Technology is undermining math and science education, argues Konstantin Kakaes, a New America Foundation fellow, on Slate. Fancy gizmos and software shortcuts waste money and weaken learning, he writes.

When Longfellow Middle School in Falls Church, Va., recently renovated its classrooms, Vern Williams, who might be the best math teacher in the country, had to fight to keep his blackboard. The school was putting in new “interactive whiteboards” in every room, part of a broader effort to increase the use of technology in education. . . . It is beginning to do to our educational system what the transformation to industrial agriculture has done to our food system over the past half century: efficiently produce a deluge of cheap, empty calories.

. . . Williams doesn’t just prefer his old chalkboard to the high-tech version. His kids learn from textbooks that are decades old—not because they can’t afford new ones, but because Williams and a handful of his like-minded colleagues know the old ones are better. The school’s parent-teacher association buys them from used bookstores because the county won’t pay for them (despite the plentiful money for technology). His preferred algebra book, he says, is “in-your-face algebra. They give amazing outstanding examples. They teach the lessons.”

The modern textbooks, he says, contain hundreds of extraneous, confusing, and often outright wrong examples, instead of presenting mathematical ideas in a coherent way.

Technology can help students learn concepts, advocates claim. In practice, that doesn’t happen, Kakaes writes. Students are even more likely to arrive in college with little understanding of math. The graphing calculator has done the work for them.

A science teacher demonstrated the superiority of her interactive whiteboard by showing him a music video featuring a Rube Goldberg machine. He wasn’t impressed. Then she showed a drawing of an electric circuit in which wires connect a light bulb to a battery. Close the circuit and the bulb lights up.

Her students like it when the bulb lights up, she says, because it reminds them of a video game. But this shortcut is dangerous. Learning how to visualize—as required when an electric circuit is drawn on a blackboard—is vital for developing the ability to think abstractly. You also have to make students manipulate real circuits with real batteries, with real wires that connect them and sometimes break. Showing them a toy circuit in computer software is an unhappy middle ground between these two useful teaching exercises: You neither learn how to trouble-shoot in the real world, nor do you think clearly about how electrons work.

Math and science require hard work, practice and perseverance, says Williams. There are no shortcuts.

Why not use the Smartboard like a black board? It really has an advantage that the blackboard doesn’t, you can save digital copies.

That’s exactly what I do. It allows me to put the actual worksheets or textbooks or graph axes on the board and write on them. I essentially use it like an overhead projector.

Presuming for the sake of discussion that the older math books–some of them–were better, what caused the change?

What was the theory that, in the event, turned out to be wrong?

Whose idea was it?

Did anybody figure out that this was a bad change, not merely a change?

Question: Since books eventually wear out or get lost, replacements must be available. Is there less money in reprinting a successful book than in making up a completely new one?

Now, I had a prof who wanted us to buy the nineteenth edition of his text. Obviously, a full turn over every year is more profitable, but why would a school board want to do the same thing? There’s no money in it for them to get a new series every so many years. Is there?

“Obviously, a full turn over every year is more profitable, but why would a school board want to do the same thing? There’s no money in it for them to get a new series every so many years. Is there?”

Now, I don’t know how things work in the public school world, but when I worked at a computer lab as a student in a state college, we would always run out of printing paper (and had no money to get more) sometime during spring quarter. But, then at the end of said spring quarter, would have to go on hardware shopping sprees (for stuff we didn’t even need) because we always had money left in that budget, and by God, it all had to be spent or we’d lose that money for next year.

So, who knows — there’s a line item for new instructional materials and that money has to get spent or taken away.

(Why does it have to be so rigid? Why can’t you just spend money on what it is you actually need? Those naive questions earned me a stupid look when I asked them. Heh.)

Richard, Good question. Textbooks and their evolution have a long and storied history. In a nutshell, math teaching in lower grades has fallen prey to inquiry-based, student-centered, problem-based, project-based and vendor-based learning. If a teacher stands at the front of the room and instructs students directly, even if he/she engages the students with questions and interactive problems, that teacher may hear about it from the powers that be. For more information on this,

See an article I wrote on this at http://educationnext.org/anamazeingapproachtomath/ and also one written by David Klein, math professor at CSU Northridge at http://www.csun.edu/~vcmth00m/AHistory.html.

