Handbook of Research Design in Mathematics and Science Education by Kelly, Anthony E. -- Read -- Imperial Library of Trantor

Index

Contents Preface I THE NEED TO ADDRESS PRIORITY PROBLEMS

1 Purposes and Assumptions of This Book

SOME OF THE BOOK’S PURPOSES SOME OPERATING ASSUMPTIONS THAT INFLUENCED DISCUSSIONS LEADING TO THIS BOOK.

Observation 1 Observation 2 Observation 3 Observation 4 Observation 5 Observation 6

WHAT PROBLEMS LED TO THE PERCEIVED NEED FOR THIS BOOK? NEW PARADIGMS CREATE THE NEED TO REVISE QUALITY ASSURANCE STANDARDS THE DECADE OF THE “STANDARDS” ACKNOWLEDGMENTS Footnotes

2 Trends and Shifts in Research Methods

SHIFTS RESEARCHERS AS INTERESTED LEARNERS: BACKGROUND FACTORS RESEARCHERS AS INTERESTED LEARNERS: FOREGROUND FACTORS RECOGNIZING THE SYSTEMS NATURE AND COMPLEXITY OF EDUCATION PROMOTING IMMEDIACY CHALLENGING THE CURRICULUM AS GIVEN CAVEATS

3 Research Agendas: Identifying Priority Problems and Developing Useful Theoretical Perspectives

WHAT FACTORS INFLUENCED OUR CHOICE OF THE RESEARCH PROCEDURES EMPHASIZED? WHY DO PROFESSIONAL ORGANIZATIONS AND FUNDING AGENCIES CHANGE THEIR RESEARCH PRIORITIES FREQUENTLY? IN WHAT WAYS DO CHANGES IN RESEARCH AGENDAS IMPACT CHOICES OF RESEARCH DESIGNS? NEW WAYS OF THINKING ABOUT COMMUNICATION BETWEEN RESEARCHERS AND PRACTITIONERS FOR PROGRESS TO BE MADE, KNOWLEDGE MUST ACCUMULATE SUMMARY Appendix I The National Science Foundation’s Program for Research on Teaching & Learning

GENERAL PROGRAM GOALS RELATIONSHIPS TO OTHER EHR PROGRAMS A MATRIX OF CURRENT FUNDING PRIORITIES THEORETICAL PERSPECTIVES AND RESEARCH METHODOLOGIES MORE ABOUT THE CELLS IN THE MATRIX OF FUNDING PRIORITIES

Preparation for Success in a Postindustrial Society Equal Access to Powerful Ideas Standards and Assessments to Document Progress Influences of Technologies on Teaching and Learning

FIVE QUESTIONS FOR PEER ASSESSMENTS OF RTL PROJECT PROPOSALS

4 The Impact of Standards-based Reform on Methods of Research in Schools

THE NEED FOR REFORM

The Legacy of Machine-Age Thinking Why Mathematics and Science Education “Failed” New Directions Implications of These Shifts for Schooling

RESEARCH QUESTIONS RESEARCH METHODS SUMMARY Footnotes

5 Improving Research and Systemic Reform Toward Equity and Quality

THREE PREMISES

Premise 1: A Need for Systemic Reform Premise 2: Equity and Quality as Complementary Goals Premise 3: A Situation of Urgency and Strategy

SPECIFIC TARGETS FOR RESEARCH ON SYSTEMIC REFORM

Target 1: Vignettes on Learning Core Ideas Target 2: Reforming the “Gatekeeper” Courses Target 3: Reform at Secondary and Postsecondary Levels Target 4: New Curricula and Implementation Strategies Target 5: School Restructuring Target 6: Assessment Pools Target 7: Effective Models for Teachers’ Professional Growth.

