A number by any other (non-English or non-French) name would make more sense.
The symbols of mathematics, like the notes of music, are in themselves merely an artificial, intrinsically meaningless script. They will convey life, meaning, richness of thought and beauty only if the ideas and the thinking which the symbols merely record are taught with as little use of symbolism as possible.
—Morris Kline
Put the above quote into your own words. Do you agree or disagree with Kline? Why?
The author of this week’s reading held in high regard the Chinese language for how well it conveys the base 10 numeration system, and also for its simplicity when spoken. While I didn’t take the time to listen to all the numbers, I got the idea after listening to 1-10 and 11-20 of Learn to count to 100 in Chinese (with Flash movies).
Last summer I attended a workshop for teachers who teach future elementary teachers. The workshop leader informed us that his wife, an elementary teacher, teaches her students to say “tenty-one” for eleven, “tenty-two” for twelve, etc. While such practices have not gained widespread popularity in the English-speaking world, they are gaining ground.
After reading this week’s required reading, let’s say you are ready to hop on the “We desperately need to change our language” wagon, will you advocate the use of “tenty-one,” or “onety-one” for eleven? How come?
I think I would advocate the onety-one because in the english language eleven is 11 and the onety-one makes more sense then tenty-one. tenty-one sounds more like 21 than 11.
Tiffany Segers
February 6, 2008
Onety-one seems better to me beacuse there are two 1s in eleven.
Tiffany Segers
February 6, 2008
I would have to say that the quote is saying that the math or just simply the numbers that we use today, do not mean anything to the “naked” eye. In other words if you are looking at our numbers or our math for the first time ever, then it is not going to make sense to you.
I think that I would have to fight what ever they were trying to change because they way that we know it now is all that I am acustom to and I am not sure if I could learn it another way. Although, it would be like learning a new language…it would be tough at first but the more we practice it the more we could get use to it.
tls1995
February 6, 2008
I’m not exactly sure what the quote is trying to say, therefore, I dont know wether to agree or disagree. I don’t think symbols are meaningless at all, actually I find them very useful!
I dont think I would be hopping on any “change our language wagon!” Absolutely not! Tenty-one for eleven , tenty-two for twelve…this seems like it would cause more confusion. I dont see the need in changing the way we teach our children numbers. I’m not sure If I had to chose one, which one I would chose. I’m not a fan of either.
rmt06
February 7, 2008
To me Kline is saying that you can use any symbols for the numbers of mathematics but it needs to be put simply, in a way that can be understood, don’t confuse it with so many things. Basically make it short and sweet.
I agree with Tiffany when she said that tenty-one sounds too much like 21 and I think that students might get easily be confused. However, it makes sense if you are teaching them to think 12 is 10+2 and when breaking 12 up to think ” tenty-two.
In the related text that you had us read, I was amazed at the students who used different body parts to count. While I can understand why they would do that ( 1-1) I think it would totally confuse me. It just goes to show we all learn differently and what works for some may not work for others.
mom22boys
February 7, 2008
The quote by Morris Kline is very true. She is saying that math is just a set of numbers and symbols. You have to put a meaning behind them. Just like a person who doesn’t know how to read music. If that person looked at the notes they would not know the music. Just like a child who hasn’t been introduced to math, or a person from a foreign country. Math is what we make it.
I would not change the way we count. It would be a long and tedious conversion. Just look at how long we have been trying to convert to the metric system. People don’t want to change. Changing the way we count would have to start off extremely gradual. Students would encounter problems later on. They would have to know both ways to count.
One thing I thought was interesting about this article was the origin of Roman Numerals. A shepherd would carve “v” and “x” to count. They did this because it was easier than carving a straight line in the wood. If anyone has ever tried to carve their initials into a tree they would know this is true!
Brandi Harbour
February 8, 2008
I truly don’t understand, but if I have to learn this I would. It would take a lot of practice. If this was something my children brought home we would all be learning it together.
cmh022007
February 9, 2008
I’m really not sure what this quote is saying. But if I had to learn how to count like they did it would be really hard at first but after a while I would eventually understand it. I agree with Tiffany that tenty-one does sound a lot like twenty one. It might confused people easily.
njd2005
February 9, 2008
I believe that Kline is saying that symbols are just synthetic. I believe that symbols are a genuine way to teach children.Just like if they see a Golden Arch when going through a town they can associate it with McDonalds,food.I used this because it is something kids enjoy and most are familiar with.I liked to use things in the environment to help my children understand.I don’t think I would ever change our language it would be a headache to convert over to another language already knowing one for so long as an adult. But we all learn in different ways and speeds so others might can do it.
