Software Design as a Learning Environment Interactive ...

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Software Design as aLearning EnvironmentIdit Harel and Seymour Papert

AbstractThis article describes a learning research called theInstructional Software Design Project (ISDP), and offersa Constructionist vision of the use of computers in edu-cation. In a Logo-based learning environment in a Bos-ton inner-city public school, a fourth-grade class wasengaged during one semester in the design and produc-tion of educational software to teach fractions. Quantita-tive and qualitative research techniques were used toassess their learning of mathematics, programming, anddesign, and their performance was compared with thatof two control classes. All three classes followed theregular mathematics curriculum, including a two-monthunit on fractions. Pre- and post-tests were administeredto the experimental and control groups. The evaluationrevealed greater mastery of both Logo and fractions aswell as acquisition of greater metacognitive skills by theexperimental class than by either control class. Selectedresults from several case studies, as well as an overallevaluation are presented and discussed. Using ISDP asa model project, a Constructionist vision of using tech-nology in learning is elaborated. The ISDP approach ofusing Logo programming as a tool for reformulatingknowledge is compared with other ways of learning andusing Logo, in particular the learning of programmingper se in isolation from a content domain. Finally, ISDP ispresented as a way of simultaneously learning program-ming and other content areas; and the claim is madethat learning both of these together results in betterlearning than if either were learned in isolation from theother.

OVERVIEW

This article has a double intention: Itadds to the description and discussion ofan experiment that formed the centerpieceof Harel's doctoral dissertation (Harel,1988), and it uses the discussion of thisparticular experiment to situate a generaltheoretical framework (developed over theyears by Papert and his colleagues) withinwhich the experiment was conceived. Theexperiment will be referred to here as the"Instructional Software Design Project"(ISDP), and the theoretical framework as"Constructionism" (e.g., Papert, 1990).

The ISDP experiment involved studyinga class of fourth grade students. Each stu-dent worked for approximately four hoursper week over a period of 15 weeks on de-signing and implementing instructionalsoftware dealing with fractions. A narrowdescription of our intention in doing this isthat we wished to turn the usual tables bygiving the learner the active position of theteacher/explainer rather than passive recip-ient of knowledge; and in the position ofdesigner/producer rather than consumer ofsoftware. This idea is in line with Construc-tionism's use of "building," "constructing,"or "knowledge-representing" as centralmetaphors for a new elaboration of the oldidea of learning by doing rather than bybeing told ("Constructionism" rather than"Instructionism").

The usual passive view of integratingcomputers into education supports Instruc-tionism and Technocentrism (Papert, 1987).ISDP, like all projects at Paper's Epistemol-ogy and Learning Group, attempted tochange this approach by giving children thecontrol over their learning with computers.Children were the agents of thinking andlearning—not the computer. Our view is:Computers cannot produce "good" learn-ing, but children can do "good" learningwith computers.

Does wood produce good houses? If I builta house out of wood and it fell down,would this show that wood doesn't pro-duce good houses? . . . These . . . ques-tions ignore people and elements that onlypeople can introduce: skill, design, aes-thetics ... (Papert, 1987. p. 24).

It ought to be equally obvious thatpeople are the agents when it comes to

Correspondence and requests for reprintsshould be sent to Idit Harel, Media Laboratory,Massachusetts Institute of Technology, 20 AmesSt. (Rm. 310) Cambridge, MA. 02139.

INTERACTIVE LEARNING ENVIRONMENTS 1, 1-32 (1990)

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I. Harel and S. Papert

thinking and learning, not computers. Peo-ple use computers to do things. If we wereto say anything meaningful about thethinking and learning involved, then weshould look at what people are doing withcomputers, and not at what "the comput-er" is allegedly doing to them. For in real-ity, there is no such thing as "the comput-er" in general—only specific uses ofcomputers in specific contexts . . . With apassive view of education, we open thedoor to technocentrism when we speakabout the computer as an "educationaltool" . . . It should not be an "educationaltool, but just a tool. Like other tools, itallows us to do things we couldn't do be-fore, or more usually, to do some thingsthat we could do before better (Falbel,1990, pp. 2-3).

Building on the computer (or with thecomputer) a piece of instructional softwareabout fractions is discussed here as a privi-leged way for children to engage with frac-tions by constructing something personal.In this, it may overlap educational tech-niques that employ materials such as cui-senaire rods, fraction bars, or patternblocks. But constructing software goes farbeyond the physical manipulations in-volved in using such materials. To the ad-age "you learn better by doing," Construc-tionism adds the rider, "and best of all bythinking and talking about what you do."Without denying the importance of teach-ing, it locates the important directions ofeducational innovation less in developingbetter methods of teaching than in develop-ing "better things to do and more powerfulways to think about what you are doing"(e.g., Papert, 1971a, 1971b).

The key research question is to deter-mine what kinds of things are "better." Inthis paper we focus on attributes such asappropriability (some things lend them-selves better than others to being madeone's own); evocativeness (some materialsare more apt than others to precipitate per-sonal thought); and integration (some ma-terials are better carriers of multiple mean-ings and multiple concepts).

We see several trends in contemporaryeducational discussion such as "situatedlearning," and "apprenticeship learning"

(e.g., Brown, Collins, & Diguid, 1989; Col-lins & Brown, 1987; Suchman, 1987) as be-ing convergent with our approach, but dif-ferent in other respects. Two features willbe discussed here as giving specificity toConstructionism in relation to this essen-tially synergistic body of literature. The firstis our emphasis on developing new kindsof activities in which children can exercisetheir doing/learning/thinking. (Turtle Ge-ometry is one example. ISDP is another.)The second is our special emphasis on pro-ject activity which is self-directed by thestudent within a cultural/social context thatoffers support and help in particularly un-obtrusive ways. ISDP provides us with in-sights into the unique ways in which con-structing instructional software generatesand supports personal reflection and socialinteraction favorable to learning.

In elaborating the Constructionist vi-sion we take the time to dissipate misun-derstandings by contrasting it with deriva-tives of Papert's early work that radicallymiss its epistemological essence. In partic-ular, we emphasize the fact that ISDP haslittle to do with the idea that learning Logois in itself either easy or beneficial.

WHAT WAS ISDP?

Context

ISDP was conducted as part of a largerproject to study the uses of computers inelementary schools. Project Headlight, as itis called, is based in an inner city publicschool, the Hennigan School, in Boston.Only one third of Hennigan students, withchildren from first through fifth grade, par-ticipate in Headlight. (The experimentalISDP class and control class C1, which diddaily programming in Logo, were both partof Project Headlight. Control class C2 wasnot). As at many Boston public schools, themajority of the student population at Hen-nigan is Black and Hispanic, and in mostways the school is quite conventionallystructured. A major purpose of Headlightwas to gain understanding of how a com-puter culture could grow in such a setting.

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Software Design as a Learning Environment

One feature that is not typical in Henniganis its building, which dates from the earlyseventies when there was a fad for "openarchitecture." When we first saw the schoolits architectural features were virtually un-used, but we viewed them as an oppor-tunity to reinforce our open-ended educa-tional philosophy through the design of thespace. We saw the physical environment asa very important factor in shaping a learn-ing culture. These open spaces allowed usto bring the technology closer (physicallyand conceptually) to students and teachers;to integrate the computer activities with theregular classroom activities; and to facili-tate movement and action around the com-puters; to reinforce communication andinformation-sharing regarding computer-based activities across grade levels andamong teachers.

