Abstract
In the past few decades, language has become an active focus of investigation in educational research, including research in mathematics education. Such a focus is a symptom of a relatively recent paradigmatic shift whose chief characteristics are a new understanding of the student and an increasing awareness of the complexities of learning contexts, such as, notably, the complexities arising from cultural and linguistic diversity.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Adler, J. (2012). The interdependence of power and mathematics in opportunities to learn: A response to Marta Civil. Proceedings of PME 36, 1, 61–64.
Adler, J., & Ronda, E. (2014). An analytical framework for describing teachers’ mathematics discourse in instruction. Proceedings of PME 38 and PME-NA 36, 2, 9–16.
Amit, M., & Jan, I. (2006). Autodidactic learning of probabilistic concepts through games. Proceedings of PME 30, 2, 49–56.
Appelbaum, P. (2012). Mathematical practice as sculpture of utopia: Models, ignorance, and the emancipated spectator. For the Learning of Mathematics. 32(2), 14–19.
Armstrong, A. (2014). Collective problem posing as an emergent phenomenon in middle school mathematics group discourse. Proceedings of PME 38 and PME-NA 36, 2, 57–64.
Arzarello, F., & Edwards, L. (2005). Gesture and the construction of mathematical meaning. Proceedings of PME 29, 1, 123–154.
Arzarello, F., Bazzini, L., Ferrara, F., Robutti, O., Sabena, C., & Villa, B. (2006). Will Penelope choose another bridegroom? Looking for an answer through signs. Proceedings of PME 30, 2, 73–80.
Askew, M., Abdulhamid, L., & Mathews, C. (2014). Embodiment in teaching and learning early counting: Grounding metaphors. Proceedings of PME 38 and PME-NA 36, 2, 65–72.
Asnis, Y. (2013). Conflicting discourses that shape mathematics teachers’ professional identity. Proceedings of PME 37, 2, 41–48.
Baber, S. A., & Dahl, B. (2005). Dealing with learning in practice: Tools for managing the complexity of teaching and learning. Proceedings of PME 29, 2, 97–104.
Bakhtin, M. M. (1981). The dialogic imagination: Four essays (M. Holquist, Ed., C. Emerson & M. Holquist, Trans.). Austin, TX: University of Texas Press.
Bardelle, C. (2010). Interpreting monotonicity functions: A semiotic perspective. Proceedings of PME 34, 2, 177–184.
Bardelle, C. (2013). The influence of verbal language in a mathematical context: A study on negation. Proceedings of PME 37, 2, 65–72.
Barwell, R. (2005). A framework for the comparison of PME research into multilingual mathematics education in different sociolinguistic settings. Proceedings of PME 29, 2, 145–152.
Barwell, R. (2007). The discursive construction of mathematical thinking: The role of researchers’ descriptions. Proceedings of PME 31, 2, 49–56.
Barwell, R. (2008). Hybrid discourse in mathematicians’ talk: The case of the hyper-bagel. Proceedings of PME 32 and PME-NA 30, 2, 129–136.
Barwell, R. (2012a). Heteroglossia in multilingual mathematics classrooms. In H. Forgasz & F. Rivera (Eds.), Towards equity in mathematics education: Gender, culture and diversity (pp. 315–332). Heidelberg, Germany: Springer.
Barwell, R. (2012b). How language shapes learners’ opportunities to learn. Proceedings of PME 36, 1, 95–100.
Barwell, R. (2013). Formal and informal language in mathematics classroom interaction: A dialogic perspective. Proceedings of PME 37, 2, 73–80.
Barwell, R. (2014). Centripetal and centrifugal language forces in one elementary school second language mathematics classroom. ZDM, 46(6), 911–922.
Barwell, R. (2016). Mathematics education, language and superdiversity. In A. Halai & P. Clarkson (Eds.), Teaching and learning mathematics in multilingual classrooms: Issues for policy, practice and teacher education (pp. 25–42). Rotterdam, The Netherlands: Sense Publishers.
