choirfarm Posted January 17, 2012 Share Posted January 17, 2012 I am currently reading Kinowing and Teaching Elementary Mathematics by Liping Ma. I've only made it through 2 chapters. The second chapter is about long multiplication. I hope the formatting stays for this as it should line up correctly. 123 x645 615 492 738 79335 They had one example lined up incorrectly and one correctly. Ok..I have NEVER seen it like that without the zeros. Most of the US teachers said it was a problem of place value if the student lined it up incorrectly BUT they had no concept of what they were doing. Some of them talked about putting in the imaginary zeroes or sometime even other object so they could keep their place. The only thing the zeros were good for were keeping their place??????? Now the Chinese left out the zeros as well many times but they had a much better grasp of the place value... The way I learned to do it was that you multiplied 5 x 123. But then you were multiplying 40 times 123. You had to have the zero there not to keep the place but because that is what you were doing. You were NOT multiplying 4 x 123. Then you are multiplying 600 x123 so once again the zeros must go there because you are NOT multiplying it by 6. So my problem looks like 123 x645 615 4920 73800 79335 To me the zeros are absolutely necessary. The Chinese teachers taught this and then had them erase the zeros since they were not necessary. I guess I do not understand how they were not necessary...to me, they are otherwise the number means something different. The American teachers thought the zeros were confusing to the students... So then I did an experiment. I asked my husband to solve the problem. HE DID IT WITHOUT THE ZEROS!!! I asked him why and he said that is because that is the way you do it. Why don't you put zeros there? Why would you need them?? he asked. He couldn't explain why he lined them up the way he did. This is a Phi Beta Kappa guy that took several calculus classes in college... I explained a little bit but he argued that he could do it as quickly as I could and maybe faster without the zeros... So then I gave it to my oldest. He did it with the zeros. I asked him why and he said it had to do with place value. He said dad's way would certainly work. I gave it to my middle boy and he did it with the zeros. I asked him why and he explained like I did because you are multiplying by 40 and by 600. ( Probably because I am the one teaching and dragging him through math!) Then he noticed that his answer differed from dad's answer..GREAT.. he said but then he realized that dad made a carrying mistake and his answer was correct. (There was great rejoicing that he got something correct.) I just thought it was funny as I have never seen or heard of lining it up that way but it is obviously taught that way. I realize that lining it up my husband's way will work, but to me it just doesn't make logical sense. It is like the numbers are just hanging out in space. Without the zeros it would be so easy to slide them over to where they are not lined up correctly. The formatting didn't work I see and I don't know how to get it to work out correctly so I hope you can get what I am trying to say. There were just spaces where zeros should be and they lined up where they SHOULD be. My example with zeros isn't lining up either. Quote Link to comment Share on other sites More sharing options...
mom2scouts Posted January 17, 2012 Share Posted January 17, 2012 I was taught to do it without the zeros. Everyone in my family who went to PS does it without the zeros. I don't require my children to use zeros either if they understand the place value, but I do teach them that they are actually multiplying by 40 and that is why they need to move it over to the tens place. Quote Link to comment Share on other sites More sharing options...
buram Posted January 17, 2012 Share Posted January 17, 2012 I just finished reading that book. I was surprised that the US teachers were teaching without the zeros because I was taught to put the zeros in. However, I was in grade school in the '70's so maybe that is why? Either way very interesting book. Quote Link to comment Share on other sites More sharing options...
boscopup Posted January 17, 2012 Share Posted January 17, 2012 I was taught without the zeros. My kid has been taught with the zeros (Math Mammoth). I understood the place value, and was basically taught that leaving off the zeros was a short cut. Quote Link to comment Share on other sites More sharing options...
kandty Posted January 17, 2012 Share Posted January 17, 2012 I was taught to use zero and so was Dh. I saw in MUS that they were teaching without the zeros. I was confused and taught it how I was taught. My Ds struggles with place value, so it was a must to put in the zero! Quote Link to comment Share on other sites More sharing options...
kristinannie Posted January 17, 2012 Share Posted January 17, 2012 I was taught with the zeros, but then stopped writing them once I understood the place value issue because writing a bunch of unnecessary zeros takes up a lot of time. What really scared me from reading her book is that the teachers didn't even know why zeros should be there! I do worry about the small sample size of the teachers, but that book was a real eye opener to me about why we are failing at teaching math in this country. There are some great ideas in that book! It is a must have for every homeschooler! Quote Link to comment Share on other sites More sharing options...
