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01 Feb 2006 - 13:46
I was just straightening up my computer files, and I came across this piece of fantastic advice on how to work word problems in algebra. Unfortunately, I didn't record the author of this advice. I think this is the text of an email Carolyn's husband, Bernie Johnston sent me back before we started writing ktm. But it may have been posted by Steve....(I'm inclined to think it's Bernie, not Steve, because Steve prefers 'isolate the variable' to 'undo what's been done to X,' assuming I read his response to Carolyn's post on the subject correctly.) I'm sure one of them will recognize this. [update: Bernie wrote it]
words to remember When you don't know something, give it a name. When you have an equation with variables on the bottom, clear the denominators. Put the x's on one side and the numbers on the other. Undo whatever has been done to x.
words to remember from Vlorbik
Include the units. Word problems have word answers.
V is right; including the units & writing word answers to word problems this is a VERY good habit to get into, right up front. I'm forcing myself to remember to do this. Interestingly, Christopher isn't hugely resistant to including the units. I thought he would be, because he's resistant to everything. Just goes to show how distant the middle-school brain is from the grown-up brain. Christopher seems to view 'including the units' as Obviously Something A Person Should Do. I wonder if it's the relative hyperspecificity of the child's brain. He may feel like an answer of '5,' when what is meant is '5 cents,' really truly isn't 5 cents. Don't know.
key words: good advice on algebra word problems good advice on how to solve algebra word problems
understanding basic algebra moves (& Comments)
good advice on solving algebra word problems
-- CatherineJohnson - 01 Feb 2006 Back to main page.
Please consider registering as a regular user.
Look here for syntax help.
Not me. -- SteveH - 01 Feb 2006
"Undo whatever has been done to x." I like my students to think in terms of opposite operations to isolate the variable. Opposite operation is an easily grasped notion. This came up before regarding a book on algebra word problems, but I'll mention it again. I find a little paperback called How to solve word problems in algebra (Johnson & Johnson) to be tremendously helpful. Many students are terrified by algebra word problems. This book presents the reasoning in a clear and concise manner with lots of examples. It can exorcise the demons of fear. -- CharlesH - 01 Feb 2006
This was a post or letter by Bernie. -- CarolynJohnston - 01 Feb 2006
good advice, indeed. here's some more. the elementary texts usually come right out
and tell you which unknown quantity
(or quantities) to "name": look at the question
and make "x" equal to whatever the answer might be.
thus, if it sez "how many quarters and how many dimes
were there in the original pile?", one puts
"x = # quarters" and "y = # dimes" (or, of course,
slightly better [but somehow unpopular with some beginners],
"q = # quarters" and "d = # dimes"). & here's another mantra for ya: include the units!
thus, when they ask, "how much beer (6% alcohol)
and how much whiskey (40% alcohol) must be mixed
to get a 16 oz. boilermaker with 10% alcohol?",
we'll begin by writing, not "b = beer", but rather
"b = oz. beer" etcetera (how can "b" be "beer"? --
all our variables represent numbers!). a-and how about this: "word problems get word answers!"?
e.g., the answer in the stated problem isn't
"b ~= 13.7, w~= 2.3", but rather,
"about 13.7 oz. beer & 2.3 oz. whiskey". shutting up. i could go on for quite some time
along these lines ... just have to imagine myself
in front of a crowd standing at a chalkboard ... -- VlorbikDotCom - 01 Feb 2006
I find a little paperback called How to solve word problems in algebra (Johnson & Johnson) Everyone loves this book (so far) It's in my Amazon cart. -- CatherineJohnson - 01 Feb 2006
For some reason, I love the 'undoing' idea. I don't know why — and I have no idea whether other students would like it and/or find it helpful. -- CatherineJohnson - 01 Feb 2006
good advice
I was just straightening up my computer files, and I came across this piece of fantastic advice on how to work word problems in algebra. Unfortunately, I didn't record the author of this advice. I think this is the text of an email Carolyn's husband, Bernie Johnston sent me back before we started writing ktm. But it may have been posted by Steve....(I'm inclined to think it's Bernie, not Steve, because Steve prefers 'isolate the variable' to 'undo what's been done to X,' assuming I read his response to Carolyn's post on the subject correctly.) I'm sure one of them will recognize this. [update: Bernie wrote it]
This reminds me of a thought I had last week. For many many algebraic or calculus computations I have a phrase that runs through my head and tells me how to proceed. If I forget what to do I simply conjure up that phrase in my head. When I've tried to tutor people I've noticed that they frequently get stuck at exactly the point where the phrase would be useful but they have no phrase in their heads. When I think back upon where the phrase came from I realize that in many cases it came from my high school algebra teacher. For example, when you start an algebra word problem, it's very difficult to know where to begin. There are a lot of words and the potential complexity of the problem is enormous. If you spend a lot of time using the front part of your brain to search for an appropriate path you may never find it. The phrase "when you don't know something, give it a name" is essentially the secret of algebra. This allows you to mentally grasp a particular thread of the problem which you can then follow through to the proper conclusion: the problem space has been cut way down in size. Another one he gave me: "When you have an equation with variables on the bottom, clear the denominators". "Put the x's on one side and the numbers on the other." "Undo whatever has been done to x." These phrases are not singing rhymes but they are quite useful. The idea that certain procedures must be memorized or learned by rote is highly unfashionable these days but I think absolutely necessary.
