Classroom Research on Mathematics and Language: Seeing Learners and Teachers Differently - Classroom Research on Mathematics and Language: Seeing Learners and Teachers Differently -

Section I: Theorising the complexity of language in mathematics teaching and learning : Developing a perspective on multiplicity in the study of language in mathematics classrooms Introduction Multilingualism and multiculturalism Multimodality Multiple levels of analysis Defining and operationalising ‘language’Defining and operationalising ‘mathematics classroom’Language as the object of study or as the medium of investigation Conclusions/ways forward Notes References : Language, paralinguistic phenomena and the (same-old) mathematics register Introduction Midstream #1: Four anecdotes Midstream #2: Somewhat picky transcriptions Midstream #3: Engaging with the purported ‘multimodal’ register Midstream #4: Communication does not only involve language University lecturer gestures Grade 3 students working on the iPad App TouchTimes In conclusion Acknowledgements Notes References : Bewitched by language: Questions on language for mathematics education research Introduction Theorizing the relation between language and mathematics Researching the relation between language and mathematics Theme 1: Linguistic mechanisms that generate mathematical objects Theme 2: The role of language in the historical emergence of mathematical discourses Theme 3: Linguistic relativity of mathematics Researching the relation between language and mathematics learning Theme 4: Linguistic changes in the process of learning mathematics Theme 5: Linguistic gaps in the classroom Theme 6: Dialogic engagement as a protection from falling into linguistic gaps Researching the relation between language and (mathematics) teaching Theme 7: Teacher’s mathematical language Theme 8: The language in which the teacher speaks about learners and learning Theme 9: The language in which the teacher speaks about her professional practices Concluding remarks Notes References : Learners’ language in mathematics classrooms: What we know and what we need to know Introduction What we know Multiple theoretical frameworks Learners’ language in mathematics classrooms is complex Learners’ mathematical language is much more than precise words Deficit views of bilingual learners’ language miss their strengths Implications for instruction What we need to know Details of how learners’ multiple languages provide resources for learning mathematics Details of learners’ informal language practices Broadening what is meant by participation Details of how learners learn to participate in formal language practices References : Content and context specificity matter in the ‘how’ of language-responsive mathematics teacher professional development Introduction The WMCS and its MDI framework Explanatory talk through naming and legitimating and extensions into a teaching framework Why, what and how of mediating language-responsive teaching in WMCS PD Principle 1: Distinguish the modelling of word use and mathematical justifications from their mediation as language-specific instructional practices Principle 2: Select/construct mediating tasks where: (a) the learner task and teacher task are clearly distinguished; (b) it is rooted in records of teaching/learning practices and focused on a specific curriculum-level mathematics; and (c) the mathematic Principle 3: Elicit and externalize teachers’ spontaneous explanatory talk for collective reflection and interrogation Principle 4: Communicate explicit evaluative criteria for improving the quality of word use and mathematical justifications in classroom talk Reflection/discussion and conclusion Acknowledgements Notes References : Conceptualising and researching mathematics classrooms as sites of communication Introduction Theoretical resources Example: Multilingual classrooms or second - language learners Communication as making functional choices Pedagogic discourse: Participation, social relations and identities Posing questions Researching classrooms as sites of communication: Analytic approaches Example 1: What kinds of mathematics?Example 2: Classroom assessment Episode 1a: An answer Episode 2: A format for answering Episode 3: A behaviour or way of feeling or being Further directions Acknowledgements Notes References Section II: Opening spaces of learning with mathematics classroom research on language : The role of mathematical vocabulary in moving from the particular to the general with visual representations Introduction Extract 1. Whole-class discussion of Figure 7.1 in Tamsin’s lesson Learning the vocabulary of mathematics The particular and the general Structures of interaction Method The case of Tamsin and the area of a triangle Extract 2. Simon and Tamsin co-construct a triangle inscribed in a rectangle The case of Talia and the moment of a force Extract 3. Sacha and Talia co-modelling the action of a wrench Extract 4. Simeon offers an alternative way of conceptualising the length of AD Extract 5. Stefan explains the particular case and Shannon offers a new method Discussion References : Mathematics through play: The influence of adult intervention on young children’s shifts between play and mathematical discourses Introduction Play and mathematics Theoretical underpinning Research method ‘Spontaneous’ play with minimal adult intervention Adult intervention during play Further reflections on ‘more’Discussion and conclusion References : Multilingual mathematics learning from a dialogic-translanguaging perspective Introduction Translanguaging in multilingual mathematics education research Exploring a dialogic stance in translanguaging Dialogic translanguaging for multilingual mathematics learning Dialogic translanguaging of diverse meanings for “baixar”Episode 1: “Going down does not mean one by one”Dialogic translanguaging of diverse meanings for “sobras”Episode 2: “I don’t think leftovers means that”Concluding remarks References : Quality dimensions for activation and participation in language-responsive mathematics classrooms Introduction Developing a theoretical framework in four dimensions and the supply and use perspective Supply-use model for framing the research overview Introducing four quality dimensions of mathematics classroom interaction Talk-related dimension Conceptual dimension Discursive dimension Lexical dimension Illustrative case for disentangling four dimensions in two perspectives Outlook: Operationalizing the dimensions for video-rating Operationalizing teachers’ intended activation (supply perspective)Operationalizing students’ participation (use perspective)Next steps towards a quantitative video-rating study Acknowledgements References : Real-world contexts in the mathematics classroom and their impact on the pupils’ language and mathematical learning Introduction Fundamental theoretical considerations The dichotomy of academic and everyday language Discourse Learning within discourses, learning within interaction Real-world contexts in mathematics education Study design Main goals of the study and research questions The fundamental methodological assumptions and methods of the study Initial results Scene 1. Class discussion at the start of the lesson: What does Croco like to eat?Scene 2. Assistance during individual work on the tasks in the workbook: Do you need help, Nabil?Concluding remarks about the impact of (narrative) real-world contexts for language use and learning opportunities References : Preservice teachers learning from teaching mathematics in multilingual classrooms Introduction Theoretical perspectives Methodology Results Episode 1: Students develop measurements units Modalities Communication Potential for learning Available identities Episode 2: The students “who struggle a bit” and language issues Modalities Communication Learning potential Available identities Discussions and concluding remarks References