In Headlight there is no long hallwayleading into one classroom called the"Computer Lab" where children take theirweekly "Computer Literacy Class." Rather,there are two large open areas (the "Pods")housing four large circles with 100 comput-ers, and each pod is surrounded by 6 class-rooms. At Headlight, children use comput-ers at least one hour a day, for working ontheir different computer projects, as an in-tegral part of their homeroom learning ac-tivities.

In Headlight there is virtually no use of"ready to use software" and little emphasison learning about computers and learningprogramming as ends in themselves. Thestudents learn programming but program-ming is a means to different ends, whichwe conceptualize as entering a new learn-ing culture—developing new ways of learn-ing and thinking.

Our vision focuses on using technologyto support excellence in teaching, in learn-ing, and in thinking with computers—technology as a medium for expression.We particularly eschew naive views of thecomputer as replacing (in the guise of im-proving) some of the functions of the teach-er. Headlight students are encouraged totackle exceptionally complex problems and

work on exceptionally large-scale projectsin a culture where they have a great respon-sibility for their own learning. They are ableto work individually and collaboratively in avariety of styles where the differences arereflected in gender, ethnicity, cognitive de-velopment, and in the individual person-ality of the teachers as well as in the per-sonality of the learners (see also, Goldman-Segall, 1989a-b; Harel, 1986, 1988,1989a-e;Motherwell, 1988; Resnick, Ocko, & Papert,1988; Resnick, 1989; Sachter, 1989; Turkle& Papert, 1990).

ISDP ProceduresDuring the period of the ISDP project,

one of the "pods" in Headlight was turnedinto a software-design studio, where 17fourth-grade students worked on construct-ing personally designed pieces of instruc-tional software; the only requirement wasthat they should "explain something aboutfractions" to some intended audience. Be-fore they started their software designwork, the students were interviewed indi-vidually and were tested on fractions andLogo programming. Presenting herself as aresearcher and a "helper," Harel explainedto the students that they were not beinggraded, but were involved in a new kind ofactivity which she wanted to observe, eval-uate, and report on for the benefit of others.Students were encouraged to think ofthemselves as collaborators in the projectand its data collection.

ISDP was open-ended, but somewhatmore structured than the other Headlightprojects. It included a series of activitiesthat all the experimental students per-formed. Each working day, before going tothe computer, the students spent 5 to 7minutes writing their plans and drawingtheir designs in their personal Designer'sNotebooks. Then, they worked at their indi-vidual computers for approximately 45 to55 minutes. They implemented their plansand designs, created new ones, and revisedold ones. When they wished, students wereallowed to work with friends, help each oth-er, or walk around to see what other stu-dents were doing. At the end of the ISDP

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daily period, students saved their dailyLogo files on a diskette. In their Designer'sNotebooks, they then wrote about the prob-lems and changes of the day (related toLogo, fractions, instructional design, teach-ing, etc.) and sometimes added designs forthe next day. The students had full freedomto choose which concepts they wanted toteach (within the domain of fractions), howto design their screens, what the sequenceof their lesson should be, and what instruc-tional games, quizzes, and tests to include,if any. In short, the Project was open-endedin terms of what the students chose to de-sign, teach, and program. The only two re-quirements were: (1) that they write in theirDesigner's Notebooks before and aftereach working session; and (2) that theyspend a specific amount of time at the com-puter each day. The purpose of this secondrequirement, regarding time limitations,was to allow the project to fit into theschedule of the class and of the school. Thisrequirement also made it possible to esti-mate and draw generalizations about whatstudents could accomplish in a project ofthis kind, within time periods that could fitinto the regular schedule of any class orschool in the future.

Several "Focus Sessions" about soft-ware design, Logo programming, and frac-tion represention were conducted in theclassroom during the project. In the firstsession, Harel briefly introduced and dis-cussed with the students, the concept ofinstructional design and educational soft-ware. Together—the children, teacher, andHarel—we defined the meaning and pur-pose of instructional software, and brieflydiscussed a few pieces of software withwhich the students were familiar. Harelshowed the students her own designs,plans, flowcharts, and screens from variousprojects she had worked on in the past. Shealso passed among the students the bookProgrammers At Work (Lammers, 1987)and asked them to look at notes, pieces ofprograms, and designs by "real" hardwareor software designers and programmers—such as the people who had designed the

Macintosh, PacMan, Lotus 1-2-3, and oth-ers. In this first session the students alsoreceived their personal diskettes and theirDesigner's Notebooks (see Appendix), andwe discussed the ways in which theyshould and could be used during the pro-ject.

Other Focus Sessions encouraged thestudents to express themselves on issuessuch as the difficulties of specific conceptsand on how they might be explained, repre-sented, or taught. For example, in two ofthese discussions, we hung two posters,one on each side of the blackboard. On oneposter we wrote, "What is difficult aboutfractions?" and on the other, "Whatscreens and representations could be de-signed for explaining these difficult con-cepts?" We asked the students to generateideas for both posters simultaneously.

Other discussions focused on specificLogo programming skills. For example, insome of these short sessions about pro-gramming, the teacher, the researcher, orone of the students, could stand next to oneof the computers that were in the class-room or in the "computer pod", in front ofthe whole class or a group of students, andexplain how to use REPEAT, IFELSE, vari-ables, etc. The students could take notes onsuch concepts and programming tech-niques in their notebooks, or go directly totheir computers and write a procedurewhich included that new programmingtechnique or concept.

In addition, the fourth-grade students/designers worked with third graders fromanother Headlight class, who visited theISDP class once a month, for the purpose oftrying out ("evaluating") the students'pieces of software as they were developed.The fourth graders gave the third graders"demos," and then, different pairs of chil-dren were engaged in discussing differentaspects of the software projects: somewere teaching/learning fractions; somewere teaching/learning Logo program-ming; some discussed design issues; and

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so forth. A great deal of teaching/learningthrough socializing went on during thesesessions. However, the actual teaching wasnot as important as the fourth graders' feel-ing that they were working on a real prod-uct that could be used and enjoyed by realpeople. It reinforced the "thinking about ex-plaining things to others" during theirproduct development, and it placed them inthe role of epistemologists.

The teacher and the researcher (Harel)collaborated and actively participated in allthe children's software design and pro-gramming sessions during the project:walked around among the students, satnext to them, looked at their programs,helped them when asked for, and discussedwith them their designs, programming, andproblems in a friendly and informal way. Ingeneral, there were no specific plans for theProject's sequence, or for our presentationsand focus discussions; rather, they wereinitiated by the teacher or by the researcher"as needed," at times when they were rele-vant to the children's work or problems, oraccording to the children's requests.

To summarize, the children's daily ac-tivities resulted in 17 different pieces of in-structional software about fractions—oneproduct for each child in the experiment—and 17 personal portfolios consisting of theplans and designs they wrote down foreach day's work, and the pieces of Logocode they had programmed, as well as theirwritten reflections at the end of each ses-sion on the problems and changes they haddealt with that day.

