Ever since the time the Augusta Metro Youth Foundation (AMYF) began sponsoring the Eagles homeschool basketball program, I've heard the following from many area basketball players: "I want to go to 'your school.'"
Well, we don't have a school. But for two decades we have been deeply involved in the educations of many of the students who have participated in our programs. So when someone recently asked me to explain a common math problem, I decided to try to show how the way I think about "education" is hopefully helpful, and probably a little different than what students get in traditional schools. Here is the problem, my way of explaining the solution, and possibly a window into my thought process regarding the "school" that we don't have:
2 divided by 1/2 equals _____
Until adulthood, when I began helping students answer such math problems, the first thing to come to my mind had been "flip the second number and multiply," meaning the path to this answer memorized in my "school life" was that multiplying the fractions 2/1 and 2/1 equals 4.
But when I began working with students, I felt the need to help them understand what such a problem actually meant, how it may be encountered in real life, and why the answer and the method used in getting the answer make sense.
So as a teacher/guide/leader or whatever I am called when helping students figure out these things, my first thought when faced with explaining this problem is something like this:
"How many halves are in two wholes?"
I believe if the youngest basketball players in our program were asked "how many half courts are in two whole courts?" all would say 4.
Coincidentally, my 7 year old just interrupted my writing this and started the following exchange:
My son: "There are 4 weeks in a month, right?"
Me: "Yes."
My son: "So two weeks is half-a-month, right?"
Me: "Yes. So how many 'half-months' are in two whole months?
My son: "4."
So I believe that the young kids in our program can answer the "how many half courts would fit in two whole courts?" question. And my son can answer the question I just posed to him. I think this is true because the context of these questions are clear and understandable.
But I think far fewer would know to "flip the second number and multiply when dividing fractions."
But this is basic stuff. I need help thinking about how to help students with the harder problems, like the one students and helpers of all ages mulled over last week at our "learning center:"
9|9-8x| = 2x+3
We figured out how this problem is solved mathematically. but If anyone can provide the context of what a problem like this really means and how it may be used in life, you can help us answer that old "when will I ever use this?" question!
Maybe the answer is as simple as "there is no one absolutely correct definmitive answer to theproblem. The 1054 answer is a repeating number type indefinite answer (infinity), unlike the fact based absolute 2 divided by 1/2 answer of 4.
ReplyDeleteIn other words, some problems do have absolute solutions and some don't. PROBLEMS INVOLVING FACT BASED SOLUTIONS VERSUS JUDGMENT BASED DECISIONS.
In fact, the more difficult issues in life usually involve and often require judgment calls. We need to gather the facts to make those judgment calls, but in the end our judgment is all we have to solve the big issues for ourselves.
Make sense?
I believe the academicians refer to this as higher order thinking or some such thing. To me it comes down to judgment.
Such as the calls Will made as point guard or the calls you coaches make about whether to press, leave a player in with three fouls and so forth.
The more facts and experience we have, and the better able we are to quickly place those facts in a proper decision making context, the better our decisions will be.
At least that's what I get out of the math questions you raised.
Thanks. Bob.