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

Probing Beneath the Surface of ExperienceIntroductionOn the Purpose of ResearchOn the Arising of Research QuestionsRecognition of a PhenomenonExample: ReversalPertinent DistinctionsReacting, Re-emoting and RespondingAccounts-of and Accounting-forForms of AttentionA Delicate Point for Educational ResearchSummaryReferencesI Teacher Noticing in Various Grade Bands and ContextsTeacher Noticing in Various Grade Bands and Contexts: CommentaryFramingConcluding RemarksReferencesFrom a Framework to a Lens: Learning to Notice Student Mathematical ThinkingTheoretical FrameworkLiterature ReviewMethodsResults and DiscussionAttendingInterpretingRespondingSummaryTypes of NoticingConclusion and ImplicationsReferencesInvestigating Secondary Preservice Teacher Noticing of Students’ Mathematical ThinkingTheoretical FrameworkTeacher NoticingIs Teacher Noticing Trainable?Productively Assessing NoticingMethodologyCurricular ModuleParticipantsData SourcesAnalysisFindingsImpact of Assignment on PSTs ’ NoticingDominant Trends in AttendingDominant Trends in InterpretingChanges Across Attending and InterpretingDominant Trends in RespondingThemes Evident in PSTs ’ Prompt ResponsesDiscussion and ImplicationsReferencesA Case Study of Middle School Teachers’ Noticing During Modeling with Mathematics TasksRelated LiteratureStandard for Mathematical Practice: Modeling with MathematicsSituating the Study in Teacher NoticingSynthesisMethodMethodologyParticipantsData CollectionData AnalysisResultsTheme 1: Structure in MathematicsTheme 2: Translating Between RepresentationsDiscussionLimitations and Future ResearchFinal ThoughtsReferencesUsing Video of Peer Teaching to Examine Grades 6-12 Preservice Teachers’ NoticingPreservice Teachers’ Abilities to NoticeTeacher NoticingMethodsContext and ParticipantsData CollectionData AnalysisResultsQuantity of CommentsFocus of CommentsDiscussionUsing Peer Video as a Context for NoticingImplications for Teacher Education and ResearchReferencesII Examining Student Thinking through Teacher NoticingExamining Student Thinking Through Teacher Noticing: CommentaryProfessional Noticing of Students’ Mathematical ThinkingThe Four StudiesThe Role of Knowledge in Deciding How to Respond to Students’ ThinkingFinal CommentsReferencesMathematical Teacher Noticing: The Key to Learning from Lesson StudyTheoretical Framework: Learning from Lesson Study Critical Lenses for Learning from Lesson StudyWhat is Mathematics Teacher Noticing?Noticing as a Way to Put on the Three Critical LensesThe Three-Point FrameworkMethodologyContext of the Two Case StudiesData CollectionData AnalysisWhat and How PSTs and ISTs Notice During Lesson Study?Teacher Noticing During Lesson PlanningTeacher Noticing During Lesson ReviewingDiscussionReferencesLearning to Notice Student Thinking About the Equal Sign: K-8 Preservice Teachers’ Experiences in a Teacher Preparation ProgramPreservice Teacher NoticingStudent Thinking About the Equal Sign and Teacher Professional NoticingMethodContextParticipantsData Collection and Data SourcesData Analysis and ResultsImplications for Teacher PreparationReferencesFollowing a Teacher’s Mathematical and Scientific Noticing Across Career Progression from Field Experiences to Classroom TeachingNoticing Students’ Mathematical ThinkingThe Role of Student Thinking in Teacher EducationContext: Iterative Model BuildingParticipantData Collection and AnalysisFindingsMikayla’s Noticing in MathematicsCross Mathematics ConclusionMikayla’s Noticing in ScienceDiscussionAttendInterpretRespondMathematics and Science ContentIterative Model Building ProcessReferencesNoticing Students’ Conversations and Gestures During Group Problem-Solving in MathematicsLiterature ReviewFrameworkNoticingConversationEffective Group TalkGestureEchoingMethodologySorting the DataResults and AnalysisAttending to the Opening of the TalkInterpreting the Opening RitualAttending to