Two points:

1. Textbook revision works like churning in stock portfolio management, where the manager gets paid for activity. What’s in it for school boards? Kickbacks from publishers. The money that system overseers spend on textbooks is not their loss. The kickbacks are their gain.

2. “There are no shortcuts”. Maybe. But there is a huge advantage, to students, in carving a direct path from whole number Arithmetic to Calculus, and not wasting time on “Rainforest Algebra”. Since the current institutional structure relates a school’s budget to the time that students spend in school, schools have no incentive to use student time efficiently.

It isn’t just, or even mostly, a result of kickbacks.

If it were prosecuting attorneys would be sending school board members off to the government hotel by the hundreds. It’d be like shooting fish in a barrel since every text book change is public record and prospective evidence of skulduggery.

Just the sort of thing a PA with political ambitions would gravitate towards. They’d be doing it for the children.

No, the textbook changes are to give the illusion of determined progress in improving the part of the public education system the school board oversees.

They’ve got to do something to indicate they’re not just napping at school board meetings and they certainly can’t point to the more compelling evidence of educational efficacy since to most of the professionals any whiff of accountability causes the rapid onset of a severe case of the vapors. So they regularly change out the text books whether the new are in any way educationally better then the old. Or even if they’re not.

Malcom

Do you know for a fact that kickbacks are involved?

A long time ago I raised the issue of school board and administration corruption on this blog and the sole teacher on this blog at the time said that was impossible.

If true, I think a young district attorney could make a big reputation trying corrupt school board members and administrators.

Was I ever offered a bribe? No. Once our department chair dated a publisher’s representative, and the department bought their wretched Alg I textbook. Another publisher’s rep took the department to dinner to pitch their books. There’s more money involved in getting books on the approved-for-all-schools list. I expect it’s more often a matter of favors than of dollar bribes. Look at the unbelievably long list of co-authors on high school Math and Science texts. In big districts, it’s very likely corrupt. Corruption in school construction contracting is certain: google “Maurice Calloway”. Why not textbooks?

If Mark Twain were even half right about school boards, the inhabitants thereof couldn’t hide any wrongdoing from a sleeping Clouseau.

Somewhere, there’d be a clown buying rounds for the house and telling everybody how he got so rich. It would only take one and, there being so many school boards, there has to be one, if kickbacks were the issue.

So, probably they’re not.

Consider the opposing view from Conrad Wolfram, certainly no lightweight in the mathematics universe himself, who espouses the complete opposite point of view.

http://www.wired.co.uk/news/archive/2010-07/19/conrad-wolfram-maths-curriculum

Having seen him speak in person, I would say he makes a very persuasive case for less mechanical focus (and more focus on technology).

As a college math professor myself, I think the problem remains the irrelevancy (for most people) of high school mathematics. STEM majors can really use rigorous mechanics and strong analytical skills; everyone needs stronger numeracy and real-life (not real world) applications. High school math tries to split the baby and fails at both.

Tom. Couldn’t agree more. In real life, everything is a story problem, usually not requiring anything more difficult than switching fractions to decimals, or long division. (Is there such a thing as short division? If not, why “long” division?)

Yes, there is such a thing as short division

Okay if I hold at long division? Jeez. Unnecessary complications.

By “high school math”, I’m assuming you mean algebra and the courses following. Conrad Wolfram seems to be opposed to teaching “hand calculation” at all. I’m assuming that he means things like long division.

So … I get the idea that maybe forcing all high school students to take a year of geometry is less than ideal. But that’s not what Conrad Wolfram is limiting himself to.

Are you also okay with most/all kids getting to high school and not knowing how to (a) add multi-digit integers, (b) multiply multi-digit integers, (c) perform long division, (d) add mixed numbers, etc? Because I think Conrad Wolfram is advocating turning all of this over to calculators.

