Page 245 - A Mind For Numbers: How to Excel at Math and Science

18 Jeffrey Karpicke and colleagues (2009) suggested the relationship between illusions of competence in
learning and the difficulty of anagrams when you see the solution as opposed to when you don’t see the
solution.
19 Henry Roediger and Mary Pyc (2012, p. 243) note: “Professors in schools of education and teachers
often worry about creativity in students, a laudable goal. The techniques we advocate show
improvements in basic learning and retention of concepts and facts, and some people have criticized this
approach as emphasizing “rote learning” or “pure memorization” rather than creative synthesis.
Shouldn’t education be about fostering a sense of wonder, discovery, and creativity in children? The
answer to the question is yes, of course, but we would argue that a strong knowledge base is a
prerequisite to being creative in a particular domain. A student is unlikely to make creative discoveries
in any subject without a comprehensive set of facts and concepts at his or her command. There is no
necessary conflict in learning concepts and facts and in thinking creatively; the two are symbiotic.”
20 Geary 2005, chap. 6; Johnson 2010.
21 Johnson 2010, p. 123.
22 Simonton 2004, p. 112.
23 This is my own rephrasing of a common sentiment in science. Santiago Ramón y Cajal cited Duclaux in
noting, “Chance smiles not on those who want it, but rather on those who deserve it.” Cajal went on to
note, “In science as in the lottery, luck favors he who wagers the most—that is, by another analogy, the
one who is tilling constantly the ground in his garden” (Ramón y Cajal 1999, pp. 67-68). Louis Pasteur
noted, “In the fields of observation chance favors only the prepared mind.” Related expressions include
the Latin-based proverb “Fortune favors the bold” and the British Special Air Service motto: “Who
dares wins.”
24 Kounios and Beeman 2009 [1897]; Ramón y Cajal 1999, p. 5.
25 Rocke 2010.
26 Thurston, 1990, p. 846–847.
27 See the foundational work of Karl Anders Ericsson on development of expertise (e.g., Ericsson 2009).
For insightful popular approaches related to the development of talent, see Coyle 2009; Greene 2012;
Leonard 1991.
28 Karpicke and Blunt 2011a; Karpicke and Blunt 2011b. For further information, see also Guida et al.
2012, p. 239.
29 Of interest is that left hemisphere prefrontal regions appear active during the encoding phase of
memorization, while right hemisphere regions are activated during retrieval. This has been reported by
many groups using a great variety of imaging techniques (Cook 2002, p. 37). Is it possible that
retrieving memorized materials creates the beginnings of diffuse-mode concept mapping-like
connections? See also Geary et al. 2008, 4-6 to 4-7.
30 There are, of course, caveats here. For example, what if a student is asked to recall material to determine
what belongs on a concept map? There are also undoubtedly disciplinary differences. Some subjects,
such as those involving communication processes in biological cells, inherently lend themselves more
readily to “concept map” approaches in understanding key ideas.
31 Brown et al. 1989.
32 Johnson 2010, p. 110.
33 Baddeley et al. 2009, chap. 8.
34 Ken Koedinger, a professor of human-computer interaction and psychology at Carnegie Mellon
University, notes, “To maximize retention of material, it’s best to start out by exposing the student to the
information at short intervals, gradually lengthening the amount of time between encounters. Different
types of information—abstract concepts versus concrete facts, for example—require different schedules
of exposure” (quoted in Paul 2012).
35 Dunlosky et al. 2013, sec. 10; Roediger and Pyc 2012; Taylor and Rohrer 2010.
36 Rohrer and Pashler 2007.
37 It appears that “mass practice” techniques of presenting the material provide an illusion of competence