Philosophy of Computer Science: Online Resources

Instructor's Manual

Last Update: Monday, 30 May 2022 — 2:00 pm

Introduction

For a full description of this course, see:

Rapaport, W.J. (2005). Philosophy of computer science: An introductory course. Teaching Philosophy, 28(4):319–341.

For the syllabus, class schedule, and supporting websites for the most recent version of the course on which this book is based, see CSE/PHI 484/584: Philosophy of Computer Science (Spring 2010)

Position Papers

The arguments that are presented in Online Resources: Position Papers are those that I have used when I have taught this course. You are invited to modify these or to create your own arguments.

Scheduling

The assignments can be scheduled at your convenience, which is why I have collected them in the Online Resources rather than placing them throughout the text. One possibility is to schedule each assignment approximately one week after the relevant topic has been covered in class. This way, the students will have the benefit of having thought about the readings before forming their own opinions.

However, another possibility is to schedule them one week before the topic is to be covered in class, so that the students will be forced to think about the issues before reading what "Authorities" (see §2.6 of the book and "Cognitive Development and the Final Exam" (below) for an explanation of this term) have had to say.

A third option is to do both: Assign the first draft before the topic is begun, then have the students do the required readings and participate in class discussions of the topic, then follow this with an optional revision or second draft of the position paper and the peer-editing session, with a third draft (or second, if the optional, post-class-discussion draft is omitted) to be turned in for instructor evaluation.

Peer Editing

Peer-editing sessions should take up a full class period. The general method is to divide the class into small groups of three or four students. (Two students will work if the number of students in the class—or latecomers!—demands it, but is not ideal. Five-student groups are too large to enable everyone to participate, especially if time is limited.)

For each student in a group:

Have the group read the student's position paper.
Have the group challenge the student's position, ask for clarification, and make recommendations for improving the student's paper.

If there are s students in a group and the peer-editing session lasts for m minutes, then the group should spend no more than m/s minutes on each student's paper. The instructor should visit each group at least once to ensure that all is going well, to answer questions, and to suggest questions if the group seems to be having trouble. If a group ends early and there is a lot of time left in the session, ask each student in the group to join another group (even if only to listen in to that group's ongoing discussion, but if that other group also ended early, then the newcomer should peer-edit one of their papers). Specific information for peer-editing sessions is given with each assignment.

After peer-editing, students should revise their position papers in the light of the editing suggestions and hand in all drafts to the instructor. I usually give the students one week for this revision.

Grading

The Quantum-Triage Philosophy of Grading

To make grading the position papers easier on the instructor and easy for students (in case the instructor decides to have students grade each other's essays), I recommend using "triage" grading. On this method, each item to be graded is given:

full credit (e.g., 3 points or 'A') if it is clearly done in a completely acceptable manner (even if it might not be entirely "correct")
partial credit (e.g., 2 points or perhaps 'C') if it is done, but is not clearly worth either full credit or minimal credit
minimal credit (e.g., 1 point or 'D') if it is done, but is clearly not done in an acceptable manner.
no credit (i.e., 0 points or 'F') if it is omitted.

Furthermore, these point values are "quantum" numbers in the sense that no fractional points are allowed. If, for example, an item is to be doubly "weighted"—perhaps giving 6 points for full credit and 2 points for minimal credit—then the only partial credit would be 4 points: It would not be possible for a student to get 1, 3, or 5 points. That way, students cannot ask for "just 1 more point".

The advantage to this method of grading is that the grader only has to decide if a response is worth full credit (i.e., shows clear understanding of what is expected) or minimal credit (i.e., shows clear mis-understaning or lack of understanding of what is expected). Any response that is not clearly one or the other is given partial credit. And failure to respond, or omission of some requirement, is given no credit. This helps make grading slightly more objective (and certainly easier for novice graders). And, perhaps more importantly, it gives the students information about the meaning of their grade.

On my grading scheme:

'B' = no direct interpretation; results from averaging 'A' and 'C' grades

'C' = neither clearly 'A' work nor clearly 'D' work

'D' = did not understand the material

'F' = did not do the work (i.e., 0 pts.);
can also result when omitting some parts and doing 'D' work on others.

