Order of Operations

You’ve all seen it. British TV, British movies, or you may have visited the UK.

They drive on the wrong side of the road there.

Of course, they’d say that we do. We drive on the right side of the road and we very sensibly put the driver’s steering wheel where that is the natural thing. But in the UK, it is the other way around.

So who’s right?

The obvious answer is, they both are. It’s just that we all have to agree on which side of the road to drive, or there would be chaos.

It’s the same in mathematics.  There is a debate among philosophers of mathematics as to whether numerical relationships are “real,” or simply a matter of convention. That is, whether “2 + 2 =4” is true because, as a matter of fact, 2 + 2 =4, or do we just define ‘2’ so that if we add it to itself, it equals 4.

That debate will be done, eventually, by intelligent cockroaches, long after human beings are gone. But there is this much truth to the position that concepts, in mathematics, are defined to be true, and that is, there are a lot of conventions in math just like in English, or, for that matter, just like in driving.

One of them is the Order of Operations.

There are several basic operations we do when we do math. We use parentheses, exponents, we add and subtract, we multiply and divide. We also square-root and some of what I’m talking about also applies to roots. When we do these operations one way, we get one result, and if we do them another way, we get a quite different result. Which is the right way?

There is no right way, if you mean which one corresponds to the reality of operations out there somewhere in Plato’s Heaven. But we all have to agree on them, just like we agree to the rules of the road.

So which is the right answer for the following:

 

4 + 2×3 = (4 + 2) ×3 = 6×3 = 18

 

Or I could multiply first:

 

4 + 2×3 = 4 + (2×3) = 4 + 6 = 10

 

Obviously, balancing a checkbook or sending a human to Mars will depend on which is right. JPL once crashed a Mars explorer when it switched from Imperial to metric in its calculations. (Yes, there is no evidence for the alternative theory that an ancient automated Martian defense system was activated. Sorry.) That’s a similar mistake.

So we agree. We do parentheses first, then exponents, then multiplication/division, then addition/subtraction.

If the operations are equal, we do them left to right.

For instance, 15 ÷ 3 × 4 is not 15 ÷ (3 × 4) = 15 ÷ 12 but is rather (15 ÷ 3) × 4 = 5 × 4, because, going from left to right, you get to the division sign first. Check it out on your calculator, you’ll see I’m right. (Or just accept that in math, I’m always right. Which would be foolish, as I make mistakes.)

What if the operations involve exponents?

4 x 3^3.

We do the exponent first, so this becomes:

4 x 9.

Which is 36.

What about 4 x (3+1) ^2?

Parentheses come first. So it is 3 +1 or 4. Then Exponents. So it is 4 x 4 (or four squared, but I don’t say it that way because when I do, I get an irresistible impulse to recite the Gettysburg Address.). 4 x 4 is 16. So this is 4 x 16, which is 64 or 4^3.

Easy, peasy. Just like driving.

But what if you have nested parentheses, that is, parentheses within parentheses?

4 + [–1(–2 – 1)] ^2.

You do the () first, which makes for -3

Then you do the [] next. Which makes it 3.

Then the exponent. Which makes it 3 x 3 or 3 squared. (Doesn’t make me recite the Gettysburg Address. Be weird if it did. Now, 4-squared? Perfectly normal to think of Lincoln.)

4 + 9 =13.

For the triskaidekaphobes out there, change the example. Make the 4 into a 5. That would make it 14. If you’re afraid of the number 14, what can I tell you? I’m a math teacher, not a psychologist.

What if it involves fractions?  Same thing. You hear that a lot in math. Same thing. That’s because a lot of things you do in math look different but are—the same thing.

 

​4(2/3 +1/4) ^2

Do what’s in the parentheses first:

2/3 + 1/4

You find a common denominator.

Everyone get 12?  Good.

So, we have 8/12 + 3/12

That makes an improper fraction, 11/12

We then square that.

121/144

Then we multiply all of that by 4

When we multiply a fraction by a whole number, we give the whole number a denominator (that’s the number on the bottom) of 1, and we get:

4/1 X 121/144 or just 4 x 121/144

Oh, hey, the order of operations again. (I knew we’d get back to it.) 4 x 121 divided by 144, as we go left to right with equal operations.

