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1. Using a New Schema Approach with Primary at Risk Students in Word Problem Solving

Author

Amiripour, Parveneh, Dossey, John Arthur, and Shahvarni, Ahmad

Abstract

This comparative study of two approaches contrasts a schema-based approach to represent a solution approach to solving whole number contextual problems for grades 2 and 3 with the traditional textbook approach. The participants are 9 to 11- year-old Afghani refugee students enrolled in non-public schools administered by NGO organization in Iran. The subjects have difficulty with grade-level mathematics and have been retained in grade at least one year. Subjects were randomly selected from four classrooms in two schools. The schema-based experimental approach is called the Problem Patterns (PP) approach. Students receiving this instructional approach were taught to break problems into data, units, and desired solution, removing irrelevant information, and make a solution model with manipulatives. Control students followed the traditional classroom approach. All classes were taught by the first researcher. Evaluation results showed the PP students had higher achievement and growth scores than the control students. The results also showed the schema building portion of instruction contributed most to the differences in performance of the experimental groups' students.

Published
2017

2. Factor Analysis of Inertia, Capacities, and Educational Performance of At-Risk Students' Training Centres According to Their Academic Failure in Mathematics

Author

Amiripour, Parvaneh, Dossey, John A., and Shahvarani, Ahmad

Abstract

Immigrants face many barriers in moving from one country to another. Today's massive migrations are dislocating students from their cultures, families, and their schooling. In Iran, such students were not able to enter Iranian schools prior to 2017. Even now, many such immigrant students are being educated in centres administered by non-governmental organisations (NGO) where the schooling is focused on providing youth with knowledge on nutrition, health care, language and mathematics, and maintaining family links where possible. Still, external and internal factors lead to many at-risk students dropping out of the programs. The researchers have focused on the failure of at-risk students in mathematics in four of these schools supported by two NGO agencies. It was clear that the inertia of both teachers and students in mathematics was influencing both teacher choices and planning and student choices in providing conceptual understanding and algorithmic performance. Given the lack of instrumentation to gauge and describe organisational and managerial aspects of the schools and meaningful assessments of students' progress, the researchers modified a questionnaire from organisational inertia for examining the administrative factors in business and created a series of mathematics tests to quantify and describe at-risk students' movement through either second or third grade mathematics classes. The data provided by an Exploratory Factor Analysis of the assessment outcomes provide a predictive picture of student persistence versus administrative changes and, more generally, on ways that teacher/educators and educational staff members can implement strategies to help immigrant at-risk students transition from mindless repetition to understanding in their mathematics school work

Published
2017

3. Impact of Organizational Inertia and Dynamic Capabilities on Educational Performance of the Charitable Societies and Its Impact on Mathematical Performance of Elementary At-Risk Students

Author

Amiripour, Parvaneh, Dossey, John A., and Shahvarani, Ahmad

Abstract

This study is an adjunct to a research effort focused on a mathematical curricular innovation in four non-governmental schools in Tehran, Iran. This study queried balanced, random sample of 100 educational personnel from the schools concerning dynamic capabilities associated with change (sensing opportunities, seizing opportunities, and reconfiguring assets) and issues surrounding organizational inertia (finding resources, confronting path dependency in change, and establishing new processes). Additional data collected described the personnel's perceptions about innovations and new processes instituted in their schools. Student performance data from the prior year's final mathematical examination were also gathered. The data describe a portion of the educational change potential of the schools, including improved student achievement. The variables informed by all of the data were evaluated by multivariate methods. The findings showed that beliefs about dynamic capabilities had a significant positive impact on educational performance and that educational performance had a positive impact on the final mathematical exam scores. The results also indicate that the organizational inertia of the schools had a significant negative impact on the educational performance of the schools. Conclusions were formed based on the analysis of the defining factors of the variables mentioned above and recommendations given for implementing change are proposed.

Published
2017

5. Problem Solving in the PISA and TIMSS 2003 Assessments. Technical Report. NCES 2007-049

Author

National Center for Education Statistics (ED), Washington, DC., Dossey, John A., McCrone, Sharon S., and O'Sullivan, Christine

Abstract

In 2003, the Program for International Student Assessment (PISA) and Trends in International Mathematics and Science Study (TIMSS) included a special focus on problem-solving. This report reviews the problem-solving aspects of each study in order to compare and contrast the nature of problem solving in each assessment. The report's authors develop and use a definition for problem solving to identify items in the two assessments that address students' problem-solving capabilities. Items that were identified as problem-solving items in the TIMSS and PISA mathematics, science, and Cross-Disciplinary problem-solving assessments were analyzed in terms of six types of item characteristics: (1) content coverage; (2) cognitive processes; (3) problem-solving attributes; (4) item formats; (5) computational aspects; and (6) translation of representations. Appended are: (1) Examples of Problem-Solving and Exercise Items; (2) Item Format Examples; (3) Examples of Problem-Solving Attributes in Items; (4) Examples of Items Requiring Translations of Representations (TIMSS); (5) Scientific Inquiry Item Examples; and (6) Technical Notes. (Contains 18 tables, 2 exhibits, and 5 footnotes.)

Published
2006

6. Student Work and Teacher Practices in Mathematics.

Author

National Center for Education Statistics (ED), Washington, DC., Mitchell, Julia H., Hawkins, Evelyn F., Jakwerth, Pamela M., Stancavage, Frances B., and Dossey, John A.

