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Constructivism in Computer Science Education [1].



Constructivism constructivism, Russian art movement founded c.1913 by Vladimir Tatlin, related to the movement known as suprematism. After 1916 the brothers Naum Gabo and Antoine Pevsner gave new impetus to Tatlin's art of purely abstract (although politically intended)  is a theory of learning, which claims that students construct knowledge rather than merely receive and store knowledge transmitted by the teacher. Constructivism has been extremely influential in science and mathematics education, but much less so in computer science education (CSE (Certified Systems Engineer) See Microsoft certification. ). This paper surveys constructivism in the context of CSE, and shows how the theory can supply a theoretical basis for debating issues and evaluating proposals. An analysis of constructivism in computer science education leads to two claims: (a) students do not have an effective model of a computer, and (b) computers form an accessible ontological on·to·log·i·cal  
adj.
1. Of or relating to ontology.

2. Of or relating to essence or the nature of being.

3.
 reality. The conclusions from these claims are that: (a) models must be explicitly taught, (b) models must be taught before abstractions, and (c) the seductive reality of the computer must not be allowed to supplant sup·plant  
tr.v. sup·plant·ed, sup·plant·ing, sup·plants
1. To usurp the place of, especially through intrigue or underhanded tactics.

2.
 construction of models.

The dominant theory of learning today is called constructivism. This theory claims that knowledge is actively constructed by the student, not passively absorbed from textbooks and lectures. Since the construction builds recursively on knowledge that the student already has, each student will construct an idiosyncratic id·i·o·syn·cra·sy  
n. pl. id·i·o·syn·cra·sies
1. A structural or behavioral characteristic peculiar to an individual or group.

2. A physiological or temperamental peculiarity.

3.
 version of knowledge. To the extent that such knowledge is not identical with "standard" scientific knowledge, the student is said to have misconceptions Misconceptions is an American sitcom television series for The WB Network for the 2005-2006 season that never aired. It features Jane Leeves, formerly of Frasier, and French Stewart, formerly of 3rd Rock From the Sun. . Teaching techniques derived from the theory of constructivism are supposed to be more successful than traditional techniques, because they explicitly address the inevitable process of knowledge construction.

Constructivism has been intensively studied by researchers of science education (Glynn, Yeany & Britton, 1991) and mathematics education (Davis, Maher, & Noddings, 1990; Ernest, 1994), to the extent that "radical constructivism represents the state of the art in epistemological e·pis·te·mol·o·gy  
n.
The branch of philosophy that studies the nature of knowledge, its presuppositions and foundations, and its extent and validity.



[Greek epist
 theories for mathematics and science education" (Ernest, 1995, p. 475). However, there has been much less work on constructivism in computer science education (CSE).

This article is logically divided into two parts. The first part--after a motivating example--is a survey of the theory of constructivism and its application in science education. The second part of the article contains the author's analysis of the theory in the context of computer science and his attempts to apply the theory to issues that are of current interest in CSE.

The discussion is concentrated within the framework of novice programmers, but constructivist con·struc·tiv·ism  
n.
A movement in modern art originating in Moscow in 1920 and characterized by the use of industrial materials such as glass, sheet metal, and plastic to create nonrepresentational, often geometric objects.
 principles are applicable at all levels of computer science education. Given the rapid rate of change of software tools and applications, most software engineers in industry and business are continually engaged in education: not only in formal training sessions, but also--perhaps more importantly--in the development of manuals, interfaces, and help files. They will find the theory and its applications to be both thought-provoking and relevant to their day-to-day work.

CSE (though not perhaps theoretical computer science) probably has more in common with engineering education than with science education. Readers with a background in engineering are invited to speculate about the applicability of these analyses to their fields.

Previous Work

There is a large amount of literature on the psychology of programming (Hoc, Green, Samurcay, & Gilmore, 1990; Soloway & Sphorer, 1989; Mayer, 1988); in particular, researchers interested in teaching programming to children or to nonmajors are often cognitive psychologists deeply immersed im·merse  
tr.v. im·mersed, im·mers·ing, im·mers·es
1. To cover completely in a liquid; submerge.

2. To baptize by submerging in water.

3.
 in Piagetian principles. Occasionally, these researchers explicitly acknowledge their commitment to constructivist principles (diSessa, Abelson, & Ploger, 1991, p. 12).

The literature on constructivism in CSE is in no way comparable with the vast literature in mathematics and physics education. Even today, a search of "constructivism" in the ACM (Association for Computing Machinery, New York, www.acm.org) A membership organization founded in 1947 dedicated to advancing the arts and sciences of information processing. In addition to awards and publications, ACM also maintains special interest groups (SIGs) in the computer field.  Digital Library returns only a handful of papers. While many computer science educators have been influenced by constructivism, only recently has this been explicitly discussed in published work (Boyle, 1996; Brandt, 1997; Gray, Boyle, & Smith, 1998; Hadjerrouit, 1998).

Motivation

What You See Is What You Get (jargon) What You See Is What You Get - (WYSIWYG) /wiz'ee-wig/ Describes a user interface for a document preparation system under which changes are represented by displaying a more-or-less accurate image of the way the document will finally appear, e.g. when printed.  (WYSIWYG (What You See Is What You Get) Pronounced "wiz-ee-wig." It refers to displaying text and graphics on screen the same as they will print on paper or display on a Web page. ) word processors are considered to be the epitome of user-friendliness, because working with them is supposed to be exactly analogous to writing with pen or pencil on a sheet of paper--a routine familiar to everyone who has graduated from elementary school elementary school: see school. . But consider the following scenario. You type in the title of your term paper, select the text and request boldface font A set of type characters that are darker and heavier than normal. A boldface font implies that each character was originally designed with a heavier appearance rather than created on the fly from a normal character. See boldface attribute. . Unfortunately, as you begin to type the text of the paper, it is also displayed in boldface font. Your pre-existing knowledge of a WYSIWYG word processor is almost certainly the metaphor of ordinary writing which consists of placing blobs of ink sequentially, but arbitrarily, on a sheet of paper (Figure 1). This metaphor cannot furnish an explanation for the phenomenon you have encountered, so you become frustrated frus·trate  
tr.v. frus·trat·ed, frus·trat·ing, frus·trates
1.
a. To prevent from accomplishing a purpose or fulfilling a desire; thwart:
, anxious, and lose self-confidence.

Of course, the explanation is trivial: the word processor is not storing blobs of ink, but symbols including implicit symbols for font changes and for indicating the end of a line (Figure 2). Here we are arbitrarily using HTML HTML
 in full HyperText Markup Language

Markup language derived from SGML that is used to prepare hypertext documents. Relatively easy for nonprogrammers to master, HTML is the language used for documents on the World Wide Web.
 notation: [less than]b[greater than]...[less than]/b[greater than] to delimit de·lim·it   also de·lim·i·tate
tr.v. de·lim·it·ed also de·lim·i·tat·ed, de·lim·it·ing also de·lim·i·tat·ing, de·lim·its also de·lim·i·tates
To establish the limits or boundaries of; demarcate.
 boldface font and [less than]br[greater than] to indicate a line break.) If your selection of the text fragment to change to boldface See boldface font.  included an invisible (!) line break character, text typed before the line break will be mysteriously displayed in boldface.

The correct explanation of WYSIWYG should now be clear. What you get is: (a) a data structure for storing text and formatting specifications, and (b) a set of operations on that data structure. What you see is: (a) a rendering of the data structure on the screen, and (b) icons and menus to invoke the operations. To learn how to use the word processor, you must: (a) create a mental model of the data structure and the effect of each operation, and (b) attribute to each icon and menu item a meaning as an operation.

Constructivism claims each individual necessarily creates cognitive structures (models) when learning to use the word processor. Furthermore, it claims that each individual will perform the construction differently, depending on his or her preexisting pre·ex·ist or pre-ex·ist  
v. pre·ex·ist·ed, pre·ex·ist·ing, pre·ex·ists

v.tr.
To exist before (something); precede: Dinosaurs preexisted humans.

v.intr.
 knowledge, learning style and personality traits. Hopefully, the construction is viable and the user can successfully use the word processor. Unfortunately, but perhaps inevitably, many users construct nonviable nonviable /non·vi·a·ble/ (-vi´ah-b'l) not capable of living.

non·vi·a·ble
adj.
Not capable of living or developing independently. Used especially of an embryo or fetus.
 models.

Teaching how to do a task can be successful initially, but eventually this knowledge will not be sufficient. As the example tries to show, a student who only knows the procedure for changing from ordinary to boldface font will be helpless when faced with this novel situation. The problem is caused not by stupidity on the part of the novice, nor by incorrectly following the instructions, but by a misconception mis·con·cep·tion  
n.
A mistaken thought, idea, or notion; a misunderstanding: had many misconceptions about the new tax program.
 that is attributable to the lack of a viable model that can explain the behavior of the word processor. The teacher must guide the student in the construction of a viable model so that new situations can be interpreted in terms of the model and correct responses formulated.