That gives us 484/144

Simplified, that’s 121/36 (We divided by 4 to simplify. You always divide by the greatest common multiple. Why? To get the smallest number as the answer. Why? Because smaller numbers are easier to work with than larger numbers.)

We do that because that’s a heck of a lot easier to divide to get the mixed number:

3 13/36

So, there you are.

I hope you enjoyed today’s lesson.

 

 

 

 

 

Advertisement

EVALUATING ALGEBRAIC EXPRESSIONS

 

 

In ordinary English, ‘to evaluate’ means to determine something’s worth or value. Or it can mean weigh the parameters as they apply to a situation and determine what course to take. You want to visit your friend, but he leaves in a rough part of town. You weigh the pleasure of visiting your friend vs the dangers to you. Given your circumstances, you may decide one way or another.

You might think, ‘Well, I haven’t seen him in a while, and I’m really rough and tough, am licensed to carry a gun and look like a sasquatch. I think I might go see him” Or you might say, “I’m a short, thin person, can’t defend myself, and there’s just been a rash of mugging where my friend lives. Maybe it’s not worth it.”

In algebra, the term evaluate is similar but has a more specific application. You are determining the value of an expression. Value is like worth, or weighing risk vs. benefits, but it has a specific numerical value. As mathematicians are, ironically, fond of simplifying, evaluation means to simplify an abstract expression down to a single set of numerical values. This is done in the application of formulas all the time.

D = M/V

Density equals mass divided by volume.  So if you have an object that weighs 14 kg and its volume is 30 liters, it’s density will be .47 kg/cm^3

Thus, the abstract formula is “simplified” to a specific concrete example.

The practical value of this is obvious, as most of the time, whether in electrical work, determining tire pressure, or how long a trip will take, we put specific values into an abstract equation. This is known as “plugging in” a value.

Plugging in a value and then you chug along to find the answer. That was fairly straightforward in the example I gave.

However, if you have minus signs, uh, oh.

Evaluate: -a^2b – c + d for a = -2, b = 3, c = -5, and d =8

There are minuses in the specific numbers to plug in and minuses in the expression. To keep track, I put everything in parentheses.

-(-2)^2)(3) –(-5) + (8)

Then I follow PEMDAS (Parentheses, exponents, multiplication/division, addition/subtraction.)

So, we get -2 squared, which is 4, then we minus that, which is -4; times that by 3, which gives us -12. Then we subtract –(-5), doing the multiplication first which makes it +5. Think of a minus sign as multiplying by -1.

Thus we have -12+5+8.

Going from left to right, we get 1. (Applause!).

Let’s suppose you have an example like this:

Evaluate (a +b) squared for a = -5, b = 3, c= -8, and d = 13

Remember PEMDAS!  You do parentheses before you do exponents. So you first add -5 to 3 and get -2, which you then square to get 4.  You don’t go -5 squared plus 3 squared, and get 25 + 9, which gives you 34, the wrong answer. Never drive left of center.

Also, note that there was no c or d in the expression. They often give you more information than you need to see if you sort it out to get the information you do need.

I hope you had fun with this. Those who don’t need any more help can stay after class and clean the erasers.

Dr. Fred Young

MATHEMATICAL REALISM

MATHEMATICAL REALISM

Numbers are real. They exist. They have a use in the real world. I love starting out with statements that everyone agrees with. But my first academic love was philosophy and philosophers, as Bertrand Russell observed, start with premises that no one in his right mind could deny and end with conclusions that no one in his right mind could believe. Let’s see what happens with the proposition, “Numbers are real.”

Have you ever written a story and thought it was horrible? Sure. We all have. So you change it. This happens in fiction all the time since we’ve been hit with prequels.  You don’t like Captain Kirk being thirty-five? You change the timeline and he’s twenty-two.  Starbuck, from Battlestar Galactica, becomes a woman, Kara Zor-El finds her mother still alive, and Shaft becomes a white guy.

Uh, wait a minute. Shaft becomes a white guy? That can’t happen.  Why not? Because he’s inherently a black guy, has the experiences of a black guy, wouldn’t make sense as a white guy. (Same thing goes– dare I say it? –in spades for Easy Rawlins. James West can be a black guy, but not Easy Rawlins.}

Numbers are like that. Even more so. You can switch the racial context in a book. Ever see “White Man’s Burden,” where America was first occupied by Africans and the Europeans were the underclass? In that society, Shaft and Easy Rawlins could be white guys. But can it be the case that 2 + 2 ≠ 4? No.

