The material of the course may be divided into three parts, that which was already covered in Algebra I, work unique to the Algebra II course (at least insofar as high school is concerned) and material covered again later in pre-calculus or calculus. Since most Algebra II students have taken geometry between Algebra I and II, they will need considerable review of much, if not most, material covered in Algebra I. Students having little interest in mathematics will generally need more review. Many capable students will find the review pointless and boring. Some will be turned off to mathematics by the tedious review.

The second caegory, matrices, determinants, systems of three or more simultaneous linear equations, is unlikely to be of much use at all for mathematically-challenged students. For those who will study mathematics further, those sections are almost worthless. I recall from my Algebra II days learning Cramer’s Rule for solving systems of equations (only in 2 or three variables). But the rule was never derived (even though it es easily done for systems of 2 equations, and is a challenging, if tedious, algebra problem in 3 variables.)

Finally there is material taught better and in more depth later in a pre-calculus or analytic geometry class. Why spend lots of class time barely covering the conic sections in the coordinate plane when it will be covered more in depth the next year with a more elite student cohort? The material is necessary for those who will pursue mathematics at a higher level, but pretty pointless for those who will not. Why give a poor emaciated presentation that won’t help those interested in mathematics, while completely bewildering with its uselessness those who are not interested?

]]>Thanks, Scott

]]>The first n is g, the second n is h, and the third n is j

]]>“Algebra II is where common responses to “Why am I learning this?” jump the tracks.

“It builds your brain like exercising build muscle.” I used this one regularly; it’s true, but only a half truth. Programming, statistics and finance can do the same with the added bonus of being unquestionably practical.

“It helps students understand where more advanced math comes from.” Playing with simulations is even better for most students in understanding why more advanced math techniques work the way they do.

“It teaches structured thinking.” Programming is even better for that and it is easier for students to see what why structure matters. Mess up the structure and programs do odd things.”

Perhaps programming/simulations, statistics,and finance might be better for those skills.

My Statistics class, which admittedly is probably the most useful math class I took (challenged only by my game theory class) took 1 full year. However, n the first quarter, we learned only the z curve. But yes, a full year of stats has more practical significance than a full year of algebra.

I’ve seen simulations and I know a little programming as well, and they definitely do teach structured thinking. And with it’s more concrete (less abstract) structure, it probably is easier to learn than algebra. So yes, a full year of programming and simulations (these are so closely related that they could be combined, don’t you think) has more value in teaching structured thinking that a full year of algebra.

However, the question we need to ask is “Does algebra have a greater TOTAL value, compared to these other courses for the same amount of time (in academic years).”

In a more mathematical sense…

Let

A= total value of algebra

B= total value of statistics

C= total value of programming/simulations

d= value of “brain building” of algebra

e= value of structured thinking of algebra

f= value of groundwork for future math of algebra

g= added value of statistics “brain building”

h= added value of programming/statistics structured thinking

j= added value of programming/statistics groundwork for future math

Assuming we are only talking about one year, The system becomes

If A= d+e+f

AND

B= 1/2((d+n)+e+f)

AND

C= 1/2(d+(e+n)+(f+n))

(Note that the 1/2 is due to the fact that they both need to fit inside the same year, and so they are being taught 1 semester each).

THEN

Does A > B+C

Or does A < B+C

Or does A = B+C

Side note: Finance is incredibly easy to teach. Depending on how deep you are going with it, it can be taught anywhere from 2 weeks to 2 years. I am of the opinion that it should be part of a "practical knowledge class."

]]>You’re focusing on the the instance of a bad argument and I’m addressing the type of bad reasoning that is common. Too many people fail to see the difference between *constant marginals* (defending against lightning or peanut butter allergies) and *non-constant marginals* (defending against terrorism.)

Your are of course exactly right that terrorists respond to incentives and

The comparison should happen at the relevant margins.

1) The Marginal Benefits and Marginal Costs of Airport Security itself. That is are we getting a level of security that is worth all the costs.

2) The Marginal Rate of Transformation between airport security and some other thing.

I think what many critics of airport security are saying is that we are “spending” a lot on airport security and we are at a point where MC>MB, further we could be spending the resources on other things with higher returns.

]]>