Math Problems

Everyone agrees that Math is Extremely Difficult and All Children Resist Math (except for those few oddballs who we can’t possibly understand or relate to).

But how true is this, really?  Consider: the proof of simplicity is that 2 + 2 = 4.  Everyone knows this, it is so logical that if 2 + 2 equals something other than 4, that is an invalid system (yes, I am thinking of Common Core here).  So everyone knows that math is extremely difficult, yet everyone uses a math equation to prove simplicity.  Which is it?

Like most paradoxes in education, it comes down to false equivalencies.  Basic math is simple and advanced calculus is not, but that does not mean that both should be avoided.  And we definitely should not teach both in the same way.  The person who is ready for even beginning calculus will be taught with certain expectations about the student’s ability, namely, that the student will understand basic addition, subtraction, multiplication and division, that the student will understand basic algebra and have the ability to manipulate equations, and that the student will be able to graph equations, especially in a Cartesian system.  If you got lost anywhere during that, I suggest that you are not ready for calculus.  But that doesn’t mean that calculus is hard.

Let’s look at it a different way.  We teach kids how to read, but we do not give them Plato’s Republic to read by themselves for their first book report.  It’s true that some would say that Plato is beyond the understanding of any but college age kids, but that is also manifestly untrue.  See Marva Collin’s work with “unteachable” kids.

But just like reading, math requires guidance from a knowledgeable teacher, one who knows  the material and knows that it is possible and even enjoyable to get from memorizing times tables to solving quadratic equations.  And we have raised a generation of teachers who are both ignorant of math and resistant to it.  And that’s what they are passing on to our children.

How easy is math?  This easy: have children memorize addition, subtraction, multiplication, and division tables from 0 to at least twelve (though 20 would be a better goal).  This is the phonics of math, and the stepping stone to higher concepts.  Math is all about pattern recognition, but it uses a special language, and all that rote memorization gets children speaking in numbers.  And it has the added benefit that 90% of the math they encounter in their daily lives will be understood with just this little bit of training.

But whatever you do, don’t start with the idea that it is too hard.


More from the good Count

This was written in 1862, but could have been written today:

After all this, compare the dogmatic school of the Middle Ages, where truths were indubitable, with our school, where nobody knows what truth is, and to which the children are nevertheless forced to go and the parents to send their children.

Tolstoy goes on to make the argument that the only form of education that could possibly justify state force would be religious, since religion is the only subject that professes eternal truth.  It seems counter intuitive at first, but that I think is more from the modern sensibility that even religion is not unchanging.  But the fact remains that it is hard, if not impossible, to demand unyielding compliance to an educational system that may be completely overturned in the next generation.

Think about it: the science books of our grandparents have no mention of electronics as we know it, and their grandparents probably learned very little about electricity at all when they were in school.  But the state, in its presumed wisdom, wants to tell us what we should be learning now.  And when challenged for a reason for their curriculum choices, they usually point to studies that are less than a decade old, and very nearly unproven in any real world setting.

What do we know?  That reading is the first key to unlocking any future hope of education, and that English, being a basically phonetic language despite all the bastardizations, can be best learned as a series of symbols to decode.  We call this phonics (although I suspect someone could make a fortune by repackaging it as “Lingual Decryption”, and for which I formally claim copyright).

That takes care of the language arts, and all that depend on it: writing, history, social studies, and every soft science.  It will even get you going in some of the harder sciences, like computer science.

But what about math?  It is universally acknowledged that Math is Very Hard.  Or even Extremely Difficult.  And the corollary is this: All Children Struggle with Math.  I think this is incorrect, and I’ll talk more about it in my next post.

The State of Education

This never fails to amaze me:

Popular education has always and everywhere afforded me an incomprehensible phenomenon. The people want education, and every separate individual unconsciously tends toward education. The more highly cultured class of people — society, the government — strive to transmit their knowledge and to educate the less educated masses. One would think that such a coincidence of necessities would satisfy both the class which furnishes the education and the one that receives it. But the very opposite takes place. The masses continually counteract the efforts made for their education by society or by the government, as the representatives of a more highly cultured class, and these efforts are frequently frustrated.

The writing feels a bit stilted, and it should: it was written in the late 1800’s.  But the sentiment is remarkably modern.  If everyone agrees that education is necessary, and desirable, then why can’t we figure it out?

Count Leo Tolstoy is best known for War and Peace and Anna Karenina, but he also wrote a lot in the philosophical realm, including essays on religion and reason.  I have only recently begun reading his thoughts on education, but it is remarkable to me that he identifies many of the same issues that vex us today: compulsory education is shows diminishing returns the more it is implemented, and yet everyone from the elites to the lower classes (nobles and peasants in Tolstoy’s culture) recognize the positive influence of education in a general sense.

So what is the best way to teach the children?  I don’t have a clear answer (though I might propose several ideas), but the empirical evidence is clear: the more we have consolidated educational standards, the lower test scores drop.  If the huge push in the mid 20th century to consolidate education at the state level resulted in a less educated populace, how could we possibly expect that nationalizing education would improve the situation?

Nothing in the Constitution addresses education.  It is a serious overreach for the federal government to even try to influence how the states educate their children, much less set the curriculum for the entire nation.