Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks

Probing Beneath the Surface of Experience Introduction On the Purpose of Research On the Arising of Research Questions Recognition of a Phenomenon Example: Reversal Pertinent Distinctions Reacting, Re-emoting and Responding Accounts-of and Accounting-for Forms of Attention A Delicate Point for Educational Research Summary References I Teacher Noticing in Various Grade Bands and Contexts Teacher Noticing in Various Grade Bands and Contexts: Commentary Framing Concluding Remarks References From a Framework to a Lens: Learning to Notice Student Mathematical Thinking Theoretical Framework Literature Review Methods Results and Discussion Attending Interpreting Responding Summary Types of Noticing Conclusion and Implications References Investigating Secondary Preservice Teacher Noticing of Students’ Mathematical Thinking Theoretical Framework Teacher Noticing Is Teacher Noticing Trainable?Productively Assessing Noticing Methodology Curricular Module Participants Data Sources Analysis Findings Impact of Assignment on PSTs ’ Noticing Dominant Trends in Attending Dominant Trends in Interpreting Changes Across Attending and Interpreting Dominant Trends in Responding Themes Evident in PSTs ’ Prompt Responses Discussion and Implications References A Case Study of Middle School Teachers’ Noticing During Modeling with Mathematics Tasks Related Literature Standard for Mathematical Practice: Modeling with Mathematics Situating the Study in Teacher Noticing Synthesis Method Methodology Participants Data Collection Data Analysis Results Theme 1: Structure in Mathematics Theme 2: Translating Between Representations Discussion Limitations and Future Research Final Thoughts References Using Video of Peer Teaching to Examine Grades 6-12 Preservice Teachers’ Noticing Preservice Teachers’ Abilities to Notice Teacher Noticing Methods Context and Participants Data Collection Data Analysis Results Quantity of Comments Focus of Comments Discussion Using Peer Video as a Context for Noticing Implications for Teacher Education and Research References II Examining Student Thinking through Teacher Noticing Examining Student Thinking Through Teacher Noticing: Commentary Professional Noticing of Students’ Mathematical Thinking The Four Studies The Role of Knowledge in Deciding How to Respond to Students’ Thinking Final Comments References Mathematical Teacher Noticing: The Key to Learning from Lesson Study Theoretical Framework: Learning from Lesson Study Critical Lenses for Learning from Lesson Study What is Mathematics Teacher Noticing?Noticing as a Way to Put on the Three Critical Lenses The Three-Point Framework Methodology Context of the Two Case Studies Data Collection Data Analysis What and How PSTs and ISTs Notice During Lesson Study?Teacher Noticing During Lesson Planning Teacher Noticing During Lesson Reviewing Discussion References Learning to Notice Student Thinking About the Equal Sign: K-8 Preservice Teachers’ Experiences in a Teacher Preparation Program Preservice Teacher Noticing Student Thinking About the Equal Sign and Teacher Professional Noticing Method Context Participants Data Collection and Data Sources Data Analysis and Results Implications for Teacher Preparation References Following a Teacher’s Mathematical and Scientific Noticing Across Career Progression from Field Experiences to Classroom Teaching Noticing Students’ Mathematical Thinking The Role of Student Thinking in Teacher Education Context: Iterative Model Building Participant Data Collection and Analysis Findings Mikayla’s Noticing in Mathematics Cross Mathematics Conclusion Mikayla’s Noticing in Science Discussion Attend Interpret Respond Mathematics and Science Content Iterative Model Building Process References Noticing Students’ Conversations and Gestures During Group Problem-Solving in Mathematics Literature Review Framework Noticing Conversation Effective Group Talk Gesture Echoing Methodology Sorting the Data Results and Analysis Attending to the Opening of the Talk Interpreting the Opening Ritual Attending to the Manner in Which Students ’ Gestures Change During the Session Interpreting Observed Gesture Size Attending to Students ’ Echoing Interpreting Echoing Attending to Developing Talk Interpreting the Developing Talk Attending to the Shifts in Group Talk Interpreting Shifts in Group Talk Conclusions and Reflections: Teaching from the Sidelines References III Extending Equitable Practices in Teacher Noticing Extending Equitable Practices in Teacher Noticing: Commentary Equity Frames Teacher Identity and Disposition Classroom-Based Practices Final Thoughts References “Everything Matters”: Mexican-American Prospective Elementary Teachers Noticing Issues of Status and Participation While Learning to Teach Mathematics Background to the Problem Conceptual Frameworks Methodology Overview Data Sources and Analysis Researcher Positionality Findings Noticing Issues of Status and Participation in Prior Experiences Noticing Issues of Status and Participation During the Mathematics Methods Semester Discussion and Conclusion References “Maybe It’s a Status Problem.” Development of Mathematics Teacher Noticing for Equity Background and Theoretical Perspectives Teacher Noticing Equity Teacher Learning in Work-Embedded Interactions Development of Mathematics Teacher Noticing for Equity Methods The Study Context Analytic Methods Coding Application of Codes to Transcript and Formation of Code Profiles of Conversations Discussion of the Data Analysis Illustrative Findings: The Case of Mr. Shaw Finding 1: Code Profiles Reveal Development of Mr. Shaw’s Noticing for Equity Finding 2: Code Profiles Reveal Ways in Which the Coach Supports Mr. Shaw’s Development of Teacher Noticing Discussion References Making Visible the Relationship Between Teachers’ Noticing for Equity and Equitable Teaching Practice Theoretical Framework Teachers ’ Pedagogical Commitments, Noticing, and Instruction What Do We Know About Equitable Noticing?Study Context and Data Collection Analytic Methods Results