George Andrews at the CRAFTY chat room 8-4-98

This was the first use of CRAFTY chat for a conference.

This excerpt begins with Professor Andrews is answering a question about what he might suggest  for faculty to think about doing over the next academic year:

ANDREWS: 1. Ban calculators.
ANDREWS: 2. I believe that large lectures allow to go unnoticed the various bad habits of students. Consequently anything that you can do in your department to keep class size down will be helpful.
ANDREWS: 3. Make sure that there is serious attention to pre-requisites. If the majority of students in your class are unprepared, your standards will unavoidably drop.[END]

FLASHMAN: These are 3 serious areas to address ... let me turn the attention briefly to item 1. You recognize that technology has some up and down sides. Perhaps you might accept a more modest proposal of making a serious examination of how technology is working an our own institutions and then come to some conclusions about its use then?

gresham_2ndtry: What specific benefits do you believe would follow from banning calculators from calc and pre-calc courses? [END]

ANDREWS: I realize that calling for a complete ban will go unheeded. Undoubtedly there are teachers who use calculators wisely. However, I feel that much too little attention is paid to how calculators serve as a crutch. While teachers can appreciate the wonderful ways that calculators can be used to expand on and apply calculus topics, student will be using them for something else. Let me give an example from my last calculus class:

ANDREWS: This was Calc II. I gave a Friday morning quiz. The first problem was to evaluate the limit as x -> 0 of tan x / sin x . As I walked up and down the aisles, I counted 28 calculators in use among the 35 students. Aha, very clever, I thought. They are putting in values of x very close to 0 in order to guess the right answer. WRONG! Without exception, they were trying to determine the cosine of 0. This mismatch between what we think they will use calculators for and what the do actually use them for is where my concern lies. I think that many become mathematical cripples.

FLASHMAN: This image of mathematical crpples is interesting. It may be a crutch, but for some students this crutch will allow them to struggle through a course that they might otherwise never experience in any way. And for those who could do the course without calculators it can allow them to see parts of the course that were never before as visible. A mountain climber usually brings some "crutches" to help in key spots. Your concern about misuse and overuse is shared by many "reformers", so why not call for serious reflection on its use, similar to your call for trying to work for effective class sizes.

johnpais: Isn't structuring class activity the instructor's responsibility? It is simple enough to control this--plan assessments in advance without using calculators. With all due respect, I consider this a flaw in the instructional strategy for that day.

gresham_2ndtry: An approach I use is to separate a quiz into two sections: 1. Papers, pencils, and brains only. Hand this in. Then 2. Calculators allowed (required for some questions!)

ANDREWS: No matter what I say, calculators won't disappear. They have numerous vocal supporters. However, I believe that as soon as they become part of a course they have a role in the lives of the students that cannot be fully controlled. Furthermore I think that the ability to use the calculator is fairly easy to acquire. I acknowledge that their abuse can be prevented with great care. But I doubt that the problems that we currently face in mathematical unpreparedness are not made worse by the fact that calculators are ubiquitous. (I will try to respond to FLASHMAN in my next line.)

ANDREWS: The entire atmosphere you (FLASHMAN) describe in your last comment is well below what I would expect for a college course on calculus. I doubt that this crutch is required for nearly the number of students who come to rely on it. I believe that we do them a disservice by allowing them to get hooked.

FLASHMAN: Perhaps what is important here is the latent issue of planning. Does an individual instructor, a group of instructors, or a department make a serious effort to plan what happens in these courses? how will calculators and pencil and paper [or slide-rules:)] get used? what kind of activities do we ask/require/demand our students to do? etc.

ANDREWS: I agree that care in planning can mitigate calculator problems. Indeed I believe that a variety of problems can be mitigated with careful planning. However, we all know that, given the demands on faculty, there will always be less planning than is desirable. Consequently adding to courses an element (calculators) that requires much careful planning is likely to wind up producing many unexpected and unplanned outcomes.[END]

McCallum: I agree with recommendations 2 and 3. As for 1, I believe it is possible to teach well using calculators, McCallum: badly using calculators, well not using calculators, and badly not using calculators.

ANDREWS: If you are a passionate believer in the value of calculators, I am sure that you can teach well using calculators. However, I still believe that it would be of great value to students to be calculator-free for at least some period in their education.

FLASHMAN: How about looking at prerequisites? How do you suggest we decide on prerequisites? How do we enforce them. How do we help students who have "passed" the prerquisites but still need to work on them ?

