Search

This volume was organized at the request of the SMSG Panel on Research for their use in identifying needed research in mathematics education. The five papers provide a review of research in each of their areas up through early 1969. Papers included are: (1) Attitudes Toward Mathematics, by Lewis R. Aiken, Jr.; (2) Classroom Teaching of Mathematics, by James T. Fey; (3) Piagetian Studies and Mathematics Learning, by D. B. Harrison; (4) Computers in Mathematics Instruction, by Larry L. Hatfield; and (5) Problem-Solving and Creative Behavior in Mathematics, by Jeremy Kilpatrick. Extensive references follow each of the papers. (RH)

Presented are 11 technical papers, position statements and instructional programs on the severely handicapped. Included are the following titles: "A Public School Program for Severely and Profoundly Handicapped Students: Zero Exclusion,""Components of Instructional Programs for Severely Handicapped Students,""Procedures of Task Analysis as Related to Developing Instructional Programs for the Severely Handicapped,""Evaluation of the Severely Retarded and Multiply-Handicapped: An Alternative,""Community Transportation: Teaching Severely Handicapped Students to Ride a Public Bus System,""Teaching Orthopedically Handicapped Adolescents to Secure Selected Products and Services from Their Community Through Functional Use of the Yellow Pages and Telephone,""A Comparison of Two Procedures for Teaching Severely Handicapped Students to Differentially Respond to Individual Components of Language Cues,""Skill Sequences and Programming for the Severely Handicapped: Use of a Math Skill Sequence in the Instruction and Evaluation of Severely Handicapped Students,""Skill Sequences and Curriculum Development: Application of a Rudimentary Developmental Math Skill Sequence in the Instruction and Evaluation of Severely Handicapped Students,""Teaching Trainable Level Multiply Handicapped Students to Use Picture Cues, Context Cues, and Initial Consonant Sounds to Determine the Labels of Unknown Words," and "Teaching Social Interaction Skills to Severely Handicapped Students." (LS)

The paper describes a study of the comparative effectiveness of certain courses in achieving specified educational objectives. Social studies, language arts, vocational/technical, math, science, and fine arts courses were compared as to their effectiveness in achieving "social education." By means of a group concensus of elementary and secondary teachers, common objectives of social education were identified, such as "builds character and good citizenship." The objectives were then arranged in an attitude scale on which teachers could register the degree to which they believed any particular course accomplished those objectives. In the study, 115 teachers responded to the scale six times, once each for the six content areas listed above. The results were compared among the six curricular areas to determine a composite teacher perception of which area was most effective in meeting the objectives of social education. Social studies objectives seemed representative of general education objectives. Objectives for individual curriculum areas did not seem to change from elementary to secondary grades. The strongest relationship existed between science and mathematics objectives. Social studies was ranked among the top third of most useful curriculum areas. (Author/AV)

Thirteen authors present twelve articles concerning the development of basic skills programs in secondary schools. These articles focus on the following topic areas: practices and strategies for teaching basic skills in secondary classrooms; language as a factor in basic skills learning; development of skills in oral communication, reading, writing, and mathematics; creation of an interdisciplinary team approach to basic skills instruction; selection of mutually reinforcing instructional materials; characteristics of tests and testing procedures used for demonstrating student achievement; the principal's role in effective development of basic skills programs; the impact of administrators' leadership styles and managerial abilities; and the significance of leadership in school administration generally. (PGD)

Intended as an example for other college libraries, this collection of 38 pathfinders and bibliographies was developed by the reference staff of the Calvin Coolidge Library at Castleton State College, Vermont. Designed to present the types of literature available in particular subject fields and those works readily available in the Coolidge Library, typical pathfinders include a cover page explaining the use of the card catalog and periodicals, and sections on research guides and bibliographies; dictionaries, encyclopedias, and handbooks; and indexes and abstracts. Each entry provides the author, title, call number, and a brief description of the reference tool. The pathfinders are as follows: (1) American History; (2) Art and Architecture; (3) Biology; (4) Business; (5) Business and Industry; (6) Careers; (7) Census Materials; (8) Chemistry; (9) Classical Literature; (10) Computer Science; (11) Criminal Justice; (12) Drunk Driving and the Drinking Age; (13) Economics; (14) Education; (15) English and American Literature; (16) English Composition; (17) European History; (18) French and Spanish Language and Literature; (19) Geography; (20) Geology; (21) Government Documents; (22) Indexes; (23) Investing in U.S. Stocks; (24) Law; (25) Marketing; (26) Mathematics; (27) Medical Aspects of Drug Abuse; (28) Mass Communications; (29) Nuclear Weapons and Disarmament; (30) Nursing; (31) Physical Education; (32) Political Science; (33) Psychology; (34) Research Papers; (35) Social Work; (36) Sociology; (37) Theater; and (38) World Literature. A sample cover page is provided. (KM)

