Search

Among the great challenges posed to democracy today is the use of technology, data, and automated systems in ways that threaten the rights of the American public. Too often, these tools are used to limit our opportunities and prevent our access to critical resources or services. These problems are well documented. In America and around the world, systems supposed to help with patient care have proven unsafe, ineffective, or biased. Algorithms used in hiring and credit decisions have been found to reflect and reproduce existing unwanted inequities or embed new harmful bias and discrimination. Unchecked social media data collection has been used to threaten people's opportunities, undermine their privacy, or pervasively track their activity--often without their knowledge or consent. To advance President Biden's vision, the White House Office of Science and Technology Policy has identified five principles that should guide the design, use, and deployment of automated systems to protect the American public in the age of artificial intelligence. "The Blueprint for an AI Bill of Rights" is a guide for a society that protects all people from these threats--and uses technologies in ways that reinforce our highest values. Responding to the experiences of the American public, and informed by insights from researchers, technologists, advocates, journalists, and policymakers, this framework is accompanied by a technical companion--a handbook for anyone seeking to incorporate these protections into policy and practice, including detailed steps toward actualizing these principles in the technological design process. These principles help provide guidance whenever automated systems can meaningfully impact the public's rights, opportunities, or access to critical needs.

Many arguments have been made against allowing examinees to review and change their answers after completing a computer adaptive test (CAT). These arguments include: (1) increased bias; (2) decreased precision; and (3) susceptibility of test-taking strategies. Results of simulations suggest that the strength of these arguments is reduced or eliminated by using specific information item selection (SIIS), under which items are selected to meet information targets, instead of the more common maximum information item selection, under which items are selected to maximize information. Because item review offers several benefits, by using SIIS and an appropriate ability estimator, allowing item review on a CAT is probably warranted. (Contains 1 table, 15 figures, and 31 references.) (Author/SLD)

New items are being calibrated for the next generation of the computerized adaptive (CAT) version of the Armed Services Vocational Aptitude Battery (ASVAB) (Forms 5 and 6). The requirements that the items be "good" three-parameter logistic (3-PL) model items and typically "like" items in the previous CAT-ASVAB tests have resulted in a set of algorithmic rules that are general enough to be of interest to researchers and others working to improve CAT tests. For CAT-ASVAB on-line calibration, a seeded-item scheme is being used. Answers to the seeded items (new) are collected along with answers to nonseeded items to allow the estimation of examinee ability and the evaluation of the quality of each new item relative to the ability scale. Six types of deficient items are discussed. The first five types lead to nonparametric item characteristic curves that cannot be fitted well with a 3-PL model. The sixth category, in which the item has insufficient information, is the most difficult to correct. A set of factors has been developed to help deal with these problems and increase the value of item information. (Contains 6 tables and 6 figures.) (SLD)

The report describes improved algorithms within a computer program for identifying spelling and word order errors in student responses. A "markup analysis" compares a student's response string to an author-specified model string and generates a graphical error markup that indicates spelling, capitalization, and accent errors, extra or missing words, and out-of-order words. The algorithm determines whether the response was acceptable or not, and computes a string of graphical error marks to be displayed below the student response. Synonyms and ignorable words can be specified and spelling errors, extra words, and word order errors can be accepted at the author's discretion. Spelling analysis is done using a dynamic programming algorithm that produces a least-cost edit trace; word order analysis is implemented using recursive branch and bound search. Improvements on earlier versions of the algorithm give more intuitive markup values. The algorithm is implemented as a HyperTalk XFCN. HyperTalk scripts can provide numerous input parameters that control the details of the matching process, and the algorithm returns a variety of fit measurements that characterize the match. Non-roman linear writing scripts are supported. The report contains detailed information on use of the function and serves as a user manual. Contains two references. (Author/MSE)

