We had a big argument in the classroom today (kindergarten/First Grade) It started by saying that a person couldn’t be less than 1 year old because they couldn't be 0. I asked a student about her dog who is 6 months. Some of the kids figured out that 6 months is 1/2 way between birth and 1 year. Others were stuck on the idea that when you were born you were 1-year old- they didn’t get that the 1st birthday signified 1 year of life. So we talked to Mrs. Nelson about her baby, when he was born, how old he is now and when he will be 1. Eventually everyone pretty much accepted that you are not 1 year old when you are born and that you are officially 1 when you have been alive for a year ( I didn’t mention some cultures start counting life from conception so they actually turn 1 aprox 3 months after being born - We had enough problems already!). Anyway…at that point I was feeling like we could move on with life but I was oh-so wrong........The next issue to arise was: "0" is not a number. I was thinking that 0 represents an amount, an amount of nothing but it does signify that there is nothing there and either side of 0 is a number representing positive or negative units of measure. Several students who go to another teacher for math insisted that Zero is nothing and since it is nothing it is not a number. They told me "Mrs. Linevitch says 0 is not a number". I told the kids I wasn’t sure and we could gather information and try to figure this out. I went on line because there is sooooooo much I don’t know about math and found a lot of contradicting information. I need help! Is Zero a number? Why do some sources say yes and others no? I have polled staff around the building and have found some believe 0 is a number while others do not. I am so confused - has my belief in 0 as a number been wrong all my life? Help!
Rebecca
Rebecca
11 comments:
Hhmm this is great!!!
But, if zero is not representing a symbol for a number, then what symbol are we going to use to write after the 1, 2, 3, for: ten, twenty, thirth, etc.????? I wonder what the Arabic, Chinese, Japanese, and any other symbol is for zero in the different languages that are not using the same number we do? I will ask my Chinese friend Monday when I see her, what the symbol for zero is in Chinese and how she writes ten, twenty, thirty, and so on in Chinese.
Thanks for posting Rebecca's reflections, Peg.
Zero. Well, you are correct Rebecca... in that there are differences of opinion out there on whether or not it is a number. But, in the end I agree with the camp that calls it a number. What is a number after all? It speaks of quantity... how many. What does zero speak of? It is still addressing the question of how many (quantity). Granted, it is a special quantity with some distinct properties. But consider a square... it also has properties that make it distinct... but that doesn't make it 'not a rectangle'. This is a bit simplistic, but it makes sense to me. Some will argue that, since infinity is not a number neither is zero. That doesn't make sense to me since infinity is not a specific quantity (more like a concept) while zero is a very specific quantity.
In the end, as much as it is interesting to contemplate the idea of zero, by far the most interesting part in my mind is simply engaging in the debate itself. The fact that zero has lit a spark in your imagination and been the catalyst for so much mathematical dialogue here, among your colleagues and in your classroom is the most fascinating part!
Suppose we engaged in the same kind of dialogue about whether the marks we make are really the math at all... if we all contemplated that idea... imagine what changes might take place!
Thank you for your inspiration.
Well, I gave my friend a "hundred chart" so she can fill in the numbers in Chinese. When I asked her the questions about whther or not zero is a number, she said yes at first, then she said well, maybe it is not. Now she is not sure what to say and she will call her friends in Taiwan and discuss this with them!!
Talking about sparking a debate, now it is going all the way to Taiwan!!!
You have started an avalanche of mangoes!! Or perhaps, children (and adults) tasting a bite or two. We start our day with announcements from our principal and frequently a question to ponder (usually math-related). So after reading the blog, I thought I'd ask our school the question "Is zero a number? Why?" Throughout the day, Marianne, Deb B. and I have received visitors bearing explanations, and notes delivered to our mailboxes from whole classes. Most said zero was a number. Some explanations were:
Yes, because . . .
. . . zero is on a calculator, number grid, and a thermometer. (The word number was underlined as if to say "hello, is this a trick question?")
. . . because me and Sam found it in the dictionary and it had a definition!
. . . without zero nine would be the highest number you could get to.
. . . if the number was 10, without the zero the number would only be worth 1.
. . . negatives are numbers and they are lower than zero. Positives are numbers and they're higher than zero. So there wouldn't be a thing that isn't a number between them. Also, if zero wasn't a number, what would it be?