Details and the theory behind the method are given in:

Rapaport, W.J. (2011). A triage theory of grading: The good, the bad, and the middling. Teaching Philosophy, 34(4):347–372
and online at "How I Grade"

Finally, I handed out each of the following analyses and grading rubrics when I returned the graded papers, so that the students would be able to understand how I graded them. As noted in the Grading Rubric for Position Paper 5, you might consider handing a version of these out before students turn in their position papers or between writing a first and second draft.

Position Paper Analyses and Grading Rubrics

Cognitive Development and the Final Exam

At least one of the goals of philosophy education ought to be the fostering of the students' development of analytical and critical thinking skills. In order to explain the nature of the sample final exam, I want to call attention to a theory of cognitive development of college students, to discuss its implications for critical thinking, and to show how it can apply to the development of writing exercises such as that final exam.

William G. Perry's scheme of cognitive development:

Perry, Jr., W.G. (1970). Forms of Intellectual and Ethical Development in the College Years: A Scheme. Holt, Rinehart and Winston, New York.
Perry, Jr., W.G. (1981). Cognitive and ethical growth: The making of meaning. In Chickering, A. and Associates, editors, The Modern American College, pages 76–116. Jossey-Bass, San Francisco.

is a descriptive theory of positions that represent students' changing attitudes towards knowledge and values as they progress through their education. There are nine positions, which fall into four groups.

These are usually referred to as "positions", rather than "stages". "Stage" terminology suggests that students "progress" from one "stage" to the next and never return to previous "stages", but that's not the case with Perry positions: A student can simultaneously be in more than one position with respect to different subjects that they are studying.

I. Dualism

Position 1. Basic Duality:

learn the correct answers

answer

You

Position 2. Dualism::
Students move to this position when faced with alternative opinions or with disagreements among different Authority figures (e.g., different instructors). For example, one literature teacher might say that Huckleberry Finn is the best American novel, but another might say that it is the worst. Dualistic students infer that one of those literature teachers' views of the golden tablets is obscured. Consequently, Dualistic students see the purpose of education as learning to find the correct answers.

Dualistic students prefer structured classes, which they see as providing the correct answers, and subjects such as math, which they see as having clear answers (all math teachers agree that the golden tablets say that 2+2=4). Conflict between instructor and text, or between two instructors, is seen threateningly as conflicts among Authority figures.

II. Multiplicity:

Position 3. Early Multiplicity:

from

know

don't

yet

methods for finding

Position 4. Late Multiplicity:
As students move along, chronologically or cognitively, they begin to see the second kind of question as being the more common one. Because it is felt that most questions are such that instructors don't have the correct answers for them, "everyone has a right to [their] own opinion; no one is wrong!" (Perry 1981, p. 79). The instructor's task, therefore, is seen as either teaching how to think or, worse, being irrelevant (after all, everyone has a right to their own opinion, including instructors—but it's just their opinion). (On science and opinion, see:

Denning, P.J. and Johnson, J. (2021). Science is not another opinion. Communications of the ACM, 84(3):36–38.

III. Contextual Relativism:

Position 5.

supported

relative to

context

IV. Commitment within Relativism:

Positions 6–9.

Finally, there is evidence that a student taking Position x will not understand—will literally not be able to make any sense out of—instruction aimed at Position x+2 (or beyond). Conversely, students at higher levels are bored by instruction aimed at lower levels.

Here is a useful anecdote (adapted from Perry) for illustrating the scheme: Suppose that a CS instructor offers three different algorithms for solving the same computational problem.

The Dualistic student will wonder which is the correct one (and why the instructor bothered to talk about the incorrect ones).
The Multiplistic student will think, "Only 3? Heck, I can come up with 6!".
The Contextual Relativist will wonder what advantages and disadvantages each theory has.
And the Commitment-oriented student will be wondering about how to decide which is most appropriate or useful in a given situation.

Data from several studies indicate that most entering college freshmen are at Positions 2 or 3:

Perry 1970
Perry 1981
Copes, L. (1982). The Perry development scheme: A metaphor for learning and teaching mathematics. For the Learning of Mathematics, 3(1):38–44.