To our pleasure, we observed that stu-dents worked with great intensity and in-volvement, over a period of four months,on a subject that more often elicits groansor yawns than excitement—namely frac-tions. What seemed to make fractions inter-esting to these students was that they couldwork with them in a context that mobilizedcreativity, personal knowledge, and a senseof doing something more important thanjust getting a correct answer.

ISDP AtmosphereProcedures answering to the descrip-

tions in the above section could be carriedout in very different atmospheres butwould then, from our point of view, consti-tute radically different projects. It is there-fore appropriate to devote some space hereto capture the particular ambience of thisproject.

The ISD environment was marked bythe deep involvement of all participants.There were interactions and reciprocal rela-tions among the students, teacher, re-searcher, members of the MIT staff, andsometimes visitors—all of whom walkedaround the computer-area, talked together,helped each other, expressed their feelingson various subjects and issues, brain-stormed together, or worked on differentprogramming projects individually and col-laboratively. Knowledge of Logo program-ming, design, and mathematics was com-municated by those involved. Children,much like the adults in this area, could walkaround and observe the various computerscreens created by their peers, or look andcompare the different plans and designs intheir notebooks.

Young students were developingknowledge and ideas with out workbooksor worksheets, working within a differentkind of a structure. They became softwaredesigners, and were representing knowl-edge, building models, and teaching con-cepts on their computer screens. They werethinking about their own thinking and otherpeople's thinking—simultaneously—to fa-cilitate their own learning. The following"snapshot" briefly illustrates the atmo-sphere of this noisy, flexible, and produc-tive learning environment.

Debbie is swinging her legs while sitting ather computer and programming in an ap-parently joyful way. To her right, Naomi isbusy programming letters in different col-ors and sizes. To her left, Michaela is en-gaged in programming and debugging ascreen that shows a mathematical word-

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problem involving fractions, comparingthirds and halves by using a representa-tion of measuring cups that are filled withdifferent amounts of orange juice and wa-ter. She is very involved with her design,typing with one hand on the keyboardwhile her other hand is moving and touch-ing the figures on her computer screen. Afew computers away, the teacher is tryingout Tommy's program, giving him feed-back on one of his explanations about"what mixed fractions are." In the back-ground, Charlie is walking around the oth-er computer circle, holding his Designer'sNotebook in one hand, and chewing on thepencil that is in his mouth. He suddenlystops next to Sharifa's computer. He chatswith her for a moment, presses a key ortwo on her keyboard, and observes Shari-fa's designs as they appear on her comput-er screen. After looking at her Logo code,moving the cursor up and down on thescreen, he calls out, "Hey Paul, come seeSharifa's fractions clock!" The noise andmovement around Michaela and Debbiedo not seem to bother them at all at thismoment. Now Naomi, who sits next to De-bbie, has just completed the "title screen"for her software, which reads: "WelcomeTo My Fractions Project! by Naomi." Sheis stretching her arms while moving herhead to the left and to the right, lookingaround to see "what is new" in her friends'programs. She then stretches towards De-bbie's computer, and asks her to show herwhat she is doing.

Debbie shows Naomi her program-ming code. "It's a long one," she says,running the cursor down the screen, veryproud of the 47 lines of code she has pro-grammed for her "HOUSE" procedure.She then gets out of the programming edi-tor to run her program, which impressesNaomi, who moves her chair even closerto Debbie's computer. In a quiet and slowvoice, pointing to the pictures on herscreen, Debbie explains to Naomi: "This ismy House Scene. All these shapes [on thescreen] are one-half. In the house, the roofhas halves, the door has two halves, and Iwill add to this scene two wooden wagonsand a sun. I'll divide them into halves too. . . The halves [the shaded parts] are ondifferent sides [of the objects]. You canuse fractions on anything. No matter whatyou use. . . Do you like the colors?" Theirconversation goes on and on.

The idea of representing halves on thedifferent sides of the objects, the objectsbeing "regular human things" in a real-lifesituation, is Debbie's. In her final versionof the teaching screen, there will be anexplanatory text accompanying the pic-

tures on the screen which says: "This is ahouse. Almost every shape is ½! am try-ing to say that you can use fractions al-most every day of your life!" Debbie is theonly child in her class who has designedsuch a screen. She is very clear about whyshe designed it: to teach other childrenthat fractions are more than strange num-bers on school worksheets. As she discov-ered, fractions can be all around us; theydescribe objects, experiences, and con-cepts in everyday life.

Debbie has painted half of each objecta different color, and left the' other halfblank. The house half is painted in lightblue, the roof half in orange, the sun half inyellow, the door half in red, the wagon halfis red, etc. While Debbie is working on this,the only advice she asks of her friendNaomi is about the colors: "Do you like thecolors?" Naomi, who has adopted a differ-ent design strategy for her software, tellsher: "It's nicer if all the halves are in thesame color." They negotiate it for a minuteor two. But Debbie doesn't agree: "No. Itwill be boring." Naomi and Debbie contin-ue to work on their projects with the com-puter keyboards on their laps . . .

EVALUATION OF ISDP

The Evaluation of ISDP was designed toexamine how students who learned frac-tions and Logo through the ISDP differedfrom students who learned fractions andLogo through other pedagogical methods.Three fourth-grade classes from the sameinner-city public school in Boston were se-

This is a house. Almost every shape is1/2! I am trying to say, thatyou can use fractionsalmost everyof your life!

Figure 1. Debbie's "House Sscene"

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lected for this evaluation. One class, fromProject Headlight (N = 17), was involved inthe ISD Project (Experimental Class). Con-trol Class 1, or C1 (N = 18), studied frac-tions only in their regular math curriculumand programmed in Logo as part of ProjectHeadlight. Control Class 2, or C2 (N = 16),studied fractions in their regular math cur-riculum, was not part of Headlight, and pro-grammed only once a week in the school's"computer laboratory."

Experimental DesignIn January 1987, all three classes were

pre-tested on specific skills and concepts infractions and Logo. Thereafter, one of theclasses participated in the four-month ISDPexperiment. All 51 pupils were then testedagain in June on their knowledge of frac-tions and of Logo (see Figure 2).

Using the set of pre-tests, it was estab-lished that no significant differences exis-ted between the experimental and the con-trol children's knowledge of fractions andLogo before the experiment began (Harel,1988, 1989e). Four months after the pre-tests, by using a similar set of post-tests,the ways in which these students differed intheir knowledge and understanding of frac-tions and Logo were investigated in detail.In addition, during the project the re-searcher and the teacher conducted carefulobservations and interviews with the ex-perimental students, and assessed (by theuse of case study methods and videotap-

ing) the development of the students in theISD Project.

Many research questions could havebeen raised concerning the ISDP experi-ment, since it involved many variableswithin a complex pedagogical situation.However, for the purpose of this study, theobjectives and questions were narroweddown to two main sets of assessments:

1. an assessment of the experimentalchildren's knowledge of basic frac-tion concepts; and

2. an assessment of the experimentalchildren's knowledge of Logo pro-gramming concepts and skills.