NEW TERRITORIES FOR RESEARCH ON SYSTEMIC REFORM

New Territory 1: Technology Education, Statistical Data Management, and Agriscience New Territory 2: Interdisciplinary Inquiry New Territory 3: Discourse Analysis and Networking New Territory 4: New Technologies New Territory 5: Methodologies

MAKING RESEARCH SYSTEMIC CONCLUSION Footnotes

II Reflecting on Instruments and Methods

6 Formulating Operational Definitions of Desired Outcomes of Instruction in Mathematics and Science Education

LIMITATIONS OF STANDARDIZED TESTS TO OPERATIONALLY DEFINE GOALS OF INSTRUCTION RELATIONSHIPS BETWEEN MEASUREMENT INSTRUMENTS AND OPERATIONAL DEFINITIONS OF UNDERLYING CONSTRUCTS ALTERNATIVE TYPES OF OPERATIONAL DEFINITIONS FOR SPECIFYING GOALS OF INSTRUCTION COMPLEX SYSTEMS HAVE DYNAMIC MULTIDIMENSIONAL PROFILES OF COMPETENCE MULTITIERED TEACHING EXPERIMENTS PROVIDE MULTIDIMENSIONAL INTERACTING TRACES OF DEVELOPMENT IN MULTITIERED TEACHING EXPERIMENTS, THE NATURE OF DEVELOPING ENTITIES EMERGES RETROSPECTIVELY WHAT ARE “WAYS OF THINKING” FOR PROGRAMS, SCHOOLS, OR SCHOOL SYSTEMS? COMPLEX SYSTEMS: TO KNOW THEM IS TO CHANGE THEM SUMMARY AND CONCLUSIONS APPENDIX A: Quality Assurance Guide APPENDIX B The Softball Problem

The ‘Crack’ of the Bat Rings Throughout Central Indiana Town and Across Fields During Summer Evenings Warm-up Questions

Key For Hitting Evaluation Coaches’ Comments

Footnotes

7 Progress in Research: The Interplay Among Theory, Research Questions, and Measurement Techniques

MATCHING THE METHODOLOGY TO THE RESEARCH QUESTIONS

Example 1: Just How “Novice” Are Novices and How “Expert” Are Experts?

Background Designing the Techniques How “the sum of the parts was greater than the whole” in refining the theory

Example 2: Probing Conceptual Understanding in Physics With a NewTechnique

Background Designing the Techniques General Comments on the Posing Techniques

CONCLUDING REMARKS ACKNOWLEDGMENTS Footnotes

8 The Corruption of a Research Design: A Case Study of a Curriculum Innovation Project

THE STORY OF THE SYSTEMS THINKING PROJECT

Objectives Project Inception A Rocky Beginning Project Expansion Lessons Learned Methodological Implications Longitudinal Design Multiple Methods Hierarchical Analyses System Dynamics

SUMMARY

III Teaching Experiments

9 Multitiered Teaching Experiments

A PRIMARY DILEMMA UNDERLYING TEACHING EXPERIMENT METHODOLOGIES DIFFICULTIES THAT LED TO THE DEVELOPMENT OF MULTITIERED TEACHING EXPERIMENTS THE NEED FOR SHARED RESEARCH DESIGNS

What Factors Are the Center of Attention? What Theoretical Windows Are Emphasized? What Practical Problems Are Treated as Priorities?

THE CONSISTENCY PRINCIPLE FOR RESEARCH DESIGNS AT ALL THREE LEVELS OF THREE-TIERED TEACHING EXPERIMENTS

Cognitive Characteristics of Investigators (Students, Teachers, and Researchers) General Mechanisms That Promote Construct Development

SIMILARITIES AND DIFFERENCES BETWEEN STUDENTS, TEACHERS, AND RESEARCHERS SIMILARITIES AND DIFFERENCES BETWEEN STUDENTS, TEACHERS, AND RESEARCHERS AN EXAMPLE: SPECIFIC WAYS TO STIMULATE AND FACILITATE CONSTRUCT DEVELOPMENT AT THE TEACHER LEVEL OF A THREE-TIERED TEACHING EXPERIMENT

Mutation Selection Propagation Preservation

AN EXAMPLE: SPECIFIC WAYS TO STIMULATE AND FACILITATE CONSTRUCT DEVELOPMENT AT THE RESEARCHER LEVEL OF A THREE-TIERED TEACHING EXPERIMENT SUMMARY, AND A COMPARISON OF MULTITIERED TEACHING STUDIES TO OTHER RESEARCH DESIGN OPTIONS