Beaud, M. (2004). A history of capitalism. Delhi, India: Aakar Books.
Berger, M. (2005). Vygotsky’s theory of concept formation and mathematics education. Proceedings of PME 29, 2, 153–160.
Berger, M. (2011). Using mathematical discourse to understand students’ activities when using Geogebra. Proceedings of PME 35, 2, 137–144.
Bergqvist, E. (2009). A verbal factor in the Pisa 2003 mathematics items: Tentative analyses. Proceedings of PME 33, 2, 145–152.
Bjuland, R., Cestari, M. L., & Borgersen, H. E. (2008). A teacher’s use of gesture and discourse as communicative strategies in the presentation of a mathematical task. Proceedings of PME 32 and PME-NA 30, 2, 185–192.
Brousseau, G. (1997). Theory of didactical situations in mathematics. Dordrecht, The Netherlands: Kluwer.
Brown, T. (2011). Rethinking objectivity and subjectivity: Re-distributing the psychological in mathematics education. Proceedings of PME 35, 2, 185–192.
Cassirer, E. (1963). The individual and the cosmos in renaissance philosophy. New York, NY: Harper Torchbooks. (Original work published in 1927)
Cavanna, J. M. (2014). Shaping mathematics classroom discourse: Relating professional development and classroom practice. Proceedings of PME 38 and PME-NA 36, 2, 257–264.
Chapman, O. (2009). Discourse to empower “self” in the learning of mathematics. Proceedings of PME 33, 2, 297–304.
Chen, C.-H., & Chang, C.-Y. (2012). An exploration of mathematics teachers’ discourse in a teacher professional learning community. Proceedings of PME 36, 2, 123–130.
Civil, M. (2008). Language and mathematics: Immigrant parents’ participation in school. Proceedings of PME 32 and PME-NA 30, 2, 329–336.
Civil, M. (2012). Opportunities to learn in mathematics education: Insights from research with “non-dominant” communities. Proceedings of PME 36, 1, 43–59.
Clarke, D., & Mesiti, C. (2010). Issue six: The possible consequences of ignoring non-English pedagogical vocabularies. Proceedings of PME 34, 1, 237–238.
Clarke, D., Xu, L. H., & Wan, M. E. V. (2010). Issue two: The contrasting approaches of research studies into classroom discourse. Proceedings of PME 34, 1, 222–226.
Clarkson, P. C. (1996). NESB migrant students studying mathematics: Vietnamese and Italian students in Melbourne. Proceedings of PME 20, 2, 225–232.
Clarkson, P., & Dawe, L. (1997). NESB migrant students studying mathematics: Vietnamese students in Melbourne and Sydney. Proceedings of PME 21, 2, 153–160.
Consogno, V., Gazzolo, T., & Boero, P. (2006). Developing probability thinking in primary school: A case study on the constructive role of natural language in classroom discussions. Proceedings of PME 30, 2, 353–360.
Cummins, J. (2000). Language, power and pedagogy: Bilingual children in the crossfire. Clevedon, UK: Multilingual Matters.
Darling, J., & Nordenbo, S. (2002). Progressivism. In N. Blake, P. Smeyers, R. Smith, & P. Standish (Eds.), The philosophy of education (pp. 288–308). Oxford, UK: Blackwell.
Dooley, T. (2011). Epistemic actions and the role of vague language. Proceedings of PME 35, 2, 281–288.
Edmonds-Wathen, C. (2010). The everyday language of mathematics: Investigation spatial frames of reference in Iwaidja. Proceedings of PME 34, 2, 321–327.
Edmonds-Wathen, C. (2014). Linguistic relativity and number. Proceedings of PME 38 and PME-NA, 2, 433–440.
Edwards, L. (2010). Doctoral students, embodied discourse and proof. Proceedings of PME 34, 2, 329–336.
