At a training session for teachers in Bellevue, Washington, an elementary teacher asks a reform math consultant what to tell parents who ask whether use of calculators will hinder children’s computational skills. Here’s a video of Phil Daro, co-director of Berkeley’s Tools for Change, telling teachers to dodge the question. (He’s preceded by Uri Treisman of the Dana Center at the University of Texas.) Cal State-LA Math Professor Wayne Bishop, writing on Math Forum, provides a transcript of Daro’s answer:

. . . it’s part of the math wars. The best advice is, Don’t answer that question. You are being asked to fight a battle on a hill that has been custom made to turn you into a fool. And there’s no way to win. So basically, the general advice I give in the math wars is Advice 1. You have to realize that their strategy is to attack you, not your ideas and

they’re going to fool you by making you think they are attacking your ideas.The first thing you do is you stand up and identify yourself to this

audience of worried and frightened parents. Tell them who you are and say I believe that all students should be able to add, subtract,

multiply, and divide without calculators. That’s the first thing you

say when the calculator issue comes up. And everything after that

when they say “calculators”, you say “technology”. If they ask about

calculators, you say, “Well, technology is important but it’s no

substitute for mathematics.”

In my experience, many parents and teachers believe introducing calculators in early elementary school hinders students’ mastery of computation, weakens their “math sense” and makes them permanently dependent. Others think there are ways to introduce calculators without letting them become a crutch. This really is about ideas, not personalities. The question deserves an honest and complete answer.

Something is very wrong in Mathland. I teach Honors chemistry in Prince George’s county Public Schools just outside of D.C. I gave the Chapter 3 Test to the Honors students which contains the type of arithmatic needed for chemistry. Scientific notation, metric conversions, unit analysis (canceling units, g/mL x mL = g for example), equation manipulation (solve for v in the equation D=m/v, density euqtion, very simple), rounding rules, and significant figures. Considering that these children are 10th through 12th graders and all have passed Algebra I and II, Geometry, with good grades and are presently taking pre-calculus or trig analysis and getting good grades, for the highest grade on a 50 question test was a 74%. Huge numbers failed the test.

Oh,…and I didn’t assume that they knew this stuff because they were Honors and getting good grades in other math classes. I knew from previous experience that they didn’t. So I spendtthe last two weeks teaching and doing activities on this material with the Honors class. But then I lerned some things.

The students don’t know the material of the math classes they got good grades in. I kid you not. These kids did not kow the law of exponents (10^n * 10^m = 10^n+m and the like), how to factor a polynomial, How to solve for an unknow in an algebraic equation, and on and on. So I wondered how this could be…

…and then this year the sciecne department ws required to follow the new grading standards just like math had to for the last 3 years. the grade in a class is calculated so: 75% effort (100% if on time, complete, and good faith effort-cannot be graded for correctness), and 25% tests and quizzes. Doing all of the effrot work and randomly answering the math test (yes…multiple choice NOT put-the-answer-from-your-work-in-the-box)with get you a B. Actually get close to passing you can get an A.

When we were given this new standard thisyear we dang near choked. The standards are being lowered like crazy. Calculator use was just hte beginning.

I can’t believe this would even be up for discussion for elementary schools, much less considered controversial. Even in first year undergrad honors physics, the prof repeated endlessly that we needed to make the calculation in our heads before hitting the calculators. There was always some fool who ignored this advice and would get pointed out when he submitted some impossible answer without thinking (for example, electrons whizzing by at 10x the speed of light due to application of a mild field).

Ms. Jacobs.

Thanks for linking this video. I actually value your judgment and may have been fooled by my own bias against calculators for figuring out nine times six.

I agree the “question deserves an honest and complete answer.” I’m surprised that there is nothing definitive after 30 years of research at our finest institutions. We are, of course, aware of progressively greater innumeracy in the population at large. There is statistical evidence based on the NAEP pointing to declining scores.

I, personally, would be unopposed to a blanket ban on the use of calculators until 10th grade when I got my first TI-50!

Raman

No K-12 student should touch a calculator in class until they start doing basic trigonometry and logarithims. For most students, that’s PreCalculus, in either 11th or 12th Grade.

(In Algebra II, you can just have the students express imperfect roots in their root forms in their final answers. For example, x = 2 + sqrt(7) would be a perfectly gradable answer. In Geometry, just have the students give their answer in terms of pi, when circles, spheres, ellipses or ellipsoids come up, or multiply it out by hand. And before Geometry? It’s nothing but integers and fractions… done by hand.)

