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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
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