASA Astrophysics Data System (ADS)

Hobson, Art

2000-04-01

Physics literacy for all students should be a top priority for every physics department. Reasons include each department's self-interest, and the health of our profession. But most importantly, as the American Association for the Adancement of Science puts it, "Without a scientifically literate population, the outlook for a better world is not promising." Because nonscientists have little need and less desire for algebra-based physics problems, these courses should be conceptual (non-algebraic) although they should certainly be numerate. Since 1976, I have developed and taught a course of this type that includes most of the major principles of physics. Its success has stemmed from (1) a conceptual approach, (2) inclusion of relevant societal topics such as energy resources, scientific methodology, pseudoscience, global warming, and technological risk, (3) modern physics topics that occupy 50instruction techniques even in (especially in!) classes of over 200. I will describe this course and conduct an "active learning" demonstration of ideas for teaching one socially relevant topic: transportation and energy efficiency. A textbook is available: Physics: Concepts and Connections, by Art Hobson (Prentice Hall, 2nd Edition 1999). Further info: http://www.uark.edu/depts/physics/about/hobson.html

Effects of California community college students' gender, self-efficacy, and attitudes and beliefs toward physics on conceptual understanding of Newtonian mechanics

NASA Astrophysics Data System (ADS)

Said, Asma

Despite the advances made in various fields, women are still considered as minorities in the fields of science and mathematics. There is a gender gap regarding women's participation and achievement in physics. Self-efficacy and attitudes and beliefs toward physics have been identified as predictors of students' performance on conceptual surveys in physics courses. The present study, which used two-way analysis of variance and multiple linear regression analyses at a community college in California, revealed there is no gender gap in achievement between male and female students in physics courses. Furthermore, there is an achievement gap between students who are enrolled in algebra-based and calculus-based physics courses. The findings indicate that attitudes and beliefs scores can be used as predictors of students' performance on conceptual surveys in physics courses. However, scores of self-efficacy cannot be used as predictors of students' performance on conceptual surveys in physics courses.

Student satisfaction in interactive engagement-based physics classes

NASA Astrophysics Data System (ADS)

Gaffney, Jon D. H.; Gaffney, Amy L. Housley

2016-12-01

Interactive engagement-based (IE) physics classes have the potential to invigorate and motivate students, but students may resist or oppose the pedagogy. Understanding the major influences on student satisfaction is a key to successful implementation of such courses. In this study, we note that one of the major differences between IE and traditional physics classes lies in the interpersonal relationships between the instructor and students. Therefore, we introduce the interpersonal communication constructs of instructor credibility and facework as possible frameworks for understanding how instructors and students navigate the new space of interactions. By interpreting survey data (N =161 respondents in eight sections of an IE introductory algebra-based physics course), we found both frameworks to be useful in explaining variance in student ratings of their satisfaction in the course, although we are unable to distinguish at this point whether instructor credibility acts as a mediating variable between facework and course satisfaction.

Predicting Course Performance in Freshman and Sophomore Physics Courses: Women Are More Predictable than Men.

ERIC Educational Resources Information Center

McCammon, Susan; And Others

1988-01-01

Investigates the extent to which thinking skills and mathematical competency would predict the course performance of freshman and sophomore science majors enrolled in physics courses. Finds that algebra ability and critical thinking skills were the best predictors. (Author/YP)

Using a flipped classroom in an algebra-based physics course

NASA Astrophysics Data System (ADS)

Smith, Leigh

2013-03-01

The algebra-based physics course is taken by Biology students, Pre-Pharmacy, Pre-Medical, and other health related majors such as medical imaging, physical therapy, and so on. Nearly 500 students take the course each Semester. Student learning is adversely impacted by poor math backgrounds as well as extensive work schedules outside of the classroom. We have been researching the use of an intensive flipped-classroom approach where students spend one to two hours each week preparing for class by reading the book, completing a series of conceptual problems, and viewing videos which describe the material. In class, the new response system Learning Catalytics is used which allows much richer problems to be posed in class and includes sketching figures, numerical or symbolic entries, short answers, highlighting text, etc in addition to the standard multiple choice questions. We make direct comparison of student learning for 1200 sudents who have taken the same tests, 25% of which used the flipped classroom approach, and 75% who took a more standard lecture. There is significant evidence of improvements in student learning for students taking the flipped classroom approach over standard lectures. These benefits appear to impact students at all math backgrounds.

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…

Austin ISD. Integrated Lesson Plans.

ERIC Educational Resources Information Center

East Texas State Univ., Commerce. Educational Development and Training Center.

This packet contains 14 lesson plans for integrated academic and vocational education courses. Lesson plans for the following courses are included: integrated physics and principles of technology; algebra and principles of technology; principles of technology, language arts, and economics; physics and industrial electronics; physics and…

Physics Almost Saved the President! Electromagnetic Induction and the Assassination of James Garfield: A Teaching Opportunity in Introductory Physics

ERIC Educational Resources Information Center

Overduin, James; Molloy, Dana; Selway, Jim

2014-01-01

Electromagnetic induction is probably one of the most challenging subjects for students in the introductory physics sequence, especially in algebra-based courses. Yet it is at the heart of many of the devices we rely on today. To help students grasp and retain the concept, we have put together a simple and dramatic classroom demonstration that…

Nontraditional approach to algebra-based general physics

NASA Astrophysics Data System (ADS)

Meltzer, David E.

1997-03-01

In order to improve the degree of conceptual learning in our algebra-based general physics course, the second semester (of a two-semester sequence) has been taught in a nontraditional format during the past year. The key characteristics of this course were: 1) Intense and continuous use of interactive-engagement methods and cooperative learning; 2) coverage of less than half of the conventional number of topics, 3) heavy emphasis on qualitative questions as opposed to quantitative problems, 4) adjustment of the pacing of the course based on continuous (twice per week) formative assessment. The students enrolled in the course were relatively poorly prepared, with weak mathematical skills. Open-book quizzes stressing qualitative concepts in electricity and magnetism were given twice per week; most were given in "group quiz" format, allowing collaboration. Exams (also open-book) were all done individually. Most of the class time was taken up by quizzes, and by interactive discussion and group work related to quiz questions. New topics were not introduced until a majority of the class demonstrated competence in the topic under discussion. Despite lengthy and intensive focus on qualitative, conceptual questions and simple quantitative problems, only a small minority of the class ultimately demonstrated mastery of the targeted concepts. Frequent testing and re-testing of the students on basic concepts disclosed tenacious persistence of misconceptions.

Promoting Quantitative Literacy in an Online College Algebra Course

ERIC Educational Resources Information Center

Tunstall, Luke; Bossé, Michael J.

2016-01-01

College algebra (a university freshman level algebra course) fulfills the quantitative literacy requirement of many college's general education programs and is a terminal course for most who take it. An online problem-based learning environment provides a unique means of engaging students in quantitative discussions and research. This article…

A Simple Mechanical Experiment on Exponential Growth

ERIC Educational Resources Information Center

McGrew, Ralph

2015-01-01

With a rod, cord, pulleys, and slotted masses, students can observe and graph exponential growth in the cord tension over a factor of increase as large as several hundred. This experiment is adaptable for use either in algebra-based or calculus-based physics courses, fitting naturally with the study of sliding friction. Significant parts of the…

Using Biomedically Relevant Multimedia Content in an Introductory Physics Course for Life Science and Pre-health Students

NASA Astrophysics Data System (ADS)

Mylott, Elliot; Kutschera, Ellynne; Dunlap, Justin C.; Christensen, Warren; Widenhorn, Ralf

2016-04-01

We will describe a one-quarter pilot algebra-based introductory physics course for pre-health and life science majors. The course features videos with biomedical experts and cogent biomedically inspired physics content. The materials were used in a flipped classroom as well as an all-online environment where students interacted with multimedia materials online and prior to engaging in classroom activities. Pre-lecture questions on both the medical content covered in the video media and the physics concepts in the written material were designed to engage students and probe their understanding of physics. The course featured group discussion and peer-lead instruction. Following in-class instruction, students engaged with homework assignments which explore the connections of physics and the medical field in a quantitative manner. Course surveys showed a positive response by the vast majority of students. Students largely indicated that the course helped them to make a connection between physics and the biomedical field. The biomedical focus and different course format were seen as an improvement to previous traditional physics instruction.

Addressing the United States Navy Need for Software Engineering Education

DTIC Science & Technology

1999-09-01

taught in MA 1996 (5 - 0). Precalculus review, complex numbers and algebra, complex plane, DeMovire’s Theorem, matrix algebra, LU decomposition...This course was designed for the METOC and Combat Systems curricula. PREREQUISITE: Precalculus mathematics. MA1996 MATHEMATICS FOR SCIENTISTS AND...description for MAI995 (5 - 0). This course was designed for the METOC and Combat Systems curricula. PREREQUISITE: Precalculus mathematics. PHYSICS/SYSTEMS

A Modeling-Based College Algebra Course and Its Effect on Student Achievement

ERIC Educational Resources Information Center

Ellington, Aimee J.

2005-01-01

In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

Reaching Out: The Bachelor of Arts Degree In Physics

NASA Astrophysics Data System (ADS)

Hobson, Art

1996-05-01

Physics degrees are not only for physicists. Our department believes that it would be healthy if attorneys, physicians, journalists, politicians, businesspeople, and others had undergraduate degrees in physics. Thus, we have begun offering a Bachelor of Arts degree in physics, for students who want to study physics as a background for other fields such as law (patents, environmental law), medical school, business (high-tech firms), journalism (science reporting, environmental reporting), music (accoustics, electronic music), and essentially any other profession. The program reaches outward, outside of physics, rather than pointing toward further work in physics. It begins with the algebra-based introductory course rather than the calculus-based course for future physicists and engineers. Two new courses are being created to provide these pre-professional students with broad science literacy and knowledge of physics-related technologies. The program is more flexible and less technical than the traditional Bachelor of Science program, allowing students time for outside electives and professional requirements in other fields.

Iterants, Fermions and Majorana Operators

NASA Astrophysics Data System (ADS)

Kauffman, Louis H.

Beginning with an elementary, oscillatory discrete dynamical system associated with the square root of minus one, we study both the foundations of mathematics and physics. Position and momentum do not commute in our discrete physics. Their commutator is related to the diffusion constant for a Brownian process and to the Heisenberg commutator in quantum mechanics. We take John Wheeler's idea of It from Bit as an essential clue and we rework the structure of that bit to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We show how the dynamical system for the square root of minus one is essentially the dynamics of a distinction whose self-reference leads to both the fusion algebra and the operator algebra for the Majorana Fermion. In the course of this, we develop an iterant algebra that supports all of matrix algebra and we end the essay with a discussion of the Dirac equation based on these principles.

Methods to Improve Performance of Students with Weaker Math Skills in an Algebra-based Physics Course

NASA Astrophysics Data System (ADS)

Smith, Leigh

2015-03-01

I will describe methods used at the University of Cincinnati to enhance student success in an algebra-based physics course. The first method is to use ALEKS, an adaptive online mathematics tutorial engine, before the term begins. Approximately three to four weeks before the beginning of the term, the professor in the course emails all of the students in the course informing them of the possibility of improving their math proficiency by using ALEKS. Using only a minimal reward on homework, we have achieved a 70% response rate with students spending an average of 8 hours working on their math skills before classes start. The second method is to use a flipped classroom approach. The class of 135 meets in a tiered classroom twice per week for two hours. Over the previous weekend students spend approximately 2 hours reading the book, taking short multiple choice conceptual quizzes, and viewing videos covering the material. In class, students use Learning Catalytics to work through homework problems in groups, guided by the instructor and one learning assistant. Using these interventions, we have reduced the student DWF rate (the fraction of students receiving a D or lower in the class) from an historical average of 35 to 40% to less than 20%.

Generalizing a categorization of students' interpretations of linear kinematics graphs

NASA Astrophysics Data System (ADS)

Bollen, Laurens; De Cock, Mieke; Zuza, Kristina; Guisasola, Jenaro; van Kampen, Paul

2016-06-01

We have investigated whether and how a categorization of responses to questions on linear distance-time graphs, based on a study of Irish students enrolled in an algebra-based course, could be adopted and adapted to responses from students enrolled in calculus-based physics courses at universities in Flanders, Belgium (KU Leuven) and the Basque Country, Spain (University of the Basque Country). We discuss how we adapted the categorization to accommodate a much more diverse student cohort and explain how the prior knowledge of students may account for many differences in the prevalence of approaches and success rates. Although calculus-based physics students make fewer mistakes than algebra-based physics students, they encounter similar difficulties that are often related to incorrectly dividing two coordinates. We verified that a qualitative understanding of kinematics is an important but not sufficient condition for students to determine a correct value for the speed. When comparing responses to questions on linear distance-time graphs with responses to isomorphic questions on linear water level versus time graphs, we observed that the context of a question influences the approach students use. Neither qualitative understanding nor an ability to find the slope of a context-free graph proved to be a reliable predictor for the approach students use when they determine the instantaneous speed.

A Quantum Groups Primer

NASA Astrophysics Data System (ADS)

Majid, Shahn

2002-05-01

Here is a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes for the Part III pure mathematics course at Cambridge University, the book is suitable as a primary text for graduate courses in quantum groups or supplementary reading for modern courses in advanced algebra. The material assumes knowledge of basic and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The volume is a primer for mathematicians but it will also be useful for mathematical physicists.

A Study of the Relationship between Student Placement Test Scores and Final Grades in Physics 121 at Pima College.

ERIC Educational Resources Information Center

Iadevaia, David G.

A study was conducted at Pima Community College to determine the relationship between the final grade received by students in an introductory, algebra-based physics course (PHY 121) and their scores on the reading, writing, and mathematics portions of the college's nonmandatory assessment test. Between 1983 and 1988, 639 students obtained a final…

Nuclear Science Curriculum and Curriculum para la Ciencia Nuclear.

ERIC Educational Resources Information Center

American Nuclear Society, La Grange Park, IL.

This document presents a course in the science of nuclear energy, units of which may be included in high school physics, chemistry, and biology classes. It is intended for the use of teachers whose students have already completed algebra and chemistry or physics. Included in this paper are the objectives of this course, a course outline, a…

The Effect of a Math Emporium Course Redesign in Developmental and Introductory Mathematics Courses on Student Achievement and Students' Attitudes toward Mathematics at a Two-Year College

ERIC Educational Resources Information Center

Bishop, Amy Renee

2010-01-01

The purpose of this research was to determine the effect of computer-based instruction on student mathematics achievement and students' attitudes toward mathematics in developmental and introductory mathematics courses, namely Elementary Algebra, Intermediate Algebra, and College Algebra, at a community college. The researcher also examined the…

Putting the spark into physical science and algebra

NASA Astrophysics Data System (ADS)

Pill, Bruce; Dagenais, Andre

2007-06-01

The presenters will describe a number of laboratory activities developed in collaboration with the Department of Electrical Engineering at the University of Delaware as part of their outreach program to help make math and science more authentic on the pre-college level. Lessons relating to electrical topics are often abstract and appropriate only for advanced students in math and science. We have devised lessons that rely on simple equipment. They promote skills that are included in National and State Standards. They emphasize the connections between math and science; they are appropriate for an algebra course, a physical science course, a PhysicsFirst course or a traditional physics course. Students benefit from seeing that what they learn in math and science courses can lead to cutting-edge work in areas such as passive wave imaging, photonics, wireless communication and high performance computing. The collaboration has been meaningful because it has motivated us to tailor our lessons to reflect what is happening in the research lab of our local university. Written materials for use in teacher training workshops will also be available.

The Universality of Time Dilation and Space Contraction.

ERIC Educational Resources Information Center

Daly, Lisa N.; Horton, George K.

1994-01-01

Describes the extended general physics course taught at Rutgers University. The course presents to students at the high school algebra level the topic of analyzing a particular thought experiment that yields the time dilation formula and subsequently space contraction, velocity addition, and other 20th-century physics concepts. (MVL)

An Unusual Apporach to the Elementary Qualitative Physics Course: Introduction to Space Science

ERIC Educational Resources Information Center

Moore, E. Neal

1975-01-01

Describes a course, without laboratory, using rudimentary algebra and covering such topics as gravitation, orbital mechanics, atomic structure, geomagnetism, electromagnetic spectrum, theory of relativity, extraterrestrial life, and interstellar travel. (GH)

Teaching Physics to Future Presidents

NASA Astrophysics Data System (ADS)

Jacobsen, Bob

2015-03-01

We present Berkeley's ``Physics for Future Presidents'' course. Created by Prof. Richard Muller, this is an introductory course aimed at preparing our students to make decisions in a physical, technological world. Organized around large topical areas like ``Energy,'' ``Gravity and Force,'' ``Nuclei and Radioactivity,'' and ``Invisible Light,'' we can cover in some depth the scientific issues involved in large-scale energy production via renewable and non-renewable resources, satellites including capabilities and limitations, nuclear power production including risk and waste, UV exposure including discussion of the ozone layer and cancer risk, etc. Although only a small bit of algebra is used, it's a deeply quantitative course. The class is structured around (1) traditional text readings and homework for basic material (2) demo- and discussion-based lectures and (3) readings and essays based on current articles and events. This third component raises student engagement and improves their reasoning & skeptical skills. It also makes the course challenging for both STEM and non-STEM students, and for future teachers.

Introducing Algebra through the Graphical Representation of Functions: A Study among LD Students

ERIC Educational Resources Information Center

Sauriol, Jennifer

2013-01-01

This longitudinal study evaluates the impact of a new Algebra 1 course at a High School for language-based learning-disabled (LD) students. The new course prioritized the teaching of relationship graphs and functions as an introduction to algebra. Across three studies, the dissertation documents and evaluates the progress made by LD high school…

Physics Almost Saved the President! Electromagnetic Induction and the Assassination of James Garfield: A Teaching Opportunity in Introductory Physics

NASA Astrophysics Data System (ADS)

Overduin, James; Molloy, Dana; Selway, Jim

2014-03-01

Electromagnetic induction is probably one of the most challenging subjects for students in the introductory physics sequence, especially in algebra-based courses. Yet it is at the heart of many of the devices we rely on today. To help students grasp and retain the concept, we have put together a simple and dramatic classroom demonstration that combines sight and sound with a compelling personal story from U.S. history. Other classroom activities dealing with induction have been discussed in this journal, but we believe that this one will be especially likely to attract and retain student interest, particularly in courses geared toward medical, biological, and other non-physics majors.

Putting the “Spark” into Physical Science and Algebra

NASA Astrophysics Data System (ADS)

Dagenais, Andre; Pill, B.

2006-12-01

The presenters will describe a number of laboratory activities developed in collaboration with the Department of Electrical Engineering at the University of Delaware as part of their outreach program to help make math and science more authentic on the pre-college level. Lessons relating to electrical topics are often abstract and appropriate only for advanced students in math and science. We have devised lessons that rely on simple equipment. They promote skills that are included in National and State Standards. They emphasize the connections between math and science; they are appropriate for an algebra course, a physical science course, a PhysicsFirst course or a traditional physics course. Students benefit from seeing that what they learn in math and science courses can lead to cutting-edge work in areas such as passive wave imaging, photonics, wireless communication and high performance computing. The collaboration has been meaningful because it has motivated us to tailor our lessons to reflect what is happening in the research lab of our local university. Written materials for use in teacher training workshops will also be available. Funded by NSF Research Experience for Teachers(RET #0322633) program under the direction of Dr. Dennis Prather, University of Delaware Electrical Engineering

Developing a magnetism conceptual survey and assessing gender differences in student understanding of magnetism

NASA Astrophysics Data System (ADS)

Li, Jing; Singh, Chandralekha

2012-02-01

We discuss the development of a research-based conceptual multiple-choice survey of magnetism. We also discuss the use of the survey to investigate gender differences in students' difficulties with concepts related to magnetism. We find that while there was no gender difference on the pre-test. However, female students performed significantly worse than male students when the survey was given as a post-test in traditionally taught calculus-based introductory physics courses with similar results in both the regular and honors versions of the course. In the algebra-based courses, the performance of female and male students has no statistical difference on the pre-test or the post-test.

Understanding measurement in light of its origins.

PubMed

Humphry, Stephen

2013-01-01

During the course of history, the natural sciences have seen the development of increasingly convenient short-hand symbolic devices for denoting physical quantities. These devices ultimately took the form of physical algebra. However, the convenience of algebra arguably came at a cost - a loss of the clarity of direct insights by Euclid, Galileo, and Newton into natural quantitative relations. Physical algebra is frequently interpreted as ordinary algebra; i.e., it is interpreted as though symbols denote (a) numbers and operations on numbers, as opposed to (b) physical quantities and quantitative relations. The paper revisits the way in which Newton understood and expressed physical definitions and laws. Accordingly, it reviews a compact form of notation that has been used to denote both: (a) ratios of physical quantities; and (b) compound ratios, involving two or more kinds of quantity. The purpose is to show that it is consistent with historical developments to regard physical algebra as a device for denoting relations among ratios. Understood in the historical context, the objective of measurement is to establish that a physical quantity stands in a specific ratio to another quantity of the same kind. To clarify the meaning of measurement in terms of the historical origins of physics carries basic implications for the way in which measurement is understood and approached. Possible implications for the social sciences are considered.

Developing CORE model-based worksheet with recitation task to facilitate students’ mathematical communication skills in linear algebra course

NASA Astrophysics Data System (ADS)

Risnawati; Khairinnisa, S.; Darwis, A. H.

2018-01-01

The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.

The Effects of Peer Instruction on Students' Conceptual Learning and Motivation

ERIC Educational Resources Information Center

Gok, Tolga

2012-01-01

The aim of this study was to investigate the effects of peer instruction on college students' conceptual learning, motivation, and self-efficacy in an algebra-based introductory physics course for nonmajors. Variables were studied via a quasi-experiment, Solomon four-group design on 123 students. Treatment groups were taught by peer instruction.…

Physics Learning with a Computer Algebra System: Towards a Learning Environment That Promotes Enhanced Problem Representations.

ERIC Educational Resources Information Center

Savelsbergh, Elwin R.; Ferguson-Hessler, Monica G. M.; de Jong, Ton

An approach to teaching problem-solving based on using the computer software Mathematica is applied to the study of electrostatics and is compared with the normal approach to the module. Learning outcomes for both approaches were not significantly different. The experimental course successfully addressed a number of misconceptions. Students in the…

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

End of Course Grades and End of Course Tests in the Virtual Environment: A Study of Correlation

ERIC Educational Resources Information Center

Philipp, Jamie Gilbert

2014-01-01

The purpose of this correlational study is to understand the relationship between end-of-course grades as assigned by teachers and standardized end-of-course scores earned by students in Algebra, Geometry, Biology, Physical Science, and U.S. History courses at one virtual charter school in the State of Georgia. Pearson Product-Moment Correlation…

Alignment of TAs' beliefs with practice and student perception

NASA Astrophysics Data System (ADS)

Chini, Jacquelyn J.; Al-Rawi, Ahlam

2013-01-01

Graduate teaching assistants (TAs) play an important role in introductory physics courses, particularly in large enrollment courses where the TA may be viewed as more approachable and accessible than the lecture instructor. Thus, while TAs may still be in the process of developing their views on teaching physics, their practices directly influence a large number of introductory students. As the first steps in reforming our introductory courses and TA training program, we collected multiple types of data on TAs teaching in traditional algebra-based physics laboratories. Drawing on prior work on TAs' pedagogical knowledge, we explore how the beliefs expressed by TAs in interviews align with their practices during a laboratory video-taped mid-semester. Additionally, we explore how both the TAs' expressed beliefs and practices align with students' responses to an end-of-semester TA evaluation survey.

A calculus based on a q-deformed Heisenberg algebra

DOE PAGES

Cerchiai, B. L.; Hinterding, R.; Madore, J.; ...

1999-04-27

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on thismore » derivative differential forms and an exterior differential calculus can be constructed.« less

Transforming a fourth year modern optics course using a deliberate practice framework

NASA Astrophysics Data System (ADS)

Jones, David J.; Madison, Kirk W.; Wieman, Carl E.

2015-12-01

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present a study of active learning pedagogies in an upper-division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15% improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier transforms, partial differential equations, and vector calculus), we expect the transformation process could be applied to most upper-division physics courses having a similar mathematical base.

42 CFR Appendix A to Part 75 - Standards for Accreditation of Educational Programs for Radiographers

Code of Federal Regulations, 2011 CFR

2011-10-01

... film evaluation; (k) Methods of patient care; (l) Pathology; (m) Radiologic physics; and (n) Radiation.... Courses in physics, chemistry, biology, algebra, and geometry are strongly recommended. (b) The number of...

42 CFR Appendix A to Part 75 - Standards for Accreditation of Educational Programs for Radiographers

Code of Federal Regulations, 2014 CFR

2014-10-01

... film evaluation; (k) Methods of patient care; (l) Pathology; (m) Radiologic physics; and (n) Radiation.... Courses in physics, chemistry, biology, algebra, and geometry are strongly recommended. (b) The number of...

42 CFR Appendix A to Part 75 - Standards for Accreditation of Educational Programs for Radiographers

Code of Federal Regulations, 2012 CFR

2012-10-01

... film evaluation; (k) Methods of patient care; (l) Pathology; (m) Radiologic physics; and (n) Radiation.... Courses in physics, chemistry, biology, algebra, and geometry are strongly recommended. (b) The number of...

42 CFR Appendix A to Part 75 - Standards for Accreditation of Educational Programs for Radiographers

Code of Federal Regulations, 2013 CFR

2013-10-01

... film evaluation; (k) Methods of patient care; (l) Pathology; (m) Radiologic physics; and (n) Radiation.... Courses in physics, chemistry, biology, algebra, and geometry are strongly recommended. (b) The number of...

A Modified Approach to Team-Based Learning in Linear Algebra Courses

ERIC Educational Resources Information Center

Nanes, Kalman M.

2014-01-01

This paper documents the author's adaptation of team-based learning (TBL), an active learning pedagogy developed by Larry Michaelsen and others, in the linear algebra classroom. The paper discusses the standard components of TBL and the necessary changes to those components for the needs of the course in question. There is also an empirically…

Do students benefit from drawing productive diagrams themselves while solving introductory physics problems? The case of two electrostatics problems

NASA Astrophysics Data System (ADS)

Maries, Alexandru; Singh, Chandralekha

2018-01-01

An appropriate diagram is a required element of a solution building process in physics problem solving and it can transform a given problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solving. We conducted an investigation in which two different interventions were implemented during recitation quizzes throughout the semester in a large enrolment, algebra-based introductory physics course. Students were either (1) asked to solve problems in which the diagrams were drawn for them or (2) explicitly told to draw a diagram. A comparison group was not given any instruction regarding diagrams. We developed a rubric to score the problem solving performance of students in different intervention groups. We investigated two problems involving electric field and electric force and found that students who drew productive diagrams were more successful problem solvers and that a higher level of relevant detail in a student’s diagram corresponded to a better score. We also conducted think-aloud interviews with nine students who were at the time taking an equivalent introductory algebra-based physics course in order to gain insight into how drawing diagrams affects the problem solving process. These interviews supported some of the interpretations of the quantitative results. We end by discussing instructional implications of the findings.

Comparison of the Effectiveness of a Traditional Intermediate Algebra Course With That of a Less Rigorous Intermediate Algebra Course in Preparing Students for Success in a Subsequent Mathematics Course

ERIC Educational Resources Information Center

Sworder, Steven C.

2007-01-01

An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

Mansfield ISD. Integrated Lesson Plans.

ERIC Educational Resources Information Center

East Texas State Univ., Commerce. Educational Development and Training Center.

This packet contains 27 lesson plans for integrated academic and vocational education courses. Lesson plans for the following courses are included: horticulture, algebra, physical science, general mechanical repair, foods and nutrition, home economics, and microcomputer applications. Some of the topics covered are as follows: seed germination,…

Identifying and addressing student difficulties with the ideal gas law

NASA Astrophysics Data System (ADS)

Kautz, Christian Hans

This dissertation reports on an in-depth investigation of student understanding of the ideal gas law. The research and curriculum development were mostly conducted in the context of algebra- and calculus-based introductory physics courses and a sophomore-level thermal physics course. Research methods included individual demonstration interviews and written questions. Student difficulties with the quantities: pressure, volume, temperature, and the number of moles were identified. Data suggest that students' incorrect and incomplete microscopic models about gases contribute to the difficulties they have in answering questions posed in macroscopic terms. In addition, evidence for general reasoning difficulties is presented. These research results have guided the development of curriculum to address the student difficulties that have been identified.

Towards Student Instrumentation of Computer-Based Algebra Systems in University Courses

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.; Hannah, John

2005-01-01

There are many perceived benefits of using technology, such as computer algebra systems, in undergraduate mathematics courses. However, attaining these benefits sometimes proves elusive. Some of the key variables are the teaching approach and the student instrumentation of the technology. This paper considers the instrumentation of computer-based…

The effect of the flipped model on achievement in an introductory college physics course

NASA Astrophysics Data System (ADS)

Winter, Joshua Brian

The flipped or inverted classroom model is one in which the time and place for traditional lecture and homework are reversed. Traditional lecture is replaced by online videos assigned as homework. This frees up time in class to be spent with more student centered activities such as discussion based concept questions and group problem solving. While growing in popularity, research on the effectiveness of this format is sparse. In this quasi-experimental study, two sections of an introductory algebra-based college physics course were examined over a five week period. Each section was taught with either the traditional or flipped model and physics knowledge achieved was compared using independent samples t-tests on both the instructor's unit exam and the Mechanics Baseline Test pre/posttest normalized gain. Results indicated that there was no statistically significant difference between the flipped model and the traditional lecture format. Avenues for further research are discussed.

Do evidence-based active-engagement courses reduce the gender gap in introductory physics?

NASA Astrophysics Data System (ADS)

Karim, Nafis I.; Maries, Alexandru; Singh, Chandralekha

2018-03-01

Prior research suggests that using evidence-based pedagogies can not only improve learning for all students, it can also reduce the gender gap. We describe the impact of physics education research-based pedagogical techniques in flipped and active-engagement non-flipped courses on the gender gap observed with validated conceptual surveys. We compare male and female students’ performance in courses which make significant use of evidence-based active-engagement (EBAE) strategies with courses that primarily use lecture-based (LB) instruction. All courses had large enrolment and often had more than 100 students. The analysis of data for validated conceptual surveys presented here includes data from two-semester sequences of algebra-based and calculus-based introductory physics courses. The conceptual surveys used to assess student learning in the first and second semester courses were the force concept inventory and the conceptual survey of electricity and magnetism, respectively. In the research discussed here, the performance of male and female students in EBAE courses at a particular level is compared with LB courses in two situations: (I) the same instructor taught two courses, one of which was an EBAE course and the other an LB course, while the homework, recitations and final exams were kept the same; (II) student performance in all of the EBAE courses taught by different instructors was averaged and compared with LB courses of the same type also averaged over different instructors. In all cases, on conceptual surveys we find that students in courses which make significant use of active-engagement strategies, on average, outperformed students in courses of the same type using primarily lecture-based instruction even though there was no statistically significant difference on the pre-test before instruction. However, the gender gap persisted even in courses using EBAE methods. We also discuss correlations between the performance of male and female students on the validated conceptual surveys and the final exam, which had a heavy weight on quantitative problem solving.

Do prescribed prompts prime sensemaking during group problem solving?

NASA Astrophysics Data System (ADS)

Martinuk, Mathew "Sandy"; Ives, Joss

2012-02-01

Many researchers and textbooks have promoted the use of rigid prescribed strategies for encouraging development of expert-like problem-solving behavior in novice students. The University of British Columbia's introductory algebra-based course for non-physics majors uses Context-Rich problems with a prescribed six-step strategy. We have coded audio recordings of group problem-solving sessions to analyze students' epistemological framing based on the implicit goal of their discussions. By treating the goal of "understanding the physics of the situation" as sensemaking, we argue that prescribed problem-solving prompts are not sufficient to induce subsequent sensemaking discussion.

