What Is It With Word Problems?
When the class does this poorly, I can't help but think it's my doing. While the test items that they struggled with the most are no news to me because these are always the word problems, I'm just tired of the status quo. Why aren't they improving? Haven't we done enough practice? Haven't I been drawing pictures, working backwards, doing a simpler problem, and employing any and all strategies in my teacher toolbox to help my students?
At least 75% of the kids were able to factor and solve quadratic equations, but when it comes to applying this skill set in a word problem, they fall apart. In my frustration I would yell at the class, "But the words are in English, people! We've been translating sentences into equations since at least sixth grade! You know what more than, twice, product of, perimeter, and volume mean, right?!" Then I yell some more, "Nobody cares if you had the skills but did not know how or when to apply them! That's like someone being great at chopping up the vegetables but can't put a meal together!" Ugh.
They are used to me yelling. They feel sorry for me.
These are the last five [word] problems on the test:
21. A triangle has an area of 77 square inches. Find the length of the base if the base is 3 inches more than the height.
22. The volume of a box is 192 cubic inches. The height is 4 inches. The width is 2 inches more than the length. Find the missing dimensions.
23. Tonisha (and why must textbooks use the vaguest names in the phone book — is this their attempt at being culturally diverse?) hit a baseball into the air with an initial upward velocity of 48 feet per second. The height h in feet of the ball above the ground can be modeled by h = -16t2 + 48t + 2, where t is the time in seconds after Tonisha hit the baseball. Find the time it takes the ball to reach 38 feet above the ground.
24. The area of a rectangular room is 238 square feet. The width is 3 feet less than the length. Find the dimensions of the room.
25. One number is 5 times another number. The product of the two numbers is 245. Find the two numbers.
Not knowing how to do a problem is one thing, but writing down a ridiculously wrong answer is another.
You know what a triangle is, you can draw it, right? They assure me they do. Can you label the base and height correctly on a triangle? They say, well yeah! Do you know how to find the area of a triangle? Isn't it base times height divided by two? Yes, it is. But you are stuck because...? It's just hard, Mrs. Nguyen! Then they go on and on about getting all nervous on the test, having brain freeze, brain fart, total amnesia.
I just need to do a better job. No one in my algebra class is enrolled in ELD, so it's not the English language itself. But the language of math is not yet spoken fluently and understood by at least half of my 8th grade algebra students. This is unacceptable to me. How do I improve — what must I do differently next year, next chapter, next week, starting tomorrow?
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There is one new thing that I'm trying. Jeff Linder, my workshop co-presenter who is a math coach and a Scrabble extraordinaire, showed me this video, My Favorite No. Ms. Alcala has her students answer a warm-up question on a 3x5 notecard. She collects the cards and chooses the incorrect solution, her "favorite no," to share with the class. The class gives input on the missteps and corrects them together. I like this a lot, but I don't have a budget for 80 daily notecards, so I'm just cutting papers up into quarters.
Categories: Teaching, Mathematics
Tags: My Favorite No Alcala word problems
Can tell you are very passionate about teaching them kids. I also encountered some issues coaching my charges when it comes to solving real-world problems. I try to get them to identify one unknown parameter which must be solved for and say: let this be x. Subsequently I make them search through the entire word problem for another parameter which would naturally be made known once the value of x is acquired. From there I will guide them in terms of assembling an appropriate quadratic equation to crack things. Works for most fundamental questions, though this approach might have to be tweaked when we venture into territory demanding higher order thinking. All the best and god bless. Peace.
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Passionate or crazy
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Thanks for sharing this idea. I'm wondering if you could sift JUST until you get to a "winner" and then start writing it out. Maybe the final/extra sifting can happen while the kids are mulling and thinking. ... Maybe you can also decide on the winner while you're walking around and just pick that one.
I also thought maybe just have the kids write their names on the back of the card and then just put up their card. I don't know if there would be issues with handwriting recognition or if that would be okay.
Anyway ... thanks and I want to try this.
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I just got an idea for this yesterday, and it would work only because I have the kids twice each day, so I could ask in the morning and collect, then during lunch or prep (right before lunch) I could sift through the answers. Yes, handwriting recognition is an issue, so I have to re-write. A few times I had shared kids' work with the names covered up, still, half the class turns toward the owners to see their reactions.
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Fawn,
I feel your frustration. I'm guessing all math teachers have had similar experiences after marking an exam, wondering why the students didn't get it, wondering if I'm the problem because I didn't teach well enough.
Perhaps an approach that enlists the students as tutors might help. Assuming that some of your students can answer a problem correctly, could they tutor others that don't get it? The problems you listed don't look that hard, providing you are thinking the right way. Maybe peer tutoring would allow those who *are* thinking mathematically to explain in words their fellow students would understand, how to think like that.
That might not be the solution; I'm just throwing out an idea. But I do think we have to somehow "get inside kids' heads" to help them to think the right way. It's not about knowing the formula or being able to factorize or carry out some other isolated skill, but being able to "see" the picture and follow the train of thought, checking along the way, to the solution.
For example, in the last question it helps to recognise that some number is going to be squared, since one number is 5 times the other. Having some sort of mental picture of the two unknown numbers and being able to deal with what *is* known while holding on to the whole picture seems to me what you have to do.
Or perhaps I'm just rambling. :)
All the best finding a way to get through.
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Peer tutoring would be ideal because I believe you learn at a deeper level when you have to teach someone else. But I hear kids say this sometimes, "I don't know... It's hard to explain." I do make them try anyway. It's common for me to ask kids to come up and explain, draw pictures, do anything they can to show the class what they did.
After giving back the graded tests, I asked everyone to re-do #21, the triangle problem. I walked around and saw that most drew a triangle, labeled the leg -- not the height -- (x) and the base (x+3). A couple of students wrote (3x) for base. Half of them wrote down A=(bh/2). Then they stopped and smiled at me.
We'll do more next week. I'm determined to help them get past this. Thanks, Peter, for your comment.
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Do you ever ask them to 'guess and check' instead of using algebra? I know they are supposed to learn algebra, but several of the typical algebra word problems are so easy to solve using guess and check that it's amazing to me.
A triangle has an area of 77 square inches. Find the length of the base if the base is 3 inches more than the height.
guess maybe the base is 10 and height is 7. Then the area is 70 / 2 = 35. OOPS too small numbers. Try 13 and 10. Then the area is 130/2 = 65. Much better. Try 14 and 11. The area is 154/2 = 77. Got it.
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Oh, I know most of them used guess-and-check. Somehow this is a "natural" first step for them. I always tell them, "use it when you're desperate," because it's better than doing nothing. So, yes, the ones who did get the correct answers to some of these problems did admit to me that they used guess-and-check.
Thanks, Maria, for dropping by!
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