As others have, I often speculate if we assembled a committee for the sole purpose of rendering a subject near useless, if that committee could possibly do a better job than the public school system has done with mathematics? Public school math has been drilled, beaten and stripped of all possible usefulness. All for what? Students hate learning it. Teachers dislike teaching it (or at the least dislike teaching it to students who dislike learning it) and still we press on. Actually it's worse; we press on without even knowing whom to point the finger. Lacking even the ability to pinpoint the problem, educators, out of desperation, begin turning their hatred toward small little rectangular objects that calculate numbers. Why? It is again the purpose of this article to answer this inquiry.

What is it about these small little calculating devices that make them such easy targets for the failure of math literacy?  Is it that these machines are doing the thinking for us? Is it that students are simply learning to punch buttons? I assume it’s possible, however, I recall an article some time ago where the author concluded that the helpfulness of most advice is inversely related to the advice-givers age; as age increased, the helpfulness of advice typically decreased. Certainly this hasn’t curtailed my desire to tell the world what I think they should do; after all, at our core, we are simply a bunch of advice-giving machines. Nevertheless, we must accept that we may suffer from this generational lag and our distaste for calculators may simply be a function of this. For example, I come from a generation of the “Resume”. I was taught the importance of the resume in job candidacy. I even outsourced my resume-making when I entered the labor force because I believed it was so vastly important. Today, studies show that networking devices such as Linked and Facebook allow many individuals to bypass the importance of building a resume by networking. It's been shown that resumes are not as important today as they were in the past, but how many of us know this? How many of you who read that previous sentence cringed and shook your head in disbelief? I did, when I first read it. This inability to place our beliefs under scrutiny creates vast problems in our advice giving. I believe this generational lag is partially responsible for the u2018blame-calculator' bias our educators support. 

Let us pretend for a second that the importance of mathematics is simply being able to produce textbook answers to standardized textbook questions. If true, then most of today's calculators could, in theory, displace most of today's math educators. A four function calculator, at a cost of about $0.99 cents, could answer 90% off all math questions for grades K-4. A scientific calculator, at a cost of about $14.99, could answer 90% of all math questions from grades K-8. A graphing calculator, with a variable solver and factoring application, could answer the majority of Algebra, Algebra II and Pre Calc questions. Most of these same graphing calculators have statistical software capable of handling most first year statistics courses. A slight step up to one of the higher end graphing calculators equips all the tools to make a first semester of calculus a breeze. In all, for about $180.00 ($100 if used), a student could purchase the majority of textbook answers from kindergarten through their freshman year of college.   

Now, clearly this says nothing about understanding the material, but, on paper, would an individual truly be able to tell the difference between the traditional paper-pencil student and the calculator student when taking standardized tests? Let me pose a question, is it possible for a student to have more understanding of the significance and methodology of a problem but be more dependent upon technology to solve it? Let me approach this problem from a different angle. For instance, in academia, I work alongside many engineers who are also adjunct math professors. They tell me they use very little of their mathematical training in their day job and many have mentioned that they have nearly forgotten much of their math training. This says nothing about their abilities as engineers; they’ve simply outsourced much of their work to software applications. The math training they went through is much more a symbol of their ability and reliability than their productivity, yet, the question still remains. Is it possible for a student to have more understanding of the significance and methodology of a problem but be more dependent upon technology to solve it? To answer this question we need to discuss the parts of a math problem. 

Conrad Wolfram, in a wonderful talk about using computers to teach mathematics, points to four parts of teaching a math problem to which I will purposefully change the titles:

1) Asking/Understanding the right question

2) Setting up the question

3) The actual computations

4) Interpreting the answer. 

Now, according to Wolfram, math students today spend about 80% of their math training on part 3, the part that our technology can do exponentially faster than we can. In fact, Wolfram has calculated that "on an average school day in the world, we use up about 106 average lifetimes learning hand calculating." Now, there are only two possible conclusions here. Either part three, the computation part, is the most important portion of the four parts of a math problem (important enough to spend 80% of classroom time, or 106 average lifetimes per day) or the other three parts are being neglected.

An example may serve, 

1) Find the interest rate r if $2,000 is compounded annually and grows to $2,420 in 2 years. 

2) A = P(1+r)^t   The formula for compound interest

$2420 = $2000(1+ r)^2

3) The Calculations

 2420 = 2000(1+ r)^2

 2420/2000 = (1+ r)^2

121/100 = (1+ r)^2

+/- SqRoot (121/100) = 1 + r

+/- 11/10 = 1 + r

-1 +/- 11/10 = r

r = 1/10 or 

r = -21/10

Check the solutions by plugging them in for r

$2420 = $2000(1+ 1/10)^2

$2420 = $2000(1.10)^2

$2420 = $2000(1.21)

$2420 = $2420

$2420 = $2000(1 – 21/10)^2

$2420 = $2000(-1.1)^2

$2420 = $2000(1.21)

$2420 = $2420

4) The rate cannot be negative, so we reject r = -21/10. r = 1/10

Now, which of the four parts do you believe took up the most time? Yet, I could have plugged part 3 into my calculator or software and churned out the answers in a matter of seconds. We could have been devoting that time to parts 1, 2 and 4. Instead of calculating, we could have been asking, 

1. Why would you want to know the answer to this question? 
2. When would you encounter this question in real life?
3. What would have happened if we incorrectly set up the problem? 
4. How would being ignorant of this math be in the interest of a lender?
5. We could have played around with different scenarios of interest, initial investment and return
6. Why do we reject negative interest rates?
7. Could negative interest ever exist? 
8. What would negative interest mean to the lender or the borrower? 

Now, one might say that we could still have asked these questions, but could we? Do we? How much could we really discuss within a 60 minute class if we are spending 80% of our time doing computations? If an educator wanted to complete, say, 5 of these types of problems after a lecture, he or she would surely be stressed for time when engaging the other three parts of a math problem. This is normally the case. Educators tend to devote the majority of their time toward practicing computations while the student is left not understanding the value of the question, how or when to set it up, or what the solution truly means. We can see this whenever we slightly change a problem. When a problem, or wording of a problem, is slightly changed, students instantly become confused. This is partially due to the fact that they never understood the question in the first place; they were simply parroting their teachers' computations. 

