Yesterday, I talked about the poetry of numbers. Seeing numbers in patterns. Finding a rhythm in numbers. Seeing sometimes symbolic meanings in the numbers themselves. And concluding that this (perhaps) fanciful interpretation of numbers opened interpretation to a poetry of numbers. This was motivated by a discussion I had with a student.

Today, I am thinking about the poetry of algebra. This was brought on by listening to The Diane Rehm show, which yesterday included an hour long segment on "Is Algebra Necessary?" a discussion driven by an opinion piece in the

I listened with interest while working. It seemed to be an argument mostly about whether requiring algebra created such a stumbling block that some students would fail out and never be able to develop their real talent versus how algebra could help with reasoning. Afterwards, I read the original opinion piece in

At it's root, everyone seems to agree that adults need some mathematical reasoning and logic skills. The questions are

As I think about the debate, I know that I benefitted from algebra (for more reasons than just that I can now help my 16 year old as he takes much of the same math that I once had) because (1) it set the foundation for calculus which was integral to my training for my academic career and (2) it did help me to expand my reasoning skills. However, I am willing to consider the possibility that my anecdotal evidence is not necessarily representative of the experience of the average person and that more data than my experience is needed.

Regardless of where we go with the debate, I would like to make a brief argument for where I see the poetry in algebra. When I think of algebra I think of turning a long-winded word problem into an elegant mathematical expression in which they symbols and numbers are used in ways that represent things that go beyond linguistic. They represent relationships that are not always obvious and that require discovery. The "Aha" moment that comes from solving a mathematical reasoning problem is like the insight that I sometimes feel from sorting out the beauty of a poem or the insight from figuring out the spiritual meaning of a verse from the Bible.

Here is some simple algebra but an example of where algebra does what I described above. Suppose a nuclear family is preparing to send its oldest child to college. Up to this point, only one parent has been working. The working parent has an annual take home pay of $45,000 and the family has managed to save $2,000 per year. The family expects college to cost $20,000 per year. If the other parent goes to work, the family anticipates that this parent will lose approximately 25% of their wages to taxes. What before tax salary would the parente returning to work have to earn so that the family would not go into debt? This can be written as :

The problem can then be solved for x (which, in this case equals $24,000). I see this as poetry because I can take a whole set of ideas and boil it down to something so simple. Some of the best poems do that. And I see the beauty in being able to say, "Now I have an answer and I understand why."

Does this mean that I ever needed quadratic equations? For this particular example, no. Does this mean that I needed to do all the graphing I learned how to do? For this particular example, again, no. But this does mean that having the skills to reason out the relationships between numbers and the algebraic toolkit to set up and solve and equation is useful for me in specific situations.

Does this require algebra the way it is currently taught in most schools--almost certainly not. If I recall correctly, the word problems were usually the end part of the learning after endless drills of pages of solving for unknowns. Why not make it much simpler? Teach the kids--here is the type of problem you are likely to encounter as an adult--or even make it more relevant to them as a kid. We could talk about saving for a new iPad, summer jobs, and savings accounts for example. Then, after they see how the logic and symbols can be used to transform a paragraph long word problem (the linguistic side) into a single line equation that can be solved after a few basic arithmetic operations and manipulations, have the practice the manipulations a bit.

I bet we can think creatively about how to teach most kids how to use mathematical reasoning in their lives with some algebraic concepts without requiring standard Algebra I. We must continue to look outside the box we have drawn for ourselves to date.

Today, I am thinking about the poetry of algebra. This was brought on by listening to The Diane Rehm show, which yesterday included an hour long segment on "Is Algebra Necessary?" a discussion driven by an opinion piece in the

*New York Times*about a month ago.I listened with interest while working. It seemed to be an argument mostly about whether requiring algebra created such a stumbling block that some students would fail out and never be able to develop their real talent versus how algebra could help with reasoning. Afterwards, I read the original opinion piece in

*The New York Times*, and in some ways I don't think that the guests were nearly as far apart as they were portrayed through the program yesterday.At it's root, everyone seems to agree that adults need some mathematical reasoning and logic skills. The questions are

*what*level,*how*to train for them,*when*to train for them,*whether*learning how to perform algebraic manipulations at a high level helps people ro learn broader problem solving skills, and*whether*there are other ways to develop problem solving/logical inference skills. The requirement that nearly everyone learn algebra (and at an increasingly early age) seems to presume a particular set of answers to these questions that (as the author of the opinion piece points out) is not necessarily proven by existing evidence.As I think about the debate, I know that I benefitted from algebra (for more reasons than just that I can now help my 16 year old as he takes much of the same math that I once had) because (1) it set the foundation for calculus which was integral to my training for my academic career and (2) it did help me to expand my reasoning skills. However, I am willing to consider the possibility that my anecdotal evidence is not necessarily representative of the experience of the average person and that more data than my experience is needed.

Regardless of where we go with the debate, I would like to make a brief argument for where I see the poetry in algebra. When I think of algebra I think of turning a long-winded word problem into an elegant mathematical expression in which they symbols and numbers are used in ways that represent things that go beyond linguistic. They represent relationships that are not always obvious and that require discovery. The "Aha" moment that comes from solving a mathematical reasoning problem is like the insight that I sometimes feel from sorting out the beauty of a poem or the insight from figuring out the spiritual meaning of a verse from the Bible.

Here is some simple algebra but an example of where algebra does what I described above. Suppose a nuclear family is preparing to send its oldest child to college. Up to this point, only one parent has been working. The working parent has an annual take home pay of $45,000 and the family has managed to save $2,000 per year. The family expects college to cost $20,000 per year. If the other parent goes to work, the family anticipates that this parent will lose approximately 25% of their wages to taxes. What before tax salary would the parente returning to work have to earn so that the family would not go into debt? This can be written as :

$2,000 + (1 - 0.25) x = $20,000

The problem can then be solved for x (which, in this case equals $24,000). I see this as poetry because I can take a whole set of ideas and boil it down to something so simple. Some of the best poems do that. And I see the beauty in being able to say, "Now I have an answer and I understand why."

Does this mean that I ever needed quadratic equations? For this particular example, no. Does this mean that I needed to do all the graphing I learned how to do? For this particular example, again, no. But this does mean that having the skills to reason out the relationships between numbers and the algebraic toolkit to set up and solve and equation is useful for me in specific situations.

Does this require algebra the way it is currently taught in most schools--almost certainly not. If I recall correctly, the word problems were usually the end part of the learning after endless drills of pages of solving for unknowns. Why not make it much simpler? Teach the kids--here is the type of problem you are likely to encounter as an adult--or even make it more relevant to them as a kid. We could talk about saving for a new iPad, summer jobs, and savings accounts for example. Then, after they see how the logic and symbols can be used to transform a paragraph long word problem (the linguistic side) into a single line equation that can be solved after a few basic arithmetic operations and manipulations, have the practice the manipulations a bit.

I bet we can think creatively about how to teach most kids how to use mathematical reasoning in their lives with some algebraic concepts without requiring standard Algebra I. We must continue to look outside the box we have drawn for ourselves to date.

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