Teaching Experiments Offer Alternatives to Expert-Novice Designs Teaching Experiments Offer Alternatives to Pretest-Posttest Designs Teaching Experiments Offer Alternatives to Simple Sequences of Tests, Clinical Interviews, or Neutral Observations Multitiered Teaching Experiments Offer the Possibility of Shared Research Designs to Coordinate the Activities of Multiple Researchers at Multiple Sites

Footnotes

10 Transformative Teaching Experiments Through Conjecture-Driven Research Design

DEVELOPING THE CONJECTURE

Ideological Stance The Conjecture The Theoretical Framework An Example: The “Splitting” Conjecture and Related Theory

DEVELOPING THE TEACHING EXPERIMENT

Refining the Conjecture and Developing Research Questions Four Design Components of Instruction Putting It All Together: The Research Design Model

DATA COLLECTION AND ANALYSES

Data Collection Preliminary Data Analysis and Curricular Revision Final Data Analysis

PRODUCTS OF TRANSFORMATIVE AND CONJECTURE-DRIVEN TEACHING EXPERIMENTS EVALUATING THE QUALITY OF A TRANSFORMATIVE AND CONJECTURE-DRIVEN TEACHING EXPERIMENT

Ensuring the Quality of the Internal Processes Assessing the Potential Impact

CONCLUSION Footnotes

11 Teaching Experiment Methodology: Underlying Principles and Essential Elements

HISTORICAL PERSPECTIVES

Reasons for the Emergence of Teaching Experiments Reasons for the Acceptance of Teaching Experiments

THE ELEMENTS OF TEACHING EXPERIMENT METHODOLOGY

Exploratory Teaching Meanings of Experiment in a Teaching Experiment Meanings of Teaching in a Teaching Experiment

PROTOCOL I PROTOCOL II PROTOCOL III

Learning and Development in a Teaching Experiment Learning as Accommodation Retrospective Analysis and Model Building

ARE TEACHING EXPERIMENTS SCIENTIFIC? FINAL COMMENTS

On Replication On Generalizability On Self-Reflexivity

ACKNOWLEDGMENTS Footnotes

12 Conducting Teaching Experiments in Collaboration With Teachers

THEORETICAL ORIENTATION

Problems and Issues

TEACHING EXPERIMENTS IN THE CONTEXT OF DEVELOPMENTAL RESEARCH

Instructional Design and Planning Experimenting in the Classroom Retrospective Analysis

GENERALIZABILITY, TRUSTWORTHINESS, AND COMMENSURABILITY

Theoretical Analyses Instructional Innovations

COLLABORATING WITH TEACHERS CONCLUSION ACKNOWLEDGMENTS Footnotes

13 Research on the Development of Mathematics Teachers: The Teacher Development Experiment

THE PSYCHOLOGICAL AND SOCIAL THEORETICAL UNDERPINNINGS OF THE TDE SITTING ON THE SHOULDERS OF GIANTS

Contributions of the Constructivist Teaching Experiment Contributions of the Whole-Class Teaching Experiment

THE TEACHER DEVELOPMENT EXPERIMENT METHODOLOGY

Overview Developmental Stance Analyzing Teaching Experiment Data: An Example Case Studies of Individual Teachers Interpretive Framework Coordinating the Analyses of the Teaching Experiments and the Case Studies of Individual Teachers Additional Issues of Data Collection and Analysis Limitations of the TDE

CONCLUSIONS Footnotes

IV Classroom-Based Research

14 Working on the Inside: Using One’s Own Practice as a Site for Studying Teaching and Learning

LOOKING AT FIRST-PERSON RESEARCH FROM A FIRST-PERSON PERSPECTIVE: A NARRATIVE RESEARCH ON AND INTO PRACTICE FROM THE PERSPECTIVE OF THE RESEARCHER-TEACHER

Lampert (1986): Inquiry Into Elementary Mathematics Teaching Heaton (1994): Inquiry into Changing One’s Practice Simon (1995): Inquiry into Mathematics Teacher Education What Is Distinctive About First-Person Research?