Edwards, L. (2011). Embodied cognitive science and mathematics. Proceedings of PME 35, 2, 297–304.
Edwards, L., Bolite Frant, J., & Radford, L. (2010). Working session: Gesture, language and embodiment in mathematics. Proceedings of PME 34, 1, 397.
Edwards, L., Bolite Frant, J., Robutti, O., & Radford, L. (2009). Gesture, multimodality, and embodiment in mathematics. Proceedings of PME 33, 1, 295.
Edwards, L., Radford, L., & Arzarello, F. (2009). Gestures and multimodality in the teaching and learning of mathematics. Educational Studies in Mathematics, 70(2), 91–215.
Edwards, L., Rasmussen, C., Robutti, O., & Frant, J. B. (2005). DG08: Embodiment in mathematics: Metaphors and gestures. Proceedings of PME 29, 1, 212.
Esmonde, I., Wagner, D., & Moschkovich, J. (2009). Equity and discourse in mathematics classrooms: A focus on students. Proceedings of PME 33, 1, 285–285.
Essien, T., & Setati, M. (2007). Exploring the English proficiency-mathematical proficiency relationship in learners: An investigation using instructional English computer software. Proceedings of PME 31, 2, 217–224.
Fernández Plaza, J. A., Ruiz Hidalgo, J. F., & Rico Romero, L. (2012). The concept of finite limit of a function at one point as explained by students of non-compulsory secondary education. Proceedings of PME 36, 2, 235–242.
Foucault, M. (2000). Power. In J. Faubion (Ed.), Essential works of Foucault, 1954–1984. New York, NY: The New York Press.
Freire, P. (2005). Pedagogy of the oppressed. New York, NY: Continuum.
García-Alonso, I., & García-Cruz, J. A. (2007). Statistical inference in textbooks: Mathematical and everyday contexts. Proceedings of PME 31, 2, 257–264.
Gates, P. (2006). The place of equity and social justice in the history of PME. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 367–402). Rotterdam, The Netherlands: Sense Publishers.
Gholamazad, S. (2007). Pre-service elementary school teachers’ experiences with the process of creating proofs. Proceedings of PME 31, 2, 265–272.
Gilbert, B., & Gilbert, M. (2011). Developing effective sociomathematical norms in classrooms to support mathematical discourse. Proceedings of PME 35, 2, 409–416.
Giroux, H. (1986). Authority, intellectuals, and the politics of practical learning. Teachers College Record, 88(1), 22–40.
Giroux, H. (1989). Schooling as a form of cultural politics: Towards a pedagogy of and for difference. In H. Giroux & P. McLaren (Eds.), Critical pedagogy, the state, and cultural struggle (pp. 125–151). Albany, NY: State University of New York Press.
Gol Tabaghi, S., & Sinclair, N. (2011). Student diagramming motion: A discursive analysis of visual images. Proceedings of PME 35, 2, 433–440.
Gress, D. (1999). Multiculturalism in history. Hellenic and Roman antiquity. Orbis, 43(4), 553–573.
Güçler, B. (2011). Historical junctures in the development of discourse on limits. Proceedings of PME 35, 2, 465–472.
Guillemette, D. (2015). L’histoire des mathématiques et la formation des enseignants du secondaire: Sur l’expérience du dépaysement épistémologique des étudiants [The history of mathematics and high school teacher education: On the students’ experience of epistemological strangeness] (Ph.D. Dissertation). Université du Québec à Montréal, Montréal, Canada.
Hardt, M., & Negri, A. (2000). Empire. Cambridge, MA: Harvard University Press.
Hegedus, S., Dalton, S., Cambridge, L., & Davis, G. (2006). Patterns of participation in networked classrooms. Proceedings of PME 30, 3, 257–264.
Heinze, A., Reiss, K., Rudolph-Albert, F., Herwartz-Emden, L., & Braun, C. (2009). The development of mathematical competence of migrant children in German primary schools. Proceedings of PME 33, 3, 145–152.