Abstract

The National Assessment of Educational Progress (NAEP) is mandated by the United States Congress to survey the educational accomplishments of U.S. students and monitor changes in those accomplishments. For more than 25 years, NAEP has assessed the educational achievement of 4th-, 8th-, and 12th-grade students in selected subject areas, making it the only nationally representative and continuing assessment of what U.S. students know and can do. NAEP assessments are based on content frameworks and specifications developed through a national consensus process involving teachers, curriculum experts, parents, and members of the general public. The frameworks are designed to reflect a balance among the emphases suggested by current instructional efforts, curriculum reform, contemporary research, and desirable levels of achievement. In 1996, NAEP assessed the abilities of students in grades 4, 8, and 12 in the subjects of mathematics and science. The first release of results from the mathematics assessment appeared in the "NAEP 1996 Mathematics Report Card", a report designed to provide policymakers and the public with a broad view of student achievement. The current report, which provides a more detailed perspective on mathematics achievement and practices in 1996, is primarily for teachers, curriculum specialists, and school administrators. To illustrate what students know and can do, the report presents examples of student work in five different content strands of mathematics. Information on current instruction in mathematics classes, as reported by students and teachers, is also included. This report presents three types of information derived from the NAEP 1996 mathematics assessment: (1) information on what students know and can do in mathematics; (2) information on course-taking patterns and current classroom practices in this subject area; and (3) information on student attitudes toward mathematics. The first portion of this information is derived from an analysis of student performance on the actual assessment exercises. The latter two portions draw upon the questionnaires completed by the students who participated in the assessment and their mathematics teachers. The chapters on student work are organized around the five content strands assessed by NAEP: (1) Number Sense, Properties, and Operations; (2) Measurement; (3) Geometry and Spatial Sense; (4) Data Analysis, Statistics, and Probability; and (5) Algebra and Functions. Discussion within these chapters also highlights students' proficiency on a number of cognitive skills that cut across the different content areas. These include conceptual understanding, procedural knowledge, and problem solving, as well as the ability to reason in mathematical situations, to communicate perceptions and conclusions drawn from a mathematical context, and to connect the mathematical nature of a situation with related mathematical knowledge and information gained from other disciplines or through observation. (ASK)

Published
1999

7. Estimation Skills, Mathematics-in-Context, and Advanced Skills in Mathematics: Results from Three Studies of the National Assessment of Educational Progress 1996 Mathematics Assessment.

Author

American Institutes for Research, Washington, DC., Mitchell, Julia H., Hawkins, Evelyn F., Stancavage, Frances B., and Dossey, John A.

Abstract

This report presents information from three special studies conducted as part of the National Assessment of Educational Progress (NAEP) 1996 mathematics assessment. It is intended primarily for mathematics educators and others concerned with mathematics education, such as curriculum specialists, teachers, and university faculty in schools of education. The three studies reported here were designed to provide greater detail on how students perform on particular types of mathematics questions. Studies include the Estimation Study, the Study of Mathematics-in-Context, and the Study of Students Taking Advanced Courses in Mathematics. The first study was designed to explore students' skills in estimation and was implemented at three grade levels. It concludes that although there has been significant improvement in mathematics performance overall since 1990 at all grade levels, the trend for student performance in estimation over the six years since the inception of the Estimation Study of 1990 is less clear. The second study was designed to assess problem-solving abilities within contexts that allow students to make connections across mathematics content areas. The Advanced study was administered at grades 8 and 12 and was designed to provide students who were taking or had taken advanced courses in mathematics an opportunity to demonstrate their full mathematical proficiency. (Contains 71 tables and figures.) (ASK)

Published
1999

8. School Policies and Practices Affecting Instruction in Mathematics: Findings from the National Assessment of Educational Progress.

Author

Educational Testing Service, Princeton, NJ., American Institutes for Research, Washington, DC., Hawkins, Evelyn F., Stancavage, Frances B., and Dossey, John A.

Abstract

The teaching and learning of mathematics continues to generate tremendous attention, both among those who support recent innovations and, more recently, among those who question the wisdom of the promulgated reforms. In order to bring an empirical basis to this debate, it is important to gather information on the policies and practices that are actually implemented. This report provides one source for such information and is the second in a series that discusses results from the National Assessment of Educational Progress (NAEP). A description of the educational policies and practices that prevailed during this period of sustained increases in mathematics achievement, giving particular attention to the relationship between these policies, practices, and student performance on the NAEP mathematics assessment. Information on the status of mathematics education in 1996 is provided, and changes that took place from the time of earlier NAEP assessments is also chronicled. (ASK)

Published
1998

9. Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (19th, Bloomington-Normal, IL, October 18-21, 1997). Volume 2.

Author

ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH., International Group for the Psychology of Mathematics Education. North American Chapter., Dossey, John A., Swafford, Jane O., and Parmantie, Marilyn

