A Word About Calculators
The use of graphing calculators and other kinds of technology is prevalent in today’s K-12 mathematics classrooms, probably more so than at the collegiate level. Consideration must be given to the amount of reliance students have on this technology. Calculator skills are certainly necessary, and the calculator can be a powerful verification tool for more difficult problems. But a careful distinction is needed between using the calculator as a tool and using a calculator due to deficiency of skills.
Certainly, students should use the calculator to confirm algebraic solutions to equations, reasonability of limits of functions and slopes of tangent lines in calculus. On the other hand, students should be able to solve equations like 36x3 = -4/3 easily without calculators.
It is expected that freshmen entering The University of Iowa are proficient in arithmetic with integers and fractions, without the use of calculators. Deficiency in this area can lead to barriers in acquiring the algebra skills needed for success in college math and math-related classes. Students need good number sense and the kind of familiarity with numbers that comes from use of paper and pencil techniques for acquiring skill in arithmetic.
Efficient use of least common denominators, for example, sets students up for success in the more advanced algebra needed at the calculus level. Students who have been allowed unrestricted use of calculators K-12 may find themselves deficient in the kinds of skills needed in college math. Of particular importance is facility with manipulating fractions – operations and simplifying.
While there are times when conversion from fractions to decimals is appropriate, it is not always productive, so that flexibility to work with fractions is important. Students who have not been expected to develop this flexibility – i.e. students who have been allowed unrestricted use of calculators for such computations – will find college math much more difficult. Also, keep in mind that instructors in mathematics courses at The University of Iowa usually want the exact answer (and how the answer was derived), not a decimal approximation. For example, 2π should be left as 2π and not approximated as 6.2832.
Consequently, students at the K-12 level should have plentiful and continuous exposure to computation in the absence of calculators so that their skills are strong enough for the acquisition of algebra and more advanced skills.
Students will probably find that graphing calculators are less used in their mathematics courses at The University of Iowa than in high school. It is departmental policy that the use of technology in a class is left up to the instructor of that course. This may range from not allowing even a scientific calculator to requiring a certain graphing calculator or that students learn to do assignments in Maple or Mathematica. Most instructors do not allow graphing calculators or calculators doing symbolic algebra on quizzes or exams.