This is important.  Numbers are mental, just like fictional characters. They are not things, but ideas. But numbers have inherent, objective properties as if they were things. Just like gold has 79 protons, a^2 +b+2=c^2. And there ain’t nothing you can do about it.

To name some of the objective properties of numbers:

1. Trichotomy. Exactly one of the following is true: y = x; y < x; y > x.
2. Transitivity. If x < y, then x + z  <  y +z
3. Order of Addition: If x < y, then x + z < y +z
4. Order of Multiplication. If z is positive and x < y, then xz < yz. If z is negative and x < y, then xz >  yz

These are called the order properties of numbers.  They are immutable. Even in a world where black is white, where impossibly young people command starships, and your dead mother is alive as she, per impossible, survived your planet’s destruction, these properties of numbers will continue.

As will these:

Communitive laws: x + y = y + x; xy =yx

Associative Laws: x + (y+z) = (x+y) + z and x(yz) =(xy)z

Distributive law:  x(y+z) =xy +xz

Identity: x +0 =x and x times 1 =x

Inverses x-x=0 and x times 1/x =1

But wait. There’s more.

These properties are true for all places, all times; they are non-local, not situated in time. They are as true in AD 5000 on the planet Mongo as they are on Earth in AD 2019. We know this even though we haven’t observed it.

Numerical relationships, such as those in algebra and geometry, though, are never perfect in the material world.  In calculus, the limit for a series of fractions is not 1, it’s .99999…In the material world, nothing is perfect. As Jesus observed, it’s all moths and rust. Hannibal Smith can make a plan come together perfectly, but you can’t. In the world of numbers, we may screw the numbers up, but the relationships, the real calculations are always precise.

This perfection of numbers led Plato to think that they existed apart from the physical world; that the physical world instantiated them. Numbers were forms; and forms were perfect, i.e., eternal (non-local). This led later philosophers to think that they existed in the mind of God. They were ideas, all right. But their objectivity meant they were not in the mind of beings that were fallible, could change their minds, could screw up and need an eraser. They must be in the mind of someone infallible and who doesn’t make mistakes. That explains their objectivity. Mathematics becomes the divine language, the code by which the universe runs. The world is imperfect, being composed of matter, which is corruptible. The forms are the really real.

So there you are. We have gone from a premise that no one can deny to a bizarre notion that numbers are eternal, they are more genuine, more real than the physical world, that there can be entities that are pure form without matter. It’s just a short leap from that to a belief in angels, folks. St. Thomas Aquinas thought angels were also pure form but limited by their properties. And God was a pure form, but unlimited.

In a later blog, we will address what skeptics think about mathematical realism.

Dr. Fred Young

http://www.agapequalitytutorial.com

 

Equations

Equations

Algebra is the science of equations. That is, it tells us how to work statements that tells us when something is equal to something else. This is tremendously convenient, especially when you are trying to figure out an unknown quantity. With algebra, you can use a known quantity to get to the unknown quantity.

There are four basic equations in algebra, corresponding to the four operations that you do in arithmetic. Those operations are: addition, subtraction, multiplication, and division.  The four basic equations involve addition, subtraction, multiplication, and division.

They are:

A+B=C

A-B=C

A(B)=C

A/B=C

The way to solve them is to do the opposite of the indicated operation. That is, in an addition equation, you subtract, in a subtraction equation, you add, in a multiplication equation, you divide, and in a division equation you multiply.

This is called the Law of Inverse Operations.

It’s a simple concept to grasp. If you have $10 and I gave you $10 more, you would have $20.  If I were to take that money back, you’d be back to $10. So, if I wanted to figure out how much money you had to begin with, I’d set up the following equation:

A+$10 =$20.

To figure out what A, the original amount, was, I’d subtract $10 from both sides of the equation and I would be left with $10.

Similarly, if someone stole $10 from you, leaving you with $10, I could restore your wealth by adding $10 back.

Multiplication works the same way.

Suppose the eight of us were to invest $8 each. A math wiz would multiply each of our holdings by $8 and come up with a total investment of $64.

If we wanted to know the original amount, we could divide the $64 by 8 and come up with it.

