The First Five Years of Teaching Mathematics (FIRSTMATH): Concepts, Methods and Strategies for Comparative International Research

Foreword
	Toward a Study of Beginning Teachers and Teaching: FIRSTMATH Proof of Concept
	References
Preface
Acknowledgments
Acronyms and Abbreviations
Contents
About the Authors
Chapter 1: The FIRSTMATH Study: Concepts, Methods, and Strategies for Comparative International Research in Mathematics Education
	Introduction
	The FIRSTMATH Study
		Rationale for the Study
		Key Findings from TEDS-M That Motivated FIRSTMATH
	FIRSTMATH as a Follow-Up to TEDS-M
	Developing and Testing Methods and Procedures
		Understanding Country Contexts
		The Field Trial
	Unique Contributions of FIRSTMATH as a Proof-of-Concept Study
		The FIRSTMATH Conceptual Framework
		FIRSTMATH Common Language, Sampling Methods and Instruments Developed Amidst Variation
		FIRSTMATH’s Alternative Model to VAM
	Overview of the Chapters in This Book
	References
Chapter 2: Design and Development of International Sampling Procedures for Comparative International Research in Mathematics Education: Challenges and Solutions
	Introduction
	Finding a Fitting Definition of a Beginning Teacher
	Developing a Stratified Multi-stage Sampling Process to Select Beginning Teachers
	Participating Countries and Regions Selected from the Countries
	Confronting Reality: Adapting to Challenges
	Toward a New Sampling Methodology
		Stratified Sequential Adaptive Cluster Sampling
	Flexibility and Adaptability
	Results and Conclusions
	References
Chapter 3: A Validity Framework for the Design of Comparative International Research in Mathematics Education
	Introduction
	Challenge 1: Validation Process
		Moving Beyond Summed Scores
	Challenge 2: Rating Scale Structure & Measurement Invariance
		Knowledge Assessments
		Questionnaires
	Challenge 3: Scaling and Scale Meaning (Reporting & Interpretation)
		Primary-Level Teacher Assessment Items
		Secondary-Level Teacher Assessment Items
		Questionnaires
	Summary
	References
Chapter 4: Design and Development of International Mathematics Assessments for Teachers and Pupils
	Introduction
	Assessment Frameworks
		Mathematical Content Knowledge Framework
		Mathematical Pedagogical Content Knowledge Framework
	Item Formats
		Developing Mathematics and Mathematics Pedagogy Items
		FIRSTMATH Comprehensive Study Field Trial
		Development of Pupil Knowledge Assessments
		Field Trial Samples
	2014 Field Trial Results
		Reporting Limitations
		Knowledge Assessment Preliminary Scoring
		Primary-Level Beginning Teacher Knowledge Assessment Distributions
		Secondary-Level Beginning Teacher Knowledge Assessment Distributions
		Primary-Level Pupil Knowledge Assessment Distributions
		Secondary-Level Pupil Knowledge Assessment Distributions
	Conclusions
	References
Chapter 5: Design and Development of International Context Questionnaires for Mathematics Teachers and Pupils
	Introduction
	Conceptual Framework
	General Methodological Approach
		Pilot Teacher Questionnaire Instrumentation
		Field Trial Teacher Questionnaire Instrumentation
	Summary of 2014 Field Trial Results
		Reporting Limitations
		Field Trial Teacher Questionnaire Interim Scoring
	Overall Summary Measures
		Beliefs About Teaching and Learning Mathematics
		Opportunities to Learn
		Teaching Practices
		School Contexts
		Inter-measure Correlations
		Teaching and Preparedness to Teach Mathematics Topics
	Pupil Questionnaire
		General Background
		Sample Sizes
		Items and Skip Rates
	Conclusions
	References
Chapter 6: Design and Development of an International Mathematics-Focused Observation Protocol
	Introduction
		Existing Protocols
	Field Trial Observation Results
		Stallings Observation Protocol Field Trial Results
		Lesson Flow Results from the Field Trial
		Holistic Item Results from the Field Trial
	Limitations and Observation Country Notes
	Conclusions and Future Directions
	References
Chapter 7: Modeling Pupil and Teacher Interactions as they Pursue Instructional Goals in Mathematics Teaching: An Alternative to VAM
	Introduction
	Challenges and Assumptions in Measuring Effectiveness of Teachers Across Countries
	Developing a Model for Relating Pupils, Teachers, and Proficiency
	Implications of the Use of the Model
	Application of This Model to International Studies
	Discussion and Conclusions
	References
Chapter 8: Comparative International Research in Mathematics Education: Lessons Learned and Future Directions
	Introduction
	FIRSTMATH PoC Accomplishments
		Common Definitions and Instruments
		Rigorous Adaptable Methods
		Insights for Teachers, Schools, and Teacher Education Professionals
	Lessons Learned Concerning Methods and Instrumentation
		Developing Common Definitions and Tailoring Sampling Frames to Contexts (Chap. 2)
		Validity Framework (Chap. 3)
		Mathematics Assessment of Teachers and Pupils (Chap. 4)
		Context Questionnaires for Teachers and Pupils (Chap. 5)
		Mathematics-Focused Observation Protocol (Chap. 6)
		Modeling Pupil/Teacher Interactions (Chap. 7)
	Expectations for the Larger Study Given PoC Study Lessons
	References