Abstract

The conference proceedings volume for PME-NA-XIX contains a total of 72 reports: 34 research reports; 20 short oral reports; 11 poster session reports; and 7 discussion group reports. Only the research reports are full reports; the others are generally one-page abstracts. The full reports include: (1) "Equity, Teaching Practices, and Reform: Mathematics Teachers Discuss the Impact of the San Jose Mathematics Leadership Project" (Richard S. Kitchen, Joanne Rossi Becker, and Barbara J. Pence); (2) "One Teacher's Solution to Reforming Mathematics Teaching" (Karen Heinz, Margaret Kinzel, Martin A. Simon, and Ron Tzur); (3) "Secondary Mathematics Teachers' Experiences Using a Reform-Oriented Curriculum To Encourage Student Cooperation and Exploration" (Gwendolyn M. Lloyd and Melvin (Skip) Wilson); (4) "A Fourth-Grade Teacher Implements the 'Spirit' of the NCTM Standards" (Diana F. Steele); (5) "Construction and Validation of the Spatial-Symbolic Pattern Instrument" (Donna F. Berlin and Arthur L. White); (6) "Views about Mathematics Survey: Design and Results" (Marilyn P. Carlson); (7) "Changes in Teachers' Beliefs and Assessments of Students' Thinking across the First Year of Implementation of Cognitively Guided Instruction" (Anita H. Bowman, George W. Bright, and Nancy N. Vacc); (8) "Sustaining Cultures of Teaching for Constructive Mathematics Education" (M. Jayne Fleener and Roland G. Pourdavood); (9) "The Educational Benefits of Being a Participant in a Research Study: One Preservice Secondary Mathematics Teacher's Experience" (Deborah A. Gober); (10) "Preservice Mathematics Teachers' Constructions of Gender Equity in the Classroom" (Denise S. Mewborn and Deborah A. Gober); (11) "The Perceptions of Preservice Elementary Teachers about the Integration of Mathematics and Reading" (Kathryn S. Reinke, Kouider Mokhtari, and Elizabeth Willner); (12) "The Impact of Math Apathy Students on One High School Teacher" (Kenneth L. Shaw and Cylle Rowell); (13) "District-Wide Reflective Teaching in Mathematics: From Changing the Story to Storing the Change" (Christine D. Thomas and Karen A. Schultz); (14) "Teachers' Beliefs about Mathematics as Assessed with Repertory Grid Methodology" (Steven R. Williams, Miriam Pack, and Lena Licon Khisty); (15) "The Geometry Classroom: The Influence of Teachers' Beliefs" (Kay A. Wohlhuter); (16) "Mathematics Students Teachers' Development of Teacher Knowledge and Reflection" (Maria L. Fernandez); (17) "Using Videos To Provide "Case-Like" Experiences in an Elementary Mathematics Methods Course" (Susan N. Friel); (18) "Mathematics Culture Clash: Negotiating New Classroom Norms with Prospective Teachers" (Betsy McNeal and Martin Simon); (19) "A Model for Studying the Relationship between Teachers' Cognitions and Their Instructional Practice in Mathematics" (Alice F. Artzt and Eleanor Armour-Thomas); (20) "Mediating Pedagogical Content Knowledge through Social Interactions: A Prospective Teacher's Emerging Practice" (Maria L. Blanton and Sarah B. Berenson); (21) "Learning To Teach Algebraic Division for Understanding: A Comparison and Contrast between Two Experienced Teachers" (Jose N. Contreras); (22)"Preservice Secondary Mathematics Teachers' Interpretations of Mathematical Proof" (Eric J. Knuth and Rebekah L. Elliott); (23) "Why Do We Invert and Multiply? Elementary Teachers' Struggle To Conceptualize Division of Fractions" (Ron Tzur and Maria Timmerman); (24) "Shape Makers: A Computer Microworld for Promoting Dynamic Imagery in Support of Geometric Reasoning" (Michael T. Battista and Caroline Van Auken Borrow); (25) "Interactive Diagrams: A New Learning Tool" (Jere Confrey, Jose Castro Filho, and Alan Maloney); (26) "Conjecturing and Representational Style in CAS-Assisted Mathematical Problem Solving" (M. Kathleen Heid, Glendon W. Blume, Karen Flanagan, Kenneth Kerr, James Marshall, and Linda Iseri); (27) "Roles of Symbolic Representation in CAS-Assisted Mathematical Problem Solving" (M. Kathleen Heid, Glendon W. Blume, Linda Iseri, Karen Flanagan, Kenneth Kerr, and James Marshall); (28) "Analyzing Students' Learning with Computer-Based Microworlds: Do You See What I See?" (Janet Bowers); (29) "Warning: Asking Questions May Lower Your Mathematical Status in Small Groups" (Kathy M.C. Ivey); (30) "Occasioning Understanding: Understanding Occasioning" (Thomas Kieren, Elaine Simmt, and Joyce Mgembelo); (31) "An Analysis of Students' Development of Reasoning Strategies within the Context of Measurement" (Kay McClain, Paul Cobb, and Koeno Gravemeijer); (32) "Coordinating Social and Psychological Perspectives To Analyze Students' Conceptions of Measurement" (Michelle Stephan and Kay McClain); (33) "Learning as Sense-Making and Property-Noticing" (David Slavit); and (34) "Proportional Reasoning of Early Adolescents: Validation of Karplus, Pulos and Stage's Model" (Linda Gellings, Donald W. Wortham, Abbe H. Herzig, and Dave Eber). (ASK)

Published
1997

10. Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (19th, Bloomington-Normal, IL, October 18-21, 1997). Volume 1.

Author

ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH., International Group for the Psychology of Mathematics Education. North American Chapter., Dossey, John A., Swafford, Jane O., and Parmantie, Marilyn

Abstract

This conference proceedings volume for PME-NA-XIX contains a total of 87 reports: one plenary session report; 39 research reports; 20 short oral reports; 25 poster session reports; and two discussion group reports. Only the plenary and research reports are full reports; the others are generally one-page abstracts. The full reports include: (1) "Participation as Fundamental in Learning Mathematics" (James G. Greeno); (2) "An Undergraduate Student's Understanding and Use of Mathematical Definitions in Real Analysis" (Barbara S. Edwards); (3) "Mis-Generalization in Calculus: Searching for the Origins" (David E. Meel); (4) "Students' Cognitive Approaches to the Concept of Rate" (Rodolfo Oliveros and Manuel Santos-Trigo); (5) "Effects of Different Instructional Approaches on Calculus Students' Understanding of the Relationship between Slope, Rate of Change, and the First Derivative" (Donald T. Porzio); (6) "The Process of Periodicity" (Gilli Shama and Nitsa Movshovitz-Hadar); (7) "The Relationship between Written and Verbal Performances: A Study of First Year Calculus Students' Understanding of the Derivative" (Kathleen G. Snook); (8) "Mathematical Patterns in the Middle Grades: Symbolic Representations and Solution Strategies" (Joyce Wolfer Bishop); (9) "The Relationship of Undergraduates' Beliefs about Learning Algebra and Their Choice of Reasoning Strategies for Solving Algebra Problems" (Albert D. Otto, Cheryl A. Lubinski, and Carol T. Benson); (10) "Teachers' Beliefs and Student Failure in Algebra" (Daniel K. Siebert); (11) "Mandated Assessment Instruments: How Do Teachers Value Them?" (Karen Bell and Thomas J. Cooney); (12) "Using Assessment Practices as a Tool for Changing Teaching Methodology" (Daniel J. Brahier); (13) "A Proposed Method for Assessing Teachers' Pedagogical Content Knowledge" (Janet Warfield); (14) "Assessing Student Work: The Teacher Knowledge Demands of Open-Ended Tasks" (Linda Dager Wilson and Patricia Ann Kenney); (15) "Mathematical Activities in Insurance Agents' Work" (Judit Moschkovich); (16) "A Semiotic Framework for Linking Cultural Practice and Classroom Mathematics" (Norma C. Presmeg); (17) "Educating Non-College Bound Students: What We Can Learn from Manufacturing Work" (John P. Smith, III); (18) "Probability Instruction Informed by Children's Thinking" (Graham A. Jones, Carol A. Thornton, and Cynthia V. Langrall); (19) "Student Understanding of Statistics: Developing the Concept of Distribution" (Melissa Mellissinos, Janet E. Ford, and Douglas B. McLeod); (20) "A Snapshot of Developmental Algebra Students' Concept Images of Function" (Phil DeMarois); (21) "Preservice Teachers' Cognitive Approaches To Variables and Functions" (David B. Klanderman); (22) "The Development of Students' Notions of Proof in High School Classes Using Dynamic Geometry Software" (Enrique Galindo with Gudmundur Birgisson, Jean-Marc Cenet, Norm Krumpe, and Mike Lutz); (23) "Understanding Angle Ideas by Connecting In-School and Out-of-School Mathematics Practice" (Joanna O. Masingila and Rapti De Silva); (24) "Defining an Exterior Angle of Certain Concave Quadrilaterals: The Role of 'Supposed Others' in Making a Mathematical Definition" (Yoshinori Shimizu); (25) "Problem-Centered Learning and Early Childhood Mathematics" (Noel Geoghegan, Anne Reynolds, and Eileen Lillard); (26) "Similarities and Differences of Experienced and Novice K-6 Teachers after an Intervention: The Use of Students' Thinking in the Teaching of Mathematics" (Cheryl A. Lubinski, Albert D. Otto, Beverly S. Rich, and Rosanna Siongco); (27) "Learning and Teaching Grade 5 Mathematics in New York City, USA, and St. Petersburg, Russia: A Descriptive Study" (Frances R. Curcio and Natalia L. Stefanova); (28) "Some Results in the International Comparison of Pupils' Mathematical Views" (Erkki Pehkonen); (29) "Views of German Mathematics Teachers on Mathematics" (Gunter Torner); (30) "Teacher Change: Developing an Understanding of Meaningful Mathematical Discourse" (Rebekah L. Elliott and Eric J. Knuth); (31) "Group Case Studies of Second Graders Inventing Multidigit Subtraction Methods" (Karen C. Fuson and Birch Burghardt); (32) "Teaching Mathematical Procedures Mindfully: Exploring the Conditional Presentation of Information in Mathematics" (Ron Ritchhart and Ellen Langer); (33) "Generating Multiple Solutions to Mathematical Problems by Prospective Secondary Teachers" (Jinfa Cai); (34) "A Problem Solving Session Designed To Explore the Efficacy of Similes of Learning and Teaching Mathematics" (Vilma Mesa and Patricio Herbst): (35) "An Expert's Approach To Mathematical Problem-Solving Instruction" (Manuel Santos-Trigo); and (36) "Relevance Judgements in Mathematical Problem Solving" (Graeme Shirley and Martin Cooper). (ASK)