Similarly, if we were to divide $64 by $8 and get $8, but wanted to reverse that, we would multiply by $8.

To solve an equation, we reverse the operation that is indicated by the equation.

To solve an equation, you do to the one side the same as to the other.

You will not be able to solve anything if you only work one side. If X +4 =16, you will never, ever learn what X was by simply subtracting the 4 from the left side. You have to do it to the right to get the answer.

Equations are a form of balance. If you and your friend are on a teeter-totter and President Trump sits on your friend’s side, you will go flying. Unless you have Chris Christy, former governor of New Jersey, sit on your side. In learning algebra, always keep the teeter-tooter in mind.

Now that we got that straight, what do we do when an equation requires more than two operations?

We do them in steps. Do the steps have any order?  Yes, they do. Remember PEMDAS? (Please Excuse My Dear Aunt Sally?) In other words, we do parentheses, exponents, multiplication/division, then addition/subtraction when doing multiple operations.

In solving an equation, we reverse that. Why? Because we want to get back to the original point. So in the following two-step equation:

2X +4 =16

We first reverse the four. To reverse addition, we do subtraction. So we subtract four from both sides.

We get:

2X =12.

Now we reverse the multiplication. We multiplied by 2, so we divide both sides by 2.

We get:

X=6.

What could be simpler?  Well, actually, one-step equations which we discussed at the beginning. Can it get more complicated? Oh, yes.

We’ll deal with that later.

Dr. Fred Young

http://www.agapequalitytutorial.com

 

 

FUNCTIONS

FUNCTIONS. WHAT THEY ARE AND WHY THEY MATTER.

Functions are a crucial concept in mathematics. You get them in algebra, in geometry, in trigonometry. You hardly ever get them at parties, but that would depend on the nature of the party, I would guess. Today, I want to explore some of the properties of a function.

A function consists of a correspondence between a first and second set. Each element in the first set corresponds to exactly one element in the second set.

Take the following:

A	1
B	2
C	3
D	4
E	5

 

This table denotes a function. For every item in the first column, there is a corresponding item in the second.

The first set is called the domain, the second, the range.

The domain is also the x-axis of a set of Cartesian Coordinates; the range is the y-axis.  This means that you can make a graph of a function!

These are graphical depictions of functions.

Now, suppose you were to draw a vertical line through one of the lines already on the chart. It would be a function. As the line represents a point on the x-axis and goes through exactly one point on the y-axis. This is called the Vertical Line Test of functions.

The above graph shows the use of functions. If we had two sets of data, we could see correlations.

Say the x-axis represented increased gun violence and the y-axis gun ownership. The first would show a direct correlation between gun violence and gun ownership; the second an inverse correlation.

Notice the vertical lines. The first defines a function, the second and third do not.

This graph isn’t a purely functional graph. The y-axis is a bit crooked. But it would show a one-on-one correlation between the x-axis and the y-axis. (It also shows that as spending on education goes up, absolutely nothing happens to students’ skills, but you already knew that.)

And here’s a graph that is called a “best fit” graph, as you can’t draw a straight line.

 

However, if you did draw a straight line, which is possible on the incident line without too much distortion, you would have a function. Mass shootings were 25 a year in 1980 and about 23 in 2010.

As should be clear by now, functions can be expressed by linear equations.  But instead of:

Y =2x+4

You say instead:

F(x)=2x +4.

We’ll continue this discussion in a future blog.

Dr. Fred Young

http://www.agapequalitytutorial.com

 

 

COIN PROBLEMS

COIN PROBLEMS

 

Word Problems.  Everyone’s favorite. From time to time, I will blog on how to solve them and other algebra problems. Today’s blog will be on coin problems. You know, the ones where you wonder why don’t the people simply look in their pockets and count? But they hone your algebra skills and allow you to understand principles involved in systems of equations and other mathematical procedures.

Here’s a typical one:

Jack and Diane have 28 coins that are nickels and dimes. If the value of the coins is $1.95, how many of each type do they have?

As with many math problems, once you simplify, the answer is a lot easier to come by. We have two variables. Ah, if we only had one.  But alas, we have two.

The first step is to get rid of that pesky fact and define one in terms of the other. This way, we only have one. Don’t worry. We will later bring back the other variable.

