contended that the slow and
gradual enrichment of knowledge is largely unconscious and that
the enrichment mechanism leads to conceptual changes in the long
run. For example, a recent experiment conducted by Siegler et al.
(2009) confirmed that stage transitions can take place suddenly, after
a given mental model has been in place for some time. They called
this transition a logarithmic-to-linear shift. In their experiment, children
estimated the position of a number in a line to represent
numeric magnitude. Their estimations showed probabilistic patterns,
whichmoved from being stable to approximating to the actual
value. This shift occurred abruptly after applying an initial approach
numerous times. In another instance, some third-grade
students in a science class strongly believed that “the earth is flat”
based on their naive theory. Even after instruction, they refused to
accept that “the earth is spherical” and continued to justify
their initial belief. Even some adults, interestingly, retain this
belief (one global society still argues that “the earth is flat”;
http://theflatearthsociety.org/forum/). After further instruction and
additional lessons, they might begin to doubt their naive theory and,
at some point, build a new one (knowledge base) that integrates
new evidence and principles to support a “spherical earth.