I have no idea.... the best and most proficient way ...
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.I agree with tkhunny but want to add that it also depends on the grade level of the student.
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.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.
I have no idea.
Why do you ask?
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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 post explains itself.
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.
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.
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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.
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.
I can't believe I've read the above posts by this guy...
(perhaps he's consumed an abundance of communion wine...)
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".2. Three college diplomas to clean my backside with. Most people only have one degree.
...I was annoyed by the tone of the replies you used with moderators here...
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".