Published
1997

11. Essential Skills in Mathematics: A Comparative Analysis of American and Japanese Assessments of Eighth-Graders.

Author

National Center for Education Statistics (ED), Washington, DC. and Dossey, John A.

Abstract

This document is a comparative report based on data that enables a different form of comparison to be made between Japanese and American eighth-graders. The data is drawn from assessments given in each country using tests developed via governmental agencies that were designed to mirror the basic curricula currently being offered to students in the two countries. This report compares the nature of these examinations, the expectations based on the curriculum, and student performance on the test items. This comparison, combined with an accompanying analysis of the curricular emphases, provides a picture of the differences in student performance that mark this study. Each of the studies examined content achievement assessments; students' and teachers' beliefs and attitudes; and environmental characteristics of the classroom, school, and community. The Japanese test items tend to present the mathematics assessed in forms that are more verbally intensive, more focused on strategies for problem solving, and more involved than the mathematics forms used in the National Assessment of Educational Progress. Sample test items, a content matrix for the U.S. test, and the framework for the Japanese test are included. Contains 29 references. (DDR)

Published
1997

12. How School Mathematics Functions: Perspectives from the NAEP 1990 and 1992 Assessments.

Author

National Assessment of Educational Progress, Princeton, NJ. and Dossey, John A.

Abstract

This report of the National Assessment of Educational Progress (NAEP) focuses on students' and teachers' reports about the classroom contexts for learning school mathematics in the top-performing one-third of schools compared to the bottom performing one-third. In 1990, 26,652 students from 1,237 schools participated in the study, while in 1992, 26,669 students from 1,582 schools were included. Data presented relate to program and curricular emphases, mathematics teachers and their classes, instructional approaches, calculators and computers, students' perceptions about mathematics, and students' mathematics course taking. Major findings were that in the two-year period from 1990 to 1992 the following signs of progress were noted: (1) Students reported taking more advanced coursework; (2) Teachers reported moving toward a more broadly-based curriculum; (3) Students and teachers reported more access to and use of calculators and computers; (4) Students were doing more daily problem solving from their textbooks; and (5) Students reported more positive attitudes about the value of mathematics. On the other hand, teachers continued to report discrepancies in resource availability and expectations between top- and bottom-performing schools, and teachers and students reported very little change in the frequency with which students were asked to engage in extended problem-solving activity. An appendix contains an overview of procedures used in NAEP's 1992 Mathematics Assessment. (MKR)

Published
1994

13. Can Students Do Mathematical Problem Solving? Results from Constructed-Response Questions in NAEP's 1992 Mathematics Assessment.

Author

National Assessment of Educational Progress, Princeton, NJ., Educational Testing Service, Princeton, NJ. Center for the Assessment of Educational Progress., and Dossey, John A.

Abstract

In the 1992 mathematics assessment of the National Assessment of Educational Progress (NAEP), approximately one-third of the questions and about half of the student response time were devoted to questions asking students to construct their own responses. Regular constructed response items required a short answer with a problem solution, while extended constructed response required demonstration of student reasoning. Analysis of student papers shows that most made a conscientious effort to respond, but that performance left much to be desired. On regular constructed response questions, the average percent correct by grade level was 42 percent of grade 4, 53 percent of grade 8, and 40 percent of grade 12. For extended constructed response questions, the average percentages of student producing correct responses were 16 percent at grade 4, 8 percent at grade 8, and 9 percent at grade 12. Results indicate that extended constructed response questions can be successfully used in large-scale assessment and that they do signify student proficiency. The levels of performance on multiple-choice items were higher than for constructed responses. Sixty tables present study findings. A procedural appendix explains study methodology, with an additional seven tables. (SLD)

Published
1993

14. The State of Mathematics Achievement: NAEP's 1990 Assessment of the Nation and the Trial Assessment of the States.

Author

National Assessment of Educational Progress, Princeton, NJ., Educational Testing Service, Princeton, NJ., Mullis, Ina V. S., Dossey, John A., Owen, Eugene H., and Phillips, Gary W.