SPECIAL VALUES AND PITFALLS OF THE FIRST-PERSON PERSPECTIVE

Research Questions: Connecting Problem and Perspective Scholarly Stance: Composing Distance and Insight Claims: Navigating the General and Particular

FIRST-PERSON RESEARCH: FACING THE RESPONSIBILITY FOR DEVELOPING A GENRE ACKNOWLEDGMENTS Footnotes

15 Paradigms for Teacher-Centered, Classroom-Based Research

THE ROLES OF TEACHERS AND RESEARCHERS KNOWLEDGE ABOUT TEACHING AND LEARNING GUIDING PRINCIPLES METHODOLOGICAL VARIATIONS WITHIN ACTION RESEARCH

Variation 1 Variation 2 Variation 3

TEACHERS AS COLLABORATIVE RESEARCHERS FOR CHANGES IN CLASSROOM ENVIRONMENTS COLLECTIVE ACTION RESEARCH FOR CHANGE IN TEACHERS’ PRACTICES COMMUNITY ACTION RESEARCH FOR CHANGES IN SCHOOL ENVIRONMENTS CONCLUSIONS ACKNOWLEDGMENTS

16 Action Research as a Research Methodology for the Study of the Teaching and Learning of Science

WHAT IS ACTION RESEARCH?

Conceptions of Action Research A Definition of Action Research Doing and Facilitating Action Research The Products of Action Research

DOING ACTION RESEARCH: AN EXAMPLE OF ACTION RESEARCH IN ONE TEACHER’S CLASSROOM

Why Classroom Research? My Classroom-Based Action Research Summary: Lessons From Doing Action Research

FACILITATING ACTION RESEARCH

Setting the Agenda Structural Concerns Constraints of Schooling The Teaching of Action Research Summary: Lessons From Facilitating Action Research

CONCLUSION ACKNOWLEDGMENTS

17 Integrating a Naturalistic Paradigm Into Research on Mathematics and Science Cognition and Learning

PRINCIPLES OF NATURALISTIC RESEARCH STUDIES

Principle 1: It Is Essential to Consider Multiple Points of View of Events Principle 2: It Is Useful to Connect Theory Verification and Theory Generation Principle 3: It Is Important to Study Cognitive Activity in Context

A DESIGN FOR INTEGRATING A NATURALISTIC PARADIGM INTO THE STUDY OF COGNITION TWO STUDIES

Making Sense of Linear Functions Hawaiian Children’s Understanding of Money

ETHNOGRAPHY AND ETHNOGRAPHIC METHODS STANDARDS OF QUALITY FOR NATURALISTIC RESEARCH STUDIES

Truth Value Applicability Consistency Neutrality

LEARNING TO USE A NATURALISTIC PARADIGM ACKNOWLEDGMENTS Footnotes

18 Interpretive Research in Science Education

QUALITY CRITERIA FOR INTERPRETIVE RESEARCH

Getting Started Data Sources Creating Viable Assertions Credibility Preparation of Research Texts The Moral Practice of Research

AUTHENTICITY CRITERIA FOR INTERPRETIVE RESEARCH AN INTERPRETIVE STUDY OF THE TEACHING AND LEARNING OF CHEMISTRY

Transferability Social Perspectives The Setting and Structure What Did We Learn?

CONCLUSIONS

V Clinical Methods

19 A Scientific Perspective on Structured, Task-Based Interviews in Mathematics Education Research

TASK-BASED INTERVIEWS SCIENTIFIC CONSIDERATIONS

Control and Design, Observation and Inference Reproducibility, Comparability, Reliability, and Generalizability Mathematical Content and Structures Cognitive Theory and Models Social, Cultural, and Psychological Contexts Interplay Among Variables

DISMISSIVE CLAIMS BASED ON EPISTEMOLOGICAL BELIEF SYSTEMS

PRINCIPLES AND TECHNIQUES FOR DESIGNING QUALITY INTERVIEWS

CONCLUSION

20 Analysis of Clinical Interviews: Foundations and Model Viability

FOUNDATIONS: FINDINGS FROM RECENT HISTORY OF SCIENCE STUDIES ON PROCESSES FOR CONSTRUCTING MODELS IN SCIENCE

Four Levels of Knowledge in Science The Need for Generative Case Studies An Example Illustrating the Role of Generative Case Studies The Construction of Explanatory Models in Science: Abduction Versus Induction Maintaining the Distinction Between Observation and Theory Using the Interpretive Analysis of Generative Clinical Interviews to Construct Models