Yet, the problem above is just simple algebra. Imagine if we were using computations to solve something more tedious? Let's call upon the same problem Wolfram used in his talk. Here is the formula of the general form of a 4th degree equation (commonly called a Quartic) 

ax4 + bx3 + cx2 + dx + e = 0

Quartics have 4 roots which can be represented in the following equations – we will produce one of the four below (click here for the other three):

(Equation 1: First Root (of four))

How many of these problems do you think we could compute within a 60 minute block of time without the help of technology? One? Are we starting to see what our students might truly be loosing with our unfounded calculator bias? 

From here the arguments start becoming warped. Many old-school math learners were forced to use paper and pencil, and thus anything newer and faster must, by definition, be lowering our math intelligence. I think this attitude could be summed up as the “order of invention bias”. In other words, the order of the invention matters to the students' development. Since the parents didn’t have software and advanced calculators when they were growing up, these technologies must not be needed, or worse, they might be detrimental. The fallacy is, of course, rooted in the limited technology of even previous generations. What did the parents of our parent's lack? Look at the history of computing, and how far we have come. One wonders if these same anti-technology arguments were made over the course of time. For example, what of those who engaged in math before recording was available? They must have performed all computations within their mind, but were they better off? The fact of the matter is "order of invention" is not important to the study of mathematics. We do not need to pretend that calculating devices are not available the same way we don’t need to pretend that writing/recording devices are not available. Instead of mindless computation we need to invest more time in asking the right questions, understanding and setting up the right questions, and understanding our solutions.

Yet, why don’t we?

Though I disagree, the skeptic in me understands why most math educators would be anti-calculator. After all, it’s probably within our interests to limit the public from these devices in order to keep demand for our skills high. Yet, why are other individuals, most of whom grew up prior to the calculator revolution, so anti-calculator? Normally their reasoning has to do with some story of the power going out while standing in a checkout line and the clerk who couldn’t add in their head. Or, some myth about how calculator users aren’t thinking. Before this, it used to be that it wasn’t fair to the students who couldn’t afford calculators (of course, it's becoming harder to make these types of arguments today). I’ve also heard the argument that standardized tests don’t allow calculators and thus more reason why they shouldn’t be used. It is my opinion that all of these arguments are weak and lacking. They are reaching at best.

Before offering a potential median for the public school math classroom, let me put forward my thoughts as to how I will personally teach mathematics to my two sons. Foremost, I will never drill multiplication/division tables (or anything for that matter) into their minds. I personally don't care if they ever remember them. At the earliest age possible I will place a calculator in their hands and free them from all this barbaric drill. I will do this so that we can jump into the more advanced topics sooner (see my blog for ways to teach math). Moreover, we will only, and I mean only, engage in real life problems where the solutions are meaningful.

• When discussing functions we'll build small bridges in my shop
• When discussing probability we'll play card games and risk.
• When discussing who between my sons is truly better at their first-person shooter video games we will gather data and analyze it.
• How angles are used in a cut to fall a tree.
• How building expressions can help you bid on landscape projects
• The blast radius of a firecrackers
• And so on…

With all this in mind, what are math educators to do? It is here that my advice is limited. That is, to simply do your best, under the circumstances, with the time you have. There are things that I would like to do in my college math classes that I haven't the time to do. There are methods of teaching that I know are inferior to others, but I haven't the time to change them. But, given the few hours I have with my students per semester, I do my best to engage as many application problems as I can. I do my best to word my test questions so that students must demonstrate mastery. I do my best to outsource the computation process to technology so that I can concentrate on the more important parts of the problems. We can only do our best…

Jeremiah Dyke [send him mail] is an adjunct professor of mathematics at LFCC, author of the children’s math book Do Natural Numbers Ever Wonder What's UnNatural and founder of Hands on Math.

The purpose of this short article is to survey the discipline problem within the public school system keeping in mind the over-arching question of why students seem to no longer respect their teachers. At the end of the article, educators will find links to unorthodox advice to aid them in their discipline problems. Now, as a disclaimer, I would like to warn you that I loved a loud classroom when I taught at public schools. Anyone who observed my classroom would attest that it was anything but silent (or what other might label a disciplined classroom). Furthermore, I'm sure I allowed many actions that other teachers didn't; it's just not in my nature to like authority. Thus, I come to you as the glutton offering you great advice on how to lose weight.  

What Are Books Telling Educators To Do? 

A short trip to my local library gave me about a weekends worth of reading on classroom discipline. I won't lie; I wasn't impressed by any of them. Of the roughly 10 books I read, I maybe jotted down a page worth of helpful pros that I could have seen myself using in the classroom. In contrast, I filled numerous pages with disappointing, self-defeating things I would never use! Truthfully, outside our lacking, and completely arbitrary, state-mandated curriculum, advice for behavioral issues is probably among the most disappointing aspects of public education. A typical classroom discipline book reminds me of a corny, twenty-first generation politically correct, Leave it to Beaver episode. Wait, did I mention corny? Yes, it's true that we don't have, and don't need, administrators or educators paddling their students whenever they make mistakes, but we also don't need rooms full of adult sissies! Students rarely respect their teachers anymore, and to counteract this lack of respect, educators attempt to guilt their students into respecting them, or worse, attempt to define who is respectable and why they are one of them. When said strategies don't work, educators instead start pampering themselves with excuses that this is just the way students are today; they lack respect for anything. What a faulty excuse. Has anyone thought that maybe  we should attempt to earn their respect? The point is that students' today lack respect for individuals who believe they can define success for them, as well as define whom they should deem to be failures. Such definitions of respect usually involve good grades, test scores, college, and knowledge of whatever subject the educator teaches. How self-serving! If a student asks me why they should have to be forced to study mathematics I don't proceed to wax on about my measly accomplishments and how important math is to colleges or employers. Even if there is merit in such verbiage, the merit is totally lacking to the students; it is simply too far removed from their life to have relevance (It’s like explaining the merits of retirement planning to a 21 year-old). Instead I take the uninterested criticism as a call to step up my lesson plans, to create better, more fun, ways for them to learn these math ideas. At the very least, if I can’t persuade them to see the relevance of math, I want them to look forward to coming to my math class. I mean, after all, their attendance is in some regards a product of force (force of the state, the parents, etc.); at least I could try to make their stay easier.  

