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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)

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)

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)

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)

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)

The focus of this study was on the processes students used in making mathematical conjectures for five divergent problem situations. The relationship of the processes to creativity factors across the problems was also examined. The results of various cluster analyses and correlational measures indicated that students use different sequences of processes for different problems; some problem types elicit more pattern searches than others; and when the processes were viewed in ordered pairs and triples, various sequences resulted. The creativity measures were all significantly correlated, but there were differences on the relationships between the creativity factors and various processes used. (Author/MP)

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)