The word-processor example illustrates two aspects of learning that are characteristic of computer science. First, since computer science deals with artifacts--programming languages and software, the creator of the artifact A distortion in an image or sound caused by a limitation or malfunction in the hardware or software. Artifacts may or may not be easily detectable. Under intense inspection, one might find artifacts all the time, but a few pixels out of balance or a few milliseconds of abnormal sound  employed a very detailed model and the learner must construct a similar, though not necessarily identical, model. Second, knowledge is not open to social negotiation. Given that the word processor is an extant artifact, you cannot argue that its method of using fonts is incorrect, discriminatory, demeaning de·mean 1  
tr.v. de·meaned, de·mean·ing, de·means
To conduct or behave (oneself) in a particular manner: demeaned themselves well in class.
, or whatever. You may be able to choose another software package, or to request modifications in an existing one, but meanwhile you must learn the existing reality. These two points will be extensively discussed in the rest of the paper.

EPISTEMOLOGY epistemology (ĭpĭs'təmŏl`əjē) [Gr.,=knowledge or science], the branch of philosophy that is directed toward theories of the sources, nature, and limits of knowledge. Since the 17th cent.  AND CONSTRUCTIVISM

Educational Paradigms

An educational paradigm is composed of four components (Ernest, 1995):

* An ontology ontology: see metaphysics.
ontology

Theory of being as such. It was originally called “first philosophy” by Aristotle. In the 18th century Christian Wolff contrasted ontology, or general metaphysics, with special metaphysical theories
 which is a theory of existence.

* An epistemology which is a theory of knowledge, both of knowledge specific to an individual and of shared human knowledge.

* A methodology for acquiring and validating knowledge.

* A pedagogy which is a theory of teaching.

(See Scheffler (1965) for an introduction to epistemology in the framework of education. Scheffler gives a slightly different decomposition decomposition /de·com·po·si·tion/ (de-kom?pah-zish´un) the separation of compound bodies into their constituent principles.

de·com·po·si·tion
n.
1.
; in particular, he includes evaluation: deciding what knowledge is reliable or important.)

This framework can be used to succinctly suc·cinct  
adj. suc·cinct·er, suc·cinct·est
1. Characterized by clear, precise expression in few words; concise and terse: a succinct reply; a succinct style.

2.
 describe the classical educational paradigm:

* There is an ontological reality. Even though scientists accept the theories of relativity and quantum mechanics quantum mechanics: see quantum theory.
quantum mechanics

Branch of mathematical physics that deals with atomic and subatomic systems. It is concerned with phenomena that are so small-scale that they cannot be described in classical terms, and it is
, the Newtonian model of absolute space and time is the model we generally use for reality. Furthermore, we function as Platonist mathematicians Mathematicians by letter: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z See also
  • Requested mathematicians articles
  • (by country, etc.)
  • List of physicists
External links
 who hold that mathematics has an existence independent of ourselves in which 2+2=4 is absolutely true.

* Epistemology is foundational. The truth is out there. We come to believe foundations--necessary truths such as 2+2=4 and empirical sensory data--and then use valid forms of logical deduction to expand the extent of true knowledge.

* The mind is a clean slate Noun 1. clean slate - an opportunity to start over without prejudice
fresh start, tabula rasa

chance, opportunity - a possibility due to a favorable combination of circumstances; "the holiday gave us the opportunity to visit Washington"; "now is your chance"
 that can be filled with knowledge. Once you know enough facts and rules of inference This is a list of rules of inference. Introduction
Rules of inference are syntactical transformation rules which one can use to infer a conclusion from a premise to create an argument.
, you can create new knowledge by logical deduction. Carroll (1990) cites the legend of the Nurnberg Funnel which can be used to "pour" knowledge directly into the learner's head.

* Listening to lectures and reading books are the primary means of knowledge transmission. Repetition (drill and practice) will ensure that the knowledge is retained.

The constructivist paradigm is dramatically different:

* Ontological reality is either rejected or at best considered irrelevant. Since we can never truly "know" anything, ontology cannot influence our educational paradigm.

* The epistemology of constructivism is nonfoundationalist and fallible fal·li·ble  
adj.
1. Capable of making an error: Humans are only fallible.

2. Tending or likely to be erroneous: fallible hypotheses.
. Absolute truth is unattainable, so there is no foundation of truth on which to build. Even 2+2=4 is not a necessary truth (Barnes, Bloor, & Henry, 1996, Chapter 7)! Knowledge is constructed by each individual and thus necessarily fallible.

* Knowledge is acquired recursively: sensory data is combined with existing knowledge to create new cognitive structures, which are in turn the basis for further construction. Knowledge is also created cognitively by reflecting on existing knowledge. These concepts come from the seminal work A seminal work is a work from which other works grow. The term usually refers to an intellectual or artistic achievement whose ideas and techniques have been adopted or responded to in later works by other people, either in the same field or in the general culture.  of Jean Piaget Noun 1. Jean Piaget - Swiss psychologist remembered for his studies of cognitive development in children (1896-1980)
Piaget
 on the acquisition of knowledge by children; Piaget's work was instrumental in the development of constructivist theories.

* Passive learning will likely fail, because each student brings a different cognitive framework to the classroom, and each will construct new knowledge in a different manner. Learning must be active: the student must construct knowledge assisted by guidance from the teacher and feedback from other students. Constructivists believe that effective learning demands not just discovery of facts, but the construction of viable mental models, and that teachers must actively guide the student in this effort. The task of the teacher in the constructivist paradigm is significantly more difficult than in the classical one, because guidance must be based on the understanding of each student's currently existing cognitive structures.

Note that constructivism does not reject classical means of instruction such as lecturing and reading books. As Mason notes, tongue-in-cheek: "Many educators espousing constructivism have been known to attend lectures on constructivism, and even to have enjoyed them!" (Mason, 1994, p. 197). The problem is not the lecture itself, but the assumption that "students know what the lecturer told them." And Mason continues with the suggestion that: "...when preparing a lecture, it is the fact of the imminent audience which enables the lecturer to contact the content in fresh ways, in a state conductive conductive

having the quality of readily conducting electric current.


conductive flooring
flooring or floor covering made specially conductive to electrical current, usually by the inclusion of copper wiring that is earthed
 to creativity and connection-finding." (Mason, 1994, p. 198) The concept that the student is trying to construct a model from what are, after all, only words is an appealing theoretical framework for an educator to use in assessing the success or failure of a lecture or other teaching activity.

Conversely, constructivism in not coextensive co·ex·ten·sive  
adj.
Having the same limits, boundaries, or scope.



coex·ten
 with "modern" teaching methods such as group projects, discovery learning and active tasks. These methods are favored by constructivists only if they are designed to enable the students' to build a viable mental model based on pre-existing knowledge. A hands-on activity is useless if "their hands are on, but their heads are out" (Resnick, 1997, p. 28).

Constructivism does have a lot in common with discovery or inquiry learning, where students are expected to discover knowledge by themselves when placed in the appropriate situation. The benefits of discovery are claimed to be:... "(l) the increase in intellectual potency, (2) the shift from extrinsic EVIDENCE, EXTRINSIC. External evidence, or that which is not contained in the body of an agreement, contract, and the like.
     2. It is a general rule that extrinsic evidence cannot be admitted to contradict, explain, vary or change the terms of a contract or of a
 to intrinsic rewards, (3) the learning of the heuristics heu·ris·tic  
adj.
1. Of or relating to a usually speculative formulation serving as a guide in the investigation or solution of a problem:
 of discovering, and (4) the aid to conserving memory" (Bruner, 1962, p. 83).

Note that Bruner (1962, p. 85) seems to agree with the constructivist viewpoint that unfettered discovery is not helpful; he distinguishes between episodic episodic

sporadic; occurring in episodes. e. falling a paroxymal disorder described in Cavalier King Charles spaniels in which affected dogs, starting at an early age, experience episodes of extensor rigidity, possibly brought on by stress. e.
 empiricism empiricism (ĕmpĭr`ĭsĭzəm) [Gr.,=experience], philosophical doctrine that all knowledge is derived from experience. For most empiricists, experience includes inner experience—reflection upon the mind and its , where the student accumulates unconnected facts, and cumulative constructionism constructionism
the use of or reliance on construction or constructive methods. — constructionist, n.
See also: Attitudes
, where the discovery is organized.

Constructivists differ among themselves as to the relative importance ascribed to the individual learner and to the group in constructing knowledge; these variants are known as radical and social constructivism, respectively. A discussion of the variants of constructivism is beyond the scope of this article; see Ernest (1995), Phillips (1995).

Constructivism in Science Education

Studies have shown that relatively few students reach an acceptable level of achievement in high-school science and mathematics (Duit, 1991). Physics teachers seem to have the worst time, as students retain a naive theory of physics despite intensive instruction in Newtonian mechanics Noun 1. Newtonian mechanics - the branch of mechanics based on Newton's laws of motion
classical mechanics

mechanics - the branch of physics concerned with the motion of bodies in a frame of reference
 (McCloskey, 1983). For constructivists this is not surprising: everyone who has ever thrown a ball--that is, everyone--knows that if you don't keep applying force, an object in motion will eventually come to rest. Apparently, these ideas are so entrenched en·trench   also in·trench
v. en·trenched, en·trench·ing, en·trench·es

v.tr.
1. To provide with a trench, especially for the purpose of fortifying or defending.

2.
 that mere lectures and even experiments have a difficult time evicting them. At most, a certain facility in manipulating formulas is achieved, but this fails as soon as the student attempts to solve a problem that requires deep understanding.