Thus, first and foremost, educators must purge themselves of this idea that, to the student, they are important. That their subject is important.  That their measly accomplishments are important. That their previous learnings are important. That, in a truly free market, one where schools are held accountable for their results, their classroom would even remotely resemble the classroom-assembly-lines we have today. Only from here can we truly begin to network with a student's mind. Only from here can we create a system of mutual respect. 

How do we do this? Well, our first task as educators is to take a second to get real. You and your students work about the same amount of hours per week, yet at the end of the month you receive a pay check and your students get squat! They are carted from their home, via a big yellow bus, where they are constantly told to be quiet and do work until the end of the day where they are carted back home, to which point in time they begin the process of working on the work you didn't have time to cover while they were in class. I can only imagine the advertisement for such a position.

The Chester County Middle School is proud to announce an opening for a full-time student beginning this fall with hours 8:00am-3:30pm Monday-Friday 

Qualifications:

• Must be willing to work 35 hours a week unpaid
• Must be willing to meet deadlines
• Must be willing to take work home
• Must be willing to set quietly for an hour at a time
• Must be responsible for learning the material presented
• Must be willing to undergo tremendous pressure from peers
• Must be willing to listen to daily pep talks about how their life will be ruined if they can't pass standardized tests 
• Finally, the job is not optional…you must attend! 

I know what you're thinking and my response is sure, they are receiving an education that is valuable for their future, but let's remember that value is subjective. To the student, they are receiving little in exchange for their time. And to indulge the topic of value within the public school system, its role is questionable. Surely the public school system props up the bottom quartile of students, but it most likely pulls down the top quartile of students. Those near the middle are questionable. The fact of the matter is, the United States spends about $123,000 per student for k-12 education. For that price we could build each kid a library at their house and offer them 24-hour tutoring from undergraduates. Therefore, before you go patting yourself on the back, you may want to question if you play any positive educational role at all in your students lives. What are you actually teaching them?   

In other words, stop trying to scare them with stories of “when they get older” or “when they get to college”. Think of it this way, planning for retirement is thought by most to be good thing, investing a little per month over the course of many years will likely lead you to a lucrative retirement. Yet, it's hard for a 20 year old to understand this because to them, retirement is forever away. The same is true for the public school student. The adulthood stories that you keep calling upon to scare them are too far removed from their life to serve any purpose.

On Discipline

Just as parents of a toddler wish some portions of their parenting were easier (be it bedtime, bath time, or eating vegetables), all teachers wish some portion of their teaching were easier. Discipline is simply a function of your own embarrassment. I have a feeling that if classroom walls were soundproof the classrooms would be different in both volume and intensity. Simply put, kids are happier when they are louder and teachers are happier when their kids are happier; therefore, I imagine educators would allow their students to be louder if they weren't afraid of being caught and I imagine that such loudness wouldn't really disrupt learning like everyone supposes it would. When I'm teaching young students, I love a loud classroom! I would rather compete with other students for their attention than to compete with sleepiness or daydreaming. Being loud at least tells me they are awake!  Many individuals are impressed by the fact that an educator can demand silence from their students for an hour by threatening, yelling, or scaring them; I am not. I think it is simply ridiculous! 

In Closing

There is no panacea for classroom discipline; each day will bring new challenges. Kids who impress you will at some point in time embarrass you, just as those who usually embarrass you will sometimes impress you. Some of the research on the subject shows that many educators spend as much as 90 percent of their disciplinary attention on less than 10 percent of the class. To translate this, within any population there are entertainers and there are the entertained; clowns will be clowns! Yet, if we can begin on a level playing field of respect we surly have a better shot at creating a meaningful relationship and productive learning environment. For advice on classroom management see here and here. For Q & A, try here.

Jeremiah Dyke [send him mail] is an adjunct professor of mathematics at LFCC, author of the children’s math book Do Natural Numbers Ever Wonder What's UnNatural and founder of Hands on Math.

The Best of Jeremiah Dyke

Homeschoolers have a rare and terrific opportunity denied to most math students throughout the country. Homeschoolers possess the ability to finally relate to mathematics in both a meaningful and instructive way by creating applications to which a solution has relevance to the student; a solution worth deriving.

The typical public educator will complain that their students care nothing about how they derived an answer, they simply want to get there. However, what you normally never hear from those on the front lines of education is why they are asking this question, or, is it even a question worth answering? It is true that students may be apathetic toward how they derived their answers, yet, what we fail to understand is this reflects less so on them and more so on the quality of the question. Good educators have become masters at making questions relevant to their students. Students do much better when the application matters, in fact, if the question is interesting enough, they may be excited to answer it! Even something as simple as adding colorful pictures to a page of drill-and-kill exercises will make the students work harder than without them.

(Is it wrong to expect more from a math class?)

Thus, what we have is that students today are too far removed from the study of math. For most, math is simply a cluster of slightly varied problems to be done in repetition until mastered. At best, the student can hope that someone, somewhere, will ask them for help on their homework problems, as far as possessing the ability to solve a real-life problem…forget about it! So, page after page, worksheet after worksheet, drill after drill, students dull their pencils in hopes of never seeing their teachers' red ink. What nonsense is this? How are students to learn meaning by simply regurgitating steps — as if mathematics were a large set of multiplication tables to be memorized?

This is where the homeschooling advantage comes in!

My suggestion to a student or homeschooling parent is to eliminate every math problem from your textbook, and I dare say from your life, except those with a purpose i.e. those that involve a purposeful application. Make every problem, from k-12, a real life word problem. One that involves using math and analysis to reach a solution.

