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1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. Student Work and Teacher Practices in Mathematics.

Author

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

Abstract

Presents three types of information derived from the National Assessment of Educational Progress (NAEP) mathematics assessment: (1) what students know and can do in mathematics; (2) course-taking patterns and current classroom practices in mathematics; and (3) student attitudes about mathematics. Student mathematics performance in the United States continues to improve. (SLD)

Published
1999

9. 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

10. 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

11. 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

12. Learning, Teaching, and Standards.

Author

Dossey, John A.

Abstract

This article is based on the 1987 presidential address to the National Council of Teachers of Mathematics. The work of George Polya is used to draw conclusions about teaching and learning mathematics. (PK)

Published
1988

13. Proceedings of the Second Mathematics Methods Conference: A Summary (Illinois State University, Normal, Illinois, June 11-13, 1980).

Author

Dossey, John A.

Abstract

The major objective of this conference was the continuation of the exchange of information on the improvement of pre-service and inservice methods courses and other program offerings in mathematics education. Topics highlighted included the effects of state mandated programs for teacher preparation, the growing shortage of qualified mathematics teachers to meet the needs of schools, and the various components of methods courses for elementary and secondary mathematics teachers. These proceedings contain: an introduction to the material, a summary of the opening session, two invited addresses, summaries of fifteen discussion sections, and an alphabetized list of conference participants and addresses. The invited address by Tom Cooney is entitled "Do Research and Teacher Education Have An Intersection"; the second address, by Perry Lanier, was entitled "Participant Observation: A Method of Inquiry in Mathematics Education." (MP)

Published
1980

14. Student/Class Results from the Second International Mathematics Study from United States Twelfth Grade Classrooms.

Author

Illinois State Univ., Normal. Dept. of Mathematics. and Dossey, John A.

Abstract

In the introductory section of this report, the Second International Mathematics Study (1981-82) is described. The study, which involved about 500 classrooms in the United States and classrooms in 24 other countries in grades 8 and 12, was designed to provide detailed information about the content of the mathematics curriculum, how mathematics is taught, and how much mathematics students learn. The intended, implemented, and attained curricula were assessed by questionnaires and achievement tests. Provisions for assuring comparability of samples are presented. Two types of twelfth-grade classes in the United States sample were studied: precalculus classes and calculus classes. The report also includes summaries of data on class size, hours of mathematics instruction, teaching assignments, teacher characteristics, how mathematics teachers spend their time, use of instructional resources, how mathematics students spend their time, homework, use of calculators, what mathematics was taught, untaught topics, and student achievement. Achievement on eight illustrative items is presented, followed by summaries of results on sex differences in achievement, changes in twelfth-grade achievement between the first study (1964) and the second study (1982), and the ranking of the United States internationally. Finally, a summary is included, plus some comments on "A Curriculum Adrift." Figures presenting data are appended. (MNS)

Published
1985

15. Brief Reports: Concept Teaching Strategy Length.

Author

Dossey, John A.

Abstract

The effect on student attainment of the number of moves in a concept teaching venture is examined. Results suggest the number of moves in short ventures had little effect on attainment of mathematical concepts. However, performance increased as the number of moves in longer ventures increased. (Author/MK)

Published
1980

16. Basic Fact Thinking Strategies for Multiplication-- Revisited.

Author

Cook, Cathy J. and Dossey, John A.

Abstract

The relative efficacy of two approaches to teaching basic multiplication facts to third graders is examined. Support was indicated for the thinking strategies approach. Results also indicated it was possible to train teachers in two days of inservice education. (MP)

Published
1982

18. Do All Graphs Have Points with Integral Coordinates?

Author

Dossey, John A.

Abstract

A discussion on the general equation of a line shows how students can be lead to discover mathematical properties, find how one discovery leads to another, see how different branches of mathematics can lead to a solution, and be provided with a starting point for studying special mathematical topics. (MP)

Published
1981

19. Learning, Teaching, and Standards.

Author

Dossey, John A.

Abstract

Article is based on the keynote address of the 1987 annual meeting of the National Council of Teachers of Mathematics. Suggests that George Polya left a legacy which has not only touched knowledge and abilities in mathematics and problem solving but also had significant effects on thoughts about teaching. (PK)

Published
1988

20. Use These Questions to Calculate the Quality of Your Math Instruction.

Author

Dossey, John A.

Abstract

Discusses four important issues influencing the current state of mathematics education: what should be taught, how to evaluate students' learning, the role of technology, and the preparation of prospective teachers. Provides a list of five questions to help administrators evaluate their schools' mathematics program. (MLH)

Published
1988

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