Calculator consequences

Chris Correa, an educational psychology graduate student, links to a study on whether K-12 calculator use affects college math grades. Researchers were surprised to find a connection.

Of our 607 students surveyed, 268 (44%) were self-declared that “In K-12, calculator usage was emphasized and encouraged.” On average, their grades were 0.20 lower.

Correa says “encouraged calculator use in K-12 education was equivalent to losing 57 points on the SAT score.”

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  1. Steve LaBonne says:

    Amen. I’ve been ranting about this for a long time. I started noticing the effects way back in 1976 when I was a first year grad student TAing a freshman chemistry lab, and was amazed to encounter students with no concept at all of significant figures- they would submit lab reports with everything to 8 decimal places. The damage has continued to get worse as calculator use has spread through all aspects of math teaching in almost all grades. I seriously advocate banning them all the way through high school.

  2. I can believe this, but I think it may be painted with too broad of a brush.

    I am a high school math teacher, and I have taught everything from Algebra I through AP Calculus. I have seen at the high school level that kids who come in calculator dependent tend to do worse in the courses that I teach – in fact, we purposely design the courses so that part of the work must be done without the use of a calculator.

    Even at the Calculus level, there are some calculators that will basically do all of the work for you (TI 89) and others that cannot (TI 83). Calculus teachers have even commented that many times the student who uses the TI 89 often doesn’t understand the concept behind what is going on – they’re too bust just punching numbers. In Calculus I can see the benefits of calculator usage to a certain extent, but having the calculator do it all leads to dependency.

    My belief – calculators should not be used at all in the elementary grades and very sparingly in the middle grades. Only when a student gets to Algebra and then moves beyond is a calculator beneficial, allowing students to work with real data and not contrived problems.

  3. Footnote: One must also realize two things from this study:

    1. There is a large contingency of college professors out there (and those in this study say that they agree) that calculators should not be used in a math classroom at all. The College Board, which oversees the AP program as well as the SAT tests, feels otherwise. That’s why calculators are allowed on the AP Calculus exam and the SAT test. These professors who have been doing it the same way for the last 30 years need to move into the 20th century and realize that calculators are here to stay.

    2. The question was asked if they had use calculators in K-12. There was very little differentiation for a student who used them only in high school or who used them all the way through school, but these two scenarios create two very different students – one who uses a calculator as a tool and one who uses a calculator as a crutch. The study doesn’t separate these groups very well.

    Yes, calculators are overused in some schools, but they are used properly in other schools.

  4. Steve LaBonne says:

    I rarely encountered college students who were able to avoid using calculators as crutches. (To such an extent, that I’m still shaking my head over simple Mendelian genetics problems, involving nothing that deserves the name of calculation, frequently receiving answers like .5625 in place of 9/16.) Whatever benfits people believe accrue to calculator use before high school at the very earliest, they seem a lot less clear than the costs. Sneering at those who question calculator use (“they need to move into the 20th century”) is unhelpful.

  5. The problem isn’t the calculator, but the “reform” math curriculum behind the calculator. Calculators should be used to increase the level of difficulty and rigor of the problems the students have to solve. Calculators should not be used to decrease the need for mastery of the basics. Calculators do not make math easier to learn. There is room for deciding exactly when a calculator should be used, but I have seen too many curricula place the calculator on the desk of Kindergarten students and it stays there throughout their whole education. It becomes a very big crutch and reduces the demand for mastery of the basics. Calculators can be powerful educational tools if they are used correctly. I haven’t seen that happen in grades K-8.

    I agree with Jill, who questioned the study:

    ” – one who uses a calculator as a tool and one who uses a calculator as a crutch.”

    There is a big difference between the two, but I think think Jill is correct in saying that calculators should not be used in the elementary grades and sparingly in the middle grades.

  6. 2. The question was asked if they had use calculators in K-12. There was very little differentiation for a student who used them only in high school or who used them all the way through school, but these two scenarios create two very different students – one who uses a calculator as a tool and one who uses a calculator as a crutch. The study doesn’t separate these groups very well.