The discrepancy between performance and understanding has also been noted in mathematics education:

The pupil's fundamental problems with such ideas as negative or complex numbers tend to be overlooked by the teacher mainly because the latter's own implicit beliefs make him or her oblivious to the possibility of somebody having a different ontological stance....Another circumstance that helps in concealing ontological difficulties is the fact that a student may become quite skilful skil·ful  
adj. Chiefly British
Variant of skillful.


skilful or US skillful
Adjective

having or showing skill

skilfully or US
 in manipulating concepts even without reifying them. (Sfard, 1994, p. 268)

Physics educators are very receptive to constructivist principles. After all, physicists have undergone two massive restructurings of their world within a short period of history: from Aristotelian physics The Greek philosopher Aristotle (384 BC – March 7, 322 BC) developed many theories on the nature of physics that somewhat differ from what are now understood as the laws of physics.  to Newtonian physics and then to Einsteinian physics. One cannot fault them for their reluctance to believe that E=[mc.sup.2] is an absolute truth. This openness is demonstrated by their willingness to attribute to the student alternative frameworks rather than misconceptions.

In fact, von Glasersfeld, a pioneer of constructivism, would never say that something is wrong, because he does not believe in the possibility of establishing universal truths. Instead, he says that concepts are viable "if they prove adequate in the contexts in which they were created" (Glasersfeld, 1995, p. 7). This is analogous to the use of the word in biology to denote an organism adapted to its environment. The box metaphor for variables, and the communications model of reference parameters (discussed later) are simply nonviable, because they cause the student to fail on programming tasks.

According to according to
prep.
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

3.
 constructivism, a teacher cannot ignore the student's existing knowledge; instead, he or she must question the student in order to understand exactly what theory the student is currently using, and only then attempt to guide the student to the "correct" theory. It is perhaps axiomatic ax·i·o·mat·ic   also ax·i·o·mat·i·cal
adj.
Of, relating to, or resembling an axiom; self-evident: "It's axiomatic in politics that voters won't throw out a presidential incumbent unless they think his challenger will
 for a constructivist that students have consistent theories--they just happen to be at variance with the (currently accepted) scientific theory.

In most fields of science Fields of science are widely-recognized categories of specialized expertise within science, and typically embody their own terminology and nomenclature.

Natural sciences

Main article: Natural science
 education including computer science, there is a large body of research that catalogs misconceptions. A constructivist would view a misconception not as a mistake, but as a logical construction based on a consistent, though nonstandard non·stan·dard  
adj.
1. Varying from or not adhering to the standard: nonstandard lengths of board.

2.
 theory, held by the student. Even Matthews--who is critical of constructivism--is careful to point out that: "It is with respect to [contemporary physics] that [students] have misconceptions, it is not with respect to the behavior of the natural world" (Matthews, 1994, p. 133).

Merely listing misconceptions is fruitless fruit·less  
adj.
1. Producing no fruit.

2. Unproductive of success: a fruitless search. See Synonyms at futile.
; a misconception must be accompanied by a description of the underlying model that caused it, and by a suggestion how to base the construction of a viable model on the existing one. Smith III, diSessa, and Roschelle (1993) go so far as to claim that misconceptions form the prior knowledge that is essential to the construction of new knowledge!

It is important not to confuse the use of computers in science education with the study of computer science. Computers are often seen as a tool to increase the constructive content of science education. For example, Hatfield (1991) considers programming, or more generally algorithmics, as constructive. However, his article is essentially concerned with the contribution of algorithmics to mathematical education, rather than to the constructivist aspects of computer science and programming. Similarly: "The role of the computer activities is...to provide an experiential basis for all other learning modes....the main point is spending the time and effort on the problem, not solving it" (Leron & Dubinsky, 1995, p. 231, 236).

In CSE, the computer is not just providing an experiential basis, nor is it creating a microworld (Harel & Papert, 1991) in order to facilitate construction of knowledge in another domain. Instead, the students are learning about computing itself--systems, algorithms, languages--and lessons from the use of computers in other fields must be applied carefully.

Criticism of Constructivism

Before continuing, we must stress that that there is strong opposition to constructivism. See the articles by Matthews, Nola, Phillips, and Ogborn in the Special Issue on Philosophy and Constructivism in Science Education (January 1997) of the journal Science & Education. The articles are also available in Matthews (1998).

One critic writes vehemently: "If radical constructivism is post-epistemological then it is also pre-Copernican and adopts views of science similar to those of the Inquisition Inquisition (ĭn'kwĭzĭsh`ən), tribunal of the Roman Catholic Church established for the investigation of heresy. The Medieval Inquisition


In the early Middle Ages investigation of heresy was a duty of the bishops.
 that interviewed Galileo" (Nola, 1997b, p. 209).

The criticism is not so much of the constructivist theory of learning, but rather of extreme conclusions drawn from constructivist epistemology Constructivism is a perspective in philosophy that views all of our knowledge as "constructed", under the assumption that it does not necessarily reflect any external "transcendent" realities; it is contingent on convention, human perception, and social experience. : "The one-step argument from the psychological premise (1) 'the mind is active in knowledge acquisition,' to the epistemological conclusion (2) 'we cannot know reality,' is endemic in constructivist writing" (Matthews, 1994, p. 151).

Carried to the extreme, radical constructivism leads to solipsism sol·ip·sism  
n. Philosophy
1. The theory that the self is the only thing that can be known and verified.

2. The theory or view that the self is the only reality.
, the philosophical claim that the world is one's own mental creation. In turn, this can lead to a rejection of ethics: if the world is my own creation, why should I care what happens to others? Boyle (1996, Section 6.4) takes radical constructivists to task for putting too much emphasis on an individual's cognition cognition

Act or process of knowing. Cognition includes every mental process that may be described as an experience of knowing (including perceiving, recognizing, conceiving, and reasoning), as distinguished from an experience of feeling or of willing.
 at the expense of the biological (Piaget) and social (Vygotsky) foundations upon which cognition must be based.

Carried to the extreme, social constructivism leads to a view of science as a merely political enterprise developed by entrenched elitist e·lit·ism or é·lit·ism  
n.
1. The belief that certain persons or members of certain classes or groups deserve favored treatment by virtue of their perceived superiority, as in intellect, social status, or financial resources.
 groups whose sole purpose is to ensure their own survival. From the fallibility fal·li·ble  
adj.
1. Capable of making an error: Humans are only fallible.

2. Tending or likely to be erroneous: fallible hypotheses.
 of scientific knowledge, one slips into relativism relativism

Any view that maintains that the truth or falsity of statements of a certain class depends on the person making the statement or upon his circumstances or society. Historically the most prevalent form of relativism has been See also ethical relativism.
 of truth, and from the sociology of scientific practice, into demands for empowerment detached from any attempt at objective evaluation of scientific knowledge. The extreme position is stated in the Edinburgh "strong programme" on the sociology of knowledge The sociology of knowledge is the study of the relationship between human thought and the social context within which it arises, and of the effects prevailing ideas have on societies. (Compare history of ideas.  (Bloor, 1991; Barnes et al., 1996); for criticism of this position see the articles in Matthews (1998).

The essential question is whether being a constructivist requires an epistemological commitment to empiricism and idealism (or social idealism), as opposed to rationalism rationalism [Lat.,=belonging to reason], in philosophy, a theory that holds that reason alone, unaided by experience, can arrive at basic truth regarding the world.  and realism that seem to come more naturally to scientists. This delicate question can perhaps be avoided by taking the position of "pedagogical ped·a·gog·ic   also ped·a·gog·i·cal
adj.
1. Of, relating to, or characteristic of pedagogy.

2. Characterized by pedantic formality: a haughty, pedagogic manner.
 constructivists":... "who concentrate solely on pedagogy, and improved classroom practices,....For [whom], the details of epistemological psychology Epistemological psychology is a multi-sided perspective in psychology uncovering simple primary hidden inklings (images) in ideas, actions, feelings and all social interactions.  are unimportant, and not worth disputing about" (Matthews, 1997, p. 8).

Empirical Results in CSE

There is no question that many students find the study of computer science extremely difficult, especially at elementary levels. Before proceeding with a theoretical analysis, it is worthwhile to survey some results that demonstrate the depth of the problem:

* Sleeman, Putnam, Baxter, & Kuspa (1988), Samurcay (1989), and Paz (1996) found that the concept of variable is extremely difficult for students. For example, students believe that a variable could simultaneously contain two values, and that after executing A:=B, the variable B no longer contains a value. The students have constructed a consistent model using the analogy of a box; the model just happens to be non-viable for successful programming.

* Haberman and Ben-David Kolikant (2001) administered a test designed to check the basic concepts of assignment, read, and write statements in Pascal. Given the statements:

read (A,B);

read (B);

write (A,B,B);

many students are not at all sure what happens when you read twice to the same variable or write twice from the variable. They find it difficult to construct a model that identifies who is doing the reading and the writing. Similarly, Samurcay (1989) claims that students' models of read CA) may not include the assignment to the variable A.

* Madison (1995) used extensive interviews to elicit the internal model of parameters (especially reference parameters) held by students in an introductory course. The students were taught a communications model for parameters, rather than a model of the implementation (copy and reference). The interviews demonstrated that students had constructed consistent, but non-viable, models of the implementation of parameters.

* Similarly, Fleury (1991) discovered "student-constructed rules" for Pascal parameters that were occasionally successful, but non-viable in the general case.