Abstract

The National Assessment of Educational Progress (NAEP), also known as "The Nation's Report Card," is a congressionally mandated survey of educational achievement of American students in a variety of curriculum areas and of changes in that achievement across time. Part 1 of this report consists of the results of NAEP's 1990 national mathematics assessment of nationally representative samples of more than 26,000 students in grades 4, 8, and 12 in more than 1,300 schools. Part 2 consists of the results of NAEP's 1990 "Trial State Assessment Program," a voluntary eighth-grade mathematics assessment administered to representative samples of 2,500 public school students at grade 8 in about a 100 schools in each of the 40 participating states and jurisdictions. This is the first time NAEP has provided results by state. The report is organized as follows: (1) executive summary; (2) NAEP history; (3) scope of the assessment; (4) results for grade 4, 8, 12, respectively; (5) results of the Trial State Assessment Program. Appendices include: contextual and background factors; participation rates; procedures; anchoring processes; and tabular data. Overall mathematics performance in the nation at each of the three grade levels tested was characterized as follows: FOURTH GRADE: 72 percent demonstrated the ability to consistently solve third grade level problems (e.g., addition and subtraction with whole numbers); 11 percent demonstrated a grasp of fifth grade level problems (e.g., multiplication). No fourth graders indicated an understanding of fractions, decimals, percents, or simple algebra. EIGHTH GRADE: 98 percent demonstrated a grasp of third grade level problems; 67 percent consistently understood fifth grade content; only 14 percent showed successful performance with seventh grade material (fractions, decimals, percents, simple algebra); no eighth graders showed the breadth of understanding necessary to begin the study of relatively advanced mathematics. TWELFTH GRADE: All high school seniors demonstrated success with third-grade materials; 91 percent showed mastery of fifth-grade material; 46 percent demonstrated a consistent grasp of seventh grade material (decimals, percents, fractions, simple algebra); 5 percent showed an understanding of geometry and algebra. Many students appear to be graduating from high school with little of the mathematics understanding required by the fastest growing occupations or for college work. Approximately half of graduating twelfth graders appear to have an understanding of mathematics that does not extend much beyond simple problem solving with whole numbers. The Trial State Assessment Program showed great variation in student achievement within each state, to the extent that the variation within states tended to exceed the variation in average performance across states. The higher performing states (e.g., North Dakota, Montana, Iowa, Nebraska, Minnesota, Wisconsin) appear to have fewer urban areas, fewer disadvantaged students, and fewer minority students. (JJK/WTB)

Published
1991

15. The State of Mathematics Achievement: NAEP's 1990 Assessment of the Nation and the Trial Assessment of the States. Executive Summary.

Author

National Assessment of Educational Progress, Princeton, NJ., Educational Testing Service, Princeton, NJ., Mullis, Ina V. S., Dossey, John A., Owen, Eugene H., and Phillips, Gary W.

Abstract

The National Assessment of Educational Progress (NAEP), also known as "The Nation's Report Card," is a congressionally mandated survey of educational achievement of American students in a variety of curriculum areas and of changes in that achievement across time. Part 1 of this report consists of the results of NAEP's 1990 national mathematics assessment of nationally representative samples of students in grades 4, 8, and 12. Part 2 consists of the results of NAEP's 1990 "Trial State Assessment Program," a voluntary eighth-grade mathematics assessment administered to representative samples of public school students at grade 8 in 40 participating states and jurisdictions. This is the first time NAEP has provided results by state. The Executive Summary (this volume) is organized as follows: (1) overall mathematics performance in the United States; (2) performance in the mathematics content areas for the nation; (3) mathematics performance by demographic subgroups; (4) home support for school; (5) mathematics performance at grade 8 in the states (based on the State Trial Assessments); (6) curricular emphases in content areas at grade 4 and 8 in the nationa and at grade 8 in the states; (7) curricular emphasis in skill areas at grades 4 and 8 in the nation and at grade 8 in the states; (8) student course taking at grade 12 in the nation; (9) summary of mathematics curriculum and course taking across the grades; (10) mathematics instruction at grades 4 and 8 in the nation and at grade 8 in the states (e.g., ability grouping, instructional materials, calculators and computers, student and teacher attitudes). (For a summary of results, see the abstract for the entire report.) (JJK/WTB)

Published
1991

16. Canadian and United States Students' Performances on the OECD's PISA 2012 Problem-Solving Assessment

Author

Dossey, John A. and Funke, Joachim

Abstract

This article presents an overview of the Organization for Economic Cooperation and Development's (OECD) Programme for International Student Assessment (PISA) 2012 Problem-Solving assessment. The assessment examined the capabilities of 15-year-olds in 40 nations and four large international cities, as well as the Canadian Provinces, to solve a set of 16 problem units presented in contextualized situations. These units each had two or three tasks for students to solve. Students' performances on these items served as a basis for developing the PISA score scale and the associated proficiency levels for each of the participating entities. Student performances on the PISA 2012 mathematics, reading, and science assessments provided an avenue to estimating student performances on the problem-solving assessment for students having similar score backgrounds in the three content areas. Student performances were also examined by item types and by differing problem situations. These latter two analyses provide interesting perspectives for comparing problem solving profiles across the participating entities. Finally, some conclusions are drawn concerning the study as a whole.

Published
2016
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19. Selected Procedures for Improving the Mathematics Curriculum: Assessment. ERIC/SMEAC Mathematics Education Digest No. 2.

Author

ERIC Clearinghouse for Science, Mathematics, and Environmental Education, Columbus, OH. and Dossey, John A.

Abstract

While 1990 was the year of reform recommendations in mathematics education, 1991 may become the year of assessment in mathematics education. The growth of assessment activities stems from the belief that the primary purpose of assessment is the improvement of teaching. The digest reviews trends in mathematics assessment. Discussed are the sudden emphasis on assessment; how schools can improve their methods of assessing students; how assessment can be used to improve instruction; what changes are taking place in state testing programs; what is happening in college entrance examinations programs; what is happening in assessment at the national level; and what schools can do to improve themselves. A list of 11 selected references is included. (CW)

Published
1990

20. Learning about Student's Mathematical Literacy from PISA 2003

Author

Soucy McCrone, Sharon M., Dossey, John A., Turner, Ross, and Lindquist, Mary Montgomery

Abstract

The article discusses the need for mathematical literacy in our world today and shares results from the 2003 PISA assessment of mathematical literacy. Some ideas are presented for incorporating similar problems in the classroom. (Contains 4 figures and 3 tables.)

Published
2008

21. Summarizing Item Difficulty Variation with Parcel Scores

Author

Camilli, Gregory, Prowker, Adam, and Dossey, John A.