The "experimental treatment" inte-grated the experimental children's learningof fractions and Logo with the designingand programming of instructional soft-ware. Since the experimental students andthe C1 class had equivalent, thoughdifferently-styled, exposure to Logo (i.e.,both classes were part of Project Head-light), it was an open question whether par-ticipation in ISDP would result in greaterLogo knowledge, but one naturally ex-pected both of these groups to exceed classC2 in this area. With respect to fractionslearning, the experimental group had addi-tional (but not formal) exposure to fractionsconcepts through ISDP, so that improvedperformance of the experimental class wasexpected in this area as well, but the as-sessment sought to determine whether thiswas in fact true and, if so, what the nature

class type

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Control 2

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Figure 2. Experimental Design and Procedure

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of the improvement was. As will be seen inthe next sections, the assessment uncov-ered some surprising results, more finely-textured than these general surmises.

Within the fractions domain, emphasiswas placed on children's ability to translatebetween various modes of fractional repre-sentations. This aspect has been shown tobe a crucial part of rational-number knowl-edge, and particularly difficult for youngchildren (e.g., Lesh & Landau, 1983; Behr,Lesh, Post, & Silver, 1983; and others). Butstandard school tests were also used,which concentrated on students' use of al-gorithms. In Logo, the evaluation investi-gated the children's knowledge, use, andunderstanding of programming com-mands, instructions, and operations. Morespecifically, it assessed whether the stu-dents from the experimental class knewand understood more programming com-mands and operations such as REPEAT,IFELSE, SETPOS, variables, and inputs intheir projects, and became better at theseskills, than the students in the two controlclasses. The evaluation also investigatedwhether the experimental students couldunderstand, implement, debug, transform,optimize, and modify someone else's pro-gramming code better than the studentsfrom the control classes. Finally, the eval-uation assessed whether the experimentalstudents were able to construct Logo rou-tines for someone else's design or pictureand were better at this than the students inthe two control classes.

Given the breadth of the learning expe-rience and the mixed methodology of theassessments—including the extensive casestudies of several students (i.e., examina-tion of the children's progress, Designer'sNotebooks, finished products, interviewswith participants during and followingcompletion of the project), as well as themore formal pre- and post-tests—it waspossible to trace in detail the microgenesisof Logo and fractions skills and concepts,exploring different approaches taken by theexperimental students with different per-sonal and learning styles (see, e.g., Deb-bie's Case in Harel, 1988, pp. 76-245; and

the Appendix in Harel's paper in Journal ofMathematical Behavior, 1990a), as well asto draw inferences concerning their acqui-sition of metacognitive skills.

The experimental design of ISDP andthe analysis of its results we present hereraise methodological issues for educationresearch. Most acutely, these concern thequestion of what kinds of rigor are appro-priate.

A simplistic position would maintainthat the highest standard of rigor is alwaysrequired. But we argued elsewhere (e.g.,Papert, 1987) that this can sometimes resultin an analog of the complementarity princi-ple in physics, stronger formal rigor some-times being obtained only at the cost ofthinner results. Thus Harel (1988) adopteddifferent kinds of rigor for different aspectsof her work, and we will do likewise in thisarticle.

The first results section demonstrateswith statistical rigor that learning tookplace: the ISDP subjects learned quan-titatively measurable skills in the program-ming and in standard school domains. Thesection that follows illustrates some as-pects of the in-depth investigations intowhat and how they learned, going beyondtest scores to obtain qualitative insightsinto the changes that occurred in students'thinking about fractions, and the dynamicof the process that lead to those changes.Finally, a discussion section follows, wherewe discuss why the students learned whatthey learned.

RESULTS

Quantitative Results from ISDP

The "thinnest" and most formally rig-orous part of the analysis shows that thesubjects in the experiment did improve intheir ability to perform on standardizedquantitative tests of performance in theirwork with fractions (as presented in the fol-lowing subsection). Here the solidity of theresults derives from the existence of a large

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established body of data on how studentsperform in such mathematics tests (e.g.,Behr et al., 1983; or Lesh et al., 1983). Wealso present some quantitative data toshow that the ISDP subjects did learn muchmore about Logo programming than thesubjects in the two control groups (as pre-sented in the subsection about Logo re-sults).

Results from the FractionsPost-Tests of the Three Classes

All the teaching of fractions, for all thethree classes, was conducted for twomonths, during regular math lessons onlyand following the city-wide curriculum andtraditional teaching methods (see Figure 2).The experimental class was not providedwith any additional formal instruction onfractions, although we note that the repre-sentations of fractions in the context of in-structional design was discussed in a fewinformal Focus Sessions. (More informa-tion about the characteristics of the pupils,teachers, and their math curriculum isavailable in the dissertation and the Appen-dix of Harel, 1988.)

The post-test included 65 multiple-choice questions. Out of these, 60 weretaken from the Rational-Number Project(RN Project, Lesh et al., 1983 pp. 309-336).The remaining five were designed by theresearcher and included word problemsand construction of representations. Of the60 RN Project questions, 43 were given tothe students in the pre-test, then again inthe post-test. As examples, Table 1 showsthe children's average percentages of cor-rect answers on the fractions pre- and post-tests; Table 2 shows the table of results for

Table 1. Average Percentage Correct of Pre-and Post-Tests on Fractions Knowledge

Table 2. Two-Way Repeated MeasurementAnalysis of Variance (The results account forthe unequal sample sizes of Factor A)

Treatment

Experimental ClassControl Class 1Control Class 2

Fraction

Pre-Test(%)

525447

Knowledge

Post-Test(%)

746656

Source

A (Groups)Subjects between

samplesWithin SubjectsB (Pre-Post)A x BB x SubjectsBetween SubjectsTotal

48

12

4851

101

d.f.

2

50

F-Statistics

15.31**

110.99**8.29**

the Two-Way Factor Analysis of Variancewith repeated measurement for the frac-tions pre- and post-test scores; and Figure3 shows the interaction diagram of the twomain factors. In general, the difference inpre- and post-test scores of the studentsfrom the experimental class was almosttwice as great as that achieved by the stu-dents from class C1, and two-and-a-halftimes as great as that of class C2.

Results from the More DifficultQuestions on the Fractions Test

We gave specific attention to the an-alyses of the most difficult translationmodes between rational-number represen-tations that the students had to carry out inthe test. Some of these translations werethe most difficult for students of all ages in

PerccitCorrect80 -

70 -

60 -

50 -

40 -

j \

tges of

?k T«$t Pojt Tes

A2 Control 1

A3 CoUrol2

t Factor B

Figure 3. Interaction Diagram of the TwoMain Factors in the Analysis of the Pre- andPost-Tests Scores

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10 I. Harel and S. Papert

previous studies, and were equally so forall students in the present study's pre-tests.In the post-tests however, these translationmodes were still relatively difficult for thecontrol students, but dramatically less sofor the experimental students. Let us con-sider an example. Lesh et al. consideredquestion 50 to be so complex that it was notgiven at all to the fourth graders in the RNProject, only to sixth, seventh, and eighth-grade students (Lesh et al., p. 326). To an-swer this question, the students had totranslate a pictorial representation into awritten (verbal) representation of a fraction.

Question 50 presented students with apolygonal region representation, with a nu-merator that was higher than 1, a denomi-nator, a representation of a rational numberlower than 1, in a discrete object that in-cluded a perceptual distraction (i.e., onepart was "outside" the triangle area). In or-der to choose one of the options, the stu-dents had to (1) translate the given pictureinto symbols or words (two fifths are shad-ed in), (2) read the question again and real-ize that the question referred to the denom-inator of the shaded fraction, and (3) findthe correct answer, which was b. Option ais confusing because it is written like a spo-ken symbol and includes "relevant"numbers—five and thirds. Option b is con-fusing because it does not mention "fifths,"but rather "five" (the denominator is"five"). Table 3 shows the scores in theirpercentage of correct answers for question50.