The University of California Catalog and Periodicals databases each have over 20 separately contributing libraries, and records for the same work can enter the MELVYL system from different campus libraries. MELVYL's goal is to have one union record for each distinct edition of a work. To promote this goal, the University's Division of Library Automation (DLA) has developed record merging algorithms that include author, title, place of publication, publisher, date, and pagination. Other data elements from the MARC record that are significant in distinguishing between different works or different editions of the same work have been added to the algorithm. This guide describes DLA's procedures for merging records, MARC fields and subfields used in merging, and bibliographic information used in merging, and provides examples of merged and nonmerged records. Records of books and in-analytic materials and records of periodicals are merged separately, and the procedures for merging records for these two formats are described separately. Some of the results of using the algorithm to merge different types of records are summarized, and it is concluded that these experiences with merging highlight how important it is to have standards for minimum record content and to use nationally- and internationally-assigned numbers for records coming into the catalog. (KRN)

Suggests that algorithms, both traditional and student-invented, are proper objects of study not only as tools for computation, but also for understanding the nature of the operations of arithmetic. (Author/NB)

Describes how open-ended writing prompts provide a window into student understanding and mathematical thinking. (YDS)

Presents an approach for illustrating, on an intuitive level, the significance of loop invariants for algorithm design and analysis. The illustration is based on mathematical games that require the exploration of regularities via problem-solving heuristics. (Author/MM)

Presents research on students' use and understanding of algorithms in Poland. Concludes that there are detrimental side effects that stem from the teaching and learning of standard written algorithms. (ASK)

Describes a multicultural enrichment project for 4th graders that highlights number systems and computation algorithms of various cultures. Discusses student responses and reactions. (KHR)

Presents several alternatives to customary algorithms for whole number arithmetic. Includes a brief history of each algorithm and discusses why each might be useful for particular kinds of children. (KHR)

Describes a calculator exercise that can help students develop a better visual and numeric feel for Newton's method. (KHR)

Presents four questions to consider when supervising elementary mathematics teachers, who come with many preconceptions about teaching and learning mathematics: What mathematical concepts, procedures, or algorithms are you teaching? Are the concepts and procedures part of a unit? What types of questions do you pose? and What understanding of concepts or knowledge of procedure do your students possess before instruction? (SM)

Debates the place of standard methods, the calculator, and mental mathematics in elementary education. Proposes a framework for computation that emphasizes a sequence for introducing computational procedures. (ASK)

Reviews the historical development of subtraction algorithms used in the United States. Discusses different algorithms used and developed throughout history that had a major impact on the way subtraction is taught today. (Contains 22 references.) (ASK)

Examines the philosophy behind the issue of computational fluency in "Principles and Standards." (Author)

Reviews the historical use of each of the three algorithms used for subtraction in the United States: (1) the equal additions; (2) the decomposition; and (3) the Austrian method. Discusses the modification to the decomposition algorithm and gives a brief overview of the current status of subtraction algorithms. Contains 12 references. (Author/ASK)

Presents an algorithm to compute the critical path in a graph representing a project evaluation research task. Once the algorithm is executed, the last matrix obtained permits the visualization of some important information which leads to the determination of the weight of the critical path. (Author/MM)

Presents a problem that requires solving a card problem by exploring patterns that will lead to a logical solution. Involves students in developing and analyzing their own algorithms as well as discussing their reasoning with peers. (ASK)

"Algorithmic counseling" is an attempt to apply recent instructional regulation techniques to graduate counselor training and research. This paper seeks to explain what algorithms are, why they could be useful, and how they can be constructed. A central motivation for studying algorithms is their utility in showing students how to accomplish a task in specific, completely understandable steps. The paper includes an algorithm designed to reflect client feelings. (Author)

A symposium with four major presentations centering on the topic of computer-based information retrieval. Also highlighted are several features of the Wisconsin Information System for Education (WISE-ONE) and the Educational Resources Information Center (ERIC) system. The first paper in the series discusses the development, current capabilities and future directions of the WISE-ONE system and the second analyzes the history and present status of ERIC. The third paper focuses on file search strategies for the WISE-ONE information retrieval system, comparing various search algorithms used in information retrieval programs and leading to an in-depth consideration of the hash coding scheme used in WISE-ONE. The final paper treats the development of search strategies for effective computerized literature searches of the ERIC data base. The use of the ERIC thesaurus and of the logical operators AND, OR, and NAND is stressed and details are provided relating to a demonstration search supported by a UNIVAC 1108 computer. (PB)