the Manner in Which Students ’ Gestures Change During the SessionInterpreting Observed Gesture SizeAttending to Students ’ EchoingInterpreting EchoingAttending to Developing TalkInterpreting the Developing TalkAttending to the Shifts in Group TalkInterpreting Shifts in Group TalkConclusions and Reflections: Teaching from the SidelinesReferencesIII Extending Equitable Practices in Teacher NoticingExtending Equitable Practices in Teacher Noticing: CommentaryEquity FramesTeacher Identity and DispositionClassroom-Based PracticesFinal ThoughtsReferences“Everything Matters”: Mexican-American Prospective Elementary Teachers Noticing Issues of Status and Participation While Learning to Teach MathematicsBackground to the ProblemConceptual FrameworksMethodologyOverviewData Sources and AnalysisResearcher PositionalityFindingsNoticing Issues of Status and Participation in Prior ExperiencesNoticing Issues of Status and Participation During the Mathematics Methods SemesterDiscussion and ConclusionReferences“Maybe It’s a Status Problem.” Development of Mathematics Teacher Noticing for EquityBackground and Theoretical PerspectivesTeacher NoticingEquityTeacher Learning in Work-Embedded InteractionsDevelopment of Mathematics Teacher Noticing for EquityMethodsThe Study ContextAnalytic MethodsCodingApplication of Codes to Transcript and Formation of Code Profiles of ConversationsDiscussion of the Data AnalysisIllustrative Findings: The Case of Mr. ShawFinding 1: Code Profiles Reveal Development of Mr. Shaw’s Noticing for EquityFinding 2: Code Profiles Reveal Ways in Which the Coach Supports Mr. Shaw’s Development of Teacher NoticingDiscussionReferencesMaking Visible the Relationship Between Teachers’ Noticing for Equity and Equitable Teaching PracticeTheoretical FrameworkTeachers ’ Pedagogical Commitments, Noticing, and InstructionWhat Do We Know About Equitable Noticing?Study Context and Data CollectionAnalytic MethodsResultsShared Teaching Practices and Associated Noticing for EquityThe Case of Parker: “Walk Away ”The Case of Raymond: “You Started Off the Period a Knucklehead”Discussion and ConclusionReferencesIV Complexities in Measuring Teacher NoticingComplexities in Measuring Teacher Noticing: CommentaryAdoption of a Conception of Teacher NoticingDesign of Data-Collection ToolsChoice of Data-Analysis LensesFinal ThoughtsReferencesMeasuring Noticing Within Complex Mathematics Classroom InteractionsMethods of Measuring NoticingMeasurement Using Categorization of InstancesMeasurement Using Point or Ranking SystemsMeasurement in Relation to a StandardFraming Our WorkContext of Our WorkMeasuring Changes in Teachers’ Noticing in Our WorkCategorization of NoticingTarget NoticingMeasuring Teacher Decision MakingMeasuring Noticing Against a StandardMeasuring What Is Not NoticedDiscussion and ConclusionsReferencesUsing Mathematical Learning Goals to Analyze Teacher NoticingDefinition of NoticingDefinition of Mathematical Learning GoalsWhy Use Mathematical Learning Goals to Analyze Data?Using Subgoals to Analyze Noticing DataDefining the Key Concepts and Subgoal CodesUsing the Key Concepts to Code Noticing DataUsing the CodesConclusionReferencesMeasuring Elementary Mathematics Teachers’ Noticing: Using Child Study as a VehicleConceptualizations of Teacher NoticingAssessing Teacher Noticing of Student ThinkingChild Study and Its Use in Promoting Teacher NoticingThe Context of the Current StudyPedagogy Course and the Child Study ProjectMethodParticipantsData and AnalysisMeasurementResultsTeacher ProfilesDiscussion and ConclusionsReferencesInvestigating the Relationship Between Professional Noticing and Specialized Content KnowledgeConceptual FrameworksMathematical Knowledge for TeachingProfessional Noticing of Children’s Mathematical ThinkingIntegration of SCK and Professional NoticingDescription of StudyMethodologyResultsOverall Professional Noticing ResultsInstances with. Evidence of SCKSCK AnalysisDiscussionImplicationsReferencesA