Courses designed to teach critical thinking skills to students through the first two years of college are thus dealing with Dualists or (early) Multiplists, and this can result in several problems that the instructor should be aware of in order to foster the students' development along the Perry scheme:

First, Dualists want to be told the correct answers. But critical-thinking courses are largely involved with criticism and argument analysis. Accordingly, the entire activity may appear to them as incomprehensible at worst and pointless at best, or may simply result in the students learning the "sport" of "dumping" on "bad" or "incorrect" arguments. Hence, such courses, including the present one, must be more than mere criticism courses; they must make a serious attempt to teach ways of constructing arguments, solving problems, or making decisions. In this way, they can offer an appropriate "challenge" to Dualistic students, especially if couched in a context of adequate "support":

Sanford, N. (1967). Where Colleges Fail. Jossey-Bass, San Francisco, Ch. 6, esp. pp. 51–52.

Second, "The highly logical argument that, 'since everybody has a right to their own opinion, there is no basis for rational choice' is very typical of Multiplistic students":

Goldberger, N.R. (1979). Developmental assumptions underlying models of general education. Paper presented at the Conference on General Education, William Patterson College, p. 7.

But a goal of critical-thinking courses should be precisely to provide bases for rational choice: logical validity, inductive strength, etc. Accordingly, Multiplistic students either will not comprehend this goal or will view it as pointless. Again, such a course can be appropriately challenging to the students, but the instructor must be aware of how the students are likely to perceive it—to "hear" students' negative comments not as marks of pseudo-sophistication or worse, but as marks of viewing the world Multiplistically.

Finally, consider the concept of logical validity. Larry Copes (personal conversation) points out that it is a "relativistic" concept: A "valid" conclusion is one that is true relative to the truth of the premises. Dualistic students searching for absolutes and Multiplistic students feeling that "anything goes" may not accept, like, or understand validity. This may explain why so many students believ that arguments with true conclusions are valid or that valid arguments require true premises—even after having dutifully memorized the definition of 'validity'!

How can an instructor simultaneously challenge students in order to help them move to a higher-numbered position, yet not threaten them, especially when a given class might have students at widely varying positions? One suggestion, based on work by Lee Knefelkamp, is to create assignments that can appeal to students at several levels.

Application to the Final Exam

The suggested final exam is one such assignment. Students are offered five questions and asked to answer any three of them.

Question 1 is similar to, but not exactly the same as, the argument in Position Paper #1, so it is a little bit challenging to the Dualistic student, but is supportive in that they have already practiced giving a response to it.
Question 2 is a brand-new argument for analysis, but one that students could have predicted that it would have appeared on a final exam, because it covers a topic that was explicitly discussed in the course yet was not the subject of a position paper. Consequently, it is challenging, because it is new. But it is also supportive, because it covers material that should be familiar. Thus, it should appeal to both Dualistic and Multiplistic students.
Questions 3 and 4 appear to be open-ended questions that should appeal to Multiplistic students, though they can be understood as questions that might appeal to Dualistic students, too. After all, they are topics that were covered in the course, and the students have been given tools for evaluating answers to such questions. The challenge here is to construct arguments for answers to the questions. Here, the student's choice of which question (3 or 4) to answer (if any) is a function of their personal interests or familiarity with the issues, which provides support.
Question 5 is the most challenging, because the student must come up with a question and then answer it. It should appeal to Multiplistic as well as Contextual Relativistic students.

If left to their own choices, students will choose the least challenging question commensurate with their current position. Thus, students need not be threatened by a question that they perceive as being too difficult or even unintelligible. But each question is just a bit more challenging than the previous one, and, because the students must answer three questions, they are offered a choice that includes at least one fully supportive question and at least one more-challenging question. (If such an exam is offered as a mid-term exam, then the final exam could begin with a least-challenging question that is more challenging than the least-challenging one on the mid-term.) In this way, students are encouraged to strive for a bit more, thus, hopefully, beginning the move to the next position of cognitive development.

It is imperative for those of us who teach such courses to learn how to challenge our students appropriately in order to foster their intellectual "growth". We must "hear" how our students inevitably make their own meaning out of what we say to them. And we must be ready to support them in the ego-threatening process of development.

Further Reading:
Perry's theory is far, far richer than I have portrayed it here. A useful survey of criticisms, together with a discussion of the relevance of the theory to mathematics education and to the history of mathematics, is Copes 1982. The relevance of the theory to philosophy is discussed in:

Rapaport, W.J. (1982). Unsolvable problems and philosophical progress. American Philosophical Quarterly, 19:289–298.

Further readings are listed at my website on "William Perry's Scheme of Intellectual and Ethical Development"