. . . if there was no 0, we would not have numbers like 50, 60, etc. Also if there was no 0, there would be no negative numbers.
. . . if you say there is 5 bikes and 5 are stolen, there would be zero bikes left.
No, because . . .
. . . zero is nothing.
. . . it's just a place holder for negative and positive numbers.
I also was approached by some of my colleagues wanting to know the answer. I think the above show this debate is far from over. More, it's just the beginning for some. A fellow teacher brought me her classes thoughts and said, "They really got into this question. I wish I'd done more like this this year. So tomorrow, I'm thinking of introducing Maggie's comment about quantity and how it relates to zero. Too fun!
That's exactly what I said at the beginning......without the zero there would not be 10, 20 etc.
Today when I asked my Read 180 students, one of them said that IF it is not a number how come we can see it??? He went further by TELLING me that if it is not a number then it must be the letter O.......now we are getting deeper here.
One of my Asian students, I believe she is Vietnamese, said that a zero in her country has a line in the middle because it means that we don't have anything, in terms of things!! You should have seen her face, because she felt so superior to have offered this piece of information!!!
However, I didn't know how to respond to that:)
Yes, you are right Karen, there wouldn't be that zero on the thermometers and the number lines.
So can we safely say that it is a number? Well, time will tell......
Maybe another word will bring some peace to this debate.
Can we say that zero is a number, but it has no value?
I use the word value as in no quantity, not to imply it has no use.
PERFECT DAVE!!!
When I introduced the number line in Grade One, a few years ago, we used a flag to indicate the start of the number line. You had to go one unit to get to the one on the number line. We also had a scroll sign to indicate that some of a number line was missing if the number line didn't start at the flag (or the zero).
The following comment was posted to me via email by Susie Guerra who is having blogging trouble.
Over to Susie...
Hi, I have tried to blog all week but have "0" capacity for remembering passwords! I am sending you my blog in hopes that you have secret powers to unlock the blog and find out what my password is...my thoughts on zero are this: I think that zero is a representation of a concept of nothing, and we all know that there is such a thing a nothing, and first graders will tell you what nothing is when they don't get a piece of the treat being shared or when there are no more legos to play with. Numbers are just symbols for the concept, right, so for teaching purposes at first and second grade levels I think it's ok to call zero a number. When our minds begin to think more abstractly then we can debate the idea!
This comment comes from Gay Sampson on Tuesday, June 9, 2009. She has asked me to post it for her as she is having blogging trouble. Over to Gay...
Zero - # or Not
After seeing Maggie's e-mail and the controversy about whether zero is a # or not. I thought I would blog first and then go back to read the other blogs. This is a very interesting topic. My first thought is that zero is a # because if we didn't have 0 we couldn't have tens, hundreds, and thousands, etc.
Lisa Parsons, Deb Smith and I had a conversation about the definition of a number " a sum of units" and came up with the same conclusion. Zero is a number.
Posted by Gay ResRm K-2(Lisa Parson's and
Deb Smith) at 5:09 PM
I tried to post this days ago, but Blog wouldn't let me in...today it will...
I also presented this question to my 7th and 8th graders. The fact that it was related to "my homework" intrigued them even more than the concept itself. The overwhelming majority of them believed that 0 is a number. They enjoyed trying to prove it...
"The dictionary gives it a definition '1. The cardinal number of the empty set, 2. the number that is one less than 1' so it must be a number"
"If we didn't have zero, we couldn't have 10, 20, 30 and so on, so it must be a number."
And my favorite...
"It stands for a quantity of something, so it's a number. For example, Mrs. Thatcher has $0 in her bank account!" (Not far from the truth!)
Only 1 (out of 10) student claimed that zero was not a number, but he was not able to provide any reasoning behind his belief, "It just isn't."
I had never really thought about this concept before. I always assumed 0 was a number. The idea that maybe it wasn't never crossed my mind. The discussions that this concept opened in my classroom were an enjoyable way to wrap up the year. As we left today (for the last time this school year), one student came up and said, "So, what's the answer?" I had to ask what she was referring to. "Zero. Is it a number or isn't it?" I told her she had the entire summer to think about it. She could come back in the fall to let me know what she had decided.
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