Partially Flipped Linear Algebra: A Team-Based Approach

ERIC Educational Resources Information Center

Carney, Debra; Ormes, Nicholas; Swanson, Rebecca

2015-01-01

In this article we describe a partially flipped Introductory Linear Algebra course developed by three faculty members at two different universities. We give motivation for our partially flipped design and describe our implementation in detail. Two main features of our course design are team-developed preview videos and related in-class activities.…

Mathematical modelling in engineering: an alternative way to teach Linear Algebra

NASA Astrophysics Data System (ADS)

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-10-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).

Consideration of learning orientations as an application of achievement goals in evaluating life science majors in introductory physics

NASA Astrophysics Data System (ADS)

Mason, Andrew J.; Bertram, Charles A.

2018-06-01

When considering performing an Introductory Physics for Life Sciences course transformation for one's own institution, life science majors' achievement goals are a necessary consideration to ensure the pedagogical transformation will be effective. However, achievement goals are rarely an explicit consideration in physics education research topics such as metacognition. We investigate a sample population of 218 students in a first-semester introductory algebra-based physics course, drawn from 14 laboratory sections within six semesters of course sections, to determine the influence of achievement goals on life science majors' attitudes towards physics. Learning orientations that, respectively, pertain to mastery goals and performance goals, in addition to a learning orientation that does not report a performance goal, were recorded from students in the specific context of learning a problem-solving framework during an in-class exercise. Students' learning orientations, defined within the context of students' self-reported statements in the specific context of a problem-solving-related research-based course implementation, are compared to pre-post results on physics problem-solving items in a well-established attitudinal survey instrument, in order to establish the categories' validity. In addition, mastery-related and performance-related orientations appear to extend to overall pre-post attitudinal shifts, but not to force and motion concepts or to overall course grade, within the scope of an introductory physics course. There also appears to be differentiation regarding overall course performance within health science majors, but not within biology majors, in terms of learning orientations; however, health science majors generally appear to fare less well on all measurements in the study than do biology majors, regardless of learning orientations.

Patterns of Incorrect Responses on the FCI and Course Success

NASA Astrophysics Data System (ADS)

Wells, James; Mokaya, Fridah; Valente, Diego

The Force Concept Inventory (FCI) is often used to measure the effectiveness of instructional pedagogy in introductory physics courses both at the algebra- and calculus-based level. Scores on the FCI are correlated with the performance of students in a class, as measured by their final course grade. We have collected data from several semesters of first-semester introductory mechanics courses at a public 4-year university, taught in large-scale classrooms with pedagogy including elements of Just-in-Time Teaching pedagogy along with active learning course components. The data collected includes pre- and post-test FCI scores, midterm exam grades, and final course grades. We examine whether certain patterns of incorrect answers on the FCI post-test are predictive of course grades, indicating whether certain specific student preconceptions are more detrimental than others to the success of students in an introductory mechanics course. Funding from UConn - College of Liberal Arts and Sciences (CLAS).

An Example of Competence-Based Learning: Use of Maxima in Linear Algebra for Engineers

ERIC Educational Resources Information Center

Diaz, Ana; Garcia, Alfonsa; de la Villa, Agustin

2011-01-01

This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

The Effect of Scheduling Models for Introductory Algebra on 9th-Grade Students, Test Scores and Grades

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…

Physics for Water and Wastewater Operators.

ERIC Educational Resources Information Center

Koundakjian, Philip

This physics course covers the following main subject areas: (1) liquids; (2) pressure; (3) liquid flow; (4) temperature and heat; and (5) electric currents. The prerequisites for understanding this material are basic algebra and geometry. The lessons are composed mostly of sample problems and calculations that water and wastewater operators have…

Carnegie Learning Curricula and Cognitive Tutor™. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2013

2013-01-01

"Carnegie Learning Curricula and Cognitive Tutor"®, published by Carnegie Learning, is a secondary math curricula that offers textbooks and interactive software to provide individualized, self-paced instruction based on student needs. The program includes pre-Algebra, Algebra I, Algebra II, and Geometry, as well as a three-course series…

Are our textbooks too good to be good? Let students own their textbooks to own the skills

NASA Astrophysics Data System (ADS)

Tao, Xiuping

The two new yearlong high school courses, AP Physics 1 and 2, are equivalent to the two-semester algebra-based introductory Physics college course. The AP courses have more than 300 instruction hours, while the college course less than 100. This partially explains why college instructors always struggle to cover the important topics to not necessarily prepared students. To make it worse, many college students are not buying or reading textbooks and rely on instructors to get the course content. The fragmented reception is preventing students from getting a complete picture of the course. Not that there is a shortage of textbooks. There are many 1000-page tomes costing 200 or more, too good to be good. All the struggles contribute to U.S. students' relatively low STEM skills. I propose to let students own their books to own the skills. Students need much shorter (thus manageable) and much more affordable books, and they need to own it for good. Cross-culture comparison reveals that students learn better when they truly own their books (without planning to resell).

Promoting Success in the Physical Sciences: The University of Wisconsin's Physics Learning Program

NASA Astrophysics Data System (ADS)

Nossal, S. M.; Jacob, A. T.

2002-05-01

The Physics Learning Program at the University of Wisconsin-Madison provides small group, academic and mentoring support for students enrolled in algebra-based introductory physics courses. Those students accepted into our program are potentially at-risk academically in their physics course or for feeling isolated at the University. They include, among others, students who have not taken high school physics, returning adults, minority students, students with disabilities, and students with English as a second language. A core component of the program is the peer-lead teaching and mentoring groups that match upper level undergraduate physics majors with students potentially at-risk in introductory physics. The tutors receive ongoing training and supervision throughout the year. The program has expanded over the years to include staff tutors, the majority of whom are scientists who seek additional teaching experience. The Physics Peer Mentor Tutor Program is run in collaboration with a similar chemistry program at the University of Wisconsin's Chemistry Learning Center. We will describe our Physics Learning Programs and discuss some of the challenges, successes, and strategies used to work with our tutors and students.

Developing and validating a conceptual survey to assess introductory physics students’ understanding of magnetism

NASA Astrophysics Data System (ADS)

Li, Jing; Singh, Chandralekha

2017-03-01

Development of validated physics surveys on various topics is important for investigating the extent to which students master those concepts after traditional instruction and for assessing innovative curricula and pedagogies that can improve student understanding significantly. Here, we discuss the development and validation of a conceptual multiple-choice survey related to magnetism suitable for introductory physics courses. The survey was developed taking into account common students’ difficulties with magnetism concepts covered in introductory physics courses found in our investigation and the incorrect choices to the multiple-choice questions were designed based upon those common student difficulties. After the development and validation of the survey, it was administered to introductory physics students in various classes in paper-pencil format before and after traditional lecture-based instruction in relevant concepts. We compared the performance of students on the survey in the algebra-based and calculus-based introductory physics courses before and after traditional lecture-based instruction in relevant magnetism concepts. We discuss the common difficulties of introductory physics students with magnetism concepts we found via the survey. We also administered the survey to upper-level undergraduates majoring in physics and PhD students to benchmark the survey and compared their performance with those of traditionally taught introductory physics students for whom the survey is intended. A comparison with the base line data on the validated magnetism survey from traditionally taught introductory physics courses and upper-level undergraduate and PhD students discussed in this paper can help instructors assess the effectiveness of curricula and pedagogies which is especially designed to help students integrate conceptual and quantitative understanding and develop a good grasp of the concepts. In particular, if introductory physics students’ average performance in a class is significantly better than those of students in traditionally taught courses described here (and particularly when it is comparable to that of physics PhD students’ average performance discussed here), the curriculum or pedagogy used in that introductory class can be deemed effective. Moreover, we discuss the use of the survey to investigate gender differences in student performance.

Principles of Stagewise Separation Process Calculations: A Simple Algebraic Approach Using Solvent Extraction.

ERIC Educational Resources Information Center

Crittenden, Barry D.

1991-01-01

A simple liquid-liquid equilibrium (LLE) system involving a constant partition coefficient based on solute ratios is used to develop an algebraic understanding of multistage contacting in a first-year separation processes course. This algebraic approach to the LLE system is shown to be operable for the introduction of graphical techniques…

Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

ERIC Educational Resources Information Center

Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

2016-01-01

Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

Making Sense of Abstract Algebra: Exploring Secondary Teachers' Understandings of Inverse Functions in Relation to Its Group Structure

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2017-01-01

This article draws on semi-structured, task-based interviews to explore secondary teachers' (N = 7) understandings of inverse functions in relation to abstract algebra. In particular, a concept map task is used to understand the degree to which participants, having recently taken an abstract algebra course, situated inverse functions within its…

Advanced Mathematics Online: Assessing Particularities in the Online Delivery of a Second Linear Algebra Course

ERIC Educational Resources Information Center

Montiel, Mariana; Bhatti, Uzma

2010-01-01

This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…

Paper 3: Content and Rigor of Algebra Credit Recovery Courses

ERIC Educational Resources Information Center

Walters, Kirk; Stachel, Suzanne

2014-01-01

This paper describes the content, organization and rigor of the f2f and online summer algebra courses that were delivered in summers 2011 and 2012. Examining the content of both types of courses is important because research suggests that algebra courses with certain features may be better than others in promoting success for struggling students.…

Algebra 1r, Mathematics (Experimental): 5215.13.

ERIC Educational Resources Information Center

Strachan, Florence

This third of six guidebooks on minimum course content for first-year algebra includes work with laws of exponents; multiplication, division, and factoring of polynomials; and fundamental operations with rational algebraic expressions. Course goals are stated, performance objectives listed, a course outline provided, testbook references specified…

Oleanna Math Program Materials.

ERIC Educational Resources Information Center

Coole, Walter A.

This document is a collection of course outlines, syllabi, and test materials designed for several high school level and lower division mathematics courses taught in an auto-tutorial learning laboratory at Skagit Valley College (Washington). The courses included are: Pre-Algebra, Basic Algebra, Plan Geometry, Intermediate Algebra, Probability and…

The Progression of Podcasting/Vodcasting in a Technical Physics Class

NASA Astrophysics Data System (ADS)

Glanville, Y. J.

2010-11-01

Technology such as Microsoft PowerPoint presentations, clickers, podcasting, and learning management suites is becoming prevalent in classrooms. Instructors are using these media in both large lecture hall settings and small classrooms with just a handful of students. Traditionally, each of these media is instructor driven. For instance, podcasting (audio recordings) provided my technical physics course with supplemental notes to accompany a traditional algebra-based physics lecture. Podcasting is an ideal tool for this mode of instruction, but podcasting/vodcasting is also an ideal technique for student projects and student-driven learning. I present here the various podcasting/vodcasting projects my students and I have undertaken over the last few years.

Deformation Theory and Physics Model Building

NASA Astrophysics Data System (ADS)

Sternheimer, Daniel

2006-08-01

The mathematical theory of deformations has proved to be a powerful tool in modeling physical reality. We start with a short historical and philosophical review of the context and concentrate this rapid presentation on a few interrelated directions where deformation theory is essential in bringing a new framework - which has then to be developed using adapted tools, some of which come from the deformation aspect. Minkowskian space-time can be deformed into Anti de Sitter, where massless particles become composite (also dynamically): this opens new perspectives in particle physics, at least at the electroweak level, including prediction of new mesons. Nonlinear group representations and covariant field equations, coming from interactions, can be viewed as some deformation of their linear (free) part: recognizing this fact can provide a good framework for treating problems in this area, in particular global solutions. Last but not least, (algebras associated with) classical mechanics (and field theory) on a Poisson phase space can be deformed to (algebras associated with) quantum mechanics (and quantum field theory). That is now a frontier domain in mathematics and theoretical physics called deformation quantization, with multiple ramifications, avatars and connections in both mathematics and physics. These include representation theory, quantum groups (when considering Hopf algebras instead of associative or Lie algebras), noncommutative geometry and manifolds, algebraic geometry, number theory, and of course what is regrouped under the name of M-theory. We shall here look at these from the unifying point of view of deformation theory and refer to a limited number of papers as a starting point for further study.

The Impact of an Elementary Algebra Course on Success in a College-Level Liberal Arts Math Course and Persistence in College

ERIC Educational Resources Information Center

Austin, Lori Ann

2017-01-01

Many students enter community college underprepared for college-level math and are placed into developmental elementary algebra without consideration if the algebra will provide a foundation for their needed college-level math course. Large percentages of those students are unable to succeed in the developmental course and, therefore, are unable…

Comparing the Impact of Traditional and Modeling College Algebra Courses on Student Performance in Survey of Calculus

ERIC Educational Resources Information Center

West, Jerry G.

2013-01-01

Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…

Math 3013--Developmental Mathematics I and II. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course that requires some previous knowledge of algebra and the ability to work at a rapid pace. Topics include the basic operations with signed integers; fractions; decimals; literal expressions; algebraic fractions; radicals;…

Motivating students to read the textbook before class

NASA Astrophysics Data System (ADS)

Pepper, Rachel E.

2016-11-01

Many faculty in STEM courses assign textbook reading in advance of lecture, yet evidence shows few students actually read the textbook. Those students that do read often do so only after the material has been presented in class. Preparing for class by reading the textbook beforehand improves student learning and is particularly critical for classes that employ active engagement strategies. Here I present strategies I have used to successfully motivate my students to read the textbook before class in physics classes ranging from introductory algebra-based physics to advanced courses for physics majors. In the introductory course, I used pre-class reading quizzes, a common strategy that has been shown effective in previous studies, but one that is somewhat time-consuming to implement. In my more advanced courses I used reading reflections, which required considerably less time. While it was typical for less than 25% of students to read the textbook before I implemented reading quizzes or reflections, after implementing these strategies 70-90% of students reported reading the textbook before class most of the time. Students also report finding both the readings themselves and the quizzes and reflections valuable for their learning.

Internet-Based Laboratory Immersion: When The Real Deal is Not Available

NASA Astrophysics Data System (ADS)

Meisner, Gerald; Hoffman, Harol

2004-11-01

Do you want all of your students to investigate equilibrium conditions in the physics lab, but don't have time for lab investigations? Do your under-prepared students need basic, careful and detailed remedial work to help them succeed? LAAPhysics provides an answer to these questions by means of robust online physics courseware based on: (1) a sound, research-based pedagogy (2) a rich laboratory environment with skills and operational knowledge transferable to the wet lab' and (3) a paradigm which is economically scalable. LAAPhysics provides both synchronous and asynchronous learning experiences for an introductory, algebra-based course for students (undergraduate, AP High School, seekers of a second degree), those seeking career changes, and pre-service and in-service teachers. We have developed a simulated physics laboratory comprised of virtual lab equipment and instruments, associated curriculum modules and virtual guidance for real time feedback, formative assessment and collaborative learning.

Curbing "Math Anxiety" with Galileo While Teaching Physicists, too

NASA Astrophysics Data System (ADS)

Schwartz, Brian P.

2006-12-01

Carthage College's introductory physics course caters to both freshmen in our program and students in general education. While "Understandings of Physics" is a conceptual overview of our discipline, physical science is necessarily quantitative. Galileo's "Dialogue Concerning the Two New Sciences" provides us with a novel way to teach the fundamentals of motion both to students who "fear" mathematics, as well as those who are adept at solving algebraic equations.

Activities for Students: Biology as a Source for Algebra Equations--The Heart

ERIC Educational Resources Information Center

Horak, Virginia M.

2005-01-01

The high school course that integrated first year algebra with an introductory environmental biology/anatomy and physiology course, in order to solve algebra problems is discussed. Lessons and activities for the course were taken by identifying the areas where mathematics and biology content intervenes may help students understand biology concepts…

Two-year colleges, Physics, and Teacher Preparation

NASA Astrophysics Data System (ADS)

Clay, Keith

2002-05-01

In the midst of a teacher shortage no field suffers more than physics. Half of our secondary physics teachers have less than a minor in physics. Meanwhile half of our future teachers start out at two-year colleges with physicists on staff. The opportunity for community colleges to have an impact on K-12 teaching is tremendous. Project TEACH has been honored as an outstanding teacher preparation program. It is a collaboration of colleges and K-12 schools dedicated to the improvement of teacher preparation, especially in science and math. Based at Green River Community College, Project TEACH unites certification institutions, community colleges, and K-12 school districts in the pre-service and in-service training of teachers. Activities of Project TEACH include recruitment and advising of future teachers, field experience for education students, creation of pre-teaching and para-educator degrees, tutoring from elementary school through college, in-service courses for current teachers, and special math and science courses aimed at future teachers. The yearlong interdisciplinary science sequence blends chemistry, physics, geology, and biology in a hands-on inquiry-based environment. The yearlong math sequence covers arithmetic, algebra, geometry, and probability with inquiry-based pedagogy. The programs developed by Project TEACH are being disseminated to colleges across Washington State and beyond.

Subsequent Success in a Mathematics Course by Students Who Received a Grade in Intermediate Algebra (Math 253) for the Fall, 2002 Semester at Saddleback College

ERIC Educational Resources Information Center

Sworder, Steve

2006-01-01

The purpose of this study was to determine the effectiveness of a typical California community college Intermediate Algebra course in preparing students for success in the transfer level mathematics courses for which Intermediate Algebra was the prerequisite. The subsequent mathematics course taken by each of the 986 students who received a grade…

Development and Assessment of a Preliminary Randomization-Based Introductory Statistics Curriculum

ERIC Educational Resources Information Center

Tintle, Nathan; VanderStoep, Jill; Holmes, Vicki-Lynn; Quisenberry, Brooke; Swanson, Todd

2011-01-01

The algebra-based introductory statistics course is the most popular undergraduate course in statistics. While there is a general consensus for the content of the curriculum, the recent Guidelines for Assessment and Instruction in Statistics Education (GAISE) have challenged the pedagogy of this course. Additionally, some arguments have been made…

Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

ERIC Educational Resources Information Center

Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

2016-01-01

The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…

Kids crash and burn: An analysis of freshmen failing science end of course exams

NASA Astrophysics Data System (ADS)

Godfrey, Tanya N.

The purpose of this study was to determine how various factors influence student achievement on the physical science EOCE so that students are provided every opportunity to be successful. An understanding of influences such as the type of mathematics course students are taking, participating in block scheduling, participating in freshmen academies, and the year students took the science course and the science EOCE should provide insight into its relationship on the physical science EOCE achievement level. The final goal was to find which factors correlate to high achievement on the physical science EOCE so that South Carolina can implement these factors. This was done by obtaining historical data on students who took physical science and determine which factors are associated with the high failure rates on the physical science EOCE. Correlational values were determined, when possible. An independent-samples t-test was used to determine the strength and directionality for each relationship. A five-way ANOVA was used to determine if there were any interaction effects between the variables. The first finding was that students who took algebra prior to physical science had higher achievement on the EOCE than students without algebra. Students had increased EOCE scores when they took physical science in a block class. More students were successful outside of a freshmen academy on the physical science EOCE. These results are important to educators and administrators that want to help students become more successful on the physical science EOCE. The findings of this study can lead to a positive change within schools and school districts when it comes to providing an atmosphere that helps students increase their science skills and knowledge.

Learning to Apply Algebra in the Community for Adults with Intellectual Developmental Disabilities

ERIC Educational Resources Information Center

Rodriguez, Anthony M.

2016-01-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This…

The Linear Algebra Curriculum Study Group Recommendations for the First Course in Linear Algebra.

ERIC Educational Resources Information Center

Carlson, David; And Others

1993-01-01

Presents five recommendations of the Linear Algebra Curriculum Study Group: (1) The syllabus must respond to the client disciplines; (2) The first course should be matrix oriented; (3) Faculty should consider the needs and interests of students; (4) Faculty should use technology; and (5) At least one follow-up course should be required. Provides a…

Curricula Alignment and Its Impact on End of Course Assessment Scores

ERIC Educational Resources Information Center

Burti, Neil, Jr.

2011-01-01

The purpose of this mixed methods study was to examine the alignment of the written, enacted, and tested Algebra I curricula in the Cherry Hill (NJ) Public School District. Furthermore, this QUAN-QUAL study sought to determine the impact of course selection (Algebra I, Enriched Algebra) on achievement as measured by the Algebra I End of Course…

Linking Computer Algebra Systems and Paper-and-Pencil Techniques To Support the Teaching of Mathematics.

ERIC Educational Resources Information Center

van Herwaarden, Onno A.; Gielen, Joseph L. W.

2002-01-01

Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

Learning to Apply Algebra in the Community for Adults With Intellectual Developmental Disabilities.

PubMed

Rodriguez, Anthony M

2016-02-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This study explores the feasibility of algebra instruction for adults with IDD through an experimental curriculum. Ten individuals with IDD participated in a 6-week course framing mathematics concepts within the context of everyday challenges in handling money. The article explores classroom techniques, discusses student strategies, and proposes possible avenues for future research analyzing mathematics instructional design strategies for individuals with IDD.

The Great Debate: Should All 8th Graders Take Algebra?

ERIC Educational Resources Information Center

McKibben, Sarah

2009-01-01

While 8th grade algebra was once reserved as a course for the gifted, today, more U.S. 8th graders take algebra than any other math course. This article discusses a report from the Brookings Institution which chronicles the history of the 8th-grade algebra surge and its impact on today's low-performing students. The report indicates that many of…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 1. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the student text for part one of a three-part SMSG algebra course for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables; operations;…

Student Reactions to Learning Theory Based Curriculum Materials in Linear Algebra--A Survey Analysis

ERIC Educational Resources Information Center

Cooley, Laurel; Vidakovic, Draga; Martin, William O.; Dexter, Scott; Suzuki, Jeff

2016-01-01

In this report we examine students' perceptions of the implementation of carefully designed curriculum materials (called modules) in linear algebra courses at three different universities. The curricular materials were produced collaboratively by STEM and mathematics education faculty as members of a professional learning community (PLC) over…

Abstract Algebra for Teachers: An Evaluative Case Study

ERIC Educational Resources Information Center

Hoffman, Andrew Joseph

2017-01-01

This manuscript describes the study of an abstract algebra course for preservice secondary mathematics teachers (PSMTs). Often, courses in abstract algebra have not been viewed as productive, beneficial learning experiences for future teachers, both by researchers and PSMTs themselves. This despite calls for increased content knowledge for…

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…

Importance of Grades and Placement for Math Attainment

ERIC Educational Resources Information Center

Tyson, Will; Roksa, Josipa

2017-01-01

Research on high school math course taking documents the advantages of starting high school at or beyond Algebra 1. Fewer studies examine differentiation into remedial, general, and honors Algebra 1 course types by course rigor. This study examines how course grades and course rigor are associated with math attainment among students with similar…

Earth Algebra.

ERIC Educational Resources Information Center

Schaufele, Christopher; Zumoff, Nancy

Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…

Who Takes College Algebra?

ERIC Educational Resources Information Center

Herriott, Scott R.; Dunbar, Steven R.

2009-01-01

The common understanding within the mathematics community is that the role of the college algebra course is to prepare students for calculus. Though exceptions are emerging, the curriculum of most college algebra courses and the content of most textbooks on the market both reflect that assumption. This article calls that assumption into question…

Curriculum Guide for Baccalaureate Oriented Courses in Mathematics.

ERIC Educational Resources Information Center

Darnes, G. Robert, Ed.

A mathematics curriculum guide is presented for the purpose of offering statewide guidelines to colleges for determining the content of those courses which might be considered standard courses in the first two years of the college curriculum. Courses covered include: intermediate algebra, college algebra, trigonometry, analytic geometry,…

Math 3007--Developmental Mathematics I. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course designed to develop student proficiency in the basic algebraic skills. This course is designed as the first of a two-semester sequence. Topics include operations with signed numbers; simple operations on monomials and…

Total Quality Management in the Classroom: Applications to University-Level Mathematics.

ERIC Educational Resources Information Center

Williams, Frank

1995-01-01

Describes a Total Quality Management-based system of instruction that is used in a variety of undergraduate mathematics courses. The courses that incorporate this approach include mathematics appreciation, introductory calculus, and advanced applied linear algebra. (DDR)

A collaborative learning approach for service-oriented introductory physics

NASA Astrophysics Data System (ADS)

Smith, Michael R.

1997-03-01

I have taught algebra-based introductory physics for six years to liberal arts students. It was primarily a service course for students majoring in Athletic Training, Physical Therapy, Geology, Biology, and Pre-Med. The typical student was characterized by having a minimal math and problem-solving proficiency. There also was a pattern of students being predisposed to memorizing facts and formulas, and attempting to solve problems by finding the correct formula and "plugging in" numbers to get an answer. The students seemed to have a minimal ability in deductive reasoning and problem solving, starting from basic principles. It is no wonder that they entered the introductory physics service course with extreme trepidation, based upon a strongly perceived physics phobia. A standard lecture format was used for the class size of approximately 25-30 students; and an attempt was always made to engage the students through the Socratic approach, by asking leading questions during the course of the lecture. The students were relatively unprepared and couldn't participate in the class, and often responded antagonistically. They indicated they didn't want to be asked to think about an issue, but would rather just be told the facts so they could take specific notes for subsequent memorization. It was clear from the results of the open book exams given during the semester that the majority of students could not approach problem solving using deductive reasoning based on basic principles, but relied on attempting to force-fit the problem into a worked example in the text (often out of context, with illogical results). The absentee rate in the classroom was usually around 30-40%. The academic administration of my liberal arts university has the policy of formal course evaluations by the students at the end of each semester. The evaluation questionnaire appears to be primarily a measurement of the stress level of the student during the course, and the evaluation score I received for the service physics course was typically on the order of 3 out of a possible 5; a score considered unsatisfactory by the administration.

The Effect of Using Concept Maps in Elementary Linear Algebra Course on Students’ Learning

NASA Astrophysics Data System (ADS)

Syarifuddin, H.

2018-04-01

This paper presents the results of a classroom action research that was done in Elementary Linear Algebra course at Universitas Negeri Padang. The focus of the research want to see the effect of using concept maps in the course on students’ learning. Data in this study were collected through classroom observation, students’ reflective journal and concept maps that were created by students. The result of the study was the using of concept maps in Elementary Linera Algebra course gave positive effect on students’ learning.

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

PubMed Central

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.

PubMed

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.

The effects of experience and attrition for novice high-school science and mathematics teachers.

PubMed

Henry, Gary T; Fortner, C Kevin; Bastian, Kevin C

2012-03-02

Because of the current high proportion of novice high-school teachers, many students' mastery of science and mathematics depends on the effectiveness of early-career teachers. In this study, which used value-added models to analyze high-school teachers' effectiveness in raising test scores on 1.05 million end-of-course exams, we found that the effectiveness of high-school science and mathematics teachers increased substantially with experience but exhibited diminishing rates of return by their fourth year; that teachers of algebra 1, algebra 2, biology, and physical science who continued to teach for at least 5 years were more effective as novice teachers than those who left the profession earlier; and that novice teachers of physics, chemistry, physical science, geometry, and biology exhibited steeper growth in effectiveness than did novice non-science, technology, engineering, and mathematics teachers.

Teaching Mathematics in the PC Lab--The Students' Viewpoints

ERIC Educational Resources Information Center

Schmidt, Karsten; Kohler, Anke

2013-01-01

The Matrix Algebra portion of the intermediate mathematics course at the Schmalkalden University Faculty of Business and Economics has been moved from a traditional classroom setting to a technology-based setting in the PC lab. A Computer Algebra System license was acquired that also allows its use on the students' own PCs. A survey was carried…

Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course

ERIC Educational Resources Information Center

Cook, John Paul

2015-01-01

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

Experiences in Evaluating Outcomes in Tool-Based, Competence Building Education in Dynamical Systems Using Symbolic Computer Algebra

ERIC Educational Resources Information Center

Perram, John W.; Andersen, Morten; Ellekilde, Lars-Peter; Hjorth, Poul G.

2004-01-01

This paper discusses experience with alternative assessment strategies for an introductory course in dynamical systems, where the use of computer algebra and calculus is fully integrated into the learning process, so that the standard written examination would not be appropriate. Instead, students' competence was assessed by grading three large…

Developing Conceptual Understanding and Definitional Clarity in Linear Algebra through the Three Worlds of Mathematical Thinking

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Michael

2016-01-01

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

Linear Algebra and the Experiences of a "Flipper"

ERIC Educational Resources Information Center

Wright, Sarah E.

2015-01-01

This paper describes the linear algebra class I taught during Spring 2014 semester at Adelphi University. I discuss the details of how I flipped the class and incorporated elements of inquiry-based learning as well as the reasoning behind specific decisions I made. I give feedback from the students on the success of the course and provide my own…

An investigation of student thinking regarding calorimetry, entropy, and the second law of thermodynamics

NASA Astrophysics Data System (ADS)

Christensen, Warren Michael

This thesis constitutes an investigation into student understanding of concepts in thermal physics in an introductory calculus-based university physics course. Nearly 90% of students enrolled in the course had previous exposure to thermodynamics concepts in chemistry and/or high-school physics courses. The two major thrusts of this work are (1) an exploration of student approaches to solving calorimetry problems involving two substances with differing specific heats, and (2) a careful probing of student ideas regarding certain aspects of entropy and the second law of thermodynamics. We present extensive free-response, interview, and multiple-choice data regarding students' ideas, collected both before and after instruction from a diverse set of course semesters and instructors. For topics in calorimetry, we found via interviews that students frequently get confused by, or tend to overlook, the detailed proportional reasoning or algebraic procedures that could lead to correct solutions. Instead, students often proceed with semi-intuitive reasoning that at times may be productive, but more often leads to inconsistencies and non-uniform conceptual understanding. Our investigation of student thinking regarding entropy suggests that prior to instruction, students have consistent and distinct patterns of incorrect or incomplete responses that often persist despite deliberate and focused efforts by the instructor. With modified instruction based on research-based materials, significant learning gains were observed on certain key concepts, e.g., that the entropy of the universe increases for all non-ideal processes. The methodology for our work is described, the data are discussed and analyzed, and a description is given of goals for future work in this area.

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…

Commentary on A General Curriculum in Mathematics for Colleges.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

This document constitutes a complete revision of the report of the same name first published in 1965. A new list of basic courses is described, consisting of Calculus I, Calculus II, Elementary Linear Algebra, Multivariable Calculus I, Linear Algebra, and Introductory Modern Algebra. Commentaries outline the content and spirit of these courses in…

Quantum Physics

NASA Astrophysics Data System (ADS)

Le Bellac, Michel

2006-03-01

Quantum physics allows us to understand the nature of the physical phenomena which govern the behavior of solids, semi-conductors, lasers, atoms, nuclei, subnuclear particles and light. In Quantum Physics, Le Bellac provides a thoroughly modern approach to this fundamental theory. Throughout the book, Le Bellac teaches the fundamentals of quantum physics using an original approach which relies primarily on an algebraic treatment and on the systematic use of symmetry principles. In addition to the standard topics such as one-dimensional potentials, angular momentum and scattering theory, the reader is introduced to more recent developments at an early stage. These include a detailed account of entangled states and their applications, the optical Bloch equations, the theory of laser cooling and of magneto-optical traps, vacuum Rabi oscillations, and an introduction to open quantum systems. This is a textbook for a modern course on quantum physics, written for advanced undergraduate and graduate students. Completely original and contemporary approach, using algebra and symmetry principles Introduces recent developments at an early stage, including many topics that cannot be found in standard textbooks. Contains 130 physically relevant exercises

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…

Examining students' views about validity of experiments: From introductory to Ph.D. students

NASA Astrophysics Data System (ADS)

Hu, Dehui; Zwickl, Benjamin M.

