Doesn’t add up

Nine-year-olds who use calculators can’t compute on their own, concludes an analysis of National Assessment of Educational Progress (NAEP) scores. Tom Loveless of the Brown Center on Education Policy at the Brookings Institution writes:

“If students are only able to compute accurately with calculators — or if their computational skills are so weak that only the simplest of calculations can be made — then students are doomed to solving only trivial mathematical problems.”

CER Newswire notes: In subtraction, students scored 89.2 percent with calculators and 59.7 without; in multiplication, 87.9 percent with calculators and 42.5 without; and in division, 77.1 percent with and 48.3 without.

Letting students use calculators on tests of computation skills makes the tests worthless, Loveless concluded.

About Joanne


  1. Margaret says:

    Duh?!?? Did anybody actually think they were testing computation skills if they allowed the kids to use the calculators to do the actual “computation” work for them? What scares me is that these kids were getting less than 97 or 98% *with* the calculator. I could attribute 2 or 3% wrong to punching errors, but these kids consistently got *over* 10% wrong with the calculator. I dread the thought of having to argue with one of these kids at a McD cash register in a few years if they make an obvious mistake but insist they are correct…

  2. Don’t worry! the registers at McD’s have the item on the register, not the price. Now, they just have to be able to read.

    Oh no!

  3. Once again I am thankful that my 6th grade math teacher refused to let us use calculators. I’m often the one in the crowd who figures up the tip or checks the bill’s addition, because I have this awesome power to do math “in my head”

  4. That’s not because of the refusal to use calculators (they weren’t around when I was in 6th grade), but because your didn’t have your mind deluded with new-new math (aka fuzzy math), and as you point out, you were forced to memorize the multiplication tables, and through numerous drills and repeating the math facts until you have had them committed to memory.

    I figure out sales tax, food orders, etc. in my head all the time, but like you, I had math teachers who taught math the old fashioned way.

  5. I similarly estimate or calculate tax and or tip in my head. On the other hand, I learned and remembered how to “manually” calculate a square root just long enough to take and pass the test back in 7th (?) grade ’59 – particularly since I learned to use a slide rule after hours in 6th grade 🙂 SOME math is useful and important to do in your head or with paper and pencil, other math is much faster and more accurate with a calculator [linear, circular, or digital] 🙂

  6. Mad Scientist says:

    This is nothing new. There are a number of really pissed off people who took the PE exam last week.

    They were pissed off because they had to use a “plain vanilla” scientific calculator. There was one individual who bragged that at a previous exam, he had four high end calculators programmed with every imaginable formula he thought he needes so he did not have to waste time. Thankfully, he did not pass.

  7. Mad Scientist – at least it was a scientific calculator – coulda made em use a “4 banger”! 🙂

  8. Mad Scientist says:

    Tough to do logs on a 4-banger. Yeah, I know, you could look them up on a table, but it was a time critical exam.

  9. In middle school the school lent the advanced math class what we called “magic calculators” because they could manipulate fractions. About halfway though the year, on a hunch, the teacher tried to have us add fractions of different denominators without the calculators, and we had forgotten how. The magic calculators went into a closet for the rest of the year.

  10. Man, I still get annoyed remembering my trig class, in which our teacher forced us to do linear interpolation… without a calculator (this was in 1989). When he finally allowed us to use calculators, my sisters kept stealing mine, so I brought my dad’s slide rule for tests. Worked just fine.

    I remember having to tell calc profs I TA’ed for that calculators now can take derivatives and do some integrals… calculators were banned from tests.

  11. Richard Heddleson says:

    Mad Scientist

    You could have used a slide rule for the logs. In fact you could use a slide rule for anything the scientific calculator could do. Man walked on the moon thanks to it alone.

  12. Margaret says:

    Meep, I think we were in the same trig class, only I think mine was 1988. Yes, linear interpolation. Ick. Those lovely tables in the back of the textbook. Only I don’t ever remember being allowed to use a calculator in trig, period. I think they were fine in physics, and almost essential in chemistry, (like how many grams per mole or whatever, it’s been a long time) but the point there was to practice the technique being applied in phyx or chemistry. We had already demonstrated our math competence in math class…

  13. Mad Scientist says:

    Oh, I know. Used to use one. Right after I handed in my abacus.

  14. Insufficiently Sensitive says:

    The benefit of those evil linear interpolations in the log tables was in the PRACTICE, particularly in learning to work methodically and efficiently. There was no other way to become proficient at numerical manipulations, and in the days before widespread calculator use it was necessary to become proficient – if you expected someone to pay you for work that involved numbers of more than two-place precision.

    There have been about two generations of ‘teachers’ now who whined like Barbie, ‘math is HARD’, and did their best to coddle the dear little students through school without inflicting the pain of learning. Calculators enabled those ‘teachers’ to succeed, and the US is now overrun with their innumerate graduates.

    Tar and feathers….

  15. Richard Nieporent says:

    You touched on one of my pet peeves. You cannot allow children to use calculators if you want them to learn basic math. They can only learn basic arithmetic by actually doing problems, not by pressing keys.