AN INITIAL DICHOTOMY OF CLINICAL INTERVIEW METHODS: GENERATIVE PURPOSES LEAD TO INTERPRETIVE ANALYSES WHEREAS CONVERGENT PURPOSES LEAD TO CODED ANALYSES

Purposes of Clinical Interview Studies Interpretive Versus Coded Analysis

THE VIABILITY OF THEORETICAL MODELS IN THE ANALYSIS OF CLINICAL INTERVIEWS

Viability Versus Validity Determinants of Viability A Constructivist Approach to Investigation The Survival of the Most Viable Model

RECOMMENDATIONS FOR FOSTERING MODEL VIABILITY

Recommendations for Increasing Model Viability in Reports on Interpretive Analyses of Generative Studies General Recommendations for Fostering Empirical Support as a Component of Viability in Both Generative and Some Convergent Studies The Quality of Subjects’ Reports

BEYOND THE GENERATIVE VERSUS CONVERGENT DICHOTOMY: A SPECTRUM OF CLINICAL INTERVIEW METHODS

Constructing New Observation Categories A Spectrum of Clinical Methods and Their Relation to Levels of Development in Observation Concepts Additional Guidelines for Fostering Model Viability in Each of the Four Types of Studies

RELIABILITY OF OBSERVATIONS: PROGRESSIVE LEVELS OF DEVELOPMENT

Reliability Concerns Observations, not Theories Varying Needs for Reliability Recommendations for Fostering Reliability

TWO TYPES OF GENERALIZABILITY

Theoretical Versus Observational Generalizability Objectivity

WHY BOTH GENERATIVE AND CONVERGENT STUDIES ALONG ALL PARTS OF THE SPECTRUM ARE IMPORTANT

Why Generative Studies Do Not Focus on Formal Measures of Reliability Higher Lettered Approaches Allow Enumerative Observations Study Sequences Maintaining a Balance Between Theoretical and Empirical Work Comparative Advantages of Generative Versus Convergent Methods

CONCLUSION ACKNOWLEDGMENTS

21 Principles for Developing Thought-Revealing Activities for Students and Teachers

PURPOSES AND GENERAL CHARACTERISTICS OF MODELELICITING ACTIVITIES WHO FORMULATED OUR CURRENT CONCEPTION OF MODEL-ELICITING ACTIVITIES? EXAMPLES OF MODEL-ELICITING ACTIVITIES CHARACTERISTICS OF STUDENTS' EARLY INTERPRETATIONS

Characteristics of Intermediate Interpretations. Characteristics of Final Interpretations

FOUR DISCLAIMERS

Disclaimer 1 Disclaimer 2 Disclaimer 3 Disclaimer 4

WHAT CREATED NEED FOR MODEL-ELICITING ACTIVITIES IN OUR OWN PAST RESEARCH PROJECTS?

Observation 1 Observation 2 Observation 3

PRINCIPLES FOR DESIGNING PRODUCTIVE MODEL-ELICITING ACTIVITIES

The Model Construction Principle The Reality Principle The Self-Assessment Principle The Construct Documentation Principle The Construct Shareability and Reusability Principle The Effective Prototype Principle

SOME COMMON MISCONCEPTIONS ABOUT MODEL-ELICITING ACTIVITIES

Why “Fun” isn’t a Primary Characteristic of Model-Eliciting Activities? Why is “Difficult” an Inaccurate Characteristic of Model-Eliciting Activities?

SUMMARY: THREE COMMON QUESTIONS ABOUT MODELELICITING ACTIVITIES

What Role(s) Should Teachers Play When Students Are Working on ProjectSize, Model-Eliciting Activities? How Can Teachers Spend So Much Time on Project-Size Activities? How Can Average-Ability Students Be Expected to Invent Significant Mathematical Ideas?