    Jill has a good point, although she does not follow up on the obvious. The way the question was framed the results were a conservative estimate of the effect of calculators. If the groups would have been divided as she suggested it is likely that the result would have been even more extreme for the students who had used calculators for an even longer period of time.

  7. “Researchers were surprised to find a connection.”

    It astonishes me that this could be written with a straight face.

  8. I’m sort of surprised that there were any students who said that they didn’t use calculators in K-12. The only time I tried to ban calculators in a college class I nearly had a mutiny on my hands (not exagerating); every student was calculator-dependant. Some of them used the calculator to divide by 1. (Again, not exagerating.) Of course Johns Hopkins (where the survey was given) is more selective than most places I’ve taught.

    I wonder if the students were allowed to use calculators in the courses which were surveyed in this study. If calculator use was forbidden in those courses, then the students who were accustomed to using calculators were at a disadvantage.

    Calculator use gives me the freedom to write test questions where the answer is not an integer near zero. They allow me to ask my students to compare algorithms for numerical integration and to consider meaningful questions in statistics.

    On the other hand, I seem to recall that the tedium of doing numerical integration by hand is what inspired Napier to develop the use of logarithms to simplify calculations.

  9. I suppose these researchers never taught a freshman calc class.

    Oh lord, the flashbacks.

    “L = 2L, thus L = 0”

    “uh, why can’t L=1?”

    Then there was the big brou-ha-ha when half the class claimed it was unfair to expect them to know the formula for the area of a circle. I could’ve been real mean and told them they could always integrate to find the area… but instead, told them that it was assumed they knew precalc, which included geometry. So perhaps they had better study what they don’t know before they failed again.

    We didn’t allow calcs on the exam. I let the profs know that the current calculators could do symbolic math, even integrals. So there they went. Poor kids, expected to know how to multiply numbers by hand…

  10. Mad Scientist says:

    I distinctly remember a Corporate Finance class where I was able to estimate the IRR of a cash flow stream to within +/- 10% of the answer (i.e., if the answer was 10%, I could estimate it in the range of 9-11%) without using a calculator.

    Would we deliberately teach the finer points of wheelchair use to people who did not need to rely on one? Then why do we do it with calculators?

  11. SRH-
    None of the students claimed to *never* use calculators in K-12 education. The survey simply asked whether calculator use was “encouraged” or “emphasized”.

    meep –
    the researchers in this study also taught calculus at the college level. Calculators were not used in the classes. They wrote:
    “Calculators are certainly a big improvement over the slide rule and books of tables. However, none of the mathematical concepts and problem solving skills we want to impart in these courses requires the use of a calculator.”

    Many good points have been raised in this thread. The survey was awfully simple, and a follow-up study should take advantage of a better survey to get a more accurate description of each student’s experience with calculators in K-12 schools.

  12. I didn’t mean to imply an all-or-nothing situation. It depends where we put the line between calculators being “used” in K12 and calculators “encouraged” or “emphasized”. The vast majority of my students (over 95% in some classes) come to college already owning a TI-83 or better; since these calculators cost over $100 each, they wouldn’t have bought them if they didn’t really need them for their HS classes. [Side note: have you seen TI’s aggressive marketing? The cigarette companies should be jealous.]

    In my ideal world, if you asked a calculator to perform basic arithmetic with single digit integers, it would mock you. And if you asked a graphing calculator to plot y=x^2 it would break out laughing and refuse to do anything else until it regained its composure. But that would damage my students’ self-esteem :).

    Anyone interested in doing a better survey? We could probably have something excellent in place for the 2005-06 school year.

  13. Just picking up on Jill’s point. A calculator is a tool and should be used that way. right tool at the right time as my old shop teacher used to say.

    I let my fifth graders use calculators when collecting data about trees in the schoolyard. This involves two and three digit multiplication which they can mostly do, but bogs them down in the math when the lesson is about trees. In that particular instance it is more important to get data about ten trees by using calculators than three trees using pencil and paper.

  14. Richard Cook says:

    Its the diference between knowing 2+2=4 and knowing why 2+2=4.

  15. John Doe says:

    Please don’t tell me kids should do proofs: GOD I hated doing proofs. The main advantage of not using calculators excessively is that it forces kids to learn how to think. Logical thinking skills are critical in the modern workplace, much more so that being able to get the right answer to a math question.

