Re: math didactics

On Thu, 04 May 2006 20:33:53 GMT, Gunnar G <debian@xxxxxxxxx> wrote:

I wish I knew how to teach maths. When I try to help my 12-y-o with her
homework, it seems like trying to teach someone colours. Yesterday she
was having difficulty solving:

u - 7 = 7.

Short of giving her the actual answer, I was trying to get her to discover
it herself. So I asked the question: "What's the difference between u and
7?" To which she replied: "One's a number, one's a letter?" (Yes,
complete
with question mark.) Give me strength.

Wonderful. You have an intelligent child. It is not only she who
needs to learn, but you. You must learn to ask the right questions.
She is clearly willing and thinking, and trying to please. She was
not being a smart aleck.

Don't worry, we've all been there. There has been an occasion when
I've asked a class a question and thought I'd been speaking Martian,
and so had to rephrase to get any response. There's also the
innocence... "Sir. How do you spell 'illiterate'?" Take all of that
into account, and the point of view that *everything* is new to them.

You might better have asked what would we have if we added 7 to the
left side? What would happen if we added 7 to the right side? Then
get into the discussion of balance of equality. You would better have
preceded the entire exercise with similar problems of equality showing
only numbers, and asking the same questions. They have not seen any
such thing before, and really don't know what you are asking until you
point the way.

E.G.

3 + 2 = 4 + 1 Are both sides equal to the same amount?

What happens if we subtract 2 from the left, and 2 from the right?
Are both sides still equal? ....... and so on.

I was visiting a friend/teacher as students were reviewing addition
and subtraction of polynomial expressions in several variables. A
girl at the blackboard was having apparent difficulty, and my friend
told me I could go ahead. I wrote the following,

5
-2
......
3

and had to quickly stem harsh glares [she thought at first I was
perhaps treating her beneath her age and intelligence] and proceeded
with a question ..."What do you have to do to the two bottom numbers
to get the top one, pointing to the quesiton in algebra she was
working on? Bingo! The light came on, and she easily finished the
exercise.

Learn to ask the right questions. It's not easy to do that at times.

.