Abstract
In this study, we investigated design processes in teacher collectives, which have been made possible by new “digital” opportunities: platforms, discussion lists, etc. The object of our study is the French Sésamath teacher association and its design of a grade 10 etextbook, more precisely the design of the “functions” chapter. We analysed it with two theoretical lenses: the documentational approach and culturalhistorical activity theory. We studied the activity system of a community of teachers designing an etextbook. At macrolevel, we observed a change of objects of the activities: from designing a “toolkit” for mathematics teachers; to interactive exercises; and finally to a more “classical etextbook”. At microlevel, we analysed the development of collective documents by the community, combining resources and schemes.
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References
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Appendix 1: list of atoms for the functions chapter in grade 10
Appendix 1: list of atoms for the functions chapter in grade 10

1.
Interpret the link between two quantities by a formula.

2.
For a function defined by a curve: identify the variable and the domain

3.
For a function defined by a table of values: identify the variable and the domain

4.
For a function defined by a formula: identify the variable and the domain

5.
For a function defined by a curve: determine the image of a number.

6.
For a function defined by a curve: research the preimages of a number.

7.
For a function defined by a table of values: determine the image of a number.

8.
For a function defined by a table of values: research the preimages of a number.

9.
For a function defined by a formula: determine the image of a number.

10.
For a function defined by a formula: research the preimage of a number.

11.
Increasing function; decreasing function.

12.
Maximum, minimum of a function over an interval.

13.
Describe, with suitable vocabulary or a table of variations, the behaviour of a function defined by a graph.

14.
Draw a graph compatible with a table of variations.

15.
When variation of a function is given by a sentence or table of variations: compare images of two numbers of an interval.

16.
Determine all numbers whose the image is greater than (or less than) a given image.

17.
Transform algebraic expressions to solve problems.

18.
Associate an algebraic expression to a given problem.

19.
Identify the most appropriate form (expanded, factorized) of an expression for solving a given problem.

20.
Expand simple polynomial expressions.

21.
Factorize simple polynomial expressions.

22.
Transform simple rational expressions.

23.
Determine equations corresponding to a problem

24.
Solve an equation by reducing it to the first degree.

25.
Find a lower and an upper bound for the root of an equation with a dichotomy algorithm.

26.
Give variations of a linear function.

27.
Give the table of signs of ax + b for given values of a and b.

28.
Represent graphically the square function.

29.
Represent graphically the reciprocal function.

30.
Knowing the variations of a polynomial function (degree 2) and the symmetry properties of its graph.

31.
Identify the domain of a homographic function.

32.
Solve graphically inequalities of the form f(x) < k.

33.
Resolve graphically inequalities of the form f(x) > k.

34.
For the same problem, combine graphical resolution and algebraic control.

35.
Solve an inequality using the sign of an expression (product, rational).

36.
Solve algebraically the inequalities needed for solving a problem.

37.
Define the sine and cosine of a real number, rolling the real axis around the unit circle.

38.
Link the previous representation with the values of sine and cosine of angle: 0°, 30°, 45°, 60°, 90°.
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Gueudet, G., Pepin, B., Sabra, H. et al. Collective design of an etextbook: teachers’ collective documentation. J Math Teacher Educ 19, 187–203 (2016). https://doi.org/10.1007/s108570159331x
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DOI: https://doi.org/10.1007/s108570159331x
Keywords
 Activity theory
 Documentational approach to didactics
 Etextbooks
 Task design
 Teaching resources
 Collective teacher work
 Teachers as partners in design