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...
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