It's no longer what is "2 + 3"? Instead it's, "if I had two apples and added three more how many apples would I now have"?

It's no longer, what percentage is 12/15? It's, "If Edward always gets 100% on Biology tests, Bella, however, answered 12 out of 15 questions correct. What percentage did Bella get right?"(click for more twilight math)

Furthermore, there is no need to follow our state's math curriculum. Math need not be segregated into little subjects called pre-algebra, algebra, algebra II, geometry, etc. Follow your interests! If you, like Bill Friedman (son of David Friedman, grandson of Milton Friedman) find yourself enjoying probability more than other math subjects simply because it gives you an advantage in board games with your friends, then pursue it! You are simply filling your toolbox with more math skills, and, eventually you will find benefit in other branches of math.

Do this and not only will your students or children have a better understanding of mathematical principles, they will finally see the relevance in math and you know, they may actually start liking it!

Jeremiah Dyke [send him mail] is an adjunct professor of mathematics at LFCC, author of the children’s math book Do Natural Numbers Ever Wonder What's UnNatural and founder of Hands on Math.

The purpose
of this article is to point out the procedural cobwebs within our
mathematics classrooms, both within our institutions of higher learning
and within our public schools.

It's always
the same. Whenever and wherever math teachers gather, the conversation
is of student deficiencies and who's to blame. Professors blame
adjuncts, adjuncts blame high school teachers, who blame middle
school teachers, who blame elementary school teachers, who blame
parents and nearly everyone blames calculators. Why? Why are these
supposed deficiencies of millennium-old mathematics of concern to
anyone? Is there really a dearth of unsolved circumferences and
areas? Is there really a shortage of algebraic equations that go
unsolved?

Certainly one
could argue there is a labor shortage of individuals who are proficient
in secondary mathematics (algebra, geometry, consumer math, statistics,
etc.) but we can hardly argue there is a shortage of answers. From
the comforts of my TI 89 calculator, I may input sets of data, acquire
all needed measures of central tendency and standard deviations,
run a regression analysis, formulate an equation, run various derivative
and integrals, plot my data, upload it to my laptop and e-mail anyone
I would like while drinking an overpriced white chocolate mocha
from my local coffee shop. I could spend a few hours teaching any
competent teenager to mimic my button inputs, and send them off
with their final exam thus saving them a semester worth of work.

Certainly this
wouldn't be within my interests as a professor and most likely wouldn't
be within the interests of the student, but we have to agree that
a small investment in technology and training could provide all
required solutions that are asked of them. In fact, these secondary
mathematics problems are so easily solvable with technology, and
said technology is so prolific, that we may safely say that there
is no demand for these skills by hand – aside from the actual
signal to employers they reveal by passing my coursework.

Yet, this simply
begs the question, what is so special about the process of deriving
solutions? Surely we would all be better spellers with the elimination
of spell check and may possibly be better writers with the elimination
of the backspace key and eraser, but exactly how would this benefit
production and consumption?

Clearly we
cannot churn out engineers and scientists by increasing the production
of Texas Instrument calculators but then again, no engineering firm
on the planet would trust their scientists or engineers without
these calculating devices. A stubborn mathematician who refuses
to employ calculating technology would be hard pressed to find work
in the fast-paced world of consulting. Simply, he is a relic; delegated
to the classroom to grade papers.

So why are
we still educating math like we did in the pre-calculator revolution
of the 1980's? I'm not sure I can provide a legitimate answer to
this question, and there is still much to debate within this topic,
but I think an extract from a favorite economist of mine (Steven
Landsburg) about quality today versus quality of the recent past
may offer some insight:

"As
far as quality of the goods we buy [today versus the past], try
picking up an electronics catalogue from oh, say, 2001 and ask
yourself whether there's anything there you'd consider owning…or,
if you prefer, take a product like health care. Would you rather
purchase today's health care at today's prices, or the health
care of say, 1970 at 1970 prices?"

Nevertheless,
as forward as I am on this topic, I would not dare call myself a
professional mathematician, as it would be an injustice to the mathematicians
I studied under as well as those I work alongside. Simply, I just
imagine a society who embraces answers instead of worshiping processes.

For more traditional
educational criticism and help/advice for educators see my Hands-on
Math website or my book "Surviving
the Trenches of Education: Unorthodox Advice from the Proudly Self-proclaimed
Worst Teacher to Ever Enter the Classroom"

October
5, 2010

Jeremiah
Dyke [send him mail]
is a professor of mathematics and author of Surviving
the Trenches of Education.
He invites you to brainstorm with him via his
website.

Well, my tenure
with public education is through, and I would be a sorry libertarian
if I didn't reflect upon the state of affairs I've seen while teaching
seventh grade mathematics. As a disclaimer, credit is not without
due. There are heroes in our schools who deserve the tip of our
hat. They are talented individuals who enjoy their job and bring
countless smiles to the little faces that walk into their classroom.

Of course,
the dilemma is that any public school teacher reading those lines
will smile with an air of self-importance. Educators seem to naturally
scarf up any broad complements and outsource all criticisms. Indeed,
modesty is not a common trait within the classroom. The majority
of public school educators, within their mind, are Mr. Holland in
due of their Opus. They are benefactors, philanthropists, Gandhi's
of society. If for some reason you find yourself not going anywhere
for awhile, just inquire these individuals' opinions on education
or child philosophy, unwrap your Snickers, and listen to the sounds
of normatives spilling from their omniscient minds. The world is
their classroom! Never have you witnessed such an extensive array
of platitudes and head bobbing till you have taken seat at a public
school faculty meeting.   

They are a
sorry lot of saps for sure, yet, my arrogance aside, let me serve
some of my opinions of the mishaps within our school system.