I have to compute everyday–frames per second, $$ per second, discounts etc. If I had to do this in my head or on paper, I’d be so slow and wrong. Why would I ever both? Does anyone in real life actually do math in their heads?

Face it–some of us in the real world aren’t math whizzes, yet we still need to work with numbers. Why make things harder than they need to be?

During my years in the kitchen, I converted thousands of recipes using fractions and my mind. I calculated food costs and labor costs in my head. All my calculations were accurate (98% accuracy was good enough for everyday life). I often corrected coworkers who made a habit of using the calculator. Using the tool itself is by no means a “bad” thing, however it must be preceded by a firm understanding of the fundamentals. Lacking those skills, one might accept a mis-keyed answer for adding 4/5 and 2/7 as being greater than or equal to 1.

The wood shop I worked in was not populated by “math whizzes” yet a calculator never made an appearance and all work was done with pencils and spare wood (and answers had to be checked). So yes, real arithmetic is done everyday, by everyday people without technology.

In the interest of full disclosure: I now teach math to 8th graders who are incapable of doing basic (4th grade) math with single digit integers with or without calculators. They can give me answers, but have no clue what it means (they’ve been using calculators for years).

There are two issues: dishonesty by math education consultants, and the role of calculators in K-12 education. The first topic one can only lament.

Calculators are important and useful. Being able to calculate is also important and useful and introducing calculators in any routine way before students have mastered arithmetic will probably hinder their mastery. But even then, in grade 4 and up, let’s say, they are frequently useful. For example, when my 10 and 11 year-olds (homeschooled) finish a worksheet, say on 3×3 multiplication (in the context of on-going practice, not learning something new!), they check it themselves with a calculator. This works fine, is quick, and for some reason they like using the calculator. But they have to know how to quickly and correctly do the arithmetic themselves.

Hung-Hsi Wu (go to http://math.berkeley.edu/~wu/ and search …)has a wise take on this. He writes that for kids to really learn fractions (a vital prerequisite to learning algebra), they need to routinely do computations with unwieldy fractions, not just 2/3 and 1/4 all the time, but 154/773 and so on. But, he says, so much arithmetic by hand will burn kids out, so let them use calculators as follows. If the have to add 485/2,973 + 193/867 then have them write out

(485×867 + 2,973×193)/(2,973×867)

and use the calculator to compute numerator and denominator (and leave it as a fraction, or divide and get the decimal expansion, as the case requires).

This is very sensible. It allows kids to do more arithmetic than they would otherwise be able to do and gets them used to handling numbers that have not been carefully chosen to “work out”. The key is that calculators can then only be used only for specific problems.

Also, KateC: you are making one of the most common errors in thinking about education, math or otherwise, which is that classroom practice should follow workplace practice. The fact that a given adult uses a calculator for all arithmetic has no bearing on the question whether students should. In fact, if they are taught to handle numbers, they will not need to use a calculator for everything when they are adults. Is there any advantage to that? Sure, sometimes it is useful to see how factors are canceling, or things like that, rather than just get a decimal number. (So the answer is 0.33333? Is it really? or is it 1/3?)

What I try to teach my kids is to recognize an easy problem when they see it; develop some judgment about what can be done with mental math, and what requires plugging and chugging on a standard algorithm; later, this will mean also deciding whether to do something by hand or by calculator. It is better to have more tools rather than only one.

p.s. Er, when I wrote “3×3 multiplication” I meant multiplying two 3-digit numbers.

Uhm, I made a mistake (didn’t check my work) 4/5 + 2/7 IS > 1.

next time I’ll use preview and check my work.

CowboyLogic nailed it. If you can’t do the fundamentals in your head, then you become a slave to the calculator, and accept the answers it gives with blind faith – even if you typed in the wrong question because you didn’t know the difference.

I see it all the time in the Math and Physics classes I teach. Calculator dependence turns students that would otherwise have regular Math skills into having poor Math skills, and those who would otherwise have poor Math skills into complete innumeracy.

The students with gifted Math skills survives despite the calculator-dependent teaching methods used in most Middle Schools, but it stunts their understanding conceptually, so even they don’t escape unscathed.