Actually what he encourages is mental math over pencil-paper math. To do mental math later in life, you still have to teach process in elementary and middle school. And I’m not entirely in agreement with him about ditching processes but I think the focus has to be on why and how it works as opposed to simply performing the calculations.

To all your questions, it’s a question of magnitude and frequency. With (a) I think mentally everyone should be able to add 3 or 4 digit numbers in your head and people who use those numbers daily should be able to handle more than that. With (b) and (c), those are exceptionally rare outside of STEM fields; people who work with numbers probably can (and should be able to) do both to a limited degree. (d) What kind of mixed numbers are we talking about? The problem is the fractions of course, not the whole parts (unless you’re carrying a whole from the sum of the fractions). Denominators of 3, 4, 6, 8 are reasonable; 23, 35, 54 less so.

Thanks

“Anyone who cannot handle mathematics is not fully human, but is at best a tolerable subhuman who has learned to bathe, wear shoes, and not make messes in the house.”

— Robert Heinlein, “Time Enough for Love”

Math as it is taught to most kids in elementary school today is a bunch of disconnected rubbish that does more to turn them off and turn them away than almost anything. The only thing worse is an elementary school math teacher telling her kids that ‘math is hard’. She should be shot, preferably where it hurts most. (Yes, this happened to my daughter. Fortunately, she didn’t listen but she did come home quite indignant. And she is working toward taking AP Calculus and AP Statistics to finish out high school. This is in spite of, not because of, her teachers. We taught her to love math as a kid by 1) teaching her the rules in a logical, organized fashion that suited her learning style, 2) playing math games such as when we were driving in the car – yes, all in our heads, and 3) showing by example that math was useful in everyday life – when mom and dad are a quality control specialist and an engineer, there is a lot to draw on. Plus we both love math anyway. I do remember one of our first dates where we discussed special relativity, quantum tunneling, and Schroedinger’s cat….

At the least, we need to stop these ignorant elementary school teachers and the stupid textbooks they use from destroying our kids’ love of math before there is time to nurture it.

Every adult should be able to do enough arithmetic so that when s/he is given a twenty-dollar bill, two one-dollar bills, two quarters, and two pennies for a $7.52 drive-through order, s/he should not have to call over a manager to have the customer explain to both the employee AND the manager why $13 change is not sufficient.

A few years ago, I handed $4 to a bakery clerk, for a $3.82 purchase, saying that I had the 2 cents. She had apparently entered $4.00 into the register, because she gave me a blank look and picked up a calculator. After she tried several times to do “something” with the calculator, I told her she owed me 20 cents. She looked even more confused, but gave me the 20 cents and disappeared. Sigh…

My experience has been that ES teachers are generally weak in math, the current spiral curricula (like Everyday Math) are inherently flawed and groupwork/projects/discovery methods of “instruction” are ineffective and inefficient. It’s a perfect storm that is almost guaranteed to produce math incompetence in a large portion of students. However, since students never have to demonstrate mastery of anything (“trust the spiral”) and are working in groups, the whole mess can be used with heterogeneous grouping (including full inclusion) and “differentiated instruction” to enable the pretense that “all” are learning. Then the kids hit about 6th-grade and most will not make the cut for real math that will allow serious HS math courses and STEM field options – and the system then blames the students for not being “engaged” or some such. The exceptions, of course, are the kids at the very top of the ability curve who have somehow managed to learn the material in spite of poor curriculum and poor instruction, and those who have been tutored (at home, Kumon etc). BTW, calculators should be absolutey forbidden until HS; they are another tool to disguise lack of mastery of arithmetic – and that’s only if the kids know how to enter the problem properly – and many don’t They really shouldn’t be used until pre-calc, but their requirement on the SATs forces earlier use.

Agreed! Students should not be using calculuators at ALL until they get into the Trig and Logarithims of PreCalculus, or the accounting of Financial Math, which is the alternative Math class for those who couldn’t handle PreCalculus – which for most students would be 11th Grade in both cases.