Exposure,
not Mastery

Somewhere in
route, the field of education substituted quantity of classes for
quality of classes. Education has become a walkthrough, a cursory
glance at the subjects. Our leaders are obsessed with exposure,
not mastery. Students finish three or more years of high school
math with little to no retention. These individuals must then spend
the first few years of college paying for remedial math classes.
Certainly I'm not knocking the need for Algebra or Geometry; they
are vital subjects of study and many of the students who struggle
in college are the ones who possess the weakest quantitative skills.
Yet the solution is more mastery not more exposure.

It is my opinion
that merely an eighth-grade education of mathematics, in which the
student surveys and masters the basics of statistics, algebra, geometry
and arithmetic, would easily prepare a student for college liberal
arts mathematics; much more so then three years of additional high
school math given the average percentage of retention.  In
time, with this trend in rushing of exposure, our middle school
students will be dabbling in integrals and derivatives as they hear,
not learn calculus. It is quite an unfunny joke.  

The
Pretense of Knowledge

Yes, Hayek's
pretense of knowledge cannot be any more apparent then within our
nearly 100,000 publicly controlled schools throughout our nation.
Each school, with its vast arrays of diversity in geography, funding,
community, parent presence, academic ability, salary, etc., is governed
from the same men, wearing the same black suits, with the same American
flag pin. Each, from the comforts of their Mont Blanc pen
delegates what they believe to be priorities.  And the schools,
competing for that federal funding, practice the art form of bureaucratic
submission.

After years
of failed attempts these talking heads now believe they have found
the recipe for educational success.

• Just sprinkle
  a little bit of emphasis on student proficiency
• coupled
  with perks for those who show progress
• add a pinch
  of math targeting.
• Finally
  set some arbitrary pass rates
• And… cook
  until burned!

What's
in an Age?

Age seems too
arbitrary of a characteristic to be the focal point of learning.
Again, what's with the ambiguity? If we’re simply going to choose
an arbitrary characteristic for clustering students, why not choose
hair color, IQ or height? At least if you clustered students based
on height you would probably have less bullying within the classroom.

Why not cluster
based on ability?     

Sure it may
be weird to have a 13-year-old learning 4th grade math,
but only because the 13-year-old believes he should be with other
13-year-olds. You may have a 4th grade math room with
a mixture of 6–13-year-olds, whereas a 13-year-old may feel
behind, but this same individual may be in an 11th
grade English room and feel they are advanced. It would certainly
require much restructure and the elimination of many of the educational
taboos — and certainly not without the "yeah, but what about…"
questions, but at least it would be a better system of deciphering
learning.   

Lower
(if not eliminate) all College Requirements for Teaching Primary
Education

You don't need
them to be a good teacher.  

Currently,
the average teacher maintains five years of education coupled with
a semester of student-teacher training. In addition, teachers must
continue their training efforts (be it through college classes,
workshops, lectures or book readings) in order to maintain their
teacher licensure. Imagine a replacement teacher with less required
educational barriers of entry to compare to our existing teacher.

To form a successful
teaching lesson, one that is characterized by student learning and
information retention takes a compilation of experience, training
and preparation time — of which experience is most significant.
Of the following mentioned, our replacement teacher falls short
in one category: training.

It may be contested
that a degree in education also contributes toward experience. Yet,
for those who have had the luxury of watching a newly inexperienced
educator fresh out of his or her program for the first time in the
classroom can attest, education degrees offer little in terms of
experience. 

In reality
teachers are overqualified given the nature of their work. It is
within all likelihood that individuals of lesser education may choose
to work year-round for the same pay or work the same hours for less
salary. Furthermore, given that the supply of potential teachers
would increase as barriers of entry decrease, it is also within
all likelihood that increased competition would translate into increased
learning.

In conclusion,
my tenure in the arena of public schools has convinced me that my
child can only receive an education from the walls of my own home.
Even a part-time home school education would set your child miles
apart from his peers.

July
2, 2010

Jeremiah
Dyke [send him mail]
is a math teacher who hails free markets and freedom of choice.

Americans have
been duped for years into thinking that by right of possessing vocal
chords they may hence disgorge whatever ramblings they have in succession
of their mind. After all it is their constitutional right, yes?

It is the purpose
of this article to show how such a conclusion is mistaken and how
this perversion is actually an enemy of liberty.

Property
Rights and Funeral Protesting

Rev. Fred Phelps
and his Westboro Baptist Church have been picketing their memorandum
of god-hate for nearly 20 years. If you are yet to witness the distasteful
hatred of anti-gay protesters waving signs outside the funerals
of dead soldiers, signs of the likes of “God hates fags” and “Thank
God for dead soldiers,” then I invite you to watch this short clip
of Hannity & Colmes. The revulsion from such film is immense,
but the question of causality is straightforward. To recap the great
giant of liberty Murray N. Rothbard, there can be no crime against
one’s image or reputation, only one’s property.

“…someone’s
‘reputation’ is not and cannot be ‘owned’ by him, since it is
purely a function of the subjective feelings and attitudes held
by other people. But since no one can ever truly ‘own’ the mind
and attitude of another, this means that no one can literally
have a property right in his ‘reputation.’ A person’s reputation
fluctuates all the time, in accordance with the attitudes and
opinions of the rest of the population.” (For
a New Liberty, chapter 6, page 117)

Therefore,
the sheer act of protest is free from liability as long as the protesters
have legal admittance to the property from which they protest. Here
is where the perversion of sidewalk communalism takes up position.

By way of common
ownership individuals cannot be barred from any specific sidewalk
unless they are in direct violation of some municipality’s accord.
Thus, anyone may travel along the sidewalks outside of businesses,
homes, churches, etc. demanding that his or her voice be heard in
the name of free speech. Even unsympathetic listeners will reframe
from quarrels in opposition to these protesters because they too
support this “supposed” freedom.   

But freedom
does not signify you right to speech; property signifies your right
to speech.

Surely freedom
of speech cannot take place from any location one chooses. Surely,
for example, someone cannot stand in my kitchen or my living room
and protest what I may eat or watch on my television. If they did
they would be in violation of my rights to ownership and potentially
held responsible for trespassing. No sane individual would argue
in opposition to this example since no sane individual would argue
against the right of property owners to make such decisions.  