GailV Posted January 17, 2012 Share Posted January 17, 2012 I don't use the zeroes. I've no memory of how I was taught, but it doesn't seem like the zeroes are really accomplishing anything by being there. Plus I've saved MINUTES over the course of my lifetime by not taking the time to write them out, not to mention the pencil lead and ink saved. I let my kids do it whichever way they want, as long as they know what they're doing and why. Quote Link to comment Share on other sites More sharing options...
boscopup Posted January 17, 2012 Share Posted January 17, 2012 Plus I've saved MINUTES over the course of my lifetime by not taking the time to write them out, not to mention the pencil lead and ink saved. Save the planet! Don't use zeros! :lol: Quote Link to comment Share on other sites More sharing options...
DianeW88 Posted January 17, 2012 Share Posted January 17, 2012 I don't use the zeros. They're not necessary. I don't teach my kids with the zeros either. Quote Link to comment Share on other sites More sharing options...
choirfarm Posted January 17, 2012 Author Share Posted January 17, 2012 I don't use the zeros. They're not necessary. I don't teach my kids with the zeros either. So you don't feel like the numbers are just hanging there? How do you keep them from sliding them over? I have to laugh at some of you. Are you being serious on the amount of time it saves you not to write zeros??? It takes a nannosecond..... Quote Link to comment Share on other sites More sharing options...
stripe Posted January 17, 2012 Share Posted January 17, 2012 I attended a private Montessori elem school, and I don't write the zeroes, but the American teachers' reaction was astonishing. Quote Link to comment Share on other sites More sharing options...
GailV Posted January 17, 2012 Share Posted January 17, 2012 (edited) So you don't feel like the numbers are just hanging there? How do you keep them from sliding them over? Okay, I now have a picture in my head of picking up my kids' math papers, giving them a shake and a horizontal twist, and ALL THE NUMBERS SLIDE ALL OVER THE PLACE! AAAAAARGH! Emergency! Emergency! Get some Place Holders in here IMMEDIATELY to nail those digits down! They're slllliiiiiiiiddddiiiiiiiinnnnnnggggggg.......... I have to laugh at some of you. Are you being serious on the amount of time it saves you not to write zeros??? It takes a nannosecond..... I have the Spiritual Gift of Sarcasm. It's one of the less-talked-about spiritual gifts. Also, I've recently (like 2 minutes ago) realized that I might have the gift of Surrealism. Edited to add: If you prefer, I'm okay saying I'm too lazy to write the zeroes. Edited January 17, 2012 by GailV Quote Link to comment Share on other sites More sharing options...
Mom-ninja. Posted January 17, 2012 Share Posted January 17, 2012 Plus I've saved MINUTES over the course of my lifetime by not taking the time to write them out, not to mention the pencil lead and ink saved. :lol::lol::lol: I use zeros. It helps me to "see" the place value. Quote Link to comment Share on other sites More sharing options...
prairiewindmomma Posted January 17, 2012 Share Posted January 17, 2012 :) I've been taught both ways. I prefer the zero as placeholder method just as a visual reference that my place columns are lined up correctly. Dh is a no-zero kinda guy. Quote Link to comment Share on other sites More sharing options...
