Professional language functions as the medium by which the academic community analyse and theorise the phenomena for which the mathematics classroom is the setting. This professional language also sets bounds on researchers’ capacity to articulate theory concerning those practices. The Sapir-Whorf hypothesis proposes that our lived experience is mediated significantly by our capacity to name and categorise our world. “We see and hear … very largely as we do because the language habits of our community predispose certain choices of interpretation,” (Sapir, 1949, p. 162).  Speakers of one language have access to terms, and therefore to perceptive possibilities, that may not be available to speakers of another language. Different communities, speaking different languages, employ different naming systems to describe the events, actions and interactions of the mathematics classroom.

A technical or professional language (in English) to describe and analyse practice in teaching has been previously reported as lacking or underdeveloped (Lortie, 1975; Lampert, 2000; Grossman 2009). Lampert (2000) has concluded that the lack of opportunities to work collaboratively with peers on the problems of practice result in “a language of practice [that] remains flat or nonexistent” (p.90). Connell (2009) has similarly observed that the organisational culture of the teaching profession does not appear to support the “the informal processes by which practical know-how is passed to new teachers in on-the-job learning” (p. 223) and that a culture that might do so needs to be purposefully fostered.

In documenting the Czech professional language of mathematics teachers, the team of researchers and experienced teachers faced similar obstacles that Czech researchers, educators and teachers in all subjects including didactics of mathematics face; that the language used in the subject didactics should form the basis for descriptions of lessons from both the researcher’s and the teacher’s perspective. However, the subject didactics in the Czech Republic are presently in the process of reconstitution. When creating new theories, researchers in subject didactics focus on development of onto-didactical and psycho-didactical dimensions of the domain and of research in the subject didactics as well as on confrontation of various directions in didactical thinking. These efforts can be expected to precise the used terminology (Janík and Stuchlíková, 2015).

This presentation draws on an international project that set out to document the professional language employed in nine countries (Australia, Chile, China, the Czech Republic, Finland, France, Germany, Japan and the USA) for the description of middle school mathematics classrooms. Our initial interest is lexical and concerns the actual terms by which students, teachers and researchers name the objects in their respective worlds. Documentation of the content and structure of classroom-related lexicons in nine countries reveals patterns of connection in the pedagogical terminology in each country, as well as the practical enactment of cultural-historical differences encrypted in the terms by which classroom phenomena are named and from which each community constructs its instruction and its theory.

If the Australian (or Czech) teacher’s conception of the mathematics classroom is constructed around activities that they can name, then it may follow that they are unlikely to engage in activities that they cannot name. Marton and Tsui (2004) suggest that categories not only express the social structure but also create the need for people to conform to the behaviour associated with these categories (p. 28). Thus teachers’ activity in the classroom is guided by those practices they are able to name, compelling their behaviour to correspond to this familiar construction of practice. Comparison of the lexicons of Australian and Czech Republic middle school mathematics teachers indicates the variation possible within two Western teaching communities with different pedagogical traditions.

The local research team in each of the countries included junior and senior researchers and at least two experienced teachers of middle school mathematics. The Australian team included three academics and three high school teachers of mathematics, two of whom had taught extensively at years seven and eight, whilst the third was a more recent member of the profession. The Czech team included three academics and two very experienced teachers that now held leadership positions in schools. Each team contributed video material, time-stamped transcripts as well as supporting material related to one lesson of year eight mathematics. These lessons were re-packaged as "three-ups", that is, three camera angles with a time-code and subtitles all visible in one viewing window. A stimulus package of nine lessons, one from each team, was constructed and distributed to each local research team for project-wide use. These nine lessons presented a variety of classroom settings and instructional approaches both familiar and unfamiliar to the research team members. Each team began with the prompt "What do you see that you can name?" and recorded their responses on a standardized template. The nine videos (one from each country) were intended to stimulate thinking about the possible terms of the lexicon, however, it was not necessary that each term recorded had to be present in the video stimulus material. The essential point was to record single words or short phrases that are familiar to at least two-thirds of middle school mathematics teachers with an agreed meaning. Operational definitions were developed for each of the terms. The essential set of elements included: the named term (in the original language); a description; examples and non-examples (in the original language and in English). National surveys were subsequently developed to collect information about teachers' level of familiarity with each of the terms, the extent to which they endorsed the descriptions, examples and non-examples, and the frequency with which they used the terms (or phrases) in conversation with their colleagues. Opportunities for commenting on the clarity and appropriateness of the descriptions and the examples and non-examples for each term were also provided. The goal was to establish that the constituent terms of the lexicon were not only familiar to the teaching community whose classroom phenomena were encoded in the lexicon, but also, that their meaning was represented in a way that teachers were happy to endorse.

The Australian lexicon consists of 61 terms and is organized into five categories as follows: Administration (8 terms); Assessment (10); Classroom Management (5); Learning Strategies (27) and Teaching Strategies (49). Twenty-four terms belong to both the Learning and Teaching Strategies categories. The Czech lexicon consists of 49 terms and is organised into ten categories as follows: Assessment (7 terms); Homework (2); Lesson Organisation (8); Lesson Stages (2); Organisational Forms of Instruction (4); Pupils' Individual Work (3); Processes Supporting Student Learning (5); Teaching Methods (10); Types of Problems (4) and Use of Didactical Means (4). In comparison, the Australian and Czech Republic lexicons offer interesting similarities and differences: (i) 16 terms are identically named in both lexicons (e.g., Scaffolding; Clarifying (Australia) and "Vysvětlování"/Clarification (ii) An additional set of 6 terms are very similarly named and have identical pedagogical intention (e.g., Whole Classroom Instruction (Australia) and "Rozhovor (učitele se žáky)"/Talk (of the teacher to the pupils)). (iii) The lexicons differ with level of specification with regard to a particular classroom phenomena. For example, whilst the Australian lexicon identifies "Assessment" as not only a term but also a category, the Czech lexicon has indicated four assessment-related terms ("Hodnocení neadresné"/Assessment-non-directed; "Hodnocení povšechné"/ Assessment - general; "Sebehodnocení"/Self-assessment; and "Vrstevnické hodnocení"/Peer-assessment). (iv) There are Czech terms that are absent from the Australian Lexicon (e.g., "Vizualizace"/Visualisation) as well as Australian terms that are absent from the Czech Lexicon (e.g., (use of a) Hook). Comparison of lexicons of teachers offers us the opportunity to reflect critically on our professional vocabulary and the pedagogical practices named, invisible or absent from our mathematics classrooms. Access to the lexicons of other countries offers possibilities for practice that may expand the professional repertoire of mathematics teachers around the world.

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