The variables will stand for our two coins—nickels and dimes. So our variables are N and D. (Pretty clever, right? I could have picked X and Y, but N and D are so much more representative of nickels and dimes, I think.)

The problem tells us that the number of nickels and dimes adds to 28. So our first equation:

N +D = 28.

The number of nickels, N, and the number of dimes, D equals 28. With me so far?  Good.

But we need another equation to solve our problem. The solution is to define the variables and the result in the equation (in this case, the $1.95) by elements they all have in common.  They are all composed of pennies. Hey, that leads us to:

5N +10D =198.

As there are 5 pennies in each nickel, ten in each dime, and 198 altogether. Beautiful. Now, all we have to do is to define one variable in terms or the other and we are all set.

Let’s define nickels in terms of dimes. We could do it the other way, but I like nickels. But maybe you like dimes. Then, you can do it for dimes.

N + D =28.

We solve for N.

N + D-D=28-D

We add the -D to D on the left, and what happens when you add the additive inverse to a number? You cancel the number. As we are in an equation and have to do to the other side what we do to the side we are working, we get the result 28-D.

Think of an equation as like a teeter-totter. You start with your friend who equals your weight. Then Donald Trump sets on your friend’s side. You go flying. Unless, of course, Chris Christy sits on your side. You are back in balance. All’s well, the world, or at least the equation is in balance.

So, N =28-D.

We substitute that for N in our equation:

5(28-D) +10D =195

We now multiply both terms of the parenthetical expression by 5 and the result is:

140-5D+10D =195

We combine like terms.

140 +5D =195

We now have your classic two-step equation. You solve it in, well, two steps.

Step 1

140-140 +5D =195-140

There’s that teeter-totter again. Maybe a less controversial example would be Nero Wolf and Cannon, two fine but large detectives. In any case, however you imagine it, you get:

5D =55

Step 2

Now, to cancel a multiplication, you do a division. To cancel five times D, you divide by 5. Again, you do it to both sides and you get:

D =11.

And Since N+D =28, and you can now substitute 11 for D, you get:

N+11 =28

You subtract the 11 from both sides, and you get 17

Next time, we might try something really hard, like how to balance your checkbook.

Dr. Fred Young

http://www.agapequalitytutorial.com

 

 

 

 

 

 

IS THERE A CONSTITUTIONAL RIGHT TO AN EDUCATION?

 

After the War between the States, Congress set standards for rebel States, if they were to be readmitted to the Union.  Mind you, they had no choice in being readmitted.  That was settled at Appomattox, the first time (and hopefully, the last time) a constitutional crisis was settled by force and not reason.  One of these standards was to provide public education.

Currently, there are lawsuits to make public education a constitutional right.  The argument goes that Article 4, Section 4 of the Constitution and the 14^th Amendment requires this.  One needs to worry when a right already established by law is being held to not exist, as this lawsuit presupposes. The idea appears to be that the States would have to provide a curriculum that adequately prepares students for citizenship.  They are:

Martinez v. Malloy

Filed: Aug. 23, 2016, in the U.S. District Court for the District of Connecticut

Argument: The Constitution guarantees substantial equality of education opportunity; Connecticut’s policies limiting charter schools, magnet schools, and interdistrict transfers violate students’ due process and equal-protection rights.

Status: Judge Alvin W. Thompson dismissed all but one claim in the lawsuit, charging the state with failing to fulfill its duty of public administration. That claim is pending.

Gary B. v. Snyder

Filed: Sept. 23, 2016, in the U.S. District Court for the Eastern District of Michigan

Argument: The Constitution contains an implied right of access to literacy instruction; state policymakers provided Detroit students with such a substandard literacy education that it fell afoul of the students’ due process and equal-protection rights.

Status: Judge Stephen J. Murphy III dismissed the lawsuit. The plaintiffs have appealed to the U.S. Court of Appeals for the 6th Circuit.

A.C. v. Raimondo

Filed: Nov. 29, 2018, in the U.S. District Court for the District of Rhode Island

Argument: The Constitution contains an implied right to an education that prepares young people to be capable citizens, including voting and serving on a jury. Rhode Island’s failure to provide this education violates multiple constitutional rights and a section of the Constitution guaranteeing a “republican form of government.”