The ISDP students scored twice as highon question 50 as did the control students,

Table 3. Contingency Table Statistics,Comparing Performance of the Study Samplewith the Performance of the BackgroundSample (Lesh et al., 1983, Average ofGrades 6-8)

ExperimentalClass

Control Class 1 &Control Class 2(Average)

(%) Correctin StudySample

66

29

(%) Correctin Background

Sample

33

33

X2 = 33.49

and twice as high as the sixth to eightgraders from the RN Project. The ChiSquare analysis shows that the differencesof frequencies are highly significant.

Perhaps there is some "transfer" fromLogo programming experience at workhere. Decomposing a given picture into itsgeometrical components is a common pro-cess in Logo programming, and a skill stu-dents usually acquire in their ongoing pro-gramming experiences. What Lesh et al.(1983) and Behr et al. (1983) consider as a"perceptual distraction" (i.e., the one littletriangle that was "outside" the big trianglearea) was probably not at all a distractionfor the students who looked at the picturewith "Logo eyes" and decomposed it intoits five geometrical components.

Another example is Question 42. It in-volved a translation of pictorial into sym-bolic representation (see Figure 5). Thisquestion, number 42, was the 13th most

50) WHAT IS THE DENOMINATOR OF THE FRACTION THAT TELLS USWHAT PART OF THE PICTURE BELOW IS SHADED?

a. f ive-thirds b. f ive c. threed. two e. not given

Figure 4. Question #50

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Software Design as a Learning Environment 11

difficult of the 18 asked in this subset. It wasthe 44th most difficult in the whole set of 60questions given in the RN Project to stu-dents from fourth through eighth grades(Lesh et al., 1983, p. 323). It included a dis-crete object representation in which therepresented rational number was less thanone; moreover, parts of this object werenot congruent and were visually distract-ing. Table 4 shows the scores (given aspercentage of correct answers) on thisquestion according to the children's divi-sion into math groups (see Harel, 1988 forthe detailed description of the mathgroups).

As seen in Table 4, none of the high-math experimental students made any mis-takes. The medium-math experimental stu-dents scored like the high-math students inthe two control classes. The experimentalclass as a whole scored 100% better on thissubset as the students in the RN Project,and 14 percentage points better and 27 per-centage points better than class C1 andclass C2, respectively. Table 5 shows thatthe Chi Square analysis of differences offrequencies is highly significant.

Results from Standard BostonPublic-Schools Math-Tests

In addition, all the pupils were tested inmath, as part of their end-of-year publicschool series of "referenced tests." Thismathematics test included 40 multiple-choice questions. The average number ofincorrect answers was 5.06 incorrect an-

Table 4. Percentage of Subjects RespondingCorrectly to Question #42, by Treatment andMathematical Ability

Treatment

Experimental classControl Class 1Control Class 2

Mathematical

Low(%)

504020

Medium(%)

726850

Ability

High(%)

1007272

Table 5. Contingency Table Statistics,Comparing Performance of the Study Samplewith the Performance of the BackgroundSample (Lesh et al., 1983, Grade 4)

ExperimentalClass

Control Class 1,Control Class 2(Average)

{%) Correctof StudySample

74

53.5

(%) Correctof Background

Sample

36

36

X2 = 42.62

swers per child in the experimental class,6.27 per child in class C1, and 9.45 per childin class C2.

Of the 40 questions, six were specifi-cally on fractions ordering and equivalence,four on decimals, four on measurements ofdistance and time that required the use offractions, and one on understanding geo-metrical shapes (i.e., this was the subset of15 questions directly related to rational-number concepts, their representations

42) WHAT FRACTION OF THE BALLS ARE TENNIS BALLS?

FOOTBALLS

TENNIS BALLS

BASKETBALLS

a. 2/8 b.3/2 c. 2/6 d.6/2 e. not given

Figure 5. Question #42

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and computation). The average number ofincorrect answers to this subset of 15rational-number questions was 1.60 perchild in the experimental class, 3.16 perchild in class C1, and 4.62 per child in classC2.

Several conclusions can be drawn fromanalyzing these results. The first is that theexperimental students, in general, didmuch better on the entire conventionalschool test than the two control classes.The second conclusion is related to the chil-dren's incorrect answers in the rational-number concepts subset of this test. In theexperimental class, only 29% of the incor-rect answers in the whole test (40 ques-tions) were incorrect answers aboutrational-number concepts. But in both classC1 and class C2, approximately 50% of theincorrect answers were on rational-numberconcepts. This shows the superiority of theexperimental class on rational-numberknowledge in particular—as measured bythis standard test. Table 6 shows the pro-portion of incorrect answers in this rational-number subset to the whole test.

The third conclusion is related to"transfer." By subtracting the average ofincorrect answers on the fractions subsetfrom the average of incorrect answers onthe whole test, we can examine the chil-dren's average of incorrect answers to allthe non-fractions questions: for the experi-mental class, 5.06 — 1.60 = an average of3.46 incorrect answers per child on non-fractions questions; for class C1, 6.27 -3.16 = 3.11; and for class C2,9.45 - 4.62 =

Table 6. Contingency Table Analysis,Comparing the Proportion of Rational-NumberSubset to Whole Test in the Boston SchoolMath Test between the Experimental andControl Classes

ExperimentalClassl%)

29

X2 = 6.631

Control 1Class(%)

51

Control 2Class(%)

48

4.83. The differences between the experi-mental class and class C1 are not signifi-cant here, but the differences betweenthese two classes and class C2 are. Thisfinding is interesting because it might bethat the experience of Project Headlight stu-dents (experimental class and class C1)with Logo programming contributed totheir general mathematical ability.

SAMPLE RESULTS FROM THELOGO POST-TESTS

In the Pencil-&-Paper Log Test the stu-dents were asked: "Please list all the Logoinstructions and commands that you knowand use—in column A; then, write an expla-nation and give an example for each one—in column B." The results for this questionwere divided into two major groups of find-ings. The first are simple findings that re-late to how many instructions and com-mands each child actually listed. Thesecond relate to the children's understand-ing of the meaning and functions of thesecommands and instructions in the Logolanguage. Table 7 represents the differ-ences between the students in terms ofhow many Logo commands, operations,function keys, control keys, etc., they listedin the post-test. The number in each slotshows the average number of commandsand instructions the children from all threeclasses listed and explained. The advan-tages of the experimental students over thestudents from the two control classes be-come clear from examining this table.

The students were also evaluated onthe quality of their definitions and exam-ples for each of the items they had listed. Inclass C1 no one was evaluated as "VeryGood," whereas in the experimental class,three students who wrote over 40 com-mands and instructions, and four whowrote over 30, and gave very good exam-ples and definitions of each, were evalu-ated as "Very Good." No one was eval-

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Table 7. Contingency Table Analysis,Comparing the Average Number of ListedLogo Commands between the Experimentaland Control Classes

ExperimentalClass

25.6

X2 = 10.8426

Control 1Class

12.0

Control 2Class

8.3

uated "Low" or "Very Low" in theexperimental class. However, four studentsin class C2 were evaluated as "Low" sincethey listed fewer than five commands andinstructions and did not provide examplesor definitions for all or most of those.

