DIFFICULTIES IN THE
INTERPRETATION OF GRAPHS OF QUADRATIC FUNCTIONS AND THE USE OF THE TI-92
GRAPHIC CALCULATOR
Martha Leticia García
Instituto Politécnico Nacional, México
Ana Isabel Sacristán
Cinvestav, México
Our study investigated students’ interpretation of graphs of quadratic functions as mediated by
the use of the TI-92 graphic calculator.
Emphasis has been placed on the importance of developing the ability to
change from one register of representation (such as the graphical one) to
another (e.g. the algebraic) (e.g., Duval, 1993). However, difficulties occur when attempting to relate the
information given in a graphical register to that in the corresponding
algebraic register: Students have
difficulties when asked to gather information from the graphic representation
of a function in order to deduce the corresponding algebraic representation
(Duval, 1993). In an extensive study of
800 subjects, Zaslavsky (1997) found and described 5 types of obstacles in the
learning of quadratic functions. Using
these obstacles as a basis for our research, we aimed to take advantage of the
representational elements provided by the graphic calculator in order to
facilitate the construction of relationships between the graphic and algebraic
registers; specifically, between the visual variables and symbolic units (see
Duval, 1993), since modification of one affects the other.
For the equations of quadratic functions, we used the form y =
ax2 + bx + c and
defined the following visual variables: (i) the concavity of the parabola
(given by the sign of a);
(ii) the width of the parabola (given by the value a); and (iii) the position
of the curve with respect to the vertical axis, in relation to the origin of
the graph (given by the value of c). Ten first-year college-level engineering students participated in
4 sessions of activities with the TI-92 calculator, designed to explore the
relationships between the visual and symbolic variables of quadratic
functions. Through direct observation,
questionnaires and clinical interviews, we observed positive results in that
many students who were previously unable to do so, were able at the end of the
study to identify the different visual and symbolic variables and construct
relationships between them.
References
Duval R. (1993).
Registres
de representation sémiotique et fonctionnement cognitif de la pensée. Annales
de Didactique et des Sciences Cognitives, 5. IREM Strasbourg.
Zaslavsky O. (1997).
Conceptual Obstacles in the Learning of the Quadratic Functions.
Focus on Learning Problems in Mathematics, Winter Edition, 19(1), pp. 20-44.