Re dy/dan An Incomplete History Of The Math Edublogosphere

The blog dy/dan by Dan Meyer has a post titled

An incomplete history of the math edublogsphere.

This has a comment thread of math teachers who blog and apparently regularly follow dy/dan.

http://algebra1teachers.com/

http://ccsstoolbox.agilemind.com/resources_samples.html

Clicking on Algebra I we get

http://ccsstoolbox.agilemind.com/pdf/Algebra%20I%20Dana%20Center%20Scope%20and%20Sequence.pdf

Page 5 of 8, we can cut and paste

==

F-­‐IF.3
(Recognize
that
sequences
are
functions,
sometimes
defined
recursively,
whose
domain
is
a
subset
of
the
integers.
For
example,
the
Fibonacci
sequence
is
defined
recursively
by
f(0)
=
f(1)
=
1,
f(n+1)
=
f(n)
+
f(n-­‐1)
for
n

1.)
F-­‐BF.1.a
F-­‐BF.2
(Write
arithmetic
and
geometric
sequences
both
recursively
and
with
an
explicit
formula,
use
them
to
model
situations,
and
translate
between
the
two
forms.★)

==

The important point being the use of recursion.  If we recall the Keith Devlin saga on repeated addition, that series ended up with Keith Devlin saying he did not advocate teaching recursion in K-12.  Yet here it is on the common core standards.

The text Pre-Algebra New Math Done Right Peano Axioms does teach recursion at below college level to define addition of natural numbers.

Here is the Devlin post from Nov 2011 on recursion as part of his multiyear series on this topic.

http://devlinsangle.blogspot.com/2011/11/how-multiplication-is-really-defined-in.html

ASIDE: This is not an article about mathematics education. How teachers introduce addition and multiplication is another issue. I am not, repeat not, suggesting we teach recursion in the K-12 system.

As we see from the above, the Common Core Standards do in fact suggest we teach recursion in the K-12 system.   Devlin’s post then makes it clear that if we do teach recursion, we should do it right.  This is what my book on Peano Axioms does.  It is the first below college level text on the Peano Axioms. 