# Vera's case context

Main elements, towards new developments

We present in this folder:

- The curricular context
- The context of the lesson to be taught
- The French context of teacher documentary work
- The context of the school
- The context of the classroom

##### 1) The curricular context

Brief elements on the French schooling system: 5 years primary + 4 years lower secondary (‘collÃ¨ge’) + 3 years upper secondary education. Some more elements can be found in (Pepin et al. 2013): "In a connected mathematics textbook study (Pepin & Haggarty 2001; Haggarty & Pepin 2002), the researchers also identified encyclopaedic traditions of school knowledge as the determining underpinning French traditions. McLean (1990) analysed European school knowledge traditions, and he supports the claim that the encyclopaedic tradition, and the associated principle of Ã©galitÃ©, were most prominently observable in the French educational system and national curricula. French encyclopaedism principally adheres to three main principles: universality; rationality; and utility. Universality contends that all students should acquire knowledge as much developed and structured as possible, and this should be standardised in curricula (reflected in yearly performance standards). Rationality, according to McLean (1990), encourages the teaching of ‘rational’ subjects (e.g. mathematics), to enable learners to understand structure and logic. The third principle, utility, sees rational knowledge to be valuable not only for its own sake, but for its societal use. Hence, encyclopaedism and egalitarian values are generic in the French National curriculum; they are historically linked to the values of the French revolution (18th century) and reinforced by the laws for public schools (‘unitary school system’- 19th century). The 20th century reforms for a “common middle school” (1974), “80% of students to pass the baccalaureat” (1985) and more recently“socle commun de connaissance” (common core of knowledge, 2005) can be seen as confirming this process of conceiving school as a ‘common home’ for each pupil’s education and further advancing and applying egalitarian principles. In terms of mathematics the period of ‘Modern Maths’ (20th century) has had a significant influence on the curriculum, and has arguably reinforced the encyclopaedic trend, situating in particular rationality and mathematical thinking at the heart of each educational process. Mathematics itself was then conceived as a ‘pure’ science, abstract and independent of social and cultural influences". In the new programs, this conception of mathematics has deeply changed (see below).

##### 2) The context of the lesson to be taught

Vera's school is a college. Pepin et al. (ibidem) situate the context of the French "Programmes du collÃ¨ge": "The French ‘Programmes du collÃ¨ge – Programmes de l’Enseignement de mathÃ©matiques’ (lower secondary curriculum for mathematics) (MinistÃ¨re de l’Education Nationale 2008), here referred to as FNC, is a lengthy document (38 pages). It comprises of a 'common introduction', concerning mathematics and science, and stressing in particular the importance of investigation. Next, it presents the content to be taught for each level, from grades 6 to 9. This content is presented in terms of knowledge/competencies with comments about these and organised according to the mathematical topic areas (e.g. data organisation and functions; numbers and computation; geometry; quantity and measure). An essential feature is that only some of the knowledge/competencies belong to the “common base”, which should be mastered by all pupils. The others are also presented, but written in italics". The "programmes du collÃ¨ge" (in French) can be found here.

The lesson at stake takes place in grade 8, and is about statistics, mor precisely percentages (programmes du collÃ¨ge, page 27, translation of the main elements below). This topic has been chosen for a set of reasons, mainly: statistics concerns not only mathematics, but each scientific field (making possible understanding and comparaison with other disciplines); teachning statistics leads to use a lot of various resources from mathematics... and every day life; the teaching of mathematics in France, since its renewing in 2000, is perceived as a difficult matter to teach (leading teachers to a particular effort of preparation... or to botch its teaching at the end of the year).

##### 3) The French context of teachers documentary work

Some elements of description can be found In Gueudet et al. 2014): "In France, teachers at secondary school work approximately 18 weekly lesson sessions (of 55 min) with their students. Typically, there is a unique ‘‘teachers’ room’’ in the school, for all teachers (there is a specific situation for science teachers, who have a ‘‘laboratory’’). The out-ofclass work is done mainly at home, and teachers only meet briefly during breaks. Each year all school staff meet the day before school starts, in order to address questions of general interest (e.g., national educational objectives, local school goals). During the year, for a given class, the teachers involved meet three times for the ‘‘class council,’’ which evaluates each pupil’s progression in terms of his/ her achievement and marks. At the end of each academic year the ‘‘subject discipline councils’’ meet, gathering all the teachers of each discipline. Among other things, at these meetings they choose textbooks (that are bought by the school and lent out to pupils for 1 year). Another opportunity for common work is the preparation of common tests.

Professional development courses are not compulsory for secondary school teachers and do not lead to career developments (apart from succeeding in specific national ‘concours’—competitive examinations). Career developments mostly depend on inspectors, who evaluate teachers’ pedagogic practice approximately every 5 years. There are, however, opportunities for professional development in different associations. In what follows we will in particular mention Sesamath, a mathematics online teacher association (Sabra and Trouche 2011), which collaboratively develops free online textbooks and various interactive resources. In summary, France offers a varied landscape for mathematics teachers’ work: no rooms and time for collective documentation work in school, but a number of occasions for such work developing at the fringes of institutional settings".

##### 4) The context of the school

Vera's college is in an urban (near city) area with ‘mixed’ population. According to Vera, it is a new and friendly school, but it does not mean that collective work with colleagues is frequent. In Gueudet et al. (ibidem), Vera gives some elements about the work with colleagues in her school: "Vera mainly mentioned collaborative work with mathematics colleagues in her own school. She made several attempts to work with a colleague in physics, or with colleagues in other schools, but these remained unsuccessful"

##### 5) The context of the classroom

Vera has the chance to work always in the same room. Then she can keep material on shelves, and arrange table and chairs according to her teaching style. She has an interactive white board in her classroom, and a laptop.

#### References

Gueudet, G., Pepin, B., & Trouche, L. (2013). Collective work with resources: an essential dimension for teacher documentation, ZDM, The International Journal on Mathematics Education, 45(7), 1003-1016.

Pepin, B., Gueudet, G., & Trouche, L. (2013). Investigating textbooks as crucial interfaces between culture, policy and teacher curricular practice: two contrasted case studies in France and Norway, ZDM, The International Journal on Mathematics Education, 45(5), 685-698.