APPENDIX A

The Sears Catalogue Problem

APPENDIX B

Using the Reality Principle to Improve Performance Assessment Activities

AN ATTEMPT TO IMPROVE “THE SOFTBALL PROBLEM'

A Teacher’s Analysis A Third Iteration of “The Softball Problem”

AN ATTEMPT TO IMPROVE “THE MILLION DOLLAR PROBLEM”

One Teacher’s Critique of “Exploring the Size of a Million Dollars”

Footnotes

22 Videorecording as Theory

DATA ARE TECHNOLOGY (AS WELL AS THEORY) LADEN

Technology and Research Practices Thinking With and Without Moving Solving Problems With/Without Whole People Teaching With and Without Acting or Listening Telling With and Without Asking or Interacting Explaining With and Without Seeing Summary and a Note About Production Values

A TERRAIN FOR (THINKING ABOUT) USING VIDEOTAPE

Trouble/Heterogeneity at Home Trouble/Heterogeneity in the Research Community Trouble/Heterogeneity Online

DISCUSSION ACKNOWLEDGMENTS Footnotes

23 Iterative Refinement Cycles for Videotape Analyses of Conceptual Change

THE ROLE OF VIDEOTAPES DEPENDS ON OTHER APPROACHES USED WITH THEM SOME ISSUES TO CONSIDER TO IMPROVE THE QUALITY OF VIDEOTAPE ANALYSES PROCEDURES FOR TESTING, REFINING, AND EXTENDING INTERPRETATIONS OF VIDEOTAPES SUMMARY APPENDIX

The Summer Jobs Problem

Footnotes

24 Choosing and Using Video Equipment for Data Collection

CHOOSING VIDEO EQUIPMENT

Tape Format Camcorders Microphones Mixers Accessories Playback VCRs Monitors Software Support for Video Analysis

USING VIDEO EQUIPMENT

Audio First! Camera Placement Videography Trade-Offs Minimizing Camera Effects About Multiple Cameras Tape Management

UNDERSTANDING BIASES IN RESEARCH VIDEOS

Misconception: Video Captures What an Observer Would See Misconception: Video Has No Point of View Misconception: Video Captures Context Misconception: A Research Video Is Like a Research Paper

METHODOLOGICAL CHALLENGES OF VIDEO DATA

Designing the Logic of a Research Project Ethics and Informed Consent Data Collection Data Analysis Presentation

CONCLUSION ACKNOWLEDGMENTS APPENDIX

Checklists

VI Curriculum Design As Research

25 Mathematics Curriculum Development as a Scientific Endeavor

A FLAWED PROCESS AN EXAMPLE: GENERAL GOALS, NEBULOUS OUTCOMES

The Lesson Plan Observation of the Final Class Discussion A Rudderless Ship

CURRICULUM DEVELOPMENT AS SCIENTIFIC ACTIVITY ELEMENTS OF A SCIENTIFIC APPROACH TO CURRICULUM DEVELOPMENT

Describe the Problem That the Curriculum Development Effort Seeks to Solve Provide a Theoretical Explanation of How the Curriculum Development Effort Should Solve the Problem Describe the Testing and Data Collection Procedures Document the Development of Instructional Activities and the Collection of Data Analyze the Data and Records of Development

THE INTERPLAY BETWEEN CURRICULUM DEVELOPMENT AND RESEARCH

Connecting Curriculum Development to Research Findings Connecting Curriculum Development to Research Perspectives Connecting Curriculum Development to Research Methodologies Benefits

POSSIBLE CRITICISMS OF SCIENTIFIC CURRICULUM DEVELOPMENT CONCLUSION ACKNOWLEDGMENT Footnotes

26 Designing Effective Software

A MODEL FOR INTEGRATED RESEARCH AND CURRICULA AND SOFTWARE DEVELOPMENT

Phase 1: Draft the Initial Goals Phase 2: Build an Explicit Model of Students’ Knowledge and Learning in the Goal Domain Phase 3: Create an Initial Design for Software and Activities Phase 4: Investigate the Components Phase 5: Assess Prototypes and Curriculum Phase 6: Conduct Pilot Tests in a Classroom Phase 7: Conduct Field Tests in Multiple Classrooms Phase 8: Recurse Phase 9: Publish