Herbel-Eisenmann, B., & Wagner, D. (2005). In the middle of nowhere: How a textbook can position the mathematics learner. Proceedings of PME 29, 3, 121–128.
Herbel-Eisenmann, B., Wagner, D., & Cortes, V. (2008). Encoding authority: Pervasive lexical bundles in mathematics classrooms. Proceedings of PME 32 and PME-NA 30, 3, 153–160.
Hodge, L. L., Zhao, Q., Visnovska, J., & Cobb, P. (2007). Revisiting discourse as an instructional resource: Practices that create spaces for learning and student contributions. Proceedings of PME 31, 3, 41–48.
Høines, M. J., & Lode, B. (2006). Positioning of a subject based and investigative dialogue in practice teaching. Proceedings of PME 30, 3, 369–376.
Hume, D. (1991). An enquiry concerning human understanding. La Salle, IL: Open Court. (originally published in 1777)
Hung, H.-C., & Leung, S.-K. S. (2012). A preliminary study on the instructional language use in fifth-grade mathematics class under multi-cultural contexts. Proceedings of PME 36, 2, 323–330.
Hunter, R. (2007). Can you convince me: Learning to use mathematical argumentation. Proceedings of PME 31, 3, 81–88.
Hunter, R. (2008). Do they know what to ask and why? Teachers shifting student questioning from explaining to justifying and generalising reasoning. Proceedings of PME 32 and PME-NA 30, 3, 201–208.
Hunter, R. (2013). Developing equitable opportunities for Pāsifika students to engage in mathematical practices. Proceedings of PME 37, 3, 97–104.
Hunter, R., Civil, M., Herbel-Eisenmann, B., & Wagner, D. (2014). Mathematical discourse that breaks barriers and creates spaces for marginalised students. Proceedings of PME 38 and PME-NA 36, 1, 244.
Hussain, M. A., Threlfall, J., & Monaghan, J. (2011). The interplay of authoritative and dialogic interactions. Proceedings of PME 35, 2, 1–8.
Ilany, B.-S., & Margolin, B. (2008). Textual literacy in mathematics: An instructional model. Proceedings of PME 32 and PME-NA 30, 3, 209–216.
Kahn, L. H., Musanti, S. I., McLeman, L. K., Menéndez-Gómez, J. M., & Trujillo, B. (2008). Teachers of Latino students reflect on the implementation of a mathematical task. Proceedings of PME 32 and PME-NA 30, 3, 233–340.
Kantor, H. (2001). In retrospect: David Tyack’s the one best system. Reviews in American History, 29(2), 319–327.
Kaufmann, J.-C. (2004). L’invention de soi : Une théorie de l’identité [The invention of self: A theory of identity]. Paris, France: Armand Colin.
Kelly, P. (2002). Multiculturalism reconsidered. Cambridge, UK: Polity.
Khisty, L. L. (2006). Language and mathematics: Toward social justice for linguistically diverse students. Proceedings of PME 30, 3, 433–440.
Kleanthous, I., & Williams, J. (2010). Cultural models of mathematics and perceived parental influence amongst immigrant students in Cyprus. Proceedings of PME 34, 3, 177–184.
Knipping, C., & Reid, D. (2013). Have you got the rule underneath? Invisible pedagogic practice and stratification. Proceedings of PME 37, 3, 193–200.
Labaree, D. (2005). Progressivism, schools and schools of education: An American romance. Paedagogica Historica, 41(1–2), 275–288.
Le Roux, K. (2014). Explaining mathematical meaning in “practical terms” and access to advanced mathematics. Proceedings of PME 38 and PME-NA 36, 4, 65–72.
Le Roux, K., & Adler, J. (2012). Talking and looking structurally and operationally as ways of acting in a socio-political mathematical practice. Proceedings of PME 36, 3, 51–58.