    While my children didn’t get to use calculators in elementary school, they did get to use graphing calculators when they took analytical geometry in high school. Oh they were really good at it. They could solve any problem on their calculator. Unfortunately, they didn’t get a basic understanding of the behavior of the trigonometric functions which is what the course is suppose to teach.

  16. My 3rd grader is learning multiplication, and I won’t let him near a calculator. There is no point for a calculator when you are learning a basic skill like arithmatic. All you need is a penicl, eraser and a piece of paper, and you should be able to solve any multiplication or division problem if you know the rules.
    And that’s all they should be given.

  17. Steven Sheets says:

    At the college level Maple and Mathematica are the sexy things to use in teaching calculus. I’ve always wondered about the usefullness of these programs since it seems the classes that use these tools cover less and the students spend too much time just trying to get Maple to spit out the right indefinite integral or what have you.

  18. Its gotten corrupt even at the top.
    I know of one professor who taught a junior-level engineering course in ordinary and partial differential equations using MATLAB… the students didn’t learn how to solve anything without just plugging it into the program… I was disgusted… this professor should have known better. The sad thing was, there actually was a textbook that was made for a MATLAB specific course… I flipped through the book… absolutely NO content… I don’t won’t these kids designing any bridge I drive over.

  19. One of my friends who teaches math at a local college tells me he should give the grade to the calculator, rather than the student !

  20. Mad Scientist says:

    I have used Maple, Matlab, and MathCad – but not until I was out of school. Very handy for taking the tedium out of the manipulations. However, you have to know how to do them.

    I remember (not so fondly) of my attempts over 6 months trying to come up with an analytic solution to the biharmonic equation in rectangular coordinates with discontinuous boundary conditions – an impossible feat (but did not know it at the time). I wound up writing a FORTRAN program to do a numerical solution.

  21. Alex Bensky says:

    A few years ago I substituted part-time in a very affluent suburban school system. I had an eighth grade math class one day, and the students had a set of problems in which they were given certain numbers and asked to find between which two integers the square root of that number would fall. Note, they weren’t asked to find the number’s square root, just be able to figure out roughly what it would be.

    They seemed stymied. It is worth noting that I subconsciously decided when I was that age to learn enough math to do baseball averages and then stopped.

    “Look,” I said, “this is easy.” I wrote one of the numbers, say 27.9, on the board. “You know that four times four is sixteen, so that’s lower. Five times five is twenty-five, and that’s still lower. Six times six is thirty-six, and that’s higher, so your answer is between five and six.”

    And I was stunned to discover about half the students could not do that in their heads, although when I told them to try it on calculators everyone got the answers.

    This is not, I repeat, in a deprived inner-city classroom.

  22. Steve LaBonne says:

    Anybody with half a brain should have been able to foresee the ill effects of handing artificial aids to students who haven’t had the pencil-and-paper practice necessary to understand what they’re doing. Yet even _after_ there’s been plenty of time for the damage to become apaprent this nonsense continues to spread, even at the college level with the continuing popularity of the disaster known as “calculus reform”.* What this says about our whole education system is profoundly depressing.

    *At the college where I had my purgatorial experience in academia, the math department had the habit of patting itself on the back as a department that could teach supposedly “rigorous” calculus courses to nonmajors and still get high student evalution numbers- they were fond of lecturing the science departments on this “achievement”. Oddly enough, though, in teaching topics like DNA renaturation kinetics to students who had gotten As and Bs in these supposedly wonderful math courses, I found that most of them were mystified by the simplest algebraic manipulations. Funny that.

  23. Well, once while serving as a teaching assistant in a college lab class for students, most of whom were from the affluent Chicago ‘burbs, I had the class estimate the size of an object based its relative size to the field of view of the microscopes they were using.

    The field of view was 1.2 mm and the object was about 1/4 the size of the field of view.

    I saw one of the students just sitting there, stymied. I went over and asked her if she had a question.

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

    After I got over my initial shock, I said “Ok, you have 1.2 millimeters. You are trying to divide that by four. You can, for the time being, ignore the decimal point [she had indicated, after I asked her a few questions, that the decimal was what she couldn’t deal with]. Imagine you are dividing 12 by 4. Then, after you’ve done that, you have one decimal place to put back. So your answer of 3 would become .3”

    Not quite the ideal teachable moment, but I was so shocked that an 18-year-old didn’t know how to divide a simple decimal that the socratic method went out the window.

    The kicker? She looked at me after that explanation, her face full of disbelief. “You can DO that?” she asked, like I had just performed some kind of alchemical experiment or told her she could spin straw into gold.

    I resisted saying “yes, if you’ve been to fifth grade you can.” (fifth grade is where I finally got really comfortable working with decimals. I think they were first introduced to me in third grade or so).

  24. Richard Cook says:


    You qual to walk into class wearing one of those wizard caps. The tall one with stars and crescent moons on it.

  25. John from OK says:

    Some points:
    1. We are assuming that scores are decreasing due to the use of calculators. Maybe they are just decreasing period. Maybe they are not decreasing, that 60%, 43%, and 48% are what our own classes would have scored.