Courtney Pollard
February 12, 2008
I also think that symbols are umportant, and that numbers without some type of meaning behind them would be meaningless. Just like a person who does not know spanish beign told to read a spanish book, the words mean nothing to them until they are taught the meaning of each word and letter. Math is the same way. I agree that changing our language would be very confusing and that we should continue to say twelve and not tenty-one, words such as those would be to easily confused.
Kendra
February 12, 2008
I think that Kline is saying that unless you have been taught the symbols for a number or the notes in music, when you look at them it would mean nothing. However, after being taught those concepts, it helps our lives make more sense.
I can see that changing to a simpler numerical system might eventually have great value in our society, but the problems that it would cause now would be enormous. I am satisfied with the way we teach our children now, and have no desire to change that.
Kelley Hale
February 13, 2008
I’m not really sure what quote is saying so I don’t really think I can agree or disagree with it. As far as learning a new language I don’t think that we as a society would change. Ever heard the comment “can’t teach a old dog new tricks”? I think this applies to many people, myself included, when it comes to even learning Spanish.
Hollie Mullins
February 13, 2008
I think Morris Kline is saying that the symbols we use in math is just symbols. The difference we need to make, as future teachers, is to give meaning to those symbols. If we ask “why” and “how”, then students will begin to understand math more than they would have with only symbols. I agree with his quote.
I would choose Onety-one because it makes more sense to me, since the numeral 11 is made up of a one and a one.
Angel Cabe
February 14, 2008
I think that now, after learning the rules of eleven through nine teen, it would be strange and complicated to learn the set as onety-one…onety-two. But if you think of it in terms of before having the knowledge, to learn onety-one just as you do ninety-one, it makes sense. One in the first place one in the second, Nine in the first place, one in second. Seems that it would be more simple than learning eleven!
xanneb
February 14, 2008
For the quote I think he is saying that all symbols of mathematics are just that symbols. If we do not teach the full meaning, and the students understand the meaning, all they will ever see are the symbols. If we as teachers can help the students understand, they will see the mathematics and understand.
I myself do not agree with changing the way the number system is taught until it is world wide and agreed upon by everyone. If we as teachers are teaching “tenty-one,” or “onety-one” to students and this has not been expressed away from school, any and all adults not associated with the school will think the students are not learning all information correctly.
hughes6871
September 10, 2008
Quote- Without understanding math you only see a bunch of number and symbols. It is like looking at a foreign language for the first time. In order to understand math you have to be able to make a connection with it and the world around you. This takes gaining experience of using and mastering concepts. Math is like a puzzle and the concepts put it all together. By learning one concept you open the door to another and build on the knowledge you are retaining. Once you learn the basic of mathematics, you begin to understand the relationship between numbers and how they work together.
If I had to choose to change our mathematical language I would pick the “tenty-one” method. Children have of way of seeing patterns and grouping things together. I think using the word “tenty” would help them to visualize a block of ten. This would automatically make a connection with the tens place. The only part that they would have to add is the ones places. If we changed to the “onety-one” method, I think children would only see symbols. They would just see that it takes two number ones to make eleven, just like our system now. I also think it would be difficult to remember and consider that onety actually represents ten ones. The word “onety” seems like it would not make a clear connection with the tens place.
burns18286
September 10, 2008
Because the symbols of mathematics are like the notes of music, they are merely meaningless to us. These symbols merely are a record. They are made to convey life, meaning, richness of thought, and beauty only when they are taught with as little symbolism as possible.
I do not agree with Kline. I believe that our symbols are very important to us. How would we understand anything if we did not have our symbols? If all we ever used were letters, how would we be able to count? We would not have a way to do so. There would be no need for money as we know it. It would be completely different. I believe that it needs to be taught with symbolism. Otherwise, we would be teaching our students nothing.