Abstract

A new method for analyzing differential item functioning is proposed to investigate the relative strengths and weaknesses of multiple groups of examinees. Accordingly, the notion of a conditional measure of difference between two groups (Reference and Focal) is generalized to a conditional variance. The objective of this article is to present and illustrate a strategy for aggregating results across sets of similar items that exhibit item difficulty variation. Logically, this aggregation strategy is related to the idea of DIF amplification, but estimation is ultimately carried out in the framework of a confirmatory multidimensional Rasch model. Grade 4 data from the 2000 National Assessment of Educational Progress are used to illustrate the technique. (Contains 1 figure, 6 tables, and 22 formulas.)

Published
2008
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24. Mathematical Literacy--It's Become Fundamental

Author

McCrone, Sharon Soucy and Dossey, John A.

Abstract

The rising tide of numbers and statistics in daily life signals a need for a fundamental broadening of the concept of literacy: mathematical literacy assuming a coequal role in the curriculum alongside language-based literacy. Mathematical literacy is not about studying higher levels of formal mathematics, but about making math relevant and empowering for everyone. Situating mathematical literacy as a major curricular focus requires making mathematics a transparent part of structuring problems and making decisions across all facets of the school curriculum. If students are to "identify and understand the role that mathematics plays in the world," they need to experience the power of mathematics in industrial technology, physical education, history, business, and physics. For this to happen, all teachers will have to buy into the need for mathematics and its applications in their disciplines. This will require efforts to coordinate the language, symbolism, and topics in non-mathematics classes with the prerequisite knowledge and skills from mathematics classes. One format for structuring classes to promote mathematical literacy is the launch-explore-reflect model employed by some of the recently developed curricular programs for middle level and high school mathematics. (Contains 1 figure.)

Published
2007

25. Setting a Course for Change Based on Beyond Crossroads

Author

Dossey, John A.

Abstract

The article provides a vision of how Beyond Crossroads can serve as a departmental guide to inducing systemic change at a two-year college. Curricular change does not mean just changing the content taught, it also means changing the way it is taught, the way learning may be assessed, and the ways in which faculty and administrators may evaluate curricular effectiveness. Beyond Crossroads provides a starting point, the rest remains in the hands of faculty committed to providing the best program possible for their students.

Published
2007

26. Estimation Skills, Mathematics-in-Context, and Advanced Skills in Mathematics.

Author

Mitchell, Julia H., Hawkins, Evelyn F., Stancavage, Frances B., and Dossey, John A.

Abstract

Presents details on how students perform on particular types of mathematics questions from the National Assessment of Educational Progress (NAEP). Data are from three special studies conducted as part of the NAEP: (1) estimation skills; (2) problem-solving abilities (mathematics in context); and (3) students taking advanced courses in mathematics. (SLD)

Published
2000

28. Mathematics Examinations

Author

Dossey, John, Madaus, George F., editor, Stufflebeam, Daniel L., editor, Britton, Edward D., editor, and Raizen, Senta A., editor

Published
1996
Full Text
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29. Comparing Examinations Across Subjects and Countries

Author

Britton, Edward, Dossey, John, Eubanks, Dwaine, Eubanks, Lucy, Gisselberg, Kjell, Hawkins, Simon, Raizen, Senta, Tamir, Pinchas, Madaus, George F., editor, Stufflebeam, Daniel L., editor, Britton, Edward D., editor, and Raizen, Senta A., editor

Published
1996
Full Text
View/download PDF

30. Illinois Secondary School Course Offerings, 1982: Special Report on Mathematics.

Author

Illinois State Board of Education, Springfield, Dept. of Planning, Research and Evaluation. and Dossey, John

Abstract

This report on the second Census of Secondary School Course Offerings, conducted in 1982, provides data on offering and enrollments in the Illinois public schools grades 7 through 12, and updates the first Census of 1977. Data were collected for 489 junior high schools (82% of the total) and 719 high schools (99% of the total). Discussed in the report are demographic characteristics, including enrollment statistics; the typical mathematics program in junior high schools and in senior high schools, including course offerings; and sex-related information on student enrollment in mathematics, including analyses by course. The summary indicated that a larger proportion of students was enrolled in mathematics courses in 1982 than in 1977. The mathematics curriculum at the high school level continues to follow a traditional pattern, with elementary algebra and plane and solid geometry the most commonly offered courses. Remedial mathematics courses are more likely to be found in large high schools than in small ones. Mathematics enrollment was greater for females than for males between 1977 and 1982. A notable increase was found in Computer Mathematics offerings and enrollment. (MNS)

Published
1984

31. Summary of the 1982 Mathematics Results of the Illinois Inventory of Educational Progress.

Author

Illinois State Board of Education, Springfield., Dossey, John A., and Brennan, Mervin M.

Abstract

A random sample of fourth, eighth, and eleventh grade Illinois students has been tested annually since 1976 by the Illinois State Board of Education. This testing program is called the Illinois Inventory of Educational Progress (IIEP). This report presents mathematics achievement results of a random sample of fourth (N=6,103), eighth (N=10,026), and eleventh grade (N=16,264) students tested in 1982, factor analysis results, and teacher survey information. The 1982 testing focused on students' knowledge of mathematical measurement. As such, a three-factor model was developed that provides for three types of measurement units (nonstandard, metric, and conventional), five categories of measurement skills (estimation, conversions within, comparisons between, selecting and/or reading instruments, and problem-solving), and five types of measurement attributes (length, area, capacity, mass, and temperature). Major findings are presented in separate chapters for each grade level. Two conclusions emerge from these results: (1) students perform at roughly the same level in all aspects of mathematical measurement tested by the IIEP and (2) students are weak in measurement. In addition, students have considerably less problems with the metric system than many people think. (Copies of test instruments, correct answer keys, a sample teacher survey instrument, and other information are included in appendices.) (JN)

Published
1984

32. Mathematics: Are We Measuring Up? The Mathematics Report Card, Executive Summary.

Author

National Assessment of Educational Progress, Princeton, NJ. and Dossey, John A.