We also tested the children's ability toanalyze given programming code and "ex-ecute" it on paper. A long, linear Logo codecomposed of short strips of Logo primitiveswas given to the students, and the studentswere asked to draw the graphics. This taskrequired that students read the given linearcode, comprehend it, understand its flow ofcontrol, build a mental model of what thecomputer would do when each of the linesin this program was executed, and draw thepicture accordingly, step by step.

Many researchers in the field of pro-gramming distinguish between writing alinear program and a modular program.These researchers consider a linear pro-gram as one which emphasizes the gener-ating of effects without any considerationand understanding of the inner structure ofthe code (e.g., Papert, 1980; Papert, Watt,diSessa, & Weir, 1979; Carver, 1987; Solo-way, 1984; several researchers in Pea &Sheingold, 1987; and others). On the otherhand, a modular program emphasizes ele-gant and efficient programming, and is ac-companied, they claim, by a higher-level ofunderstanding of programming in general,and of the programming language charac-teristics in particular.

Our results show that students who hadwritten linear as well as modular programs

during their process of learning to programwere better able to understand and cor-rectly execute this confusing linear pro-gram. The students in C2, who only knewhow to write linear programs, were not ableto solve this problem accurately unlikemany of the ISDP students. We should notethat ISDP students often introduced struc-ture (i.e., subprocedures and functionalnaming) into their programs only after along period of purely linear programming,and only when they themselves decided itwas necessary; it was not imposed on themfrom the outside. They learned to introducestructure, modularity, and elegant codingwhen they themselves realized the need forit in maintaining their long programs, inadding new parts to them, or in re-using(instead of re-writing) certain subproce-dures in several places in their programs.

Another interesting aspect of these re-sults came to view in the "number of trials"category. Many of the ISDP students triedmore than once to draw the picture on pa-per, and finally found the right solution; butthe students in the control classes who hadgotten it wrong in their first trial were ap-parently not motivated or determined to tryagain or to find the right solution. Many ofthem simply wrote "I don't know how to doit," and went on to the next task on the test.

Finally, we mention that on a "Debug-ging Task" given to the students on thecomputer, the ISDP students were faster atidentifying the bugs, locating them, andthen re-evaluating the program in order tocreate an output that corresponded perfect-ly with the original goal given to them. Thedata in Table 8 shows the results for "Tasks1 and 2" on the computer, which requiredthat the students run a given bugged pro-gram, analyze the features of the resultantgraphics, identify the discrepancies be-tween them and the desired graphics, enterthe Logo code on the computer, locate thedifferent bugs causing the discrepancies,fix the program on the computer, and addthe corrections on the program that werewritten on the paper.

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Table 8 speaks for itself. The superiorityof the ISDP students over the other pupils isclear, as is that of class C1 over class C2.Table 9 shows a Chi Square Analysis ofthese results.

In addition to the above quantitative re-sults we made a number of qualitative ob-servations about the children's debuggingstrategies. For example, the first thing allthe ISDP students did was to change the HT(Hide Turtle) command at the very begin-ning of the procedure, to ST (Show Turtle),so that they could follow the turtle as itexecuted the code. On the other hand, thefirst strategy that most of the students inclass C2 and many in class C1 used was tocopy the program given to them on paper(in sub-task 2) into the Logo CommandCenter and execute it line by line. This strat-egy worked well until they reached the RE-PEAT statements, which were written onmore than one line. Then, the students gotconfused because the program still did notwork, though they were sure that they hadlocated a bug. Instead of trying a new strat-egy, these students then erased everythingand started to copy the procedure into thecomputer in "direct mode" again, whichresulted in the same thing happeningagain, and so on.

In "Tasks 3 and 4 on the computer," thestudents were asked to optimize the codegiven to them in Tasks 1 and 2, and make itclearer and shorter. In order to solve thesesub-tasks, the students had to cease operat-

ing on the individual command level, andstart thinking in a procedural mode, usingREPEATS, procedures, and inputs. To sum-marize these results, the experimental stu-dents were more flexible and attempted toexplore a greater variety of ways for pro-ducing the same Logo drawings. They un-derstood and reached a more modular levelof code, and many of them tried to userepeats, sub-procedures, and variables.The experimental students also performedsignificantly better than the control stu-dents on the three other items of this test,covering use of inputs, modification of pro-cedures according to specific requests, andprediction of results of short but confusinggraphics programs (see Harel, 1988; 1989b,d,e).

Interestingly, all the ISDP students, whohad already performed much better thanthe control students in the similar pencil-&-paper tasks, performed even better whenusing the computer. But the students fromclass C2 got more confused at the comput-er, and performed less well than they hadon the pencil-&-paper task. Class C1 wassomewhere in between: the high-math stu-dents, like those from the ISDP class, per-formed much better at the computer, andthe medium- and low-math students per-formed similarly to those from class C2—far less successfully than they had in thepencil-&-paper task.

Similar trends were found in the resultsof the Logo post-tests and in the Fractions

Table 8. Results from the Debugging Task

Experimen.classN = 17

Control 1N = 18

Control 2N = 16

No. of Bugs Foundand Fixed

16—all bugs1—one bug

9—all bugs4—one bug5—none2—all bugs4—one bug10—none

Identify & Fix Bugsin Computer Prog.

17 children—yes100% succeeded

13 children—yes5 children—no70% succeeded6 children—yes10 children—no37% succeeded

Identify & Fix Bugsin Paper Program

17 children—yes100% succeeded

8 children—yes10 children—no44% succeeded2 children—yes14 children—no12% succeeded

Average Time forSolving 1 & 2

15 min per child

35 min per child

55 min per child

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Table 9. Contingency Table Analysis,Comparing the Number of Bugs Found in theDebugging Task between the Experimentaland Control Classes

Bugs found:210

ExperimentalClass

9460

Control 1Class

502228

Control 2Class

132562

X2 = 138.92

post-test: the ISDP students consistentlyscored higher than the other two classes;but class C1 usually scored higher thanclass C2. Also, the high-math students fromclass C1 made up a special group. Theywere never as good as the high-math ISDPstudents, but most of the time they were asgood as the medium-math ISDP students.Their scores in the fractions test were oftenhigher than those of the students from theRN Project, and stood out from those of theother control students. What does thismean? It seems as though only the high-math students in class C1 strongly bene-fited from Project Headlight experiencewith respect to the pictorial-to-symbolictranslation of fractions. This was probablydue to their programming expertise, whichcontributed to their ability to translate pic-ture representations into written ones, andvice versa. This phenomenon requires fur-ther investigation. It is an interesting one,since it suggests a correlation between thechildren's level of understanding and in-volvement in Logo programming, and theirability to understand different representa-tional systems.