Network Analysis is an observational system focusing on the relationships of individuals within a system--their subgroups, their leaders, and the frequency of their communications. The strength of relationships can be measured by examining the incidence and duration of intercommunications. Using data accumulated by questioning each member of the organization, the computer employs a prescribed set of algorithms, the Network Analysis Program (NEGOPY), to yield a topological interpretation of individuals, subgroups, and inte communications. (EMH)

This student textbook is designed to incorporate programable calculators in grade 11 mathematics. The eight chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Exponents and Logarithms; (3) Trigonometry of the Right Triangle; (4) Trigonometry Beyong the Right Triangle; (5) Graphs of the Trigonometric Functions and Their Inverses; (6) Solution of Oblique Triangles and Other Applications of Trigonometry; (7) The Quadratic and Other Polynomial Functions; and (8) Sequences and Series. Each chapter is further subdivided into topic sections. Each section concludes with a set of calculator-oriented exercises geared towards the material covered. (MP)

This student textbook is designed to incorporate programable calculators in grade 12 mathematics. The seven chapters contained in this document are: (1) Using Calculators in Mathematics; (2) Sequences, Series, and Limits; (3) Iteration, Mathematical Induction, and the Binomial Theorem; (4) Applications of the Fundamental Counting Principle; (5) Polynomial Functions; (6) Exponents and Logarithms; and (7) Trigonometric Functions. Each chapter is further subdivided into topic sections. Each section concludes with a set of calculator-oriented exercises geared towards the material covered. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate and secondary students. The contents of this French language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Spanish language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate and secondary students. The contents of this Greek language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Creole language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

Presented is an overview of some specific schemes that have been used successfully by teachers throughout New York State to strengthen basic mathematics skills. Components offer ideas that have been successful with primary, intermediate, and secondary students. The contents of this Italian language edition are identical to the English language and other foreign language editions. In addition to the Foreword, there are sections on: (1) Some Brief Observations About Strengthening Mathematics Skills; (2) The Balanced Mathematics Program; (3) "Par"--Puzzles+Arithmetic=Remediation; (4) Regrouping in Subtraction; (5) Money Games; (6) A Visual Sequence for Teaching Fractions; (7) A Space to Carry in Simple Addition and Multiplication Examples; (8) Grid Paper Computation; (9) The Need for Math Reading Skills; (10) A Structural Approach to Multiplication; (11) The Electronic Calculator in Remedial Mathematics; (12) Nature's Mathematics; and (13) Additional Teacher Designed Ideas. (MP)

This paper outlines the development of an activity that uses the computer's unique capabilities to provide students with a meaningful and highly motivating experience with the graphing of equations. The basic design of the game calls for the computer to display a coordinate grid on which it graphs any equations that are typed in by the student. Thirteen "Green Globs," each about .7 units in diameter, are scattered about the grid. The goal of the game is to explode all of the green globs by hitting them with graphs specified by typing in equations. If a shot misses the expected targets, diagnostic feedback is provided to debug the ideas used. The game is scored using an algorithm which encourages cleverly planned shots and provides a wide range of achievable scores. The decision to exclude the possibility of trigonometry functions in favor of other options is discussed. A provision of the game allows students to view any of the ten top scoring games and see what shots and strategies the top players have used. Highlights of classroom use of Green Globs are provided, including descriptions of techniques used by some of the more advanced students. One reference is cited. (CHC)

This material contains two units which view applications of computer science. The first of these examines Horner's scheme; and is designed to instruct the user on how to apply both this scheme and related algorithms. The second unit aims for student understanding of standard bisection, secant, and Newton methods of root finding and appreciation of their limitations and strong points. An introduction to more recent root finding methods is also provided. Both modules contain exercises, and answers to these problems are given at the conclusion of each unit. (MP)