2018-06-01

We investigated physics students' epistemological views on measurements and validity of experimental results. The roles of experiments in physics have been underemphasized in previous research on students' personal epistemology, and there is a need for a broader view of personal epistemology that incorporates experiments. An epistemological framework incorporating the structure, methodology, and validity of scientific knowledge guided the development of an open-ended survey. The survey was administered to students in algebra-based and calculus-based introductory physics courses, upper-division physics labs, and physics Ph.D. students. Within our sample, we identified several differences in students' ideas about validity and uncertainty in measurement. The majority of introductory students justified the validity of results through agreement with theory or with results from others. Alternatively, Ph.D. students frequently justified the validity of results based on the quality of the experimental process and repeatability of results. When asked about the role of uncertainty analysis, introductory students tended to focus on the representational roles (e.g., describing imperfections, data variability, and human mistakes). However, advanced students focused on the inferential roles of uncertainty analysis (e.g., quantifying reliability, making comparisons, and guiding refinements). The findings suggest that lab courses could emphasize a variety of approaches to establish validity, such as by valuing documentation of the experimental process when evaluating the quality of student work. In order to emphasize the role of uncertainty in an authentic way, labs could provide opportunities to iterate, make repeated comparisons, and make decisions based on those comparisons.

A Fresh Look at Longitudinal Standing Waves on a Spring

NASA Astrophysics Data System (ADS)

Rutherford, Casey

2013-01-01

Transverse standing waves produced on a string, as shown in Fig. 1, are a common demonstration of standing wave patterns that have nodes at both ends. Longitudinal standing waves can be produced on a helical spring that is mounted vertically and attached to a speaker, as shown in Fig. 2, and used to produce both node-node (NN) and node-antinode (NA) standing waves. The resonant frequencies of the two standing wave patterns are related with theory that is accessible to students in algebra-based introductory physics courses, and actual measurements show good agreement with theoretical predictions.

An Analysis of Higher-Order Thinking on Algebra I End-of-Course Tests

ERIC Educational Resources Information Center

Thompson, Tony

2011-01-01

This research provides insight into one US state's effort to incorporate higher-order thinking on its Algebra I End-of-Course tests. To facilitate the inclusion of higher-order thinking, the state used "Dimensions of Thinking" (Marzano et al., 1988) and "Bloom's Taxonomy" (Bloom et al., 1956). An analysis of Algebra I test…

Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

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)

An Appropriate Culminating Mathematics Course.

ERIC Educational Resources Information Center

Haver, Bill; Turbeville, Gwen

1995-01-01

Describes a freshman level mathematics course designed as an alternate to algebra for non-science majors. Mathematical content is based on real-world situations, student activities include small and large projects done in groups or individually, and lecture time is held to a minimum. (MKR)

Examining gender differences on FCI performance in algebra and calculus based physics courses

NASA Astrophysics Data System (ADS)

Kreutzer, Kimberley; Boudreaux, Andrew

2009-05-01

The Force Concept Inventory (FCI) has been widely used to asses student understanding of Newtonian principles. Studies have shown a marked difference in the performance of men and women on both pre- and post-tests [1,2] and also indicate that experiential based instruction may lead to a reduction in this gender gap [1,3]. This poster presents FCI data collected at Western Washington University. Initial analysis of gender differences are consistent with those reported nationally. We also discuss factors that may contribute to the differences in performance and propose instructional strategies that are designed to address the gender gap. [4pt] [1] M. Lorenzo, et. al., ``Reducing the gender gap in the physics classroom,'' AJP 74(2), 118-122 (2006) [0pt] [2] J. Docktor and K. Heller, ``Gender Differences in Both Force Concept Inventory and Introductory Physics Performance,'' Proceedings at the 2008 PERC [0pt] [3] S. Pollack, et. al., ``Reducing the gender gap in the physics classroom: How sufficient is interactive engagement?'' PRST-PER 3 (2007)

Is classical mechanics a prerequisite for learning physics of the 20th century?

NASA Astrophysics Data System (ADS)

Walwema, Godfrey B.; French, Debbie A.; Verley, Jim D.; Burrows, Andrea C.

2016-11-01

Physics of the 20th century has contributed significantly to modern technology, and yet many physics students are never availed the opportunity to study it as part of the curriculum. One of the possible reasons why it is not taught in high school and introductory physics courses could be because curriculum designers believe that students need a solid background in classical mechanics and calculus in order to study physics of the 20th century such as the photoelectric effect, special and general relativity, the uncertainty principle, etc. This presumption may not be justifiable or valid. The authors of this paper contend that teaching physics of the 20th century aids students in relating physics to modern technology and the real world, making studying physics exciting. In this study, the authors correlated scores for matched questions in the Mechanics Baseline Test and a physics of the 20th century test in order to examine the trend of the scores. The participants included undergraduate students attending an introductory algebra-based physics course with no intention of taking physics at a higher level. The analysis of the scores showed no significant correlation for any of the matched pairs of questions. The purpose of this article is to recommend that even without a solid background in classical mechanics, teachers can introduce physics of the 20th century to their students for increased interest.

Increasing Student Success in Large Survey Science Courses via Supplemental Instruction in Learning Centers

NASA Astrophysics Data System (ADS)

Hooper, Eric Jon; Nossal, S.; Watson, L.; Timbie, P.

2010-05-01

Large introductory astronomy and physics survey courses can be very challenging and stressful. The University of Wisconsin-Madison Physics Learning Center (PLC) reaches about 10 percent of the students in four introductory physics courses, algebra and calculus based versions of both classical mechanics and electromagnetism. Participants include those potentially most vulnerable to experiencing isolation and hence to having difficulty finding study partners as well as students struggling with the course. They receive specially written tutorials, conceptual summaries, and practice problems; exam reviews; and most importantly, membership in small groups of 3 - 8 students which meet twice per week in a hybrid of traditional teaching and tutoring. Almost all students who regularly participate in the PLC earn at least a "C,” with many earning higher grades. The PLC works closely with other campus programs which seek to increase the participation and enhance the success of underrepresented minorities, first generation college students, and students from lower-income circumstances; and it is well received by students, departmental faculty, and University administration. The PLC staff includes physics education specialists and research scientists with a passion for education. However, the bulk of the teaching is conducted by undergraduates who are majoring in physics, astronomy, mathematics, engineering, and secondary science teaching (many have multiple majors). The staff train these enthusiastic students, denoted Peer Mentor Tutors (PMTs) in general pedagogy and mentoring strategies, as well as the specifics of teaching the physics covered in the course. The PMTs are among the best undergraduates at the university. While currently there is no UW-Madison learning center for astronomy courses, establishing one is a possible future direction. The introductory astronomy courses cater to non-science majors and consequently are less quantitative. However, the basic structure of small groups focusing on fundamental understanding taught mostly by dedicated undergraduates should transfer well.

Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

NASA Astrophysics Data System (ADS)

Nazarov, Anton

2012-11-01

In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent algorithm based on generalization of Weyl character formula. We also offer alternative implementation based on the Freudenthal multiplicity formula which can be faster in some cases. Restrictions: Computational complexity grows fast with the rank of an algebra, so computations for algebras of ranks greater than 8 are not practical. Unusual features: We offer the possibility of using a traditional mathematical notation for the objects in representation theory of Lie algebras in computations if Affine.m is used in the Mathematica notebook interface. Running time: From seconds to days depending on the rank of the algebra and the complexity of the representation.

A Concurrent Support Course for Intermediate Algebra

ERIC Educational Resources Information Center

Cooper, Cameron I.

2011-01-01

This article summarizes the creation and implementation of a concurrent support class for TRS 92--Intermediate Algebra, a developmental mathematics course at Fort Lewis College in Durango, Colorado. The concurrent course outlined in this article demonstrates a statistically significant increase in student success rates since its inception.…

Alternative Delivery Systems for Introductory Algebra.

ERIC Educational Resources Information Center

Keating, John; And Others

Since 1988, Massachusetts' Massasoit Community College has offered two alternative introductory algebra courses for students receiving low scores on mathematics admission tests. One alternative course provides 5 hours of instruction per week, rather than the 3 hours per week in the traditional course, while the other segments the traditional…

The Physics Learning Center at the University of Wisconsin-Madison

NASA Astrophysics Data System (ADS)

Nossal, S. M.; Watson, L. E.; Hooper, E.; Huesmann, A.; Schenker, B.; Timbie, P.; Rzchowski, M.

2013-03-01

The Physics Learning Center at the University of Wisconsin-Madison provides academic support and small-group supplemental instruction to students studying introductory algebra-based and calculus-based physics. These classes are gateway courses for majors in the biological and physical sciences, pre-health fields, engineering, and secondary science education. The Physics Learning Center offers supplemental instruction groups twice weekly where students can discuss concepts and practice with problem-solving techniques. The Center also provides students with access on-line resources that stress conceptual understanding, and to exam review sessions. Participants in our program include returning adults, people from historically underrepresented racial/ethnic groups, students from families in lower-income circumstances, students in the first generation of their family to attend college, transfer students, veterans, and people with disabilities, all of whom might feel isolated in their large introductory course and thus have a more difficult time finding study partners. We also work with students potentially at-risk for having academic difficulty (due to factors academic probation, weak math background, low first exam score, or no high school physics). A second mission of the Physics Learning Center is to provide teacher training and leadership experience for undergraduate Peer Mentor Tutors. These Peer Tutors lead the majority of the weekly group sessions in close supervision by PLC staff members. We will describe our work to support students in the Physics Learning Center, including our teacher-training program for our undergraduate Peer Mentor Tutors

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.…

Assessment of student knowledge of the weak and strong nuclear forces

NASA Astrophysics Data System (ADS)

Shakya, Pramila

The purpose of this study was to determine if the use of active-learning activities to teach weak force and strong force to students enrolled in various courses at The University of Southern Mississippi, Hattiesburg campus and Gulf Park campus at different class times would increase their knowledge. There were eighty-six students that took part in this study. The study was conducted in the lab classes of an introductory astronomy survey course (AST 111), an introductory algebra-based physics course (PHY 112), and an introductory calculus-based physics course (PHY 202) during fall semester, 2014. Each class was randomly assigned as active-learning or direct instruction. A pretest followed by lecture was administered to all groups. The active-learning group performed four activities whereas the direct group watched a video irrelevant to the lesson. At the end of the lesson, the same post-test was given to all groups. Various statistical methods were used to analyze the differences in mean pretest and posttest scores. Overall, results show that the mean posttest scores were higher than the mean pretest scores. Findings support the use of active-learning activities work to the small number of students or the equal number of students in a group. The mean posttest scores of the direct instruction classes were higher than those of the active-learning groups.

Mobile Learning: Integrating Text Messaging into a Community College Pre-Algebra Course

ERIC Educational Resources Information Center

Bull, Prince; McCormick, Carlos

2012-01-01

This study investigated the use of text messaging as an educational tool in a pre-algebra course at a community college in the central region of North Carolina. The research was conducted in two pre-algebra classes with thirty-three students and one instructor. Data were gathered using qualitative and quantitative methods. A mixed method design…

Flipping College Algebra: Effects on Student Engagement and Achievement

ERIC Educational Resources Information Center

Ichinose, Cherie; Clinkenbeard, Jennifer

2016-01-01

This study compared student engagement and achievement levels between students enrolled in a traditional college algebra lecture course and students enrolled in a "flipped" course. Results showed that students in the flipped class had consistently higher levels of achievement throughout the course than did students in the traditional…

Math 3008--Developmental Mathematics II. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for an introductory college algebra course designed to develop student proficiency in the basic algebraic skills. This is designed as the second of a two-semester sequence. Topics include performing operations with radicals and exponents; learning to solve equations;…

Algebra 2u, Mathematics (Experimental): 5216.26.

ERIC Educational Resources Information Center

Crawford, Glenda

The sixth in a series of six guidebooks on minimum course content for second-year algebra, this booklet presents an introduction to sequences, series, permutation, combinations, and probability. Included are arithmetic and geometric progressions and problems solved by counting and factorials. Overall course goals are specified, a course outline is…

Conceptual physics differences by pedagogy and gender: Questioning the deficit model

NASA Astrophysics Data System (ADS)

Majors, Twanelle Deann Walker

The differences in physics performance between males and females have been studied extensively (Blue & Heller, 2003; Coletta, 2015; Madsen, McKagan, & Sayre 2013; McCullough, 2002, 2004, 2011; Pollock, Finkelstein, & Kost, 2007; Zohar & Sela, 2003). The purpose of this study was to look at the ways teaching methods and assessment choices have fabricated a gender gap. Deficit ways of thinking have further marginalized women by renegotiating prior acts of power that initiated and perpetuated marginalization. Outside of the deficit model, the blame for the underperformance of females has been attributed to discourses of power as well as less-than-critical ways of evaluating learning and schooling. Students in introductory algebra-based physics courses from 2008-2014 at Tennessee Technological University were self-enrolled in PHYS2010 sections that were taught using either a traditional or constructivist, interactive-engagement Learner-centered Environment for Algebra-based Physics (LEAP) pedagogy. Propensity scoring on all feasible and relevant independent variables was used to adjust for the probability of students choosing either LEAP or traditional sections. The Force Concept Inventory (FCI) and Gender Force Concept Inventory (GFCI) were used as the measures to gauge students' performance on physics concepts. The results showed that there were no differences in the FCI or GFCI performance of males and females. Results also showed that when accounting for pretest performance and the likelihood of choosing a LEAP section, LEAP pedagogy accounted for roughly 30% of performance differences. Not only was this true on the average, it was true for both genders. This meant that the main effect of LEAP pedagogy was even stronger and more generalizable. Gender did not moderate pedagogy, indicating that a pedagogy gap focus was more appropriate for evaluating physics learners.

PREFACE: Workshop on Higher Symmetries in Physics

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, Rutwig; María Ancochea, José; Castrillón, Marco

2009-07-01

This volume of Journal of Physics: Conference Series contains the Proceedings of the Workshop on Higher Symmetries in Physics (WHSP), held at the Universidad Complutense of Madrid (UCM) on 6-8 November 2008. This meeting constituted one of the activities of the research group GEODISIM-920920 of the Universidad Complutense, through the research project CCG07/ESP-2922 of the UCM/CAM for the academic year 2008/2009. The objective of this meeting was to provide a forum to facilitate the opportunity for interaction between specialists working in different fields of physics and mathematics, but who share a common interest in group theoretical, geometrical and symmetry methods applied to physical phenomena. This goal was achieved by means of lectures and technical presentations on different subjects, the only constraint being the current academic interest. The multidisciplinary character of the meeting allowed an effective exchange of ideas between different topics having a symmetry background, like higher order and n-Lie algebras and their cohomology theories, supergravity backgrounds, the geometric approach to the Quantum Hall effect, integrable and superintegrable systems, loop quantum gravity, master symmetries, constants of motion, Gowdy cosmological models, new methods for the Kronecker product decomposition of multiplets, the internal labelling problem or recent developments concerning Grand Unified Theories. The workshop consisted of three microcourses of three hours each and some plenary talks of one hour, as well as a small number of short communications. The Proceedings have been divided into two main sections, according to the structure of the meeting. The first one corresponds to the papers of the courses, which in addition to the material presented in the lectures also contain new and original results. The second part is devoted to the papers of the plenary talks and the remaining contributions. In some cases, the corresponding contributions are completely original, and expand or complement the topic presented at the workshop. Unfortunately, some of the speakers were not able to submit their contributions in time, for which reason they do not appear in these Proceedings. In addition to the contributions of the participants, other specialists in the field that could not attend the meeting, as well as some members of the scientific committee, were also invited by the Editors to submit their papers for this volume. The main motivation for the three courses was to provide a short and updated introduction to to current research topics, as well as to provide an overview for the non-specialists. We briefly describe the principal results of these lectures. The first course, given by Professor J A de Azcárraga (IFIC and University of Valencia) dealt with generalized Lie algebras and Filippov algebras. These structures, which enlarge naturally the notion of ordinary Lie algebras, have been shown to be of interest for the description of various physical phenomena, like the low energy dynamics of coincident M2-branes. The lecture presented an exhaustive review of the mathematical apparatus of these generalized structures, and recent developments on their cohomological properties were announced. The paper underlying these lectures expands the material covered during the course, and new results concerning the non-existence of central extensions and the cohomological rigidity of Filippov algebras are obtained. Professor J M Figueroa-O'Farrill (Maxwell Institute, University of Edinburgh) presented recent results concerning the homogeneity conjecture for supergravity backgrounds. The procedure to associate a Lie (super)algebra to a spin manifold with additional geometrical constraints was explained, and the most important examples of supersymmetric supergravity backgrounds commented. The lecture focused on two main results: on one hand, the recovery of the compact forms of the simple algebras B4, F4 and E8 by means of geometrical techniques, and the construction of the Killing superalgebra of 11-dimensional supergravity backgrounds. Criteria ensuring local homogeneity were described in terms of supersymmetry. Finally, the course of Professor M Rausch de Traubenberg (IPHC, Université de Strasbourg) reviewed the present status of higher order extensions of the Poincaré algebra. In this lecture, basing on some features of the Wess-Zumino model, additional algebraic structures are added in order to obtain a hierarchy of non-trivial extensions of the Poincaré algebra. Two different types, with interesting applications in the corresponding context, are presented. The first type corresponds to finite dimensional cubic extension in D-dimensional space-time. The latter induces a symmetry on generalized gauge fields, and the corresponding invariant Lagrangians are constructed explicitly. The remaining possibility is shown to be an infinite dimensional higher order extension inducing a symmetry that allows to connect relativistic anyons. This procedure presents some analogies with supersymmetry. All papers published in this volume of Journal of Physics: Conference Series contains have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing. This meeting was possible thanks to the financial and infrastructural assistance of the following Spanish institutions and projects: Universidad Complutense de Madrid (UCM) Instituto de Matemática Interdisciplinar (I.M.I.) of the UCM The Geometry, Mechanics and Control Network (GMC) CCG07/ESP-2922 of the UCM/Comunidad Autónoma de Madrid MTM2005-00173 of the Ministerio de Educación y Ciencia (MEC) MTM2006-09152 of the Ministerio de Educación y Ciencia (MEC) Consolider-Ingenio 2010 ''Programa de Investigación Intensiva sobre Mecánica Geométrica y Teoría de Control'' Finally, on behalf of the Organizing Committee, we would like to express our gratitude to the participants and assistants in the WHSP meeting for their presence and contributions, as well as to the members of the Scientific Committee for their help and outstanding efforts, with special mention to E Padrón from the Universidad de La Laguna and the GMC Network. R Campoamor-Stursberg, M Castrillón López and J M Ancochea Bermúdez Universidad Complutense de Madrid Editors of the WHSP Proceedings

STEPS at CSUN: Increasing Retention of Engineering and Physical Science Majors

NASA Astrophysics Data System (ADS)

Pedone, V. A.; Cadavid, A. C.; Horn, W.

2012-12-01

STEPS at CSUN seeks to increase the retention rate of first-time freshman in engineering, math, and physical science (STEM) majors from ~55% to 65%. About 40% of STEM first-time freshmen start in College Algebra because they do not take or do not pass the Mathematics Placement Test (MPT). This lengthens time to graduation, which contributes to dissatisfaction with major. STEPS at CSUN has made substantial changes to the administration of the MPT. Initial data show increases in the number of students who take the test and who place out of College Algebra, as well as increases in overall scores. STEPS at CSUN also funded the development of supplemental labs for Trigonometry and Calculus I and II, in partnership with similar labs created by the Math Department for College Algebra and Precalculus. These labs are open to all students, but are mandatory for at-risk students who have low scores on the MPT, low grades in the prerequisite course, or who failed the class the first time. Initial results are promising. Comparison of the grades of 46 Fall 2010 "at-risk" students without lab to those of 36 Fall 2011 students who enrolled in the supplementary lab show D-F grades decreased by 10% and A-B grades increased by 27%. A final retention strategy is aimed at students in the early stages of their majors. At CSUN the greatest loss of STEM majors occurs between sophomore-level and junior-level coursework because course difficulty increases and aspirations to potential careers weaken. The Summer Interdisciplinary Team Experience (SITE) is an intensive 3-week-long summer program that engages small teams of students from diverse STEM majors in faculty-mentored, team-based problem solving. This experience simulates professional work and creates strong bonds between students and between students and faculty mentors. The first two cohorts of students who have participated in SITE indicate that this experience has positively impacted their motivation to complete their STEM degree.

A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

NASA Astrophysics Data System (ADS)

Tuminaro, Jonathan

Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of mathematical use in the context physics, and (2) a detailed understanding, in terms of the proposed theoretical framework, of the errors that students make when using mathematics in the context of physics.

Expanding the FCI to Eevaluate Conceptual Mastery of Energy, Momentum, and Rotational Dynamics

NASA Astrophysics Data System (ADS)

Chediak, Alex; Hay, Katrina

2010-03-01

Normalized gain on the Force Concept Inventory (FCI) has deservedly become a widely accepted assessment tool to evaluate conceptual mastery in a high school, college, or university-level mechanics course. Left out of this assessment, however, are important physics concepts typically presented in the same course. Conservation of energy and momentum as well as rotational motion receive scant (if any) coverage on the FCI (or, for that matter, the Mechanics Baseline Test). Yet these concepts are foundational for popular majors such as mechanical engineering, where high failure rates are often a concern. A revised assessment tool is presented, one that incorporates the strengths of the FCI (and preserves the straightforward multiple choice format), but assesses these other mechanics-related concepts. Ten additional questions are included, inspired in part by material from the Physics Education Group at the University of Washington and in part by the authors' own experiences with common student misperceptions. The questions are given as pre- and post tests at the authors' institutions, California Baptist University and Pacific Lutheran University, in both calculus-based and algebra-based mechanics courses, exploring breadth of applicability for our findings. We present normalized gain data for the traditional thirty FCI questions and for our ten additional questions.

Some applications of mathematics in theoretical physics - A review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bora, Kalpana

2016-06-21

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical toolsmore » are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.« less

Some applications of mathematics in theoretical physics - A review

NASA Astrophysics Data System (ADS)

Bora, Kalpana

2016-06-01

Mathematics is a very beautiful subject-very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like-differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Transforming an Introductory Linear Algebra Course with a TI-92 Hand-Held Computer.

ERIC Educational Resources Information Center

Quesada, Antonio R.

2003-01-01

Describes how the introduction of the TI-92 transformed a traditional first semester linear algebra course into a matrix-oriented course that emphasized conceptual understanding, relevant applications, and numerical issues. Indicates an increase in students' overall performance as they found the calculator very useful, believed it helped them…

Impact of Maple(TM) on the design, instruction and performance in an undergraduate physics mathematical methods course

NASA Astrophysics Data System (ADS)

Runge, Alan Paul

1997-10-01

A traditional undergraduate physics course on mathematical methods has been redesigned to incorporate the use of Maplesp{sc {TM}}, a computer algebra program, during all aspects of the course. Topics covered were: complex number theory; series approximations; matrix theory; partial differentiation; vector algebra; and vector calculus. Five undergraduate students were enrolled, from sophomore to senior in academic class standing. A qualitative case study methodology was used to describe the changes in the course design resulting from the incorporation of Maplesp{sc {TM}} and their impact on the instruction of the course, and to determine the effects on the students' learning and development of problem solving skills in physics using Maplesp{sc {TM}} as a problem solving tool. The impact of using Maplesp{sc {TM}} on the number and types of interactions is presented. The entire semester long course was included in this study. Each class session is described in detail. Examples of the Maplesp{sc {TM}} materials used are given. The use of the Maplesp{sc {TM}} program was allowed on all homework and exams with each student having their own computer during class. Constraints were made so that the assessment emphasis remained on the mathematics and the conceptual understanding of the problem solving methods. All of the students demonstrated some level of proficiency in using Maplesp{TM} to solve the assigned problems. Strategies for effectively using Maplesp{TM} were presented and were individualized by the students. The students reported positive and negative impacts of using Maplesp{sc {TM}}. All of the students satisfactorily completed the course requirements, receiving final course grades from B to A+. All of them continued to voluntarily use Maplesp{sc {TM}} during the following semester. Instructional methods used included various lecture techniques without Maplesp{sc {TM}} assistance, lectures and demonstrations using only Maplesp{sc {TM}}, and student tasks assigned in class worked with the aid of Maplesp{sc {TM}}. Maplesp{sc {TM}} was used in one of these aspects in all but 3, out of 45, class periods. The use of Maplesp{sc {TM}} constituted about half of the overall class time.

Topics in elementary particle physics

NASA Astrophysics Data System (ADS)

Jin, Xiang

The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

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,…

Algebras Generated by Geometric Scalar Forms and their Applications in Physics and Social Sciences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Keller, Jaime

2008-09-17

The present paper analyzes the consequences of defining that the geometric scalar form is not necessarily quadratic, but in general K-atic, that is obtained from the K{sup th} power of the linear form, requiring {l_brace}e{sub i};i = 1,...,N;(e{sub i}){sup K} = 1{r_brace} and d-vector {sigma}{sub i}x{sub i}e{sub i}. We consider the algebras which are thus generated, for positive integer K, a generalization of the geometric algebras we know under the names of Clifford or Grassmann algebras. We then obtain a set of geometric K-algebras. We also consider the generalization of special functions of geometry which corresponds to the K-order scalarmore » forms (as trigonometric functions and other related geometric functions which are based on the use of quadratic forms). We present an overview of the use of quadratic forms in physics as in our general theory, we have called START. And, in order to give an introduction to the use of the more general K-algebras and to the possible application to sciences other than physics, the application to social sciences is considered.For the applications to physics we show that quadratic spaces are a fundamental clue to understand the structure of theoretical physics (see, for example, Keller in ICNAAM 2005 and 2006)« less

Software for Training in Pre-College Mathematics

NASA Technical Reports Server (NTRS)

Shelton, Robert O.; Moebes, Travis A.; VanAlstine, Scot

2003-01-01

The Intelligent Math Tutor (IMT) is a computer program for training students in pre-college and college-level mathematics courses, including fundamentals, intermediate algebra, college algebra, and trigonometry. The IMT can be executed on a server computer for access by students via the Internet; alternatively, it can be executed on students computers equipped with compact- disk/read-only-memory (CD-ROM) drives. The IMT provides interactive exercises, assessment, tracking, and an on-line graphing calculator with algebraic-manipulation capabilities. The IMT provides an innovative combination of content, delivery mechanism, and artificial intelligence. Careful organization and presentation of the content make it possible to provide intelligent feedback to the student based on performance on exercises and tests. The tracking and feedback mechanisms are implemented within the capabilities of a commercial off-the-shelf development software tool and are written in the Unified Modeling Language to maximize reuse and minimize development cost. The graphical calculator is a standard feature of most college and pre-college algebra and trigonometry courses. Placing this functionality in a Java applet decreases the cost, provides greater capabilities, and provides an opportunity to integrate the calculator with the lessons.

Graduate teaching assistants in a reformed introductory physics course: Synthesis of quantitative analyses of instructor action and qualitative analyses of instructor attitudes and perspectives

NASA Astrophysics Data System (ADS)

Calder, Austin Michael

Physics Education Research (PER) has shown us that when students have opportunities to make sense of concepts they tend to remember them better and can apply them more appropriately to new situations. PER has also revealed that an interactive, cooperative, small group environment is more conducive to achieving this than traditional lecture and recitation sections. It is useful to consider the aims of reformed instruction from the point of view of the graduate teaching assistants (GTAs) in physics, who are facilitating the instruction. The data in this dissertation comes from audio-recordings of GTAs teaching in an algebra-based introductory course; I develop a rubric for assessing the teaching practices of the GTAs which separates teaching into five categories according to the reformed practices present. The rubric and technique developed here could be used as a diagnostic for GTAs new to a reformed classroom. I also conducted surveys of the GTA participants, as well as semi-structured interviews to gain more information about the attitudes and perspectives toward reformed physics instruction. Results from this work include: (1) A diagnostic tool for teaching improvement and (2) a detailed understanding of the GTA facilitators' teaching practices in the reformed physics laboratory.

Educational Outcomes of Synchronous and Asynchronous High School Students: A Quantitative Causal-Comparative Study of Online Algebra 1

ERIC Educational Resources Information Center

Berry, Sharon

2017-01-01

This study used a quantitative, causal-comparative design. It compared educational outcome data from online Algebra 1 courses to determine if a significant difference existed between synchronous and asynchronous students for end-of-course grades, state assessments scores, and student perceptions of their course. The study found that synchronous…

Reducing "Math Anxiety" in College Algebra Courses Including Comparisons with Elementary Statistics Courses.

ERIC Educational Resources Information Center

Bankhead, Mike

The high levels of anxiety, apprehension, and apathy of students in college algebra courses caused the instructor to create and test a variety of math teaching techniques designed to boost student confidence and enthusiasm in the subject. Overall, this proposal covers several different techniques, which have been evaluated by both students and the…

Innovative Interactive Lecture Demonstrations Using Wireless Force Sensors and Accelerometers for Introductory Physics Courses

NASA Astrophysics Data System (ADS)

Yoder, G.; Cook, J.

2010-12-01

Interactive lecture demonstrations1-6 (ILDs) are a powerful tool designed to help instructors bring state-of-the-art teaching pedagogies into the college-level introductory physics classroom. ILDs have been shown to improve students' conceptual understanding, and many examples have been created and published by Sokoloff and Thornton.6 We have used the new technology of Vernier's Wireless Dynamics Sensor System (WDSS)7 to develop three new ILDs for the first-semester introductory physics (calculus-based or algebra-based) classroom. These three are the Force Board, to demonstrate the vector nature of forces, addition of vectors, and the first condition of equilibrium; the Torque Board, to demonstrate torque and the second condition for equilibrium; and the Circular Motion Board, to discover the nature of the acceleration an object exhibiting uniform circular motion. With the WDSS, all three of these ILDs are easy to set up and use in any classroom or laboratory situation, and allow more instructors to utilize the technique of interactive lecture demonstrations.

Teaching mathematics in the PC lab - the students' viewpoints

NASA Astrophysics Data System (ADS)

Schmidt, Karsten; Köhler, Anke

2013-04-01

The Matrix Algebra portion of the intermediate mathematics course at the Schmalkalden University Faculty of Business and Economics has been moved from a traditional classroom setting to a technology-based setting in the PC lab. A Computer Algebra System license was acquired that also allows its use on the students' own PCs. A survey was carried out to analyse the students' attitudes towards the use of technology in mathematics teaching.

Constructive Learning in Undergraduate Linear Algebra

ERIC Educational Resources Information Center

Chandler, Farrah Jackson; Taylor, Dewey T.

2008-01-01

In this article we describe a project that we used in our undergraduate linear algebra courses to help our students successfully master fundamental concepts and definitions and generate interest in the course. We describe our philosophy and discuss the projects overall success.

Interactive, Collaborative, Electronic Learning Logs in the Physics Classroom

NASA Astrophysics Data System (ADS)

Gosling, Chris

2006-12-01

I describe my experiences using Hickman's Interactive Collaborative Electronic Learning Logs teaching HS Physics. ICE Learning Logs are written in student groups to answer questions posed by the instructor, who then in turn responds to each group’s entry before the next class. These logs were used with non-physics majors in both algebra and calculus-based introductory physics courses, and also at the high school level. I found ICE Learning Logs were found to be a clear improvement over traditional student journals. Excerpts from group entries will be presented to demonstrate the group identities that formed as well as the utility of the journals to probe for conceptual understanding. In addition, the ICE Learning Logs served as an excellent resource for students to review before exams and also to examine for critical moments to reflect on in formal essays. Hickman, P. (2000). Assessing student understanding with interactive-electronic-collaborative learning logs. ENC Focus, 7(2), 24-27. Sponsored by the National Science Foundation DUE0302097 and SUNY-Buffalo State Physics

Applicability of the Newtonian gravity concept inventory to introductory college physics classes

NASA Astrophysics Data System (ADS)

Williamson, Kathryn; Prather, Edward E.; Willoughby, Shannon

2016-06-01

The study described here extends the applicability of the Newtonian Gravity Concept Inventory (NGCI) to college algebra-based physics classes, beyond the general education astronomy courses for which it was originally developed. The four conceptual domains probed by the NGCI (Directionality, Force Law, Independence of Other Forces, and Threshold) are well suited for investigating students' reasoning about gravity in both populations, making the NGCI a highly versatile instrument. Classical test theory statistical analysis with physics student responses pre-instruction (N = 1,392) and post-instruction (N = 929) from eight colleges and universities across the United States indicate that the NGCI is composed of items with appropriate difficulty and discrimination and is reliable for this population. Also, expert review and student interviews support the NGCI's validity for the physics population. Emergent similarities and differences in how physics students reason about gravity compared to astronomy students are discussed, as well as future directions for analyzing the instrument's item parameters across both populations.