Lee, C. (2006). Language for learning mathematics. Assessment for learning in practice. London, UK: Open University Press.
Lerman, S. (2006). Socio-cultural research in PME. In A. Gutiérrez & P. Boero (Eds.), Handbook of research on the psychology of mathematics education: Past, present and future (pp. 347–366). Rotterdam, The Netherlands: Sense Publishers.
Leung, A., & Or, C. M. (2007). From construction to proof: Explanations in dynamic geometry environment. Proceedings of PME 31, 3, 177–184.
Lim, C., & Ellerton, N. (2009). Malaysian experiences of teaching mathematics in English: Political dilemma versus reality. Proceedings of PME 33, 4, 9–16.
Lunney Borden, L. (2009). The ‘verbification’ of mathematics. Proceedings of PME 33, 4, 41–48.
Makar, K., & Canada, D. (2005). Preservice teachers’ conceptions of variation. Proceedings of PME 29, 3, 273–280.
Manu, S. (2005). Growth of mathematical understanding in a bilingual context: Analysis and implications. Proceedings of PME 29, 3, 289–296.
Mellone, M., Verschaffel, L., & Van Dooren, W. (2014). Making sense of word problems: The effect of rewording and dyadic interaction. Proceedings of PME 38 and PME-NA 36, 4, 202–209.
Mesa, V., & Chang, P. (2008). Instructors’ language in two undergraduate mathematics classrooms. Proceedings of PME 32 and PME-NA 30, 3, 367–374.
Metz, M. H. (1978). Classrooms and corridors: The crisis of authority in desegregated secondary schools. Berkeley, CA: University of California Press.
Meyer, M. (2014). An inferential view on concept formation. Proceedings of PME 38 and PME-NA 36, 4, 218–225.
Misailidou, C. (2007). Detecting the emergence and development of mathematical discourse: A novel approach. Proceedings of PME 31, 3, 273–280.
Morera, L., & Fortuny, J. M. (2012). An analytical tool for the characterisation of whole-group discussions involving dynamic geometry software. Proceedings of PME 36, 3, 233–240.
Morgan, C., & Tang, S. (2012). Studying changes in school mathematics over time through the lens of examinations: The case of student positioning. Proceedings of PME 36, 3, 241–248.
Moschkovich, J., Gerofsky, S., & Esmonde, I. (2010). Discourse and equity in mathematics classrooms: A focus on students. Proceedings of PME 34, 1, 394.
Nachlieli, T., Heyd-Metzuyanim, E., & Tabach, M. (2013). Proceedings of PME 37, 3, 345–352.
Neill, A. S. (1992). Summerhill school: A new view of childhood. New York, NY: St. Martin’s Griffin. (Original work published 1960)
Ng, O.-L. (2014). The interplay between language, gestures, dragging and diagrams in multilingual learners’ mathematical communications. Proceedings of PME 38 and PME-NA 36, 4, 290–297.
Nkambule, T., Setati, M., & Duma, B. (2010). One mathematics classroom, multiple languages. Proceedings of PME 34, 3, 345–352.
Ohtani, M. (2007). Designing unit for teaching proportion based on cultural-historical activity theory: Process of symbolizing through collective discourse. Proceedings of PME 31, 4, 33–40.
Pace, J., & Hemmings, A. (2007). Understanding authority in classrooms: A review of theory, ideology, and research. Review of Educational Research, 77(1), 4–27.
Planas, N., & Civil, M. (2008). Voices of non-immigrant students in the multiethnic mathematics classroom. Proceedings of PME 32 and PME-NA 30, 4, 121–127.
Planas, N., & Civil, M. (2010). Mathematical thinking and language switching as seen by Latin American students in Barcelona. Proceedings of PME 34, 4, 49–56.
Planas, N., Iranzo, N., & Setati, M. (2009). Language switching with a group of bilingual students in a mathematics classroom. Proceedings of PME 33, 4, 393–400.