    2. How is it that students are better able to divide longhand (48%) than to multiply longhand (43%)? I always found division to be harder.

    3. Why is it so much harder to divide using a calculator (77%) than to multiply (88%) or subtract (89%) using a calculator?

  26. Regarding computer programs for collegiate math (Maple, Mathematica, etc.), they really are useful, especially for systems that can’t be solved exactly, but need to be estimated numerically (such as in my differential equations class). But we aren’t even allowed to use a four-function calculator on tests, we just have separate labs (which are hard, and require difficult write-ups) with the computers. That strikes me as the best way to use technology.

  27. John, the research wasn’t comparing students today with students in the past. As I understand it, today’s students were tested with and without calculators on similar problems. Taking away their calculators greatly depressed their scores.

  28. M. J. Wise says:

    The only time I was allowed to use a calculator in K-8 was occasionally in the 8th grade, but only for special math “labs.”

    In high school we were expected to have graphing calculators, but the teachers were savvy enough on them to know how to write tests that emphasize logical thinking over button pressing.

    In college, it’s been a mix. Some calculus classes allowed them, others didn’t. Allowed usage really didn’t help me — unless there was some long arithmetic calculation, which was rare.

    Now my current math course (Engineering Statistics II) basically requires the usage of a graphing calculator plus computer software (such as Minitab and R). Trust me, you do _NOT_ want to (try to) do a multiple linear regression with 10 independent variables by hand. Heck, even with 2 IVs, it is fairly painful.

    So, I think it’s really a matter of the computational difficulty of the material faced. But I really can’t see doing basic arithmetic with them in grade school. And how the heck do they still miss > 10% even WITH the calculators? Are their fingers extraordinarily stubby?

  29. Harvey Chao says:

    1) Unless a student understands enough of the basics, calculators won’t tell them whether they need to divide miles by galons or vice versa to calculate simple problem such as a car’s fuel economy.
    2) Unless students finally assume the minimal “rigor” to carry “units” through their problem solving, they miss a significat clue on how to manipulate the numbers they have (ref 1) above.
    3) I have interviewed new college Electrical Eng. grads (or about to grad) who have used network analyzers in labs to evaluate circuits. Yet if I ask them to draw a block diagram, not having a network analyzer available, but a whole room full of available test equipment of any other kind (meters, signal generators, oscilloscopes, plotters, …) on how they would put together a test setup to measure the basic power output response of a simple “hi-fi” audio amplifier across the frequency band (“x volts into z ohms +/- y dB)- a frightening number had absolutely NO idea of how to proceed, and I suspect more than a few didn’t even grasp what I was asking them to measure.
    4) Failing 3 above I considered the possibility that they were too theoretically oriented and insufficiently “hands on” experienced (potentially lack of lab opportunity), so I would ask a simple question of them to explain the implications of “tilt” across the top of a square wave in two cases, rising/tilt left to right, and then rising/tilting right to left. Most of them couldn’t explain that either.

    Least you consider me an engineering genius/interviewing ogre, consider that I graduated from college in 1968 with a piece of paper that SAID I was an EE, but NEVER had the opportunity to become a PRACTICING engineer and have spent my career initially as a junior officer in USAF, and then a mixture of various software test and integration, systems engineering, program staff and program management and similar activities. NO industry expeience/ojt to develop into a REAL circuit design engineer. My questions are based on what I recall from BASIC theory classes 36+ years ago (and practical experience in high school taking radios and TVs apart trying to kill myself on tube high voltage circuits) . I EXPECT students fresh out of engineering college to be a WHOLE lot better than that! Way too often, I am seriously appaled and disappointed.

  30. For a novel reading assignment, the students had a certain number of days to read their chosen novel. I told them to figure out how many pages they would need to read each day in order to stay on track.

    Each class, at least ten of thirty kids complained they couldn’t do Math in their English class. Another third pulled out their calculators, and most of the other third waited to use a friend’s calculator since they didn’t bring it to English.

  31. Steve LaBonne says:

    That sounds like some former students of mine who resented doing statistics for genetics labs- after all, it was a biology course, not math! Some students also would give answers to simple Mendelian genetics problems, most naturally figured (with no need for a calculator)as fractions like 3/4 or 9/16, in decimals, a telltale sign that they were unused to doing even the simplest arithmetic without the crutch. Calculators should be banned until grad school. 😉

  32. Harvey,

    A few years ago, I went back and visited my old college p-chem professor and we got to talking about about students over the last 20 years or so, the one conclusion which came to the forefront was that each year the crop of students he sees for general chemistry I (Chem 115) is just slightly less intelligent then the group that came before them. I’m not surprised that EE’s today can’t do anything without what they have been exposed to (i.e. – asking them to think outside the box == disaster).

  33. why cant there be a website that atleast helps children with assignments because i have to do some assignment on networks and why you can only draw some of them without taking your pen off the paper and i cant find a thing and it is really getting on my nerves and just because you use a calculater doesnt mean your dumb because im in advanced maths and sometimes on our sheets it says use a calculater anyways can someone make a website about Sir Montague Snuffles and networks because i cant find anything on it


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