Abstract

This executive summary presents key findings from the 1986 National Assessment of Educational Progress (NAEP) in mathematics. It is designed to alert leaders in classrooms, families, and councils of government to the state of mathematics education in the United States. "Why Mathematics Counts" is summarized in the first section. Then, highlights from the assessment are given: the trend in mathematics performance is encouraging, particularly for students at ages 9 and 17 and for Black and Hispanic students. However, the gains have been confined primarily to lower-order skills. Other findings concerning achievement, instructional patterns, technology, course-taking, and attitudes are succinctly presented. Next, the assessment procedures are summarized, followed by some reflections on the findings. Trends in mathematics proficiency is the concern of the next section, with a graph highlighting overall trends and a chart showing the percentage of students in each age group (9, 13, and 17) in the last three assessments (1978, 1982, and 1986). Implications for instruction are considered in terms of students' perception of mathematics, patterns of classroom instruction, and the place of mathematics in the curriculum. Finally, a summary stresses the need to teach not only skills, but also higher-order thinking strategies. (MNS)

Published
1988

33. The Mathematics Report Card: Are We Measuring Up? Trends and Achievement Based on the 1986 National Assessment.

Author

National Assessment of Educational Progress, Princeton, NJ. and Dossey, John A.

Abstract

This report presents results from the 1986 National Assessment of Educational Progress (NAEP) in mathematics. Students aged 9, 13, and 17 were tested, as in the previous four mathematics assessments. Part I reports on the data, with chapter 1 considering signs of progress, noting national trends and trends by race/ethnicity, gender, and region. In chapter 2, how students did at several proficiency levels is presented. The third chapter concerns students' relative performance in particular mathematics content areas. In the second part of the document, the quality of mathematics education is analyzed. Chapter 4 considers patterns and trends in classroom instruction. Materials for mathematics instruction are considered in chapter 5, with calculator and computer use of particular concern. Chapter 6 analyzes students' perceptions of mathematics, while chapter 7 considers school and home expectations. In chapter 8, data on course-taking and the program of study in secondary school are discussed. A Procedural Appendix presents background information on conducting the study and analyzing the data, and a Data Appendix presents results for various proficiency levels for the total group and by sex, ethnicity/race, region, and parental education, with comparisons with earlier assessments. (MNS)

Published
1988

35. Confronting the Core Curriculum: Considering Change in the Undergraduate Mathematics Major. Proceedings of the West Point Core Curriculum Conference in Mathematics (West Point, New York, April 23-24, 1994). Notes 45.

Author

Mathematical Association of America, Washington, DC. and Dossey, John A.

Abstract

This document contains the proceedings of a conference held at the U.S. Military Academy to consider the question of core requirements for the courses often employed by partner disciplines, what concepts and procedural skills are really central, and how these questions might lead to the creation of a new undergraduate set of requirements that meet both the needs of mathematics departments and those of their partner disciplines. Chapters include: (1) "Core Curriculum in Context: History, Goals, Models, Challenges" (Lynn Arthur Steen); (2) "Response To Core Curriculum in Context: History, Goals, Models, Challenges" (Joan Ferrini-Mundy); (3) "Core Mathematics at the United States Military Academy: Leading into the 21st Century" (David C. Arney, William P. Fox, Kelley B. Mohrmann, Joseph D. Myers, and Richard A. West); (4) "Discrete Mathematics in the Core Curriculum" (Alan Tucker); (5) "Response to Discrete Mathematics in the Core Curriculum" (Martha Siegel); (6) "Calculus in the Core" (Wayne Roberts); (7) "Response to Calculus in the Core I: Parallels in Calculus" (David Heckman); (8) "Response to Calculus in the Core II: Calculus and Other 7-into-4 Issues" (Stephen Rodi); (9) "Calculus after High School Calculus" (Don Small); (10) "Response to Calculus after High School I" (Frank Wattenberg); (11) "Response to Calculus after High School Calculus II" (Jeanette Palmiter); (12) "Linear Algebra in the Core Curriculum" (Donald R. LaTorre); (13) "Response to Linear Algebra in the Core I" (David Carlson); (14) "Response to Linear Algebra in the Core II" (Anita E. Solow); (15) "Response to Linear Algebra in the Core III" (Steve Friedberg); (16) "Differential Equations in the Core Curriculum" (James V. Herod); (17) "Response to Differential Equations in the Core I" (Donald Bushaw); (18) "Response to Differential Equations in the Core II: ODEs Renewed" (Courtney Coleman); (19) "Response to Differential Equations in the Core III: Data Sets in the First Course of Differential Equations" (David O. Lomen); (20) "Probability and Statistics in the Core Curriculum" (David S. Moore); (21) "Response to Probability and Statistics in the Core I" (Ann E. Watkins); (22) "Response to Probability and Statistics in the Core II" (R.A. Kolb); (23) "Probability and Statistics in the Core III: Is It Really Such a Tight Squeeze?" (Sheldon P. Gordon); (24) "Evaluation of Mathematics Core Curriculum Conference, April 22-24, 1994" (Robert Orrill); (25) "A Curriculum Reform Workshop/Retreat" (Don Small); (26) "Carroll College Mathematics Curriculum Reform Project" (John Scharf and Marie Vanisko); (27) "A Preliminary Plan for Curriculum Change at Harvey Mudd College: N-into-Four" (Robert Borrelli, Robert Keller, and Michael Moody); (28) "Core Curriculum Reform Model for the Oklahoma State University" (James Choike); and (29) "Plan To Integrate Calculus II and III Curricula at University of Redlands" (J. Beery, P. Cornell, A. Killpatrick, and A. Koonce). (ASK)

Published
1998

37. The Relative Effectiveness of Four Strategies for Teaching Disjunctive Concepts in Mathematics.

Author

Dossey, John A. and Henderson, Kenneth B.

Abstract

Programmed materials presenting twelve mathematical concepts were developed to investigate disjunctive concept learning relative to four teaching strategies involving characterization and exemplification (CEC, EC, CE, ECE). Prospective elementary teachers in an undergraduate mathematics course were randomly assigned to one of eight treatment programs after stratification according to mental ability. Achievement tests designed to test concept attainment at the levels of Knowledge and Comprehension (Level 1), Application (Level 2), and Analysis, Synthesis, and Evaluation (Level 3) yielded the following results: (1) upper ability groups did significantly better than low ability groups; and (2) exemplar moves were more effective than non-exemplar moves for Level 1 performance, but the CEC strategy was better than ECE for Levels 2 and 3. No meaningful interactions were found. (Author/JG)

Published
1972

38. Mathematics, Pedagogy, and Secondary Teacher Education.

Author

Cooney, Thomas J., Brown, Stephen I., Dossey, John A., Schrage, Georg, Wittmann, Erich Ch, Cooney, Thomas J., Brown, Stephen I., Dossey, John A., Schrage, Georg, and Wittmann, Erich Ch