Poirier, A. (2006). Research with teachers: The model of collaborative research: Study of joint development mechanisms for an approach to the teaching of mathematics to Inuit children in kindergarten and primary Grades 1 and 2. Proceedings of PME 30, 1, 105–115.
Prediger, S., Renk, N., Büchter, A., Gürsoy, E., & Benholz, C. (2013). Family background or language disadvantages? Factors for underachievement in high stakes tests. Proceedings of PME 37, 4, 49–56.
Radford, L. (2000). Signs and meanings in students’ emergent algebraic thinking: A semiotic analysis. Educational Studies in Mathematics, 42(3), 237–268.
Radford, L. (2002). The seen, the spoken and the written. A semiotic approach to the problem of objectification of mathematical knowledge. For the Learning of Mathematics, 22(2), 14–23.
Radford, L. (2011). Embodiment, perception and symbols in the development of early algebraic thinking. Proceedings of PME 35, 4, 17–24.
Radford, L. (2012). Education and the illusions of emancipation. Educational Studies in Mathematics, 80(1), 101–118.
Radford, L. (2014). On teachers and students: An ethical cultural-historical perspective. Proceedings of PME 38 and PME-NA 36, 1, 1–20.
Radford, L., Bardini, C., Sabena, C., Diallo, P., & Simbagoye, A. (2005). On embodiment, artifacts, and signs: A semiotic-cultural perspective on mathematical thinking. Proceedings of PME 29, 4, 113–120.
Radford, L., Demers, S., Guzmán, J., & Cerulli, M. (2003). Calculators, graphs, gestures, and the production of meaning. Proceedings of PME 27 and PME-NA 25, 4, 55–62.
Radford, L., Edwards, L., & Arzarello, F. (2009). Beyond words. Educational Studies in Mathematics, 70(2), 91–95.
Radford, L., Miranda, I., & Guzmán, J. (2008). Relative motion, graphs and the heteroglossic transformation of meanings: A semiotic analysis. Proceedings of PME 32 and PME-NA 30, 4, 161–168.
Reiss, T. (1997). Knowledge, discovery and imagination in early modern Europe. The rise of aesthetic rationalism. Cambridge, UK: Cambridge University Press.
Robutti, O., Edwards, L., & Ferrara, F. (2012). Enrica’s explanation: Multimodality and gesture. Proceedings of PME 36, 4, 27–33.
Roth, W.-M., & Radford, L. (2011). A cultural-historical perspective on mathematics teaching and learning. Rotterdam, The Netherlands: Sense Publishers.
Ruwisch, S., & Neumann, A. (2014). Written reasoning in primary school. Proceedings of PME 38 and PME-NA 36, 5, 73–80.
Sakonidis, H., & Klothou, A. (2007). On primary teachers’ assessment of pupils’ written work in mathematics. Proceedings of PME 31, 4, 153–160.
Sánchez, V., & García, M. (2011). Socio-mathematical and mathematical norms in pre-service primary teachers’ discourse. Proceedings of PME 35, 4, 105–112.
Setati, M. (2006). Access to mathematics versus access to the language of power. Proceedings of PME 30, 5, 97–104.
Sfard, A. (2008). Thinking as communicating: Human development, the growth of discourses, and mathematizing. Cambridge, UK: Cambridge University Press.
Sfard, A. (2010). Issue one: The challenges of researching discursive practice in classrooms. Proceedings of PME 34, 1, 217–221.
Shinno, Y. (2013). Semiotic chaining and reification in learning of square root numbers: On the development of mathematical discourse. Proceedings of PME 37, 4, 209–216.
Shuard, H., & Rothery, A. (Eds.). (1984). Children reading mathematics. London, UK: Murray.
Sinclair, N., & Kaur, H. (2011). Young children’s understanding of reflectional symmetry in a dynamic geometry environment. Proceedings of PME 35, 4, 193–200.