Hearing Math: Algebra Supported eText for Students With Visual Impairments.

PubMed

Bouck, Emily C; Weng, Pei-Lin

2014-01-01

Supported eText for students with visual impairments in mathematics has a promising, emerging literature base, although little of the existing research focuses on implementation within a classroom setting. This qualitative study sought to understand the use of supported eText to deliver algebra to students with visual impairments enrolled in algebra mathematics courses. The study also sought to explore supported eText in contrast to students' traditional means of accessing an algebra text. The main results suggest supported eText holds potential in terms of delivering mathematics content; however, more research and more reflection on the field is needed regarding this approach as a sole means of presenting text. Implications for teacher professional development and implementation practices are discussed.

Effects of 8th Grade Algebra on High School Course-Taking and Math Achievement: Evidence from Changing Practices in a Large Urban District

ERIC Educational Resources Information Center

Rickles, Jordan; Phillips, Meredith; Yamashiro, Kyo

2014-01-01

Between 1990 and 2012, the percentage of 13-year-olds (most of whom are 8th graders) taking algebra more than doubled, from 15% to 34% (National Center for Education Statistics, 2013). Yet recent education policy changes suggest that this movement to encourage algebra-taking in 8th grade has begun to reverse course. Existing research suggests that…

How Do Algebra I Course Repetition Rates Vary among English Learner Students by Length of Time to Reclassification as English Proficient? REL 2017-222

ERIC Educational Resources Information Center

Jaquet, Karina; Fong, Anthony B.

2017-01-01

Research has found high repetition rates for students in Algebra I, with one study finding a repetition rate of 44 percent for students in a large urban high school district. Less is known about how math performance and Algebra I course repetition rates vary among students with different levels of English proficiency. This report examines Algebra…

Factors That Have an Effect on Students' Scores on the Florida Algebra 1 End-of-Course Assessment in Algebra 1 Classrooms Using Interactive Whiteboard Tools

ERIC Educational Resources Information Center

Kelley, Ginno Paoli

2012-01-01

This study examined the factors that have an effect on student scores on the Florida End-of-Course (EOC) Assessment in four secondary Algebra 1 classrooms using interactive whiteboard tools (IWTs). Four teachers and 335 students were observed in one public suburban school in central Florida during the second half of the spring term. Hierarchical…

A Tale of Two Students

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2008-01-01

The article describes the performance of several individual students in a college algebra/precalculus course that focuses on the development of conceptual understanding and the use of mathematical modeling and discusses the likely differences in outcome if the students took a traditional algebra-skills focused course.

The Effects of Guided Discussion on Math Anxiety Levels, Course Performance, and Retention in a College Algebra Internet Class

ERIC Educational Resources Information Center

Emig, Christa

2009-01-01

The study sought to test the hypotheses that effective, guided discussions that facilitate meaningful dialogue about math anxiety would reduce levels of math anxiety in college algebra students, and would enhance course performance and course retention at a large community college in South Texas. The study was quantitative with a qualitative…

Who Repeats Algebra, and How Does Initial Performance Relate to Improvement When the Course Is Repeated?

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…

Cooperative Learning in a Community College Setting: Developmental Coursework in Mathematics

ERIC Educational Resources Information Center

Rivera, Natalie

2013-01-01

This action research study, set in a community college in the southwestern United States, was designed to investigate the effects of implementing cooperative learning strategies in a developmental mathematics course. Introductory algebra was formerly taught in a lecture based format, and as such regularly had a low course completion rate. To…

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

PubMed

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

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…

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…

Journal Writing: Enlivening Elementary Linear Algebra.

ERIC Educational Resources Information Center

Meel, David E.

1999-01-01

Examines the various issues surrounding the implementation of journal writing in an undergraduate linear algebra course. Identifies the benefits of incorporating journal writing into an undergraduate mathematics course, which are supported with students' comments from their journals and their reflections on the process. Contains 14 references.…

The Impact of the Louisiana State University Physics Entrance Requirement on Secondary Physics in Louisiana

NASA Astrophysics Data System (ADS)

McCoy, Michael Hanson

State Department of Education data was examined to determine the number of students enrolled in physics, physics class number, physics teacher number, and physics teacher certification. Census data from public and nonpublic school teachers, principals, and superintendents was analyzed. Purposive sampling of seven public and four nonpublic schools was used for site visitation including observations of physics classes, interviews of teachers and principals, and document acquisition. The literature base was drawn from a call for an increase in academic requirements in the sciences by the National Commission on Excellence in Education, the Southern Regional Education Board, the American Association for Advancement in the Sciences, and numerous state boards of education. LSU is the only major state university to require physics as an academic admission standard. Curriculum changes which influenced general curriculum change were: leveling of physics classes; stressing concepts, algebra, and doing problems in level-one; stressing trigonometry and problem solving in level-two; and increased awareness of expectations for university admission. Certified physics teachers were positive toward the requirement. The majority adopted a "wait-and-see" attitude to see if the university would institute the physics standard. Some physics teachers, nonphysics majors, were opposed to the requirement. Those who were positive remained positive. Those who developed the wait-and-see adopted the leveled physics course concept in 1989 and were positive toward the requirement. College-bound physics was taught prior to the requirement. The State Department of Education leveled physics in 1989. Level-one physics was algebra and conceptual based, level-two physics was trigonometry based, and a level-three physics, advanced placement was added. Enrollment doubled in public schools and increased 40% in nonpublic schools. African-American enrollment almost doubled in public and nonpublic schools. Oriental enrollment increased 40% in public schools. Hispanic enrollment increased 120% in public schools. Female enrollment in public schools increased 27.6% and 10% in nonpublic schools. The number of physics faculty members increased 33% in public schools and 25% in nonpublic schools. Newly certified physics teachers increased 80% although demand exceeded teacher supply. The proportion of certified to noncertified public school physics teachers declined 12% and spiraled downward 25% for nonpublic school physics teachers.

A Meta-Analysis of Algebra Interventions for Learners with Disabilities and Struggling Learners

ERIC Educational Resources Information Center

Hughes, Elizabeth M.; Witzel, Bradley S.; Riccomini, Paul J.; Fries, Karen M.; Kanyongo, Gibbs Y.

2014-01-01

The need for global competence in mathematics is apparent. Algebra is considered a gateway course to prepare students for the demands of a competitive global market. Many students demonstrate low performance in algebra; this is especially true for students with disabilities. Effective algebra instruction is essential to increase algebra…

Using Linguistics in the Teaching of Developmental and Remedial Algebra.

ERIC Educational Resources Information Center

Lesnak, Richard J.

Basic algebra at Robert Morris College (RMC) in Pittsburgh, Pennsylvania, is a remedial course for students with virtually no algebra background, and for students whose previous experiences with algebra have created math blocks and math anxiety. A study was conducted in an effort to measure quantitatively the benefits of using linguistic methods…

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…

On the structure of quantum L∞ algebras

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Fuchs, Michael; Traube, Matthias

2017-10-01

It is believed that any classical gauge symmetry gives rise to an L∞ algebra. Based on the recently realized relation between classical W algebras and L∞ algebras, we analyze how this generalizes to the quantum case. Guided by the existence of quantum W algebras, we provide a physically well motivated definition of quantum L∞ algebras describing the consistency of global symmetries in quantum field theories. In this case we are restricted to only two non-trivial graded vector spaces X 0 and X -1 containing the symmetry variations and the symmetry generators. This quantum L∞ algebra structure is explicitly exemplified for the quantum W_3 algebra. The natural quantum product between fields is the normal ordered one so that, due to contractions between quantum fields, the higher L∞ relations receive off-diagonal quantum corrections. Curiously, these are not present in the loop L∞ algebra of closed string field theory.

Cognitive development in introductory physics: A research-based approach to curriculum reform

NASA Astrophysics Data System (ADS)

Teodorescu, Raluca Elena

This project describes the research on a classification of physics problems in the context of introductory physics courses. This classification, called the Taxonomy of Introductory Physics Problems (TIPP), relates physics problems to the cognitive processes required to solve them. TIPP was created for designing and clarifying educational objectives, for developing assessments that can evaluate individual component processes of the problem-solving process, and for guiding curriculum design in introductory physics courses, specifically within the context of a "thinking-skills" curriculum. TIPP relies on the following resources: (1) cognitive research findings adopted by physics education research, (2) expert-novice research discoveries acknowledged by physics education research, (3) an educational psychology taxonomy for educational objectives, and (4) various collections of physics problems created by physics education researchers or developed by textbook authors. TIPP was used in the years 2006--2008 to reform the first semester of the introductory algebra-based physics course (called Phys 11) at The George Washington University. The reform sought to transform our curriculum into a "thinking-skills" curriculum that trades "breadth for depth" by focusing on fewer topics while targeting the students' cognitive development. We employed existing research on the physics problem-solving expert-novice behavior, cognitive science and behavioral science findings, and educational psychology recommendations. Our pedagogy relies on didactic constructs such as the GW-ACCESS problem-solving protocol, learning progressions and concept maps that we have developed and implemented in our introductory physics course. These tools were designed based on TIPP. Their purpose is: (1) to help students build local and global coherent knowledge structures, (2) to develop more context-independent problem-solving abilities, (3) to gain confidence in problem solving, and (4) to establish connections between everyday phenomena and underlying physics concepts. We organize traditional and research-based physics problems such that students experience a gradual increase in complexity related to problem context, problem features and cognitive processes needed to solve the problem. The instructional environment that we designed allows for explicit monitoring, control and measurement of the cognitive processes exercised during the instruction period. It is easily adaptable to any kind of curriculum and can be readily adjusted throughout the semester. To assess the development of students' problem-solving abilities, we created rubrics that measure specific aspects of the thinking involved in physics problem solving. The Colorado Learning Attitudes about Science Survey (CLASS) was administered pre- and post-instruction to determine students' shift in dispositions towards learning physics. The Force Concept Inventory (FCI) was administered pre- and post-instruction to determine students' level of conceptual understanding. The results feature improvements in students' problem-solving abilities and in their attitudes towards learning physics.

The State of the Gate: A Description of Instructional Practice in Algebra in Five Urban Districts

ERIC Educational Resources Information Center

Litke, Erica G.

2015-01-01

Algebra is considered a linchpin for success in secondary mathematics, serving as a gatekeeper to higher-level courses. Access to algebra is also considered an important lever for educational equity. Yet despite its prominence, large-scale examinations of algebra instruction are rare. In my dissertation, I endeavor to better understand what…

The Role of Mothers' Communication in Promoting Motivation for Math and Science Course-Taking in High School.

PubMed

Hyde, Janet S; Canning, Elizabeth A; Rozek, Christopher S; Clarke, Emily; Hulleman, Chris S; Harackiewicz, Judith M

2017-03-01

In the context of concerns about American youths' failure to take advanced math and science (MS) courses in high school, we examined mothers' communication with their adolescent about taking MS courses. At ninth grade, U.S. mothers (n = 130) were interviewed about their responses to hypothetical questions from their adolescent about the usefulness of algebra, geometry, calculus, biology, chemistry, and physics. Responses were coded for elaboration and making personal connections to the adolescent. The number of science, technology, engineering, and mathematics courses taken in 12th grade was obtained from school records. Mothers' use of personal connections predicted adolescents' MS interest and utility value, as well as actual MS course-taking. Parents can play an important role in motivating their adolescent to take MS courses. © 2016 The Authors. Journal of Research on Adolescence © 2016 Society for Research on Adolescence.

Exceptional quantum geometry and particle physics

NASA Astrophysics Data System (ADS)

Dubois-Violette, Michel

2016-11-01

Based on an interpretation of the quark-lepton symmetry in terms of the unimodularity of the color group SU (3) and on the existence of 3 generations, we develop an argumentation suggesting that the "finite quantum space" corresponding to the exceptional real Jordan algebra of dimension 27 (the Euclidean Albert algebra) is relevant for the description of internal spaces in the theory of particles. In particular, the triality which corresponds to the 3 off-diagonal octonionic elements of the exceptional algebra is associated to the 3 generations of the Standard Model while the representation of the octonions as a complex 4-dimensional space C ⊕C3 is associated to the quark-lepton symmetry (one complex for the lepton and 3 for the corresponding quark). More generally it is suggested that the replacement of the algebra of real functions on spacetime by the algebra of functions on spacetime with values in a finite-dimensional Euclidean Jordan algebra which plays the role of "the algebra of real functions" on the corresponding almost classical quantum spacetime is relevant in particle physics. This leads us to study the theory of Jordan modules and to develop the differential calculus over Jordan algebras (i.e. to introduce the appropriate notion of differential forms). We formulate the corresponding definition of connections on Jordan modules.

High Level Technology in a Low Level Mathematics Course.

ERIC Educational Resources Information Center

Schultz, James E.; Noguera, Norma

2000-01-01

Describes a teaching experiment in which spreadsheets and computer algebra systems were used to teach a low-level college consumer mathematics course. Students were successful in using different types of functions to solve a variety of problems drawn from real-world situations. Provides an existence proof that computer algebra systems can assist…

Undergraduate Mathematics Students' Emotional Experiences in Linear Algebra Courses

ERIC Educational Resources Information Center

Martínez-Sierra, Gustavo; García-González, María del Socorro

2016-01-01

Little is known about students' emotions in the field of Mathematics Education that go beyond students' emotions in problem solving. To start filling this gap this qualitative research has the aim to identify emotional experiences of undergraduate mathematics students in Linear Algebra courses. In order to obtain data, retrospective focus group…

Enumerating Small Sudoku Puzzles in a First Abstract Algebra Course

ERIC Educational Resources Information Center

Lorch, Crystal; Lorch, John

2008-01-01

Two methods are presented for counting small "essentially different" sudoku puzzles using elementary group theory: one method (due to Jarvis and Russell) uses Burnside's counting formula, while the other employs an invariant property of sudoku puzzles. Ideas are included for incorporating this material into an introductory abstract algebra course.…

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…

Preliminary Success and Retention Rates in Selected Math Courses. Research Report.

ERIC Educational Resources Information Center

Cuesta Coll., San Luis Obispo, CA. Matriculation and Research Services.

This report presents findings of exploratory research on success, retention, and persistence in math courses at Cuesta College. The following research questions were addressed: (1) How do success rates in Math 23 (elementary algebra) and Math 27 (intermediate algebra) compare with traditional and computer-assisted formats? (2) What are the…

An Introduction to Geometric Algebra with some Preliminary Thoughts on the Geometric Meaning of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Horn, Martin Erik

2014-10-01

It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics.

Mathematics in the Real World.

ERIC Educational Resources Information Center

Borenstein, Matt

1997-01-01

The abstract nature of algebra causes difficulties for many students. Describes "Real-World Data," an algebra course designed for students with low grades in algebra and provides multidisciplinary experiments (linear functions and variations; quadratic, square-root, and inverse relations; and exponential and periodic variation)…

Student Logical Implications and Connections between Symbolic Representations of a Linear System within the Context of an Introductory Linear Algebra Course Employing Inquiry-Oriented Teaching and Traditional Lecture

ERIC Educational Resources Information Center

Payton, Spencer D.

2017-01-01

This study aimed to explore how inquiry-oriented teaching could be implemented in an introductory linear algebra course that, due to various constraints, may not lend itself to inquiry-oriented teaching. In particular, the course in question has a traditionally large class size, limited amount of class time, and is often coordinated with other…

A Mathematics Entrance Exam for General (Non-Majors) Physics

ERIC Educational Resources Information Center

Chediak, Alex

2010-01-01

In a previous issue of "The Physics Teacher", John Hubisz explained how a mathematics background check has been used at three different colleges to determine the appropriate physics sequence for incoming students. Based on their performance, students are placed into either calculus-based physics (CBP), algebra-trig physics (ATP), or a year of…

Investigating the Use of Mastery-Style Online Homework Exercises in Introductory Algebra-Based Mechanics in a Controlled Clinical Study

ERIC Educational Resources Information Center

Evans, William R.; Selen, Mats A.

2017-01-01

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs. traditional-style homework with students in both algebra-based and…

Algebra for All: California's Eighth-Grade Algebra Initiative as Constrained Curricula.

PubMed

Domina, Thurston; Penner, Andrew M; Penner, Emily K; Conley, Annemarie

2014-08-01

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. (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? 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. 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%. 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 prior achievement. We find that students' odds of taking higher level mathematics courses increased as this district implemented the state's Algebra mandate. However, even as the district implemented a constrained curriculum strategy, mathematics achievement growth between 6th sixth and 10th grade slowed and the achievement advantages associated with 8th eighth grade Algebra declined. Our analyses suggest that curricular intensification increased the inclusiveness and decreased the selectivity of the mathematics tracking regime in Towering Pines middle schools. However, the findings suggest that this constrained curriculum strategy may have may have unintended negative consequences for student achievement.

Using Dynamic Geometry and Computer Algebra Systems in Problem Based Courses for Future Engineers

ERIC Educational Resources Information Center

Tomiczková, Svetlana; Lávicka, Miroslav

2015-01-01

It is a modern trend today when formulating the curriculum of a geometric course at the technical universities to start from a real-life problem originated in technical praxis and subsequently to define which geometric theories and which skills are necessary for its solving. Nowadays, interactive and dynamic geometry software plays a more and more…

The Role of Logic in the Validation of Mathematical Proofs. Technical Report. No. 1999-1

ERIC Educational Resources Information Center

Selden, Annie; Selden, John

1999-01-01

Mathematics departments rarely require students to study very much logic before working with proofs. Normally, the most they will offer is contained in a small portion of a "bridge" course designed to help students move from more procedurally-based lower-division courses (e.g., abstract algebra and real analysis). What accounts for this seeming…

Middle School Math Acceleration and Equitable Access to Eighth-Grade Algebra: Evidence from the Wake County Public School System

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…

It's a Wonderful Life: Using Public Domain Cinema Clips To Teach Affective Objectives and Illustrate Real-World Algebra Applications.

ERIC Educational Resources Information Center

Palmer, Loretta

A basic algebra unit was developed at Utah Valley State College to emphasize applications of mathematical concepts in the work world, using video and computer-generated graphics to integrate textual material. The course was implemented in three introductory algebra sections involving 80 students and taught algebraic concepts using such areas as…

A Worked Example for Creating Worked Examples

ERIC Educational Resources Information Center

McGinn, Kelly M.; Lange, Karin E.; Booth, Julie L.

2015-01-01

Researchers have extensively documented, and math teachers know from experience, that algebra is a "gatekeeper" to more advanced mathematical topics. Students must have a strong understanding of fundamental algebraic concepts to be successful in later mathematics courses. Unfortunately, algebraic misconceptions that students may form or…

Training Undergraduate Physics Peer Tutors

NASA Astrophysics Data System (ADS)

Nossal, S. M.; Jacob, A. T.

2004-05-01

The University of Wisconsin's Physics Peer Mentor Tutor Program matches upper level undergraduate physics students in small study groups with students studying introductory algebra-based physics. We work with students who are potentially at-risk for having academic trouble with the course. They include students with a low exam score, learning disabilities, no high school physics, weak math backgrounds, and/or on academic probation. We also work with students from groups under represented in the sciences and who may be feeling isolated or marginal on campus such as minority, returning adult, and international students. The tutors provide a supportive learning environment, extra practice problems, and an overview of key concepts. In so doing, they help our students to build confidence and problem solving skills applicable to physics and other areas of their academic careers. The Physics Peer Mentor Tutor Program is modeled after a similar program for chemistry created by the University of Wisconsin's Chemistry Learning Center. Both programs are now run in collaboration. The tutors are chosen for their academic strength and excellent communication skills. Our tutors are majoring in physics, math, and secondary-level science education. The tutors receive ongoing training and supervision throughout the year. They attend weekly discipline-specific meetings to discuss strategies for teaching the content currently being discussed in the physics course. They also participate in a weekly teaching seminar with science tutors from chemistry and biochemistry to discuss teaching methods, mentoring, and general information relating to the students with whom we work. We will describe an overview of the Physics Peer Mentor Tutor Program with a focus on the teacher training program for our undergraduate tutors.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buchstaber, V M; Ustinov, A V

We describe the coefficient rings of universal formal group laws which arise in algebraic geometry, algebraic topology and their application to mathematical physics. We also describe the homomorphisms of these coefficient rings coming from reductions of one formal group law to another. The proofs are based on the number-theoretic properties of binomial coefficients. Bibliography: 37 titles.

Middle School Mathematics: 2006-07 to 2008-09. Impact Evaluation. E&R Report No. 10.11

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

In 2006-07, seven Wake County Public School System (WCPSS) middle schools piloted Algebraic Thinking as an alternate approach to teaching middle school mathematics. Algebraic Thinking was developed to help students in grade 6 reach higher mathematics courses by combining the regular and advanced middle school mathematics courses into one…

Team Teaching and Cooperative Groups in Abstract Algebra: Nurturing a New Generation of Confident Mathematics Teachers

ERIC Educational Resources Information Center

Grassl, R.; Mingus, T. T. Y.

2007-01-01

Experiences in designing and teaching a reformed abstract algebra course are described. This effort was partially a result of a five year statewide National Science Foundation (NSF) grant entitled the Rocky Mountain Teacher Enhancement Collaborative. The major thrust of this grant was to implement reform in core mathematics courses that would…

Proof and Reasoning in Secondary School Algebra Textbooks

ERIC Educational Resources Information Center

Dituri, Philip

2013-01-01

The purpose of this study was to determine the extent to which the modeling of deductive reasoning and proof-type thinking occurs in a mathematics course in which students are not explicitly preparing to write formal mathematical proofs. Algebra was chosen because it is the course that typically directly precedes a student's first formal…

Teaching Special Relativity Without Calculus

NASA Astrophysics Data System (ADS)

Ruby, Lawrence

2009-04-01

I 2007 many AAPT members received a booklet that is the first chapter of a physics textbook available on a CD. This book espouses the new educational philosophy of teaching special relativity as the first item in the topic of mechanics. Traditionally, special relativity is part of one or more modern physics chapters at the end of the text,2 and very often this material is never utilized due to time constraints. From a logical standpoint, special relativity is important in satellite communications and in cosmology, as well as in modern physics applications such as atomic theory and high-energy physics. The purpose of this paper is to show that the new philosophy can be carried out in a noncalculus physics course, by demonstrating that all of the principal results of special relativity theory can be obtained by simple algebra. To accomplish this, we shall propose alternate derivations for two results that are usually obtained with calculus. Textbooks2 typically obtain the equations for time dilation and for length contraction from simple considerations based on Einstein's second postulate.3 We shall start from this point.

Emphasizing language and visualization in teaching linear algebra

NASA Astrophysics Data System (ADS)

Hannah, John; Stewart, Sepideh; Thomas, Mike

2013-06-01

Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his approach in both lectures and tutorials, and how he employed visualization and an emphasis on language to encourage conceptual thinking. We use Tall's framework of three worlds of mathematical thinking to reflect on the effect of these activities in students' learning. An analysis of students' attitudes to the course and their test and examination results help to answer questions about the value of such an approach, suggesting ways forward in teaching linear algebra.

MULTIVARIATERESIDUES : A Mathematica package for computing multivariate residues

NASA Astrophysics Data System (ADS)

Larsen, Kasper J.; Rietkerk, Robbert

2018-01-01

Multivariate residues appear in many different contexts in theoretical physics and algebraic geometry. In theoretical physics, they for example give the proper definition of generalized-unitarity cuts, and they play a central role in the Grassmannian formulation of the S-matrix by Arkani-Hamed et al. In realistic cases their evaluation can be non-trivial. In this paper we provide a Mathematica package for efficient evaluation of multivariate residues based on methods from computational algebraic geometry.

The Effects of Teacher Collective Responsibility on the Mathematics Achievement of Students Who Repeat Algebra

ERIC Educational Resources Information Center

Morales-Chicas, Jessica; Agger, Charlotte

2017-01-01

In this article, the authors use the national High School Longitudinal Study of 2009 (HSLS:09) dataset to explore (a) if repeating algebra in the eighth grade was associated with overall mathematics grades and course-taking patterns by twelfth grade, (b) if repeating algebra in the eighth grade was associated with students' final grade in algebra,…

Emotional Component in Teaching and Learning

NASA Astrophysics Data System (ADS)

Ponnambalam, Michael

2018-02-01

The laws of physics are often seen as objective truth, pure and simple. Hence, they tend to appear cerebral and cold. However, their presentation is necessarily subjective and may vary from being boring to being exciting. A detailed analysis of physics education reform efforts over the last three decades finds that interactive instruction results in greater learning gains than the traditional lecture format. In interactive engagement, the emotional component plays a far greater role than acknowledged by many. As an experienced physics teacher [(i) Four decades of teaching and research in four continents (teaching all courses to undergraduate physics majors and algebra-based physics to high school seniors as well as college freshmen), (ii) 11 years of volunteer work in Physics Popularization in six countries to many thousands of students in elementary, middle, and high schools as well as colleges and universities, and (iii) eight years as a Master Teacher and mentor], I feel that the emotional component in teaching and learning physics has been neglected. This paper presents the role of the emotional component in transforming ordinary teaching and learning of physics into an enjoyable and exciting experience for students as well as teachers.

Teaching group theory using Rubik's cubes

NASA Astrophysics Data System (ADS)

Cornock, Claire

2015-10-01

Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure elective based on physical examples. Abstract concepts, such as subgroups, homomorphisms and equivalence relations are explored with the cubes first. In addition to this, conclusions about the cubes can be made through the consideration of algebraic approaches through a process of discovery. The teaching, learning and assessment methods are explored in this paper, along with the challenges and limitations of the methods. The physical use of Rubik's cubes within the classroom and examination will be presented, along with the use of peer support groups in this process. The students generally respond positively to the teaching methods and the use of the cubes.

Funny Face Contest: A Formative Assessment

ERIC Educational Resources Information Center

Colen, Yong S.

2010-01-01

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

University of Chicago School Mathematics Project (UCSMP) Algebra. WWC Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

Pre-Algebra Lexicon.

ERIC Educational Resources Information Center

Hayden, Dunstan; Cuevas, Gilberto

The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…

Application of Computer Graphics to Graphing in Algebra and Trigonometry. Final Report.

ERIC Educational Resources Information Center

Morris, J. Richard

This project was designed to improve the graphing competency of students in elementary algebra, intermediate algebra, and trigonometry courses at Virginia Commonwealth University. Computer graphics programs were designed using an Apple II Plus computer and implemented using Pascal. The software package is interactive and gives students control…

Improving Algebra Preparation: Implications from Research on Student Misconceptions and Difficulties

ERIC Educational Resources Information Center

Welder, Rachael M.

2012-01-01

Through historical and contemporary research, educators have identified widespread misconceptions and difficulties faced by students in learning algebra. Many of these universal issues stem from content addressed long before students take their first algebra course. Yet elementary and middle school teachers may not understand how the subtleties of…

Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type

NASA Astrophysics Data System (ADS)

Hermann, Robert

1982-07-01

Recent work by Morrison, Marsden, and Weinstein has drawn attention to the possibility of utilizing the cosymplectic structure of the dual of the Lie algebra of certain infinite dimensional Lie groups to study hydrodynamical and plasma systems. This paper treats certain models arising in elementary particle physics, considered by Lee, Weinberg, and Zumino; Sugawara; Bardacki, Halpern, and Frishman; Hermann; and Dolan. The lie algebras involved are associated with the ''current algebras'' of Gell-Mann. This class of Lie algebras contains certain of the algebras that are called ''Kac-Moody algebras'' in the recent mathematics and mathematical physics literature.

Exploring Attitudes and Achievement of Web-Based Homework in Developmental Algebra

ERIC Educational Resources Information Center

Leong, Kwan Eu; Alexander, Nathan

2013-01-01

The purpose of this study was to understand how students' attitudes were connected to their mathematics learning. This investigation was specific to web-based homework in developmental courses in the community college environment. The mixed-methods approach was used to analyze the relationship between students' attitudes and mathematical…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 1, Teacher's Commentary. Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part one of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables;…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 2. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real numbers, subtraction and division…

The Effects of Computer Algebra System on Undergraduate Students' Spatial Visualization Skills in a Calculus Course

ERIC Educational Resources Information Center

Karakus, Fatih; Aydin, Bünyamin

2017-01-01

This study aimed at determining the effects of using a computer algebra system (CAS) on undergraduate students' spatial visualization skills in a calculus course. This study used an experimental design. The "one group pretest-posttest design" was the research model. The participants were 41 sophomore students (26 female and 15 male)…

School and District Policies and Strategies That Impact Student Performance on the Missouri End-of-Course Algebra 1 NCLB Assessment

ERIC Educational Resources Information Center

Nevels, Nevels

2012-01-01

The dissertation study reported here describes various policies and strategies used by school districts that impact student performance on the Missouri Algebra 1 End-of- Course (EOC) assessment. Analysis of state testing data, teacher survey data, and interview data were used to describe policies and strategies used by 42 teachers and…

The Effects of Migration to a Blended Self-Paced Format for a Remedial Pre-College Algebra Mathematics Course

ERIC Educational Resources Information Center

Deshler, Jessica; Fuller, Edgar

2016-01-01

Approximately 30% of students entering West Virginia University (WVU) are not ready for college mathematics. The WVU Department of Mathematics has been tasked with remediating these students and has worked over the last decade to find the most efficient way to teach the Pre-College Algebra Workshop; the prerequisite course students must complete…

Using Topic Order to Reinforce Student Algebra Skills in a Community College Introductory Chemistry Course

ERIC Educational Resources Information Center

Blakely, Alan W.

2011-01-01

This article describes the impact of starting with gases in an introductory chemistry course at a community college. Students in the author's class frequently are very weak in algebra skills, and this has a cumulative impact over time that culminates in student struggles when moles and reaction stoichiometry are discussed. The rationale behind…

Programmed First Course in Algebra, Revised Form H, Student's Text, Part I, Unit 60.

ERIC Educational Resources Information Center

Buck, R. Creighton; And Others

This is part one of a two-part SMSG Programed Algebra Text for high school students. The general plan of the course is to build upon the student's experience with arithmetic. The student is initially led to extract from his or her experience the fundamental properties of addition and multiplication. The text then introduces negative real numbers…

Explicating mathematical thinking in differential equations using a computer algebra system

NASA Astrophysics Data System (ADS)

Zeynivandnezhad, Fereshteh; Bates, Rachel

2018-07-01

The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance students' mathematical thinking by implementing a computer algebra system and active learning pedagogical approaches. students' mathematical thinking processes were analyzed while completing specific differential equations tasks based on posed prompts and questions and Instrumental Genesis. Data were collected from 37 engineering students in a public Malaysian university. This study used the descriptive and interpretive qualitative research design to investigate the students' perspectives of emerging mathematical understanding and approaches to learning mathematics in an undergraduate differential equations course. Results of this study concluded that students used a variety of mathematical thinking processes in a non-sequential manner. Additionally, the outcomes provide justification for continued use of technologies such as computer algebra systems in undergraduate mathematics courses and the need for further studies to uncover the various processes students utilize to complete specific mathematical tasks.

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.)

Catching Up on Algebra

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…

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…

Ready, Set, Algebra?

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,…

Just-in-Time Algebra: A Problem Solving Approach Including Multimedia and Animation.

ERIC Educational Resources Information Center

Hofmann, Roseanne S.; Hunter, Walter R.