Does anyone in real life actually do math in their heads?Yes, in meetings, and other situations where people don’t have calculators to hand. Technology is nice, but your brain is always with you.

In 2007, Singapore changed its national math curriculum to allow for calculator usage in level 5 (equivalent to 4th grade in the US). Now educators here are holding their collective breaths, waiting to see if/how this change affects students’ success on the big PSLE exams in level 6 and the TIMSS. Should be interesting….

Actually, what Mr. Smith said doesn’t surprise me, in an introductory course in informatics I took last year (college course), the 2nd exam covered basic statistics (mean, mode, std. dev, variance, probability, etc), and no calculators allowed. I got a 95 on that exam (of course, I had the benefit of learning how to do math w/out a calculator in my youth). The class average on this exam was 69.7% (and the student body was typically under the age of 25).

The over-reliance on calculators has ruined the math ability of an entire generation of students, and will continue to do so for generations to come, in my opinion.

Kate C said, “Does anyone in real life actually do math in their heads?”

Yes, those of us who were actually taught how to compute do math in their heads. ALL THE TIME. Of course, we went to school in the 50s and 60s. I don’t use calclators for much of anything in everyday life because I don’t have to–I can do basic math in my head or on paper and do it quickly. Alas, like reading and writing, math computation is becoming another lost “art.” Sad.

By the way, the so-called experts in the video are several of the many reasons why people outside the field of education laugh at us. Education is an insulated world that is not self-critical nor does the field respond to criticism from outside the field. As many have noted elsewhere, that is a recipe for disaster. The disaster is the public schools.

I had a kid who couldn’t multiply by ten. I told him to move the decimal point one place to the right. He freaked out and said “but you told me to multiply by ten!”, as if I was suggesting something different.

This is not that unusual.

Admin types are impressed with calculators because they’re “technology”.

Kate C said, “Does anyone in real life actually do math in their heads?”

Um. Yes. After six years of Singapore Math my kid does most of his math in his head. It’s nearly impossible to get him to show his work. I bought him a calculator from the dollar store. He thought it was kind of neat for a few days and then lost it somewhere in his room…

BTW, I can compute tips, sales taxes, store discounts and adjust recipes all in my head!! I guess I’m a genius!!

I’ve had more than one gen-X’er cashier pull out a calculator to figure out change…. Pretty soon, even McD’s is going to have to outsource their work to India….

“Does anyone in real life actually do math in their heads? ”

I don’t do things in my head, but I do them on scratch paper all the time. I’m an engineer and I recently worked out a high school physics kinematics problem in the middle of a meeting. The answer probably saved the US taxpayer millions of dollars in expensive (and unnecessary as it turns out) testing.

Anything much more complicated than high school physics will be farmed out to computers, which means I’ve only had to work out the solutions to those problems once or twice in order to do the programming and verify that the computer is working properly.

Vandal Savage’s suggestion of exact answers is also brilliant. If and when the kids get to higher level sciences and computer programming, everything will be in terms of variables. You can’t just put variable names into a calculator and have it spit out the solution equation. You have to manipulate it the hard way or go to more expensive and much less common symbolic manipulation tools.

Nicksmama and others are making this point: people who can do arithmetic in their heads (whether estimating or exactly)will do so. People who can walk won’t always take a wheeled conveyance. It is probably hard to explain to someone who cannot calculate in their head why anyone would want to, but the simple fact is, people who have the ability use it.

As I wrote earlier, calculators are great. I frequently use one, but not as frequently as I calculate in my head or on paper. After a while you get a feel for which is better for what problem.

I recommend a book like “Secrets of Mental Math”. Engineers do stuff like this all the time. In the real world a quick and approximate first answer can be useful especially when discussing ideas with other engineers. Using a calculator is just to slow and cumbersome for this purpose.

I’ll echo what bky stated, that calculators are useful and important. Used properly, they can enhance education. I recall my high school Chemistry teacher sharing with me that due to the availability of calculators, he could assign a variety of problems involving balanced equations instead of one or two. Students could focus on the chemistry of each problem and not spend 90% of their effort on the math. Of course you have to have the requisite math skills in the first place.

