opinion of algebra

[WalterMitty]

discuss

[RI]

Middle/high school algebra or real algebra?

[angus]

Very useful.  Just yesterday I was using simple algebra to show my son some things.

Algebra was invented long ago by the Arabs but did not come into general use in Europe until the 17th Century.  Imagine how hard it was for the champion of Copernican heliocentrism, Galileo, to explain the motion of heavenly bodies using his dialogues and the geometry of the Greeks!  I shudder thinking of it.

I'm not sure how hard it is so I didn't vote, but I'm a big fan of mastering it.

[WalterMitty]

Middle/high school algebra or real algebra?

all algebra is 'real.'

this is going to turn into another discussion on what year the euros had algebra in their 'maths' class.

[Starbucks Union Thug HokeyPuck]

Freedom maths.

The development of algebra led to defining the algebraic number, which led to the discovery of transcendental numbers, which led to the discovery that most of the number line is transcendental, which led to the realization that the language of nature (and therefore nature itself) is so much stranger than we imagined, which led to the openings of many great minds...

FM, you see.  

[Grumpier Than Thou]

It sucks

[muon2]

I think we too easily confuse algebraic principles with the formal system of symbolic manipulation. As such it can be either easy, hard or somewhere between depending on the level of abstraction.

Many basic properties of arithmetic operations are essentially algebra. For instance a true multiplication table includes rows and columns like this:

x	1	2	3	4	5
1	1	2	3	4	5
2	2	4	6	8	10
3	3	6	9	12	15
4	4	8	12	16	20
5	5	10	15	20	25

One can memorize this table and from it get 3 x 5 = 15 using 3 from the row and 5 from the column. Separately one can get 5 x 3 = 15 by using the row with 5 and the column with 3. That's arithmetic.

However, most students learn that multiplication has a property that allows the order to be inverted without changing the result. Then one only needs to remember one of the two choices in the multiplication table. Some students even learn that is is called the commutative property, and not all operations have it. That's algebra.

One can go further and instead invoke the commutative property of multiplication to rearrange a symbolic expression in order to simplify it. Thus one can take b(3a+2b) = b3a + b2b = 3ab + 2b². The step in the middle is usually skipped, but technically it requires the algebraic commutative property to go to the third step. It's the same property we use to know that 3 x 5 = 5 x 3.

Then one can apply this to systems where some quantities commute and others do not. If a and b above are matrices, then that extra step above becomes important since not all matrices commute under multiplication. That is you might be stuck with 3ba + 2b² instead of 3ab + 2b².

This increasing level of abstraction and complexity is where many find algebra hard. Yet, the same concept can be applied at simple levels.

[ElectionsGuy]

Looking back at it, it was very easy and something I should've done better on. It is actually useful in life too (but anything above Algebra II isn't)

[Torie]

Word problems, which require translating words into a formula, I found hard in Algebra 2 in 7th grade, in part because the teacher was useless, and the textbook almost equally so, as to giving some help as to how to so translate words into formulas, with x's and y's, and the word clues to look for to assist, and what the basic 15 or so patterns were. Learn all of that, and you have broken the code, and can just do it all on autopilot, stoned out of your mind. The rest was like sailing with a steady tail wind - a piece of cake - just cranking out, knowing a few rules, the formulas presented. It got boring after awhile. That was true more or less for me all the way through calculus. Algebra 2 was the ultimate bitch for me. I was just so frustrated!

By the way, I have used simultaneous algebraic equations with x's and y's quite valuable in my legal practice, because when you try to evaluate what a property is worth, based on net income after expenses, you have property taxes going up as an expense as values go up, so you have two variables acting together at once. You can either use trial and error on a spreadsheet, somewhat more laborious, or use a simultaneous equation. I think that is why Newton invented calculus. Getting delta function rate of change calculations done, is just too laborious with algebra. He realized it sucked, and had an insight as to how to finesse that all.

And that, my friends, is the grand unified theory of math, from a lawyer, not a math major, who has no hesitation to opine about anything. I have a license to do so!

[muon2]

Torie has hit on one of the great problems in math education: how to anchor the abstract problems of algebra II in real world examples. I think that the solution lies in breaking down the artificial lines between arithmetic, algebra, geometry and trigonometry that appear in middle and high school. Replace them instead with math I, II, III, etc. and create separate tracks at each level.

I can see that as an approach that looks at math as a collection of tools to attack real problems rooted in numeric values. Each year in school one covers a range of topics, and each year the applications require more thought, new tools, and combining old tools in new ways. Those on a STEM track can get their math with examples that are preparation for the math needed in science and engineering. Others who are not so inclined would get applications in business and home finance - including just the sort of application Torie alluded to.

[Atlas Has Shrugged]

I can't do any type of math above a seventh grade level .

[angus]

Torie has hit on one of the great problems in math education: how to anchor the abstract problems of algebra II in real world examples. I think that the solution lies in breaking down the artificial lines between arithmetic, algebra, geometry and trigonometry that appear in middle and high school. Replace them instead with math I, II, III, etc. and create separate tracks at each level.

I can see that as an approach that looks at math as a collection of tools to attack real problems rooted in numeric values. Each year in school one covers a range of topics, and each year the applications require more thought, new tools, and combining old tools in new ways. Those on a STEM track can get their math with examples that are preparation for the math needed in science and engineering. Others who are not so inclined would get applications in business and home finance - including just the sort of application Torie alluded to.

apologist.

[Indy Texas]

It was invented by the Muslims. Therefore it's the Devil's mathematics and we ought to stop using it.

[Free Bird]

Depends on the section

[J-Mann]

I use it often, to a degree ... advanced Excel formulas and whatnot.

[GaussLaw]

Looking back at it, it was very easy and something I should've done better on. It is actually useful in life too (but anything above Algebra II isn't)

Actually, taking calculus is useful as it gives you a really good intuition for reading graphs.  This can come in handy when you think about things like rate of change.

[Ntwadumela]

very cool

[badgate]

College algebra was hard, but more because of the textbook and teacher. High school algebra was easy.

[TDAS04]

Mostly easy, but it depends on the level.  It can be fun, and it's definitely freedom math. 

[Torie]

Torie has hit on one of the great problems in math education: how to anchor the abstract problems of algebra II in real world examples. I think that the solution lies in breaking down the artificial lines between arithmetic, algebra, geometry and trigonometry that appear in middle and high school. Replace them instead with math I, II, III, etc. and create separate tracks at each level.

I can see that as an approach that looks at math as a collection of tools to attack real problems rooted in numeric values. Each year in school one covers a range of topics, and each year the applications require more thought, new tools, and combining old tools in new ways. Those on a STEM track can get their math with examples that are preparation for the math needed in science and engineering. Others who are not so inclined would get applications in business and home finance - including just the sort of application Torie alluded to.

apologist.

I think "sagacious" would be a better word to use here, don't you angus?