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Every day for about ten minutes, elementary teachers using the Think Math program are supposed to engage the class in an exercise called “Headline Stories”.
This unique feature, the “Headline Stories,” provides open-ended situations in which specific mathematical ideas are embedded. It has three main purposes:
• to develop students’ skills at deriving real-world meaning from mathematical statements and deriving mathematical meaning from real-world situations,
• to develop students’ skills at using both natural language and mathematical language to describe ideas drawn from mathematics or the physical world, and
• to help students learn to solve word problems by understanding how they are built.
Like a newspaper headline, Headline Stories give clues about what might follow, but they leave out the details. Only rarely do they pose a specific problem. Envisioning a story and asking the right questions are left to the students. Part of the learning goal for students is to discover what mathematical questions are possible to ask, or answer, about a situation.
Apparently, the teacher reads aloud or writes a “headline” and then leads the class in a discussion, occasionally journaling. The teacher’s guide gives examples of appropriate mathematical responses for each story.
For instance:
In my hand I have 9¢.
Sample responses: Can it be shared evenly among three people? How can it be made? That’s 2¢ more than I had yesterday. I used to have a dime, but I spent a penny.
There are 6 cookies. _____ children could have _____ cookies each.
Sample responses: 3 children could have 2 cookies each, or 6 children could have 1 cookie each. 4 children could have a cookie each, and 2 cookies would be left over. Up to 12 children can have half a cookie each.
Liam earned $1.00 on Monday, $2.00 on Tuesday, $4.00 on Wednesday, $8.00 on Thursday,
Sample responses: Each day he earned more than the day before. By Thursday, Liam earned $15. 1 + 2 + 4 + 8 = 15. I think he’ll earn $16 on Friday. If this pattern keeps up, Liam is going to be quite rich! How much did he earn so far? If the pattern keeps up, how much will he earn next Monday? I don’t think the pattern can continue.
I don’t fully understand the relative benefits of this exercise. From doing this, a student is supposed to learn how to pull out relevant math information from a statement. However, couldn’t this be better accomplished using actual word problems? Is this a typical time wasting reform exercise? Or, is this a good way to have students construct and learn key math concepts. Also, does successful implementation of this exercise require exceptional teaching skills and math knowledge?
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17 comments:
These are much too unfocused. A better use of time is found in the textbooks I used when a mere lad but now viewed by those "in the know" as math as it used to be taught 50 years ago, which they then claim "failed". This is from the 4th grade "Arithmetic We Need" textbook, written in 1955, by Buswell, Brownell and Sauble. On p. 230 is something called "Making a Quilt". What follows are some statements from which students are then to make problems out of. Here are some of them.
Jean's club is making a quilt for the fair. Jean's mother is helping.
The pattern for the quilt calls for a total of 744 squares of cloth. Each of the 6 girls in the club will bring her share of the squares.
They already have finished 365 of the squares. One of the girls says that she has enough cloth left to make 95 more squares.
They have finished putting squares together to make 4 rows for the quilt. They used 24 squares in each row.
Jean's mother estimates that in all it will take about 80 hours of work to make the quilt. She told the girls that they have finished about 1/2 the work.
"I don’t think the pattern can continue."
Why not? Maybe Liam cut a really good deal.
"I don't think the pattern can continue" is subjective. Liam might be like Rani in the folktale One Grain of Rice.
Many years ago, there lived a selfish raja in India. He ruled that all the people should give him almost all of their rice for safekeeping, so that in a time of need there would be rice to eat. One year, a famine hit and no one had any rice to eat, but the raja would not give the stored rice to the people because he wanted to save it for himself. One day a clever girl named Rani created a plan to help the starving people of India. She asked the raja for one grain of rice and for each day for thirty days she asked the raja to double the amount of rice given the day before. The raja did not realize how much one grain of rice would amount to if it were doubled every day for one month. The raja learned a valuable lesson about selfishness and Rani saved the people of India from starvation through her cunningness and her understanding of math.
The schools seem determined to shred whatever is left of legitimacy they possess.
Spoken as one who has just sent the superintendent a legal opinion re: group punishment.
The entire middle school is to undergo collective punishment tomorrow at lunchtime.
The principal gives kids literature on hand-anal touching, but the kids are the ones serving detention.
Here's a question taken from page 49 in Mathematics 6 by Enn Nurk and Aksel Telgmaa:
202.
Two trains leave simultaneously from different cities heading toward one another. The speed of the first train is 54.4 km/h and the speed of the second is 60.8 km/h. Come up with an appropriate question and answer it.
I don't like non-questions. "Appropriate" is too vague. Here's my question. Which train is going faster? Also, there is something missing (like distance or time) from the train question.
Q. Why are the speeds in km/h instead of m/h?
A. No reason.
Q. Are the trains on the same track so they will smash into each other?
A. I hope not.
Q. How did the trains instantly accelerate to such high speeds?
A. Magic.
Q. How do the trains keep their speeds exactly constant?
A. They are on auto-pilot.
Q. Are the people on the first train reading health brochures about sex?
A. I'm sorry but this is an inappropriate question.
"Q. Are the people on the first train reading health brochures about sex?"
Good one! I think it's quite appropriate. Real world math. You are connecting math with sex. Now everyone will be happy to go to math class. I'm sure we could come up with some great probability questions.
If the instructions were to “make up a problem” or come up with an “appropriate question” for the story, then I would find that useful and productive. That is more focused, and it seems much easier for the teacher to judge whether a student’s response is correct or acceptable.
On the other hand, just trying to imagine all the possible responses a typical class might come up with “headline stories, how will teachers feel confident that any given response is appropriate?
Too vague, I think. Or, maybe I don’t give teachers enough credit.
I don't like non-questions.
Me neither. And, I have a son who doesn’t like them. There’s something in our brains that dislikes sitting around and discussing possible appropriate questions about vague mathematical statements. Maybe, it seems too much like group therapy.
Not to knock group therapy. I’m sure it’s fine for some people and for some issues. Just not for math.
Some responses are only appropriate for Irvington students.
Liam earned $1.00 on Monday, $2.00 on Tuesday, $4.00 on Wednesday, $8.00 on Thursday,
Appropriate response: Does Liam have enough money to buy a dental dam on Friday?
There are 6 cookies. _____ children could have _____ cookies each.
Appropriate response: Can the children catch HIV from sharing cookies?
In my hand I have 9¢.
Appropriate response: Where is my other hand?
In my hand I have 9¢.
Appropriate response: Where is my other hand?
You win!
Those are very creative responses!
Just wondering . . . in light of the healthy eating craze, I'm just wondering if it is politically incorrect for word problems to include cookies??
The health fair is sounding more and more like a prison riot.
Remember Doug's middle school motto in the middle school motto contest?
Irvington Middle School
Frequently Better Than Prison
headline stories are cr**
that's pretty much where i am tonight
Ed has just left to teach in Paris for two weeks; Andrew has been walking around the house carrying a turd in his hand; etc.
Chris has group punishment at lunch tomorrow ----
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