However, relying on the calculator and not having the ability to estimate the correct answer and therefore not recognizing an obvious wrong answer is a problem in everyday life. Too often I have seen a cashier or speaker insist the value was correct because that’s what the machine calculated. Recently my wife (a L&D nurse) was at a meeting where the speaker stated the number of babies deliveries per month for the year was up significantly. My wife divided the monthly total that was presented by 30 (in her head!) and the daily figure was well above average. Yet the speaker held fast to the original value as true, because, well she calculated a monthly average, not a daily average. Although in this case a wrong value on a slide may have just been a minor embarrassment or at worst lead to slightly inefficient staffing, I believe at least some of the dosing mistakes are due to medical personnel not able to recognize math errors.

I frequently do math in my head. I may be working out an example for my class at the chalkboard and not have a calculator at hand. (Granted, I choose the “made up numbers” for the example so that it’s something relatively easy for me to do – like winding up dividing by 3 for example).

But yes. I also do math in my head when shopping (“how much will I have to pay for all of this” or “okay, this is 40% off and it was 67.00, what will I pay for it now?”) or when planning a craft project (“this sweater takes 14 balls of yarn that has 100 yards per ball, how many fewer can I get away with for this yarn that has 120 yards per ball.” Granted, in that case I may resort to pencil and paper but I still do know how to do it in my head).

My dad also taught me to calculate gas mileage based on miles traveled vs. gallons bought, but I tend to be too lazy to do it with my car.

“The best advice is, Don’t answer that question. You are being asked to fight a battle on a hill that has been custom made to turn you into a fool. And there’s no way to win.

There is, if you’re correct.

“So basically, the general advice I give in the math wars is Advice 1. You have to realize that their strategy is to attack you, not your ideas and they’re going to fool you by making you think they are attacking your ideas.”

Public school advocates have been attacking people for decades.

I constantly do math in my head: calculating tips (move the decimal & double it), converting celsius to farenheit (ballpark number – double the temp & add 30), and once upon a time I could convert binary to decimal & vice versa (very handy when figuring out subnets on networks). What I don’t use, I lose, and it’s been several years since I’ve done the binary/decimal conversions, so I can’t do those in my head anymore.

But figuring out the approx square footage of my yard, so I know how much weed-n-seed to buy? In my head.

Multiplying or dividing a recipe? In my head.

Figuring how much gas I’ll get if I just put $10 worth in my tank, or how far I can go on a tank of gas? In my head.

Counting my change so I can roll it up? In my head.

I’ll use a calculator if I have a large pile of numbers to add up, but I usually double-check myself with pen/paper, because I’ve been known to leave numbers out on the calculator.

And I’m just an average person with a liberal arts degree who later chose to work in the computer industry (hence the subnetting). I didn’t go past Geometry in high school, and I was a sophomore (almost junior) in college before I ever knew what a logarithm was. Never used a slide rule (those went away right before I got to the grade where I would have needed one), never learned how to calculate a square root. On my college entrance exams, my math scores were several hundred points below the verbal scores. And yet, I can do all these common, everyday arithmetic tasks in my head, BECAUSE I LEARNED ARITHMETIC BEFORE CALCULATORS WERE COMMON.

Calculators are a nice tool, but I rarely have one handy, and as someone else said, my brain is always with me (although sometimes it does seem to take vacations without me).

An editor at a newspaper where I once worked thought she needed a calculator to figure out whether a school-bond issue had passed or not, in a very close election that required a 2/3 vote for passage. (She didn’t; multiply the number of no votes by two and compare that to the number of yes votes.) So she used the calculator. And she got it wrong, in a screaming banner headline in huge type on the front page.

“I had a kid who couldn’t multiply by ten. I told him to move the decimal point one place to the right. He freaked out and said “but you told me to multiply by ten!”, as if I was suggesting something different. This is not that unusual.”

No, it is not unusual. I have college students who cannot carry and borrow on paper or in their heads. Long division? Fugitabout it! Fractions? Heaven forbid! 10% of 100? No way! You know what they’re going to be called after 2-3 more years? Teachers!

anon- I once had a student (this was in a freshman-level college class), when we were doing a lab that involved estimating how large an object was under the microscope based on the size of the field-of-view, who had to divide 1.2 by 10.

“I can’t do this.” she said, “I left my calculator at home.”

I explained how to do it by moving the decimal place.

She looked at me as if I had invented fire. “You can DO that?”

I resisted the impulse to say, “Yeah, and I’ve been doing that since I was in fourth grade.” Because that would be just too snarky.

“Yes, in meetings … Technology is nice, but your brain is always with you.”

