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comment left by Lauren:
I'm not a fuzzy math advocate by any means and I agree with most of the warning signs on this list. However, I do not understand why connecting math concepts to real world situations is an indication of a fuzzy math program. My algebra students came alive this year when I showed them how the distance formula is used in programming video games. When I taught middle school, I connected everything from percentages to coordinate pairs to real world examples. Math doesn't have to be abstract and irrelevant. Making real world connections can increase student interest in math which may lead to lower drop out/failure rates.
from Barry:
It depends on how one defines "real world". Those who rail against the so-called rote-ridden, formulaic traditional math, point to problems such as work, distance, and mixture problems as irrelevant to students' interests. Other criticism includes that such problems contain all the information that the student needs, they work out neatly, they don't represent the messiness of problems one encounters in the "real world". The solution, in the reformists' mind, is to present students with assignments requiring them to collect data, come to conclusions about such data that they may or may not be prepared to do.
For example, in one assignment I saw, students were to throw various types of paper airplanes, measure how far they traveled, how long they were in the air, and other parameters. These data were then given to another group of students who then were to come up with a scheme for rating which plane flew "the best."
In the documentation of this assignment, it was evident the students were not familiar with the distance = rate · time formula, though some of the brighter kids seem to stumble on it. The whole assignment was one of stumbling and fumbling, which passes for discovery and further passes for learning. It is neither. That they were engaged is irrelevant. The assignment had no value because they were unable to make connections to previous learned and (hopefully) mastered material.
What you have done in your algebra class does relate to previous learned and mastered material. And the students enjoyed being able to put what they've learned into practice.
But many of these so-called real world assignments are nothing more than data collection and data mongering with some statistics thrown in. Not much application of previously learned material takes place. Nor discovery. Nor learning. But onlookers ooh and ahh when they see how "engaged" the students are.
10 comments:
Thank you, Barry, for the quick reply you gave to Lauren's comment.
Another problem with "real world" math, at least at my intermediate 5th level, is the inappropriateness for the grade level. What might be an excellent "real world" connection at 8th or 9th grade is pushed down to 4th and 5th grade! The laboriousness of having to figure it all out is so lengthy and involved for 5th graders that they quickly lose interest. And it's nothing that they, at their age, could conceive of ever using or needing to use. "Stumbling and fumbling" is a good description of what happens.
I often wonder how long it's been since these "math gurus" have taught in a classroom. Five minutes into one of these "connected to the real world adventures", the students are completely disengaged.
And I loved what you said about "previously learned and mastered material". Not only have my 5th graders not mastered the material and concepts needed to do these time consuming assignments. They haven't even been introduced.
And the teacher ends up doing the entire assignment for them!!! Which, if I understand, misses the entire point. I, the teacher, am the only one discovering anything on my own and it's not anything that I would ever conceive of ever wanting to know!!
Oh, about throwing paper airplanes -- would you believe it? Just this past spring, a second-grade teacher at our school had her class out in the hall doing just that -- throwing paper airplanes. Students were running back and forth, throwing and chasing after the planes. The teacher was trying to get them to measure (which may have been the purpose of this exercise), but the children were just playing. And the teacher was the only one keeping any kind of record. I asked her about it and she openly said that they didn't really know what they were doing, referring to how to make the planes fly. It was obvious the class had not yet studied about "flight" or "speed" or "lift" or "airfoils" or even how the shape of the nose of the plane could help. It looked more like "indoor recess" than class.
Well I wasn't going to say anything more about discovery learning etc, but it seems that in avoiding working on my article about same, and avoiding trimming the bushes in the front of my house in 90 degree heat (which I undertook to avoid writing said article), I am forced to do so.
Take a look at the PowerPoint (yes, a PowerPoint) that Deborah Ball, Dean of U of Michigan Ed School put together on a math lab she held last summer. A discovery lesson. No. It isn't a "real world" math type lesson. This was given to rising 5th graders. I was reminded of it because of Concerned Teacher's comment: Not only have my 5th graders not mastered the material and concepts needed to do these time consuming assignments. They haven't even been introduced.
Apparently, Deb Ball introduces the material via scaffolding though it isn't obvious from the PowerPoint how this was done. I'll give her the benefit of the doubt and blame PowerPoint. The rest of you can chime in as you wish.
Well, I guess we have to give Dr. Ball praise that the "Social and Intellectual Culture" was addressed. After all, we want all of the students to feel good about themselves as they go through this train-building exercise.
And referring to her Conclusion that the students "can be interested in and sustain work on a complex proof" -- Did you notice the body language of the two students nearest the camera in slide 14? One boy is lying down so far in his chair that one more inch and he will be on the floor. I would say it is a stretch that these two students are demonstrating the above stated conclusion. They prove my point completely.
Thank you for answering my question about real world math. I understand the distinction you made. It never even occurred to me that real world connections would be made prior to the introduction of math concepts.
My daughter attends a private school that uses a traditional math curriculum so I have not encountered any of the fuzzy elementary programs. I use McDougal Littell's classic series by Dolciani, Brown, et al with my high school students but I have seen the failure of IMP in other schools.
Thanks for informing the public and please continue to advocate for higher math standards.
Lauren, it is certainly important for students to know why they are learning what they are learning. They need to know "what's the purpose for learning how to do this, anyway?" That was the whole purpose of word problems, story problems. So, we have to use those word problems for our ideas to do "real world" problems. Here is an example and I hope I can explain it satisfactorily here.
After we've learned to multiply 2/3 X 18 or something similar, and after we've learned that "of" = "X", then students need to learn how to use that in "real life".
So the story problem might be, "Mrs. John had 18 tomato plants and planted 2/3 of them. How many did she plant?" At first a student just looks at the words, or raise their hands and ask for help. So I ask them to read the words again out loud to me, and then have them writwe down "2/3 OF 18". And as soon as they write that down, they will say, "Ohhhhh!" and a wonderful smile will spread across their face.
I didn't want you to think that real life is ignored. It just needs to be appropriate to the grade level and to what they're learning or have learned.
We all learned how to divide fractions by fractions, but I never knew how I would use that in real life. I was never taught how to use that. So, I understand the "new math" people wanting students to understand "real world" situations. I want students to know that also. But the exercise doesn't have to become such a project that it takes hours, maybe a couple of days, to complete.
And I make it a goal every year to be sure my 5th grade students learn when they will use division of fractions. And I tell them "if you are making bows for your friends hair and you need 7/8 yard per bow and you 15 1/2 yards, you will be able to quickly know how many you can make." Or "if you are a boy scout with 24 yds. of rope, and you are responsible for making sure every boy gets a piece "so many inches" long, now you can quickly determine if you have enough rope. Those are "real life" situations that students can use.
So real life problems at the appropriate grade level are important and certainly should be taught. I just wanted to clear that up.
Isn't there a study somewhere that students learn better without the "real world" connection? I hope Catherine has it -- I recall the study said abstract was a better way of teaching to mastery.
The second point I'd throw into the mix is that the "real world connections" in math are incredibly time consuming. Time spent throwing paper airplanes or playing with blocks or taking pictures of geometric angles is time taken away from mastering the skills needed to succeed.
Students shouldn't have the impression that math is useless unless there is an immediate real world application for every topic in the curriculum. Students should understand that math is a tool for rigorously training the mind and that has value in its own right.
I thought this comic semi-related to the issue:
http://xkcd.com/435/
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