This document contains two units that examine integral transforms and series expansions. In the first module, the user is expected to learn how to use the unified method presented to obtain Laplace transforms, Fourier transforms, complex Fourier series, real Fourier series, and half-range sine series for given piecewise continuous functions. In the second unit, the student is expected to use the method presented to find a function when given the Laplace transform, the Fourier transform, the coefficient transform, or the Fourier series expansion of a function. Each module contains exercises and a model exam. Answers to all questions are provided. (MP)

Applied mathematics is seen often to involve the solution of single equations or systems of equations. A particular technique for solving equations in the context of functions on the real line is examined. This technique includes an iterative process, which is viewed as an algorithm that can be implemented readily on inexpensive and widely available calculators. Some examples of physical problems in which the equations of interest arise are presented. This module includes exercises and a model exam. Answers to problems in the exercises and on the test are provided in the material. (MP)

This module is designed to apply mathematical models to nuclear deterrent problems, and to aid users in developing enlightened skepticism about the use of linear models in stability analyses and long-term predictions. An attempt is made at avoiding overwhelming complexities through concentration on land-based missile forces. It is noted that after the Second World War, the United States' monopoly on nuclear weapons permitted it to attempt to deter aggression through a policy of "massive retaliation." The history of change from this policy is outlined, and the chances for reaching an equilibrium in the nuclear arms race are examined through probabilistic models. Exercises are provided, and the answers to these problems are given at the end of the unit. (MP)

These modules view aspects of computer use in the problem-solving process, and introduce techniques and ideas that are applicable to other modes of problem solving. The first unit looks at algorithms, flowchart language, and problem-solving steps that apply this knowledge. The second unit describes ways in which computer iteration may be used effectively in problem solving, and shows ways in which two other forms of iteration may be applied in algorithm construction. Both modules include exercises, and each has a model exam. Answers to all problems presented are provided. (MP)

This unit is 1 of 12 developed for the university classroom portion of the Mathematics-Methods Program (MMP), created by the Indiana University Mathematics Education Development Center (MEDC) as an innovative program for the mathematics training of prospective elementary school teachers (PSTs). Each unit is written in an activity format that involves the PST in doing mathematics with an eye toward application of that mathematics in the elementary school. This document is one of four units that are devoted to the basic number work in the elementary school. In addition to an introduction to the unit, the text has sections on the conceptual development of multiplication and division, developing the basic multiplication and division facts, and computational algorithms for multiplication and division. (MP)

Arithmetic programming for students with mild mental disabilities requires a comprehensive perspective that includes attention to curriculum, instruction, and appraisal. Arithmetic computation should not dominate educational programming, but should be included in ways that are functionally relevant and meaningfully presented within a framework of problem-solving and applied experiences. The teaching of counting depends on an understanding of two basic concepts, one-to-one and many-to-one relationships. Instruction in these areas can take place in the forms of arrangements, patterns, and sets. A scheme referred to as the Interactive Unit makes instruction both systematic and flexible by organizing instruction, with four instructor inputs (manipulate, display, say, write) and four learner behavior changes (manipulate, identify, say, write). Within the schemata of the Interactive Unit, the teacher can develop an unlimited number of instructional activities and accompanying materials. In the use of arithmetic algorithms, it is important that the teacher become familiar with a variety of algorithms and correct only errors rather than the student's performance style. Other recommended practices include presenting addition as a process of joining sets, and using expanded notation to numerically represent each place value position. Examples are provided to illustrate how these methods can be used in the classroom. Eight figures are included. (JDD)

After an introduction including a brief history of measurement, conversion of units within the customary system, within the metric system, and from customary to metric and vice versa are discussed. A fraction/multiplication system is introduced to teach correct alignment of units of measurement and to direct proper multiplication and division of conversion factors. A number of solved examples are given, as well as several problems to be solved by the reader. It is suggested that successful completion of the problems should increase confidence in the student's ability to convert between measurement systems. (Author/PK)