If I had a choice, I would not change the way we say our numbers or words. I believe that this would be very confusing to young students. I would not want them to go through learning the way we have always said it, to changing to a new way to say the word. I do not believe that it would be good for the students.
deedowdy
September 10, 2008
The saying “You can’t teach an old dog new tricks” certainly comes to mind as I read these articles and responses. I did see more of a possibility of onety-one being 11 than tenty-one. Onety-one just “looks” more like 11 to me. In my opinion, it would be too easily confused with twenty-one and twenty-two if the terms tenty-one and tenty-two became the new words. I believe that the idea of the Chinese having shorter words for their numbers is an interesting point. I don’t think that the country is ready for a complete change in our number words, but gradually done, it might work.
lockhart8292
September 11, 2008
Kline’s comment, to me, is basically saying that our number system would be “Greek” to someone who used a different system for counting. If it were not used in everyday communication we would not know what each symbol (1,2,3,4,etc.) meant. Other countries have different terminologies for their number systems, but if that is the environment you were raised in or had to live in, you would learn that terminology to shop, order food, and pay for purchases. Our numbers are just symbols that we have learned to associate with different activities to live more completely.
If I had to choose between “tenty-one” and “onety-one” as a new number for eleven, I might chose “onety-one” for the natural transition of eleven consisting of 1 and 1. On the other hand, “tenty-one” also makes sense because of the place value of 1 ten and 1 one being eleven. Either way, it would take at least one generation to have the new number incorporated into our math. I know from my own perspective that it has taken the last 20 or so years to find a symbolence of comfort using the metric system. When I went to school as a young child, I was taught the “standard” feet-inches, ounces-gallon, ounces-pound, and feet-yard-mile measurements.By the time I started college, liter bottles of soda started showing up in grocery stores. Needless to say it took some time to transition. Any change will take time and effort from the entire country to change a number in an already established numerical system.
weaver17536
September 13, 2008
I believe that what Kline is trying to say is that without knowing the meaning of the symbols for things such as numbers in mathematics and notes of music then the symbols are useless. I think that what he is also trying to say is that symbols have a meaning, but the symbols need to be taught as little as possible, and the meaning stressed more than ever. Teachers need to start associating a meaning or a value with a symbol. To many times than none, young children can count from 1 to 10 and write the numbers 1 through 10, but do they really know the values of the symbol? Honesty, I do not know which phrase I would use if I had to advocate the use of one of the above. I would probably advocate the use of “onety-one” for eleven and then as the students became familiar with this phrase, I would introduce “tenty-one” as also having the value of eleven. I just think that having a student say “tenty-one” is too close to our “twenty-one” and would cause mass confusion. However, tenty-one does make more sense when dealing with the base ten method, because children can associate the “ten” in “tenty” with a group of tens or the tens place. I do not think that onety-one makes near as much sense as tenty-one for eleven, but I would still use onety-one to prevent confusion. In a way onety-one makes sense, because onety-one, is 1 then 1, or 11 and so forth and so on. But with this method just the symbols are being stressed and not so much the value as seen with the tens.
I also agree with hughes6871. I don’t think that we should change our number language until it is agreed upon worldwide and students can see it outside of school. Because isn’t this where children’s number sense comes from in the first place?
sam5712
September 28, 2008
I do think that if we did not know what the numbers were we would be lost, but we do use them in everyday life. It is our job as teachers to incorporate it into our students lives so they understand that 1 is 1 and not anything else. I think if I were just now looking at 11 I would probably call it onety one based on it coming after ten. When I went to school I also learned using feet, inches, tsp, etc. Now in college we use milligrams and meters. It is a big change, but once you learn what these units are you can use it as well as what you already know.
pearce4471
October 10, 2008
I interpret Kline’s quote as meaning symbols are necessary, but in order for them to be effective, they need to be as simple as possible or else the message is lost.
I am reminded of a term that I was recently introduced to in one of my classes; Ockham’s razor, a rule interpreted to mean that the simplest of two or more competing theories is preferable and that an explanation for unknown phenomena should first be attempted in terms of what is already known.
Sometimes simple is better, and initiating something new is not always an improvement. The field of mathematics is an example of such a time. How is a parent expected to be involved in his or her child’s schoolwork when the child is taught a completely new language of mathematics; it’s hard enough as it is.
sefrancis
October 19, 2008