Why are sidewalks
so different from other property?

If sidewalks
were privatized then owners would have the right to remove any individual
whom they deem bothersome as well as charge individuals for their
use.

(Most knee-jerk
reactions will involve something along the lines of “what if the
sidewalk owner entraps you” or "why should I have to pay
to walk down the block." Although these questions have been
addressed elsewhere, it is beyond the scope of this article. I
encourage readers seek such answers through The
Privatization of Roads and Highways: Human and Economic Factors
Block, Walter. 2009.)

Therefore,
if Fred Phelps and his Westboro Baptist Church wish to hang out
on the street corner and protest their stupidity, they must pay
for it. Yet, because there is currently no fee associated with sidewalk
use these individuals have thus freely picketed more than 20,000
street corners within a span of 20 years.

Therefore,
this situation is not one of freedom of speech versus defamation
of character, or freedom of speech versus reverence for one's country;
it is not concerning freedom of speech at all, since freedom of
speech presupposes a platform from which to speak.

It is about
property!

Who owns the
property from which the protesters shout? If the answer to this
question is uncertain or bleak, then you have located your problem.

Therefore,
let us reexamine this scenario under the lens of property rights.
If anti-gay activists wish to celebrate the deaths of gay soldiers
or police officers then they must first purchase the right to do
so. They must either rent or buy the space from which they desire
to shout.

Furthermore,
family members of dead soldiers or gays would have the option of
choosing funeral homes that contract no anti-gay protests. Or family
members could agree to allow such protests at a discounted price.

Therefore,
in the end, anti-gay protesters must be willing to subsidize the
funerals of gays in order to wave their signs.

April
6, 2010

Jeremiah
Dyke [send him mail]
is a math teacher who hails free markets and freedom of choice.

If you hang
around your local gas station or food mart long enough, a scruffy-looking
man will toddle in the door and request $25.00 of gas on pump nine,
a pack of Camels Lights, one mega-million card and three of your
dollar scratchers. He will then proceed to scratch the tickets as
his gas pumps, only to return with a $2.00 winner that he would
like to exchange for two more tickets. He will proceed to scratch
the tickets again, discard them in the trash, and leave. You will
not see this man again until next payday.

Gambling is
a moron's retirement plan, and it is certainly not our positive
obligations to help morons. Yet, unlike the casinos, what is it
about state lotteries that make these acts so contemptible?

By means of
mandatory K-12 drill-and-kill public education, the state ill-educates
the public into a pool of mathematical ignorance. Most high school
students graduate without a single course in probability/statistics.
Sure, in seventh grade they learn about the probability of pulling
an ace out of a deck of cards, but permutations and combinations
like that needed to calculate the odds of winning the mega-millionaire
jackpot is only taught to the top percentile of high school students,
which is usually recommended as an elective, not as a course of
learning.

How convenient.

The state not
only promotes the public's ignorance in probabilities, but then
maximizes that ignorance via a monopoly on gambling.

Thus, simple
equations like the one below are foreign to the majority of the
populace.

Not only is
the math foreign, but even the term "your odds of winning"
is foreign to most individuals. What does 1 out of 80 million even
denote to the average citizen?

Let us translate
this into something more tangible that common individuals can comprehend.

Here is a penny

If this penny
represents the chance of you winning the mega-lottery jackpot, then
here is how many pennies you must choose from.

(See The
Mega Penny Project)

Yet, you will
find nothing of this nature on the lottery websites or the back
of the cards. Instead you will find this:

LOTTERY

TYPE

Odds
1 Chance in:

US PowerBall

5/45
+ 1/42

80,089,128

US The
Big Game

5/50
+ 1/36

76,275,360

(According
to The
Lottery Site)

Again, I am
not highlighting that casinos and other private gambling venues
should highlight such depictions of probability, but at least these
private institutions are upfront about their self-indulgence. The
state, however, promotes such ignorance from their constituents
under the veil of moral good. States will even advertise the various
"good things" it does with its lotto earnings (like promoting
more public education or other state funding), while all along it's
the impoverished saps that keep giving away their money.

But whose money
are they giving away?

What percentage
of transfer payments like welfare, unemployment, disability or social
security simply returns to the state via the "stupid tax"?
More bluntly, what percentages of OUR paychecks are being given
away?

Now, maybe
the naysayer will argue that state gambling is indeed evil, but
deregulated gambling would lead to even higher improbabilities of
losing, and thus why we should outlaw gambling all together?

I don't believe
this to be true.

Sidestepping
the issue that no one has the moral authority to assert what others
may or may not do with their own money, competition in gambling
would actually lead to higher probabilities of winning or some other
form of payout. For example, casinos litter their hotels with free
festivities and offerings so that consumers feel as though they
are getting something for their money. Consumers may travel to Vegas,
blow one month's pay, and still have a great time. Casinos offer
these extras not out of the good of their hearts, but because of
the competition with other casinos.

When is the
last time the state lottery offered such extras? Sure, you may write
the losses off your income taxes (as if they actually own the income
they tax) but that's it! At least I can be sure that under a private
lottery I would get some free gas, coffee, Reese Cups or some other
kickback from the convenience store from which I bought the lottery
ticket. If not, I will buy his competitors ticket.

Therefore,
let us return one more time to the convenience of our malevolent
state-controlled lottery. The state may choose what math is important
for study, exploit that ignorance in mathematics, and veil its racketeering
under the label of social good all from the comforts of its monopoly.

March
30, 2010

Jeremiah
Dyke [send him mail]
is a math teacher who hails free markets and freedom of choice.

The purpose
of this article is to fry but a small fish in a vast pond of governmental
inefficiency.

Those who typically
support the construction and operation of the aircraft carrier employ
the following argument "the navy's ability to carry out the
U.S. military strategies is highly dependent on its ability to supply
tactical air power at sea…" (see David Isenberg: The
Illusion of Power), yet at what cost? It is estimated
that a Nimitz Class aircraft carrier costs, on average,
$22 billion dollars each (see below), of which we currently harbor
ten — with an additional three in the pipeline of procurement.