Status: Pending

Source: Education Week

 

 

Now, ok, I agree that there should be charter schools, magnet schools, no limits on interdistrict transfers.  All of those policies buttress up the public schools’ monopoly. And indeed, when public schools provide substandard instruction, then there is inequity.  But should we, as a nation, impose these things on States?

I should simply whisper, “Betsy Voss” to progressives who want national education and see them have hysterics.  My point is to question the whole idea of national standards.  Look at “Core Curriculum,” which has math problems that are incomprehensible, even to mathematicians.

You may ask yourself what the question is.  Beats me.

As to federal standards for citizenship?

The Medford, Oregon school district got a bargain of history books that annotated the Constitution.  (Guess which Amendments got annotations that favored one side over the other in interpretation.  You guessed The Second Amendment?  Congratulations.)  The School Board finally decided to use the books (Don’t look a gift horse in the mouth) but decided maybe the actual Constitution should be passed out as a supplement.

You can argue that education is a right.  That “republican institutions” presupposed it.  I suppose, as long as teachers stop indoctrinating their views on the electoral college and the powers of the Presidency.  (It isn’t ‘undemocratic,’ unless you think that 18 counties imposing their will on everybody else is the high point of democracy, and no, the President doesn’t get to subsidize companies or do an end run around the law.) Adam Smith thought public education was essential to capitalism.  But what of parents’ rights?

Shouldn’t you be able to raise your children according to your religion?  Shouldn’t a Christian community have a nativity scene at the local school?  Institutionalized atheism wasn’t what the radical Republicans had in mind when they imposed public education on rebel States.  They wanted literacy and arithmetic.  They wanted you to be able to read the notice that said there was a meeting to discuss public policy—and no content was imposed.  Meetings that took place including union organizing and suffragettes, but also the KKK.

Education may be a right, but “re-education” isn’t.

Dr. Fred

 

 

ENSURING YOUR STUDENT GETS THE BEST EDUCATION POSSIBLE

How do you ensure that your children are getting the best education?  There is no right or conclusive answer to that question.  There are so many factors in education.  But one thing is certain—you should never leave it up to the schools.

Don’t get me wrong.  There are excellent public school systems.  The one in Beverly Hills competes well with any private schools.  Of course, if you’re not lucky enough to live in a rich school district?  You can accept a second class education or consider private schools. But this caveat, do not leave your child’s learning applies to private schools as well.  The thing is, schools have their own agendas.

There was a study done in the ‘eighties’ that argued very well that school boards reflect the needs of their community’s businesses.  And one of the reasons for the rise in public schools was that business realized that it needed a skilled workforce and a public school system would shift the burden and costs of training to the schools.  So, if you live in a mining town, you can expect that the school’s curriculum will reflect that.  Or you can go to a private school, 90% of which are religious; the other 10%, largely military.  So, unless you’re of the school’s faith, or want your child to serve in the military, you may be in trouble.  Again, there is nothing wrong with a religious education or with wanting your child to serve his or her country.

Common core fixed the problem of the schools having their own agenda, right?  No, it standardized and gave a federal agenda to the process of your child’s education.  You may be happy with Betsy Voss and Donald Trump deciding what is best for your child, but you really shouldn’t be.

And consider this.  A survey by the American Federation of Teachers and Badass Teachers Association, released on Monday, shows that teachers are feeling especially stressed and are less enthusiastic about their jobs that before.  And the retention rate among teachers is still abysmal.  So, you want to leave your child’s education to overworked, stressed out, unenthusiastic teachers who will probably end up in another job where they can make gobs more money, right?  Again, there are good teachers, but roll that around in your mind for a while.

So how to ensure that your children are getting the best education?  Here are some tips:

1. Consider homeschooling. You are in control of your child’s education every step of the way.
2. Be involved. You may not have the time to homeschool.  Maybe your child is science-bent, and you don’t have the means to provide a science education.  Maybe you like the idea of public schools.  But in that case, you need to attend PTA meetings, consult regularly with your child’s teachers, research the schools, and find out what special help is available if your child has special needs.
3. Hire a tutor. A tutor is a teacher that is responsible to you, not to a school board, a teacher’s union, or Betsy Voss.
4. Help your child with his or her studies. If they are beyond you, see tip 3 above.

Above all, make learning fun.  You will be rewarded and so will your kids.