ElizabethB Posted January 17, 2012 Share Posted January 17, 2012 I have to laugh at some of you. Are you being serious on the amount of time it saves you not to write zeros??? It takes a nannosecond..... But, those nanoseconds add up, eventually, you've saved seconds and then minutes! My daughter still uses zeros but will be allowed to drop them when she is more proficent, currently the zeros help her remember what she's doing. I don't use zeros because I value my nanoseconds, I'm into efficiency! (OK, I'm lazy.) I expect that my son will be allowed to drop his zeros much sooner than my daughter, but he needs a lot more repetition with phonics, she needs more repetition with math. Quote Link to comment Share on other sites More sharing options...
Rivka Posted January 17, 2012 Share Posted January 17, 2012 I was taught to do it with zeroes in an American public school. Quote Link to comment Share on other sites More sharing options...
kandty Posted January 18, 2012 Share Posted January 18, 2012 But, those nanoseconds add up, eventually, you've saved seconds and then minutes! I don't use zeros because I value my nanoseconds, I'm into efficiency! (OK, I'm lazy.) :lol: Too bad all of you nanosecond savers just used all of them up posting on this thread. Years of non-zero writting all gone. :D Quote Link to comment Share on other sites More sharing options...
stripe Posted January 18, 2012 Share Posted January 18, 2012 Imagine what I could accomplish if I stopped dotting "i." Quote Link to comment Share on other sites More sharing options...
choirfarm Posted January 18, 2012 Author Share Posted January 18, 2012 :lol::lol: Imagine what I could accomplish if I stopped dotting "i." Quote Link to comment Share on other sites More sharing options...
Farrar Posted January 18, 2012 Share Posted January 18, 2012 Having actually taught a class of 6th graders remedial math... I think the zeros are useful for kids simply because they have cruddy handwriting and can't line things up properly.:glare: The zeros help them do that. Of course, they aren't necessary for the math. And any child who doesn't understand what they're doing... yada yada yada... you all have read Liping Ma... you know what I'm on about. ETA: And the really interesting question is... is it "zeros" or "zeroes"? My spellchecker infuriatingly thinks both are correct, which, maybe they are. Quote Link to comment Share on other sites More sharing options...
GailV Posted January 18, 2012 Share Posted January 18, 2012 ETA: And the really interesting question is... is it "zeros" or "zeroes"? My spellchecker infuriatingly thinks both are correct, which, maybe they are. "Zeros" takes less time to write. I just saved nanoseconds by not typing that extra E. Of course, I then squandered them with a bunch of typos like "nonoseconds" (which I actually sort of like as a concept). Quote Link to comment Share on other sites More sharing options...
LizzyBee Posted January 18, 2012 Share Posted January 18, 2012 (edited) I just finished reading that book. I was surprised that the US teachers were teaching without the zeros because I was taught to put the zeros in. However, I was in grade school in the '70's so maybe that is why? Either way very interesting book. I was also in grade school in the '70s, but we taught to do it without the zeros. To me, the zeros just clutter up the space. :tongue_smilie: I'm surprised how many people were taught with the zeros. I just assumed that "everyone" learned it the same way my school taught it. lol. Edited January 18, 2012 by LizzyBee Quote Link to comment Share on other sites More sharing options...
Posted January 18, 2012 Share Posted January 18, 2012 (edited) How important is it to really understand place value? I went to PS many years ago, and we were taught to do multiplication without the zeros. In retrospect, I remember my second grade teacher using bundles of ten tongue depressors wrapped up with a rubber band to teach borrowing and place value, but I never really understood the meaning at the time. I certainly learned the procedures for borrowing and carrying, and multiplication and long division. However, I never (well, maybe not until high school) learned why they worked. But, I don't think that lack hurt me any. I always seemed to do as well as my peers on math tests. Up until this moment, I don't think I've ever really thought about why long division works, but that hasn't stopped me from using it successfully, or doing well in math classes. How important is it to teach the meanings of these procedures in the early years? Edited January 18, 2012 by GGardner Quote Link to comment Share on other sites More sharing options...
