Thursday, April 9, 2015

Are the new Dark Ages coming?

Does the new math mean no math?  A professor of psychiatry opined on Bloomberg that boys and girls should not learn math past the basic levels of addition and subtraction.  Wisdom is ignorance. Foolishness is brilliance.  Dr. Susan Engel wrote:

The U.S. has a math problem. Despite all the time, energy and money the country has thrown into finding better ways to teach the subject, American children keep scoring poorly and arriving at college woefully unprepared. Just as bad, if not worse, too many students think they hate math.

I propose a solution: Stop requiring everyone to take math in school.

People typically offer some combination of four reasons children should learn math: for everyday functions such as doing taxes, buying groceries and reading the news; for getting a job in an increasingly technologically advanced market; as a powerful way of thinking and understanding the world; to tackle high school or get into a good college.

Let's consider these one by one. To some degree, children naturally learn basic arithmetic just by spending time with people who use it, and by carrying out such tasks as setting the table, going to the store or sharing toys with friends. Research shows that even illiterate children can compute sums quite quickly and accurately in familiar settings (such as selling produce on the street). Babies are born with an intuitive knowledge of numbers. It wouldn’t take much for schools to teach every child how to add, subtract, multiply and divide.

Those interested in highly quantitative fields such as technology, finance or research are likely to have a natural inclination for math. They can obtain the knowledge they need later, in a much more effective and profound way, in college or beyond. People who invent new industries are rarely using math they learned in school, and often aren’t using any at all. Why drag all elementary school students through a compulsory curriculum that turns off as many as it prepares, on the off chance that a few might need it?

True, learning math can give us intellectual strengths different from the ones we get reading novels, studying history or poking around in a petri dish. However, these kinds of thinking are not necessarily tied to numbers, certainly not at the novice level. Advanced mathematics requires students to reason logically, be patient, methodical and playful in trying out solutions to a problem, imagine various routes to the same end, tolerate uncertainty and search for elegance. They need to know when to trust their quantitative intuitions and when to engage in counterintuitive thinking.

However, such abilities are usually precluded by the typical K-12 curriculum -- a dizzying array of isolated skills and procedures, which many college professors say they spend too much time getting students to "unlearn." Research has shown that many students who do perfectly well on math tests often can't apply a single thing they have learned in any other setting. We end up missing a chance to teach them what they would really need in order to go on to higher-level math or to think well.

Instead of a good score in algebra, children need three things:

1. Time. For the most part, children think concretely when they are young, and become more capable of abstract thought later. A huge industry has grown up around the idea that we can game the human system and teach children to think abstractly before they are ready. Such strategies haven’t been very successful, and they preclude activities that would be much more compelling and useful to young minds.

2. Reading. Research has demonstrated that literacy is crucial to abstract thought. Children who read become capable of specific kinds of conceptual and logical thought not available to others. This opens the door to thinking about things that are not part of one’s immediate tangible experience, a crucial aspect of higher mathematics.

3. Intellectual challenges. Children who are immersed in informal quantitative reasoning come to more formal math tasks, at a later age, with much greater ease. Similarly, children who are asked to give reasons for their thinking, or speculate about the past and future, are well positioned to learn various kinds of logic and argument.

So here’s the plan. Teach young children arithmetic, a task that would probably take 20 minutes a day through the end of third grade. Spend the extra time on reading, and on the kinds of play that involve abstract thinking and problem solving. For young children, this could include building blocks, dominoes and playing store. For older children -- chess, "Minecraft," cryptography and the mental puzzles that can be found in a few outstanding math books, as well as in the brain teaser section of many supermarkets. Ask students to come up with reasons and evidence for what they say, and engage in serious sustained arguments with one another.

By about ninth grade, those drawn to mathematics could take interesting, rigorous classes. Others could pursue subjects more suited to their interests and strengths. Teachers who love math could offer activities as a way of teaching good thinking rather than as an obligatory form of preparation for future math classes. Those who are adept at some other way of teaching good thinking would be free to do so.

Teachers and students alike would no longer be locked into a compulsory curriculum that is too much for some, too little for others, and leads very few children to true mathematical ability. We would give up little of worth, and make more room for truly valuable learning. That seems like a good solution to me. Column.

Shades of Rousseau's Emile. Emile wasn't forced to sit through rigorous lectures or follow a curriculum. Emile could learn at his own pace. He could pick what subjects he wanted to study. One can only imagine what other schemes this Know-Nothing advocates.   One can only imagine the day when readin' and 'rithmetic are considered to be areas of special knowledge known by only a few.  One can only imagine the outrage if Bilbo and the Klan had proposed this crap for black kids.  Make it a lily-white liberal professor in the ivory tower in Massachusetts and it is suddenly "innovative".   Such learnedness will be the end of us all.


