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[helpful]

Thanks, I guess I do that intuitively. I would be a horrible math teacher as I do all math intuitively.

I can't even explain how one does equivalencies...ie. 3/4= x/15. I just know what I have to do. I always have trouble explaining to my spouse, who is math phobic, why I do it the way I do it, because I have always done it that way.

I guess I am a product of the "old math".

(If someone can explain why one does the equivalency the way I do it, let me know....ie. in my example, 3 x 15 = 4x, then 45 divided by 4 = .)

[cgfunmathguy]

Somehow, it seems like I hijacked this thread unintentionally. I believe the original discussion was trying to get our students to "think" in class rather than inanely repeating what they have been told by others.

[voxprincipalis]

Somehow, it seems like I hijacked this thread unintentionally. I believe the original discussion was trying to get our students to "think" in class rather than inanely repeating what they have been told by others.

That's OK, cgfunmathguy. In about two seconds, it was going to morph into "students squared," so we would have been OK.

In my studio music lessons, I run up against this all the time when I work with students on technique. In the first term of the freshpeep year, I get a lot of "but my old teacher told me to do it X way." To which I usually reply, "yes, and when you were five your mother told you to always hold someone's hand when you cross the street. Do you still do that, too?"

The only person I'm interested in having them quote is me.

(I'm just kidding about that. Mostly.)

VP

[gennidad]

My point was that I had to spend a lot of time teaching High school Juniors and Seniors math they should have learned in elementary school or at least Jr. High. 

[cgfunmathguy]

My point was that I had to spend a lot of time teaching High school Juniors and Seniors math they should have learned in elementary school or at least Jr. High. 

I realize that, gennidad. I have the same problem at the college level. I believe part of it is the fact that elementary and middle-school teachers aren't confident in their answers to the ubiquitous (sp?) question "Why?". So, they don't answer that question, and a piece of information that would help the student understand goes missing. It is kind of like building a house without a foundation. These students come to college with very little exposure to the process of critical thinking and making arguments, even after taking high-school geometry (does anyone teach proofs anymore?). Now, instead of the students learning this skill in high school, it is delayed until college, causing exactly the kind of problems the OP is having.

Okay, time to get off the soapbox. I do like that view, though. ;-)

[helpful]

My point was that I had to spend a lot of time teaching High school Juniors and Seniors math they should have learned in elementary school or at least Jr. High. 

I realize that, gennidad. I have the same problem at the college level. I believe part of it is the fact that elementary and middle-school teachers aren't confident in their answers to the ubiquitous (sp?) question "Why?". So, they don't answer that question, and a piece of information that would help the student understand goes missing. It is kind of like building a house without a foundation. These students come to college with very little exposure to the process of critical thinking and making arguments, even after taking high-school geometry (does anyone teach proofs anymore?). Now, instead of the students learning this skill in high school, it is delayed until college, causing exactly the kind of problems the OP is having.

Okay, time to get off the soapbox. I do like that view, though. ;-)

So to satisfy my curiosity can you tell me Why? I do equivalencies the way I do it? (other than saying, that is how I was taught it!)

[cgfunmathguy]

So to satisfy my curiosity can you tell me Why? I do equivalencies the way I do it? (other than saying, that is how I was taught it!)

Not having seen your homework paper, I cannot. There are several approaches to the problem you posted, and unless I see your work, I cannot tell you the mathematical basis for your approach. However, I'm guessing that your approach is based on the concept of common denominators.

[gennidad]

My turn on the soapbox. 

I discovered that many of the lower grade teachers were not passing on the the why so much as they didn't have time to give the answers and encourage the critical thinking that are needed in the higher grades and in college.  I know that in my classes I had about 30 students in a class.  Out of those 30 I had maybe 4 that wanted to learn the material to get into college, another 10 or so who paid attention but didn't really care, 6 cl*** *****s, 6 slackers, and 4 who were diagnosed with a learning disability.  Out of the last 4 I had one or two that were mainstreamed into my class, meaning that they have almost no hope of being able to do the work but I had to spend extra time with them trying to get them to pass.   This means that instead spending my time preparing and encouraging the students that want to go to college I had to try to help the ones who didn't care or who couldn't to keep up.

Ok.  That is my rant for the day.  You are right about the view from up here.