id: 06639328
dt: j
an: 2016f.01000
au: Tanguay, Denis; Venant, Fabienne
ti: The semiotic and conceptual genesis of angle.
so: ZDM, Math. Educ. 48, No. 6, 875-894 (2016).
py: 2016
pu: Springer, Berlin/Heidelberg
la: EN
cc: G40 C30 U20 D30
ut: angle; measure; mathematical working space; semiotic genesis; semiotic
bundle; sense vs meaning; amalgamation vs disentanglement
ci:
li: doi:10.1007/s11858-016-0789-5
ab: Summary: In the present study, we try to understand how students at the end
of primary school conceive of angle: Is an angle a magnitude for them
or a geometric figure, and how do they manage to coordinate the two
aspects in their understanding of the concepts of angle and of angle
measurement? With the aim of better grasping the way {\it angle} is
conceptualized, we submitted to a 6th grade class (11‒12 years old) a
questionnaire about angles. The analysis of the answers allows tracking
a muddled meaning allotted to angle and shared by these students, in
which measure prevails widely and where the measured figure is fuzzy,
leaning on strongly iconic representations, of a blurred theoretical
status. The analysis of two textbook collections used as guidelines by
primary level teachers in the school under consideration suggests that
the outlined conceptualizations are elicited by the way instruments and
semiotic representations are being used in the teaching situations
proposed in the textbooks. The study enabled us to build a better and
deeper understanding, in that context, of two dialectical genetic
processes that we name and describe as ‘disentanglement’ and
amalgamation, and which help to bring to light the interactions between
the different meanings in construction.
rv: