tag:blogger.com,1999:blog-32744448.post7633610006550811557..comments2023-10-08T06:20:56.637-06:00Comments on Learning and Laptops: A Learning Adventureanneshttp://www.blogger.com/profile/00573450327737964454noreply@blogger.comBlogger269125tag:blogger.com,1999:blog-32744448.post-74558356862828320892008-10-03T13:33:00.000-06:002008-10-03T13:33:00.000-06:00Sorry, I got cut off.What I was trying to say was ...Sorry, I got cut off.<BR/>What I was trying to say was that if the number system was based of the number of fingers we have (you can do 5 for one hand, 10 for both, 8 eith no thumbs, etc.) why would all of these different places have the same way of counting?<BR/>The numbers must have originated from a particular place to be so similar. I think it was greece because they had contact with every civilization and could have spread the system.BernardoT2012https://www.blogger.com/profile/07494728940464981630noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-53204998572216675572008-10-03T09:25:00.000-06:002008-10-03T09:25:00.000-06:00Mr Fisch- A great point about the fingers. In resp...Mr Fisch- A great point about the fingers. In response I have to follow the style of the hitchikers guide to the galaxy.<BR/>If we based the world's most common system of logic and arithmetic on the completely random sequence of DNA that caused our race to develop 10 fingers as opposed to some other random quantity. <BR/>Did we base the world's main system of logical quantities on random DNA that affected us most billions of years ago and could change at any point as far as we know?<BR/>I know it's strange but it' worth considering<BR/><BR/>Gary- You bring up a great point. I took french for a while and I also speak portuguese fluently.<BR/>Both languages (Latin languages in general) use the same basic system for counting.<BR/>0-10 are different words<BR/>11-19 are variations of 1-9<BR/>and 20-99 are combinations of a variation of 1-9 (in the tens place) and the same words for 1-9 used in the first few digits (in the ones place)<BR/>After 100 a similar system continues with variations of the digits 1-9 for the hundreds place.BernardoT2012https://www.blogger.com/profile/07494728940464981630noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-43163655257831020862008-10-01T22:13:00.000-06:002008-10-01T22:13:00.000-06:00hannahl, I've been thinking about your comment for...hannahl, I've been thinking about your comment for a couple of days. I think what Orwell was trying to show with Winston being tortured to believing that 2+2=5 was that the power of the government was absolute, that anything they said was true. It's sad that sometimes maths seems like that.<BR/><BR/>But what we've been talking about here is not demanding that one answer is right, but to explore what other answers might be right. The freedom to question, to ask impertinent questions, to explore unlikely answers is the key to fighting fascist behaviors. It's not about math, per se, it's about opening your mind to the world and seeing possibilities where no one else has before.Sylviahttps://www.blogger.com/profile/07197716318141984888noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-35604643773637102082008-09-26T08:36:00.000-06:002008-09-26T08:36:00.000-06:00I think that math should be required simply for th...I think that math should be required simply for the reason that people are hungry and other large world problems we need those people that know math and science well enough to be able to go and change the world and solve major problems. Also, if you never are forced into math how will you know if you like it or how good you are at it? Just because you don't like something doesn't always mean you're bad at it. And I think that the U.S. needs more world class mathematicians and scientists to solve the world's problems and if noone tries to make it that far then noone ever will.AustinW2012https://www.blogger.com/profile/08837049750703185679noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-75749070941853121472008-09-25T18:45:00.000-06:002008-09-25T18:45:00.000-06:00Mr. Fisch- I really enjoyed your scenario about 2...Mr. Fisch- I really enjoyed your scenario about 2 + 2 = 3. It was creative. I couldn't help but think of the passage in "1984 when Winston is being tortured by O'Brian into believing that 2+2=5, which in this case represented the ability of the government to brain-wash people into believing untrue things. However, I do think the math class is basically pointless past fifth grade unless one plans to go into a field involving math, such as engineering or chemistry. I understand that we must learn simple multiplication/division and other elementary concepts in our day-to-day lives, but for anyone not planning to be a scientist or mathematician, math in no way benefits them in their careers or their lives. Personally, I have no use for it. I plan to be a dancer and an English teacher or novelist. None of this requirest that I know how to form a quadratic equation and graph it. Seriously people, people are starving, genocides are occuring, and people around the world can't afford a roof over their heads, there are more important things to learn than y = 8x + 6. And, the way math is taught in today's schools is corrupt. We take notes, do problems from the book, take a test, and take a final. That is the complete extent of our curriculum in math. No matter how fun the teacher is (I love my math teacher to death) there is no way you can convince me that my time in those classes are well-spent. This doesn't mean students should not do their best every day, but I just think we either need a radical change in the way we teach math, or we need to make it an optional thing at the high school level.hannahlhttps://www.blogger.com/profile/05592505763451118754noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-24422292131417697032008-09-24T16:11:00.000-06:002008-09-24T16:11:00.000-06:00Also a YouTube video of counting to 100 in French....Also a <A HREF="http://www.youtube.com/watch?v=ywIWYKamyCY" REL="nofollow">YouTube video</A> of counting to 100 in French.Karl Fischhttps://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-3083601212739364202008-09-24T16:08:00.000-06:002008-09-24T16:08:00.000-06:00Gary: Wow. I am glad you mentioned that to me, bec...Gary: Wow. I am glad you mentioned that to me, because frankly I had no idea that's how it worked. For the rest, <A HREF="http://french.about.com/library/begin/bl_numbers.htm" REL="nofollow">here is what I found.</A> (Look where it says "notes.")<BR/><BR/>I suspect that a system like that evolves out of colloquialisms, and possibly a cultural tendency to break relatively common numbers up into more manageable chunks.<BR/><BR/>In response to Mr. Fisch, I think that we would probably count in base 12 (or 24 or 6) if we had 12 fingers. And we might be better for it. Doing a little <A HREF="http://en.wikipedia.org/wiki/Numeral_system" REL="nofollow">more research</A> after this topic initially got me thinking, I found that base 12 has been put in place, somewhat artificially, because it is easier to break into parts.BenHhttps://www.blogger.com/profile/14962067325143948683noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-53072793326733397562008-09-24T09:02:00.000-06:002008-09-24T09:02:00.000-06:00So, if it's because we have 10 fingers, then there...So, if it's because we have 10 fingers, then there's nothing magical about base 10. If humans happened to have 12 fingers, do you think we might be using base 12?<BR/><BR/>(Except, of course, we'd still write it as 10 if we had developed the same naming conventions, we'd just have a new single digit symbol for our current 10 and 11, much like hexadecimal - base 16 - uses A for 10, B for 11, etc.)Karl Fischhttps://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-28887882533824054872008-09-24T08:53:00.000-06:002008-09-24T08:53:00.000-06:00Ben,Check out how one counts to 100 in French.Ben,<BR/><BR/>Check out how one counts to 100 in French.Garyhttps://www.blogger.com/profile/16005284607047954745noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-82791861167372008222008-09-24T08:02:00.000-06:002008-09-24T08:02:00.000-06:00I'll take a shot at why we use base 10. We have 10...I'll take a shot at why we use base 10. We have 10 fingers. It is natural to start "regrouping" when you run out of fingers to count on.<BR/><BR/>Similar variations have been used by the majority of cultures throughout history. The Maya used 20 (fingers and toes), many cultures used 5 (one hand), and some used 8 (no thumbs). The Sumerians used base 60. I have no idea what they were thinking. I'm just glad we moved past that.BenHhttps://www.blogger.com/profile/14962067325143948683noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-77695074043901296542008-09-23T08:57:00.000-06:002008-09-23T08:57:00.000-06:00Mr. Fisch – From the quotes, I drew that the answe...Mr. Fisch – From the quotes, I drew that the answer isn’t really what matters in a problem (whether it be mathematics or not), it’s how the answer was found. From the quote, “One can always reason with reason.” One can always think of another comeback for what someone else says. People have different opinions; in math, the reasoning people have for their answers, anyone can come back and have a different reasoning to contradict. Different people understand mathematics in different ways.chelseac2012https://www.blogger.com/profile/03781011097442911273noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-47573113890438821342008-09-23T08:39:00.000-06:002008-09-23T08:39:00.000-06:00Mr. Zack Allen-I think you pose a wonderful questi...Mr. Zack Allen-<BR/>I think you pose a wonderful question! Of course, that is a wonderful way to look at things. I think I know what you may be talking about. In simple terms, here is what I think you mean:<BR/>Answer : 4<BR/>Equations: 2+2, 2X2, 6-2, 10x0.4, And many other equations. Thank you for the great opportunity to look at things a completely different way!<BR/>And, for you second question, no I don't believe that the answer has to be a whole number. I think the others' examples with whole numbers was purely because it is an easier way to start understanding these "there is more than one answer" problems. I believe there are zillions (not a real number, I know!) of answers to the simple question, 2+2.<BR/>Again, thanks!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-32744448.post-42584019340481546242008-09-22T21:55:00.000-06:002008-09-22T21:55:00.000-06:00Mr. Fisch has done an excellent job of getting eve...Mr. Fisch has done an excellent job of getting everyone to start thinking about critical numeracy. There is a saying "numbers don't lie", or do they? There is another saying "50% of all statistics are made up on the spot." You can twist numbers to say what ever you want them to. Being able to critically think about numbers and statistics is an important life skill.<BR/><BR/>Instead of chiming in with another answer to the 2 + 2 problem, I will pose a thought. Maybe what you think of as the question is the answer, and what you are really trying to figure out is "what is the question." 2 + 2 is only one side of the equation. Does the "answer" on the right side of the equals sign have to be a whole number?Zack Allenhttps://www.blogger.com/profile/14081110560172261887noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-34669717033885293052008-09-22T20:29:00.000-06:002008-09-22T20:29:00.000-06:00We learn mathematics not only so we can learn numb...We learn mathematics not only so we can learn numbers and how they work, but to understand life and how to work with it to come up with what is perceived to be the best solution to each of the decisions we make. With each new decision there becomes a new problem and with each correct answer we get the clearer everything becomes. For an example if someone were to ask if you wanted a cigarette and you said, “No thanks I would rather not.” Then your path becomes clearer and you would know that you have a better chance of not having lung cancer compared to someone who would have said yes to the person who had offered them the cigarette.<BR/>I also agree with Justin when it comes to the 2+2= D) all of the above.sammiet2012https://www.blogger.com/profile/03808818914310688912noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-79777579754018652792008-09-22T19:45:00.000-06:002008-09-22T19:45:00.000-06:00Hey everyone,It looks like you have a nice convers...Hey everyone,<BR/>It looks like you have a nice conversation going about Macbeth and all but I got lost when the whole 2+ 2 thing came into the conversaition. Anyhow, hope that you enjoy Macbeth with Mrs. Smith!Anonymoushttps://www.blogger.com/profile/12756426265527503133noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-70296267327100949942008-09-22T18:56:00.000-06:002008-09-22T18:56:00.000-06:00@kailynw2012 - thanks for taking a shot at why we ...@kailynw2012 - thanks for taking a shot at why we use base 10. The digits 0 through 9 certainly add up to 10 digits, but only in base 10. Kind of a circular explanation, there. If we used base 6, we'd have 10 digits as well (stay with me here, 10 in base 6 is the same as 6 in base 10), 0 through 5, so that argument would hold up just as well.Karl Fischhttps://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-58925594201310216682008-09-22T18:52:00.000-06:002008-09-22T18:52:00.000-06:00@chelseac2012 - very interesting quotes. When you ...@chelseac2012 - very interesting quotes. When you put them all together, what does that tell you about mathematics?Karl Fischhttps://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-72831864875374374182008-09-22T18:51:00.000-06:002008-09-22T18:51:00.000-06:00More food for thought from early 2007.More <A HREF="http://thefischbowl.blogspot.com/2007/02/formula-for-success.html" REL="nofollow">food for thought</A> from early 2007.Karl Fischhttps://www.blogger.com/profile/11121548023409279686noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-22390604735476819352008-09-22T17:37:00.000-06:002008-09-22T17:37:00.000-06:00Karl,To answer this question I think that I must d...Karl,<BR/><BR/>To answer this question I think that I must define what mathematics means to me first. I believe that mathematics is many different methods for solving multiple problems. We are some information and are expected to fill in the gaps to find the answer. So to answer the question why we learn mathematics, I think that it is not just for the obvious reasons like being able to add and subtract number for we which we learn math. Furthermore, I do not even think that it is really about the numbers at all. It is just practice solving problems in a myriad of different ways; for example, global warming!AllisonM2012https://www.blogger.com/profile/02263156636607706085noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-29597176410005026282008-09-22T15:43:00.000-06:002008-09-22T15:43:00.000-06:00I was thinking more on the topic of mathematics an...I was thinking more on the topic of mathematics and thought I would look up some quotes… Also, I thought that I may get a better understanding of how 2+2 has more answers than just 4. This is what I found (note: I did not put my interpretations of all the quotes, only a few):<BR/>Aristotle – “To Thales the primary question was not what do we know, but how do we know it.” It doesn’t matter so much as what the answer is, it matters how the answer was found.<BR/>Aristotle – “We cannot ... prove geometrical truths by arithmetic.”<BR/>Heri Bergson – “One can always reason with reason.”<BR/>George Cantor – “The essence of mathematics is its freedom.” There are many different ways for math to be understood.<BR/>George Cantor – “In mathematics the art of proposing a question must be held of higher value than solving it.”chelseac2012https://www.blogger.com/profile/03781011097442911273noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-66252927239581382422008-09-22T13:05:00.001-06:002008-09-22T13:05:00.001-06:00Karl, You make us lean mathematics because learnin...Karl,<BR/> You make us lean mathematics because learning is a necessary experience, learning mathematics gives students experience learning. The better you can learn the more successful you will be in life. The only real job teachers have is to prepare their students for life outside of school and being a great learner is the key to doing well outside of school.Zivenc2012https://www.blogger.com/profile/07993175265974847782noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-78913710997746150812008-09-22T13:05:00.000-06:002008-09-22T13:05:00.000-06:00Anna, I thought that math was an abbreviation for ...Anna, I thought that math was an abbreviation for mathematics,I don't think there is a difference!kailynw2012https://www.blogger.com/profile/08482719947306738508noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-22006676135514174342008-09-22T13:04:00.002-06:002008-09-22T13:04:00.002-06:00In preschool and elementary we learn the the bacic...In preschool and elementary we learn the the bacics of addition, subtraction and mltiplication. However, we miss the real ideas and "philosophies" if you please. Mathematics reach far ther than these simple equation and problems of additon but having the ideas that you learn, being applicable to the situations that you encounter in every day life. I know I sound redundant, since I sort of said this in my previous comment but its not just arithmetic but the prinicples you learn. This is so different for me to explain because I never really have thought deeper into this than just the surface of the things I learn in school. Most of my teachers through my education have always bipassed the real fundamentals of it. I felt like they just focused on the grade you got at the end of the semester. Back to mathematics, to be totally honeset, I'm not completely sure. Basically in the simpliest terms I can say is that its learning how to learn and teach your self ideas and new ways to solve the problems that arise.lsadler2012https://www.blogger.com/profile/02527622504779757267noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-2090772448796894752008-09-22T13:04:00.001-06:002008-09-22T13:04:00.001-06:00I agree with bridget. There is always a way to mak...I agree with bridget. There is always a way to make something what you want. I'm only in geometry myself but there is always some underlying foundation of the problem that can be altered to pu must first alter the foundation.roduce the desired answer. If you want to cange the shape of a building then yokelseyc2012https://www.blogger.com/profile/05404260920455905469noreply@blogger.comtag:blogger.com,1999:blog-32744448.post-24052677831045709072008-09-22T13:04:00.000-06:002008-09-22T13:04:00.000-06:00I agree with Bridget. Depending on the type of thi...I agree with Bridget. Depending on the type of thinker the person is they can agree or disagree with any answers and have perfectly good support for their answer too. One answer may make more sense to someone, but that doesn't mean the others are wrong or even right. Who knows, this could go on forever.katiez2012https://www.blogger.com/profile/16025966907226976716noreply@blogger.com