kiana Posted January 18, 2012 Share Posted January 18, 2012 How important is it to really understand place value? I went to PS many years ago, and we were taught to do multiplication without the zeros. In retrospect, I remember my second grade teacher using bundles of ten tongue depressors wrapped up with a rubber band to teach borrowing and place value, but I never really understood the meaning at the time. I certainly learned the procedures for borrowing and carrying, and multiplication and long division. However, I never (well, maybe not until high school) learned why they worked. But, I don't think that lack hurt me any. I always seemed to do as well as my peers on math tests. Up until this moment, I don't I've ever really thought about why long division works, but that hasn't stopped me from using it successfully, or doing well in math classes. How important is it to teach the meanings of these procedures in the early years? Some people can easily remember a procedure without understanding -- other people cannot remember a procedure without understanding. This caused issues in early elementary when I was absolutely unable to do long division because what we were doing did not make sense. Secondly, understanding why the procedure works will imo make future generalizations of said procedure (i.e. from long division to polynomial division) easier. YMMV. Quote Link to comment Share on other sites More sharing options...
Farrar Posted January 18, 2012 Share Posted January 18, 2012 How important is it to really understand place value? I went to PS many years ago, and we were taught to do multiplication without the zeros. In retrospect, I remember my second grade teacher using bundles of ten tongue depressors wrapped up with a rubber band to teach borrowing and place value, but I never really understood the meaning at the time. I certainly learned the procedures for borrowing and carrying, and multiplication and long division. However, I never (well, maybe not until high school) learned why they worked. But, I don't think that lack hurt me any. I always seemed to do as well as my peers on math tests. Up until this moment, I don't think I've ever really thought about why long division works, but that hasn't stopped me from using it successfully, or doing well in math classes. How important is it to teach the meanings of these procedures in the early years? I would say read the book. Really. Quote Link to comment Share on other sites More sharing options...
Snowfall Posted January 18, 2012 Share Posted January 18, 2012 I would say read the book. Really. I agree. I was taught to write the zeroes, but the teachers always told us it was to hold our place. They never explained anything about place value, that I recall. Quote Link to comment Share on other sites More sharing options...
ElizabethB Posted January 18, 2012 Share Posted January 18, 2012 :lol: Too bad all of you nanosecond savers just used all of them up posting on this thread. Years of non-zero writting all gone. :D Well, I've wasted a lot of nanoseconds here, but I enjoy it! Writing zeros, on the other hand, has no benefit for me. ETA: And the really interesting question is... is it "zeros" or "zeroes"? My spellchecker infuriatingly thinks both are correct, which, maybe they are. Wasting more nanoseconds for this, a question that has plagued people here for at least a few nanoseconds, maybe even a dozen. Making plurals: 1. After hissing sounds, add –es 2. After non-hissing sounds, just add -s Words ending in an o can add either -s or -es. (And, words ending in an o add their endings with no apparent rhyme or reason as far as I know, and apparently some words can be both -s and -es, but I'm not wasting any more nanoseconds researching the issue.) Quote Link to comment Share on other sites More sharing options...
Rosie_0801 Posted January 18, 2012 Share Posted January 18, 2012 Up until this moment, I don't think I've ever really thought about why long division works, but that hasn't stopped me from using it successfully, or doing well in math classes. How important is it to teach the meanings of these procedures in the early years? I'd say it is very important, assuming the child is able to learn it. Some just aren't ready to absorb that kind of info. A long time ago, I was pretty good at the plug the number stuff that passed as maths at my school. Then I suffered a few bouts of mamma brain and I can no longer remember any of the formulas I used to know. I can only use the maths I actually understood because I have no way of reinventing formulas for the rest of it, so I'm pretty much limited to the four basic operations. And I feel quite pathetic about it. (Yes, I will start relearning maths next year if not sooner. :) ) Rosie Quote Link to comment Share on other sites More sharing options...
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