Rather than droning on about each subject in math at this point, I'm going to make a shift. I'm currently engaged in a conversation with a friend, and my most recent reply to him expresses my opinion on how math is being taught today:

...The beauty of math is something that I have seen most of my life, and it stands in my mind as one of my fundamental motivations for studying math.

As a person with that emotional tie to math, I realize that many students would find it difficult to identify with my assertion that math is beautiful. As a result, I often take a stance that might be a little self-protective, and offer an answer that seems to be weaker but more universal.

In short, some aspects of math are of universal benefit, such as the skill of basic calculation, or the benefits of mental exercise. There are some benefits that apply only to a portion of the population, such as the ability to factor polynomials, or to find missing sides of triangles. Both of these arguments address the utility of math. In addition to this, there is the beauty of math. Whether or not a student sees that beauty is largely up to the teacher and the learning environment and culture.

Consider the distinctions between these questions:

Why do I (Peter) study math?

What are my rewards for studying math?

What rewards every student who takes math?

What rewards only some students who take math?

Why is math a required subject today?

What was the original reason for making math a required subject?

Why do I (the student) have to learn this?

A little broader: Why are gym and math required subjects in high school, while art and music are not? The fact is that all of these pursuits carry potential short and long term rewards. These rewards include personal satisfaction and enrichment, general personal growth, and possible future career application.

In my mind, this boils down to the fact that students are asking the question in the first place. In an overwhelming plurality of cases (is that a thing?) math is taught to students in a way that seems to have been designed to remove any element of fun and joy.

An analogy that I have used recently is this: Picture a literature class that is covering a unit on the mystery novel as a genre. At the start of every class, a new book is considered. They start by giving away the ending. The fact is, much of the joy of learning anything is that sensation of tension and release. That is to say, I am curious, and my curiosity motivates me. When I engage in a pursuit motivated by curiosity, learning is its own reward.

Once we have given away the ending, the joy has been stolen, and the only motivation left is utilitarian. I say this more as a description of the way things tend to be in mathematics education, than as an assertion of a basic law of the universe. In a sense, answering the question, "Why do we have to learn this?", is to try to defend the indefensible. The question itself is really an accusation. When a frustrated student asks this question, it is a sign that damage has already been done.

On the other hand, when I consider the question, "Why do I study math?" it is not a whimper. If someone asks me that question, my face lights up, and I warn them, "Don't get me started!" I then proceed to wax eloquent like an adolescent with a new crush.

I am curious about the thoughts of others on this topic.

As a person with that emotional tie to math, I realize that many students would find it difficult to identify with my assertion that math is beautiful. As a result, I often take a stance that might be a little self-protective, and offer an answer that seems to be weaker but more universal.

In short, some aspects of math are of universal benefit, such as the skill of basic calculation, or the benefits of mental exercise. There are some benefits that apply only to a portion of the population, such as the ability to factor polynomials, or to find missing sides of triangles. Both of these arguments address the utility of math. In addition to this, there is the beauty of math. Whether or not a student sees that beauty is largely up to the teacher and the learning environment and culture.

Consider the distinctions between these questions:

Why do I (Peter) study math?

What are my rewards for studying math?

What rewards every student who takes math?

What rewards only some students who take math?

Why is math a required subject today?

What was the original reason for making math a required subject?

Why do I (the student) have to learn this?

A little broader: Why are gym and math required subjects in high school, while art and music are not? The fact is that all of these pursuits carry potential short and long term rewards. These rewards include personal satisfaction and enrichment, general personal growth, and possible future career application.

In my mind, this boils down to the fact that students are asking the question in the first place. In an overwhelming plurality of cases (is that a thing?) math is taught to students in a way that seems to have been designed to remove any element of fun and joy.

An analogy that I have used recently is this: Picture a literature class that is covering a unit on the mystery novel as a genre. At the start of every class, a new book is considered. They start by giving away the ending. The fact is, much of the joy of learning anything is that sensation of tension and release. That is to say, I am curious, and my curiosity motivates me. When I engage in a pursuit motivated by curiosity, learning is its own reward.

Once we have given away the ending, the joy has been stolen, and the only motivation left is utilitarian. I say this more as a description of the way things tend to be in mathematics education, than as an assertion of a basic law of the universe. In a sense, answering the question, "Why do we have to learn this?", is to try to defend the indefensible. The question itself is really an accusation. When a frustrated student asks this question, it is a sign that damage has already been done.

On the other hand, when I consider the question, "Why do I study math?" it is not a whimper. If someone asks me that question, my face lights up, and I warn them, "Don't get me started!" I then proceed to wax eloquent like an adolescent with a new crush.

I am curious about the thoughts of others on this topic.