Skog, K., & Andersson, A. (2013). Immigrant mathematics teacher students’ subject positioning. Proceedings of PME 37, 4, 233–240.
Tatsis, K., & Rowland, T. (2006). Vague language in Greek and English mathematical talk: A variation study in face-work. Proceedings of PME 30, 5, 257–264.
Thornton, S., & Reynolds, N. (2006). Analysing classroom interactions using critical discourse analysis. Proceedings of PME 30, 5, 273–280.
Todorov, T. (1984). The conquest of America: The question of the other (Richard Howard, Trans.). New York, NY: Harper & Row. (Paris, France: Editions du Seuil, 1982)
Toscano, R., Sánchez, V., & García, M. (2013). Norms and perspectives in pre-service secondary mathematics teachers’ discourse. Proceedings of PME 37, 4, 289–296.
Tyack, D. (1974). The one best system. Cambridge, MA: Harvard University Press.
Valero, P. (2007). A socio-political look at equity in the school organization of mathematics education. ZDM, 39(3), 225–233.
Vergnaud, G. (2001). Forme opératoire et forme prédicative de la connaissance [Operational and predicative forms of knowledge]. In J. Portugais (Ed.), Actes du colloque GDM-2001 (pp. 1–22). Montréal, Canada: Université de Montréal.
Verhoef, N. C., & Broekman, H. G. B. (2005). A process of abstraction by representations of concepts. Proceedings of PME 29, 4, 273–279.
Vertovec, S. (2007). Super-diversity and its implications. Ethnic and Racial Studies, 30(6), 1024–1054.
Verzosa, D. B., & Mulligan, J. (2012). Teaching children to solve mathematical word problems in an imported language. Proceedings of PME 36, 4, 203–210.
Viirman, O. (2011). Discursive practices of two university teachers on the concept of ‘linear transformation’. Proceedings of PME 35, 4, 313–320.
Wagner, D. (2014). Privileging local cultures and demographics in the mathematics classroom. Proceedings of PME 38 and PME-NA 36, 1, 61–66.
Walkerdine, V. (1988). The mastery of reason: Cognitive development and the production of rationality. London, UK: Routledge.
Walshaw, M. (2014). Who can know mathematics? For the Learning of Mathematics, 34(2), 2–6.
Walter, J. G., & Johnson, C. (2007). Elementary teachers’ linguistic inventions and semantic warrants for mathematical inferences. Proceedings of PME 31, 4, 233–240.
Wang, T.-Y., Hsieh, F.-J., & Schmidt, W. H. (2012). Comparison of mathematical language-related teaching competence of future teachers from Taiwan and the United States. PME 36, 4, 211–213.
Warren, E., Miller, J., & Cooper, T. J. (2011). Exploring young children’s functional thinking. Proceedings of PME 35, 4, 329–336.
Wille, A. M. (2011). Activation of inner mathematical discourses of students about fractions with the help of imaginary dialogues: A case study. Proceedings of PME 35, 4, 337–344.
Williams, J., & Ryan, J. (2014). Bakhtinian dialogue and Hegelian dialectic in mathematical and professional education. Proceedings of PME 38 and PME-NA 36, 5, 377–384.
Ye, R., & Czarnocha, B. (2012). Universal and existential quantifiers revisited. Proceedings of PME 36, 4, 235–242.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Sense Publishers
About this chapter
Cite this chapter
Radford, L., Barwell, R. (2016). Language in Mathematics Education Research. In: Gutiérrez, Á., Leder, G.C., Boero, P. (eds) The Second Handbook of Research on the Psychology of Mathematics Education. SensePublishers, Rotterdam. https://doi.org/10.1007/978-94-6300-561-6_8
Download citation
DOI: https://doi.org/10.1007/978-94-6300-561-6_8
Publisher Name: SensePublishers, Rotterdam
Online ISBN: 978-94-6300-561-6
eBook Packages: EducationEducation (R0)