Standardized Approach for Measuring Teachers’ Professional Vision: The Observer Research ToolProfessional Vision as an Indicator of the Quality of Knowledge Application to PracticeThe Idea of Professional VisionThe Conceptualization of Professional VisionVideotaped Classroom Situations as Representations of PracticeCriterion-Based Selection of VideosCriterion-Based Validation of the Selected VideosRating Items as Measures of the Quality of Knowledge RepresentationThe Observer Research Tool as a Formative Assessment ApproachThe Usability of the Observer Research ToolSuitability for Empirically Capturing Reasoning SkillsSensitiveness to Measure DevelopmentsConclusionReferencesChallenges in Measuring Secondary Mathematics Teachers’ Professional Noticing of Students’ Mathematical ThinkingChallenges of Collecting Data on Teachers’ NoticingObservations and InferenceReflections on PracticeVideo and Student Work from Others ’ ClassroomsChallenges Specific to Studying Secondary TeachersComparison of Analyses: K-3 Teachers Versus Secondary TeachersParticipantsChallenge 1—Availability of Artifacts Used in MeasuresChallenge 2—Determining Relative Sophistication of ResponsesChallenge 3—Access to Expert ResponsesDiscussion and ConclusionLack of a Research Base of Students ’ Conceptions of Secondary Mathematics TopicsCulture of Secondary Mathematics ClassroomsReferencesV Exploring the Boundaries of Teacher Noticing Exploring the Boundaries of Teacher Noticing: CommentaryTeacher Noticing: A Construct Under DevelopmentNew Approaches to Extending Teacher NoticingReferencesShifting Perspectives on Preservice Teachers’ Noticing of Children’s Mathematical ThinkingDefining Teacher NoticingExpert-Novice Differences in NoticingPreservice Teachers’ Noticing of CMTSituating Our Perspective on NoticingThe VPEM ProjectVPEM Online PlatformEvidence of NoticingIssues Emerging from Our ResearchInterrelationship Between Attending and InterpretingComplexity of Video RepresentationsConcluding ThoughtsReferencesCurricular Noticing: Theory on and Practice of Teachers’ Curricular UseResearch on Teachers’ Curriculum Use and NoticingNoticingTransferability of the Noticing ConstructStudies Aimed at Examining and Developing Curricular NoticingDiscussionConclusionReferencesThe FOCUS Framework: Characterising Productive Noticing During Lesson Planning, Delivery and ReviewResearch DesignDesign Research ParadigmParticipants and SettingData Collection, Condensation and AnalysisThe FOCUS FrameworkAn Explicit FocusFocusing NoticingSnapshot of Noticing: From Planning to ReviewingVignette 1: Analysing James’ Noticing During Task DesignVignette 2: Analysing James’ Noticing During Lesson DeliveryVignette 3: Analysing James’ Noticing During Post-lesson DiscussionConcluding RemarksReferencesNoticing Distinctions Among and Within Instances of Student Mathematical ThinkingNoticing Within and AmongThe MOST Analytic FrameworkNoticing Within and Among Using the MOST Analytic FrameworkIllustration of the Within and Among InteractionDiscussion and ConclusionReferencesTeachers’ Professional Noticing from a Perspective of Key Elements of Intensive, One-to-One InterventionMethodFindings of Research on KEsA Collection of KEs of One-to-One InstructionSet A of KEs: DescriptionsSet B of KEs: DescriptionsProblematic Teacher BehaviorsProblematic Teacher Behaviors: DescriptionsFramework of KEs for Analyzing One-to-One InstructionLinking KEs and Professional NoticingAn Example of Linking Professional Noticing and the Use of KEsDiscussionConclusion and RecommendationsReferencesThe Ascendance of Noticing: Connections, Challenges, and QuestionsThe Fundamental Nature of Teacher NoticingThe Relationship Between Teacher Noticing ComponentsThe Measurement of Teacher NoticingDevelopment of Teacher NoticingAn Unanswered Question—What Do Teachers Think About All of This?Concluding RemarksReferences
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