14 ÷ 7 = 2
35 x 3 = 105
1 + 2 + 3 = 6
Q. If I give the Staples lady 10.00 for a 8.99 package of labels, how much will she give to me?
A. She will give me $1.01 and my address labels.
√64 = __
How much of this can you take? Are these mindless drills? Do you drop over asleep in 20 seconds?
I don't. I can do problems like this all day. I like to solve problems that I can solve correctly. I'm not afraid of failure but I do like success.
We have some customers who say:
If the work is easy, it's not worth doing. If you succeed right away, it's been a waste of time doing the work. If it isn't hard, it can't be any good. If the kids aren't struggling, they aren't learning.
Why do any math at all that's easy? Why do we using spiraling instruction in our curriculum? Give them lots of chances to solve similar problems, over one or more years?
Well, because lots of other things in any kid's day are hard. Like catching the bus on time, choosing what to have for lunch, surviving the criticism of friends, striking out in the softball game, remembering to take books home (or back to school), getting a flu shot.
As adults we sometimes forget how traumatic these little things can be. We don't want math to be the pinnacle of pain for kids. We need to give them a chance to know they are right and they solved the problem correctly.
Math is not exactly like crossing the street, but there are lots of ways to do it correctly or incorrectly. I love this poster - I got it in Switzerland about 25 years ago. Can you see how many ways NOT to cross the street?
A related question is this - are answers always either right or wrong? Could there be shades of grey? (gray?) Here's an example:
- Was Lincoln the first president of the United States? No Correct
- Was Lincoln a president of the United States? Yes Correct
- Was Lincoln the thirteenth president of the United States? I don't know True but not the answer
- Name one president and two other men Abraham Lincoln, Madonna, my dog Spot
If I don't phrase the questions correctly, and kids arrive at two different answers, I get harassed by customers. Fair enough. To any single, precisely-worded problem there should be one correct answer.
But for the question What is the best way to teach? there is no one right answer. We use spiraling and repetition because we don't know in what order the light goes on for you.
Will you get the problem the first time? Possibly not if you have math right after lunch on a hot day. Will you get the problem after seeing it the second time, or after doing a similar but parallel problem in another context? Or after doing it 5 times over a period of 5 months? Or seeing it phrased in another way?
We think you have a better chance through spiraling than if you study a concept for a week and move along to something else.
C'mon now, try it again.
What is the square root of 64? 8