Over the years, I have watched my kids learn a variety of math strategies, most of which bear no resemblance to how I learned math. If they work, I'm all for them. Really, I am.
Among these has been "counting on," which essentially has the student
figure out an addition or subtraction problem by simply following the
counting pattern. It works, it makes sense, and it is kind of
comforting, because it lets you use what you already know to solve a
problem you've never seen. It's just not the most efficient strategy
when you have a lot of problems to do.
Most of us practice "counting on" each day. Though we
may not be using this strategy to add or subtract, we are planning our lives with
it. If something was a certain way yesterday or last month or last
summer, we "count on" it being that way today, tomorrow, or next summer. If a method worked for us last time, we "count on" it to work this time as well.
The problem is, just as "counting on" is not necessarily an efficient
math strategy, it turns out not to be a consistently efficient life strategy either.
While there may be nothing wrong with using past experiences to predict
future ones, life (unlike addition) tends to change. So if we "count
on," assuming circumstances we know, we may come to the wrong
conclusions when circumstances have changed.
So, it appears that in life, as in math, it is important to have more than one
strategy. If you rely only on what you "count on," you will often be
confused and disappointed. Sometimes, it takes looking at a problem in a
new way, not just the way you know, to find its solution. And
sometimes, it is only when we move past the security and comfort of
"counting on" that we can really add to our experience, and move ahead.