[Edu-sig] Re: Beyond CP4E

[Lee Harr]

Where is the balance we must strike between
      experiment, see new things, and play!
and
      practice to assimilate new patterns, forms, and structures
and
      identifying and meeting goals for learning

It is interesting.
We need to be more intentional with learning.
I see so many students struggling with math, and I believe
the problem is that they just see it as one more thing to
learn. As if memorizing the quadratic formula is all there is
to it, when in fact that is just the first step. Is memorizing
the quadratic formula important? Heck yeah. Now what?
Start playing. You might even find something interesting.
huh... what does sqrt(-17) mean?

a=5+3j
a
(5+3j)
sqrt(a)
Traceback (most recent call last):
 File "<stdin>", line 1, in ?
TypeError: can't convert complex to float; use abs(z)
a=0+3j
a
3j
sqrt(a)
Traceback (most recent call last):
 File "<stdin>", line 1, in ?
TypeError: can't convert complex to float; use abs(z)
a=-10+0j
sqrt(a)
Traceback (most recent call last):
 File "<stdin>", line 1, in ?
TypeError: can't convert complex to float; use abs(z)
abs(a)
10.0
def _sqrt(real):
...     if real >= 0:
...         return sqrt(real)
...     else:
...         return sqrt(-real) * (0+1j)
...
_sqrt(-10)
3.1622776601683795j
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