## Have You Ever Studied The Relationship Between Quality And Quantity?

May, 2011
This waddle of penguins picture was taken on 12/30/2010, by my cousin, while he was on a trip to Antarctica. Do you think mathematical thinking helped him appreciate and enjoy this scene? Consider how your mind uses quantity and quality while viewing the picture.

Have you ever studied the relationship between quality and quantity? I’ll bet you have. In fact, there is hardly an American over six years old who hasn’t. And, if you have a high school education, no matter how well you did in school, you have formally studied the relationship.

Am I thinking mathematically?

Before I go any further with this, consider the following question. “What do we call the mental act of quantifying quality and qualifying quantity?” A confusing mess! :-) Yes, it might be confusing, but I believe it’s something you do everyday. What?? Let me explain.

Once, I asked a critical thinking expert (Richard Paul):What is mathematics?” He responded by asking me what I thought it was? I responded by saying: “Mathematics is the logical study of shape, arrangement and quantity.” That was the definition of mathematics I had memorized and used since I was in college. He then said: “Well, your definition is fine, but is it what you think, or is it what someone else thinks and you are just using it?” I told him that I wasn’t really sure, since I had been using the definition for such a long time that it seemed to be a part of me. He then said: “I think mathematics involves both quantity and quality – put those two together and you have mathematics!” I said: “How about quantifying quality and qualifying quantity?” He said: “Sounds reasonable.”

Are you thinking about quality and quantity as you look at me?

That conversation has been in my mind for the past fourteen years. I think the, “quantifying quality and qualifying quantity,” description is a short and to-the-point way of viewing this thing we call math. Having stated that, I must admit that when I share this description of math with others, I often get a confused look for a response. I think it is such a different way of viewing mathematics that most find it lacking any concrete meaning. That doesn’t make it bad – it just makes it interesting.:-)

Ok, so where am I going with this? Well, recently, I was looking at some fun and interesting statistics. As I was reading through a list of statistical facts, the above description of math came to mind. You see, statistics is where I think we can see the “quantifying quality and qualifying quantity” vividly illustrated in our minds.

Let’s explore this view of mathematical thinking using the following statistical statement:Although everyone knows how many divorces there are, only 12% of married people thought they would get divorced.” If we leave out the quantity words of “many” and “12%,” then we have the unquantified qualities of divorces and married people. If we leave out the quality words of “divorces” and “married,” we have the unqualified quantities of “many” and “12%.” When mathematical thinking is being used in real life situations, it’s difficult to separate the quantity and quality and still have a meaningful thought.

Look where I found quantifying quality and qualifying quantity!

Have you ever studied the relationship between quality and quantity? Answer yes, if you’ve ever studied mathematics. :-)

I will end this post with some fun and interesting statistics and let you mentally watch your mathematical thinking.

**The number of mobile phones eaten by dogs in the U.K. every year: 1 million

**Percentage of those who leave their spouses and then go on to marry the person they were having an affair with: 10

**Did you know that 3 billion people worldwide live on less than \$2 a day?

**Percentage of divorced or separated Americans who believe marriage should be for life: 80

Five Americans are injured by shopping carts every hour!

**Number of calories you burn by kissing for one minute: 26

**Did you know that 3.7 million Americans claim to have been abducted by aliens?

**Five Americans are injured by shopping carts every hour.

**Percentage of third marriages that end in divorce: 90

**Number of people who could be provided with sources of clean drinking water per year for the cost of a submarine: 60 million

Did you know that women own only one percent of the world assets?

**Percentage of children born to cohabiting couples who will live with both parents until the age of at least 16: 36 (compares with 70 for the children of married couples)

**Number of miles driven by the average American car before it emits its own weight in carbon dioxide: 10,000

**U.S. still spends \$96 million every day on nuclear weapons.

**Percentage by which you are more likely to get ill if you are in an unhappy marriage: 35

**Women own only one percent of the world assets.

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## What Should We Call The Mental Act Of “Quantifying Quality And Qualifying Quantity?”