QUALITATIVE RESULTSABOUT WHAT AND HOW THESTUDENTS LEARNED

Thicker descriptions than "getting bet-ter at" fractions or Logo in the school'sterms were derived from an analysis of alarge body of qualitative data derived inthree ways: formal interviews, preservation

of students' work, and observations of pro-cess. The 51 students in the experimentaland control groups were interviewed be-fore and after the ISDP experience. TheISDP students' work was preserved in De-signer Notebooks and in computer filesshowing the state of their software projectsat the end of each day. In addition to directdaily observations by the researcher andteacher, videotape made in two modesgave many opportunities for micro-analysisof behaviors: in one mode the videocamerawas carried by an observer and directed atinteresting events, in the other it wasplaced in one position on a tripod for anentire session and simply allowed to run.These sources of data allowed us to seesubjects discovering new ways of talkingabout fractions and relating to fractionsspatially and kinesthetically as well as lin-guistically and conceptually (e.g., Harel,1990b).

The interpretative nature of such con-clusions required rigor that is different inkind from statistical analysis that checkswhether or not the probability of differ-ences in scores could be due to chance. Butit is the richness of observation obtainedfrom so many different sources that yieldeda coherent sense of the development of in-dividual subjects as well as of shared devel-opmental trends, and this gave us confi-dence in our conclusions that we could nothave obtained by any other means. To ap-preciate this coherence in full it is neces-sary to refer to finer textured case studiespublished elsewhere (Harel, 1988, 1990a).Here we focus on four issues which welabel as development of concept, appro-priation of project, rhythm of work, andcognitive awareness and control.

Development of Concept. Under therubric development of concept we analyzethe movement from rigidity, particularlyand isolatedness toward flexibility, gener-ality, and connectedness. In the initial inter-views questions such as "What is a frac-tion?" or "When you close your eyes andthink about fractions what images do you

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have?" or "Can you give me an example ofa fraction?" revealed several aspects of par-ticularity. There was particularity in the useof particular rational numbers (usually onehalf or one fourth) as prototypes. Moststrikingly there was particularity of restric-tion to the spatial: A fraction is a part ofsomething, and "something" means some-thing physical or geometrical. Of coursechildren from an early age use fractionwords linguistically to refer to parts of otherkinds of entities, such as time ("half anhour" or "I am eight-and-three-quarters")and money ("a quarter"). But in the inter-views they very seldom seemed to connectsuch usages to a general notion of a frac-tion. When specifically prompted to look forfractions in a real calendar or clock, sub-jects gave answers referring to the squareson the calendar or shapes on the clock face.One student even referred to the patternstrap-watch-strap as analogous to the nu-merator, the slash, and the denominator inthe school representation of fractions! Andeven within the spatial there was a highdegree of particularity in choosing exam-ples that happened to coincide with thoseone expects to meet in school books: "a

fraction is a half a pie" or "a fraction is likean apple or an orange divided in the mid-dle." When asked to draw a fraction mostcommonly they would draw a circle or asquare, divide it vertically (not necessarilyequally), and shade some parts. In somecases the degree and rigidity of the partic-ularity bordered on the bizarre. For exam-ple, Debbie was committed to the idea thata fraction is the right shaded part of a circledivided by a vertical diameter. When askedwhether the unshaded part of the circle is afraction, she said, "No. It's not a fraction.It's nothing." Such tendencies were alsoseen in the choice and modes of represen-tation of fractions in the very first examplesof computer screens made in the experi-mental students' software projects.

All this changed dramatically in thecourse of the project. The content of thesoftware as well as the post-interviews re-vealed a widening diversity of kinds of ex-amples and representations among theISDP students. Even more significantly,there was often a conscious—indeed, onemight well say philosophical, recognition ofthe achievement of greater generality. In

2/4=1/2iiiiiiiiiiiiiii

§8

iIII

:::::::n

si

this is 1 /2 of a circle This is a square, and1 /4 is shaded in.

Debbie1 /2 of a computer screen

MichaelaA half of a circle

TommyA fourth of a square

This is a half of atriangle!

This is a whole of atriangle!

This is One Half:

SharifaA half of a triangle

SharifaA whole triangle

DavidThe Vhole is two squares

Figure 6. Some Children's InitialRepresentations on the Computer

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Figure 7 we show a few examples of somechildren's further representations. Al-though it is difficult to capture the colorful-ness and playfulness of those animations inthis static black and white medium, the chil-dren's general ideas, their diversity, andcomplexity is captured here.

Consider Debbie again. After a wholemonth of explaining about fractions—bycreating a representation showing a half ofher computer screen, and different geomet-rical shapes divided into halves andfourths—Debbie discovered something.Her discovery was expressed in her choos-

One of these measuring cups is filled with1/3 juice and 2/3 water. The second is with2/3 juice and 1/3 water. Which one isMORE concentrated? (Type Left

J ,;.wX;!v,

:x*Xv>:

VELCOM TO MY KITCHEN!

ing to teach an idea of a different, more"philosophical" nature than how to cut ashape into thirds or how to add a third anda half.

She chose to explain that, "there arefractions everywhere . . . you can put frac-tions on anything." To teach this idea, Deb-bie designed a representation of a "house,a sun, and two wooden wagons" (see Fig-ure 1). She worked very hard on imple-menting this representation using somequite complex Logo programming code(see Harel 1988, pp. 118-140 for a detaileddescription of her lengthy and complex

$ $ $ FRACTIONS & HONEY

1/4

- + - = 1 -=• + •=-= 1

Figure 7a. Michaela's Kitchen Scene Figure 7b. Nicole's Money Scene

Naomi's"SESAMESTSEETSCENE"

Which on* doesn't ielong?

so o

kTvpt AB C D.ii I::::::

ITthe ustr typed C:I If the user typed A, B, or D:

cdYOU

IIIH• tai

• ! • !

QlASE

C

II PI mmA GENIUS

AOiLook,

-far, -w

oyou"

ky m

lirrTC comeess mj i

[la. otler voris Try

Li™a.

toes&'t1 |IIIi!lIIflIl!

t&isl

a^iia:

iiiijiif 1

Figure 7c.

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THE TIME IS HIKE O'CLOCK Now the time is nine and a half.

Half an HourISALiJfofONE HOUR!

And (Ms is & fraction, too!

Shirifi's Clock Scent. Shirifi created in mimilion. The minute hand is moving irouni the clock.The Turtle draws the "minute lines" until it reaches 9:30.

Figure 7d.

programming process and her work on thisparticular screen).

Debbie was not alone. A few weeks la-ter, Tommy's House appeared, and thenPaul's. The idea that it is important to teachothers that "fractions are everywhere," andthat one could "find fractions in regular hu-man things" was spreading around the De-sign Studio.

Michaela and Sharifa, who used Deb-bie's software and received her full set ofexplanations about it, also chose to teachthe same principle, but in another way.Sharifa selected to represent fractions byusing a clock, teaching her users that "Halfan hour is a half of ONE hour!" Her enthusi-asm in announcing to the world that, "halfof an hour is a fraction too!" (and her use ofexclamation points) is evidence for the

2

4

There are 5 Halloween Goasts in the picture. Tvo are colored inWhite. We say that 2 /5 Goasts are shaded in. We call itTWO FIFTHS. Press any key to continue.

Figure 7e.

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In this picture there axe 12 airplanes.HOV many axe big airplains?Tyep: 4112, 4/8, 8/4, 1/3, 1/2.1/3You are right because 4/12=1/3 Both answers are correct!