2003-01-01

Describes a beginning algebra course that places stronger emphasis on learning to solve problems and introduces topics using real world applications. Students learn estimating, graphing, and algebraic algorithms for the purpose of solving problems. Indicates that applications motivate students by appearing to be a more relevant topic as well as…

Foundations of Algebra: 2009-10. Implementation Insights. E&R Report No. 10.28

ERIC Educational Resources Information Center

Paeplow, Colleen

2010-01-01

This report examined the implementation of Foundations of Algebra, a course designed to provide high school students with low mathematics performance an extra opportunity to review and study foundational mathematics concepts prior to enrolling in Introductory Mathematics and subsequently Algebra I. In the fall of 2009, 877 high school students…

Resources for Teaching Linear Algebra. MAA Notes Volume 42.

ERIC Educational Resources Information Center

Carlson, David, Ed.; And Others

This book takes the position that the teaching of elementary linear algebra can be made more effective by emphasizing applications, exposition, and pedagogy. It includes the recommendations of the Linear Algebra Curriculum Study Group with their core syllabus for the first course, and the thoughts of mathematics faculty who have taught linear…

Emphasizing Language and Visualization in Teaching Linear Algebra

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Mike

2013-01-01

Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his…

Teaching the "Diagonalization Concept" in Linear Algebra with Technology: A Case Study at Galatasaray University

ERIC Educational Resources Information Center

Yildiz Ulus, Aysegul

2013-01-01

This paper examines experimental and algorithmic contributions of advanced calculators (graphing and computer algebra system, CAS) in teaching the concept of "diagonalization," one of the key topics in Linear Algebra courses taught at the undergraduate level. Specifically, the proposed hypothesis of this study is to assess the effective…

A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry

ERIC Educational Resources Information Center

Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew

2012-01-01

In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

Early Integration of Tutorial Support in Beginning Algebra

ERIC Educational Resources Information Center

Copus, Colleen; McKinney, Betsy

2016-01-01

Anecdotal observations reveal that most students with strong arithmetic skills will succeed in the Beginning Algebra course even if they have no previous experience with algebra. In trying to quantify this with an initial teacher-created survey of arithmetic skills, it was observed, for three consecutive semesters, that students who scored in the…

Balancing the Equation: Do Course Variations in Algebra 1 Provide Equal Student Outcomes?

ERIC Educational Resources Information Center

Kenfield, Danielle M.

2013-01-01

Historically, algebra has served as a gatekeeper that divides students into academic programs with varying opportunities to learn and controls access to higher education and career opportunities. Successful completion of Algebra 1 demonstrates mathematical proficiency and allows access to a sequential and progressive path of advanced study that…

Algebra for All: California’s Eighth-Grade Algebra Initiative as Constrained Curricula

PubMed Central

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 prior achievement. Findings/Results We find that students’ odds of taking higher level mathematics courses increased as this district implemented the state’s Algebra mandate. However, even as the district implemented a constrained curriculum strategy, mathematics achievement growth between 6th sixth and 10th grade slowed and the achievement advantages associated with 8th eighth grade Algebra declined. Conclusions/Recommendations Our analyses suggest that curricular intensification increased the inclusiveness and decreased the selectivity of the mathematics tracking regime in Towering Pines middle schools. However, the findings suggest that this constrained curriculum strategy may have may have unintended negative consequences for student achievement. PMID:26120219

Letters

NASA Astrophysics Data System (ADS)

2001-09-01

The Editor welcomes letters, by e-mail to ped@iop.org or by post to Dirac House, Temple Back, Bristol BS1 6BE, UK. Contents: M-set as metaphor The abuse of algebra M-set as metaphor 'To see a World in a Grain of Sand And a Heaven in a Wild Flower Hold Infinity in the palm of your hand And Eternity in an hour' William Blake's implied relativity of spatial and temporal scales is intriguing and, given the durability of this worlds-within-worlds concept (he wrote in 1803) in art, literature and science, the blurring of distinctions between the very large and the very small must strike some kind of harmonious chord in the human mind. Could this concept apply to the physical world? To be honest, we cannot be absolutely sure. Most cosmological thinking still retains the usual notions of a finite universe and an absolute size scale extending from smallest to largest objects. In the boundless realm of mathematics, however, the story is quite different. The M-set was discovered by the French mathematician Benoit Mandelbrot in 1980, created by just a few simple lines of computer code that are repeated recursively. As in Blake's poem, this 'world' has no bottom we have an almost palpable archetype for the concept of infinity. I would use the word 'tangible', but one of the defining features of the M-set is that nowhere in the labyrinth can one find a surface smooth enough for a tangent. Upon magnification even surfaces that appeared to be smooth explode with quills and scrolls and lightning bolts and spiral staircases. And there is something more, something truly sublime. Observe a small patch with unlimited magnifying power and, as you observe the M-set on ever-smaller scales, down through literally endless layers of ornate structure, you occasionally come upon a rapidly expanding cortex of dazzling colour with a small black structure at its centre. The black spot appears to be the M-set itself! There is no end to the hierarchy, no bottom-most level, just endless recursive worlds within worlds within worlds. Scale is no longer fixed and absolute, but is purely relative. These beautiful symmetries convey an immediate aesthetic pleasure and also compel one to think about these strange concepts of self-similarity, infinity and relativity of scale. Our present science tends to favour reductionism. We surmise that the physics of our world has a most fundamental level and all phenomena are built up from these quarks or strings. Mathe-matics need not be so limited: here the mind is set free to dream of universes with the most exquisite symmetries and infinities. I urge you to explore the M-set. The epiphanies you experience will be worth the effort. Robert L Oldershaw Physics Department, Amherst College, Amherst, MA 01002, USA rlolders@unix.amherst.edu Video copies of The Colors of Infinity are available from Humanities, Inc. Princeton, New Jersey, priced 30. There are also several websites such as www.softlab.ntua.gr/mandel/mandel.html or tqd.advanced.org/3288. The abuse of algebra What a pleasure it is to read the work of students whose reasoning is easy to follow, who observe the rules of grammar in all their writing, and who remember that an algebraic equation is and must be a sentence in their native language, albeit written in a universal shorthand. About thirty years ago the ASE encouraged us all to use 'Quantity Algebra' consistently rather than to muddle on with inconsistent (and therefore incorrect) hybrids of 'Number' and 'Quantity' Algebra. Number Algebra is tedious if used correctly in physics. But Quantity Algebra seems to petrify Maths departments, whose incoherent practices undermine the efforts of Physics teachers to persuade their pupils to reason both logically and clearly. When I read a pupil's work, the final answer (or conclusion) interests me far less than the reasoning that leads to that conclusion. I want to be able to check the work as I read it, and it helps greatly if units are included when values are substituted for symbols. Textbooks which set out their worked examples in Quantity Algebra are especially appreciated, not only for illustrating the 'good practice' we want to encourage, but, of course, in helping the student keep sight of the physics throughout. Physics texts which do not use Quantity Algebra in their worked examples invariably demonstrate faulty logic ... besides hiding the physics. Here is a very simple example: Good practice: Force = 70 kg × 10 N/kg = 700 N Bad practice: Force = 70 × 10 = 700 (or Force = 700 N) The final 'slide-rule' manipulation is of numbers, of course; but we should keep sight of the route to those numbers. Years ago the Head of Maths at a large comprehensive school described how he persuaded all departments to convert to Quantity Algebra. But he ended with an admission: that such an initiative must come from the Head of Maths. That enlightened man understood the problem: his fellow mathematicians. Tim Watson Worcester

Using the Logarithmic Concentration Diagram, Log "C", to Teach Acid-Base Equilibrium

ERIC Educational Resources Information Center

Kovac, Jeffrey

2012-01-01

Acid-base equilibrium is one of the most important and most challenging topics in a typical general chemistry course. This article introduces an alternative to the algebraic approach generally used in textbooks, the graphical log "C" method. Log "C" diagrams provide conceptual insight into the behavior of aqueous acid-base systems and allow…

Grouping Within Algebra I: A Structural Sieve With Powerful Effects for Low-Income, Minority, and Immigrant Students

ERIC Educational Resources Information Center

Paul, Faith G.

2005-01-01

A key element in educational reform has been to increase mathematical proficiency. We look at how five urban high schools with virtually all low-income, minority, and immigrant students have arranged for students to take algebra I, and we examine the course enrollments and grades of these student in the core college prep courses. Both preparation…

Perceptions of 9th and 10th Grade Students on How Their Environment, Cognition, and Behavior Motivate Them in Algebra and Geometry Courses

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…

Exploring Interactive and Dynamic Simulations Using a Computer Algebra System in an Advanced Placement Chemistry Course

ERIC Educational Resources Information Center

Matsumoto, Paul S.

2014-01-01

The article describes the use of Mathematica, a computer algebra system (CAS), in a high school chemistry course. Mathematica was used to generate a graph, where a slider controls the value of parameter(s) in the equation; thus, students can visualize the effect of the parameter(s) on the behavior of the system. Also, Mathematica can show the…

Computer Aided Instruction for a Course in Boolean Algebra and Logic Design. Final Report (Revised).

ERIC Educational Resources Information Center

Roy, Rob

The use of computers to prepare deficient college and graduate students for courses that build upon previously acquired information would solve the growing problem of professors who must spend up to one third of their class time in review of material. But examination of students who were taught Boolean Algebra and Logic Design by means of Computer…

A Regression Analysis of South Carolina Algebra I End-of-Course Exam Scores by Schedule Type

ERIC Educational Resources Information Center

Smith, Dawn M.

2017-01-01

The purpose of this study was to examine the relationship between scheduling and first-year-high-school students' exam scores on the South Carolina Algebra I End-of-Course (EOC) assessment. The study compared existing empirical data from two southeastern high schools from the same school district using 4 X 4 block schedules from 2011-2014 and…

Place-Based Mathematics: A Conflated Pedagogy? Working Paper No. 43

ERIC Educational Resources Information Center

Showalter, Daniel A.

2012-01-01

Place-based mathematics education (PBME) has the potential to engage students with the mathematics inherent in the local land, culture, and community. However, research has identified daunting barriers to this pedagogy, especially in abstract mathematics courses such as algebra and beyond. In this study, 15 graduates of a doctoral program in rural…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 2, Teacher's Commentary. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real…

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…

Linear Algebra Revisited: An Attempt to Understand Students' Conceptual Difficulties

ERIC Educational Resources Information Center

Britton, Sandra; Henderson, Jenny

2009-01-01

This article looks at some of the conceptual difficulties that students have in a linear algebra course. An overview of previous research in this area is given, and the various theories that have been espoused regarding the reasons that students find linear algebra so difficult are discussed. Student responses to two questions testing the ability…

Student and Instructor Perceptions of a Flipped College Algebra Classroom

ERIC Educational Resources Information Center

Jaster, Robert W.

2017-01-01

Each year about half a million students fail to make planned academic progress due to college algebra, hence the need for researchers to find ways of improving the quality of instruction in the course. Recent research suggests that flipping college algebra to allow time for active learning in the classroom may improve student performance. Also,…

A Quantitative Study Analyzing Predictive Factors That Affect Achievement on Florida's Algebra I End-of-Course Exam (EOC)

ERIC Educational Resources Information Center

Holley, Hope D.

2017-01-01

Despite research that high-stakes tests do not improve knowledge, Florida requires students to pass an Algebra I End-of-Course exam (EOC) to earn a high school diploma. Test passing scores are determined by a raw score to t-score to scale score analysis. This method ultimately results as a comparative test model where students' passage is…

Efficacy of Online Algebra I for Credit Recovery for At-Risk Ninth Grade Students: Evidence from Year 1

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…

Finding golden mean in a physics exercise

NASA Astrophysics Data System (ADS)

Benedetto, Elmo

2017-07-01

The golden mean is an algebraic irrational number that has captured the popular imagination and is discussed in many books. Indeed, some scientists believe that it appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts. Generally, the golden mean is introduced in geometry and the textbooks give the definition showing a graphical method to determine it. In this short note, we want to find this number by studying projectile motion. This could be a way to introduce the golden mean (also said to be the golden ratio, golden section, Fidia constant, divine proportion or extreme and mean ratio) in a physics course.

Teaching Basic Algebra Courses at the College Level

ERIC Educational Resources Information Center

Mallenby, Michel L.; Mallenby, Douglas W.

2004-01-01

Three dysfunctional behaviors of basic algebra students are described: Silence as Camouflage, Wing and a Prayer, and Ignorance is OK. These behavior patterns are explained, and beneficial teaching methods that address the weaknesses are presented.

The link between middle school mathematics course placement and achievement.

PubMed

Domina, Thurston

2014-01-01

The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. © 2014 The Author. Child Development © 2014 Society for Research in Child Development, Inc.

Using Example Generation to Explore Students' Understanding of the Concepts of Linear Dependence/Independence in Linear Algebra

ERIC Educational Resources Information Center

Aydin, Sinan

2014-01-01

Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…

The Struggle to Pass Algebra: Online vs. Face-to-Face Credit Recovery for At-Risk Urban Students

ERIC Educational Resources Information Center

Heppen, Jessica B.; Sorensen, Nicholas; Allensworth, Elaine; Walters, Kirk; Rickles, Jordan; Taylor, Suzanne Stachel; Michelman, Valerie

2017-01-01

Students who fail algebra are significantly less likely to graduate on time, and algebra failure rates are consistently high in urban districts. Identifying effective credit recovery strategies is critical for getting students back on track. Online courses are now widely used for credit recovery, yet there is no rigorous evidence about the…

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…

Using Standardized Tests to Identify Prior Knowledge Necessary for Success in Algebra: A Predictive Analysis

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…

Algebra Matters: An Ethnographic Study of Successful African American Male Algebra 1 Students in a Suburban Middle School

ERIC Educational Resources Information Center

Kirkwood, Kirk

2012-01-01

Alarming statistics reveal that African American male students are encountering long-standing challenges in K-12 mathematics. However, few studies have explored the phenomena associated with African American males and K-12 mathematics education, particularly at the middle school level in the context of an Algebra 1 course of study. The purpose of…

Factors Related to Problem Solving by College Students in Developmental Algebra.

ERIC Educational Resources Information Center

Schonberger, Ann K.

A study was conducted to contrast the characteristics of three groups of college students who completed a developmental algebra course at the University of Maine at Orono during 1980-81. On the basis of a two-part final examination, involving a multiple-choice test of algebraic concepts and skills and a free-response test of problem-solving…

Relationships between Student and Instructional Factors and Algebra Achievement of Students in the United States and Japan: An Analysis of TIMSS 2003 Data

ERIC Educational Resources Information Center

House, J. Daniel; Telese, James A.

2008-01-01

Algebra knowledge is a critical part of middle-school mathematics achievement, and success in algebra is necessary for taking higher level mathematics courses and leads to higher scores on standardized tests. The purpose of this study was to simultaneously examine relationships between mathematics beliefs, classroom instructional strategies, and…

A Study to Determine Differences in the Level of Perceived Preparedness in Teaching Algebra to Eighth Graders between Teachers in the United States and Teachers in Lebanon

ERIC Educational Resources Information Center

Khajarian, Seta

2011-01-01

Algebra is a branch in mathematics and taking Algebra in middle school is often a gateway to advanced courses in high school. The problem is that the United States and Lebanon had low scores in Algebra in the 2007 Trends in Mathematics and Sciences Study (TIMSS), an international assessment administered to 4th and 8th graders every 4 years. On the…

Research on Group Learning and Cognitive Science: A Study of Motivation, Knowledge, and Self-Regulation in a Large Lecture College Algebra Class

ERIC Educational Resources Information Center

Miller, David; Schraeder, Matthew

2015-01-01

At a research University near the east coast, researchers restructured a College Algebra course by formatting the course into two large lectures a week, an active recitation size laboratory class once a week, and an extra day devoted to active group work called Supplemental Practice (SP). SP was added as an extra day of class where the SP leader…

An Application of Cartesian Graphing to Seismic Exploration.

ERIC Educational Resources Information Center

Robertson, Douglas Frederick

1992-01-01

Describes how college students enrolled in a course in elementary algebra apply graphing and algebra to data collected from a seismic profile to uncover the structure of a subterranean rock formation. Includes steps guiding the activity. (MDH)

Partial Fractions via Calculus

ERIC Educational Resources Information Center

Bauldry, William C.

2018-01-01

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to…

Teaching Determinants Using Rook Arrangements

ERIC Educational Resources Information Center

Hendrickson, Anders O. F.

2018-01-01

Teaching determinants poses significant challenges to the instructor of a proof-based undergraduate linear algebra course. The standard definition by cofactor expansion is ugly, lacks symmetry, and is hard for students to use in proofs. We introduce a visual definition of the determinant that interprets permutations as arrangements of…

A real signal and its states

NASA Astrophysics Data System (ADS)

Basiladze, S. G.

2017-05-01

The paper describes the general physical theory of signals, carriers of information, which supplements Shannon's abstract classical theory and is applicable in much broader fields, including nuclear physics. It is shown that in the absence of classical noise its place should be taken by the physical threshold of signal perception for objects of both macrocosm and microcosm. The signal perception threshold allows the presence of subthreshold (virtual) signal states. For these states, Boolean algebra of logic ( A = 0/1) is transformed into the "algebraic logic" of probabilities (0 ≤ a ≤ 1). The similarity and difference of virtual states of macroand microsignals are elucidated. "Real" and "quantum" information for computers is considered briefly. The maximum information transmission rate is estimated based on physical constants.

Using isomorphic problems to learn introductory physics

NASA Astrophysics Data System (ADS)

Lin, Shih-Yin; Singh, Chandralekha

2011-12-01

In this study, we examine introductory physics students’ ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the recitation in which they had to first learn from a solved problem provided and take advantage of what they learned from it to solve another problem (which we call the quiz problem) which was isomorphic. Previous research suggests that the multiple-concept quiz problem is challenging for introductory students. Students in different recitation classes received different interventions in order to help them discern and exploit the underlying similarities of the isomorphic solved and quiz problems. We also conducted think-aloud interviews with four introductory students in order to understand in depth the difficulties they had and explore strategies to provide better scaffolding. We found that most students were able to learn from the solved problem to some extent with the scaffolding provided and invoke the relevant principles in the quiz problem. However, they were not necessarily able to apply the principles correctly. Research suggests that more scaffolding is needed to help students in applying these principles appropriately. We outline a few possible strategies for future investigation.

Math Remediation for the College Bound: How Teachers Can Close the Gap, from the Basics through Algebra

ERIC Educational Resources Information Center

Khatri, Daryao

2011-01-01

Algebra is the language that must be mastered for any course that uses math because it is the gateway for entry into any science, technology, engineering, and mathematics (STEM) discipline. This book fosters mastery of critical math and algebraic concepts and skills essential to all of the STEM disciplines and some of the social sciences. This…

Individual and Collective Analyses of the Genesis of Student Reasoning Regarding the Invertible Matrix Theorem in Linear Algebra

ERIC Educational Resources Information Center

Wawro, Megan Jean

2011-01-01

In this study, I considered the development of mathematical meaning related to the Invertible Matrix Theorem (IMT) for both a classroom community and an individual student over time. In this particular linear algebra course, the IMT was a core theorem in that it connected many concepts fundamental to linear algebra through the notion of…

Redesigning the Quantum Mechanics Curriculum to Incorporate Problem Solving Using a Computer Algebra System

NASA Astrophysics Data System (ADS)

Roussel, Marc R.

1999-10-01

One of the traditional obstacles to learning quantum mechanics is the relatively high level of mathematical proficiency required to solve even routine problems. Modern computer algebra systems are now sufficiently reliable that they can be used as mathematical assistants to alleviate this difficulty. In the quantum mechanics course at the University of Lethbridge, the traditional three lecture hours per week have been replaced by two lecture hours and a one-hour computer-aided problem solving session using a computer algebra system (Maple). While this somewhat reduces the number of topics that can be tackled during the term, students have a better opportunity to familiarize themselves with the underlying theory with this course design. Maple is also available to students during examinations. The use of a computer algebra system expands the class of feasible problems during a time-limited exercise such as a midterm or final examination. A modern computer algebra system is a complex piece of software, so some time needs to be devoted to teaching the students its proper use. However, the advantages to the teaching of quantum mechanics appear to outweigh the disadvantages.

Curricular Reforms That Improve Students' Attitudes and Problem-Solving Performance

ERIC Educational Resources Information Center

Teodorescu, Raluca E.; Bennhold, Cornelius; Feldman, Gerald; Medsker, Larry

2014-01-01

We present the most recent steps undertaken to reform the introductory algebra-based course at The George Washington University. The reform sought to help students improve their problem-solving performance. Our pedagogy relies on didactic constructs such as the" GW-ACCESS problem-solving protocol," "instructional sequences" and…

Districts Add Web Courses for Summer

ERIC Educational Resources Information Center

Borja, Rhea R.

2005-01-01

More and more school districts, as well as for-profit companies and nonprofit organizations, are offering Internet-based summer classes in core subjects, such as algebra and reading, and electives such as creative writing. In this article, the author discusses the growth of enrollment in online education for summer. The logistical ease of…

Video Based Developmental Mathematics Learning System For Community College Students.

ERIC Educational Resources Information Center

Gormley, Tyrone D.

The University of Maine at Augusta uses an individualized video-taped mathematics instructional system to eliminate students' math weaknesses before they attempt college math. The course, "1 Mth Developmental Mathematics," is part of the Educational Assistance Program and teaches basic skills and concepts of arithmetic and algebra. The…

Physics gains attraction?

NASA Astrophysics Data System (ADS)

2000-01-01

A recent report from the American Institute of Physics has indicated that high school enrolments in physics in the USA have reached their highest level since World War II. Figures for the last decade show an increase in the proportion of high school students taking physics from 20 to 28% (800Â 000 students now), according to Physics Today (October 1999, p 68). The report, Maintaining Momentum: High School Physics for a New Millennium , was based on a 1997 survey of high school physics teachers, the fourth such since the mid-1980s. One conclusion drawn by the report's authors was that a broader range of physics courses is now offered, with increased popularity of `conceptual' physics courses using little algebra or trigonometry over the last ten years. The proportion of students with the strongest maths abilities now taking advanced placement or second-year physics has doubled since 1987. In addition the physics appeal has been noted among high school girls, where the percentage taking physics has risen from 39 to 47% in the ten years to 1997. These female students do not, however, seem to extend their studies into advanced placements or even into teaching physics (women constitute just a quarter of high school teachers of the subject). Sadly the good news is outweighed by the fact that physics still registers the lowest enrolments of all the high school sciences - about half those in chemistry for example. Indeed only around 1% of high school students have taken two years of physics before they graduate, which represents a much lower proportion than in many European and Asian countries. The full report can be viewed at the AIP's statistics division's homepage: www.aip.org/statistics/trends/hstrends.htm whilst summaries of the document are available free from the AIP, Education and Employment Statistics Division, One Physics Ellipse, College Park, MD 20740, USA.

Applications of a Sequence of Points in Teaching Linear Algebra, Numerical Methods and Discrete Mathematics

ERIC Educational Resources Information Center

Shi, Yixun

2009-01-01

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…

Inquiry experiences as a lecture supplement for preservice elementary teachers and general education students

NASA Astrophysics Data System (ADS)

Marshall, Jill A.; Dorward, James T.

2000-07-01

The study reported here was designed to substantiate the findings of previous research on the use of inquiry-based laboratory activities in introductory college physics courses. The authors sought to determine whether limited use of inquiry activities as a supplement to a traditional lecture and demonstration curriculum would improve student achievement in introductory classes for preservice teachers and general education students. Achievement was measured by responses to problems designed to test conceptual understanding as well as overall course grades. We analyzed the effect on selected student outcome measures in a preliminary study in which some students engaged in inquiry activities and others did not, and interviewed students about their perceptions of the inquiry activities. In the preliminary study, preservice elementary teachers and female students showed significantly higher achievement after engaging such activities, but only on exam questions relating directly to the material covered in the exercises. In a second study we used a common exam problem to compare the performance of students who had engaged in a revised version of the inquiry activities with the performance of students in algebra and calculus-based classes. The students who had engaged in inquiry investigations significantly outperformed the other students.

From Earth Algebra to Earth Math: An Expansion and Dissemination of the Methods of Earth Algebra [and] Proceedings, Earth Math Conference (Kennesaw, Georgia, April 19-20, 1996).

ERIC Educational Resources Information Center

Zumoff, Nancy; Schaufele, Christopher

This final report and appended conference proceedings describe activities of the Earth Math project, a 3-year effort at Kennesaw State University (Georgia) to broaden and disseminate the concept of Earth Algebra to precalculus and mathematics education courses. Major outcomes of the project were the draft of a precalculus textbook now being…

What Do the California Standards Test Results Reveal about the Movement toward Eighth-Grade Algebra for All?

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…

Trends in Algebra II Completion and Failure Rates for Students Entering Texas Public High Schools. REL 2018-289

ERIC Educational Resources Information Center

Stoker, Ginger; Mellor, Lynn; Sullivan, Kate

2018-01-01

This study examines Algebra II completion and failure rates for students entering Texas public high schools from 2007/08 through 2014/15. This period spans the time when Texas students, beginning with the 2007/08 grade 9 cohort, were required to take four courses each in English, math (including Algebra II), science, and social studies (called the…

Numerical Problem Solving Using Mathcad in Undergraduate Reaction Engineering

ERIC Educational Resources Information Center

Parulekar, Satish J.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

A Nonlinear, Multiinput, Multioutput Process Control Laboratory Experiment

ERIC Educational Resources Information Center

Young, Brent R.; van der Lee, James H.; Svrcek, William Y.

2006-01-01

Experience in using a user-friendly software, Mathcad, in the undergraduate chemical reaction engineering course is discussed. Example problems considered for illustration deal with simultaneous solution of linear algebraic equations (kinetic parameter estimation), nonlinear algebraic equations (equilibrium calculations for multiple reactions and…

Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers

ERIC Educational Resources Information Center

Evans, Brian R.

2012-01-01

It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…

Teaching Students to Formulate Questions

ERIC Educational Resources Information Center

Jensen-Vallin, Jacqueline

2017-01-01

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

Independent Study Workbooks for Proofs in Group Theory

ERIC Educational Resources Information Center

Alcock, Lara; Brown, Gavin; Dunning, Clare

2015-01-01

This paper describes a small-scale research project based on workbooks designed to support independent study of proofs in a first course on abstract algebra. We discuss the lecturers' aims in designing the workbooks, and set these against a background of research on students' learning of group theory and on epistemological beliefs and study habits…

An Inquiry-Based Quantitative Reasoning Course for Business Students

ERIC Educational Resources Information Center

Piercey, Victor; Militzer, Erin

2017-01-01

Quantitative Reasoning for Business is a two-semester sequence that serves as an alternative to elementary and intermediate algebra for first-year business students with weak mathematical preparation. Students who take the sequence have been retained at a higher rate and demonstrated a larger reduction in math anxiety than those who take the…

Original Recipes for Matrix Multiplication

ERIC Educational Resources Information Center

Hallman-Thrasher, Allyson; Litchfield, Erin T.; Dael, Kevin E.

2016-01-01

Matrices occupy an awkward spot in a typical algebra 2 textbook: sandwiched between solving linear systems and solving quadratics. Even teachers who do not base their course timeline and pacing on the class textbook may find a disconnect between how matrices are taught (procedurally) and how other topics are taught (conceptually or with real-world…

A Study of the Effectiveness of the Louisiana Algebra I Online Course

ERIC Educational Resources Information Center

O'Dwyer, Laura M.; Carey, Rebecca; Kleiman, Glenn

2007-01-01

Student enrollment in K-12 online learning programs showed a tenfold expansion in the years between 2002 and 2005. Despite increased implementation to fulfill critical local needs, there is very little evidence-based research available to inform education leaders' decisions relating to these initiatives. To address the important question of…

The Effectiveness of Alternative Certification Teachers versus Traditionally Trained Teachers in Three School Districts in Texas on Hispanic Students' Scores in 9th Grade Algebra I: What Leaders Should Know

ERIC Educational Resources Information Center

Trevino, Anysia R.

2013-01-01

The purpose of this quantitative study is to measure the effectiveness of alternative certification teachers versus traditionally trained teachers of 9th grade Hispanic students enrolled in Algebra I. The dependent variable, teacher effectiveness, will be measured by the students' raw score on the Texas Algebra I End Of Course (EOC) Assessment.…

Investigating the use of mastery-style online homework exercises in introductory algebra-based mechanics in a controlled clinical study

NASA Astrophysics Data System (ADS)

Evans, William R.; Selen, Mats A.

2017-12-01

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs traditional-style homework with students in both algebra-based and calculus-based introductory mechanics. Results indicate a benefit from mastery-style over traditional-style homework, principally for weaker students who are less familiar with the material being covered and on questions that are nearer transfer to the study materials.

Case Study Projects for College Mathematics Courses Based on a Particular Function of Two Variables

ERIC Educational Resources Information Center

Shi, Y.

2007-01-01

Based on a sequence of number pairs, a recent paper (Mauch, E. and Shi, Y., 2005, Using a sequence of number pairs as an example in teaching mathematics, "Mathematics and Computer Education," 39(3), 198-205) presented some interesting examples that can be used in teaching high school and college mathematics classes such as algebra, geometry,…

The ALARM Experiment

ERIC Educational Resources Information Center

Gerhardt, Ira

2015-01-01

An experiment was conducted over three recent semesters of an introductory calculus course to test whether it was possible to quantify the effect that difficulty with basic algebraic and arithmetic computation had on individual performance. Points lost during the term were classified as being due to either algebraic and arithmetic mistakes…

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…

Targeting Summer Credit Recovery

ERIC Educational Resources Information Center

Eno, Jared; Heppen, Jessica

2014-01-01

Algebra is considered a key gatekeeper for higher-level mathematics course-taking in high school and for college enrollment (Adelman, 2006; Gamoran & Hannigan, 2000). Yet, algebra pass rates are consistently low in many places (Higgins, 2008; Ham & Walker, 1999; Helfand, 2006), including Chicago Public Schools (CPS). This is of particular…

Developing Compressed Beginning and Intermediate Algebra Courses

ERIC Educational Resources Information Center

Walker, Sylvia E.

2017-01-01

The purpose of this project was two-fold. First, it would provide an opportunity for students to complete the developmental math course sequence more quickly, thereby enabling students to proceed to a college-level mathematics course sooner. To accomplish this, the classroom was designed with computer-assisted homework courses that blended…

Math 3310--Technical Mathematics I. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for a college pre-calculus designed as the first course in a two-semester sequence for students in a Bachelor of Technology program. The course emphasizes engineering technology applications and verbal problems. Topics include a review of elementary algebra; factoring…

Algebra and topology for applications to physics

NASA Technical Reports Server (NTRS)

Rozhkov, S. S.

1987-01-01

The principal concepts of algebra and topology are examined with emphasis on applications to physics. In particular, attention is given to sets and mapping; topological spaces and continuous mapping; manifolds; and topological groups and Lie groups. The discussion also covers the tangential spaces of the differential manifolds, including Lie algebras, vector fields, and differential forms, properties of differential forms, mapping of tangential spaces, and integration of differential forms.

Quantitative critical thinking: Student activities using Bayesian updating

NASA Astrophysics Data System (ADS)

Warren, Aaron R.

2018-05-01

One of the central roles of physics education is the development of students' ability to evaluate proposed hypotheses and models. This ability is important not just for students' understanding of physics but also to prepare students for future learning beyond physics. In particular, it is often hoped that students will better understand the manner in which physicists leverage the availability of prior knowledge to guide and constrain the construction of new knowledge. Here, we discuss how the use of Bayes' Theorem to update the estimated likelihood of hypotheses and models can help achieve these educational goals through its integration with evaluative activities that use hypothetico-deductive reasoning. Several types of classroom and laboratory activities are presented that engage students in the practice of Bayesian likelihood updating on the basis of either consistency with experimental data or consistency with pre-established principles and models. This approach is sufficiently simple for introductory physics students while offering a robust mechanism to guide relatively sophisticated student reflection concerning models, hypotheses, and problem-solutions. A quasi-experimental study utilizing algebra-based introductory courses is presented to assess the impact of these activities on student epistemological development. The results indicate gains on the Epistemological Beliefs Assessment for Physical Science (EBAPS) at a minimal cost of class-time.