• Construction
  Costs — $4.5 billion
• Mid-life
  Overhaul Costs — $2.3 billion
• Operating
  and Support Costs — $14 billion
• Other
  Costs — $1 billion
• Total
  Average Cost — $22 billion each

(As
estimated in life-cycle costs of 1997 dollars)

However, the
costs outlined above do not fully inform the taxpayer of actual
overheads. Like the forty-five carat Hope Diamond, these expensive
naval ships spend more time being secured than actually employed.
According to defense analyst Edward N. Luttwak, it is estimated
"that more than $6 billion worth of ships, as well as salaries,
benefits, and pensions for 8,000 people are needed to keep a carrier-based
air wing of 90 planes at sea (Pentagon
and the Art of War)."

Yet, aside
from their expensive nature what benefits are gained from the procurement
of such expensive vessels? For example, if the U.S. operated under
the banner of neutrality, whereas military expenditures were dedicated
only to the cause of protection, would such expensive acquisitions
be condoned? Indeed, if oceans
or militaries
were privatized would we see such expensive acquisitions? The answer
within such a political environment as we have today is likely no.
In all, these large war devices have no place outside an aggressive
hegemony

There just
is no threat aside from continued tax theft!

At an annual
budget of roughly $650+ billion
dollars, the United States spends as much on its military per
year as the top 21 competing nations. Or in other language, at the
rank of number one for military expenditures the U.S. outspends
ranks 2–21 combined per year on their military (see below).

Rank  

Country  

Military
expenditures (USD)  

u2014

World
Total

1,470,000,000,000

u2014

NATO Total

1,049,875,309,000

1

United
States

663,700,000,000

2

People’s
Rep. of China

70,308,600,000

3

United
Kingdom

65,149,500,000

4

Japan

48,860,000,000

5

France

47,421,250,000

6

Germany

45,930,000,000

7

Turkey

40,936,000,000

8

Italy

40,050,000,000

9

Russian
Federation

39,600,000,000

10

India

32,700,000,000

11

Iraq

32,400,000,000

12

Saudi
Arabia

31,050,000,000

13

South
Korea

28,500,000,000

14

Brazil

23,972,836,012

15

Australia

23,040,500,000

16

Canada

19,038,161,370

17

Spain

18,974,000,000

18

Israel

13,300,000,000

19

Netherlands

12,000,000,000

20

Poland

11,791,000,000

21

Republic
of China (Taiwan)

10,500,000,000

(See
CIA
website or List
of countries by military expenditures)

Furthermore,
at an annual operating and supporting cost of roughly $300
million dollars per carrier, the United States spends more per
year on their 10 aircraft carriers than most countries spend on
their entire military budget!

Thus, before
this country can begin to realize the temperament of domestic security
it must first be stripped of such aggressive and cumbersome armament.
Let these bulky naval bodies be pawned off to carnival cruise lines
or salvaged for it materials. Let this be the end of the era of
large navy ships.

October
21, 2009

Jeremiah
Dyke [send him mail]
is a math teacher who hails free markets and freedom of choice.

Witness as
my students slave over long division and fraction addition with
hundred-year-old technologies, while those rectangular calculating
instruments are sitting forgotton on our dusty shelves. Soon the
teaching will begin as will the daydreaming, yet maybe I will play
foolish games today in order to keep my students’ attention. After
all, is it not common to employ individuals who have a graduate
education to play computation bingo and other math games 180 days
a year? Surely no one devoid of six years of education is capable
of playing games like these, cloaked under the rubric of learning.

For the amount
of work I do my salary is more than sufficient but sometime this
week I may swing by the teacher lounge so that I can hear how dreadful
we educators have it. I am contracted to work 180 days a year for
nearly $40,000. After my two personal days and at least five sick
days I will only have worked 173 days. Of course, we must factor
in at least a week’s worth of snow day cancellations or delays,
about six early release days, five assemblies, three field trips
and numerous teacher work days. All in all I probably work 160 days
a year for 40,000 dollars or roughly $31 dollars an hour (40,000/160days/8hours).
Yet, since my day only involves four one-hour classes of teaching,
lunch, study hall (shut up and read time) and planning period (listen
to radio time) my hourly figure should probably be adjusted upward.
Nevertheless, enough about me, on to my students

My typical
classroom consists of 15 average Joes, 3 gifted kids and 3 Forest
Gump's (thanks to no child left behind). The 3 gifted kids provide
copying opportunities to at least six average Joes who exploit them
to their fullest. In return, the gifted kids may be allowed to sit
at their lunch table or be picked to play football during gym or
recess. The Forrest Gump's provide plenty of laughing stock for
the rest of the class as well as add an outlier into the curriculum
pace. This works out well for them, for they get to pick their nose
while staring into space, have their emotions tested by their peers,
all so that they can sit in the same classroom under the label "normal."

Grading is
easy. No one is allowed a grade under 50 percent. So, you may do
half of your homework (50%), turn in your homework late (50%) or
not do your homework (50%). The same applies for quiz or test grades.
Therefore, a child need only do 10% of the work in a year in order
to receive a passing grade of 60%, though this is too much for some
and thus we must pay teachers additional money to teach them over
the summer. Yet, times are tough. This year our district didn't
possess the funding to pay teachers to teach summer school, so,
we just passed everyone!

My supervisors
are numerous and their oversight is always felt. I am frequently
observed by my principal, assistant principal, team lead, school
math dean, district math dean, state dean of mathematics, the instructional
specialist, and, on occasion, school board members and though they
all give me contradicting advice (more games, less games, etc.),
they truly only care about the end of the school year state test.
As long as a specific percentage of my kids pass their SOL test
(and it is my job to find out who those "golden kids"
are and to devote the majority of my attention to them) they are
happy.

This my friends
is the unearthly inefficient system of public schools.

September
14, 2009

Jeremiah
Dyke [send him mail]
is a math teacher who hails free markets and freedom of choice.