September, 2009
What do we call the mental act of quantifying quality and qualifying quantity? A confusing mess! :-)
Once I asked a critical thinking expert (Richard Paul) what mathematics is. He responded first by asking me what I thought it was? I responded by saying mathematics is the logical study of shape, arrangement and quantity. That was the definition of mathematics I had memorized and used since I was in college. He then said, “well, your definition is fine, but is it what you think or is it what someone else thinks and you are just using it?” I told him that I wasn’t really sure, since I had been using the definition for such a long time that it seemed to be a part of me. He then said, “I think mathematics involves both quantity and quality – put those two together and you have mathematics!” I said, “how about quantifying quality and qualifying quantity?” He said, “sounds reasonable.”
That conversation has been in my mind for the past fourteen years. I think “the quantifying quality and qualifying quantity” description is a short and “to the point” way of viewing this thing we call math. Having stated that, I must admit when I share this description of math with others, I often get a confused look for a response. I think it is such a different way of viewing mathematics that most find it lacking any “concrete meaning.” That doesn’t make it a bad – it just makes it interesting. :-)
Ok, so where am I going with this? Recently, I was looking at some “fun and interesting” statistics. As I was reading through a list of statistical facts the above description of math came to mind. You see, statistics is where I think we see the “quantifying quality and qualifying quantity” vividly illustrated in our mind. Take, for example, the following statement: “Although everyone knows how many divorces there are, only 12% of married people thought they would get divorced.” If we leave out the “quantity words” of “many” and 12%, then we have an unquantified quality of “divorces and married people.” If we leave out the “quality words” of “divorces” and “married,” we have the unqualified quantity of “many” and 12%. When mathematical thinking is being used for real life situations, we really can’t separate the quantity and quality and have a meaningful thought.
I will end this with some more fun and interesting statistics and let you mentally watch your mathematical thinking. Please consider increasing my “comment statistic.” :-)
**The number of mobile phones eaten by dogs in the U.K. every year: 1 million
**Percentage of those who leave their spouses that then go on to marry the person they were having an affair with: 10
**Did you know that 3 billion people worldwide live on less than \$2 a day?
** Percentage of divorced or separated Americans who believe marriage should be for life: 80
** Number of calories you burn by kissing for one minute: 26
**Did you know that 3.7 million Americans claim to have been abducted by aliens?
** Percentage of people who say they want to be rid of their current partner: 8
**Five Americans are injured by shopping carts every hour
** Percentage of third marriages that end in divorce: 90
**Number of people who could be provided with sources of clean drinking water per year for the cost of a submarine: 60 million
** Percentage of children born to cohabiting couples who will live with both parents until the age of at least 16: 36 (compares with 70 for the children of married couples)
** Percentage of Australian married men who have sex at least twice a week: 43
**Number of miles driven by the average American car before it emits its own weight in carbon dioxide: 10,000
** Percentage of Australian single men who have sex at least twice a week: 26
**U.S. still spends \$96 million every day on nuclear weapons
** Percentage of people who claim to be satisfied with their sex life: 49
** Average number of times French people have sex every year: 130 (the most in Europe)
** Percentage by which you are more likely to get ill if you are in an unhappy marriage: 35
**Women own only one percent of world assets

How big is it?

What do we call the mental act of quantifying quality and qualifying quantity? A confusing mess! :-)

Will you still love me when I’m …..?

Once I asked a critical thinking expert (Richard Paul) what mathematics is? He responded first by asking me what I thought it was? I responded by saying, “mathematics is the logical study of shape, arrangement and quantity.” That was the definition of mathematics I had memorized and used since I was in college. He then said, “well, your definition is fine, but is it what you think, or is it what someone else thinks and you are just using it?” I told him that I wasn’t really sure, since I had been using the definition for such a long time that it seemed to be a part of me. He then said, “I think mathematics involves both quantity and quality – put those two together and you have mathematics!” I said, “how about quantifying quality and qualifying quantity?” He said, “sounds reasonable.”

That conversation has been in my mind for the past fourteen years. I think “the quantifying quality and qualifying quantity” description is a short and to-the-point way of viewing this thing we call math. Having stated that, I must admit when I share this description of math with others, I often get a confused look for a response. I think it is such a different way of viewing mathematics that most find it lacking any “concrete meaning.” That doesn’t make it a bad – it just makes it interesting. :-)

A “quality” 7.

A “7” that lacks quality :-)

Ok, so where am I going with this? Recently, I was looking at some “fun and interesting” statistics. As I was reading through a list of statistical facts, the above description of math came to mind. You see, statistics is where I think we see the “quantifying quality and qualifying quantity” vividly illustrated in our mind. Take, for example, the following statement: “Although everyone knows how many divorces there are, only 12% of married people thought they would get divorced.” If we leave out the quantity words of “many” and “12%,” then we have an unquantified quality of “divorces and married people.” If we leave out the quality words of “divorces” and “married,” we have the unqualified quantity of “many” and 12%. When mathematical thinking is being used for real life situations, we really can’t separate the quantity and quality and have a meaningful thought.

I will end this with some fun and interesting statistics and let you mentally watch your mathematical thinking. Please consider increasing my “comment statistic.” :-)

**The number of mobile phones eaten by dogs in the U.K. every year: 1 million

**Percentage of those who leave their spouses and then go on to marry the person they were having an affair with: 10

**Did you know that 3 billion people worldwide live on less than \$2 a day?

** Percentage of divorced or separated Americans who believe marriage should be for life: 80

** Number of calories you burn by kissing for one minute: 26

**Did you know that 3.7 million Americans claim to have been abducted by aliens?

**Five Americans are injured by shopping carts every hour.

** Percentage of third marriages that end in divorce: 90

**Number of people who could be provided with sources of clean drinking water per year for the cost of a submarine: 60 million

** Percentage of children born to cohabiting couples who will live with both parents until the age of at least 16: 36 (compares with 70 for the children of married couples)

**Number of miles driven by the average American car before it emits its own weight in carbon dioxide: 10,000

**U.S. still spends \$96 million every day on nuclear weapons.

** Percentage by which you are more likely to get ill if you are in an unhappy marriage: 35

**Women own only one percent of the world assets.

I’m writing quantity and quality.