The Quantitative Reasoning for College Science (QuaRCS) Assessment in non-Astro 101 Courses II

NASA Astrophysics Data System (ADS)

Kirkman, Thomas W.; Jensen, Ellen

2017-06-01

The Quantitative Reasoning for College Science (QuaRCS) Assessment[1] aims to measure the pre-algebra mathematical skills that are often part of "general education" science courses like Astro 101. In four majors STEM classes, we report comparisons between QuaRCS metrics, ACT math, GPAO, and the course grade. In three of four classes QuaRCS QR score and ACT math were statistically significantly correlated (with r˜.6), however in the fourth course —a senior-level microbiology course— there was no statistically significantly correlation (in fact, r<0). In all courses —even in courses with seemingly little quantitative content— course grade was statistically significantly correlated to GPAO and QR. A QuaRCS metric aiming to report the students belief in the importance of math in science was seen to grow with the course level. Pre/post QuaRCS testing in Physics courses showed fractional sigma gains in QR, self-estimated math fluency and math importance, but not all of those increases were statistically significant. Using a QuaRCS map relating the questions to skill areas, we found graph reading, percentages, and proportional reasoning to be the most misunderstood skills in all four courses.[1] QuaRCS, Follette, et al.,2015, DOI: http://dx.doi.org/10.5038/1936-4660.8.2.2

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…

A Linear Algebraic Approach to Teaching Interpolation

ERIC Educational Resources Information Center

Tassa, Tamir

2007-01-01

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach…

Teaching Linear Algebra: Proceeding More Efficiently by Staying Comfortably within Z

ERIC Educational Resources Information Center

Beaver, Scott

2015-01-01

For efficiency in a linear algebra course the instructor may wish to avoid the undue arithmetical distractions of rational arithmetic. In this paper we explore how to write fraction-free problems of various types including elimination, matrix inverses, orthogonality, and the (non-normalizing) Gram-Schmidt process.

A Guided Reinvention of Ring, Integral Domain, and Field

ERIC Educational Resources Information Center

Cook, John Paul

2012-01-01

Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by exposing them to structures that form its foundation--it arguably approximates the actual practice of mathematics better than any…

Embodied, Symbolic and Formal Thinking in Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2007-01-01

Students often find their first university linear algebra experience very challenging. While coping with procedural aspects of the subject, solving linear systems and manipulating matrices, they may struggle with crucial conceptual ideas underpinning them, making it very difficult to progress in more advanced courses. This research has sought to…

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

The Simulation of an Oxidation-Reduction Titration Curve with Computer Algebra

ERIC Educational Resources Information Center

Whiteley, Richard V., Jr.

2015-01-01

Although the simulation of an oxidation/reduction titration curve is an important exercise in an undergraduate course in quantitative analysis, that exercise is frequently simplified to accommodate computational limitations. With the use of readily available computer algebra systems, however, such curves for complicated systems can be generated…

Systems with outer constraints. Gupta-Bleuler electromagnetism as an algebraic field theory

NASA Astrophysics Data System (ADS)

Grundling, Hendrik

1988-03-01

Since there are some important systems which have constraints not contained in their field algebras, we develop here in a C*-context the algebraic structures of these. The constraints are defined as a group G acting as outer automorphisms on the field algebra ℱ, α: G ↦ Aut ℱ, α G ⊄ Inn ℱ, and we find that the selection of G-invariant states on ℱ is the same as the selection of states ω on M( G M(Gmathop × limits_α F) ℱ) by ω( U g)=1∨ g∈ G, where U g ∈ M ( G M(Gmathop × limits_α F) ℱ)/ℱ are the canonical elements implementing α g . These states are taken as the physical states, and this specifies the resulting algebraic structure of the physics in M( G M(Gmathop × limits_α F) ℱ), and in particular the maximal constraint free physical algebra ℛ. A nontriviality condition is given for ℛ to exist, and we extend the notion of a crossed product to deal with a situation where G is not locally compact. This is necessary to deal with the field theoretical aspect of the constraints. Next the C*-algebra of the CCR is employed to define the abstract algebraic structure of Gupta-Bleuler electromagnetism in the present framework. The indefinite inner product representation structure is obtained, and this puts Gupta-Bleuler electromagnetism on a rigorous footing. Finally, as a bonus, we find that the algebraic structures just set up, provide a blueprint for constructive quadratic algebraic field theory.

Teachers' Beliefs about Improving Transfer of Algebraic Skills from Mathematics into Physics in Senior Pre-University Education

ERIC Educational Resources Information Center

Tursucu, Süleyman; Spandaw, Jeroen; Flipse, Steven; de Vries, Marc J.

2017-01-01

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers' beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using a…

Triangles with Integer Side Lengths and Rational Internal Radius P and External Radius R

ERIC Educational Resources Information Center

Zelator, Konstantine

2005-01-01

This paper is written on a level accessible to college/university students of mathematics who are taking second-year, algebra based, mathematics courses beyond calculus I. This article combines material from geometry, trigonometry, and number theory. This integration of various techniques is an excellent experience for the serious student. The…

Apprehending Mathematical Structure: A Case Study of Coming to Understand a Commutative Ring

ERIC Educational Resources Information Center

Simpson, Adrian; Stehlikova, Nada

2006-01-01

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

Using Toulmin Analysis to Analyse an Instructor's Proof Presentation in Abstract Algebra

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy

2014-01-01

This paper provides a method for analysing undergraduate teaching of proof-based courses using Toulmin's model (1969) of argumentation. It presents a case study of one instructor's presentation of proofs. The analysis shows that the instructor presents different levels of detail in different proofs; thus, the students have an inconsistent set of…

Development of a Diagnostic and Remedial Learning System Based on an Enhanced Concept--Effect Model

ERIC Educational Resources Information Center

Panjaburees, Patcharin; Triampo, Wannapong; Hwang, Gwo-Jen; Chuedoung, Meechoke; Triampo, Darapond

2013-01-01

With the rapid advances in computer technology during recent years, researchers have demonstrated the pivotal influences of computer-assisted diagnostic systems on student learning performance improvement. This research aims to develop a Diagnostic and Remedial Learning System (DRLS) for an algebra course in a Thai lower secondary school context…

Surveying Turkish high school and university students' attitudes and approaches to physics problem solving

NASA Astrophysics Data System (ADS)

Balta, Nuri; Mason, Andrew J.; Singh, Chandralekha

2016-06-01

Students' attitudes and approaches to physics problem solving can impact how well they learn physics and how successful they are in solving physics problems. Prior research in the U.S. using a validated Attitude and Approaches to Problem Solving (AAPS) survey suggests that there are major differences between students in introductory physics and astronomy courses and physics experts in terms of their attitudes and approaches to physics problem solving. Here we discuss the validation, administration, and analysis of data for the Turkish version of the AAPS survey for high school and university students in Turkey. After the validation and administration of the Turkish version of the survey, the analysis of the data was conducted by grouping the data by grade level, school type, and gender. While there are no statistically significant differences between the averages of various groups on the survey, overall, the university students in Turkey were more expertlike than vocational high school students. On an item by item basis, there are statistically differences between the averages of the groups on many items. For example, on average, the university students demonstrated less expertlike attitudes about the role of equations and formulas in problem solving, in solving difficult problems, and in knowing when the solution is not correct, whereas they displayed more expertlike attitudes and approaches on items related to metacognition in physics problem solving. A principal component analysis on the data yields item clusters into which the student responses on various survey items can be grouped. A comparison of the responses of the Turkish and American university students enrolled in algebra-based introductory physics courses shows that on more than half of the items, the responses of these two groups were statistically significantly different, with the U.S. students on average responding to the items in a more expertlike manner.

Using Group Explorer in teaching abstract algebra

NASA Astrophysics Data System (ADS)

Schubert, Claus; Gfeller, Mary; Donohue, Christopher

2013-04-01

This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in abstract algebra. A total of 26 participants in an undergraduate course studying group theory were surveyed regarding their experiences using Group Explorer. Findings indicate that all participants believed that the software was beneficial to their learning and described their attitudes regarding the software in terms of using the technology and its helpfulness in learning concepts. A multiple regression analysis reveals that representational fluency of concepts with the software correlated significantly with participants' understanding of group concepts yet, participants' attitudes about Group Explorer and technology in general were not significant factors.

An Algebra-Based Introductory Computational Neuroscience Course with Lab.

PubMed

Fink, Christian G

2017-01-01

A course in computational neuroscience has been developed at Ohio Wesleyan University which requires no previous experience with calculus or computer programming, and which exposes students to theoretical models of neural information processing and techniques for analyzing neural data. The exploration of theoretical models of neural processes is conducted in the classroom portion of the course, while data analysis techniques are covered in lab. Students learn to program in MATLAB and are offered the opportunity to conclude the course with a final project in which they explore a topic of their choice within computational neuroscience. Results from a questionnaire administered at the beginning and end of the course indicate significant gains in student facility with core concepts in computational neuroscience, as well as with analysis techniques applied to neural data.

Balancing the Equation: The Effect of Alternate Course Formats on Retention and Performance of Adult Elementary Algebra Learners

ERIC Educational Resources Information Center

Gilbert, Jeremiah A.

2010-01-01

With the rise of nontraditional students at the college level, nontraditional course formats have been added to address student need. These alternate course formats include online, weekend, short-term, and computer assisted instruction courses. The purpose of this study was to look at the effect of these alternate course formats on student…

Algebraic geometry and Bethe ansatz. Part I. The quotient ring for BAE

NASA Astrophysics Data System (ADS)

Jiang, Yunfeng; Zhang, Yang

2018-03-01

In this paper and upcoming ones, we initiate a systematic study of Bethe ansatz equations for integrable models by modern computational algebraic geometry. We show that algebraic geometry provides a natural mathematical language and powerful tools for understanding the structure of solution space of Bethe ansatz equations. In particular, we find novel efficient methods to count the number of solutions of Bethe ansatz equations based on Gröbner basis and quotient ring. We also develop analytical approach based on companion matrix to perform the sum of on-shell quantities over all physical solutions without solving Bethe ansatz equations explicitly. To demonstrate the power of our method, we revisit the completeness problem of Bethe ansatz of Heisenberg spin chain, and calculate the sum rules of OPE coefficients in planar N=4 super-Yang-Mills theory.

Algebra I. Curriculum Guide. Bulletin 1580. Revised 1984.

ERIC Educational Resources Information Center

Louisiana State Dept. of Education, Baton Rouge. Div. of Academic Programs.

This guide, developed by a statewide committee in response to the legislature's mandate to develop statewide curriculum standards for required subjects, presents the content that should be taught in Algebra I. It was piloted by teachers in representative school systems and subsequently revised. Six goals for the course are listed, followed by a…

The Role of Technology in Increasing Preservice Teachers' Anticipation of Students' Thinking in Algebra

ERIC Educational Resources Information Center

Rhine, Steve; Harrington, Rachel; Olszewski, Brandon

2015-01-01

The collision between a growing, inexperienced teaching force and students' algebra struggles should be one of great concern. A collaboration of four public and private universities in Oregon restructured mathematics methods courses for preservice teacher candidates by using the affordances of technology to counteract this loss of experience. Over…

Math/Measurement Literacy for Upgrading Skills of Industrial Hourly Workers. Math Manual.

ERIC Educational Resources Information Center

McMahon, Joan L.

This manual contains materials for a numeracy course for adult industrial workers. In addition to assessment tests, seven units are provided. Unit topics are whole numbers; fractions; decimals; percents, median, and range; measurement and signed numbers; ratio/proportion and introduction to algebra; and computer literacy using algebra software.…

Computer Algebra Systems in Education Newsletter[s].

ERIC Educational Resources Information Center

Computer Algebra Systems in Education Newsletter, 1990

1990-01-01

Computer Algebra Systems (CAS) are computer systems for the exact solution of problems in symbolic form. The newspaper is designed to serve as a conduit for information and ideas on the use of CAS in education, especially in lower division college and university courses. Articles included are about CAS programs in several colleges, experiences…

Principal Component Analysis: Resources for an Essential Application of Linear Algebra

ERIC Educational Resources Information Center

Pankavich, Stephen; Swanson, Rebecca

2015-01-01

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and extension of the Spectral Theorem and is commonly used within a variety of fields, including statistics,…

University of Chicago School Mathematics Project 6-12 Curriculum. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2011

2011-01-01

The "University of Chicago School Mathematics Project ("UCSMP") 6-12 Curriculum" is a series of yearlong courses--(1) Transition Mathematics; (2) Algebra; (3) Geometry; (4) Advanced Algebra; (5) Functions, Statistics, and Trigonometry; and (6) Precalculus and Discrete Mathematics--emphasizing problem solving, real-world applications, and the use…

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…

Student Connections of Linear Algebra Concepts: An Analysis of Concept Maps

ERIC Educational Resources Information Center

Lapp, Douglas A.; Nyman, Melvin A.; Berry, John S.

2010-01-01

This article examines the connections of linear algebra concepts in a first course at the undergraduate level. The theoretical underpinnings of this study are grounded in the constructivist perspective (including social constructivism), Vernaud's theory of conceptual fields and Pirie and Kieren's model for the growth of mathematical understanding.…

Advanced Linear Algebra: A Call for the Early Introduction of Complex Numbers

ERIC Educational Resources Information Center

Garcia, Stephan Ramon

2017-01-01

A second course in linear algebra that goes beyond the traditional lower-level curriculum is increasingly important for students of the mathematical sciences. Although many applications involve only real numbers, a solid understanding of complex arithmetic often sheds significant light. Many instructors are unaware of the opportunities afforded by…

A Study of the Use of a Handheld Computer Algebra System in Discrete Mathematics

ERIC Educational Resources Information Center

Powers, Robert A.; Allison, Dean E.; Grassl, Richard M.

2005-01-01

This study investigated the impact of the TI-92 handheld Computer Algebra System (CAS) on student achievement in a discrete mathematics course. Specifically, the researchers examined the differences between a CAS section and a control section of discrete mathematics on students' in-class examinations. Additionally, they analysed student approaches…

Lack of Set Theory Relevant Prerequisite Knowledge

ERIC Educational Resources Information Center

Dogan-Dunlap, Hamide

2006-01-01

Many students struggle with college mathematics topics due to a lack of mastery of prerequisite knowledge. Set theory language is one such prerequisite for linear algebra courses. Many students' mistakes on linear algebra questions reveal a lack of mastery of set theory knowledge. This paper reports the findings of a qualitative analysis of a…

A Framework for Mathematical Thinking: The Case of Linear Algebra

ERIC Educational Resources Information Center

Stewart, Sepideh; Thomas, Michael O. J.

2009-01-01

Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…

Definitions Are Important: The Case of Linear Algebra

ERIC Educational Resources Information Center

Berman, Abraham; Shvartsman, Ludmila

2016-01-01

In this paper we describe an experiment in a linear algebra course. The aim of the experiment was to promote the students' understanding of the studied concepts focusing on their definitions. It seems to be a given that students should understand concepts' definitions before working substantially with them. Unfortunately, in many cases they do…

Using Group Explorer in Teaching Abstract Algebra

ERIC Educational Resources Information Center

Schubert, Claus; Gfeller, Mary; Donohue, Christopher

2013-01-01

This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in…

Proof in Algebra: Reasoning beyond Examples

ERIC Educational Resources Information Center

Otten, Samuel; Herbel-Eisenmann, Beth A.; Males, Lorraine M.

2010-01-01

The purpose of this article is to provide an image of what proof could look like in beginning algebra, a course that nearly every secondary school student encounters. The authors present an actual classroom vignette in which a rich opportunity for student reasoning arose. After analyzing the proof schemes at play, the authors provide a…

Student learning and perceptions in a flipped linear algebra course

NASA Astrophysics Data System (ADS)

Love, Betty; Hodge, Angie; Grandgenett, Neal; Swift, Andrew W.

2014-04-01

The traditional lecture style of teaching has long been the norm in college science, technology, engineering, and mathematics (STEM) courses, but an innovative teaching model, facilitated by recent advances in technology, is gaining popularity across college campuses. This new model inverts or 'flips' the usual classroom paradigm, in that students learn initial course concepts outside of the classroom, while class time is reserved for more active problem-based learning and practice activities. While the flipped classroom model shows promise for improving STEM learning and increasing student interest in STEM fields, discussions to date of the model and its impact are more anecdotal than data driven - very little research has been undertaken to rigorously assess the potential effects on student learning that can result from the flipped classroom environment. This study involved 55 students in 2 sections of an applied linear algebra course, using the traditional lecture format in one section and the flipped classroom model in another. In the latter, students were expected to prepare for the class in some way, such as watching screencasts prepared by the instructor, or reading the textbook or the instructor's notes. Student content understanding and course perceptions were examined. Content understanding was measured by the performance on course exams, and students in the flipped classroom environment had a more significant increase between the sequential exams compared to the students in the traditional lecture section, while performing similarly in the final exam. Course perceptions were represented by an end-of-semester survey that indicated that the flipped classroom students were very positive about their experience in the course, and particularly appreciated the student collaboration and instructional video components.

Measurement theory in local quantum physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Okamura, Kazuya, E-mail: okamura@math.cm.is.nagoya-u.ac.jp; Ozawa, Masanao, E-mail: ozawa@is.nagoya-u.ac.jp

In this paper, we aim to establish foundations of measurement theory in local quantum physics. For this purpose, we discuss a representation theory of completely positive (CP) instruments on arbitrary von Neumann algebras. We introduce a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with the NEP and statistical equivalence classes of measuring processes. We show that every CP instrument on an atomic von Neumann algebra has the NEP, extending the well-known result for type I factors. Moreover, we show that every CP instrument on an injective von Neumann algebra is approximated bymore » CP instruments with the NEP. The concept of posterior states is also discussed to show that the NEP is equivalent to the existence of a strongly measurable family of posterior states for every normal state. Two examples of CP instruments without the NEP are obtained from this result. It is thus concluded that in local quantum physics not every CP instrument represents a measuring process, but in most of physically relevant cases every CP instrument can be realized by a measuring process within arbitrary error limits, as every approximately finite dimensional von Neumann algebra on a separable Hilbert space is injective. To conclude the paper, the concept of local measurement in algebraic quantum field theory is examined in our framework. In the setting of the Doplicher-Haag-Roberts and Doplicher-Roberts theory describing local excitations, we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a CP instrument with the NEP, provided that the split property holds for the net of local algebras.« less

Math 3011--College Algebra and Trigonometry. Course Outline.

ERIC Educational Resources Information Center

New York Inst. of Tech., Old Westbury.

This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…

Numerical algebraic geometry: a new perspective on gauge and string theories

NASA Astrophysics Data System (ADS)

Mehta, Dhagash; He, Yang-Hui; Hauensteine, Jonathan D.

2012-07-01

There is a rich interplay between algebraic geometry and string and gauge theories which has been recently aided immensely by advances in computational algebra. However, symbolic (Gröbner) methods are severely limited by algorithmic issues such as exponential space complexity and being highly sequential. In this paper, we introduce a novel paradigm of numerical algebraic geometry which in a plethora of situations overcomes these shortcomings. The so-called `embarrassing parallelizability' allows us to solve many problems and extract physical information which elude symbolic methods. We describe the method and then use it to solve various problems arising from physics which could not be otherwise solved.

Course Placement Influences on Student Motivation

ERIC Educational Resources Information Center

Simzar, Rahila; Domina, Thurston; Conley, AnneMarie; Tran, Cathy

2013-01-01

A national initiative encourages STEM careers to prepare students to succeed in an increasingly competitive economy (National Research Council, 2011). The STEM pipeline is dependent on students' mathematics course-taking trajectories, which are determined once a student enrolls in his/her first Algebra course. Despite efforts to increase access to…

College Preparatory Curriculum for All: Academic Consequences of Requiring Algebra and English I for Ninth Graders in Chicago

ERIC Educational Resources Information Center

Allensworth, Elaine; Nomi, Takako; Montgomery, Nicholas; Lee, Valerie E.

2009-01-01

There is a national movement to universalize the high school curriculum so that all students graduate prepared for college. The present work evaluates a policy in Chicago that ended remedial classes and mandated college preparatory course work for all students. Based on an interrupted time-series cohort design with multiple comparisons, this study…

Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities

NASA Astrophysics Data System (ADS)

Spill, Fabian

In the following paper, which is based on the author's PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular, in relation with S-matrices. One of the main themes in this work is that, after a careful study of the mathematics of the symmetry algebras one finds that in an integrable model, one can directly reconstruct S-matrices just from the algebra. It has been known for a long time that S-matrices in integrable models are fixed by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation, crossing and unitarity, which constrain the S-matrix in integrable models, are often taken to be separate, independent properties of the S-matrix. Here, we construct scattering matrices purely from the Yangian, showing that the Yangian is the right algebraic object to unify all required symmetries of many integrable models. In particular, we reconstruct the S-matrix of the principal chiral field, and, up to a CDD factor, of other integrable field theories with 𝔰𝔲(n) symmetry. Furthermore, we study the AdS/CFT correspondence, which is also believed to be integrable in the planar limit. We reconstruct the S-matrices at weak and at strong coupling from the Yangian or its classical limit. We give a pedagogical introduction into the subject, presenting a unified perspective of Yangians and their applications in physics. This paper should hence be accessible to mathematicians who would like to explore the application of algebraic objects to physics as well as to physicists interested in a deeper understanding of the mathematical origin of physical quantities.

Examining the Conceptual Organization of Students in an Integrated Algebra and Physical Science Class.

ERIC Educational Resources Information Center

Westbrook, Susan L.

1998-01-01

Compares the conceptual organization of students in an integrated algebra and physical science class (SAM 9) with that of students in a discipline-specific physical science class (PSO). Analysis of students' concept maps indicates that the SAM9 students used a greater number of procedural linkages to connect mathematics and science concepts than…

The Effect of Assessment Style on Student Epistemologies in Introductory Physics

ERIC Educational Resources Information Center

Bowen, Mark Ryan

2011-01-01

Epistemologies were measured across two separate lecture sections of introductory algebra-based physics at UC Davis. Remarkable differences in epistemologies, as measured by the MPEX II survey were noted with one section's students (section A) showing significantly better gains in almost all epistemological categories than the other (section…

A note on derivations of Murray-von Neumann algebras.

PubMed

Kadison, Richard V; Liu, Zhe

2014-02-11

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray-von Neumann algebras. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements.

Relating Understanding of Inverse and Identity to Engagement in Proof in Abstract Algebra

ERIC Educational Resources Information Center

Plaxco, David

2015-01-01

In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of…

The Effect of Graphing Calculators on Student Achievement in College Algebra and Pre-Calculus Mathematics Courses

ERIC Educational Resources Information Center

Hatem, Neil

2010-01-01

This study investigates the relationship between the use of graphing calculators employed as Type II technology and student achievement, as determined by assessing students' problem solving skills associated with the concept of function, at the college algebra and pre-calculus level. In addition, this study explores the integration of graphing…

Discovering Theorems in Abstract Algebra Using the Software "GAP"

ERIC Educational Resources Information Center

Blyth, Russell D.; Rainbolt, Julianne G.

2010-01-01

A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…

The Effect of the Math Emporium Instructional Method on Students' Performance in College Algebra

ERIC Educational Resources Information Center

Cousins-Cooper, Kathy; Staley, Katrina N.; Kim, Seongtae; Luke, Nicholas S.

2017-01-01

This study aims to investigate the effectiveness of the Emporium instructional method in a course of college algebra and trigonometry by comparing to the traditional lecture method. The math emporium method is a nontraditional instructional method of learning math that has been implemented at several universities with much success and has been…

Updating Algebra for All?: Evidence of a Middle-Grades Math Acceleration Policy

ERIC Educational Resources Information Center

Dougherty, Shaun M.; Goodman, Joshua; Hill, Darryl; Litke, Erica; Page, Lindsay

2014-01-01

The Wake County Public School System (WCPSS) in North Carolina recently addressed the issue of advancement in and equitable access to advanced mathematics. Under a recent policy, WCPSS uses a SAS-generated predicted probabilities of students' success in obtaining a passing score on the NC Algebra I End-of-Course (EOC) exam, to determine…

Using a Square to Complete the Algebra Student: Exploring Algebraic and Geometric Connections in the Quadratic Formula

ERIC Educational Resources Information Center

Yarema, Connie H.; Hendricks, T. David

2010-01-01

Recommendations and standards from various stakeholders in the mathematical preparation of teachers, such as "The Mathematical Education of Teachers" (http://www.cbmsweb.org/MET_Document/chapter_2.htm) and "Beyond Crossroads" (http://beyondcrossroads.amatyc.org/doc/CH6.html), call for courses that emphasize connections within topics in…

Experiences of Adults with Developmental Disability and a Teacher of Mathematics in the Money Club

ERIC Educational Resources Information Center

Rodriguez, Anthony M.

2012-01-01

In my experiences, students with Developmental Disability (DD) are routinely excluded from Algebra and other high-level mathematics courses. People with DD do not have the opportunity to learn Algebra, which may support the understanding and provide purpose for learning money and budgeting skills that, perhaps, could help them avoid financial…

Like Terms: What's in a Name?

ERIC Educational Resources Information Center

de Groot, Cornelis; Boyajian, Meredith

2015-01-01

In introductory algebra and later mathematics courses, students seem to struggle with the concepts of like terms and combining like terms with algebraic expressions. These ideas appear to be unfamiliar to students and do not seem to relate to any mathematics that they have done in the past. In an attempt to link with something that the students do…

Elliptic surface grid generation on minimal and parmetrized surfaces

NASA Technical Reports Server (NTRS)

Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.

1995-01-01

An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.

A note on derivations of Murray–von Neumann algebras

PubMed Central

Kadison, Richard V.; Liu, Zhe

2014-01-01

A Murray–von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray–von Neumann algebras. We show that the “extended derivations” of a Murray–von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray–von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer’s seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements. PMID:24469831

Recalling Prerequisite Material in a Calculus II Course to Improve Student Success

ERIC Educational Resources Information Center

Mokry, Jeanette

2016-01-01

This article discusses preparation assignments used in a Calculus II course that cover material from prerequisite courses. Prior to learning new material, students work on problems outside of class involving concepts from algebra, trigonometry, and Calculus I. These problems are directly built upon in order to answer Calculus II questions,…

Using e-Learning Platforms for Mastery Learning in Developmental Mathematics Courses

ERIC Educational Resources Information Center

Boggs, Stacey; Shore, Mark; Shore, JoAnna

2004-01-01

Many colleges and universities have adopted e-learning platforms to utilize computers as an instructional tool in developmental (i.e., beginning and intermediate algebra) mathematics courses. An e-learning platform is a computer program used to enhance course instruction via computers and the Internet. Allegany College of Maryland is currently…

The Predictive Validity of Coordinate Algebra Common District Assessments on High-Stakes Coordinate Algebra End of Course Assessment

ERIC Educational Resources Information Center

Ainsworth, Jessica Marie

2016-01-01

Formative assessments have been deemed the key to effectively measuring if students have mastered the understanding of curriculum standards. Thus, allowing teachers to use the results to tailor remediation and use other efforts to support mastery of student learning before the end of the school year has positive effects on student achievement.…

The Use of Instructional Animations in a College Algebra Course: Can It Facilitate Learning of Concepts and Skill Development?

ERIC Educational Resources Information Center

Serfaty de Markus, Alicia

2018-01-01

This quasi-treatment study, using a non-equivalent group design, explored how a set of animations related to various concepts in algebra impacted students' ability to learn as measured by changes in quiz and test scores. The concepts that were investigated were addition and subtraction of rational expressions, solving equations involving rational…

Tracking the Success of Pre-College Algebra Workshop Students in Subsequent College Mathematics Classes

ERIC Educational Resources Information Center

Fuller, Edgar; Deshler, Jessica M.; Kuhn, Betsy; Squire, Douglas

2014-01-01

In 2007 the Department of Mathematics at our institution began developing a placement process designed to identify at-risk students entering mathematics courses at the College Algebra and Calculus levels. Major changes in our placement testing process and the resulting interventions for at-risk students were put in place in Fall of 2008. At the…

Studying the Effectiveness of Online Homework for Different Skill Levels in a College Algebra Course

ERIC Educational Resources Information Center

Mathai, Elizabeth; Olsen, Darlene

2013-01-01

A comparison of the performance on the final exam for subpopulations of students in College Algebra was used to assess the effectiveness of online homework. Data was collected for two small groups of students, one with traditional paper homework and the other with online homework. The groups of students were further classified by incoming skill…

A REPORT ON EXPERIMENTATION IN THE TEACHING OF THE FIRST COURSE IN ALGEBRA AT EL CAMINO COLLEGE.

ERIC Educational Resources Information Center

MANSFIELD, HENRY, JR.

AN INITIAL ATTEMPT TO EVALUATE PROGRAMED INSTRUCTIONAL MATERIAL IN ALGEBRA CLASSES LED TO FURTHER EXPERIMENTATION WITH A VARIETY OF PROCEDURES. IN 1964-65, NO SIGNIFICANT DIFFERENCES WERE FOUND IN THE PERCENT OF STUDENTS SUCCEEDING IN PROGRAMED AND CONVENTIONAL CLASSES, THOUGH STUDENTS IN PROGRAMED SECTIONS DID NOT SEEM MOTIVATED TO WORK AT THEIR…

A Method for Using Adjacency Matrices to Analyze the Connections Students Make within and between Concepts: The Case of Linear Algebra

ERIC Educational Resources Information Center

Selinski, Natalie E.; Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle

2014-01-01

The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation…

The Use of Concept Maps to Assess Preservice Teacher Understanding: A Formative Approach in Mathematics Education

ERIC Educational Resources Information Center

Brakoniecki, Aaron; Shah, Fahmil

2017-01-01

The research reported in this article explored the methods by which concept maps served as formative assessment by capturing changes in the ways preservice mathematics teachers represented their understanding of algebra. The participants were enrolled in a course on high school algebra for teachers and created the maps on the first and last day of…

What is special about the group of the standard model?

NASA Astrophysics Data System (ADS)

Nielsen, H. B.; Brene, N.

1989-06-01

The standard model is based on the algebra of U 1×SU 2×SU 3. The systematics of charges of the fundamental fermions seems to suggest the importance of a particular group having this algebra, viz. S(U 2×U 3). This group is distinguished from all other connected compact non semisimple groups with dimensionality up to 12 by a characteristic property: it is very “skew”. By this we mean that the group has relatively few “generalised outer automorphisms”. One may speculate about physical reasons for this fact.

Physics Based University Courses

ERIC Educational Resources Information Center

Beeby, J. L.

1974-01-01

Two physics courses which serve as alternatives to general college courses in physics are outlined: physics with astrophysics and physics with electronics. Details are given of the structure of the courses and third year options are specified. (DT)

"MONSTROUS MOONSHINE" and Physics

NASA Astrophysics Data System (ADS)

Pushkin, A. V.

The report presents some results obtained by the author on the quantum gravitation theory. Algebraic structure of this theory proves to be related to the commutative nonassociative Griess algebra. The theory symmetry is the automorphism group of Griess algebra: "Monster" simple group. Knowledge of the theory symmetry allows to compute observed physical values in the `zero' approximation. The report presents such computed results for values {m_{p}}/{m_{c}} and α, for the latter the `zero' approximation accuracy, controlled by the theory, being one order of magnitude higher than the accuracy of modern measurements.