Anonymous said...

When the Nazis subjugated Poland, they defined Poles as 'Subhuman'. It was decreed that they need not learn to count beyond 500. And while the official opinion was that they should be taught to write their own names, their learning to read was considered overkill.

Perhaps Americans are now viewed as being a population of Subhuman slaves. Why should the slaves learn math?

Anonymous said...

I think that there's something to be said for not teaching algebra to everyone, but arithmetic? Sheesh.

Anonymous said...

I've taught Psychiatrists. Some are as dumb as a box of rocks.
Not knowing math is a great shortcut to a lifetime of minimum wage jobs.
Not understanding exponential interest rates is a good way to be suckered by BS from politicians from both political parties.
Are most of this blogs readers aware that in the mid-20th century in some states (no names, please ) African-Americans could graduate from high school after 11 years? Apparently the powers that be [or beed :-)] thought that was sufficient education to be a maid or a gardener.

Anonymous said...

"One can only imagine the day when readin' and 'rithmetic are considered to be areas of special knowledge known by only a few"

Been there, done that - it looks like some professor needs to re-read Frederick Douglass about what happens when a slave dares to learn how to read.

Anonymous said...

We'll they've accomplished allowing kids to graduate without being able to spell. Math is next I guess.

Anonymous said...

... Having read the excerpt, not just the misleading post title, I see that she does indeed say that arithmetic should be taught.

I would think a hard-hittin', truth-tellin' blog like JJ would be open to discussing whether high schools really need to treat a college-prep curriculum as a prerequisite to graduation.

Anonymous said...

We don't need no education!

Anonymous said...

What we're gonna do right here is go back, way back, back into time.
When the only people that existed were troglodytes...cave men...
cave women...Neanderthal...troglodytes

Anonymous said...

Ok, I'm coming back with some 2d-year algebra problems for the commenters to solve ...

Anonymous said...

I graduated with honors from Harvard Law and wrote my thesis on a law and econ topic that intensely data driven ... and I actually kind of agree with her. So does a high school classmate of mine who is a prominent surgeon.

Maths are languages for understanding and articulating with precision phenomena in the physical world. But once you get beyond arithmetic (or maybe Algebra I), the vast majority of high school teachers are neither capable of nor interested in teaching math as a language. They simply memorize pat formulas, rules and mnemonic devices to solve prefabricated problems. They have no idea what real-world phenomena those problems represent.

Students in these cases just go through the motions along with the teachers, which is worse than useless. Unless a student is in the .1% of people who will actually use advanced math in their career, the ONLY value of high school math is exploring the logic behind the problems. And frankly, most students don't have the intellectual horsepower to do that. And they never have. But we've been making them memorize theorems and mnemonics to pretend that they do, much like we used to make them memorize a smattering of Latin so they could pretend they had a classical education by the 12th grade.

It's pure pretense. It's like teaching a bunch of out-of-shape karate students a pre-scripted kata and pretending they know how to fight. In most cases, it would be better to try to improve their logical reasoning abilities through exercises that are more their speed, which typically involve words and less precise abstract concepts.

All that to say, I'm interested in quantifiable analysis of real-world problems, and I can say without hesitation that my Mississippi public high school math education was a complete waste of time. I would have been much better off building an engine or solving brain-teasers than regurgitating memorized formulas to some in-over-her-head teacher.

Anonymous said...

Hey Harvard Law! Less is more. Take a breath. No one reads blogs for long winded diatribes. I only read the first three words of yours. By the way, were you a classmate of Obama?

Anonymous said...

"the ONLY value of high school math is exploring the logic behind the problems. And frankly, most students don't have the intellectual horsepower to do that."

Not in that indirect manner, true. They'd be better off studying logic straight-up, preferably in conjunction with rhetoric.

I have a similar gripe about science, which in h.s. should be taught from a much more practical level, like the chemistry of the stuff under the kitchen sink, and the physics of the internal combustion engine. How's electricity work? (It is easier to find pop-science books on the origin of the universe or the frontiers of quantum theory than to find books about how the electricity running your computer is generated & transmitted.)

One problem is that h.s curricula are developed by professors, who opt for a slightly dumbed-down version of college classes rather than building from scratch.

Anonymous said...

Young people minds are like putty. They can formed to love and learn math if presented to them in the correct manner. Math is like a language. It has to be used everyday. If we fail to give them math we will fall behind the Russians and Chinese. Correction, we will fall even further behind the Russians and Chinese.