Provides an annotated bibliography of the 39 best science and technology books from 1993 in the areas of animal life, astronomy, biography, chemistry, earth science, environmental sciences, evolution, mathematics, medical sciences, natural history, paleontology, philosophy of science, physics, psychology, general science, and technology. Ethical issues addressed by the publications are noted. (LRW)

This monograph from the University of Minnesota General College (GC) discusses theoretical perspectives on developmental education from both new and established standpoints. GC voluntarily eliminated its degree programs in order to focus on preparing under-prepared students for transfer to the university system. GC's curricular model includes a multi-disciplinary range of base curriculum courses integrating both skills and academic content. This model, which does not focus on traditional skills-based models for developmental education, provides students with a range of perspectives and academic training for continuing work directly in their majors. In this monograph, GC faculty and staff offer perspectives on the theoretical foundations of developmental education. Papers are divided into the following categories: (1) New and Revisited Theories for Developmental Education, with articles by Carl J. Chung, Jeanne L. Higbee, Patrick Bruch, and Dana Britt Lundell and Terence Collins; (2) Culture and Constructivism, with articles by Heidi Lesley Brajas, Mark H. Pedelty and Walter R. Jacobs, Rashne Jehangir, and David L. Ghere; (3) Literacy and Composition, with articles by Amy M. Lee, Thomas Reynolds, and Ditlev S. Larsen; and (4) Theories for Math and Science, with articles by Randy Moore, Allen B. Johnson, Thomas Brothen and Cathrine A. Wambach, and D. Patrick Kinney. Each paper contains references. (NB)

This paper reports on a class assignment written by preservice teachers on the use of mathematics in different professions. The professions included licensed practical nurse, auto mechanic, research and development product manager for industrial cleaning products, dental office assistant, snack bar employee at a beach club, beauty salon owner and operator, apple orchard and fruit stand owner, secretary at a university alumni hall, bus person at a restaurant, video store clerk, professional mover, convenience store assistant manager, pizza restaurant server, meteorologist, and land surveyor. (YDS)

This chapter mines some of the powerful consequences of the basic measure theory in Chapter V. Sections 1-3 establish properties of Lebesgue measure and other Borel measures on Euclidean space and on open subsets of Euclidean space. The main general property is the regularity of all such measures—that the measure of any Borel set can be approximated by the measure of compact sets from within and open sets from without. Lebesgue measure in all of Euclidean space has an additional property, translation invariance, which allows for the notion of the convolution of two functions. Convolution gives a kind of moving average of the translates of one function weighted by the other function. Convolution with the dilates of a fixed integrable function provides a handy kind of approximate identity. Section 4 gives the final form of the comparison of the Riemann and Lebesgue integrals, a preliminary form having been given in Chapter III. Section 5 gives the final form of the change-of-variables theorem for integration, starting from the preliminary form of the theorem in Chapter III and taking advantage of the ease with which limits can be handled by the Lebesgue integral. Sard's Theorem allows one to disregard sets of lower dimension in establishing such changes of variables, thereby giving results in their expected form rather than in a form dictated by technicalities. Section 6 concerns the Hardy-Littlewood Maximal Theorem in N dimensions. In dimension 1, this theorem implies that the derivative of a 1 -dimensional Lebesgue integral with respect to Lebesgue measure recovers the integrand almost everywhere. The theorem in the general case implies that certain averages of a function over small sets about a point tend to the function almost everywhere. But the theorem can be regarded as saying also that a particular approximate identity formed by dilations applies to problems of almost-every where convergence, as well as to problems of norm convergence and uniform convergence. A corollary of the theorem is that many approximate identities formed by dilations yield almost-everywhere convergence theorems. Section 7 redevelops the beginnings of the subject of Fourier series using the Lebesgue integral, the theory having been developed with the Riemann integral in Section I.10. With the Lebesgue integral and its accompanying tools, Fourier series are meaningful for more functions than before, Dini's test applies even to a wider class of Riemann integrable functions than before, and Fejér's Theorem and Parseval's Theorem become easier and more general than before. A completely new result with the Lebesgue integral is the Riesz-Fischer Theorem, which characterizes the trigonometric series that are Fourier series of square-integrable functions. Sections 8-10 deal with Stieltjes measures, which are Borel measures on the line, and their application to Fourier series. Such measures are characterized in terms of a class of monotone functions on the line, and they lead to a handy generalization of the integration-by-parts formula. This formula allows one to bound the size of the Fourier coefficients of functions of bounded variation, which are differences of monotone functions. In combination with earlier results, this bound yields the Dirichlet-Jordan Theorem, which says that the Fourier series of a function of bounded variation converges pointwise everywhere, the convergence being uniform on any compact set on which the function is continuous. Section 10 is a short section on computation of integrals. [ABSTRACT FROM AUTHOR]

