# Calculator Policies in NIU Math Courses

Since there are a variety of opinions about the value of calculators in the mathematics classroom, the development of these guidelines has required careful reflection. Some key ideas informing our decisions are discussed here for the benefit of those interested in the development of pedagogical practice.

## Advantages and Disadvantages of Calculator Use in the Classroom

Our calculator requirements have been designed with the best interest of the students in mind. Our goal is to help you understand and use mathematics, and we believe a judicious use of technology is most likely to enhance your learning. This includes calculators as appropriate tools for faculty to demonstrate, and for you to explore, some of the concepts as they appear. However, most exams and some homework assignments are not designed for exploration; you are expected to demonstrate that you have mastered the underlying concepts.

An essential component of proper calculator use is the ability to determine when it is appropriate to use a calculator, and when it's not. For example, it would be unproductive for you to divide 0.9738 by 0.30103 by hand; the same is not true when dividing 1 by (1/20), since the likelihood of mistyping exceeds the likelihood of getting a wrong answer by hand.

Parallel examples exist with the use of symbolic calculators in college-level mathematics classes. Should you learn to compute partial-fractions decompositions by hand? It is important in calculus to understand the principles of this decomposition to be able to integrate 1/(x2-1), and to work with Laplace transforms in a later differential equations course. So it is certainly appropriate for instructors to expect you to learn in Calculus 2 the steps for constructing such a decomposition. On the other hand, a bit of preliminary effort is enough to convince even the most determined student that little light is shed on the problem of integrating 1/(x5-1) using Partial Fractions; once the principles are clear, it is reasonable to ask a symbolic calculator to compute the integral.

We see that a student who is working needlessly complicated examples by hand is learning little and could be a more productive learner by leaving those routine computations to a machine. At the same time, we see that a student who is working very simple examples by machine is learning little and could be developing a more authentic understanding of the material by trying those computations by hand.

## Different Policies Apply to Different Courses

The importance of working without calculators is especially clear when you are learning ideas which are used in courses for which a given course is a prerequisite. In these courses, it is very important for you to work large numbers of examples and to be familiar with concepts and procedures, as well as with examples likely to require more computation than can be done by hand. It is in these courses which you are expected to demonstrate mastery of ideas without the use of calculators. So, in courses with the lowest course numbers you should not expect to be able to use any calculator on exams.

On the other extreme are courses primarily designed for applications, or terminal math courses. Here it is important for you to be accustomed to using a calculator to work "real" problems, more similar to expected later applications. Thus, you are expected to have calculators, especially during exams.

Intermediate-level courses must be treated with some care - some are terminal courses, some are prerequisites and some may be both. And for any course, instructors may find it necessary to limit or prohibit the use of calculators for procedural reasons.

### Not All Calculators are alike

We attempt to direct students to the appropriate tool for each job.

Four-function calculators are inexpensive and widely available, and make it essentially impossible to derive an undue advantage on an exam; they also offer little useful help towards learning, except to remove the distraction of routine arithmetic.

"Scientific" calculators are capable of more complex numerical functions. You are expected to be able to use these to compute nontrivial trigonometric values, to compute statistical measures of data and to handle real data in models using logarithm and exponential functions. Some may be programmed, which is usually a useful exercise for learning algorithms such as numerical integration, but of course overuse can enable you to avoid learning what numerical integration really means.

"Graphing" calculators produce a pixelated approximation of graphs, curves and other planar figures. These can be invaluable if you are investigating properties of functions which are new to you, and are useful for tracing or deriving other data from functions whose overall behavior you already understand. On the other hand, students who rush to use these prematurely often appear not to see any connection between a function and its graph than memorized associations.

"Symbolic" calculators are capable of algebraic manipulations of functions of one or more variables, and in particular may be able to factor polynomials, differentiate or integrate, and evaluate series and limits. They typically include an alphabetic keypad and may have a text-storage area which of course may be used to store notes. Software for computation of symbolic algebra is known to be subject to many errors. These calculators typically have a graphic display; some claim a 3-dimensional graphics capability but the displays are usually too primitive to be very helpful.

Computers are typically used by students on their own or in computer labs and not in classrooms. There is a wide variety of software capable of professional-quality numerical computations, symbolic manipulation and graphical display, as well as educational and testing software of mixed quality. Most software requires personalized instruction and training.

### Exams Are Special Situations

Students often prefer to have a calculator available to check simple arithmetic during exams, and we try to allow that when appropriate.

We would like during an exam to test your ability to use truly representative data, so we do ask you to have a calculator available in some of these mid-level service courses.

Calculator use is not appropriate when you are being tested on your basic conceptual understanding. A common approach fruitfully used by some instructors is to use two-part exams, one part allowing calculators and the other not, as appropriate for the concepts being tested.

The use of a calculator's text-storage feature must be limited during closed-notes exams, the use of a calculator as a communications device must be limited if group-work is forbidden and the use of programmable calculators must be limited during an exam designed to test understanding of algorithms. Some instructors may be able to permit appropriate calculator use during exams. Others, particularly when teaching large lecture sections, may prohibit calculators altogether.

During final examinations in lower-division courses, graphing calculators are allowed only on any specifically-designated portions of two-part exams as described above. These exams will reflect what these instructors are actually doing with their classes, and what they expect the students to understand.

### Policy Development

We continue to experiment with a variety of teaching and testing strategies. To the extent that our expectations of the students' use of technology change, we will of course adjust the final-exam policies.