Key concept in elementary math needs a notation

The key concept in elementary math is successor.   That is after function.  Functions we already have at least two notations. The ordered pair (x,y) and a function symbol y=f(x).  We also have operator notations like +.

x+y = S(x,y)

Where S(x,y) means start at x and take successor y times.

S(x,0) = x

S(x,1) = S(x) = x’

The successor function is the base function of numbers.

(n,n’) is the link ordered pair.

We need these notations to teach concepts at lower age levels.

If lower age levels have a harder time learning not to leave steps out of proofs, i.e. explanations, then we need props to help them learn what the steps or structure is.

Manipulatives are at least partly using props to help teach concepts this way.

The successor function notations are a type of manipulative.

So are truth tables.

The more that young minds have a harder time with abstract critical thinking, the more we need symbolic structure to show them explicitly what rests on top of what.

Advertisements

About New Math Done Right

Author of Pre-Algebra New Math Done Right Peano Axioms. A below college level self study book on the Peano Axioms and proofs of the associative and commutative laws of addition. President of Mathematical Finance Company. Provides economic scenario generators to financial institutions.
This entry was posted in Uncategorized. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s