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49

tr iangle. ther e is of course no need to stop at this point;

an equation may be lik ened to a balance. but we k now that to man y

v ided a bov e the bea m of the ba la nce, so th at negati v e w eights

ances. thus t

ar atus could be extended to show mor e stages if this w er e

students wor ds mean very little. w hy talk about a balance? w hy

pulling upwar ds could be ar r anged. the situation show n in figur e

a false step, a

. the a dva ntage of this dev ice was th at it gav e a class

not have a balance ther e in the room?' accor dingly he construct-

14 cor r esponds to the equation 4 — x = x — 2 . on the left, w e see

if the studen

ng to look at and think about dur ing a discussion of the

ed a balance, on which a simple equation could be r epr esented. for

four nuts pulling dow n and a matchbox x counter acting them; on

he might r ea

l theor em, and con veyed a certain fa miliar it y w ith and

w eights w hitworth nuts w er e used. matchboxes w er e mar k ed x,

the search for patter n r ight, a matchbox x pulls dow n, w ith two

stage the ma

for the cor r esponding distr ibutions of mater ia l, w hich

nuts counter acting it. the best way of using the balance is for the i n s t r u c t o r » Name student to w r ite dow n w hat he thinks the next step should be,

thr ee nuts. in

w r iting the numbers might w ell have failed to give. math-

and a teacher would put nuts into these boxes, the sa me number c l a s s » Title in each. even a homemade balance is r emar k ably sensitive, and this

through the hand the algebr aic balance the device show n

sensitivity had to be cut dow n by putting in some extr a fr iction;

and then to alter the w eights on the balance so as to r epr esent

the idea see

e 14 was used r ight at the begin ning of an algebr a course.

otherwise the scale might appear to be out of balance simply because

the new equation. if he has made a mistak e, the scales w ill imme-

question abo

piece. r ather