Quick -- which is bigger: 1/3 or 1/4? Apparently, there is a significantly large proportion of the American Public that believes that 1/3 is less than 1/4. After all, 3 is smaller than 4.
Evidence is cited in the New York Times Magazine, July 27, 2014 in the article (New Math)-(New Teaching)= Failure, by Elizabeth Green. The premise of the article is that "the common core is the best way to teach math, but no one has shown the teachers how to teach it." The example above appears in the article.
Follow this link; it has the same article but with a different title that's a little more provocative. Read enough of the article to find the reference to the McDonald's restaurant competitor that offered the "third" pounder to be in competition with McDonald's "quarter" pounder. In your response to this blog, be sure to mention the more provocative title AND the name of the competitor restaurant, just so I know you read at least a little of the article.
I'd like your response to anything in this article in a meaningful but brief essay. Some ideas follow: (Go ahead, be provocative!)
Do you think it's the education system? Do you think it's the poor education of our math teachers in this country? Many of your teachers (like me) at independent schools (like AA) have never received any formal training in math teaching. What's up with that?
Why do you think we have so much "innumeracy" in our fellow Americans (to use a vocabulary word coined by John Allen Paulos). If we had as much "illiteracy" as "innumeracy," then people would be up-in-arms. Why are folks not so upset about the "innumeracy"? What's up with that?
Do you have examples of innumeracy that you'd like to share? I wrote a post on this last year; I've made it available again if you'd like to see that. (Find it below....)
Due Date: The THIRD day 9 in our semester 2 occurs Feb 17. If you do not have class that day, of course it's due Feb 18.
Monday, January 12, 2015
Wednesday, January 7, 2015
To Infinity and Beyond. Due Feb 2
Infinity. Several things we said in class:
Consider a segment of length 1 mm. Then consider a line of infinite length in both directions. There is a one-to-one correspondence between each point on the segment and each point on the line. Yep, there's the same number of points on the segment (infinite) as there is on the line (infinite).
Let's say you are the proprietor of a hotel with an infinite number of rooms. You have the good fortune of having all rooms rented. Yet when a new customer walks in the door and asks about lodging for the night, you say, "Why yes, of course, I have space for you...." There's a variety of ways that can happen, but the solution requires involvement with infinity.
We can also use infinite sets in calculating probability. The example given in class: If a Natural Number is chosen randomly, what's the probability that the number will be a multiple of 8? (1/8).
Do these examples blow your mind? Find another story about infinity and write about it in your post. Have fun; include jokes if you'd like. But the jokes must have some kind of foundation or understanding or exploration of the infinite.
Consider a segment of length 1 mm. Then consider a line of infinite length in both directions. There is a one-to-one correspondence between each point on the segment and each point on the line. Yep, there's the same number of points on the segment (infinite) as there is on the line (infinite).
Let's say you are the proprietor of a hotel with an infinite number of rooms. You have the good fortune of having all rooms rented. Yet when a new customer walks in the door and asks about lodging for the night, you say, "Why yes, of course, I have space for you...." There's a variety of ways that can happen, but the solution requires involvement with infinity.
We can also use infinite sets in calculating probability. The example given in class: If a Natural Number is chosen randomly, what's the probability that the number will be a multiple of 8? (1/8).
Do these examples blow your mind? Find another story about infinity and write about it in your post. Have fun; include jokes if you'd like. But the jokes must have some kind of foundation or understanding or exploration of the infinite.
PreCalculus. BIG Numbers. Due Feb 2
So it's back in hunter-gatherer times for our species; around the campfire one night, there's a couple of cave people geeking out and talking about numbers.
Thor: "I can think of a number bigger than you can."
Lana: "Oh yeah? Try me."
Thor: "Two."
Lana: "Three."
Thor: "Oh man. Got me."
So how big is big? We can talk in class about a billion seconds as being a lot of seconds -- nearly 32 years worth -- and say WOW that's awesome...what big numbers..... but what about the number of seconds that's in a billion years? That number makes our billion seconds seem pretty trivial. Just as we may chuckle at Lana and Thor, there may be a group of people several thousand years hence (assuming we don't kill ourselves before then) that laughs at our inability to contemplate what they consider to be large numbers. This is almost like my 1986 computer I told you about where 40 megs was SO MUCH SPACE that people thought, "What is she ever going to do with that space?"
So how big is big? Exponential functions (with a base greater than one) are rapidly increasing functions and just beg the question: how big is that big number? Choose your method of describing large numbers; give some kind of numerical idea of how we might contemplate large ideas. Other than Jenny Lee's or Tony Borek's idea of how much time is equal to 1 billion seconds, what are other ways that might allow us to wrap our minds around large numbers? That's your task. Yep, pretty open-ended and this asks you to think a little creatively and outside the box. Google whatever you'd like, but be original and write your own stuff.