CONCLUSIONS Footnotes

27 Technology Design as Educational Research: Interweaving Imagination, Inquiry, and Impact

CHARACTERISTICS OF SUCCESSFUL PROJECTS

Integrated Attention to Learning, Curriculum, and Technology Technology Design as Iterative and Transformative

THE DILEMMA OF IMPACT OPEN PROJECT ARCHITECTURE PRINCIPLED DESIGN EXPERIMENT CONSORTIA REUSABLE SOFTWARE KITS CONCLUSION ACKNOWLEDGMENTS

28 The Role of Historical Studies in Mathematics and Science Educational Research

HISTORICAL BACKGROUND AS AN ADDENDUM TO TRADITIONAL CURRICULA NEW CURRICULA INSPIRED BY ORIGINAL HISTORICAL SOURCE MATERIAL SOCIAL HISTORY OF CURRICULA AND IMPLIED VALUES CONCLUSIONS ACKNOWLEDGMENTS

VII Toward Assessment Design

29 Subgroup Differences on the GRE Quantitative Test Based on the Underlying Cognitive Processes and Knowledge

A BRIEF SUMMARY OF THE RULE-SPACE MODEL OBTAINING ATTRIBUTE PROBABILITIES USING THE RULE-SPACE MODEL

The Data Set Phase 1: Obtaining an Incidence Matrix for Use in Rule-Space Analysis

Identifying the Attributes Developing the Incidence Matrix Validating the Incidence Matrix

Phase 2: Rule-Space Analysis

Determining Ideal Item-Response Patterns, Latent Knowledge States, Latent Classes Classification Validity of the 14 Attributes: Variance of the IRT Ability Measure Accounted for by the 14 Attributes

ANALYSIS OF THE RULE-SPACE CLASSIFICATION RESULTS

Cluster Analysis Discriminant Analysis for the Majors Discriminant Analysis for Racial-Ethnic Groups Discriminant Analysis for the Gender Differences

CONCLUSIONS DISCUSSION ACKNOWLEDGMENTS APPENDIX A

Major Fields of Study

Humanities and Art Natural Sciences Physical Sciences: Nonengineering Physical Sciences: Engineering Social Sciences and Business Social Work and Education

APPENDIX B

Attributes Required by Examinees to Answer Correctly Items on the GRE Quantitative Test

Content Variables Context Variables

Footnotes

30 Cautions and Considerations: Thoughts on the Implementation and Evaluation of Innovation in Science Education

TECHNOLOGY-BASED PROGRAMS IN SCIENCE CURRICULA EVALUATING TECHNOLOGY-BASED PROGRAMS

Difficulties in Implementing Innovation Evaluation Protocols

CONCLUSION

31 Assessing Learning as Emergent Phenomena: Moving Constructivist Statistics Beyond the Bell Curve

TAKING THE MEASURE OF MEASURING

Reconsidering the Beginnings and Ends of Assessment What’s in a Number? How Does Standard Numerical Assessment Depict Learning?

CRITIQUE OF STANDARD GROUP ASSESSMENT METHODOLOGY: REJECTING THE EFFICACY OF METHODS WITHOUT MODELS

Heuristic Realism and the Gaussian Distribution An Early Example of a Constructivist Statistic

TOWARD A NONUNIVERSAL CONSTRUCTIVE! STATISTIC

Outlines of an Emergent Framework Limitations of the Nonstandard Methodology

THE COEVOLUTION OF TECHNOLOGY, METHOD, AND EPISTEMOLOGY Footnotes

32 When Using the Mean Is Meaningless: Examples From Probability Theory and Cardiology

ASSUMPTIONS ON WHICH THE MEAN IS BASED THE MEAN IS NOT DEFINED FOR FRACTALS HISTORICAL BACKGROUND AN EXAMPLE WHERE THE MEAN EXISTS: A GAUSSIAN COIN GAME AN EXAMPLE WHERE THE MEAN IS NOT DEFINED: THE ST. PETERSBUG PARADOX, A FRACTAL COIN GAME AN EXAMPLE FROM HEART DATA SUMMARY ACKNOWLEDGMENT

References Author Index Subject Index

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