Copyright of Advanced Algebra is the property of Springer eBooks and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Advanced Algebra is the property of Springer eBooks and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This chapter develops some general theory for field extensions and then goes on to study Galois groups and their uses. More than half the chapter illustrates by example the power and usefulness of the theory of Galois groups. Prerequisite material from Chapter VIII consists of Sections 1-6 for Sections 1-13 of the present chapter, and it consists of all of Chapter VIII for Sections 14-17 of the present chapter. Sections 1-2 introduce field extensions. These are inclusions of a base field in a larger field. The fundamental construction is of a simple extension, algebraic or transcendental, and the next construction is of a splitting field. An algebraic simple extension is made by adjoining a root of an irreducible polynomial over the base field, and a splitting field is made by adjoining all the roots of such a polynomial. For both constructions, there are existence and uniqueness theorems. Section 3 classifies finite fields. For each integer q that is a power of some prime number, there exists one and only one finite field of order q, up to isomorphism. One finite field is an extension of another, apart from isomorphisms, if and only if the order of the first field is a power of the order of the second field. Section 4 concerns algebraic closure. Any field has an algebraic extension in which each nonconstant polynomial over the extension field has a root. Such a field exists and is unique up to isomorphism. Section 5 applies the theory of Sections 1-2 to the problem of constructibility with straightedge and compass. First the problem is translated into the language of field theory. Then it is shown that three desired constructions from antiquity are impossible: "doubling a cube," trisecting an arbitrary constructible angle, and "squaring a circle." The full proof of the impossibility of squaring a circle uses the fact that π is transcendental over the rationals, and the proof of this property of π is deferred to Section 14. Section 5 concludes with a statement of the theorem of Gauss identifying integers n such that a regular n-gon is constructible and with some preliminary steps toward its proof. Sections 6-8 introduce Galois groups and develop their theory. The theory applies to a field extension with three properties—that it is finite-dimensional, separable, and normal. Such an extension is called a "finite Galois extension." The Fundamental Theorem of Galois Theory says in this case that the intermediate extensions are in one-one correspondence with subgroups of the Galois group, and it gives formulas relating the corresponding intermediate fields and Galois subgroups. Sections 9-11 give three standard initial applications of Galois groups. The first is to proving the theorem of Gauss about constructibility of regular n-gons, the second is to deriving the Fundamental Theorem of Algebra from the Intermediate Value Theorem, and the third is to proving the necessity of the condition of Abel and Galois for solvability of polynomial equations by radicals-that the Galois group of the splitting field of the polynomial have a composition series with abelian quotients. Sections 12-13 begin to derive quantitative information, rather than qualitative information, from Galois groups. Section 12 shows how an appropriate Galois group points to the specific steps in the construction of a regular n-gon when the construction is possible. Section 13 introduces a tool known as Lagrange resolvents, a precursor of modern harmonic analysis. Lagrange resolvents are used first to show that Galois extensions in characteristic 0 with cyclic Galois group of prime order p are simple extensions obtained by adjoining a pauth root, provided all the pauth roots of 1 lie in the base field. Lagrange resolvents and this theorem about cyclic Galois groups combine to yield a derivation of Cardan's formula for solving general cubic equations.… [ABSTRACT FROM AUTHOR]

This volume collects together revised papers originally presented at the 7th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 2006). LOFT is a key venue for presenting research at the intersection of logic, economics and computer science, and the present collection gives a lively and wide-ranging view of an exciting and rapidly growing area.