Let me give you some starter examples of what you can think about: How many blades of grass are there on AA property? How about how many gallons of water are in Lake Superior? How many pennies would you stack together to reach the moon?
Have fun. If you have questions, let me know.
Thor: "I can think of a number bigger than you can."
Lana: "Oh yeah? Try me."
Thor: "Two."
Lana: "Three."
Thor: "Oh man. Got me."
So how big is big? We can talk in class about a billion seconds as being a lot of seconds -- nearly 32 years worth -- and say WOW that's awesome...what big numbers..... but what about the number of seconds that's in a billion years? That number makes our billion seconds seem pretty trivial. Just as we may chuckle at Lana and Thor, there may be a group of people several thousand years hence (assuming we don't kill ourselves before then) that laughs at our inability to contemplate what they consider to be large numbers. This is almost like my 1986 computer I told you about where 40 megs was SO MUCH SPACE that people thought, "What is she ever going to do with that space?"
So how big is big? Exponential functions (with a base greater than one) are rapidly increasing functions and just beg the question: how big is that big number? Choose your method of describing large numbers; give some kind of numerical idea of how we might contemplate large ideas. Other than Jenny Lee's or Tony Borek's idea of how much time is equal to 1 billion seconds, what are other ways that might allow us to wrap our minds around large numbers? That's your task. Yep, pretty open-ended and this asks you to think a little creatively and outside the box. Google whatever you'd like, but be original and write your own stuff.
Let me give you some starter examples of what you can think about: How many blades of grass are there on AA property? How about how many gallons of water are in Lake Superior? How many pennies would you stack together to reach the moon?
Have fun. If you have questions, let me know.
Saturday, January 3, 2015
Geo/Algebra 2, misspelled: Sets of Numbers Due Jan 15
Watch Sal Khan talk about sets of numbers.
Compare what he talks about to what we do/did in class about sets of numbers. I hope that his lesson will help clarify the sets of numbers discussion from class. Know that you can always use his lectures/site for helping you learn the material from class. I know some of you already do. If you don't know of this resource on line, then this blog is all about having you learn about Khan Academy.
In your blog, please write about how YOU will learn to keep these sets of numbers straight. Find a mnemonic device that will help you remember, for example, the difference between the integers and rational numbers. Go ahead, google to see if there's something that someone else has already come up with that you think will be helpful. Or come up with your own idea.
Before you start on this blog, be sure that you make yourself familiar with the blog grading rubric.
Also, I'm thinking that we'll do a better job with blogs this semester; we'll have a blog due every day 9. I'd like your responses, positive and negative, to this.
Compare what he talks about to what we do/did in class about sets of numbers. I hope that his lesson will help clarify the sets of numbers discussion from class. Know that you can always use his lectures/site for helping you learn the material from class. I know some of you already do. If you don't know of this resource on line, then this blog is all about having you learn about Khan Academy.
In your blog, please write about how YOU will learn to keep these sets of numbers straight. Find a mnemonic device that will help you remember, for example, the difference between the integers and rational numbers. Go ahead, google to see if there's something that someone else has already come up with that you think will be helpful. Or come up with your own idea.
Before you start on this blog, be sure that you make yourself familiar with the blog grading rubric.
Also, I'm thinking that we'll do a better job with blogs this semester; we'll have a blog due every day 9. I'd like your responses, positive and negative, to this.
Precalculus: Welcome Back! Topic: Transcendental Functions. Due Jan 15
What does the word, "Transcendental" mean? In English literature, you may (or may not) have studied the "transcendentalists" like Emerson or Thoreau. Why are these authors called the Transcendentalists?
In mathematics, we discuss "Transcendental Functions." Trigonometric functions are transcendental. We are now exploring exponential and logarithmic functions which are also transcendental. Why? How? What does this have to do with the use of the word, "Transcendental" in English literature?
Before you write this blog, you'll want to read the instructions and rubric as posted on canvas. Be sure you are doing what you need to be doing to earn all the credit you need in this blog.
Also, in your blog, let me know how often you think it's reasonable to write a blog. Is once each cycle good? That's about once every 2 weeks. I'm thinking that we could make the blog due every day 9, unless of course, there's a test that day. I'd like your response to that.
In mathematics, we discuss "Transcendental Functions." Trigonometric functions are transcendental. We are now exploring exponential and logarithmic functions which are also transcendental. Why? How? What does this have to do with the use of the word, "Transcendental" in English literature?
Before you write this blog, you'll want to read the instructions and rubric as posted on canvas. Be sure you are doing what you need to be doing to earn all the credit you need in this blog.
Also, in your blog, let me know how often you think it's reasonable to write a blog. Is once each cycle good? That's about once every 2 weeks. I'm thinking that we could make the blog due every day 9, unless of course, there's a test that day. I'd like your response to that.
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