Page 240 - A Mind For Numbers: How to Excel at Math and Science

Chapter 1: Open the Door

1 I’d like to point educators toward the book Redirect, by psychology professor Timothy Wilson, which
describes the seminal importance of failure-to-success stories (Wilson 2011). Helping students change
their inner narratives forms one of the important goals of this book. A leader in describing the
importance of change and growth in mindset is Carol Dweck (Dweck 2006).
2 Sklar et al. 2012; Root-Bernstein and Root-Bernstein 1999, chap. 1.

Chapter 2: Easy Does It: Why Trying Too Hard Can Sometimes Be Part of the Problem

1 Default-mode network discussions: Andrews-Hanna 2012; Raichle and Snyder 2007; Takeuchi et al.
2011. More general discussion of resting states: Moussa et al. 2012. In a very different line of
investigation, Bruce Mangan has noted that William James’s description of the fringe includes the
following feature: “There is an ‘alternation’ of consciousness, such that the fringe briefly but frequently
comes to the fore and is dominant over the nucleus of awareness” (Cook 2002, p. 237; Mangan 1993).
2 Immordino-Yang et al. 2012.
3 Edward de Bono is the grand master of creativity studies, and his vertical and lateral terminology is
roughly analogous to my use of the terms focused and diffuse (de Bono 1970).
Astute readers will notice my mention that the diffuse mode seems to sometimes work in the
background while the focused mode is active. However, research findings show that the default-mode
network for example (which is just one of the many resting state networks), seems to go quiet when the
focused mode is active. So which is it? My sense as an educator and a learner myself is that some
nonfocused activities can continue in the background when focused work is taking place, as long as the
focused attention is shifted away from the area of interest. In some sense, then, my use of the term
diffuse mode might be thought of as “nonfocused mode activities directed toward learning” rather than
simply “default-mode network.”
4 There are also a few tight links to more distant nodes of the brain, as we’ll explore later with the
attentional octopus analogy.
5 The diffuse mode may also involve prefrontal areas, but it probably has more connections overall and less
filtering out of seemingly irrelevant connections.
6 Psychologist Norman Cook has proposed that “the first elements in a central dogma for human
psychology can be expressed as (1) the flow of information between the right and left hemispheres and
(2) between the “dominant” [left hemisphere] and the peripheral effector mechanisms used for verbal
communication” (Cook 1989, p. 15). But it should also be noted that hemispheric differences have been
used to launch countless spurious overextrapolations and inane conclusions (Efron 1990).
7 According to the National Survey of Student Engagement (2012), engineering students spend the most
time studying—senior engineering students spend eighteen hours on average per week preparing for
class, while senior education students spend fifteen hours and senior social science and business
students spend about fourteen hours. In a New York Times article titled “Why Science Majors Change
Their Minds (It’s Just So Darn Hard),” emeritus engineering professor David E. Goldberg has noted that
the heavy demands of calculus, physics, and chemistry can initiate the “math-science death march” as
students wash out (Drew 2011).
8 For a discussion of evolutionary considerations in mathematical thinking, see Geary 2005, chap. 6.
Of course, many abstract terms aren’t related to mathematics. A surprising number of these types of
abstract ideas, however, relate to emotions. We may not be able to see those terms, but we can feel them,
or at least important aspects of them.