Chapter 6, page 91
Political
world
A nation is a political entity
with a central government,
which can take many forms,
including democracies.- Some elementary school children think that “nations” are
simply large tracts of land. - Other elementary school children develop a feudal
conception of government of nations. There is a single
central power who gives laws to local officials such as
mayors, who then give orders to the population.
Equals
sign
The equals sign in
mathematics indicates that the
two quantities on each side of
the equal sign are equivalent.- Many elementary school (and even older) children think
that the equals sign is an instruction to carry out an
operation. For example, in the problem “3 x 15 = _,”
students the equals sign is taken to mean “multiply 3 and 15
and then write down the product on the right side.” When
students see problems such as = 5 + 8, they may object
that this is illegitimate, because the equals sign is telling you
to do something to the numbers on its left, but there are no
numbers on the left.”
Sources: (Ambos et al., 2007; Berti, 2005; Berti & Bombi, 1988; Berti & Vanni, 2000; Chinn,
1997; Ergazaki, Komis, & Zogza, 2005; Kaput, Carraher, & Blanton, 2008; Lin & Hu, 2003;
Nakhleh & Samarapungavan, 1999; Nakhleh et al., 2005; Webley, 2005; Winer et al., 2002)
Students exhibit alternative conceptions on many topics covered in the K-12 curriculum. Table 6.6
presents examples of several other alternative conceptions. We have seen that students’ alternative
conceptions can be grounded in their own experiences, as when children’s idea that the earth is flat is
grounded in their experiences that things fall downward and the earth looks flat. We have now seen that
students’ alternative conceptions can also be grounded in successful prior learning, as when students’
mastery of the natural number system interferes with learning fractions in later grades. Regardless of the
source of the prior conceptions, it is important for teachers to learn about conceptions such as these in
order to design more effective instruction.