* Deep misconceptions are not limited to elementary programming. Holland, Griffiths, and Woodman (1997) show the extent of the misconceptions held by students studying object-oriented programming object-oriented programming, a modular approach to computer program (software) design. Each module, or object, combines data and procedures (sequences of instructions) that act on the data; in traditional, or procedural, programming the data are separated from the . They found inappropriate conflation (database) conflation - Combining or blending of two or more versions of a text; confusion or mixing up. Conflation algorithms are used in databases.  of the concept of an object with other concepts like variable, class, and textual representation.

* The difficulties that students have in elementary computer science studies are often attributed to the need to spend too much time on the syntax of low-level procedural languages A programming language that requires programming discipline, such as C/C++, Java, COBOL, FORTRAN, Perl and JavaScript. Also called an "imperative language," programmers writing in such languages must develop a proper order of actions in order to solve the problem, based on a knowledge of  like Pascal and C. But similar phenomena are encountered even when teaching Prolog (PROgramming in LOGic) A programming language used for developing AI applications (natural language translation, expert systems, abstract problem solving, etc.). Developed in France in 1973, "Programmation en Logique" is used throughout Europe and Japan and is gaining , a language whose syntax is about as simple as can be imagined. Taylor (1990) studied novice Prolog programmers and found that students constructed models that were not viable:

Prolog's behavioral component is complex, and because its syntax is noncommittal, learners are tempted to hallucinate hal·lu·ci·nate  
v. hal·lu·ci·nat·ed, hal·lu·ci·nat·ing, hal·lu·ci·nates

v.intr.
To undergo hallucination.

v.tr.
To cause to have hallucinations.
 onto it whatever they think appropriate, rather than referring to an interpretation based upon underlying domain knowledge. (Taylor, 1990, p. 308)

* Algorithm and software visualization Software visualization (Diehl, 2002; Knight, 2002) is concerned with the static or animated 2-D or 3-D (Marcus et al., 2003) visual representation of information about software systems based on their structure (Staples & Bieman, 1999), size (Lanza, 2004), history (Girba et al,  is an extremely active field of CSE research. Yet Mulholland (1997) found that software visualization in itself does not necessarily help the student unless the visualization is based on a careful analysis of the pedagogic ped·a·gog·ic   also ped·a·gog·i·cal
adj.
1. Of, relating to, or characteristic of pedagogy.

2. Characterized by pedantic formality: a haughty, pedagogic manner.
 task.

Constructivism in the Context of CSE

To what extent is constructivism applicable to CSE? According to constructivism, students construct knowledge by combining the experiential world with existing cognitive structures. The author claims that the application of constructivism to CSE must take into account two characteristics that do not appear in natural sciences:

1. A (beginning) computer science student has no effective model of a computer.

2. The computer forms an accessible ontological reality.

Effective model means a cognitive structure that the student can use to make viable constructions of knowledge based upon sensory experiences such as reading, listening to lectures and working with a computer. Accessible ontological reality means that a "correct" answer is easily accessible, and moreover, successful performance requires that a normative model of this reality must be constructed. The rest of this section expands on these claims.

The important word is effective. The naive theory of physics held by students is clearly effective, as anyone who has seen professional ball players can testify. They have intuitive models that enable them to implicitly calculate the forces required to achieve superb accuracy when throwing or kicking a ball. Note that diSessa (1988) does not believe that students' intuitive concepts form a well-developed theory. Rather, he claims that they have a large number of fragments called p-prims, short for phenomena logical primitives. This does not materially change the argument; as it is doubtful that intuitive knowledge about computers reaches even the level of diSessa's p-prims.

The empirical results cited earlier (especially the work by Taylor (1990)) show just as clearly that intuitive models of computers are doomed to be non-viable. At most, the model is limited to the grossly anthropomorphic Having the characteristics of a human being. For example, an anthropomorphic robot has a head, arms and legs.  giant brain, hardly a useful metaphor when studying computer science. Pea (1986) gives the name "superbug su·per·bug
n.
Any of various disease-causing bacteria that develop a resistance to drugs normally used to control or eradicate them.



superbug
" to the idea that a "hidden mind" within the programming language has intelligence.

At the novice level, the claim is supported by many studies:

Even if no effort is made to present a view of what is going on 'inside' the learners will form their own. (duBoulay, 1989, p. 285)

... [we] attribute students' fragile knowledge of programming in considerable part to a lack of a mental model of the computer.... (Perkins, Schwartz, & Simmons, 1988, p. 162)

... even after a full semester of Pascal, students' knowledge of the conceptual machine underlying Pascal can be very fuzzy. (Sleeman, Putnam, Baxter, & Kuspa, 1988, p.251)

The lack of an effective, even if flawed, model of a computer can be a serious obstacle to teaching computer science if we accept the claim by Smith III et al. (1993) that prior knowledge, even in the form of misconceptions, is essential to the construction of new knowledge.

Turning now to the question of ontological reality, the computer science student is faced with immediate and brutal feedback on conclusions drawn from his or her mental model. More graphically, alternative frameworks cause bugs. Computer science is unlike school physics: the consequences of misconceptions are exposed immediately, not when you get your homework back a week later. Similarly, from the social viewpoint, there is not much point negotiating models of the syntax or semantics of a programming language.

This claim is based on the fact that almost all introductory computer science instruction includes programming. If, as Dijkstra (1989) suggested, we taught programs as mathematical objects John Backus argued that if computer programming is to turn more into a science (let alone an engineering discipline) and less of an art, it first has to become a truly mathematical discipline.  that need not be executed on a computer, the normal constructivist principles would apply. We could talk about the viability of denotational semantics (theory) denotational semantics - A technique for describing the meaning of programs in terms of mathematical functions on programs and program components. Programs are translated into functions about which properties can be proved using the standard mathematical theory of , or the social processes responsible for the belief in the Church-Turing Thesis. If the latter were ever superseded, we would experience a shock no less intense than that experienced by physicists in the early twentieth-century. Clearly, since computer science is unlikely to become a subject that is primarily theoretical, we must generate the motivation to examine our teaching practices without the benefit of an epistemological shock.

The claim cuts at the heart of constructivist epistemology, which is nonfoundationalist and fallible. But the pedagogy of constructivism is relatively independent of its epistemology. A physicist has no way of determining if E=[mc.sup.2] is true, but few of us can resist the temptation to use a computer if it helps us construct knowledge about a language or system. In fact, one of the ultimate tests of your prowess as a computer programmer or software engineer comes when you have to deal with a bug in the underlying hardware, operating system operating system (OS)

Software that controls the operation of a computer, directs the input and output of data, keeps track of files, and controls the processing of computer programs.
 or language compiler. Since you have come to look upon them as ontological reality--as arbiters of truth so to speak--it is extremely difficult to diagnose a problem in the implementation of your mental model, as opposed to a problem in your personal task such as writing a program.

APPLICATION OF CONSTRUCTIVISM IN CSE

Many phenomena of CSE can be explained by constructivism:

* The construction of even elementary computer science concepts is haphazard hap·haz·ard  
adj.
Dependent upon or characterized by mere chance. See Synonyms at chance.

n.
Mere chance; fortuity.

adv.
By chance; casually.
, leading to frustration and to the perception that computer science is hard. This is due to the fact that--in the absence of a viable preexisting model--models must be self-constructed from the ground up.

* Autodidactic au·to·di·dact  
n.
A self-taught person.



[From Greek autodidaktos, self-taught : auto-, auto- + didaktos, taught; see didactic.
 programming experience is not necessarily correlated with success in academic computer science studies. These students, like most physics students, come with firmly held mental models that are not viable for academic studies.

* Graphical user interfaces graphical user interface (GUI)

Computer display format that allows the user to select commands, call up files, start programs, and do other routine tasks by using a mouse to point to pictorial symbols (icons) or lists of menu choices on the screen as opposed to having to
 (GUI (Graphical User Interface) A graphics-based user interface that incorporates movable windows, icons and a mouse. The ability to resize application windows and change style and size of fonts are the significant advantages of a GUI vs. a character-based interface. ) are often touted as "intuitive" and "userfriendly", yet many people earn a comfortable living giving courses to anxiety-ridden users. Icons, scroll bars A vertical bar on the right side of a window or a horizontal bar at the bottom of a window that is used to move the window contents up and down or left and right. The bar contains a box with square or rounded corners, which together look like an elevator in a shaft.  and menus are merely representations, and seeing a representation alone contributes very little to the construction of a model.

* The reality feedback obtained by working on a computer can be discouraging to students who prefer a more reflective or social style of learning.

In the rest of the article, constructivist principles will be applied to specific issues in CSE. To avoid misunderstanding, it is important to clarify what is being claimed here. The author is not (necessarily) saying that one approach is superior to another; rather, he is saying that certain conclusions seem to follow directly from constructivist principles, so that if one accepts constructivism--which you are not required to do of course--then one must be willing to analyze his/her teaching methods in light of these conclusions.