Clearly you haven’t been attending the same meetings I have.

I’m afraid that this is one of those topics that makes otherwise intelligent people appear less than intelligent.

The belief that the use of calculators hinders the learning of basic arithmetic is a myth.

It’s a myth that springs from ignorance and fear and probably from watching too much of Fox News.

You’ll find more science teachers who reject evolution than you will find math teachers who object to calculators.

Don’t take the word of an adult who’s proud that he can do math in his head. Look at the research. It’s clear. Also, talk to math teachers who, day after day, have to put theory into practice.

It frightens me how people hold on to myths.

Talk to math teachers. Look at the research.

…and turn off Fox News.

Robert,

You make a number of proclamations without evidence; perhaps you could link to research you fail to cite.

ps. your prejudices are showing. Fox is not the only source of propaganda in the media.

Tom West, sometimes in meetings my brain has exuded strong impulses in favour of jumping out the window, never mind if we’re ten floors up. Having your brain always with you is not always a good thing.

“Look at the research.”

What research is there that the early routine use of calculators does not interfere with mastering arithmetic? Note this: by using a calculator in the 3rd grade classroom, for example, you remove opportunities for a third-grader to practice doing arithmetic. So how are they going to learn this stuff? The question of whether math teachers object to calculators is irrelevant, since math teachers are frequently the very people who preside over the non-learning of arithmetic in the first place.

You’ll find more science teachers who reject evolution than you will find math teachers who object to calculators.I’ve never encountered a science teacher who rejects evolution, but my 7th form maths teachers objected to calculators.

Admittedly he came to class once fuming because our principal had offered him a classroom in the new school building that was opening next year, which would have taken him away from his shoddy 40-year old “temporary” pre-fab with no insulation. From his reaction you’d’ve thought she’d asked if they could sacrifice his first-born son to placate evil spirits on the building’s opening. But he was a good maths teacher.

“The belief that the use of calculators hinders the learning of basic arithmetic is a myth. It’s a myth that springs from ignorance and fear and probably from watching too much of Fox News.”

Oh, Robert, and here I thought you were actually going to provide some evidence on this issue. But, when evidence is absent, your resort to the favorite practice of left wingers, the ad hominem attack. This type of attack provides evidence for my earlier point. Education is an insulated world that is not self-critical nor does the field respond to criticism from outside the field. As many have noted elsewhere, that is a recipe for disaster. The disaster is the public schools.

Here are a few things I remember from my studies as an educator: Our brains need “exercise”. Memory is created by making strong connections and reinforced by repeating them. Children’s neural plasticity puts them in a unique situation to benefit from knowledge and skill acquisition more efficiently and effectively than adults. Brain games and regular mental exercises may produce positive effects on mental performance in a number of different and surprising realms unrelated to the subject of the exercise (like driver safety).

To me this reinforces the value of kids learning to do math on their own. There is value in kids developing mathematic knowledge and skill in their longterm memories; there is value in the act of doing math for their brains as a whole. Some of this value is simply not measured by the education system. In my own life I recognize value in nearly every course I’ve ever taken. Why? Variety, mental exercise, and the fact that you never know when a particular fact, concept, or approach is going to help you solve a problem–regardless of the realm.

Calculators therefore seem like an unnecessary crutch in K-6. After 6? I’d hypothesize that they have little or no negative impact, and probably a positive one, especially when used in science courses, such as chemistry and physics, where math is necessary but not the focus of learning objectives.

Ah, typical eduspeak. Make assertion. Pretend it’s obvious.

Countries where calculator usage is delayed or minimized kick US butt in math.

I see the results of calculator damage in students all the time. No number sense whatsoever. A student will fat finger some keys, get an absurd number, and pronounce it correct, because the calculator said so.

I don’t watch Fox News. And I don’t see how it could ever be a Fox News issue anyway. Isn’t being pro-calculator a part of being pro-technology, which is highly pro-business?

Why not?

You mean educational research? The laughingstock of academia? I’ve seen enough “research” to last me a lifetime.

Yes, it is. It’s clear that the overuse of calculators impacts kids’ math abilities. Kids who can’t add fractions on paper because they’ve used calculators for such operations can’t then deal with expressions like a/b + c/d algebraically.

First, not all math teachers would agree with you.