Abstract

This book is intended for both preservice and inservice teachers who wish to experience some of the fundamental ideas expressed in the documents published by the National Council of Teachers of Mathematics (NCTM) that are commonly referred to as the Standards. The text encourages the reader to seek connections between pedagogy and content in a number of ways. Pedagogical ideas are part of the substance of each piece. Often these ideas are exemplified in various classroom vignettes or in a variety of interview settings. Readers are also encouraged to imagine the implications of their own experiences as learners for teaching. Consequently, both the content and the format of the text differ significantly from most texts that address the teaching of mathematics at the secondary level. Chapters include: (1) "Thinking about Being a Mathematics Teacher" (Thomas J. Cooney); (2) "Developing a Topic across the Curriculum" (Thomas J. Cooney); (3) "Designing Teaching: The Pythagorean Theorem" (Erich Ch. Wittman); (4) "Analyzing Subject Matter: Fundamental Ideas of Combinatorics" (Georg Schrage); (5) "Modeling with Functions" (John Dossey); and (6) "Posing Mathematically: A Novelette" (Stephen I. Brown). (ASK)

Published
1996

39. American Perspectives on the Seventh International Congress on Mathematical Education.

Author

National Council of Teachers of Mathematics, Inc., Reston, VA. and Dossey, John A.

Abstract

This publication is a collection of papers portraying an American view of the happenings of the Seventh International Congress on Mathematical Education (ICME-7). Papers included: (1) "ICME-7 and Tertiary Level Mathematics: Une Petite Affaire" (Shirley Hill); (2) "Technology and Mathematics Education at ICME-7" (James T. Fey); (3) "Assessment in Mathematics Education Around the World" (Norman Webb); (4) "Poster Sessions: A Reflection of Work in Progress" (Bonnie Shulman); (5) "Just One More Computer, Please" (Jacqueline Mayo); (6) "The Impact of the Calculator on the Elementary School Curriculum: Reflections on ICME-7" (Betty K. Lichtenberg); (7) "Impressions of a Secondary School Teacher at ICME-7" (Arnold Perham); (8) "ICME-7, Quebec, Canada" (Richard Sander); (9) "Computers, Mathematics, and Learning: Notes from ICME-7" (Paul Zorn); (10) "Less Theory, More Action" (Florence E. Klimas); (11) "Assessing Gender Differences in Mathematics" (Denisse R. Thompson); (12) "Unity and Diversity: Some Observations on ICME-7" (Mark Saul); (13) "What Mathematics Is, Will Be, Should Be" (Richard A. Gibbs); (14) "Art and Mathematics at ICME-7" (Catalina Reyero); (15) "Impressions Regarding the Program of ICME-7" (Karen Sharp); (16) "Misconceptions" (Marilyn Mays); (17) "A Sampling of International Perspectives at ICME-7: We're All the Same, but Different" (Eric W. Hart); (17) "Personal Outcomes from ICME-7" (Bernadette H. Perham); (18) "Emergent Themes at ICME-7" (Diana V. Lambdin); (19) "Reflections on ICME-7" (Jerry P. Becker); (20) "My Fifth Dance at the ICME Balls" (Thomas J. Cooney); (21) "Mathematician, Mathematics Educator, Teacher: The Intersection Is Not Empty" (Genevieve M. Knight); (22) "ICME-7" (Arthur Johnson, II); (23) "Preservice and In-service Teacher Education" (Margaret Shoukry); (24) "ICME-7: Personal Reflections about Mathematics Education" (Vania Maria Pereira dos Santos); (25) "ICME-7 and Learning To Teach Mathematics" (Glenda Lappan); (26) "Reflections on ICME-7, the International Congress on Mathematical Education" (Sharon Crumpton); (27) "Cultural Diversity and Bonding in Mathematics" (Eileen L. Poiani); (28) "Innovative Assessment of Students in the Mathematics Classroom" (Winnie Miller); (29) "Assessing: The Distance from Research To Practice" (Patricia L. Duckhorn); (30) "ICME-7: An Assessment" (Evan B. Alderfer); (31)"Mathematics as Communication: A Universal Endeavor" (Frances R. Curcio); (32) "Mathematical Communication in the Classroom" (Marta Civil); (33) "Some Remarks on ICME-7" (Floyd L. Williams); (34) "My Diary of ICME-7" (Susan L. Ganter); (35) "ICME--Is It for Precollege Teachers?" (Cynthia Lanius); (36) "Mathematical Modeling in the Classroom" (Bart Braden); and (37) "Theories of Learning and the Theory and Practice of Proof" (Susanna Epp). (ASK)

Published
1993

40. American Perspectives on the International Congress on Mathematical Education (7th, Quebec City, Quebec, Canada, August 17-23, 1992).

Author

National Council of Teachers of Mathematics, Inc., Reston, VA. and Dossey, John A.

Abstract

A pervasive theme running throughout a conference on mathematical education was the transformation of the learning and teaching of mathematics using technology. This publication is a collection of papers representing an American view of the events of the international conference. The papers share the views of collegiate mathematicians, elementary school teachers, teacher educators, researchers in mathematics education, middle and secondary school teachers, two-year-college faculty members, and others. The first three authors focus on the special aspects of the relationship between prior ICME meetings and higher education (S. Hill), technology and mathematics education (J. T. Fey), and assessment around the world (N. Webb). The remaining 35 papers report the activities, insights, and growth of many of the 40 individuals who received support awards for attending the Congress through a National Science Foundation grant to the National Council of Teachers of Mathematics. (MDH)

Published
1993

41. Discrete Mathematics and the Secondary Mathematics Curriculum.

Author

National Council of Teachers of Mathematics, Inc., Reston, VA. and Dossey, John

Abstract

Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that material should be taught in the classroom. This document details a set of recommendations on the infusion of topics from discrete mathematics into the secondary school (grades 7-12) mathematics curriculum. The suggestions are accompanied by a list of resources, including software, which will aid in the development of specific topics. Modeling, use of technology, algorithmic thinking, recursive thinking, decision making, and mathematical induction as a way of knowing are six unifying themes that emerge when discrete mathematics is studied and applied. Recommended topics for emphasis in discrete mathematics before algebra, with algebra, and with geometry are included. Appended is an outline for a semester course in discrete mathematics. (KR)

Published
1990

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