As a part of the teacher licensure program at the graduate level at The University of Tennessee at Chattanooga (UTC), the M.Ed. Licensure candidate is required to complete an action research project during a 3-semester-hour course that coincides with the 9-semester-hour student teaching experience. This course, Education 5900 Culminating Experience, requires the student to implement an action research plan designed through (a) the Education 5000 Introduction to Inquiry course or the Education 5010 Methods of Educational Research course, (b) one of the two learning assessments required during student teaching, or (c) a newly-designed project not used as one of the learning assessments. With funding through a UTC Teaching, Learning, and Technology Faculty Fellows award, the Education 5900 course is conducted through the use of an online, course management system (Blackboard), allowing for asynchronous discussion and use of the digital drop box feature for submitting required papers. The action research projects from, fall semester 2010, are presented below. Papers include: (1) Student Perceptions of Layered Curriculum[R] vs. Traditional Coursework on Class Grades for 11th-12th Grade Economics and Government Students (Heidi Beckham); (2) What Motivates Young Readers to Read? (Sarah Bolton); (3) Just Story Time? An Evaluation of the Effects of Reading Aloud to Secondary-aged Students (Keeton Christian); (4) Using a Behavioral Management Reward System to Decrease the Behavioral Problems in a High School Setting (Amber Collins); (5) Ready for Middle School Math? (Dorothy L. Finch); (6) Improving Vocabulary Acquisition and Grammar Comprehension in The Second Language through Five Minutes of In-class Reading Time (Veronica V. Herrera); (7) Technology and Mathematics: Classroom Companions for the Future (April J. Huddleston); (8) Perceptions of Fourth-Grade Math Students on Computer-Based Homework (Amanda I. H. Legge); (9) Do Students Retain More Information through Real Life Images or through Clip Art Cartoon Images? (Courtney Sloane Phillips); (10) The Visual Aspect of Vocabulary: Increasing Comprehension and Retention (Nicole Pinkerton); (11) Increasing Grammar Accuracy in the TPRS Classroom (Erin Segroves); (12) Effective Differentiated Instructional Strategies of Middle Grades' Mathematics Instructors (Elizabeth W. Stewart); (13) Vocational Education: Is It Meeting the Needs of the Community? (Stephen Tompkins); (14) The Effect of Daily Quizzes on Student Scores and Class Participation: A Study on High School Economic Students (Elizabeth Warren); and (15) Math-ercise...Could It Fatten Up Scores? (Wendi Worley). (Individual papers contain references, figures, and appendices.) [For "Culminating Experience Action Research Projects, Volume 16, Spring 2010," see ED518906. Abstract modified to meet ERIC guidelines.]

This book contains the full text of the mathematical notebooks of Helmut Hasse (1898-1979), who was one of the leading mathematicians of the 20th century. The originals have been preserved in the Handschriftenabteilung at the Göttingen University Library. There are a total of seven volumes which contain 98 entries all together; these span the time period from July 1923 to February 1935. Each of the entries is preceded by a short comment. An extensive bibliography is provided. Compared to the other documents and papers from Hasse Nachlass at Göttingen, these papers are quite different. They detail Hasse‘s mathematical background, interests and his way of approaching problems. Many of the entries are inspired by Hasse‘s discussions with other mathematicians (for example, Emil Artin is often mentioned). One of the notable highlights in the entries is the first documentation of Artin‘s conjecture on primitive roots (1927), which Hasse noted down after a discussion with Artin. Another example is the first proof of the Riemann hypothesis for an extended class of function fi elds of high genus, namely those of the generalised Fermat fields with a finite field of constants (1932), after corresponding with Harold Davenport.

This is the first of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains combinatorial and homological surveys. The combinatorial papers document some of the increasing focus in commutative algebra recently on the interaction between algebra and combinatorics.

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.The second portion of the book introduces trigonometry. Trig is introduced through an integrated circle/triangle approach. Identities are introduced in the first chapter, and revisited throughout. Likewise, solving is introduced in the second chapter and revisited more extensively in the third chapter. As with the first part of the book, an emphasis is placed on motivating the concepts and on modeling and interpretation.In addition to the paper homework sets, algorithmetically generated online homework is available as part of a complete course shell package, which also includes a sample syllabus, teacher notes with lecture examples, sample quizzes and exams, printable classwork sheets and handouts, and chapter review problems. If you teach in Washington State, you can find the course shell in the WAMAP.org template course list. For those located elsewhere, you can access the course shell at MyOpenMath.com. A self-study version of the online course exercises is also available on MyOpenMath.com for students wanting to learn the material on their own, or who need a refresher.

This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics. "This new and expanded edition is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge Colleges for conditional offers in mathematics. They are also used by some other UK universities and many mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics bridges the gap between school and university mathematics, and prepares students for an undergraduate mathematics course. The questions analysed in this book are all based on past STEP questions and each question is followed by a comment and a full solution. The comments direct the reader’s attention to key points and put the question in its true mathematical context. The solutions point students to the methodology required to address advanced mathematical problems critically and independently. This book is a must read for any student wishing to apply to scientific subjects at university level and for anyone interested in advanced mathematics.

Summary: This book is a reprint of papers in the Special Issue published in Education Sciences under the title "Online and Distance Learning during Lockdown Times: COVID-19 Stories". It includes papers covering Higher Education (post-secondary) sector representing international experience of teaching and learning from the start of the first episode of lockdown due to the Covid-19 pandemic.