Comprachico Education

You couldn’t get a more motley crew together if you tried:  Paul Goodman, playwright and anarchist, Victor Hugo, novelist, Ayn Rand, philosopher-novelist, and Anthony Flew, philosopher.  But they all had one thing in common:  opposition to the current state of education.  All advocated a radically different approach to how we teach our kids, and it all centered on parents, or the community in lieu of parents, taking responsibility for their kids.

Paul Goodman, in Compulsory Miseducation (1964) argued that the fatal flaw of progressive education was that it always ate its own children.  Each generation of progressives tried to undo what the last generation wanted.  The core problem was in its centralist approach to education–school boards, large classrooms, top down education. This has just gotten worse with a federal dimension to schooling, with standardized tests and teaching to them.  Every individual is unique, according to Goodman, and some might not even need a formal education.  Children should be allowed to explore what they consider to be fruitful avenues of knowledge.  If this is done, then the spark of curiosity, so keen in children, will not go out, as it does by high school.  Goodman believed every stage of formal education had to undo what the earlier stage had done:  you unlearn elementary school in high school, you unlearn high school in college, and you unlearn college in the school of hard knocks.

Ayn Rand likened educators to “comprachicos of the mind.” (1975) Victor Hugo coined the term, and he used it to describe the child buyers of medieval times.  They would condition children for tasks and sell them for that task.  Some would be put into a pot and grow in the perfect shape of a pot.  A later industrial practice did the same.  Child labor was justified in coal mines, as their bones would adapt to the stooped environment that they found themselves in.  Rand believed educators did the same thing–only to the mind.  They would put kids in spiritual pots and they would grow into the grotesques that would demonstrate and yell, but never understand the needs of human life. There have been studies to show that school boards reflect the needs of the corporations or industry of an area and not that of the children.

Anthony Flew, in The Politics of Procrustus (1981) talked about compulsory egalitarianism.  Procrustus was an inn keeper who had but one bed.  If you were too short for the bed, he’d put you on the rack and stretch you; if you were too long, he would cut you down to size.  Flew believed that public institutions did just that, including the schools.  You dumb down the smart; you try to bring to average those who don’t measure up.

What would Goodman, Rand, and Flew think of today’s education–with standardized tests, a return to learning that requires mathematics beyond what the student is comfortable with, and imposes a particular view of history?  In Medford, the school board wrestled with history books that depicted the framers as rich white slave owners, dedicated to their own privileges, and which cut out or amended parts of the Constitution.  They decided to allow the book as long as the actual constitution was passed out and discussed. Both left and right politicians complain about the brainwashing that goes into the schools.  It seems both the first and second amendment, the one giving basic freedoms and the one protecting them, are anathema in a lot of schools.

What is the solution?  Too easy to say homeschooling, that won’t work for many.  Ditto, private education.  What will work is for parents to get actively involved in the educational process–every step of the way.  Only when you can’t teach your child what you need yourself should you involve the schools.  Far better to hire a tutor than to hand your children over to nameless bureaucrats.

Would you sell you children to a carnival?

I CAN’T READ…

In my dojo, when people were learning a new technique, if they said, “I Can’t,” they were made to do push-ups.  This was painful, and was an adverse association with “I Can’t,” and it helped build muscle strength.  Thus the punishment came with positive benefits.  Why punish “I Can’t?”

Because it tells your subconscious that you’re incapable and wires in powerlessness.  It is a form of learned helplessness.  This is behavior that is self-limiting.

What if Trump had believed all the press–“No way can he win.   He will be crushingly defeated.”  “Hillary has the numbers.”  Uh, huh.  Doesn’t matter whether you like Trump or not.  He was the ant moving the rubber tree plant.

Or Helen Keller.  Unable to communicate but became a world renown thinker.  Due to her will and the fact that Ann Sullivan did not give up on her.

When I hear “I Can’t,” I never give up on the student.  It challenges me–and I know “I Can” reach them.

I know this because I’m not just like Ann Sullivan, I’m like Trump and Helen Keller.  I went from a wimp to a Black Belt.  If I can do it, anyone can do it.

I’ve seen how attitude works.  How students who were labeled “uneducable” by their schools came to me and became successful.

So next time you say “I Can’t,” drop and give me twenty.  It will do you good.