id: 06270707
dt: j
an: 2014b.00253
au: Duval, Raymond
ti: Commentary: linking epistemology and semio-cognitive modeling in
visualization.
so: ZDM, Int. J. Math. Educ. 46, No. 1, 159-170 (2014).
py: 2014
pu: Springer, Berlin/Heidelberg
la: EN
cc: D20 D40
ut: visualization; epistemology; semio-cognitive modeling
ci:
li: doi:10.1007/s11858-013-0565-8
ab: Summary: To situate the contributions of these research articles on
visualization as an epistemological learning tool, we have employed
mathematical, cognitive and functional criteria. Mathematical criteria
refer to mathematical content, or more precisely the areas to which
they belong: whole numbers (numeracy), algebra, calculus and geometry.
They lead us to characterize the “tools" of visualization according
to the number of dimensions of the diagrams used in experiments. From a
cognitive point of view, visualization should not be confused with a
visualization “tool," which is often called “diagram" and is in
fact a semiotic production. To understand how visualization springs
from any diagram, we must resort to the notion of figural unity. It
results methodologically in the two following criteria and questions:
(1) In a given diagram, what are the figural units recognized by the
students? (2) What are the mathematically relevant figural units that
pupils should recognize? The analysis of difficulties of visualization
in mathematical learning and the value of “tools" of visualization
depend on the gap between the observations for these two questions.
Visualization meets functions that can be quite different from both a
cognitive and epistemological point of view. It can fulfill a help
function by materializing mathematical relations or transformations in
pictures or movements. This function is essential in the early
numerical activities in which case the used diagrams are specifically
iconic representations. Visualization can also fulfill a heuristic
function for solving problems in which case the used diagrams such as
graphs and geometrical figures are intrinsically mathematical and are
used for the modeling of real problems. Most of the papers in this
special issue concern the tools of visualization for whole numbers,
their properties, and calculation algorithms. They show the semiotic
complexity of classical diagrams assumed as obvious to students. In
teaching experiments or case studies they explore new ways to introduce
them and make use by students. But they lie within frameworks of a
conceptual construction of numbers and meaning of calculation
algorithms, which lead to underestimating the importance of the
cognitive process specific to mathematical activity. The other papers
concern the tools of mathematical visualization at higher levels of
teaching. They are based on very simple tasks that develop the ability
to see 3D objects by touch of 2D objects or use visual data to reason.
They remain short of the crucial problem of graphs and geometrical
figures as tools of visualization, or they go beyond that with their
presupposition of students’ ability to coordinate them with another
register of semiotic representation, verbal or algebraic.
rv: