Students really do say the funniest things. Here is a record of some comments, conversations, etc from the first semester. Enjoy!
**Me: If your swearing becomes habitual, then you will have to stay after school [instead of doing pushups].
Student: Does habitual count?
**Me: You’ll probably break that (using a badminton racket with a volleyball)
Student: If you break it, we won’t tell. Just bury it.
**Teacher 1: You need a sphere (best item for projectile motion)
Teacher 2: We could make spears!
**Student: Sometimes I feel like I’m too smart.
**Student: I’m not checking you out. I’m finding your derivative.
**Me: I can’t say the letter r.
Student: That explains why you sound like a pirate.
**Student: Do you know why it’s (the graphing calculator) trying to teach me French?
**Student: If you use big words like constitutes, it makes it seem like you use the word-a-day toilet paper.
**Student: What is this unidentified object on my [calculator] screen?
**Student: Can we turn the air off? [I’m freezing.]
Me: That’s the heat.
**Student: We pompous calc students should do great on the *pre-calc test
**Student: Is this the ruler ______ chewed on?
Me: Yes, but he hasn’t chewed on it this week.
Thursday, December 22, 2011
Friday, November 11, 2011
Is math invented or discovered?
I had my students write their initial thoughts on the question: Is mathematics invented or discovered? Then they had to read a few people's opinions, discuss their ideas with the class, and then write down their final thoughts. Here are three student responses:
I believe that mathematics is a combination of both discovery and invention. As Dr.Mellendorf had stated, “What was discovered was how to mold the model to fit reality. What was invented was the model itself.” It was discovered how to use mathematics. Yet, the processes and whatnot were invented. As Einstein once questioned, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” Even Einstein believed that there had to be some for of math on the earth before we invented the process of mathematics.
The use of mathematics has been there since the beginning of time. However, it took human thought to develop forms of mathematics. For centuries, our world was using math without knowing what exactly it was called. People have always used forms of addition and subtraction without knowing the technical terms. Math hadn’t come out of thin air, it was discovered. We had just invented the processes and technical terms for the different areas of math. All in all, math has been on the earth since the day it was created. It just took humans some time to pinpoint exactly what mathematics was.
People say that it is there to be discovered, that if it was only invented
anyone could come out and say that 2+2=4. They say that math is there for us to discover. But yet
there are people out there that say math is invented, made by us, that math was not there before
humans. I am somewhere in between the two viewpoints on this topic. I believe that math has
always been there, created by God along with everything else to make the universe go round. I
believe that Newton discovered gravity, he did not invent it. But, I believe that we invented the
system, or the language, that we use to interpret mathematics, but not the “math behind the
math”. Take Newton and Leibnitz for example. Both discovered calculus around the same time,
yet when you look at their theorems, they have many different notations and ways of expressing
the same thing. The calculus they both discovered is the same thing, but they invented different
ways of interpreting it. It would be next to impossible for men who have virtually no way of
communicating to both invent the same thing around the same time. Say the great mathematicians
of old had decided that 1 was really 2 and 2 was really three. Wouldn’t that mean 2+2 would equal
3 when there were really only 2 objects there? (If we were adding objects) Theoretically if the
mathematicians wanted everything to equal tree, then our notation would be different types of
trees, but it would mean the same thing as what we have today. After reading Eugene Vigner’s
quote that said mathematics is a gift, when you think about it, it really is. Mathematics, along with
everything, is a gift from God, therefore not invented, but discovered.
I think that it is both. I believe that the actual concept of math was invented, but I would say that the inner workings of it must be discovered. I’m assuming that people first started to use math in order to make building and other such tasks less difficult, so like discovering fire, it made our lives easier. It’s a tool. Although on the other hand, mathematicians today are still looking to divulge themselves into deeper knowledge of the subject. A prime example of how parts of math have been discovered is Calculus. Regardless of whether or not it was Leibnitz or Newton who discovered it, the fact remains the same; Calculus was discovered. It’s these new discoveries that expand our knowledge of mathematic world.
- Later on, we found that what made this so difficult to answer was the definition of “Math.” After a lot of discussing, we came to the conclusion that math can be defined as both the language of math, and how we use it / describe it, as well as the actual math itself. The actual math itself can be described as the truths and the fact that everything fits and how it works, which is discovered. The part that’s invented is the language of math.
I believe that mathematics is a combination of both discovery and invention. As Dr.Mellendorf had stated, “What was discovered was how to mold the model to fit reality. What was invented was the model itself.” It was discovered how to use mathematics. Yet, the processes and whatnot were invented. As Einstein once questioned, “How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?” Even Einstein believed that there had to be some for of math on the earth before we invented the process of mathematics.
The use of mathematics has been there since the beginning of time. However, it took human thought to develop forms of mathematics. For centuries, our world was using math without knowing what exactly it was called. People have always used forms of addition and subtraction without knowing the technical terms. Math hadn’t come out of thin air, it was discovered. We had just invented the processes and technical terms for the different areas of math. All in all, math has been on the earth since the day it was created. It just took humans some time to pinpoint exactly what mathematics was.
People say that it is there to be discovered, that if it was only invented
anyone could come out and say that 2+2=4. They say that math is there for us to discover. But yet
there are people out there that say math is invented, made by us, that math was not there before
humans. I am somewhere in between the two viewpoints on this topic. I believe that math has
always been there, created by God along with everything else to make the universe go round. I
believe that Newton discovered gravity, he did not invent it. But, I believe that we invented the
system, or the language, that we use to interpret mathematics, but not the “math behind the
math”. Take Newton and Leibnitz for example. Both discovered calculus around the same time,
yet when you look at their theorems, they have many different notations and ways of expressing
the same thing. The calculus they both discovered is the same thing, but they invented different
ways of interpreting it. It would be next to impossible for men who have virtually no way of
communicating to both invent the same thing around the same time. Say the great mathematicians
of old had decided that 1 was really 2 and 2 was really three. Wouldn’t that mean 2+2 would equal
3 when there were really only 2 objects there? (If we were adding objects) Theoretically if the
mathematicians wanted everything to equal tree, then our notation would be different types of
trees, but it would mean the same thing as what we have today. After reading Eugene Vigner’s
quote that said mathematics is a gift, when you think about it, it really is. Mathematics, along with
everything, is a gift from God, therefore not invented, but discovered.
I think that it is both. I believe that the actual concept of math was invented, but I would say that the inner workings of it must be discovered. I’m assuming that people first started to use math in order to make building and other such tasks less difficult, so like discovering fire, it made our lives easier. It’s a tool. Although on the other hand, mathematicians today are still looking to divulge themselves into deeper knowledge of the subject. A prime example of how parts of math have been discovered is Calculus. Regardless of whether or not it was Leibnitz or Newton who discovered it, the fact remains the same; Calculus was discovered. It’s these new discoveries that expand our knowledge of mathematic world.
- Later on, we found that what made this so difficult to answer was the definition of “Math.” After a lot of discussing, we came to the conclusion that math can be defined as both the language of math, and how we use it / describe it, as well as the actual math itself. The actual math itself can be described as the truths and the fact that everything fits and how it works, which is discovered. The part that’s invented is the language of math.
Tuesday, September 27, 2011
rough notes on interest rates, loans, etc
If you teach math, perhaps your students ask this: When will I ever need this in "real life?"*
We have been studying exponential growth and decay, and I was just waiting for this question. The past few days we have looked at car depreciation and why that is a big deal in "real life," but I wanted to take it up a notch.
Here are the rough notes for a project I am going to do with my advanced math students. I worked with my brother who is in the financial industry to help me design it. I still don't know how I am going to have the kids present what they learned to me. Perhaps I will do interviews, have them make a recording, or write a paper.
Project:
You need to take enough notes so that you'll be able to tell me what you learned. Take notes, screen shots, etc. so that you can reference them.