McCallum: I don't believe that courses requiring calculators require any more or less preparation than those that do not, nor do they require passionate belief.
McCallum: However, I do believe that instructors who are forced to use a method against their will will probably

ANDREWS: I assume that in most colleges and universities (certainly in mine) teachers have control over the prerequisites. In other words, we can prevent enrollment by students we deem unqualified (either by failing an entrance exam or not having specified pre-requisite courses). If (as may well be the case) standards have fallen disastrously in all courses, then it will be impossible to fix just one course. However, this is either an individual or departmental problem that surely can be addressed if enough faculty think it important.[end]

FLASHMAN: the fact that faculty have control doesn't mean that the apparently simple solutions will be effective if the desired result is to have more students learn more mathematics. The responsiblity for desgning these courses- precalculus through de's is one that you rightly place on departments. Unfortunately many departments see the resposiblity satisfied by listing topics a portion of which must be passed to pass a course and selecting a tecxtbook for the courses. This is not an adequate response for most of the situations faced today..the client departments want and deserve more effort.

McCallum: Our client departments often do not enforce mathematics prerequisites. I found that one engineering course which required calculus had on two thirds of tis students who had acactually taken calculus.

ANDREWS: I agree (with FLASHMAN). You are highlighting one of my concerns: faculty responsibility. I do not have global answers to this problem. However, until this problem is solved (or at least...

McCallum: I wanted to say before that I don't think technology should be forced on unwilling instructors.
McCallum: Nor do I think that instructors who wish to use technology should be prohibited from using it.

ANDREWS: I agree that technology should not be forced on unwilling instructors. This, however, poses major policy problems at large universities. In order to provide reasonable uniformity, we have to have a "technology policy" for all sections of calculus. This turns out to be unpleasant for one side or the other.[end]

FLASHMAN: Faculty responsibility is a key here. Making accomodation for instructors preferences and fears is difficult and can sometimes ignore harder decisions on what might be in the best interest of some/all of our students.


McCallum: Yes, it may be necessary to have a uniform policy within one course at one institution. However, it is

FLASHMAN: So if we are to make headway on these harder decisions perhaps we need to call a moratorium on extreme rhetoric on all sides [inside and outside :)] and try to keep a focus on addressing these hard issues.

ANDREWS: I agree that keeping focus on the main problems should be of paramount importance.

FLASHMAN: Perhaps we could agree on a list of the areas where discussion time should be spent in the future. For instance:

McCallum: Yes, I was about to say, it is not necessary, nor is desirable, to impose a uniform technology policy more broadly thatn that.
McCallum: I would like to see more discussion of assessment. What questions do you ask your students on the final exam.
McCallum: It's the final exam, and the students' performance on it, that really tells you the content of the course: not the syllabus, not the teaching style, not the use of technology.

FLASHMAN: 1. level of competence at basic pencil/paper skills; 2. level of competence at appropriate technology skills; 3. Appropriate class size and organization for student faculty staff intereaction; 4. ....

ANDREWS: (Response to McCallum). Obviously assessment depends heavily on the course being taught. I do not agree that just one of the items you chose tells the content (you say final exam). Clearly your choices on the other items will have to be synchronized with the final exam. If the final exam is not harmonized with the other choices comething is terribly wrong. (I will reply to FLASHMAN in the next line)

FLASHMAN: I'm not sure I agree.... there are some ways to structure a program (e.g. USMA I think) where assessment accumulates over many courses. I often have suggested that if our final exams were to be used as a starte for the next course, indicating where students needed to work more even though they had passsed we would be able to identify and perhaps correct student difficulities before they compound further.

McCallum: Yes, it is important to harmonize. The other items (syllabus, teaching style, technology) determine the intended content of the course. The final exam shows the content actually achieved.

ANDREWS: (response to FLASHMAN) Clearly if we were in the same faculty meeting we would likely have some stasrk disagreements on your item 2. There is a way, however, in which I do believe that this list approach fails to face the real problem. The real problem is: Are we serious about this? If we are, there are numerous ways to skin a cat. If on the other hand, the other obligations of faculty life crowd out our teaching concerns, then we will never improve instruction. The big question is: How do we go about making teaching really important ?[end]

McCallum: (Response to Andrews.) Yes, you are absolutely right, that is the most important question.

FLASHMAN: This is true at larger and research oriented universities...but at many institutions -for example the California State University which is the largest single university system in the US, the priority of teaching is #1 as far as I know.

ANDREWS: I regret that other obligations require that I sign off now. I am grateful to have had this opportunity to interact on these important topics. So long! [end]

FLASHMAN: We've be on for about an hour now... so before the few people who have stayed leave, I want to thank Professor Andrews and you all for participating in this conference.
FLASHMAN: It has been slow but perhaps that has allowed us all time to think before we speak. As a first attempt I know it shows me some of the problems and potential of a chat conference.
FLASHMAN: If you would like to see more such conferences and/or have other suggestions for how to use the chatroom please contact me via e-mail

FLASHMAN: Bye too all and thanks.

Back to the CRAFTY home page.