WHY ALGEBRA? WHAT ALGEBRA?. How can we reshape the algebra curriculum, so that it has more immediate...

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?……………..