Shared Teaching Practices and Associated Noticing for Equity The Case of Parker: “Walk Away ”The Case of Raymond: “You Started Off the Period a Knucklehead”Discussion and Conclusion References IV Complexities in Measuring Teacher Noticing Complexities in Measuring Teacher Noticing: Commentary Adoption of a Conception of Teacher Noticing Design of Data-Collection Tools Choice of Data-Analysis Lenses Final Thoughts References Measuring Noticing Within Complex Mathematics Classroom Interactions Methods of Measuring Noticing Measurement Using Categorization of Instances Measurement Using Point or Ranking Systems Measurement in Relation to a Standard Framing Our Work Context of Our Work Measuring Changes in Teachers’ Noticing in Our Work Categorization of Noticing Target Noticing Measuring Teacher Decision Making Measuring Noticing Against a Standard Measuring What Is Not Noticed Discussion and Conclusions References Using Mathematical Learning Goals to Analyze Teacher Noticing Definition of Noticing Definition of Mathematical Learning Goals Why Use Mathematical Learning Goals to Analyze Data?Using Subgoals to Analyze Noticing Data Defining the Key Concepts and Subgoal Codes Using the Key Concepts to Code Noticing Data Using the Codes Conclusion References Measuring Elementary Mathematics Teachers’ Noticing: Using Child Study as a Vehicle Conceptualizations of Teacher Noticing Assessing Teacher Noticing of Student Thinking Child Study and Its Use in Promoting Teacher Noticing The Context of the Current Study Pedagogy Course and the Child Study Project Method Participants Data and Analysis Measurement Results Teacher Profiles Discussion and Conclusions References Investigating the Relationship Between Professional Noticing and Specialized Content Knowledge Conceptual Frameworks Mathematical Knowledge for Teaching Professional Noticing of Children’s Mathematical Thinking Integration of SCK and Professional Noticing Description of Study Methodology Results Overall Professional Noticing Results Instances with. Evidence of SCK SCK Analysis Discussion Implications References A Standardized Approach for Measuring Teachers’ Professional Vision: The Observer Research Tool Professional Vision as an Indicator of the Quality of Knowledge Application to Practice The Idea of Professional Vision The Conceptualization of Professional Vision Videotaped Classroom Situations as Representations of Practice Criterion-Based Selection of Videos Criterion-Based Validation of the Selected Videos Rating Items as Measures of the Quality of Knowledge Representation The Observer Research Tool as a Formative Assessment Approach The Usability of the Observer Research Tool Suitability for Empirically Capturing Reasoning Skills Sensitiveness to Measure Developments Conclusion References Challenges in Measuring Secondary Mathematics Teachers’ Professional Noticing of Students’ Mathematical Thinking Challenges of Collecting Data on Teachers’ Noticing Observations and Inference Reflections on Practice Video and Student Work from Others ’ Classrooms Challenges Specific to Studying Secondary Teachers Comparison of Analyses: K-3 Teachers Versus Secondary Teachers Participants Challenge 1—Availability of Artifacts Used in Measures Challenge 2—Determining Relative Sophistication of Responses Challenge 3—Access to Expert Responses Discussion and Conclusion Lack of a Research Base of Students ’ Conceptions of Secondary Mathematics Topics Culture of Secondary Mathematics Classrooms References V Exploring the Boundaries of Teacher Noticing Exploring the Boundaries of Teacher Noticing: Commentary Teacher Noticing: A Construct Under Development New Approaches to Extending Teacher Noticing References Shifting Perspectives on Preservice Teachers’ Noticing of Children’s Mathematical Thinking Defining Teacher Noticing Expert-Novice Differences in Noticing Preservice Teachers’ Noticing of CMT Situating Our Perspective on Noticing The VPEM Project VPEM Online Platform Evidence of Noticing Issues Emerging from Our Research Interrelationship Between Attending and Interpreting Complexity of Video Representations Concluding Thoughts References Curricular Noticing: Theory on and Practice of Teachers’ Curricular Use Research on Teachers’ Curriculum Use and Noticing Noticing Transferability of the Noticing Construct Studies Aimed at Examining and Developing Curricular Noticing Discussion Conclusion References The FOCUS Framework: Characterising Productive Noticing During Lesson Planning, Delivery and Review Research Design Design Research Paradigm Participants and Setting Data Collection, Condensation and Analysis The FOCUS Framework An Explicit Focus Focusing Noticing Snapshot of Noticing: From Planning to Reviewing Vignette 1: Analysing James’ Noticing During Task Design Vignette 2: Analysing James’ Noticing During Lesson Delivery Vignette 3: Analysing James’ Noticing During Post-lesson Discussion Concluding Remarks References Noticing Distinctions Among and Within Instances of Student Mathematical Thinking Noticing Within and Among The MOST Analytic Framework Noticing Within and Among Using the MOST Analytic Framework Illustration of the Within and Among Interaction Discussion and Conclusion References Teachers’ Professional Noticing from a Perspective of Key Elements of Intensive, One-to-One Intervention Method Findings of Research on KEs A Collection of KEs of One-to-One Instruction Set A of KEs: Descriptions Set B of KEs: Descriptions Problematic Teacher Behaviors Problematic Teacher Behaviors: Descriptions Framework of KEs for Analyzing One-to-One Instruction Linking KEs and Professional Noticing An Example of Linking Professional Noticing and the Use of KEs Discussion Conclusion and Recommendations References The Ascendance of Noticing: Connections, Challenges, and Questions The Fundamental Nature of Teacher Noticing The Relationship Between Teacher Noticing Components The Measurement of Teacher Noticing Development of Teacher Noticing An Unanswered Question—What Do Teachers Think About All of This?Concluding Remarks References