GUI and WYSIWYG Angst angst 1
n.
A feeling of anxiety or apprehension often accompanied by depression.



angst 2
abbr.
angstrom
 

Turkle and Papert (1990) wax poetic on the virtues of icons. Yet an icon is just a representation; it is useful only to the extent that the user can construct a mental model of object being represented. The icon must undergo semiosis Semiosis is any form of activity, conduct, or process that involves signs, including the production of meaning. The term was introduced by Charles Sanders Peirce to describe a process that interprets signs as referring to their objects, as described in his theory : "the process whereby something comes to stand for something else, and thus acquires the status of a sign" (Husen & Postlethwaite, (1994) p. 5411). Today's software packages, both those intended for the general public such as word processors and professional software such as integrated development environments See IDE.

integrated development environment - interactive development environment
, display dozens of icons. From a semiotic semiotic /se·mi·ot·ic/ (se?me-ot´ik)
1. pertaining to signs or symptoms.

2. pathognomonic.
 point of view, it may be true that that an icon is better than text, but from a constructivist point of view, what is important is the construction of the model and not the sign that denotes it.

Icons are intuitive to the extent that the analogy between the object shown and the object represented is perfect. But as Glynn (1991) shows, analogies are rarely, if ever, perfect, so one must not lose patience with a novice who has yet to construct a viable model of the underlying machine. For example, consider an icon for the paste operation. The icon is two steps removed from the operation. First, the icon must be deciphered de·ci·pher  
tr.v. de·ci·phered, de·ci·pher·ing, de·ci·phers
1. To read or interpret (ambiguous, obscure, or illegible matter). See Synonyms at solve.

2. To convert from a code or cipher to plain text; decode.
 as representing the word paste. (This first step can be skipped if paste is selected from a menu.) Second, the word whose original meaning is "form a permanent chemical bond between one item and another" must be related to the operation "insert a copy of the material held in an internal buffer into the current working document at the place pointed to by the cursor." To understand this operation, one must have a mental model that enables you to understand the four concepts in this sentence. Even if the word "paste" is avoided, it is hard to see how so many concepts can be contained wi thin an icon.

WYSIWYG is another concept that could benefit from constructivist analysis In mathematics, constructive analysis is mathematical analysis done according to the principles of constructivist mathematics. This contrasts with classical analysis  as we showed above. The relevance for CSE is this: courses, help files, and tutorials must explicitly address the construction of a model, and not limit themselves to behaviorist Behaviorist

1. One who accepts or assumes the theory of behaviorism (behavioral finance in investing.) 2. A psychologist who subscribes to behaviorism.

Notes:
When it comes to investing, people may not be as rational as they think.
 practices of the form "to do X, following these steps." It is a reasonable conjecture CONJECTURE. Conjectures are ideas or notions founded on probabilities without any demonstration of their truth. Mascardus has defined conjecture: "rationable vestigium latentis veritatis, unde nascitur opinio sapientis;" or a slight degree of credence arising from evidence too weak or too  that document preparation systems with transparent models like LaTeX and HTML should engender en·gen·der  
v. en·gen·dered, en·gen·der·ing, en·gen·ders

v.tr.
1. To bring into existence; give rise to: "Every cloud engenders not a storm" 
 less anxiety among their users than WYSIWYG systems on complex tasks. If the underlying model is not accessible, there is a genuine trepidation trepidation /trep·i·da·tion/ (trep?i-da´shun)
1. tremor.

2. nervous anxiety and fear.trep´idant


trep·i·da·tion
n.
1. An involuntary trembling or quivering.
 associated with trying out new or advanced features, for fear that the document will be irrevocably trashed trashed  
adj. Slang
Drunk or intoxicated.

Our Living Language Expressions for intoxication are among those that best showcase the creativity of slang.
; with a transparent model you can easily insert and then comment-out or remove the explicit commands. Many users of WYSIWYG systems overcome the anxiety and eventually construct viable models, but the anxiety returns as new features are tried or familiar ones used in new contexts. Of course the claims in this paragraph are anecdotal an d need empirical verification.

Explicitly Teach the Model

If the student does not bring a preconceived pre·con·ceive  
tr.v. pre·con·ceived, pre·con·ceiv·ing, pre·con·ceives
To form (an opinion, for example) before possessing full or adequate knowledge or experience.
 model to class, we must ensure that a viable hierarchy of models is constructed and then refined as learning progresses. This means that the model of a computer--CPU, memory, I/O (Input/Output) The transfer of data between the CPU and a peripheral device. Every transfer is an output from one device and an input to another. See PC input/output.

I/O - Input/Output
 peripherals--must be explicitly taught and discussed, not left to haphazard construction and not glossed over with facile (language) Facile - A concurrent extension of ML from ECRC.

http://ecrc.de/facile/facile_home.html.

["Facile: A Symmetric Integration of Concurrent and Functional Programming", A. Giacalone et al, Intl J Parallel Prog 18(2):121-160, Apr 1989].
 analogies. Furthermore, the choice of language is not arbitrary (as is often claimed) because the "simplicity and visibility of the notional machine can be spoiled by poor language design or implementation" (du Boulay, O'Shea, & Monk, 1989, p. 436).

Teaching the model can be done using diagrams Mayer (1975) or epistemic ep·i·ste·mic  
adj.
Of, relating to, or involving knowledge; cognitive.



[From Greek epistm
 games--formalized procedures for constructing knowledge--such as a model computer (Sherry, 1995) or a notional machine (duBoulay, 1989). Kieras and Bovair (1984) showed that a block diagram A chart that contains squares and rectangles connected with arrows to depict hardware and software interconnections. For program flow charts, information system flow charts, circuit diagrams and communications networks, more elaborate graphical representations are usually used.  of an instrument facilitates the learning of an operational procedure, and Mulholland showed that software visualization (SV) of Prolog programs is most successful if "there is a clear, simple mapping between the SV and the underlying source code" (Mulholland, 1997). Based on observations of expert programmers and electronics engineers, Petre (1991) believes that declarative de·clar·a·tive  
adj.
1. Serving to declare or state.

2. Of, relating to, or being an element or construction used to make a statement: a declarative sentence.

n.
 reasoning does not really occur; instead, the experts reason operationally in terms of an underlying machine.

An important question is: how detailed should a model be? Does an introductory computer science student have to construct a model in terms of the electronic properties of semiconductors?! The extent and fidelity of the model that must be taught to the students can only be discovered from the experience of teachers of the subject. Sherry's model seems to be too detailed; a better approach is demonstrated by Naps and Stenglein (1996) who created a visualization of a specific concept--parameter passing. Much can be done even with noncomputerized epistemic games. For example, take thee cheap calculators and attach them to a board (Figure 3), covering up all the non-numeric keys except for '='. Each calculator represents one variable and it is possible to practice assignment statements without ever touching a programmable computer.

Don't Start with Abstractions

The author's conclusion that a model of the computer be explicitly taught has implications for the teaching of object-oriented programming (OOP See object-oriented programming.

OOP - object-oriented programming
) in introductory courses. The abstraction inherent in OOP is essential as a way of forgetting detail, and software development would be impossible without abstraction, but it appears that there must be an object-oriented paradox: how is it possible to forget detail that you never knew or even imagined? If students find it difficult to construct a viable model of variables and parameters, why should we believe that they can construct a viable model of an object such as a window object? Advocates of an objects-first approach seem to be rejecting Piaget's view that abstraction (or accommodation) follows assimilation.

Professional software engineers who use abstractions generally have a fairly good idea of the underlying model. For example, few software engineers have actually written programs for manipulating windows on a screen. But even a general understanding of how images are represented in the computer by bitmaps should be sufficient to enable the engineer to construct a viable model.

The author appreciates the attractiveness of an objects-first approach; the gap between the standard libraries (especially the GUI libraries) of a modern programming environment and the model of a computer is so great that motivating beginners has become a serious problem. Furthermore, OOP can be used to teach good software development practice from the beginning because "OOP allows-even encourages-one to address the "big picture" by emphasizing a strategic approach to programming" (Dekker & Hirshfeld, 1993, p.271).

Turkle and Papert go further and claim that OOP is: "... not only more congenial con·gen·ial  
adj.
1. Having the same tastes, habits, or temperament; sympathetic.

2. Of a pleasant disposition; friendly and sociable: a congenial host.

3.
 to those who favor concrete approaches, but it also puts an intellectual value on a way of thinking that is resonant resonant

giving an intense, rich sound on percussion; exhibiting resonance.
 with their own" (Turkle & Papert, 1990, p. 155). This claim is strange, because the point of-studying OOP is to learn to create abstractions, not just to use existing concrete objects. The concreteness of reading and using objects is at most a steppingstone step·ping·stone  
n.
1. A stone that provides a place to step, as in crossing a stream.

2. An advantageous position for advancement toward a goal.
 to modifying, extending, and defining them, as advocates of OOP are careful to point out (Dekker & Hirshfeld, 1993).

Given these advantages of the objects-first approach, it cannot be dismissed out of hand; on the contrary, the trade-offs probably favor this approach. But if the constructivist viewpoint is valid, teachers of introductory courses that use OOP should be very, very careful not to assume that the students will construct the model that the instructor has, nor even to assume that they will construct a viable model at all.

This viewpoint is supported by the literature on teaching OOP:

* While Adams (1996) opposes deferring the teaching of OOP until late in the curriculum by which time it is difficult to cure students of the lowlevel paradigms they have developed, neither does he believe that OOP should be taught first when the students are not mature enough to master the concepts involved:

CS1 novices do not have the cognitive framework to grasp the concepts underlying object-oriented design Transforming an object-oriented model into the specifications required to create the system. Moving from object-oriented analysis to object-oriented design is accomplished by expanding the model into more and more detail. , because they have no experience dealing with types and functions, much less classes, function members or inheritance (Adams, 1996, p.79).