Metacognitive gimmicks and their use by upper level physics students

NASA Astrophysics Data System (ADS)

White, Gary; Sikorski, Tiffany-Rose; Landay, Justin

2017-01-01

We report on the initial phases of a study of three particular metacognitive gimmicks that upper-level physics students can use as a tool in their problem-solving kit, namely: checking units for consistency, discerning whether limiting cases match physical intuition, and computing numerical values for reasonable-ness. Students in a one semester Griffiths electromagnetism course at a small private urban university campus are asked to respond to explicit prompts that encourage adopting these three methods for checking answers to physics problems, especially those problems for which an algebraic expression is part of the final answer. We explore how, and to what extent, these students adopt these gimmicks, as well as the time development of their use. While the term ``gimmick'' carries with it some pejorative baggage, we feel it describes the essential nature of the pedagogical idea adequately in that it gets attention, is easy for the students to remember, and represents, albeit perhaps in a surface way, some key ideas about which professional physicists care.

Teacher Mindset and the Nature of Feedback Provided to Students in the Pennsylvania Keystone Courses

ERIC Educational Resources Information Center

Prevost, Kimberly Ann Jones

2017-01-01

This study explored the nature of feedback strategies that teachers of Pennsylvania's Keystone courses (Algebra I, biology, and literature) used to prepare their students to meet the minimum proficiency standard on the corresponding Keystone exam, taken at the end of the course. Teachers reported highest usage of the following feedback types:…

Using the Computer Algebra System "Maple" to Generate Research Questions for Pre-Service Teachers in a Capstone Course

ERIC Educational Resources Information Center

Farley, Rosemary Carroll

2013-01-01

At Manhattan College, secondary mathematics education students take a capstone course designed specifically for them. In this course, students revisit important topics in the high school curriculum from a mathematically advanced perspective; incorporating the mathematical knowledge they have attained in their college mathematics classes to an…

Geometric Probability. New Topics for Secondary School Mathematics. Materials and Software.

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, Inc., Reston, VA.

These materials on geometric probability are the first unit in a course being developed by the Mathematics Department at the North Carolina School of Science and Mathematics. This course is designed to prepare high school students who have completed Algebra 2 for the variety of math courses they will encounter in college. Assuming only a knowledge…

A Correlation of Community College Math Readiness and Student Success

NASA Astrophysics Data System (ADS)

Brown, Jayna Nicole

Although traditional college students are more prepared for college-level math based on college admissions tests, little data have been collected on nontraditional adult learners. The purpose of this study was to investigate relationships between math placement tests and community college students' success in math courses and persistence to degree or certificate completion. Guided by Tinto's theory of departure and student retention, the research questions addressed relationships and predictability of math Computer-adaptive Placement Assessment and Support System (COMPASS) test scores and students' performance in math courses, persistence in college, and degree completion. After conducting correlation and regression analyses, no significant relationships were identified between COMPASS Math test scores and students' performance (n = 234) in math courses, persistence in college, or degree completion. However, independent t test and chi-squared analyses of the achievements of college students who tested into Basic Math (n = 138) vs. Introduction to Algebra (n = 96) yielded statistically significant differences in persistence (p = .039), degree completion (p < .001), performance (p = .008), and progress ( p = .001), indicating students who tested into Introduction to Algebra were more successful and persisted more often to degree completion. In order to improve instructional methods for Basic Math courses, a 3-day professional development workshop was developed for math faculty focusing on current, best practices in remedial math instruction. Implications for social change include providing math faculty with the knowledge and skills to develop new instructional methods for remedial math courses. A change in instructional methods may improve community college students' math competencies and degree achievement.

Current algebra, statistical mechanics and quantum models

NASA Astrophysics Data System (ADS)

Vilela Mendes, R.

2017-11-01

Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.

Contractions from grading

NASA Astrophysics Data System (ADS)

Krishnan, Chethan; Raju, Avinash

2018-04-01

We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically via identifying appropriate Zm-gradings (and their generalizations) on the parent algebra. This includes various types of flat space/Carroll limits of finite and infinite dimensional (A)dS algebras, as well as Galilean and Galilean conformal algebras. Our observations can be regarded as providing a natural context for the Grassmann approach of Krishnan et al. [J. High Energy Phys. 2014(3), 36]. We also introduce a related notion, which we call partial grading, that arises naturally in this context.

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hong-Biao, E-mail: zhanghb017@nenu.edu.cn; Lu, Lu

2013-12-15

Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derivedmore » naturally from the polynomial su(1, 1) algebras built by us.« less

Responsibility for proving and defining in abstract algebra class

NASA Astrophysics Data System (ADS)

Fukawa-Connelly, Timothy

2016-07-01

There is considerable variety in inquiry-oriented instruction, but what is common is that students assume roles in mathematical activity that in a traditional, lecture-based class are either assumed by the teacher (or text) or are not visible at all in traditional math classrooms. This paper is a case study of the teaching of an inquiry-based undergraduate abstract algebra course. In particular, gives a theoretical account of the defining and proving processes. The study examines the intellectual responsibility for the processes of defining and proving that the professor devolved to the students. While the professor wanted the students to engage in all aspects of defining and proving, he was only successful at devolving responsibility for certain aspects and much more successful at devolving responsibility for proving than conjecturing or defining. This study suggests that even a well-intentioned instructor may not be able to devolve responsibility to students for some aspects of mathematical practice without using a research-based curriculum or further professional development.

Conditional Independence in Applied Probability.

ERIC Educational Resources Information Center

Pfeiffer, Paul E.

This material assumes the user has the background provided by a good undergraduate course in applied probability. It is felt that introductory courses in calculus, linear algebra, and perhaps some differential equations should provide the requisite experience and proficiency with mathematical concepts, notation, and argument. The document is…

Socorro ISD. Integrated Lesson Plans.

ERIC Educational Resources Information Center

East Texas State Univ., Commerce. Educational Development and Training Center.

This packet contains 29 lesson plans for integrated academic and vocational education courses. Lesson plans for the following courses are included: algebra, health occupations education, English, biology, laboratory mathematics, and health care sciences. Some of the topics covered are as follows: statistics, vital signs, graphing, ethics, special…

Students' confidence in the ability to transfer basic math skills in introductory physics and chemistry courses at a community college

NASA Astrophysics Data System (ADS)

Quinn, Reginald

2013-01-01

The purpose of this study was to examine the confidence levels that community college students have in transferring basic math skills to science classes, as well as any factors that influence their confidence levels. This study was conducted with 196 students at a community college in central Mississippi. The study was conducted during the month of November after all of the students had taken their midterm exams and received midterm grades. The instrument used in this survey was developed and validated by the researcher. The instrument asks the students to rate how confident they were in working out specific math problems and how confident they were in working problems using those specific math skills in physics and chemistry. The instrument also provided an example problem for every confidence item. Results revealed that students' demographics were significant predictors in confidence scores. Students in the 18-22 year old range were less confident in solving math problems than others. Students who had retaken a math course were less confident than those who had not. Chemistry students were less confident in solving math problems than those in physics courses. Chemistry II students were less confident than those in Chemistry I and Principals of Chemistry. Students were least confident in solving problems involving logarithms and the most confident in solving algebra problems. In general, students felt that their math courses did not prepare them for the math problems encountered in science courses. There was no significant difference in confidence between students who had completed their math homework online and those who had completed their homework on paper. The researcher recommends that chemistry educators find ways of incorporating more mathematics in their courses especially logarithms and slope. Furthermore, math educators should incorporate more chemistry related applications to math class. Results of hypotheses testing, conclusions, discussions, and recommendations for future research are included.

Graphs in kinematics—a need for adherence to principles of algebraic functions

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej

2017-11-01

Graphs in physics are central to the analysis of phenomena and to learning about a system’s behavior. The ways students handle graphs are frequently researched. Students’ misconceptions are highlighted, and methods of improvement suggested. While kinematics graphs are to represent a real motion, they are also algebraic entities that must satisfy conditions for being algebraic functions. To be algebraic functions, they must pass certain tests before they can be used to infer more about motion. A preliminary survey of some physics resources has revealed that little attention is paid to verifying if the position, velocity and acceleration versus time graphs, that are to depict real motion, satisfy the most critical condition for being an algebraic function; the vertical line test. The lack of attention to this adherence shows as vertical segments in piecewise graphs. Such graphs generate unrealistic interpretations and may confuse students. A group of 25 college physics students was provided with such a graph and asked to analyse its adherence to reality. The majority of the students (N  =  16, 64%) questioned the graph’s validity. It is inferred that such graphs might not only jeopardize the function principles studied in mathematics but also undermine the purpose of studying these principles. The aim of this study was to bring this idea forth and suggest a better alignment of physics and mathematics methods.

Black holes, information, and the universal coefficient theorem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Patrascu, Andrei T.

2016-07-15

General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is based on the principle of unitary evolution. In this article, I provide a possible answer to the black hole information paradox by means of homological algebra and pairings generated by the universal coefficient theorem. The unitarity of processes involving black holes is restored by the demanding invariance of the laws of physics to the change of coefficient structures in cohomology.

A Study of the Predictability of Praxis I Examination Scores from ACT Scores and Teacher Education Program Prerequisite Courses

ERIC Educational Resources Information Center

Henderson, Allen R.

2013-01-01

This study investigated the relationship between student enrollment in certain college courses and Praxis I scores. Specifically, the study examined the predictive nature of the relationships between students' grades in college algebra, their freshman English course of choice, their ACT scores, and their Praxis I scores. The subjects consisted of…

Math Refresher Workshop Series as an Aid to Registrants of a College Level Math Course.

ERIC Educational Resources Information Center

Boyd, Vivian; And Others

Because the failure rate for Math 110 (a college algebra course for non-science/technology-oriented majors at the University of Maryland) was so high, it was decided to offer selected registrants the opportunity to take a free refresher workshop series to improve their mathematics skills before they took the course. In summer 1985, 809 students…

The Effects of Recorded Lectures on Passing Rates in Online Math Courses

ERIC Educational Resources Information Center

Fital-Akelbek, Sandra; Akelbek, Mahmud

2018-01-01

In this mixed method study we investigate the impact of recorded lectures on passing rates in an online math course. For three years, we collected data from approximately 380 students enrolled in a first-year undergraduate online course, College Algebra. The data was used to compare the amount of time students spent watching recorded lectures and…

The structure and Gel'fand patterns inherent in the Heisenberg supergenerator algebra of dual Liouville-space ||kq{K-tilde.}(k1 - kn)[lambda- tilde],scriptn>> tensors and the Cayley algebra of scalar invariants over a (k1 - kn) field

NASA Astrophysics Data System (ADS)

Temme, F. P.

1991-06-01

For many-body spin cluster problems, dual-symmetry recoupled tensors over Liouville space provide suitable bases for a generalized torque formalism using the Sn-adapted density operator in which to discuss NMR and related techniques. The explicit structure of such tensors is considered in the context of the Cayley algebra of scalar invariants over a field, specified by the inner ki rank labels of the Tkq(kl-kn)s. The pertinence of both lexical combinatorial architectures over inner rank sets and SU2 propagative topologies in specifying the structure of dual recoupling tensors is considered in the context of the Sn partitional aspects of spin clusters. The form of Heisenberg superoperator generators whose algebra underlies the Gel'fand pattern algebra of SU(2) and SU(2)×Sn tensor bases over Liouville space is presented together with both the related s-boson algebras and a description of the associated {||2k 0>>} pattern sets of CF29H carrier space under the appropriate symmetry. These concepts are correlated with recent work on SU(2)×Sn induced symmetry hierarchies over Liouville spin space. The pertinence of this theoretical work to an understanding of multiquantum NMR in Liouville space formalisms is stressed in a discussion of the nature of pathways for intracluster J coupling, which also gives a valuable physical insight into the nature of coherence transfer in more general spin-1/2 systems.

75 FR 79350 - Notice of Submission for OMB Review

Federal Register 2010, 2011, 2012, 2013, 2014

2010-12-20

... postsecondary world; and what courses, majors, first job, and careers students decide to pursue when, why, and how, especially, but not solely, in regards to science, technology, engineering, and math courses, majors, and careers. This study includes a new student assessment in algebraic skills, reasoning, and...

Incorporating Writing in an Integrated Calculus, Linear Algebra, and Differential Equations Sequence.

ERIC Educational Resources Information Center

Kelly, Susan E.; LeDocq, Rebecca Lewin

2001-01-01

Describes the specific courses in a sequence along with how the writing has been implemented in each course. Provides ideas for how to efficiently handle the additional paper load so students receive the necessary feedback while keeping the grading time reasonable. (Author/ASK)

Cultivating Deductive Thinking with Angle Chasing

ERIC Educational Resources Information Center

Edwards, Michael todd; Quinlan, James; Harper, Suzanne R.; Cox, Dana C.; Phelps, Steve

2014-01-01

Despite Common Core State Standards for Mathematics (CCSSI 2010) recommendations, too often students' introduction to proof consists of the study of formal axiomatic systems--for example, triangle congruence proofs--typically in an introductory geometry course with no connection back to previous work in earlier algebra courses. Van Hiele…

The Relationship between School-Facilitated Parental Involvement and Academic Math Achievement of High School Students in Virginia Who Receive Special Education Services

ERIC Educational Resources Information Center

Stein, Allison

2017-01-01

This study examined how school-facilitated parental involvement affects Standards of Learning (SOL) end-of-course exams for high school students in Virginia who are receiving special education services. This study examined test results from the 2012-2013, 2013-2014, and 2014-2015 school years for the Algebra I, Geometry, and Algebra II SOL exams,…

Reducing the failure rate in introductory physics classes

NASA Astrophysics Data System (ADS)

Saul, Jeff; Coulombe, Patrick; Lindell, Rebecca

2017-01-01

Calculus-based introductory physics courses are often among the most difficult at many colleges and universities. With the national movement to increase STEM majors, the introductory calculus-based courses need to be less of a weed-out course and more of a course that propels students forward into successful majors. This talk discusses two approaches to reduce DFW rates and improve student retention: studio courses and parachute courses. Studio courses integrate lecture/laboratory into one course where the primary mode of instruction is small group activities. Typically, any students enrolled in the college or university can enroll in a studio version of the course. Parachute courses on the other hand, focus on the poor performing students. Designed so that students not doing well in an introductory physics course can switch into the parachute class mid-semester without harm to their GPA. In addition, the parachute course focuses on helping students build the knowledge and skills necessary for success when retaking the calculus-based Physics course. The studio course format has been found to reduce DFW rates at several universities by 40-60% compared with separate lecture and laboratory format versions of the same courses, while parachutes courses were less successful. At one university, the parachute course succeeded in helping 80% of students maintain their GPA, but only helped 20% successfully pass the calculus-based physics course.

An analysis of science content and representations in introductory college physics textbooks and multimodal learning resources

NASA Astrophysics Data System (ADS)

Donnelly, Suzanne M.

This study features a comparative descriptive analysis of the physics content and representations surrounding the first law of thermodynamics as presented in four widely used introductory college physics textbooks representing each of four physics textbook categories (calculus-based, algebra/trigonometry-based, conceptual, and technical/applied). Introducing and employing a newly developed theoretical framework, multimodal generative learning theory (MGLT), an analysis of the multimodal characteristics of textbook and multimedia representations of physics principles was conducted. The modal affordances of textbook representations were identified, characterized, and compared across the four physics textbook categories in the context of their support of problem-solving. Keywords: college science, science textbooks, multimodal learning theory, thermodynamics, representations

Locally Compact Quantum Groups. A von Neumann Algebra Approach

NASA Astrophysics Data System (ADS)

Van Daele, Alfons

2014-08-01

In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68-92] locally compact quantum groups are also studied in the von Neumann algebraic context. This approach is independent of the original C^*-algebraic approach in the sense that the earlier results are not used. However, this paper is not really independent because for many proofs, the reader is referred to the original paper where the C^*-version is developed. In this paper, we give a completely self-contained approach. Moreover, at various points, we do things differently. We have a different treatment of the antipode. It is similar to the original treatment in [Ann. Sci. & #201;cole Norm. Sup. (4) 33 (2000), 837-934]. But together with the fact that we work in the von Neumann algebra framework, it allows us to use an idea from [Rev. Roumaine Math. Pures Appl. 21 (1976), 1411-1449] to obtain the uniqueness of the Haar weights in an early stage. We take advantage of this fact when deriving the other main results in the theory. We also give a slightly different approach to duality. Finally, we collect, in a systematic way, several important formulas. In an appendix, we indicate very briefly how the C^*-approach and the von Neumann algebra approach eventually yield the same objects. The passage from the von Neumann algebra setting to the C^*-algebra setting is more or less standard. For the other direction, we use a new method. It is based on the observation that the Haar weights on the C^*-algebra extend to weights on the double dual with central support and that all these supports are the same. Of course, we get the von Neumann algebra by cutting down the double dual with this unique support projection in the center. All together, we see that there are many advantages when we develop the theory of locally compact quantum groups in the von Neumann algebra framework, rather than in the C^*-algebra framework. It is not only simpler, the theory of weights on von Neumann algebras is better known and one needs very little to go from the C^*-algebras to the von Neumann algebras. Moreover, in many cases when constructing examples, the von Neumann algebra with the coproduct is constructed from the very beginning and the Haar weights are constructed as weights on this von Neumann algebra (using left Hilbert algebra theory). This paper is written in a concise way. In many cases, only indications for the proofs of the results are given. This information should be enough to see that these results are correct. We will give more details in forthcoming paper, which will be expository, aimed at non-specialists. See also [Bull. Kerala Math. Assoc. (2005), 153-177] for an 'expanded' version of the appendix.

The development and nature of problem-solving among first-semester calculus students

NASA Astrophysics Data System (ADS)

Dawkins, Paul Christian; Mendoza Epperson, James A.

2014-08-01

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate this blended instruction as a local representative of the US calculus reform movements that helped foster it. These reform movements tended to emphasize problem-solving as well as multiple mathematical registers and quantitative modelling. Our statistical analysis reveals the influence of the blended traditional/reform calculus instruction on students' ability to solve calculus-related, non-routine problems through repeated measures over the semester. The calculus instruction in this study significantly improved students' performance on non-routine problems, though performance improved more regarding strategies and accuracy than it did for drawing conclusions and providing justifications. We identified problem-solving behaviours that characterized top performance or attrition in the course. Top-performing students displayed greater algebraic proficiency, calculus skills, and more general heuristics than their peers, but overused algebraic techniques even when they proved cumbersome or inappropriate. Students who subsequently withdrew from calculus often lacked algebraic fluency and understanding of the graphical register. The majority of participants, when given a choice, relied upon less sophisticated trial-and-error approaches in the numerical register and rarely used the graphical register, contrary to the goals of US calculus reform. We provide explanations for these patterns in students' problem-solving performance in view of both their preparation for university calculus and the courses' assessment structure, which preferentially rewarded algebraic reasoning. While instruction improved students' problem-solving performance, we observe that current instruction requires ongoing refinement to help students develop multi-register fluency and the ability to model quantitatively, as is called for in current US standards for mathematical instruction.

Care and Feeding of a Paperless, Calculus-based Physics Course

NASA Astrophysics Data System (ADS)

Moore, Christopher; Fuller, Robert; Plano-Clark, Vicki L.; Dunbar, Steven R.

1997-04-01

Technology is playing an increasing role in our lives at home, at work, and in the classroom. We have begun a calculus-based introductory physics course to integrate mathematics and multimedia with the traditional physics content. This course relies on the use of technology to teach physics. We formulated the following rule for the conduct of the course: ''No paper is transferred between instructional staff and students that contains course information or assignments for grading.'' Implementing and maintaining this physics course within the context of the instructor goals will be discussed. Preliminary results of feedback from the students and an evaluation team will be presented.

Conceptual Precalculus: Strengthening Students' Quantitative and Covariational Reasoning

ERIC Educational Resources Information Center

Madison, Bernard L.; Carlson, Marilyn; Oehrtman, Michael; Tallman, Michael

2015-01-01

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…

Integration of CAI into a Freshmen Liberal Arts Math Course in the Community College.

ERIC Educational Resources Information Center

McCall, Michael B.; Holton, Jean L.

1982-01-01

Discusses four computer-assisted-instruction programs used in a college-level mathematics course to introduce computer literacy and improve mathematical skills. The BASIC programs include polynomial functions, trigonometric functions, matrix algebra, and differential calculus. Each program discusses mathematics theory and introduces programming…

Core-Plus Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

"Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…

Student Learning and Perceptions in a Flipped Linear Algebra Course

ERIC Educational Resources Information Center

Love, Betty; Hodge, Angie; Grandgenett, Neal; Swift, Andrew W.

2014-01-01

The traditional lecture style of teaching has long been the norm in college science, technology, engineering, and mathematics (STEM) courses, but an innovative teaching model, facilitated by recent advances in technology, is gaining popularity across college campuses. This new model inverts or "flips" the usual classroom paradigm, in…

What Are the ACT College Readiness Benchmarks? Information Brief

ERIC Educational Resources Information Center

ACT, Inc., 2013

2013-01-01

The ACT College Readiness Benchmarks are the minimum ACT® college readiness assessment scores required for students to have a high probability of success in credit-bearing college courses--English Composition, social sciences courses, College Algebra, or Biology. This report identifies the College Readiness Benchmarks on the ACT Compass scale…

Fundamentals of Digital Logic.

ERIC Educational Resources Information Center

Noell, Monica L.

This course is designed to prepare electronics personnel for further training in digital techniques, presenting need to know information that is basic to any maintenance course on digital equipment. It consists of seven study units: (1) binary arithmetic; (2) boolean algebra; (3) logic gates; (4) logic flip-flops; (5) nonlogic circuits; (6)…

Open Source Software in Teaching Physics: A Case Study on Vector Algebra and Visual Representations

ERIC Educational Resources Information Center

Cataloglu, Erdat

2006-01-01

This study aims to report the effort on teaching vector algebra using free open source software (FOSS). Recent studies showed that students have difficulties in learning basic physics concepts. Constructivist learning theories suggest the use of visual and hands-on activities in learning. We will report on the software used for this purpose. The…

Marriages of mathematics and physics: A challenge for biology.

PubMed

Islami, Arezoo; Longo, Giuseppe

2017-12-01

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences. Copyright © 2017. Published by Elsevier Ltd.

Math in the Real World: Early Findings from a Study of the Dana Center Mathematics Pathways. Research Brief

ERIC Educational Resources Information Center

Rutschow, Elizabeth Zachry; Diamond, John; Serna-Wallender, Elena

2017-01-01

Until recently, most colleges required students to pass a college-level algebra course in order to earn a degree. As many as 50 percent to 70 percent of community college students enter college unprepared to take these courses, and fewer than 20 percent of such students ever successfully complete a college-level math course; the rest are…

An Analysis of Final Course Grades in Two Different Entry Level Mathematics Courses between and among First Year College Students with Different Levels of High School Mathematics Preparation

ERIC Educational Resources Information Center

Muir, Carrie

2012-01-01

The purpose of this study was to compare the performance of first year college students with similar high school mathematics backgrounds in two introductory level college mathematics courses, "Fundamentals and Techniques of College Algebra and Quantitative Reasoning and Mathematical Skills," and to compare the performance of students…

Transversality of Electromagnetic Waves in the Calculus--Based Introductory Physics Course

NASA Astrophysics Data System (ADS)

Burko, Lior M.

2009-05-01

Introductory calculus--based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments are at a level appropriate for students of courses based on such books, and could be readily used by instructors of such courses. Here, we discuss two physical arguments (based on polarization experiments and on lack of monopole electromagnetic radiation), and the full argument for the transversality of (plane) electromagnetic waves based on the integral Maxwell equations. We also show, at a level appropriate for the introductory course, why the electric and magnetic fields in a wave are in phase and the relation of their magnitudes. We have successfully integrated this approach in the calculus--based introductory physics course at the University of Alabama in Huntsville.

The Adidactic Interaction with the Procedures of Peers in the Transition from Arithmetic to Algebra: A "Milieu" for the Emergence of New Questions

ERIC Educational Resources Information Center

Sadovsky, Patricia; Sessa, Carmen

2005-01-01

The purpose of the present article is to give an account of the emergence of knowledge pertaining to the transition from arithmetic to algebra in the course of a debate in a grade 7 classroom. This debate follows two other instances of work: (1) the adidactic interaction between each student and a given problem, (2) the adidactic interaction of…

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miyadera, Takayuki; Imai, Hideki; Graduate School of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551

This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloningmore » on effect algebras and hidden variables.« less

Affine Kac-Moody symmetric spaces related with A1^{(1)}, A2^{(1)},} A2^{(2)}

NASA Astrophysics Data System (ADS)

Nayak, Saudamini; Pati, K. C.

2014-08-01

Symmetric spaces associated with Lie algebras and Lie groups which are Riemannian manifolds have recently got a lot of attention in various branches of Physics for their role in classical/quantum integrable systems, transport phenomena, etc. Their infinite dimensional counter parts have recently been discovered which are affine Kac-Moody symmetric spaces. In this paper we have (algebraically) explicitly computed the affine Kac-Moody symmetric spaces associated with affine Kac-Moody algebras A1^{(1)}, A2^{(1)}, A2^{(2)}. We hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems.

The conceptual basis of mathematics in cardiology: (I) algebra, functions and graphs.

PubMed

Bates, Jason H T; Sobel, Burton E

2003-02-01

This is the first in a series of four articles developed for the readers of. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease, abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to cardiovascular medicine and biology.

A Genetically Optimized Predictive System for Success in General Chemistry Using a Diagnostic Algebra Test

NASA Astrophysics Data System (ADS)

Cooper, Cameron I.; Pearson, Paul T.

2012-02-01

In higher education, many high-enrollment introductory courses have evolved into "gatekeeper" courses due to their high failure rates. These courses prevent many students from attaining their educational goals and often become graduation roadblocks. At the authors' home institution, general chemistry has become a gatekeeper course in which approximately 25% of students do not pass. This failure rate in chemistry is common, and often higher, at many other institutions of higher education, and mathematical deficiencies are perceived to be a large contributing factor. This paper details the development of a highly accurate predictive system that identifies students at the beginning of the semester who are "at-risk" for earning a grade of C- or below in chemistry. The predictive accuracy of this system is maximized by using a genetically optimized neural network to analyze the results of a diagnostic algebra test designed for a specific population. Once at-risk students have been identified, they can be helped to improve their chances of success using techniques such as concurrent support courses, online tutorials, "just-in-time" instructional aides, study skills, motivational interviewing, and/or peer mentoring.

Studio Physics at the Colorado School of Mines: A model for iterative development and assessment

NASA Astrophysics Data System (ADS)

Kohl, Patrick; Kuo, Vincent

2009-05-01

The Colorado School of Mines (CSM) has taught its first-semester introductory physics course using a hybrid lecture/Studio Physics format for several years. Based on this previous success, over the past 18 months we have converted the second semester of our traditional calculus-based introductory physics course (Physics II) to a Studio Physics format. In this talk, we describe the recent history of the Physics II course and of Studio at Mines, discuss the PER-based improvements that we are implementing, and characterize our progress via several metrics, including pre/post Conceptual Survey of Electricity and Magnetism (CSEM) scores, Colorado Learning About Science Survey scores (CLASS), failure rates, and exam scores. We also report on recent attempts to involve students in the department's Senior Design program with our course. Our ultimate goal is to construct one possible model for a practical and successful transition from a lecture course to a Studio (or Studio-like) course.

Expectations of Internet Education: Casper College's Experience.

ERIC Educational Resources Information Center

Nelson, Gerald E.

The Internet Based Distance Learning (IBDL) classes provided in Wyoming's Casper College have the potential to benefit all involved. The "Cyber Semester," which began in the spring of 1997, consisted of four typical freshman classes (Physical Geography, Precalculus Algebra, English Composition I, and Political Science) that were offered…

Computers as Cognitive Tools.

ERIC Educational Resources Information Center

Lajoie, Susanne P., Ed.; Derry, Sharon J., Ed.

This book provides exemplars of the types of computer-based learning environments represented by the theoretical camps within the field and the practical applications of the theories. The contributors discuss a variety of computer applications to learning, ranging from school-related topics such as geometry, algebra, biology, history, physics, and…

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra

PubMed Central

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-01-01

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail. PMID:24225900

Novel characteristics of energy spectrum for 3D Dirac oscillator analyzed via Lorentz covariant deformed algebra.

PubMed

Betrouche, Malika; Maamache, Mustapha; Choi, Jeong Ryeol

2013-11-14

We investigate the Lorentz-covariant deformed algebra for Dirac oscillator problem, which is a generalization of Kempf deformed algebra in 3 + 1 dimension of space-time, where Lorentz symmetry are preserved. The energy spectrum of the system is analyzed by taking advantage of the corresponding wave functions with explicit spin state. We obtained entirely new results from our development based on Kempf algebra in comparison to the studies carried out with the non-Lorentz-covariant deformed one. A novel result of this research is that the quantized relativistic energy of the system in the presence of minimal length cannot grow indefinitely as quantum number n increases, but converges to a finite value, where c is the speed of light and β is a parameter that determines the scale of noncommutativity in space. If we consider the fact that the energy levels of ordinary oscillator is equally spaced, which leads to monotonic growth of quantized energy with the increment of n, this result is very interesting. The physical meaning of this consequence is discussed in detail.

Hawking fluxes, fermionic currents, W{sub 1+{infinity}} algebra, and anomalies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bonora, L.; Cvitan, M.; Theoretical Physics Department, Faculty of Science, University of Zagreb Bijenicka cesta 32, HR-10002 Zagreb

2009-10-15

We complete the analysis carried out in previous papers by studying the Hawking radiation for a Kerr black hole carried to infinity by fermionic currents of any spin. We find agreement with the thermal spectrum of the Hawking radiation for fermionic degrees of freedom. We start by showing that the near-horizon physics for a Kerr black hole is approximated by an effective two-dimensional field theory of fermionic fields. Then, starting from two-dimensional currents of any spin that form a W{sub 1+{infinity}} algebra, we construct an infinite set of covariant currents, each of which carries the corresponding moment of the Hawkingmore » radiation. All together they agree with the thermal spectrum of the latter. We show that the predictive power of this method is based not on the anomalies of the higher-spin currents (which are trivial) but on the underlying W{sub 1+{infinity}} structure. Our results point toward the existence in the near-horizon geometry of a symmetry larger than the Virasoro algebra, which very likely takes the form of a W{sub {infinity}} algebra.« less

Geometric and Applied Optics, Science (Experimental): 5318.04.

ERIC Educational Resources Information Center

Sanderson, Robert C.

This unit of instruction presents a laboratory-oriented course which relates the sources and behaviors of light to man's control and uses of light. Successful completion of Algebra I and Plane Geometry is strongly recommended as indicators of success. The course is recommended if the student plans further studies in science, optical technology, or…

Problems before Procedures: Systems of Equations

ERIC Educational Resources Information Center

Allen, Kasi C.

2013-01-01

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

Bridging Algebra & Geometry with "n"-Gram Proofs

ERIC Educational Resources Information Center

Craven, Joshua D.

2010-01-01

For many students, geometry is the first course in which mathematical proof takes center stage. To help ease students into writing proofs, the author tries to create lessons and activities throughout the year that challenge students to prove their own conjectures by using tools learned in previous mathematics courses. Teachers cannot get all…

Sound Off! Don't Sacrifice Geometry on the Common Core Altar

ERIC Educational Resources Information Center

Nirode, Wayne

2013-01-01

Although high school geometry could be a meaningful course in exploring, reasoning, proving, and communicating, it often lacks authentic proof and has become just another course in algebra. This article examines why geometry is important to learn and provides an outline of what that learning experience should be.