Yet, forget
about the books on debt, weight loss and natural cures they don't
want you to know about… what about the "Welfare Cures"
they don't want you to know about?

Eliminate
the min wage

In spite of
that "brand new" regression model brewing in the hallways
of Cornell or the eternally touted New Jersey experiment, min wage
laws are not helping the poor! There is no new data that proves
economic tradition incorrect; there are only additional tiny fractions
of data whirling in a sea of formulae. Statisticians (code for economists
before graduate school) may simply elect or exclude whatever data
they wish — be it too hard or too expensive to measure — in order
to reach their proper margin of error. Yet, if these data-pushers
could truly sift through a world of six billion intricately networked
individuals, they would find their answer sitting on the lap of
a college freshman in econ 101 — price supports cause scarcity!

Abolishing
the FED

A malicious
printing, credit granting, monster lives amongst us. Not only is
this monster responsible for the relative decline of our purchasing
power it is partnered-in-scheme to redistribute wealth from the
vast toward the selective. Behind their secrecy and double speak
linger the inflationary henchman of a banking confederacy, the Fed.
Using various monetary concoctions, the Federal Reserve has the
capacity, and resilience, to redistribute wealth by means of inflation.
Yet, unlike Robin Hood, this form of redistribution is absent of
a feel-good mechanism often accompanying taxation. There is no wealth
transferred from "greedy rich" to the "innocent poor";
in fact, much like Friedman's negative income tax, the distribution
is inverse. Wealth is thus transferred, via inflation, from the
vast bulk of the populace to the selective few of the rich — the
connected? How you may ask? When money is inflated its purchasing
power declines, yet, the decline is not instant, there is a lag.
Therefore, those of initial receiving are liberated from the eventual
decline of purchasing power, whereas, those on the final stages
of receiving are left with idle wealth and inflated prices. These
individuals on the lower ends of the totem pole are the wounded.

Eliminate
Subsidizations of Employment, Unemployment and Employer

Indulge me
for a second as I parallel subsidizing to American Idol. We all
love watching the first two weeks of singing rejects get their feelings
hurt by Simon, we wonder, how can they not know? Well, like a world
of ever-smiling mothers (and Paula Abduls), no one wanted to break
their hearts or singing dreams. No one wanted to tell these screeching
soloists that they were not quality singers, and so, their inflated
self-image became a byproduct of polite-subsidization. Now, once
in competition, these inferior singers quickly realize their lack
of talent, courtesy of those who stand to lose from such inflated
promises. Very few would disagree with this example, yet, carry
this analogy to other markets of employment and you will find more
ridiculous polite-subsidization. Only, the culprits won't be smiling
mothers or Paula Abdul's, it will be inferior employees begging
for more charity, or inferior employers squawking for a helping
hand.

Eliminate
Taxation of Income

According to
Ron
Paul "We could eliminate the income tax, replace it
with nothing, and still fund the same level of big government we
had in the late 1990s." Yet, an even deeper question involves
defining a public sector? Aside from the various assembles of inefficient
services offered to the public, in reality, a swollen public sector
is by definition a sunken private sector, for, the public sector
is but a parasite feeding upon its citizens' labor. How can one
define wasting resources to collect resources in order to redistribute
resources a proper path toward prosperity?

Alas, in spite
of all these welfare cures we now know about, individuals of little
welfare will likely burrow at the troughs of our leadership so as
to continue in squander.

September
8, 2009

Jeremiah
Dyke [send him mail]
is a math teacher who hails free markets and freedom of choice.

Yet, is this truly it? Is this the best our intelligentsia has to offer? A cornucopia of Rich-Dad-Poor-Dad books trailing repeated episodes of Jim Cramer's Mad-Yelling!

It's not enough to quote another survey relating rates of returns between portfolio managers and monkeys throwing darts…though, these humiliations are still fun to indulge. Yet, who are these charlatans and where did they get such amazing foresight? The answer is simple really, these actors are pawning to you yesterdays news from behind the veil of their crystal ball.

Though you may not speak the jargon of your financial heroes, their jargoned forecasting is probably only marginally better than your own forecasting. Similarly their complicated models for predicting asset prices or unemployment rates are most likely only marginally better than your own model. This is of course not to suggest that the asset prices are random, or detached from the inter-connectivity of human action. It simply suggests that comprehensive marketplace predicting is dismal at best and thus the wrong is in the question, not person. This exact inter-connectivity of human action is what places economic variables in the realm of "Extremistan," highly subjected and impacted by the outlier writes Nassim Taleb.

So what good is economics if it is unable to forecast? And more importantly, why are we still listening to economists?

This is where economics goes defunct! Economics rests on basic fundamental a priori principles of self-interest. Economics cannot tell us what the unemployment is, was or will be! It can merely tell us that individuals will pursue employment of their labor when the exchange of that labor for other goods is beneficial. Moreover, economics can tell us that if you increase taxes on labor, you have inadvertently changed the ratio of exchange. Labor is thus less beneficial when the fruits of its undertaking are eroded by taxation. Similarly, economics can tell us that if you pay someone to leisure, there is less incentive to labor. Thus, economics can predict such effects with accuracy while still not having the ability to predict policy outcomes. Meaning, economics can tell you likelihoods based on presuppositions of self-interest but are at a loss to predict an outcome when hundreds of these policies are pursued at the matching times. This is why there is weight in the term ceteris paribus.

While the vast array of social scientists may laugh at economists for interjecting such capricious language as ceteris paribus the language, when used appropriately, is a testament of honesty. Economists honestly don't know the answer to the questions of aggregate outcomes without holding all other courses of action constant. Similarly, a mechanical engineer is ineffective at predicting the outcome of randomly slamming on the accelerator and breaks of a moving vehicle. This incapability derives not from the basic premises but from the series of self-canceling actions.

This is where economics derives its power, not from quacks in expensive suits.

Jeremiah Dyke [send him mail] is a math teacher who hails free markets and freedom of choice.