He advocates a middle road where objects are introduced early but only after sufficient procedural programming This article is about the computer programming paradigm. For the method of algorithmic content creation, see procedural generation.

Procedural programming
 has been learned to provide an underlying mental model.

* Wolz and Conjura (1994) propose a three-tiered model for teaching introductory computer science which includes mathematical theory (unusual but refreshing!), implementation and mechanical trivia. They report that teaching OOP using C++ in CS2 is successful because students are able to build on previous knowledge learned from CS1: expressing algorithms procedurally in Scheme. On the other hand, they claim that: "There is no reason that students in a first course can't learn to use [data types such as queues, stacks, lists, trees and graphs] before learning how they are implemented" (Wolz & Conjura, 1994, p.224).

From a constructivist point of view, one must evaluate the mental models these students construct; if they are non-viable, they can impede further study.

* Holland et al., (1997) summarize students' misconceptions in an introductory course that uses OOP. Many of these misconceptions are due to conflation of concepts (object/variable, object/class) that can be attributed to the lack of an effective mental model. Based on experience in other disciplines of science education, cataloging and analyzing misconceptions will not be sufficient to improve students' understanding. Instead, research must be done to identify the mental models that cause these specific misconceptions, and guidelines must be developed so that teachers can diagnose and correct the problems.

For an objects-first approach to work, teachers will have to develop ways of explaining the underlying models without destroying the abstractions. My current belief is that introductory CSE should be based on the functional or logic programming paradigm A programming paradigm is a fundamental style of programming regarding how solutions to problems are to be formulated in a programming language. (Compare with a methodology, which is a style of solving specific software engineering problems). , not only because these languages minimize mechanical trivia, but also (and primarily) because the underlying models can be explained in relatively high-level, hardware-free terms.

Bricolage bri·co·lage  
n.
Something made or put together using whatever materials happen to be available: "Even the decor is a bricolage, a mix of this and that" Los Angeles Times.
 

Bricolage is a term coined by the anthropologist Claude Levi-Strauss Noun 1. Claude Levi-Strauss - French cultural anthropologist who promoted structural analysis of social systems (born in 1908)
Levi-Strauss
, who used it in a derogatory de·rog·a·to·ry  
adj.
1. Disparaging; belittling: a derogatory comment.

2. Tending to detract or diminish.
 sense for the "science of the concrete" in primitive societies, as opposed to abstract European science. Turkle and Papert (1990) transferred the concept to the context of learning to program, and vehemently defend it as a learning style as valid as the normative "planning" style that we attempt to teach. This is consistent with a constructivist view of education: different students will approach the construction of knowledge in different ways, and the educational environment must be supportive of these differences.

The manifestation of bricolage in computer science is endless debugging (programming) debugging - The process of attempting to determine the cause of the symptoms of malfunctions in a program or other system. These symptoms may be detected during testing or use by real users. : try it and see what happens. While we all practice a certain amount of bricolage and while concrete thinking can be especially helpful--if not essential--for students in introductory courses, bricolage is not an effective methodology for professional programming, nor an effective epistemology for dealing with the massive amount of detailed knowledge must be constructed and organized in levels of abstraction (cf., object-oriented programming). The normative planning style called software engineering must eventually be learned and practiced.

This belief is likely to be shared by anyone who has studied or worked on non-deterministic systems involving concurrency Operations that are performed simultaneously within the computer. For example, dual-core CPUs provide complete overlapping of two independent processes. See dual core, hyperthreading, multiprocessing, multitasking, multithreading, SMP and MPP.

concurrency - multitasking
, real-time or communications, subjects that are simply not amenable to bricolage and can be mastered only through abstract techniques. Students who excel at Verb 1. excel at - be good at; "She shines at math"
shine at

excel, surpass, stand out - distinguish oneself; "She excelled in math"
 bricolage often cannot make the transition to master the thought patterns and methods required by these systems. This claim has implications for counseling students. If software development is ultimately about abstraction, a student incapable of or uncomfortable with abstract thought should be discouraged from studying for the profession of software engineer.

Gender

Turkle and Papert (1990) published their article arguing for tolerance of concrete thinking in a journal subtitled sub·ti·tle  
n.
1. A secondary, usually explanatory title, as of a literary work.

2. A printed translation of the dialogue of a foreign-language film shown at the bottom of the screen.

tr.v.
 Women in Culture and Society, and they chose two women to exemplify college students who are concrete thinkers. Since the concrete way of thinking advocated by Turkle and Papert can only go so far in computer science, their coupling of a learning style with a gender stereotype would lead to the unacceptable conclusion that women are not suited for careers as computer scientists.

On the other hand, constructivism--especially social constructivism--has much to say about the task of the teacher and the role of peers in education, and the theory can contribute to the analysis of the well-documented social difficulties faced by women in the computer science classroom and laboratory.

Minimalism minimalism, schools of contemporary art and music, with their origins in the 1960s, that have emphasized simplicity and objectivity. Minimalism in the Visual Arts
 

Minimalism (Carroll, 1990, 1998) is an approach to instruction that arose in the design of manuals for software documentation. It is apparently little known outside of this community. (For a good introduction see Van der Meij and Carroll (1998).) The minimalist min·i·mal·ist  
n.
1. One who advocates a moderate or conservative approach, action, or policy, as in a political or governmental organization.

2. A practitioner of minimalism.

adj.
1.
 approach to training and documentation can be summarized as follows:

... (1) allowing learners to start immediately on meaningful realistic tasks, (2) reducing the amount of reading and other passive activity in training, and (3) helping to make errors and error recovery less traumatic and more pedagogically ped·a·gog·ic   also ped·a·gog·i·cal
adj.
1. Of, relating to, or characteristic of pedagogy.

2. Characterized by pedantic formality: a haughty, pedagogic manner.
 productive. (Carroll, 1990, p. 7)

Minimalism has much in common with constructivism as explicitly noted by Van der Meij (1997, P. 7) and Carroll and Van der Meij (1998, p. 84):

* A preference for active learning to enable the student to construct mental models.

* Recognition of the importance of pre-existing knowledge.

* The employment of the inevitable errors and misconceptions as a pedagogical device rather than as a symptom of failure.

Minimalism seems to part company with constructivism in its emphasis--even insistence--on eliminating conceptual material, or at least on deferring it as long as possible:

It is quite common for training manuals to present a "welcome to the system" preface, a conceptual model of how the system works, ...And none of this, even in the end, does much to facilitate the user's desire to get started on meaningful activity. Rather, it obstructs this goal. (Carroll, 1990, p. 80)

The success of minimalism has been empirically demonstrated in straightforward training tasks such as learning to use a word processor. But once the user needs to go beyond elementary tasks, the absence of a viable mental model means that the user's attempts to master advanced material will be frustrating frus·trate  
tr.v. frus·trat·ed, frus·trat·ing, frus·trates
1.
a. To prevent from accomplishing a purpose or fulfilling a desire; thwart:
 and lead to a reluctance to learn new concepts.

To test this conjecture, the author performed an experiment, which required the subjects to modify documents in Microsoft Word A full-featured word processing program for Windows and the Macintosh from Microsoft. Included in the Microsoft application suite, it is a sophisticated program with rudimentary desktop publishing capabilities that has become the most widely used word processing application on the market.  (Ben-Ari, 1999). The tasks were chosen to be easy if you understand the underlying concepts, but quite difficult if you do not. The (sophisticated) subjects almost invariably in·var·i·a·ble  
adj.
Not changing or subject to change; constant.



in·vari·a·bil
 used bricolage. They restricted themselves to elementary techniques learned in a minimalist setting-- behaviorist explanations from colleagues--and made no attempt to investigate the concepts or even to use the Help facility.

Some authors now claim that the dismissal of conceptual material by naive minimalism was mistaken and some way must be found to strike a balance. See the articles by Rosenbaum, Hackos, Redish, Farkas, and Draper in the retrospective volume by Carroll (1998). For example: "...a manual must: Help users grasp the big picture of the product, that is, help users develop a mental model that helps them predict what to do" (Redish, 1998, p. 240).

Given the empirically proven success of minimalism in the narrow field of technical documentation, it would be interesting to explore a closer integration of minimalist writing techniques The literature on journalling and creative writing has generated various writing techniques to encourage self-discovery and self-expression for those who may wish to expand their techniques or address issues of writer's block.  with constructivist teaching techinques.

Don't Run to the Computer

Constructivism suggests that programming exercises should be delayed until class discussion has enabled the construction of a good model of the computer. Too often students become infatuated in·fat·u·at·ed  
adj.
Possessed by an unreasoning passion or attraction.



in·fatu·at
 with the absolute ontology supplied by the computer. Premature attempts to write programs lead to bricolage and delay the development of viable models. While formal methods in CSE are extremely important, you need not go to the extreme that Dijkstra (1989) advocates and entirely give up compilation and execution of programs. There is nothing wrong with experimentation and bricolage-style debugging, as long as it supplements, rather than supplants, planning and formal methods.

Unfortunately, CSE is heavily weighted on the side of bricolage. A high-school course we are developing comes in for scathing criticism from many students (and some teachers!) because we insist on "wasting time" on algorithm development and analysis, instead of just getting on with writing and debugging programs.