This guidebook is designed for data analysts who are working with computer data files that contain records with incomplete data. It indicates choices the analyst must make and the criteria for making those choices in regard to the following questions: (1) What resources are available for performing the imputation? (2) How big is the data file? (3) What is the purpose for imputing missing data? (4) What structures exist in the recorded variables? (5) What is the pattern of missing data? (6) What assumptions are acceptable for this imputation? Answers to these questions constitute recommendations for imputation procedures. Several alternative recommendations and the conditions that determine the appropriateness of use are considered. The final section of the guidebook contains instructions for using PROC IMPUTE created by the Statistical Analysis Group in Education for the National Center for Education Statistics, and for interpreting its results. Appendices include: (1) Processing Time by Numbers of Variables and PROC IMPUTE; and (2) Sample Statistical Analysis System Program to Reweight for Total Nonresponse. (JAZ)

Compares methods of subtraction used by children and teachers. Suggests ways to encourage children to invent their own subtraction algorithms. (CCM)

Argues that there is a whole class of physiological topics that are best taught using dynamic diagrams, a series of diagrams generated through simple animations and based on user-provided inputs. Uses the theory of neural generation as an example. (DDR)

Suggests that issues surrounding the teaching of algorithms focus not on whether to teach them but rather on balancing and connecting the development of algorithmic thinking. Presents an approach to help students develop their algorithmic thinking. Contains 18 references. (ASK)

Indicates that there has been a lot of work done and that a great deal needs to be done in the future to explore the world of children's early number. Discusses the counting, the use of algorithm, practical mathematics, the use of manipulatives, individual differences and pedagogical concerns, and classroom applications. Contains 18 references. (ASK)

Describes use of the little-known Shuttle Puzzle in computer programming to elucidate the process of analyzing a problem and synthesizing observations into an algorithm that can be used to generate a programming solution. The process used to solve the problem reflects one that an expert uses. The method could be adapted for small-group cooperative learning. (Author/MSE)

This volume is the twenty-fourth in a series of 29 coordinated MINNEMAST units in mathematics and science for kindergarten and the primary grades. Intended for use by third-grade teachers, this unit guide provides a summary and overview of the unit, a list of materials needed, and descriptions of four groups of lessons and activities. The purposes and procedures for each activity are discussed. Examples of questions and discussion topics are given, and in several cases ditto masters, stories for reading aloud, and other instructional materials are included in the book. This unit covers both computational and measurement ideas. In the two sets of lessons on computation, the class simulates a computer in activities designed to promote understanding of addition and subtraction in a place value system. Measurement activities are related to liquid volume, length and time. Two job booklets, one on pouring and the other on balancing as methods of measurement, provide activities for independent work by students. (SD)

Parts one and two of a one-year computer-oriented calculus course (without analytic geometry) are presented. The ideas of calculus are introduced and motivated through computer (i.e., algorithmic) concepts. An introduction to computing via algorithms and a simple flow chart language allows the book to be self-contained, except that material on programming languages is excluded in order to allow the use of any language. Chapter topics include sequences, integrals, applications, functions, maxima, chain rule, derivatives, logarithmic and exponential functions, infinite series, and differential equations. (MP)

This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being taught to classes of children, extensive discussion notes, and detailed guides for correcting written lessons. This booklet contains exercises on rules moving two points and composition of number line rules, a summary of the problems in the film "Rules Moving Two Points," and the supplement. (MK)

This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being taught to classes of children, extensive discussion notes, and detailed guides for correcting written lessons. This booklet contains exercises on artificial operations and competing rules, and a summary of the problems from the film "Some Artificial Operations." (MK)

This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being taught to classes of children, extensive discussion notes, and detailed guides for correcting written lessons. This booklet contains exercises on work with artificial operations, a summary of the problems in the film "Frames and Number Line Jumping Rules," and the supplement. (MK)

This is one of a series of 20 booklets designed for participants in an in-service course for teachers of elementary mathematics. The course, developed by the University of Illinois Arithmetic Project, is designed to be conducted by local school personnel. In addition to these booklets, a course package includes films showing mathematics being taught to classes of children, extensive discussion notes, and detailed guides for correcting written lessons. This booklet contains exercises on the use of lower brackets, a summery of the problems in the film "Lower and Upper Brackets," and the supplement. (MK)