Anonymous said...

Sorry, 9:17. I forget that for some people reading five paragraphs is a substantial undertaking.

Anonymous said...

Let's just get government out of the education business altogether, except for military academies, etc., and then let people buy whatever education they want, or not.

But don't complain when you can't figure out anything for yourself and have to vote Democrat to get the smart people to give you everything you have.

Anonymous said...

We could look at the teaching methods in countries whose students do better at math.

We could take an multi-discipline approach to solving our educational problems including math.

There's plenty of research about how the human brain develops differently and that not all humans learn in the same way...some are visual learners and some are oral learners, for example. We teach with a " one size fits all" approach.

I hated math until I finally had a first rate professor my freshman year who understood that the tedium and excruciatingly boring text books made my eyes glaze over. He understood I didn't want to memorize formulas but understand why they worked! And, that was easily done and magical!

I realized my math teachers had just memorized math. They hadn't understood it's value in explaining the world! They had turned the ability to create a skyscraper into ditch digging!

Anonymous said...

I agree with Harvard Guy.

Anonymous said...

Hey, KF, you've got a Harvard Law grad hanging out on your little 'ol blog. But, KF, don't get the big head. It moreso suggests how far he* has fallen as to how far your blog has risen.

* Use of the word "he" is intended and is hopefully found to be offensive to the hand wringing bed wetters.

Anonymous said...

Bring it on, at 6:12.

Anonymous said...

Hey Harvard Law - pronounce "corpsman" for us. Then name all 57 states.

Anonymous said...

Typical (of this blog) responses to a thoughtful analysis. The guy qualifies his reasoned point by setting forth his substantial education, and most of you jokers don't read past "Harvard". Obviously, because he went to Harvard, he must be an ivory tower egghead.

The celebration of ignorance continues. I attended one of the best schools in the state in high school, and took math courses up through AP calculus. I never understood the logic behind the math, and instead just memorized the formulas to get through the class.

Later in life, after I had some context and basis for the application of higher math (in college, in my major), I was able to functionally grasp calculus, and math is now beautiful to me.

The point is that rote memorization of difficult concepts is useless across the broad spectrum. Start useful applications for math at a young age (such as shop, mechanics, household chemistry) and then watch those young minds learn to use higher math within context.

Anonymous said...

11:36 You said in a few sentences, and without invoking any authority other than your unnamed high school and college, what Harvard Law failed to express convincingly in an overlong screed. My post at 11:02 was just to deflate his immediate brag (as if we think law school automatically entitles one to claim expertise in higher mathematics).

As far as your "celebration of ignorance" claim - as someone who has served on the full-time faculty of two Ivy League medical schools (NB: you don't find many med school grads embarrassing their alma maters as in the example I cited at 11:02) I felt obligated to shut down that pompous appeal to authority (read: brag) as soon as it appeared.

For the record, my oldest aced AP Calc, and I expect the younger one to take it as well. Neither one is interested in a minimum wage "career" of hair nets and name tags (thank you, "Wayne's World").

Anonymous said...

Hey. Teacher. Leave those kids alone.

Anonymous said...

12:15, give it up. Harvard wasn't bragging. He was illustrating that it's not just uneducated people who think math as currently taught is lousy. It's a fair response to the implication that the original author risks returning us to the "dark ages." He's not Obama, any more than he's Scalia. You were being petty. Now stop.

Anonymous said...

I graduated with honors from Harvard Law and wrote my thesis on a law and econ topic that intensely data driven ... and I actually kind of agree with her. So does a high school classmate of mine who is a prominent surgeon.

ANOTHER damn anonymous APPEAL to AUTHORITY and know ANNA inside and out.


Col. Reb Sez said...

The guy is partially right. Some people simply aren't very good at math.

My son taught himself to multiply a single-digit number and a two-digit number while still in kindergarten, provided all of the numbers were below six, which was as far as he knew the multiplication table. So we challenged him by asking him math problems that included a six, then a seven, and so on. In first or second grade the kids made fun of him on the bus because he knew how to calculate squares, cubes, and their roots. That was the end of his doing squares and cubes.

Meanwhile, my daughter, who is quite bright verbally, is mediocre at math. I don't think she ever did really learn her multiplication tables. In my view there is no need for her to have Algebra II or Calculus.

All students should master basic algebra, and virtually everyone should get more geometry than they do now. But we don't need a society in which every student is great at math.

Anonymous said...

"I graduated with honors from Harvard Law and wrote my thesis on a law and econ topic that intensely data driven .." Classic.

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