Laboratory Organization

One of the debates in CSE concerns the choice between closed labs--where students work on assignments at an appointed time in a supervised setting, and open labs--where students work on assignments whenever convenient. From a constructivist viewpoint, especially from a social constructivist one, closed labs should be preferable, not only because they soften the brutality of the interaction with the computer, but also because they facilitate the social interaction that is apparently necessary for successful construction. In fact, Thweatt (1994) found empirical evidence for the superiority of closed labs over open labs.

The type of problems assigned is also important; as opposed to minimalism's emphasis on task performance, problems should encourage cognitive operations such as reflection and exploration:

Another common failing in lab design is to make every task so constrained and explicit that students never need to think about what techniques to use...The production of an ill-structured problem is likely to add an element of reality to the lab, and allows the students to have their own Eureka!s about the underlying nature of the exercise. (Fekete & Greening, 1996, pp. 295, 298)

Assessment

Performance on a test is a poor guide to the students' construction of the rich conceptual models of computer science. A student's failure to construct a viable model is a failure of the educational process, even if the failure is not immediately apparent. Furthermore, in the case of group work, performance-based assessment can mask the misconceptions of individual students. Ideally, constructivist-inspired assessment would be based on an instructor's observation and questioning of students engaged in an unconstrained activity such as a lab project. Unfortunately, this is almost always impractical, and instructors must attempt to design written questions that elicit information about the student's mental model rather than about the contents of his or her factual memory.

Implications for Research

In their book, Maykut and Morehouse (1994) claim that practitioners of qualitative research Qualitative research

Traditional analysis of firm-specific prospects for future earnings. It may be based on data collected by the analysts, there is no formal quantitative framework used to generate projections.
 must understand its philosophical underpinnings, which are essentially constructivist in nature. The claim can be turned around: a researcher working from a constructivist viewpoint should use qualitative methods.

We are now starting to see more empirical research Noun 1. empirical research - an empirical search for knowledge
inquiry, research, enquiry - a search for knowledge; "their pottery deserves more research than it has received"
 in CSE done using qualitative methods (Madison, 1995; Mulholland, 1997). These techniques, which elicit the internal structures of the student, are far more helpful than research that measures performance alone and then draws conclusions on the success of a technique.

As computer literacy Understanding computers and related systems. It includes a working vocabulary of computer and information system components, the fundamental principles of computer processing and a perspective for how non-technical people interact with technical people.  becomes common, if not universal, students will begin their academic studies with an effective model of a computer. Research must be done to determine if these models are stepping-stones to the construction of effective models, or obstacles like naive physics.

A GUIDE FOR EDUCATORS

To summarize the article, here is a guide for educators on the practical application of constructivism.

* Regardless of your teaching technique (lectures, labs, assignments), you must articulate to yourself the cognitive change that you wish to bring about in the students and structure the activity to achieve this aim. Merely transferring knowledge is not a meaningful aim.

* You must dig underneath your own expert knowledge to expose the prior knowledge needed to construct a viable model of the material that you are teaching. You must ensure that that the students have this prior knowledge.

* In any particular course you will be teaching a specific level of abstraction The level of complexity by which a system is viewed. The higher the level, the less detail. The lower the level, the more detail. The highest level of abstraction is the single system itself. ; you must explicitly present a viable model one level beneath the one you are teaching.

* When a student makes a mistake or otherwise displays a lack of understanding, you must assume that the student has a more-or-less consistent, but non-viable, mental model. Your task as a teacher is to elicit this model and guide the student in its modification.

* You must provide as much opportunity as possible for individual reflection (for example, analysis of errors) and social interaction (for example, group labs). Clearly, each educator must decide how to apply these aphorisms in a concrete situation.

CONCLUSION

The author's analysis of constructivism has led him to conclude that the epistemology of computer science is significantly different than that of, say, physics. Nevertheless, the basic tenet of the theory--that knowledge is constructed by the student--applies to computer science, and its central implication is that models must be explicitly taught.

Given the central place of constructivist learning theory and its influence on pedagogy, computer science educators should study the theory, perform research, and analyze their educational proposals in terms of constructivism. Software and language designers should be guided by constructivist principles; though the individuality of the construction by learners implies that no system will ever be universally easy-to-learn, and we educators must learn how to teach these extant artifacts artifacts

see specimen artifacts.
.

Acknowledgements

I would like to thank Abraham Arcavi, Yifat Ben-David Kolikant, Tom Boyle, Bat-Sheva Eylon, Ann Fleury, Sandra Madison and the referees for their critiques of drafts of this article.

Note

(1.) This article is an extended version of a paper that was presented at the Twenty-Ninth SIGCSE SIGCSE Special Interest Group on Computer Science Education  Technical Symposium on Computer Science Education, Atlanta, GA, 1998.

References

Adams, J.C. (1996). Object-centered design: A five-phase introduction to object-oriented programming in CS 1-2. SIGCSE Bulletin, 28(1), 78-82.

Barnes, B., Bloor, D., & Henry, J. (1996). Scientific knowledge: A sociological analysis. Chicago, IL: University of Chicago.

Ben-Ari, M. (1999). Bricolage forever! Eleventh workshop of the psychology of programming interest group (53-57). Leeds, UK.

Bloor, D. (1991). Knowledge and social imagery (2nd edition). Chicago, IL: University of Chicago.

Boyle, T. (1996). Design for multimedia learning. Hemel Hempstead Hemel Hempstead (hĕm`əl), town (1991 pop. 80,110), Hertfordshire, SE England. Hemel Hempstead was designated one of the new towns in 1946 to alleviate overpopulation in London. It is a market town and London suburb. : Prentice-Hall I.

Brandt, D.S D.S Drainage Structure (flood protection) . (1997). Constructivism: Teaching for understanding of the Internet. Communications of the ACM (publication) Communications of the ACM - (CACM) A monthly publication by the Association for Computing Machinery sent to all members. CACM is an influential publication that keeps computer science professionals up to date on developments. , 40(10), 112-117.

Bruner, J.S. (1962). On knowing: Essays for the left hand. Cambridge, MA: Harvard University Harvard University, mainly at Cambridge, Mass., including Harvard College, the oldest American college. Harvard College


Harvard College, originally for men, was founded in 1636 with a grant from the General Court of the Massachusetts Bay Colony.
.

Carroll, J.M. (1990). The Nurnberg Funnel: Designing minimalist instruction for practical computer skill. Cambridge, MA: MIT MIT - Massachusetts Institute of Technology  Press.

Carroll, J. M. (Ed.), (1998). Minimalism beyond the Nurnberg Funnel. Cambridge, MA: MIT Press.

Carroll, J.M., & Van der Meij, H.(1998). Ten misconceptions about minimalism. In J. M. Carroll (Ed.), Minimalism beyond the Nurnberg Funnel (55-90). Cambridge, MA: MIT Press.

Davis, R.B., Maher, C.A., & Noddings, N. (Eds.), (1990). Constructivist views of the teaching and learning of mathematics, Reston, VA: National Council for the Teaching of Mathematics.

Dekker, R., & Hirshfeld, S. (1993). Top-down teaching: Object-oriented programming in CSI CSI Crime Scene Investigator
CSI CompuServe, Inc.
CSI Commodity Systems, Inc.
CSI Commodity Systems Inc. (Boca Raton, FL)
CSI Crime Scene Investigation (CBS TV show)
CSI Christian Schools International
. SIGCSE Bulletin, 25(1) 270-273.

Dijkstra, E.W. (1989). On the cruelty of really teaching computer science. Communications of the ACM, 32(12), 1398-1404.

diSessa, A.A. (1988). Knowledge in pieces. In G. Forman & P.B. Pufall (Eds.), Constructivism in the computer age (49-70). Hillsdale, NJ: Lawrence Erlbaum.

diSessa, A.A., Abelson, H., & Ploger, D. (1991). An overview of Boxer. Journal of Mathematical Behavior, JO, 3-15.

du Boulay, B. (1989). Some difficulties of learning to program. In E. Soloway & J.C. Spohrer (Eds.), Studying the novice programmer (283-299). Hillsdale, NJ: Lawrence Erlbaum.

du Boulay, B., O'Shea, T., & Monk, J. (1989). The black box inside the glass box: Presenting computing concepts to novices. In E. Soloway & J.C. Spohrcr (Eds.), Studying the novice programmer (431-446). Hillsdale, NJ: Lawrence Erlbaum.

Duit, R. (1991). Students' conceptual frameworks For the concept in aesthetics and art criticism, see .

A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to a system analysis project.
: Consequences for learning science. In S.M. Glynn, R.H. Yeany, & B.K. Britton (Eds.), The psychology of learning science (65-85) Hillsdale, NJ: Lawrence Erlbaum.

Ernest, P. (Ed.). (1994). Constructing mathematical knowledge: Epistemology and mathematics education. London: The Falmer Press.

Ernest, P. (1995). The one and the many. In L.P. Steffe & J. Gale (Eds.), Constructivism in education (459-486). Hillsdale, NJ: Lawrence Erlbaum.

Fekete, A., & Greening, A. (1996). Designing closed laboratories for a computer science course. SIGCSE Bulletin, 28(1), 295-299.

Fleury, A.E. (1991). Parameter passing: The rules the students construct. SIGCSE Bulletin, 23(1), 283-286.

Glasersfeld, E. von. (1995). A constructivist approach to teaching. In L. P. Steffe & J. Gale (Eds.), Constructivism in education (3-15). Hillsdale, NJ: Lawrence Erlbaum.

