SEMINARIO NAZIONALE - University of Melbourne

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). 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).

THEORETICAL REFLECTION 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 bodyrelated metaphors in mathematical

thinking. New content based approach and

New methodological approach 2

y x 4 x 4 2 y x 4 Compare these two

formulas from an algebraic and graphical point of view ...

(Bazzini, Boero & Garuti, 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) d d

t t

d d t

t (Arzarello & Robutti, 2001)

Which technology? Which changes in classroom organisation? Which changes in teacher education?

..