WHY ALGEBRA?
WHAT ALGEBRA?
How can we reshape the algebra curriculum, so that it has more immediate value to individuals?
…so that specific difficult ideas are more easily accessed?
HAVING THE STUDENT IN MIND
IN A TECHNOLOGICAL ERA
DIFFICULTIES ON
INEQUALITIES
Invalid connections between the solution of a quadratic equation and its related inequality (Linchevski & Sfard, 1991;
Tsamir, Tirosh, & Almog, 1998, Tsamir & Bazzini, 2001).
THEORETICAL REFLECTION
Tendency to regard transformable inequalities as being equivalent (Linchevski & Sfard, 1991, Bazzini, 1997).
Difficulties in solving inequalities with “R” or ““ as
truth set (Tsamir & Almog, 1999) and difficulties in
parametric
inequalities (Bazzini & Tsamir, 2001).
HOW CAN WE FACE SUCH SITUATIONS?
On the basis of experimental data.....
…a new approach to the theme
Equations and inequalities introduced by means of a functional approach...
and
… legitimacy and relevance of body-related metaphors in mathematical
thinking.
New content based approach
and
New methodological approach
42 xyCompare these two
formulas from an algebraicand graphical point
of view
………...
442 xxy
(Bazzini, Boero & Garuti, 2001)
VERBALISATION
GESTURES
EMBODIED COGNITION
EMBODIMENT AND
TECHNOLOGY
COULD THEY BE LINKED IN SCHOOL MATHS?
Connecting motion with an algebraic representation
(Thornton, 1990 ; Isoda, 2001; Doerr, 2001; Arzarello & Robutti, 2001)
t
d
t
d
t
d
t
d
(Arzarello & Robutti, 2001)
Which technology?
Which changes in classroom organisation?
Which changes in teacher education?……………..