Glynn, S.M. (1991). Explaining science concepts: A teaching-with-analogies model. In S.M. Glynn, R.H. Yeany, & B.K. Britton (Eds.), The psychology of learning science (219-240). Hillsdale, NJ: Lawrence Erlbaum.

Glynn, S.M., Yeany, R.H., & Britton, B.K. (Eds.). (1991). The psychology of learning science. Hillsdale, NJ: Lawrence Erlbaum.

Gray, J., Boyle, T., & Smith, C. (1998). A constructivist learning environment implemented in Java. SIGCSE Bulletin, 30(3), 94-97.

Haberman, B., & Ben-David Kolikant, Y. (2001). Activating "black boxes" instead of opening "zippers"--a method of teaching novices. Proceedings of the Sixth Annual Conference on Innovation and Technology in Computer Science Education, Canterbury, UK (in press).

Hadjerrouit, S. (1998). A constructivist framework for integrating the Java paradigm into the undergraduate curriculum. SIGCSE Bulletin, 30(3), 105-107.

Harel, I., & Papert, S. (Eds.). (1991). Constructionism. Norwood, NJ: Ablex.

Hatfield, L.L. (1991). Enhancing school mathematical experience through constructive computing activity. In L.P. Steffe (Ed.), Epistemological foundations of mathematical experience (238-259). New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
: Springer-Verlag.

Hoc, J., Green, T., Samurcay, R., & Gilmore, D. (1990). Psychology of programming. London: Academic Press.

Holland, S., Griffiths, R., & Woodman, M. (1997). Avoiding object misconceptions. SIGCSE Bulletin, 29(1), 131-134.

Husen, T., & Postlethwaite, T.N. (Eds.). (1994). The international encyclopedia of education. Oxford: Pergamon.

Kieras, D.E., & Bovair, S. (1984). The role of a mental model in learning to operate a device. Cognitive Science cognitive science

Interdisciplinary study that attempts to explain the cognitive processes of humans and some higher animals in terms of the manipulation of symbols using computational rules.
, 8, 255-273.

Leron, U., & Dubinsky, E. (1995). An abstract algebra
This article is about the branch of mathematics. For other uses of the term "algebra" see algebra (disambiguation).


Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules,
 story. American Mathematical Monthly The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894. It is currently published 10 times each year by the Mathematical Association of America. , 102(3), 227-242.

Madison, S.K. (1995). A study of college students' construct of parameter passing: Implications for instruction. Doctoral dissertation, University of Wisconsin.

Mason, J. (1994). Enquiry in mathematics and mathematics education. In P. Ernest (Ed.), Constructing mathematical knowledge: Epistemology and mathematics education (190-200). London: The Falmer Press.

Matthews, M.R. (1994). Science teaching: The role of history and philosophy of science The history and philosophy of science (HPS) is an academic discipline that encompasses the philosophy of science and the history of science. Although many scholars in the field are trained primarily as either historians or as philosophers, there are degree-granting departments of . New York: Routledge.

Matthews, M.R. (1997). Introductory comments on philosophy and constructivism in science education. Science & Education, 6(1-2), 5-14.

Matthews, M.R. (Ed.). (1998). Constructivism in science education. Dordrecht: Kluwer Academic.

Mayer, R.E. (1975). Different problem-solving competencies established in learning computer programming with and without meaningful models. Journal of Educational Psychology, 67(6), 725-734.

Mayer, R.E. (Ed.). (1988). Teaching and learning computer programming. Hillsdale, NJ: Lawrence Erlbaum.

Maykut, P., & Morehouse, R. (1994). Beginning qualitative research. London: The Falmer Press.

McCloskey, M. (1983). Naive theories of motion. In D. Gentner & A.L. Stevens (Eds.), Mental models (299-323). Hillsdale, NJ: Lawrence Erlbaum.

Mulholland, P. (1997). Using a fine-grained comparative evaluation technique to understand and design software visualization tools. Paper presented at the Empirical Studies Empirical studies in social sciences are when the research ends are based on evidence and not just theory. This is done to comply with the scientific method that asserts the objective discovery of knowledge based on verifiable facts of evidence.  of Programmers: Seventh Workshop. Alexandria, VA.

Naps, T.L., & Stenglein, J. (1996). Tools for visual exploration of scope and parameter passing in a programming languages course. SIGCSE Bulletin, 28(1), 295-299.

Nola, R. (1997a). Constructivism in science education: A philosophical critique. Science & Education, 6(1-2), 55-83.

Nola, R. (1997b). Book review of Kenneth Tobin (Ed.), The practice of constructivism in science education. Science & Education, 6(1-2), 197-214.

Ogborn, J. (1997). Constuctivist metaphors in science learning. Science & Education, 6(1-2), 121-133.

Paz, T. (1996). Computer science for vocational high-school students: Processes of learning and teaching. Masters thesis, Technion--Israel Institute of Technology (in Hebrew).

Pea, R.D. (1986). Language-independent conceptual "bugs" in novice programming. Journal of Educational Computing Research, 2(1), 25-36.

Perkins, D., Schwartz, S., & Simmons, R. (1988). Instructional strategies for the problems of novice programmers. In R.E. Mayer (Ed.), Teaching and learning computer programming (153-178). Hillsdale, NJ: Lawrence Erlbaum.

Petre, M. (1991). Shifts in reasoning about software and hardware systems: do operational models underpin declarative ones? Paper presented at the Third Psychology of Programming Interest Group Workshop. Huddersfield, UK.

Phillips, D.C. (1995). The good, the bad, and the ugly: The many faces of constructivism. Educational Researcher, 24(7), 5-12.

Phillips, D.C. (1997). Coming to grips with radical social constructivism. Science & Education, 6(1-2), 85-104.

Redish, J. (1998). Minimalism in technical communication: Some issues to consider. In J.M. Carroll (Ed.), Minimalism beyond the Nurnberg Funnel (219-245). Cambridge, MA: MIT Press.

Resnick, M. (1997). Turtles, termites, and traffic jams: Explorations in massively parallel See MPP.  microworlds. Cambridge, MA: MIT Press.

Samurcay, R. (1989). The concept of variable in programming: Its meaning and use in problem-solving by novice programmers. In E. Soloway & J.C. Spohrer (Eds.), Studying the novice programmer (161-178). Hillsdale, NJ: Lawrence Erlbaum.

Scheffler, I. (1965). Conditions of knowledge: An introduction to epistemology and education. Chicago, IL: University of Chicago.

Sfard, A. (1994). Mathematical practices Introductory Section
Mathematical practice is used to distinguish the working practices of professional mathematicians (e.g. selecting theorems to prove, using informal notations to persuade themselves and others that various steps in the final proof can be formalised,
, anomalies and classroom communications problems. In P. Ernest (Ed.), Constructing mathematical knowledge: Epistemology and mathematics education (248-273). London: The Falmer Press.

Sherry, L. (1995). A model computer simulation as an epistemic game. SIGCSE Bulletin, 27(2), 59-64.

Sleeman, D., Putnam, R.T., Baxter, J.A., & Kuspa, L. (1988). An introductory Pascal class: A case study of student errors. In R.E. Mayer (Ed.), Teaching and learning computer programming (237-257). Hillsdale, NJ: Lawrence Erlbaum.

Sleeman, D., Putnam, R.T., Baxter, J.A., & Kuspa, L. (1989). A summary of misconceptions of high school Basic programmers. In E. Soloway, & J.C. Spohrer (Eds.), Studying the novice programmer (301-314). Hillsdale, NJ: Lawrence Erlbaum.

Smith III, J.P., diSessa, A.A., & Roschelle, J. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of The Learning Sciences The Journal of the Learning Sciences (JLS) is an official publication of the International Society of the Learning Sciences (ISLS) covering research on learning and education. , 3(2), 115-163.

Soloway, E., & Spohrer, J.C. (Eds.). (1989). Studying the novice programmer. Hillsdale, NJ: Lawrence Erlbaum.

Steffe, L.P., & Gale, J. (Eds.). (1995). Constructivism in education. Hillsdale, NJ: Lawrence Erlbaum.

Taylor, J. (1990). Analysing novices analysing Prolog: What stories do novices tell themselves about Prolog. Instructional Science, 19, 283-309.

Thweatt, M. (1994). CS1 closed lab vs. open lab experiment. SIGCSE Bulletin, 26(1), 80-82.

Turkle, S., & Papert, S. (1990). Epistemological pluralism: Styles and cultures within the computer culture. Signs: Journal of Women in Culture and Society, 16(1), 128-148.

Van der Meij, H. (1992). A critical assessment of the minimalist approach to documentation. In Tenth annual ACM conference on systems documentation (SIGDOC SIGDOC Special Interest Group on Documentation 92) (7-17). Ottawa, Canada.

Van der Meij, H., & Carroll, J.M. (1998). Principles and heuristics for designing minimalist instruction. In J.M. Carroll (Ed.), Minimalism beyond the Nurnberg Funnel (19-53). Cambridge, MA: MIT Press.

Wolz, U., & Conjura, E. (1994). Integrating mathematics and programming into a three tiered model for computer science education. SIGCSE Bulletin, 26(1), 223-227.
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Author:BEN-ARI, MORDECHAI
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Date:Mar 22, 2001
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