Explorations in Elementary Mathematical Modeling

ERIC Educational Resources Information Center

Shahin, Mazen

2010-01-01

In this paper we will present the methodology and pedagogy of Elementary Mathematical Modeling as a one-semester course in the liberal arts core. We will focus on the elementary models in finance and business. The main mathematical tools in this course are the difference equations and matrix algebra. We also integrate computer technology and…

Detracking and Tracking Up: Mathematics Course Placements in California Middle Schools, 2003-2013

ERIC Educational Resources Information Center

Domina, Thurston; Hanselman, Paul; Hwang, NaYoung; McEachin, Andrew

2016-01-01

Between 2003 and 2013, the proportion of California eighth graders enrolled in algebra or a more advanced course nearly doubled to 65%. In this article, we consider the organizational processes that accompanied this curricular intensification. Facing a complex set of accountability, institutional, technical/functional, and internal political…

Detracking and Tracking Up: Mathematics Course Placements in California Middle Schools, 2003-2013

ERIC Educational Resources Information Center

Domina, Thurston; Hanselman, Paul; Hwang, NaYoung; McEachin, Andrew

2016-01-01

Between 2003 and 2013, the proportion of California 8th graders enrolled in Algebra or a more advanced course nearly doubled to 65 percent. In this paper, we consider the organizational processes that accompanied this curricular intensification. Facing a complex set of accountability, institutional, technical/functional, and internal political…

Calculus of Elementary Functions, Part II. Teacher's Commentary. Revised Edition.

ERIC Educational Resources Information Center

Herriot, Sarah T.; And Others

This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This teacher's guide is for Part II of the course. It is designed to follow Part I of the text. The guide contains background information, suggested instructional…

Calculus of Elementary Functions, Part I. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Herriot, Sarah T.; And Others

This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This text, Part I, contains the first five chapters of the course and two appendices. Chapters included are: (1) Polynomial Functions; (2) The Derivative of a Polynomial…

Instructional Objectives for a Junior College Course in Intermediate Algebra.

ERIC Educational Resources Information Center

Starkweather, Ann, Comp.

These instructional objectives have been selected from materials submitted to the Curriculum Laboratory of the Graduate School of Education at UCLA. Arranged by major course goals, these objectives are offered simply as samples that may be used where they correspond to the skills, abilities, and attitudes instructors want their students to…

A Comprehensive Probability Project for the Upper Division One-Semester Probability Course Using Yahtzee

ERIC Educational Resources Information Center

Wilson, Jason; Lawman, Joshua; Murphy, Rachael; Nelson, Marissa

2011-01-01

This article describes a probability project used in an upper division, one-semester probability course with third-semester calculus and linear algebra prerequisites. The student learning outcome focused on developing the skills necessary for approaching project-sized math/stat application problems. These skills include appropriately defining…

Using Student Performance to Judge the Difficulty of Examinations

ERIC Educational Resources Information Center

Roegner, Katherine

2015-01-01

This contribution focuses on a scheme developed to characterize the level of difficulty of an examination in the course "Linear Algebra for Engineers" and on the transfer of the underlying idea to a similar scheme for examinations in the course "Analysis I for Engineers". Using these schemes, it is possible to define standards…

Mainstreaming Remedial Mathematics Students in Introductory Statistics: Results Using a Randomized Controlled Trial

ERIC Educational Resources Information Center

Logue, Alexandra W.; Watanabe-Rose, Mari

2014-01-01

This study used a randomized controlled trial to determine whether students, assessed by their community colleges as needing an elementary algebra (remedial) mathematics course, could instead succeed at least as well in a college-level, credit-bearing introductory statistics course with extra support (a weekly workshop). Researchers randomly…

Tensile and shear strength of adhesives

NASA Technical Reports Server (NTRS)

Stibolt, Kenneth A.

1990-01-01

This experiment is conducted in a freshman-level course: Introduction to Engineering Materials. There are no prerequisites for the course although students should have some knowledge of basic algebra. The objectives are to tension and shear test adhesives and to determine the tensile and shear properties of adhesives. Details of equipment of procedure are given.

Case Study of a College Mathematics Instructor: Patterns of Classroom Discourse

ERIC Educational Resources Information Center

Tsay, Jenq-Jong; Judd, April B.; Hauk, Shandy; Davis, Mark K.

2011-01-01

In the United States, undergraduates--regardless of their field of study--generally must complete a mathematics course to meet breadth-of-study requirements. This report is aimed at providing a research foundation for practical efforts to improve teaching and learning in such college mathematics service courses (e.g., college algebra, liberal arts…

Trends in Achievement Gaps in First-Year College Courses for Racial/Ethnic, Income, and Gender Subgroups: A 12-Year Study. ACT Research Report Series 2013 (8)

ERIC Educational Resources Information Center

Lorah, Julie; Ndum, Edwin

2013-01-01

Prior research has demonstrated gaps in the academic success of college student subgroups defined by race/ethnicity, income, and gender. We studied trends over time in the success of students in these subgroups in particular first-year college courses: English Composition I, College Algebra, social science courses, and Biology. The study is based…

Affine group formulation of the Standard Model coupled to gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chou, Ching-Yi, E-mail: l2897107@mail.ncku.edu.tw; Ita, Eyo, E-mail: ita@usna.edu; Soo, Chopin, E-mail: cpsoo@mail.ncku.edu.tw

In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder’s affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang–Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang–Mills and Higgs energy densities, are composed with York’s integrated time functional. The result, when combined with the imaginary part of themore » Chern–Simons functional Q, forms the affine commutation relation with the volume element V(x). Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant. -- Highlights: •Wheeler–DeWitt equation (WDW) quantized as affine algebra, realizing Klauder’s program. •WDW formulated for interaction of matter and all forces, including gravity, as affine algebra. •WDW features Hermitian generators in spite of fermionic content: Standard Model addressed. •Constructed a family of physical states for the full, coupled theory via affine coherent states. •Fundamental uncertainty relation, predicated on non-vanishing cosmological constant.« less

Toward the classification of differential calculi on κ-Minkowski space and related field theories

NASA Astrophysics Data System (ADS)

Jurić, Tajron; Meljanac, Stjepan; Pikutić, Danijel; Štrajn, Rina

2015-07-01

Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincaré Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.

A grid spacing control technique for algebraic grid generation methods

NASA Technical Reports Server (NTRS)

Smith, R. E.; Kudlinski, R. A.; Everton, E. L.

1982-01-01

A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.

Facilitating Case Reuse during Problem Solving in Algebra-Based Physics

ERIC Educational Resources Information Center

Mateycik, Frances Ann

2010-01-01

This research project investigates students' development of problem solving schemata while using strategies that facilitate the process of using solved examples to assist with a new problem (case reuse). Focus group learning interviews were used to explore students' perceptions and understanding of several problem solving strategies. Individual…

A heuristic way of obtaining the Kerr metric

DOE Office of Scientific and Technical Information (OSTI.GOV)

Enderlein, J.

1997-09-01

An intuitive, straightforward way of finding the metric of a rotating black hole is presented, based on the algebra of differential forms. The representation obtained for the metric displays a simplicity which is not obvious in the usual Boyer{endash}Lindquist coordinates. {copyright} {ital 1997 American Association of Physics Teachers.}

A spatial operator algebra for manipulator modeling and control

NASA Technical Reports Server (NTRS)

Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

1991-01-01

A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.

Professional Development Graduate Courses and a Masters of Arts in Physics Education with Web Based Course Components

NASA Astrophysics Data System (ADS)

Lindgren, Richard; Thornton, Stephen

2010-02-01

Professional development courses offered in physical/Earth science and physics by the Department of Physics are delivered by different venues to accommodate the needs of the K-12 teaching community. The majority of teachers take our courses off-site or through our distance-learning web-based program on the Internet for endorsement or recertification, but with a gradually increasing number enrolling in our 30 credit Masters of Arts in Physics Education degree (MAPE) program. The purpose of the Masters program is to provide increased physics content to those teachers who feel inadequately prepared to teach high school physics. The increase in numbers and success of this program is partly due to the convenience of taking online web-based courses which is made possible by using the latest communication technologies on the high speed internet. There is also a residential component of the MAPE program, which requires the candidates to earn 14 credits of calculus-based core physics in residence in the summer at the University. We have graduated a total of 91 teachers since the program began in 2000. )

Color Algebras

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.

A Algebraic Approach to the Quantization of Constrained Systems: Finite Dimensional Examples.

NASA Astrophysics Data System (ADS)

Tate, Ranjeet Shekhar

1992-01-01

General relativity has two features in particular, which make it difficult to apply to it existing schemes for the quantization of constrained systems. First, there is no background structure in the theory, which could be used, e.g., to regularize constraint operators, to identify a "time" or to define an inner product on physical states. Second, in the Ashtekar formulation of general relativity, which is a promising avenue to quantum gravity, the natural variables for quantization are not canonical; and, classically, there are algebraic identities between them. Existing schemes are usually not concerned with such identities. Thus, from the point of view of canonical quantum gravity, it has become imperative to find a framework for quantization which provides a general prescription to find the physical inner product, and is flexible enough to accommodate non -canonical variables. In this dissertation I present an algebraic formulation of the Dirac approach to the quantization of constrained systems. The Dirac quantization program is augmented by a general principle to find the inner product on physical states. Essentially, the Hermiticity conditions on physical operators determine this inner product. I also clarify the role in quantum theory of possible algebraic identities between the elementary variables. I use this approach to quantize various finite dimensional systems. Some of these models test the new aspects of the algebraic framework. Others bear qualitative similarities to general relativity, and may give some insight into the pitfalls lurking in quantum gravity. The previous quantizations of one such model had many surprising features. When this model is quantized using the algebraic program, there is no longer any unexpected behaviour. I also construct the complete quantum theory for a previously unsolved relativistic cosmology. All these models indicate that the algebraic formulation provides powerful new tools for quantization. In (spatially compact) general relativity, the Hamiltonian is constrained to vanish. I present various approaches one can take to obtain an interpretation of the quantum theory of such "dynamically constrained" systems. I apply some of these ideas to the Bianchi I cosmology, and analyze the issue of the initial singularity in quantum theory.

Computer-assisted instruction in programming: AID

NASA Technical Reports Server (NTRS)

Friend, J.; Atkinson, R. C.

1971-01-01

Lessons for training students on how to program and operate computers to and AID language are given. The course consists of a set of 50 lessons, plus summaries, reviews, tests, and extra credit problems. No prior knowledge is needed for the course, the only requirement being a strong background in algebra. A student manual, which includes instruction for operating the instructional program and a glossary of terms used in the course, is included in the appendices.

Transversality of electromagnetic waves in the calculus-based introductory physics course

NASA Astrophysics Data System (ADS)

Burko, Lior M.

2008-11-01

Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments are at a level appropriate for students of courses based on such books, and could be readily used by instructors of such courses. Here, we discuss two physical arguments (based on polarization experiments and on lack of monopole electromagnetic radiation) and the full argument for the transversality of (plane) electromagnetic waves based on the integral Maxwell equations. We also show, at a level appropriate for the introductory course, why the electric and magnetic fields in a wave are in phase and the relation of their magnitudes.

Beyond Concepts: Transfer From Inquiry-Based Physics To Elementary Classrooms

NASA Astrophysics Data System (ADS)

Harlow, Danielle B.; Otero, Valerie K.

2007-01-01

Physics education researchers have created specialized physics courses to meet the needs of elementary teachers. While there is evidence that such courses help teachers develop physics content knowledge, little is known about what teachers transfer from such courses into their teaching practices. In this study, we examine how one elementary teacher changed her questioning strategies after learning physics in a course for elementary teachers.

Peer Learning as a Tool to Strengthen Math Skills in Introductory Chemistry Laboratories

ERIC Educational Resources Information Center

Srougi, Melissa C.; Miller, Heather B.

2018-01-01

Math skills vary greatly among students enrolled in introductory chemistry courses. Students with weak math skills (algebra and below) tend to perform poorly in introductory chemistry courses, which is correlated with increased attrition rates. Previous research has shown that retention of main ideas in a peer learning environment is greater when…

Completing Algebra II in High School: Does It Increase College Access and Success?

ERIC Educational Resources Information Center

Kim, Jeongeun; Kim, Jiyun; DesJardins, Stephen L.; McCall, Brian P.

2015-01-01

Noting the benefits of mathematics in students' future educational attainment and labor market success, there is considerable interest in high school requirements in terms of course-taking in mathematics at the national, state, and school district level. Previous research indicates that taking advanced math courses in high school leads to positive…

Implementation Challenges and Results

ERIC Educational Resources Information Center

Walters, Kirk; Sorensen, Nicholas

2013-01-01

This paper describes the implementation of the online and f2f summer algebra courses that were delivered in summers 2011 and 2012. These data will be used to frame the impact results presented in an earlier paper. In particular, the paper will provide a detailed picture of how the online course was structured and the types of supports provided to…

Using Maple to Implement eLearning Integrated with Computer Aided Assessment

ERIC Educational Resources Information Center

Blyth, Bill; Labovic, Aleksandra

2009-01-01

Advanced mathematics courses have been developed and refined by the first author, using an action research methodology, for more than a decade. These courses use the computer algebra system (CAS) Maple in an "immersion mode" where all presentations and student work are done using Maple. Assignments and examinations are Maple files downloaded from…

A Study of Placement and Grade Prediction in First College Mathematics Courses

ERIC Educational Resources Information Center

Madison, Bernard L.; Linde, Cassandra S.; Decker, Blake R.; Rigsby, E. Myron; Dingman, Shannon W.; Stegman, Charles E.

2015-01-01

A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test…

A Follow-up Study of Two Methods of Teaching Mathematics: Traditional versus New Math

ERIC Educational Resources Information Center

Walton, Gene A.; And Others

1977-01-01

When high school mathematics grades and test scores were analyzed, findings showed that high- and middle-ability students who had a modern mathematics course in the seventh grade received significantly higher grades in Algebra I, II, III, and Geometry than did students who had a traditional seventh grade mathematics course. (DT)

Particle-like structure of coaxial Lie algebras

NASA Astrophysics Data System (ADS)

Vinogradov, A. M.

2018-01-01

This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number of steps from two elementary constituents, called dyons and triadons. Here we consider the problems of the construction and classification of those Lie algebras which can be assembled in one step from base dyons and triadons, called coaxial Lie algebras. The base dyons and triadons are Lie algebra structures that have only one non-trivial structure constant in a given basis, while coaxial Lie algebras are linear combinations of pairwise compatible base dyons and triadons. We describe the maximal families of pairwise compatible base dyons and triadons called clusters, and, as a consequence, we give a complete description of the coaxial Lie algebras. The remarkable fact is that dyons and triadons in clusters are self-organised in structural groups which are surrounded by casings and linked by connectives. We discuss generalisations and applications to the theory of deformations of Lie algebras.

The 1984 ARI Survey of Army Recruits: Supplementary User’s Manual for October 1984/February 1985 Administration

DTIC Science & Technology

1986-05-01

league baseball playoffs 106. World Series 116. Which of the following mathematics 107. NBA basketball and technical courses, if any, did you take and pass...baseball playoffs 94. World Series (Mark all that apply) 95. NBA bdsketball A. Elementary Algebra B. Plane Geometry e 96. College basketball C...in high school? 108. College basketball (Mark all that apply) 109. NHL hockey A. Elementary Algebra 110. Professional wrestling S. Plane Geometry C

Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence.

PubMed

Ozaktas, Haldun M; Yüksel, Serdar; Kutay, M Alper

2002-08-01

A linear algebraic theory of partial coherence is presented that allows precise mathematical definitions of concepts such as coherence and incoherence. This not only provides new perspectives and insights but also allows us to employ the conceptual and algebraic tools of linear algebra in applications. We define several scalar measures of the degree of partial coherence of an optical field that are zero for full incoherence and unity for full coherence. The mathematical definitions are related to our physical understanding of the corresponding concepts by considering them in the context of Young's experiment.

Developing the Learning Physical Science Curriculum: Adapting a Small Enrollment, Laboratory and Discussion Based Physical Science Course for Large Enrollments

ERIC Educational Resources Information Center

Goldberg, Fred; Price, Edward; Robinson, Stephen; Boyd-Harlow, Danielle; McKean, Michael

2012-01-01

We report on the adaptation of the small enrollment, lab and discussion based physical science course, "Physical Science and Everyday Thinking" (PSET), for a large-enrollment, lecture-style setting. Like PSET, the new "Learning Physical Science" (LEPS) curriculum was designed around specific principles based on research on learning to meet the…

Inquiry-Based Course in Physics and Chemistry for Preservice K-8 Teachers

ERIC Educational Resources Information Center

Loverude, Michael E.; Gonzalez, Barbara L.; Nanes, Roger

2011-01-01

We describe an inquiry-based course in physics and chemistry for preservice K-8 teachers developed at California State University Fullerton. The course is one of three developed primarily to enhance the science content understanding of prospective teachers. The course incorporates a number of innovative instructional strategies and is somewhat…

New phases of D ge 2 current and diffeomorphism algebras in particle physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tze, Chia-Hsiung.

We survey some global results and open issues of current algebras and their canonical field theoretical realization in D {ge} 2 dimensional spacetime. We assess the status of the representation theory of their generalized Kac-Moody and diffeomorphism algebras. Particular emphasis is put on higher dimensional analogs of fermi-bose correspondence, complex analyticity and the phase entanglements of anyonic solitons with exotic spin and statistics. 101 refs.

Projectile motion without calculus

NASA Astrophysics Data System (ADS)

Rizcallah, Joseph A.

2018-07-01

Projectile motion is a constant theme in introductory-physics courses. It is often used to illustrate the application of differential and integral calculus. While most of the problems used for this purpose, such as maximizing the range, are kept at a fairly elementary level, some, such as determining the safe domain, involve not so elementary techniques, which can hardly be assumed of the targeted audience. In the literature, several attempts have been undertaken to avoid calculus altogether and keep the exposition entirely within the realm of algebra and/or geometry. In this paper, we propose yet another non-calculus approach which uses the projectile’s travel times to shed new light on these problems and provide instructors with an alternate method to address them with their students.

Undergraduate Students' Perceptions of an Inquiry-Based Physics Course

NASA Astrophysics Data System (ADS)

Ballone Duran, Lena; McArthur, Julia; van Hook, Stephen

2004-04-01

The purpose of this study was to examine middle childhood students'' perceptions of the learning environment in a reform-based physics course. A lecture-style, introductory physics course was modified into an inquiry-based course designed for preservice middle childhood teachers through the collaborative efforts of faculty in the Colleges of Education and Arts and Sciences. Focus group interviews were conducted to examine students'' perceptions. The results suggested that the students initially felt a level of frustration with a new constructivist experience; however, they were able to embrace the inquiry method and expressed a desire for additional specialized content courses for preservice teachers.

Affine Kac-Moody symmetric spaces related with A{sub 1}{sup (1)}, A{sub 2}{sup (1)}, A{sub 2}{sup (2)}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nayak, Saudamini, E-mail: anumama.nayak07@gmail.com; Pati, K. C., E-mail: kcpati@nitrkl.ac.in

Symmetric spaces associated with Lie algebras and Lie groups which are Riemannian manifolds have recently got a lot of attention in various branches of Physics for their role in classical/quantum integrable systems, transport phenomena, etc. Their infinite dimensional counter parts have recently been discovered which are affine Kac-Moody symmetric spaces. In this paper we have (algebraically) explicitly computed the affine Kac-Moody symmetric spaces associated with affine Kac-Moody algebras A{sub 1}{sup (1)},A{sub 2}{sup (1)},A{sub 2}{sup (2)}. We hope these types of spaces will play similar roles as that of symmetric spaces in many physical systems.

76 FR 57721 - Notice of Submission for OMB Review

Federal Register 2010, 2011, 2012, 2013, 2014

2011-09-16

... for HSLS:09, especially, but not solely, in regards to science, technology, engineering, and math courses, majors, and careers. This study includes a new student assessment in algebraic skills, reasoning...

Time-reversal-based SU(2) x Sn scalar invariants as (Lie Algebraic) group measures: a structured overview of generalised democratic-recoupled, uniform non-Abelian [AX]n NMR spin systems, as abstract [Formula: see text] chain networks.

PubMed

Temme, F P

2004-03-01

The physics of dual group scalar invariants (SIs) as (Lie algebraic) group measures (L-GMs) and its significance to non-Abelian NMR spin systems motivates this overview of uniform general-2n [AX](2n) spin evolution, which represents an extensive addendum to Corio's earlier (essentially restricted) view of Abelian spin system SU(2)-based SI-cardinalities. The [Formula: see text] values in [J. Magn. Reson., 134 (1998) 131] arise from strictly linear recoupled time-reversal invariance (TRI) models. In contrast, here we discuss the physical significance of an alternative polyhedral combinatorics approach to democratic recoupling (DR), a property inherent in both the TRI and statistical sampling. Recognition of spin ensemble SIs as being L-GMs over isomorphic algebras is invaluable in many DR-based NMR problems. Various [AX]n model spin systems, including the [AX]3 bis odd-odd parity spin system, are examined as direct applications of these L-GM- and combinatorial-based SI ideas. Hence in place of /SI/=15 (implied by Corio's [Formula: see text] approach), the bis 3-fold spin system cardinality is seen now as constrained to a single invariant on an isomorphic product algebra under L-GMs, in accord with the subspectral analysis of Jones et al. [Canad. J. Chem., 43 (1965) 683]. The group projective ideas cited here for DR (as cf. to graph theoretic views) apply to highly degenerate non-Abelian problems. Over dual tensorial bases, they define models of spin dynamical evolution whose (SR) quasiparticle superboson carrier (sub)spaces are characterised by SIs acting as explicit auxiliary labels [Physica, A198 (1993) 245; J. Math. Chem., 31 (2002) 281]. A deeper [Formula: see text] network-based view of spin-alone space developed in Balasubramanian's work [J. Chem. Phys., 78 (1983) 6358] is especially important, (e.g.) in the study of spin waves [J. Math. Chem., 31 (2002) 363]. Beyond the specific NMR SIs derived here, there are DR applications where a sporadic, still higher, 2n-fold regular uniform spin ensemble exhibits a topological FG duality to some known modest /SI/(2i<2n) cardinality--in principle providing for the (sparce) existence of other /SI/(2n) DR-based values.

Testing Nonassociative Quantum Mechanics.

PubMed

Bojowald, Martin; Brahma, Suddhasattwa; Büyükçam, Umut

2015-11-27

The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead to nonassociative algebras. Their quantum physics has remained obscure. This Letter presents the first derivation of potentially testable physical results in nonassociative quantum mechanics, based on effective potentials. They imply new effects which cannot be mimicked in usual quantum mechanics with standard magnetic fields.

The Care and Feeding of Pre-Meds

NASA Astrophysics Data System (ADS)

Magleby, Stephanie

2009-05-01

Most physics instructors will at some point in their teaching career face a room full of students bound for medical or dental school. This particular student clientele presents a host of distinctive challenges. My presentation will discuss insights gained while teaching premed sections of algebra-based College Physics over the last ten semesters. Topics will include syllabus structure, grading techniques, testing strategies, letters of recommendation and most importantly: how to get a good teaching evaluation from a Pre-Med.

The Care and Feeding of Pre-Meds

NASA Astrophysics Data System (ADS)

Magleby, Stephanie

2008-10-01

Most physics instructors will at some point in their teaching career face a room full of students bound for medical or dental school. This particular student clientele presents a host of distinctive challenges. My presentation will discuss insights gained while teaching premed sections of algebra-based College Physics over the last ten semesters. Topics will include syllabus structure, quiz techniques, testing strategies, letters of recommendation and how to get a good teaching evaluation from a pre-med.

Computing with impure numbers - Automatic consistency checking and units conversion using computer algebra

NASA Technical Reports Server (NTRS)

Stoutemyer, D. R.

1977-01-01

The computer algebra language MACSYMA enables the programmer to include symbolic physical units in computer calculations, and features automatic detection of dimensionally-inhomogeneous formulas and conversion of inconsistent units in a dimensionally homogeneous formula. Some examples illustrate these features.

Architecture and Impact of an Open, Online, Remixable, and Multimedia-Rich Algebra 1 Course

ERIC Educational Resources Information Center

Bissell, Ahrash N.

2012-01-01

Less than half of the students in the United States graduate from high school and are ready to take college-level math courses. Many years and varieties of remedial math programs have failed to dramatically improve outcomes, especially at scale. The question we face is whether technology in general, and open educational resources in particular,…

The Effects of Blue Ink Print on Students' Memory Retention of Math Terms and Definitions.

ERIC Educational Resources Information Center

Din, Feng S.; Barnes, Kahlon

This study investigated whether students' memory retention rate improved when they were provided with blue ink printed material. A pretest, treatment, posttest with control group design was used. The participants were 93 10th and 11th grade students in algebra and geometry courses, and there were 2 classes in each course. The treatment lasted for…

Formula 1--A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

ERIC Educational Resources Information Center

Gerny, Marianne; Alpers, Burkhard

2004-01-01

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple[R], which provides the means…

Quantization of noncompact coverings and its physical applications

NASA Astrophysics Data System (ADS)

Ivankov, Petr

2018-02-01

A rigorous algebraic definition of noncommutative coverings is developed. In the case of commutative algebras this definition is equivalent to the classical definition of topological coverings of locally compact spaces. The theory has following nontrivial applications: • Coverings of continuous trace algebras, • Coverings of noncommutative tori, • Coverings of the quantum SU(2) group, • Coverings of foliations, • Coverings of isospectral deformations of Spin - manifolds. The theory supplies the rigorous definition of noncommutative Wilson lines.

Playing with Quantum Toys: Julian Schwinger's Measurement Algebra and the Material Culture of Quantum Mechanics Pedagogy at Harvard in the 1960s

NASA Astrophysics Data System (ADS)

Gauvin, Jean-François

2018-03-01

In the early 1960s, a PhD student in physics, Costas Papaliolios, designed a simple—and playful—system of Polaroid polarizer filters with a specific goal in mind: explaining the core principles behind Julian Schwinger's quantum mechanical measurement algebra, developed at Harvard in the late 1940s and based on the Stern-Gerlach experiment confirming the quantization of electron spin. Papaliolios dubbed his invention "quantum toys." This article looks at the origins and function of this amusing pedagogical device, which landed half a century later in the Collection of Historical Scientific Instruments at Harvard University. Rendering the abstract tangible was one of Papaliolios's demonstration tactics in reforming basic teaching of quantum mechanics. This article contends that Papaliolios's motivation in creating the quantum toys came from a renowned endeavor aimed, inter alia, at reforming high-school physics training in the United States: Harvard Project Physics. The pedagogical study of these quantum toys, finally, compels us to revisit the central role playful discovery performs in pedagogy, at all levels of training and in all fields of knowledge.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-02-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-12-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-11-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

The Mathematics of "Star Trek"--An Honors Colloquium

ERIC Educational Resources Information Center

Karls, Michael A.

2011-01-01

After the success of a course on cryptography for a general audience, based on Simon Singh's "The Code Book" [49], I decided to try again and create a mathematics course for a general audience based on "The Physics of Star Trek" by Lawrence Krauss [32]. This article looks at the challenges of designing a physics-based mathematics course "from…

Problems Relating Mathematics and Science in the High School.

ERIC Educational Resources Information Center

Morrow, Richard; Beard, Earl

This document contains various science problems which require a mathematical solution. The problems are arranged under two general areas. The first (algebra I) contains biology, chemistry, and physics problems which require solutions related to linear equations, exponentials, and nonlinear equations. The second (algebra II) contains physics…

Asymptotic identity in min-plus algebra: a report on CPNS.

PubMed

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

PubMed Central

Li, Ming; Zhao, Wei

2012-01-01

Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions. PMID:21822446

A Lab-Based, Lecture-Free General Physics Course

NASA Astrophysics Data System (ADS)

Schneider, Mark B.

1997-04-01

The past four years have seen the development of a discovery style, lecture-free, lab-based General Physics course at Grinnell College. Similar in spirit to Priscilla Laws' Workshop Physics (P. Laws, Physics Today, Dec. 1991, p. 24.), this course is a calculus- based, two-semester sequence, which is offered in parallel with more conventional lecture sections, allowing students choice of pedagogical styles. This new course is taught without a text, allowing a somewhat atypical ordering of topics and the early inclusion of a modern introduction to quantum and statistical mechanics. A complete set of laboratory materials was developed at Grinnell for this course, with activities considerably different in most cases than Laws' activities. A quick overview of the pedagogical style and topics covered will be given, and then several specific activities will be described in greater detail. The course has been shown to be a popular and viable alternative to the more conventional sections for majors and non-majors; ongoing efforts to assess the course will be described, especially those that make comparisons between this course and more conventional sections.

Using interviews to understand the assignment mechanism in a nonexperimental study: the case of eighth grade algebra.

PubMed

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.

Classical versus Computer Algebra Methods in Elementary Geometry

ERIC Educational Resources Information Center

Pech, Pavel

2005-01-01

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

Linear algebraic methods applied to intensity modulated radiation therapy.

PubMed

Crooks, S M; Xing, L

2001-10-01

Methods of linear algebra are applied to the choice of beam weights for intensity modulated radiation therapy (IMRT). It is shown that the physical interpretation of the beam weights, target homogeneity and ratios of deposited energy can be given in terms of matrix equations and quadratic forms. The methodology of fitting using linear algebra as applied to IMRT is examined. Results are compared with IMRT plans that had been prepared using a commercially available IMRT treatment planning system and previously delivered to cancer patients.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chung, Won Sang, E-mail: mimip4444@hanmail.net; Hounkonnou, Mahouton Norbert, E-mail: norbert.hounkonnou@cipma.uac.bj; Arjika, Sama, E-mail: rjksama2008@gmail.com

In this paper, we propose a full characterization of a generalized q-deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed q-number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and discussed.

Gender-based performance differences in an introductory physics course

NASA Astrophysics Data System (ADS)

McKinnon, Mark Lee

Cognitive research has indicated that the difference between males and females is negligible. Paradoxically, in traditionally-taught college level introductory physics courses, males have outperformed females. UC Davis' Physics 7A (the first class of a three-quarter Introduction to Physics sequence for Life-Science students), however, counters this trend since females perform similarly to males. The gender-based performance difference within the other two quarters (Physics 7B & 7C) of the radically restructured, active-learning physics sequence still echo the traditionally-taught courses. In one experiment, I modified the laboratory activity instructions of the Physics 7C course to encourage further group interaction. These modifications did not affect the gender-based performance difference. In a later experiment, I compared students' performance on different forms of assessment for certain physics concepts during the Physics 7C course. Over 500 students took weekly quizzes at different times. The students were given different quiz questions on the same topics. Several quiz questions seemed to favor males while others were more gender equitable. I highlighted comparisons between a few pairs of questions that assessed students' understanding of the same physical concept. Males tended to perform better in responding to questions that seemed to require spatial visualization. Questions that required greater understanding of the physical concept or scientific model were more gender neutral.

A case study of successful e-learning: a web-based distance course in medical physics held for school teachers of the upper secondary level.

PubMed

Jönsson, Bo-Anders

2005-09-01

Learning activities and course design in the new context of e-learning, such as in web-based courses involves a change both for teachers and students. The paper discusses factors important for e-learning to be successful. The development of an online course in medical physics and technology for high school teachers of physics, details of the course, and experience gained in connection with it are described. The course syllabus includes basics of radiation physics, imaging techniques using ionizing or non-ionizing radiation, and external and internal radiation therapy. The course has a highly didactic approach. The final task is for participants to design a course of their own centered on some topic of medical physics on the basis of the knowledge they have acquired. The aim of the course is to help the teachers integrate medical physics into their own teaching. This is seen as enhancing the interest of high school students in later studying physics, medical physics or some other branch of science at the university level, and as increasing the knowledge that they and people generally have of science. It is suggested that the basic approach taken can also have applicability to the training of medical, nursing or engineering students, and be used for continuing professional development in various areas.

Parametric Equations: Push 'Em Back, Push 'Em Back, Way Back!

ERIC Educational Resources Information Center

Cieply, Joseph F.

1993-01-01

Stresses using the features of graphing calculators to teach parametric equations much earlier in the curriculum than is presently done. Examples using parametric equations to teach slopes and lines in beginning algebra, inverse functions in advanced algebra, the wrapping function, and simulations of physical phenomena are presented. (MAZ)