words to remember When you don't know something, give it a name. When you have an equation with variables on the bottom, clear the denominators. Put the x's on one side and the numbers on the other. Undo whatever has been done to x.
words to remember from Vlorbik
Include the units. Word problems have word answers.
V is right; including the units & writing word answers to word problems this is a VERY good habit to get into, right up front. I'm forcing myself to remember to do this. Interestingly, Christopher isn't hugely resistant to including the units. I thought he would be, because he's resistant to everything. Just goes to show how distant the middle-school brain is from the grown-up brain. Christopher seems to view 'including the units' as Obviously Something A Person Should Do. I wonder if it's the relative hyperspecificity of the child's brain. He may feel like an answer of '5,' when what is meant is '5 cents,' really truly isn't 5 cents. Don't know.
key words: good advice on algebra word problems good advice on how to solve algebra word problems
understanding basic algebra moves (& Comments)
good advice on solving algebra word problems
-- CatherineJohnson - 01 Feb 2006 Back to main page.
Comments
After entering a comment, users can login anonymously as KtmGuest (password: guest) when prompted.Please consider registering as a regular user.
Look here for syntax help.
Not me. -- SteveH - 01 Feb 2006
"Undo whatever has been done to x." I like my students to think in terms of opposite operations to isolate the variable. Opposite operation is an easily grasped notion. This came up before regarding a book on algebra word problems, but I'll mention it again. I find a little paperback called How to solve word problems in algebra (Johnson & Johnson) to be tremendously helpful. Many students are terrified by algebra word problems. This book presents the reasoning in a clear and concise manner with lots of examples. It can exorcise the demons of fear. -- CharlesH - 01 Feb 2006
This was a post or letter by Bernie. -- CarolynJohnston - 01 Feb 2006
good advice, indeed. here's some more. the elementary texts usually come right out
and tell you which unknown quantity
(or quantities) to "name": look at the question
and make "x" equal to whatever the answer might be.
thus, if it sez "how many quarters and how many dimes
were there in the original pile?", one puts
"x = # quarters" and "y = # dimes" (or, of course,
slightly better [but somehow unpopular with some beginners],
"q = # quarters" and "d = # dimes"). & here's another mantra for ya: include the units!
thus, when they ask, "how much beer (6% alcohol)
and how much whiskey (40% alcohol) must be mixed
to get a 16 oz. boilermaker with 10% alcohol?",
we'll begin by writing, not "b = beer", but rather
"b = oz. beer" etcetera (how can "b" be "beer"? --
all our variables represent numbers!). a-and how about this: "word problems get word answers!"?
e.g., the answer in the stated problem isn't
"b ~= 13.7, w~= 2.3", but rather,
"about 13.7 oz. beer & 2.3 oz. whiskey". shutting up. i could go on for quite some time
along these lines ... just have to imagine myself
in front of a crowd standing at a chalkboard ... -- VlorbikDotCom - 01 Feb 2006
I find a little paperback called How to solve word problems in algebra (Johnson & Johnson) Everyone loves this book (so far) It's in my Amazon cart. -- CatherineJohnson - 01 Feb 2006
For some reason, I love the 'undoing' idea. I don't know why — and I have no idea whether other students would like it and/or find it helpful. -- CatherineJohnson - 01 Feb 2006
| WebLogForm | |
|---|---|
| Title: | good advice |
| TopicType: | WebLog |
| SubjectArea: | HighSchoolMath, ParentsTeachingKids, TeachersTeachingKids |
| LogDate: | 200602010845 |