Teaching Fractions

mathdad

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What is the best and most proficient way to teach fractions, in your opinion?
 

tkhunny

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Whichever way the student understands.
 

Jomo

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I agree with tkhunny but want to add that it also depends on the grade level of the student.
 

Otis

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tkhunny

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I agree with tkhunny but want to add that it also depends on the grade level of the student.
Excellent. And this is exactly my point. If one decides there is a very best way to proceed, will one judge grade level or previous experience in selecting the very best way for THAT STUDENT? Better to keep a full box of tools at your disposal and reach all the students you can, rather than just the few you choose.
 

Jomo

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Excellent. And this is exactly my point. If one decides there is a very best way to proceed, will one judge grade level or previous experience in selecting the very best way for THAT STUDENT? Better to keep a full box of tools at your disposal and reach all the students you can, rather than just the few you choose.
Teaching how to add fractions to a student in my opinion has the same problems as teaching someone how to add/subtract signed numbers. I always tell my students to try to learn their own way of seeing this.

The main problem is that as an instructor there is no way of teaching multiple ways of doing these two processes. I have tried and students complained that I was confusing them-- and it takes a lot of classroom time to do this. I just choose a method where students can see why it works rather than memorizing some boring unsuccessful steps.

Of course the real issue is having a class of over 25 students of varying ability. I remember teaching a summer remedial math class of 6 students. I was able to get through to each of the students by spending time with each of them individually. I had a 100% passing rate which is unheard of in a remedial math course. Sure I did a good job teaching that course but the fact that the class size was very small made it extremely easy to get everyone to pass.
 

mathdad

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JeffM

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Although I agree that ideally whatever method works best for the individual student is what should be taught, that is impractical for large (?) classes. Moreover, teaching multiple methods is resisted by students who are prejudiced against math in the first place. What I have done with reasonable success is to show why there is a necessity to find a common denominator and a universal method to find a common denominator. Once the student sees a reason and a method, the student, particularly a student that has some commitment to learning the material, will usually buckle down and learn the method.

In other words, I do not try to teach a method without context. I provide a context first and only then provide a method that always works.

Notice that I do not bother with least common denominator at all. With pocket calculators virtually ubiquitous, the advantage of least common denominator is greatly reduced, and the advantage of a least common denominator frequently does not extend to non-integer denominators or to algebra. I fully understand why the use of a least common denominator was advantageous in the past, but it is a complexity that has less and less practical benefit going forward.
 

Otis

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The post explains itself.
Oops. I didn't ask for an explanation of the post. (I understand the content.) I'm curious to know why you're soliciting opinions about the best, most proficient way. There must be a reason. Maybe you're thinking about how to revisit ratios, or maybe you want to tutor someone. If you'd rather not say, then it's okay to say that. (No biggie.)

The reason for my question is that I like to know something about purpose when deciding whether (or how) to contribute. Cheers.

😎
 
Last edited:

mathdad

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Teaching how to add fractions to a student in my opinion has the same problems as teaching someone how to add/subtract signed numbers. I always tell my students to try to learn their own way of seeing this.

The main problem is that as an instructor there is no way of teaching multiple ways of doing these two processes. I have tried and students complained that I was confusing them-- and it takes a lot of classroom time to do this. I just choose a method where students can see why it works rather than memorizing some boring unsuccessful steps.

Of course the real issue is having a class of over 25 students of varying ability. I remember teaching a summer remedial math class of 6 students. I was able to get through to each of the students by spending time with each of them individually. I had a 100% passing rate which is unheard of in a remedial math course. Sure I did a good job teaching that course but the fact that the class size was very small made it extremely easy to get everyone to pass.
Private schools are far better than public schools due to small amount of students vs a big class of 25 or more. In my opinion, 25 students is actually TWO classes in one. Public schools are notorious for bombarding classrooms with an unlimited supply of students. I consider myself a victim of NYC public school so-called education.

The entire reason for my post here has a lot to do with learning math well in the early grades to prepare for middle school and beyond. For example, students in middle school should be able to add algebraic fractions if they learned regular fractions well in the lower grades. When I face, for example, (a/b) + (b/c), I use the same steps for adding (1/2) + (3/4). See my point?
 

mathdad

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Oops. I didn't ask for an explanation of the post. (I understand the content.) I'm curious to know why you're soliciting opinions about the best, most proficient way. There must be a reason. Maybe you're thinking about how to revisit ratios, or maybe you want to tutor someone. If you'd rather not say, then it's okay to say that. (No biggie.)

The reason for my question is that I like to know something about purpose when deciding whether (or how) to contribute. Cheers.

😎
You are becoming a problem for me here. Read my reply to Jomo.
 

mathdad

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Although I agree that ideally whatever method works best for the individual student is what should be taught, that is impractical for large (?) classes. Moreover, teaching multiple methods is resisted by students who are prejudiced against math in the first place. What I have done with reasonable success is to show why there is a necessity to find a common denominator and a universal method to find a common denominator. Once the student sees a reason and a method, the student, particularly a student that has some commitment to learning the material, will usually buckle down and learn the method.

In other words, I do not try to teach a method without context. I provide a context first and only then provide a method that always works.

Notice that I do not bother with least common denominator at all. With pocket calculators virtually ubiquitous, the advantage of least common denominator is greatly reduced, and the advantage of a least common denominator frequently does not extend to non-integer denominators or to algebra. I fully understand why the use of a least common denominator was advantageous in the past, but it is a complexity that has less and less practical benefit going forward.
Read my reply to Jomo.
 

mathdad

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Excellent. And this is exactly my point. If one decides there is a very best way to proceed, will one judge grade level or previous experience in selecting the very best way for THAT STUDENT? Better to keep a full box of tools at your disposal and reach all the students you can, rather than just the few you choose.
Read my reply to Jomo. Learn to have fun with math. We are no longer in school. This is a math site not a college classroom.
 

Denis

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I can't believe I've read the above posts by this guy...
(perhaps he's consumed an abundance of communion wine...)
 

mathdad

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I can't believe I've read the above posts by this guy...
(perhaps he's consumed an abundance of communion wine...)
This guy? A little bit about me.

1. Former Navy sailor
2. Three college diplomas to clean my backside with. Most people only have one degree.
3. I am 54 years old and missing my youth daily.
4. I work very, very hard just to pay bills. Ha!
5. Traveling through life hoping for a better day tomorrow but tomorrow never comes.
6. Hoping to find female companionship but females run away from math guys.
7. Always here, Denis, to answer any questions you may have about the last days.
8. I am still living in the 1970s.
9. I love classic sitcoms and despise modern day so-called comedies.
10. Earnestly and anxiously waiting for the rapture of the church to occur.

Denis:

You love drawing attention to yourself. You enjoy connecting negativity to ALL MY QUESTIONS and ANSWERS. Brother, do you know how to be positive for a change? It really is not difficult to be nice to other people. You are older than me by more than 10 years, right? Are you an older man going through the crazy teen years again? Honestly, "this guy" is negativity to a New Yorker like myself.
 

Denis

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...I was annoyed by the tone of the replies you used with moderators here...
 

tkhunny

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2. Three college diplomas to clean my backside with. Most people only have one degree.
The standard percentage in the U.S. is about 30% without any college degree, so it's difficult to make such claims about "most people".
 

mathdad

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...I was annoyed by the tone of the replies you used with moderators here...
Relationships on the internet and/or in life outside the web are not always a bed of roses.
 

mathdad

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The standard percentage in the U.S. is about 30% without any college degree, so it's difficult to make such claims about "most people".
Yes but you know what I mean. I am learning disabled. This is a huge accomplishment for me.
 
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