Page 243 - A Mind For Numbers: How to Excel at Math and Science

archivist with the Thomas Edison National Historical Park. He noted, “I have heard the story of Edison
and the ball bearings but have never seen any documentation that would confirm it. I’m also not sure
about the story’s origin. This may be one of those anecdotes that had some basis in reality but became
part of the Edison mythology.”
6 Dalí 1948, p. 36.
7 Gabora and Ranjan 2013, p. 19.
8 Christopher Lee Niebauer and Garvey 2004. Niebauer refers to the distinction between object and meta-
level thinking. The third, paradoxical error in the sentence, incidentally, is that there is no third error.
9 Kapur and Bielczyc 2012, contains an excellent review on the importance of failure in problem solving.
10 For a nice discussion of the many variations of what Edison actually might have said or written, see
http://quoteinvestigator.com/2012/07/31/edison-lot-results/
11 Andrews-Hanna 2012; Raichle and Snyder 2007.
12 Doug Rohrer and Harold Pashler (2010, p. 406) note: ”. . . recent analysis of the temporal dynamics of
learning show that learning is most durable when study time is distributed over much greater periods of
time than is customary in educational settings.” How this relates to alternation between focused and
resting state networks is an important topic for future research. See Immordino-Yang et al. 2012. In
other words, what I’ve described is a reasonable supposition for what occurs while we learn, but needs
to be borne out by further research.
13 Baumeister and Tierney 2011.
14 I want to make it clear that these are only my “best guess” ideas about what might promote diffuse-mode
thinking, based on where people seem to get many of their most creative, “aha!” insights.
15 Bilalić et al. 2008.
16 Nakano et al. 2012.
17 Kounios and Beeman 2009, p. 212.
18 Dijksterhuis et al. 2006.
19 Short-term memory is the activated information that is not actively rehearsed. Working memory is the
subset of short-term memory information that is the focus of attention and active processing (Baddeley
et al. 2009).
20 Cowan 2001.
21 If you’re interested in the neural geography underlying all of this, it looks like both long-term memory
and working memory use overlapping regions in the frontal and parietal lobes. But the medial temporal
lobe is used only for long-term memory—not working memory. See Guida et al. 2012, pp. 225–226, and
Dudai 2004.
22 Baddeley et al. 2009, pp. 71–73; Carpenter et al. 2012. Spaced repetition is also known as distributed
practice. Dunlosky et al. 2013, sec. 9, provides an excellent review of distributed practice.
Unfortunately, as noted in Rohrer and Pashler 2007, many educators, particularly in mathematics,
believe overlearning is a good way to boost long-term retention—hence many similar problems are
assigned that ultimately devolve to make-work with little long-term benefit.
23 Xie et al. 2013.
24 Stickgold and Ellenbogen 2008.
25 Ji and Wilson 2006; Oudiette et al. 2011.
26 Ellenbogen et al. 2007. The diffuse mode may also be related to low latent inhibition—that is, being
rather absentminded and easily distractable (Carson et al. 2003). There’s creative hope for those of us
who tend to switch thoughts in the middle of a sentence!
27 Erlacher and Schredl 2010.
28 Wamsley et al. 2010.

Chapter 4: Chunking and Avoiding Illusions of Competence: The Keys to Becoming an
“Equation Whisperer”