Calculators in the Classroom?

    For research pertaining to usage of calculators in the classroom, there are two very interesting meta-analyses that have been published (requires VT PID):  "Effects of hand-held calculators in precollege mathematics education: A meta-analysis" by Hembree and Dessart, and "A Meta-Analysis of the Effects of Calculators on Students' Achievement and Attitude levels in Precollege Mathematics Classes" by Elington. The following is a review I have written on these two articles.

Review of Meta-Analysis

    For both of the “Review of Research on Graphing Calculators” articles, meta-analysis of calculator in the classroom research showed that calculators are beneficial to student learning and skills.  In the Hembree article, calculators are found to have a positive effect on problem solving and computational skills in all grades except grade 4, where calculators were found to be detrimental towards basic skills.  In the Elington article, calculators were found to be generally beneficial for operational and problem solving skills, with not enough evidence to single out detrimental effects by grade.  Since the Elington article went more in depth (and certainly was lengthier), most of my observations will stem from it instead of the Hembree article.
    I agree with the article in feeling strongly that calculators can aid in the building of conceptual knowledge in classroom settings.  However, as far as other building other skills I am very skeptical.  Although the article builds a very positive image for the use of graphing calculators and the like in classes, it still leaves me very skeptical on two issues: the building of computational abilities and operational skills.
    I found it interesting in the Ellington article that the difference between students who are allowed calculators on tests versus those not allowed calculators (both having had instruction with tests) is that skills for computation and conceptual understanding improve for the calculator group.  I feel that promoting this “improvement” as a positive is a bit misleading—don’t we all usually get correct numbers when punching in input to a calculator? I don’t believe that punching buttons is the equivalent of possessing computational skills.  As an example, in tutoring two years at the Math Emporium at Virginia Tech, I have seen perhaps 3 people—overall—that have multiplied fractions such as 1/3 and 3/4 together by hand.  Usually, with either slide rule or a graphing/scientific calculator, students will enter 1 ÷ 3 = [receive .333… repeating as a result] x (3 ÷4) =, and then get .25 as a result.  On several, several occasions, 1/4 is often an answer choice on a practice quiz the student is taking, and he/she doesn’t understand why the correct answer is not there.  On several other occasions, the student has entered all answer choices from the practice quiz on the screen into the calculator to see which one is right: 2 ÷ 5, 3 ÷8, 4 ÷ 7, until finally they enter 1 ÷ 4 and determine that 1/4 = .25.  Although this is technically a valid approach and this method of computation is sound, this can hardly be considered possession of a computational skill.  One wrong key press, and your “skill” is gone.  Thus it seems to me that this is an exaggeration of student abilities in taking tests with calculators.
    Similarly, displaying that one possesses conceptual knowledge on tests is often hindered by computational errors, and thus I think the non-calculator assessment group’s lack of conceptual abilities may be exaggerated.  In teacher-graded tests where partial credit is given, this may be easier to notice.  However, with mass careless computational errors of even simple things like adding and subtracting, it can be hard to determine that a student has deep conceptual understanding of a topic.  On standardized tests where an answer is either right or wrong with no in betweens, it is impossible.
    I also am intrigued by the apparent improvement of operational skills of students who are taught with calculators.  In operationalizing the variable, Elington claimed that operational skills were those needed to do well on tests measuring student achievement.  Yet again, this seems open to me in that teacher created tests are very different from standardized tests and this was not specified. 
For example, In using teacher-created tests, there may be some intrinsic property of teachers that simultaneously causes them to decide to use or not use calculators in instruction, makes them write more or fewer “operational” questions, and/or renders them better or worse at teaching “operational skills.”  Teaching style would definitely come in to play here much stronger than usage of calculators in students’ acquisition of knowledge.
And in the case of basing comparison on standardized tests, this seems a bit confusing:  In states such as Virginia, the current teaching practice seems to be using calculators as a tool to thwart the testing system.  (At least as far as my classes, the classes of friends in high school, and the classes of friends’ siblings who are currently still in secondary school.)  Many schools who know their students will be using calculators teach toward the “plug and check” method on tests of mathematical knowledge.  Even students that don’t have or use calculators who are taught this method acquire it fairly well since it often is less challenging than using the conceptual method of solving for a problem’s solution.  (Many students at the Virginia Tech Math Emporium still use this as a primary method for problem solving, and they often do poorly on word problems where formulas to plug answers in are not especially clear.)  And as I’ve mentioned above: on tests such as these, a few computational errors can make those that do understand conceptual material appear as if they don’t.
I can see a place in the classroom for calculators in terms of building conceptual knowledge.  Graphing calculators and other technology provide a fast way of letting students see math as it happens.  Students—especially those who are visual learners—often have a very hard time understanding certain concepts that they can’t visualize.  In some cases, activities that build these pictures for students may be a tremendous benefit, especially when they are time-consuming or cumbersome to do by hand.  (For example, comparing several graphs of different functions may take time if one draws them all out instead of using a calculator to graph them.)  In this case, technology is truly a great aid in conceptual understanding. 
However, I truly feel that calculators are overused in the classroom, and are contributing to an erosion of basic mathematical skills in the general population: if my experiences at the Emporium were with undergraduates of reasonable enough ability to be accepted to Virginia Tech, what of the students that were not capable of getting into college?  I feel that more conclusive and better-defined research should be done to determine very specifically what calculators actually do help and hurt.

PDF Copy of this file
Back to the Main Page