Read http://www.bankrate.com/finance/auto/the-price-of-long-auto-loans.aspx. What does it mean to be "upside down" in a loan?
Find a new car and use http://www.money-zine.com/Calculators/Auto-Loan-Calculators/Car-Depreciation-Calculator/ to figure out what value of car will be in 2 years. (I think we underestimated using 15% in class.) [Remember that you put in 0 for current age.]
Go to loan amortization sheet.
http://financialsoft.about.com/gi/o.htm?zi=1/XJ&zTi=1&sdn=financialsoft&cdn=compute&tm=32&f=10&su=p284.9.336.ip_p504.1.336.ip_&tt=11&bt=1&bts=1&zu=http%3A//www.mdmproofing.com/iym/products/loan-amortization/
Use 5.25% as the APR and 1/1/12 as the start date.
Compare total payment of loans for 3, 4, 5, 6, and 7 years. What happens to the total amount you have to pay? Why?
Compare your car value at 2 years to each of these loan values. What do you notice?
Read http://www.lendingtree.com/auto-loans/advice/buying-a-new-car/how-much-to-put-down-on-a-car/.
Now go back to the loan amortization sheet and put $5,000 down in the first payment. Now what do you notice? According to this article, can you be "upside down" in a loan even if you take out a 3-year loan?
Reflection questions
Why do most financial experts advise consumers to take car loans of 4 years or less?
Why do people take out loans for longer than 5 years and what can happen?
About what % of a car's value should you put down and why?
At my first job, I brought home approximately $23,000. Suppose my typical month of bills was $900, what advice would you give me if I wanted to buy a new car?
*I do acknowledge this is a valid and important question. I just wanted to set the tone of the blog. :)
We have been studying exponential growth and decay, and I was just waiting for this question. The past few days we have looked at car depreciation and why that is a big deal in "real life," but I wanted to take it up a notch.
Here are the rough notes for a project I am going to do with my advanced math students. I worked with my brother who is in the financial industry to help me design it. I still don't know how I am going to have the kids present what they learned to me. Perhaps I will do interviews, have them make a recording, or write a paper.
Project:
You need to take enough notes so that you'll be able to tell me what you learned. Take notes, screen shots, etc. so that you can reference them.
Read http://www.bankrate.com/finance/auto/the-price-of-long-auto-loans.aspx. What does it mean to be "upside down" in a loan?
Find a new car and use http://www.money-zine.com/Calculators/Auto-Loan-Calculators/Car-Depreciation-Calculator/ to figure out what value of car will be in 2 years. (I think we underestimated using 15% in class.) [Remember that you put in 0 for current age.]
Go to loan amortization sheet.
http://financialsoft.about.com/gi/o.htm?zi=1/XJ&zTi=1&sdn=financialsoft&cdn=compute&tm=32&f=10&su=p284.9.336.ip_p504.1.336.ip_&tt=11&bt=1&bts=1&zu=http%3A//www.mdmproofing.com/iym/products/loan-amortization/
Use 5.25% as the APR and 1/1/12 as the start date.
Compare total payment of loans for 3, 4, 5, 6, and 7 years. What happens to the total amount you have to pay? Why?
Compare your car value at 2 years to each of these loan values. What do you notice?
Read http://www.lendingtree.com/auto-loans/advice/buying-a-new-car/how-much-to-put-down-on-a-car/.
Now go back to the loan amortization sheet and put $5,000 down in the first payment. Now what do you notice? According to this article, can you be "upside down" in a loan even if you take out a 3-year loan?
Reflection questions
Why do most financial experts advise consumers to take car loans of 4 years or less?
Why do people take out loans for longer than 5 years and what can happen?
About what % of a car's value should you put down and why?
At my first job, I brought home approximately $23,000. Suppose my typical month of bills was $900, what advice would you give me if I wanted to buy a new car?
*I do acknowledge this is a valid and important question. I just wanted to set the tone of the blog. :)
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