  16. John — if logical thinking skills are so critical in the workplace (which I agree with, btw), it would seem even more important that proofs should be taught. Yes, I disliked them also, but they form the foundation of mathematics.

  17. SRH –
    You’re right; many students should regularly use calculators for certain topics in high school. The survey results are counterintuitive in a way because students who take advanced classes in high school that really do require calculators should be doing better, not worse, in college courses. Of course, those students may be outnumbered by the students who relied on calculators in seventh grade… we can’t really tell with their survey.

    What kind of college course(s) do you teach?

  18. Karen Savage says:

    I would like to have the name and phone number of the attorney handling the Wal-Mart Case

  19. Hi, someone sent me this site and since I’m the primary author of the paper being discussed I thought I’d chime in.

    First, let me comment on the “we were surprised” phrase. We were not surprised. We were curious. We had a great deal of difficulty getting the paper published. Most people in charge of education journals do not want to hear that maybe calculators are not really a good thing. I put that in the paper in hopes of getting more sympathy since what I expected didn’t seem to be and shouldn’t have been relevant. Our calculator story is but a tidbit. I know of a couple of significant papers by college math professors about college performance of students who have been through particular reform programs in K-12 and how they have failed (as a group) miserably in college. They cannot get papers like this published. I was “lucky”.

    In our attempt to get the paper published it was very short and lots of things were left unsaid. Some of the courses surveyed allowed calculators on exams and some didn’t. Our courses tend to go very very fast and we don’t have the luxury of exporing difficult problems, in fact, I just wish students could grasp the material and be able to solve a few multi step problems. Aparently some of you teach in environments where you have students who have a solid grasp of the basic and have the time to go after the interesting hard problems. I wish you’d send your students to me! But, I assume you are sending all those students to Harvard or MIT. There are very few of those students.

    On a personal level, I don’t pay much attention to calculators. I don’t need them for the concepts I teach and I don’t need them for testing whether a student has learned what I’ve taught so I don’t allow them.

    Yes, I do teach calculus, regularly, since 1972. In fact, I’m a bit burnt out on it so last year I taught linear algebra to a total of about 300 students. A good 15% of them learned it well.

    As for joining the 20th century, well, I’m not sure I have the time for that. Well, seriously, who should drive the curriculum? We, in the math dept at JHU have no control over what we teach. In most universities almost all the students are taking course required by their (non-math) major. Those other depts determine what is taught in those courses, not us. If we screw it up then we hear from them. We are not getting lots of pressure from them to incorporate calculators into our service course. Why then should we bow to the pressure from K-12 educators to do so? As for the SAT and the College Board, yes, when I heard that their exams allowed calculators I got sort of upset, they had clearly given in to the k-12 educators. Representatives came down to Baltimore to talk to me and give me copies of the exams and I concluded that, yes, you could use a calculator, but the questions were real math questions and most didn’t actually require a calculator, so I left them alone. They’ve made a bit of a compromise. Yes, you can use a calculator, but, gosh, you still have to know the math. I could live with that.

    I believe that we pointed out in our paper that our question was rather coarse and it would be nice if people refined it a bit. I’ve been trying to get some big state universities to ask a refined question on their placement test and then compare with the results of the placement test and with the grades in courses they take. JHU really isn’t a very good place to do this kind of study.

    Even though the question was coarse, students clearly didn’t take it to mean using calculators a lot for a year or two. If I asked in class how many had calculators encourage or emphasized for one year or more then the percent doubled.

    I will tell you all a story that we didn’t put in the paper (because we didn’t notice it until later). All our students have pretty high SAT scores, but if you looked at the results by quartile then
    the middle 50% seemed to be unaffected and the top 25%
    (in our case 760-800 math SAT) and the bottom 25% were doubly affected. I have no idea what this means and would be very pleased to hear ideas from any of you. It would appear that those most hurt by calculator usage are the very top, but what
    does that mean in a world where most of the students are “tops”?

    I don’t know how this posting works so I don’t know if this gets seen or if I’ll hear from anyone. Steve

    Thanks for reading the paper!