Incorrect instruction - split from quadratic

Jeff,
Here is the issue. You are probably right that if the students are taught correctly they will use, in this case, cross multiplication correctly. The problem is that if you teach at a college the students come to you knowing/not knowing how to use cross multiplication. Most times when a student takes algebra or arithmetic in college it is because they did not learn it well in high school. More often then not, they did not learn when to cross multiply. I can assure you that these students fight and argue with you when you even show them how to solve x/a = b/c w/o cross multiplying. It may be sad but it is the case.
 
Jomo said:
Jeff,
Here is the issue. You are probably right that if the students are taught correctly they will use, in this case, cross multiplication correctly. The problem is that if you teach at a college the students come to you knowing/not knowing how to use cross multiplication. Most times when a student takes algebra or arithmetic in college it is because they did not learn it well in high school. More often then not, they did not learn when to cross multiply. I can assure you that these students fight and argue with you when you even show them how to solve x/a = b/c w/o cross multiplying. It may be sad but it is the case.
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I agree. I taught at community college and volunteer there in the math-resource center. I have seen - in these types of problems at least - whenever I say "calculate the LCM" - their eyes glaze over and immediate response "Isn't there a shorter way?". I see the importance of learning the shorter way (correctly) in tests like SAT, etc. But for HW, I had insisted that "go through LCM - and you'll be rewarded".
 
Subhotosh Khan said:
I see the importance of learning the shorter way (correctly) in tests like SAT, etc. But for HW, I had insisted that "go through LCM - and you'll be rewarded".
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If one learns how to use short cuts correctly, then i support it's use. I support anything that gets a student to think mathematically.
 
Well, I am not going to argue with observed experience. If both of you say that college students don't know how to solve

[MATH]\dfrac{x}{a} = b \implies x = ab[/MATH] without cross muliplication and instead go

[MATH]\dfrac{x}{a} = \dfrac{b}{1} \implies \dfrac{x}{b} = \dfrac{a}{1} = a[/MATH],

I have to believe you. The problem is clearly insoluble for college students.?
 
Jomo said:
If one learns how to use short cuts correctly, then i support it's use. I support anything that gets a student to think mathematically.
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The key word is - correctly. But that cannot be judged till and until they make horrible mistakes. The problem like:

x/a + c/b = y/d + e/f

They want to write:

x * df + c * df = y * ab + e * ab ......[It must be right - I did "criss-cross"]

Then you say -- "you CAN do that AFTER you do the addition on each side of the = sign"

Then they say - "But PEMDAS says multiplication before addition"

Oh brother .... where art thou.....
 
Subhotosh Khan said:
The key word is - correctly. But that cannot be judged till and until they make horrible mistakes. The problem like:

x/a + c/b = y/d + e/f

They want to write:

x * df + c * df = y * ab + e * ab ......[It must be right - I did "criss-cross"]

Then you say -- "you CAN do that AFTER you do the addition on each side of the = sign"

Then they say - "But PEMDAS says multiplication before addition"

Oh brother .... where art thou.....
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Gee thanks. What you wrote will make me ill for the whole day!
What you wrote is the perfect example of why students do poorly in math. They do steps without understanding why it works, if it does in fact work. Students from early on accept math facts without questioning them at all. This is suicidal for a student to do.
High school math teacher, usually, are educator (having earned a degree in education) and not mathematicians (even low level mathematicians who only have a BS or MS in math). As educators they are taught methods to get the best grade out of students. For example they will tell their students time after time that a b/c = (ac+b)/c without saying why. I would fire ever teacher that does not say why! It is nothing advanced, as it is just adding fractions but they are usually not taught why. Fine, some students will not get it or not care to get it but in my opinion you still have to say the why! Whenever I received my paycheck as a community college professor I always felt good accepting that check and it had nothing to do with the grades my students were getting. It was always because of the quality of education I gave them.
 
Jomo said:
Gee thanks. What you wrote will make me ill for the whole day!
What you wrote is the perfect example of why students do poorly in math. They do steps without understanding why it works, if it does in fact work. Students from early on accept math facts without questioning them at all. This is suicidal for a student to do.
High school math teacher, usually, are educator (having earned a degree in education) and not mathematicians (even low level mathematicians who only have a BS or MS in math). As educators they are taught methods to get the best grade out of students. For example they will tell their students time after time that a b/c = (ac+b)/c without saying why. I would fire ever teacher that does not say why! It is nothing advanced, as it is just adding fractions but they are usually not taught why. Fine, some students will not get it or not care to get it but in my opinion you still have to say the why! Whenever I received my paycheck as a community college professor I always felt good accepting that check and it had nothing to do with the grades my students were getting. It was always because of the quality of education I gave them.
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Mission accomplished!!!:devilish::devilish::devilish::devilish:
 
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