Personal Experiences Teaching Inside Your Calculator

Gerald R. Rising

Inside Your Calculator has been written as a book for the general reader. As one result of this, it contains no exercises. The book may, however, serve as a text on which may be based a variety of lecture series or courses for adults or students in secondary schools and colleges.

I have taught just such a course, a three semester hour seminar for undergraduate honors students at the University at Buffalo. Early versions of the text chapters served as reading assignments, we explored in class extensions of the text material , and I assigned rather demanding tasks appropriate to these extremely bright students.

As an aside, I note that I was regularly surprised at how much that we covered the students told me was "new" to them. Even some of the content that is standard to the secondary school curriculum was not recognized by many students. Their generous end-of-course evaluations indicated how much they appreciated their new depth of understanding of the course topics.

Few teachers will have an opportunity to work with such exceptional students and your instruction will have to reflect the quality and kind of audience you will meet. I have found, however, that the content of various parts of this text "works" with students of a wide range of ability. The key to the presentation is your interpretation of the content.

Here, however, are some suggestions about teaching that should apply to any course based on my experiences:

  1. A central activity of this book is programming and it is appropriate that you spend time at the outset familiarizing your students with preparing simple programs for the calculators they will be using.

    Today students have a wide range of programming ability, but you will find that remarkably few, even including those who have taken computer courses, are skilled at programming their calculator. Even students who have owned graphic calculators for some time will often never have written a program for their instrument. They will almost certainly have used the calculator's graphics capabilities, but their other use will have been restricted to carrying out calculations. For this reason you will be well advised to provide assistance in developing a few first programs.

    I have provided a series of programming exercises, many of which I used in my course, that build from very simple to quite sophisticated tasks. I suggest that you assign longer range programming projects. (If you do not have your own preferred tasks, you can select or have your students select their project from some of those that appear on the list.) In doing so, I urge you to require your students to prepare a written report in support of their program. Such a report should include a description of what the program is doing and how it is doing it.

  2. You will need to decide how to handle the programming tasks in the classroom. I began many classes by introducing a problem and asking for help in solving it. For example, one session late in the semester I began with a concern, "Many of you have probably worked the Sudoku puzzles in your newspaper. Clearly each puzzle has a unique solution. Is there a way we can program our calculators to provide such solutions?" This led the class to develop a backtracking program that solves such puzzles. What impressed (and pleased) the class most about this activity was the fact that they could often beat the calculator to a solution, the processing took such a long time. As two other class projects we developed the BIGMULT and BIGDIV programs for multiplying and dividing integers with many digits. The BIGMULT program is now found in Appendix L of the text and BIGDIV as Appendix T in the applications section of this website.
  3. If your experience is anything like mine, you will find that debugging programs is an important part of course activities. Students learn through mistakes and sometimes those errors are not easy to identify. I found that having students work together on such problems before coming to me - as a kind of source of last resort - saved a good deal of my time. In fact, usually their problems were solved in this way. Unfortunately, however, you will find that the problems that then do reach you are tough ones.
  4. You will soon identify student experts on whom you can rely for esoteric uses of their calculator. This represents a mixed blessing. These students can be of help to you in some situations but they can also flaunt their knowledge. You will find that such students will become much less of a problem as the level of difficulty of your assigned tasks increases.
  5. My course did not include examinations and grades were based on homework, class participation and a term project. One of my last tasks in the development of this website (still only half done as I write) will be the development of some sample test questions. Obviously, because this is an open site, these will only serve as suggested kinds of exercises.

    Some of the appendices of Inside Your Calculator also provide the basis for student projects.