Second, those that do have put us in the dismal situation we’re in.

i saw some comments suggesting the middle school teachers make a practice of allowing students to depend on calculators. i teach middle school, and i find that they come to 6th grade without knowing their times tables and God forbid you ask them to divide anything. They are shaky at best at adding and subtracting multi-digit numbers, mostly because they don’t aren’t even sure about single digit addition and subtraction.

so, i’ve now taught 6th and 8th grade math. the choices are: spend a frustrating amount of time reteaching 3rd grade content, or allow them to continue the stupid calculator dependence that the elementary schools started. for the sake of teaching 6th (now 8th) grade content, i allow them to use calculators. in fact, our administrators insist on it, b/c they can use them on the PSSA.

now after the PSSA? i drill them to death doing multiplication and division by hand. and you know what? they actually LOVE long division.

Some appallingly high percentage of Ivy League graduates become consultants.

It’s a very insulated world. Who needs to be right? The rich keep paying each other and keeping their kids in private schools.

Gag me with a spoon.

Oh, by the way, I do math in my head, too. People who weren’t shoved calculators and told not to learn talk each other into thinking that it’s too hard. Unfortunately, some of them are teachers.

The theory in our school district is to have the kids spend a lot of time on concepts that they haven’t been taught and try to figure it out themselves – then they will supposedly be better at it when they do get taught the material. This seems to only be useful for the kids who are very good at math. The rest struggle, get frustated and hate math. They should be spending more time getting their basic math facts down – kids that aren’t that great at math need lots of repetition (without a calculator) instead of doing odd touchy feely problems.

I’ve been teaching Math, Physics, and basic Electronics for almost a decade. I’ve taught Grades 8-12 (on both extremes and all the grades in the middle) and at the community college level.

Overdependence on calculators is NOT a myth. It’s as real as anything real can be. For many students who end up in this situation, it permanantly damages their number sense – which in turn permanantly damages their ability to reason scientifically and logically.

“You mean educational research? The laughingstock of academia? I’ve seen enough ‘research’ to last me a lifetime.”

No kidding. If someone ever made a version of MST3K that made fun of academic research instead of movies, 95% of their episodes would be research from Education Departments. 😛

P.S. – Knowing how to do Math in your head doesn’t automatically qualify one’s statements about teaching Math. Knowing how to eat isn’t the same skill as knowing how to cook.

Calculators don’t create a dependence.

That’s counter-intuitive, clearly, but so was the idea that two objects of different weight dropped from the Tower of Pisa would land at the same time.

And that’s the value of research. Sometimes what is assumed to be common sense turns out to be wrong.

And on this issue the research is not just clear–it is overwhelming.

Of course, overwhelming research means nothing if you are the kind of opinion holder who steadfastly refuses to believe in evolution or global warming. “My mind is made up; don’t confuse me with the facts!”

If you have an open mind and want to look at the research, just google it.

Here’s an example:

Aimee J. Ellington

November 2003, Volume 34, Issue 5, Pages 433 – 463

Abstract

The findings of 54 research studies were integrated through meta-analysis to determine the effects of calculators on student achievement and attitude levels. Effect sizes were generated through Glassian techniques of meta-analysis, and Hedges and Olkin’s (1985) inferential statistical methods were used to test the significance of effect size data. Results revealed that students’ operational skills and problem-solving skills improved when calculators were an integral part of testing and instruction. The results for both skill types were mixed when calculators were not part of assessment, but in all cases, calculator use did not hinder the development of mathematical skills. Students using calculators had better attitudes toward mathematics than their noncalculator counterparts.

Better attitudes towards math (rotflmao). I’ve seen people who couldn’t figure out change from a $10 bill for a $6.45 receipt with the cash register helping them.

It’s amazing, but all we want to do as a nation is dumb down our population (that’s what will make us eventually a 3rd world nation), and the easy way to control a population is to make sure they cannot think for themselves (thinking is dangerous, don’t ya know).

If you really want a no nonsense read on math, read the book by Charles Sykes “The Dumbing Down of America: Why Johnny can’t read, write, or perform math, but feels good about himself” (it’s probably the biggest eye opener any parent could read in a lifetime).

What if these studies you cite contradict years of first-hand experience? What then? Do you consider my first hand experience worthless, because it wasn’t in a study?

Golobus – well, the trouble with your first-hand experience is that it’s very very easy for people to fool ourselves and see what we want to see. This is why double-blind tests are used in medicine, because doctors can be very biased observers.