Figure 7f. Pay attention to the options Oai gave to his users (4/12, 4/8, 8/4, 1/3, 1/2). Heprobably had an idea of what could be their problems with understanding this representation.He programmed it so both the answers 4/12 and 1/3 would receive the same feedback ("youare right . . ."). He also had an explanation for the users for why their answers were incorrect.

philosophical importance of the break-through as she experienced it. Michaelachose to teach this principle through usinga representation of "two measuring cupsfilled with different quantities of orangejuice, water, or flour—depends on the frac-tion . . ." Later she confessed, "I found somany fractions in my kitchen . . . I told mymom about it too . . ."

These observations are consistent withthe ways in which ethnographers such asScribner and Lave (1984) have demon-strated the separation of school knowledgeof mathematics from practical, everydayknowledge. But we note something furtherthat has a disquieting as well as an educa-tionally hopeful aspect. The disconnectionseems to be well entrenched within boththe practical and everyday side and on theschool side, as shown for example by thefact that Sherifa had to discover a connec-tion between "half an hour" and "half anapple." On the other hand, she did makethe discovery, and did so without explicit ordirective prompting by adults. Similarly, wesee clear evidence that many students do

not see "a quarter" as related to either the¼ in their school worksheets or the "25%off" in a store's sale pricing.

Our conjecture is that "disconnection ofknowledge" must not be seen primarily asa limitation of "schoolish" knowledge butrather as a universal characteristic of howknowledge develops, first as "knowledge inparts" (to use Andrea diSessa's phrase)and then by the unifying effect of controlmechanisms such as those described byLawler in Computer Experience and Cogni-tive Development (1985), by Minsky in Soci-ety of Mind (1986), and by Papert in Mind-storms (1980).

Appropriation of the Project. Our sec-ond rubric, appropriation of the project, re-fers to observations about a shift from areluctant, impersonal, and mechanicalmode of working to a growing personal en-gagement, assertive individuality, and cre-ativity. Debbie's case once more illustratesthis process. Her initial response to the pro-ject was globally very negative. She simplydid not want to develop software about

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fractions. In the culture we tried to main-tain, she was allowed to hold back but grad-ually began to succumb to generalized so-cial pressures. So by the end of the secondweek, she was beginning to put fractionson her computer screen. But what she putup was still a direct reflection of the stereo-typed model of fractions she had derivedfrom math class. However, a new processwas also beginning. We would say that shewas "working through" her ideas (and nodoubt her feelings too) about fractions. Ittook her approximately a month to achieveher break-through. Now she had an individ-ual philosophical position which she pur-sued with something of a missionary zeal.She had given herself the task of leadingthe rest of the world to her discovery.

Time Frame and Rhythm of Work. Thiscategory appears to be an essential ele-ment of the process of appropriation.Switching in and out of projects in the frag-mented time of the regular school, simplydoes not provide the conditions for person-al appropriation and expression of personalintellectual style. Observations in the ISDPalso show the importance of pace in thestudent's rhythm of daily work and in theradical differences in individual style ofwork, action, and thought. Analysis of vid-eotapes set up to run continuously at fixedplaces show a pattern of work in strikingcontrast with the regular school notion of"efficient time on task." In the videos, wedo see periods of intense concentration.But we also see periods in which students'attention is elsewhere: sometimes lookingat a neighbour's work, sometimes engagedin play, chatting, and interactions that haveno discernible connection with the project.Is this an "inefficient" use of time? Whilewe did not measure this with any rigor, itappears to us that the rhythms of workadopted by the individual students have anintegrity that contributes to getting the jobdone and especially to getting it done cre-atively. And in making this assertion wefeel supported by such ethnographic stud-ies as Bruno Latour's (1987) description ofthe ways in which engineers and scientistsat work mix "serious" talk about the prob-

lems in hand with intrusions from everydaylife and personal concerns.

Metacognitive Awareness. In thisrubric we describe in what ways ISDP en-couraged children's metacognitive aware-ness (i.e., children's thinking about theirown thinking), their cognitive control (i.e.,planning, self-management, and thinkingabout these processes), and their meta-conceptual thinking (i.e., children's thinkingabout their own knowledge and under-standing of concepts).

Through the project the students devel-oped problem-finding skills. For fourmonths, students involved themselves indiscovering problems they wished to solve.No one specified the problems for them;rather, they were the ones in charge of de-ciding, for example, what was difficultabout fractions, what screens to design toexplain fractions, what Logo proceduresto create and how, etc. Students also de-veloped an awareness of the skills andprocesses needed to solve the variousproblems they posed. The Designer's Note-books, as another example, required thatchildren design and think about theirscreens on paper. Their initial drawings andplans demonstrated that they were not veryaware of either the programming or thefractions knowledge and skills needed toaccomplish their designs; however, as theproject progressed they rarely came upwith a design they could not manage inLogo. They also had to be aware of theirtarget users' knowledge of fractions so thatthey could make the representations theyhad created on the computer comprehen-sible to them. Not only did children becomeaware of strategies to solve a problem athand, they also learned to activate them.The Logo post-tests, for example, showedthat the experimental children were able tooptimize, modularize, and debug Logo pro-cedures better and faster within given timeconstraints.

Over the course of the project, childrendeveloped the ability to discard inefficientdesigns, plans, and solutions and to search

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for better alternatives. In other words, theydeveloped cognitive flexibility. During theproject they learned to adjust their cogni-tive efforts to match the difficulty of theproblem. They would often begin to imple-ment their designs in Logo, but when theyrealized that too much effort was needed toaccomplish a simple or "unimportant" de-sign, they stopped working on it andmoved on to a screen that was more crucialfor their software or decided to redesignthe screen that was giving them problems.As a result the ISDP students were not rigidin their solution processes in the Logo post-tests, and did not stop working on difficultproblems (unlike many of the control chil-dren who simply answered "I don't know"),but kept trying until they found the solu-tion.

Another thing they learned was how tocontrol distractions and anxiety. In this pro-ject (and in Project Headlight in general),children worked in an open area next totheir classroom. Different children workedon different problems, with other children,teachers, and visitors often walking around.Children learned to keep their attention fo-cused on the problems they were workingon, and to resist being distracted by exter-nal stimulation. They also learned to con-trol their anxiety when a problem was diffi-cult. Post-tests showed that ProjectHeadlight children (both ISDP and C1) didbetter in avoiding anxiety, focusing effi-ciently on the problems given to them andnot letting external interference distractthem from their thinking and writing.

The community supported a practice ofcontinual evaluation: Children evaluatedtheir own and each other's performance ev-ery day when they ran their software andmade entries in their Designer's Note-books, and when they looked at other chil-dren's software—sometimes making sug-gestions or borrowing ideas. They wereconstantly relating their current perfor-mance and implementation phases to thegeneral goals of the task and making appro-priate changes if the result was too slow orunclear.

The students learned to monitor theirsolution processes. Since they were incharge of their own learning and produc-tion, they knew that when they had a prob-lem or difficulty they could look first tothemselves for a solution. They developedself-reliance and faith in their thinking.

Finally, the students became articulatenot only about general planning and spe-cific design tasks, but about the subject do-main as well. They talked, thought about,and actually related to fractions, bothduring their involvement in the project andin the interviews and tests that took placeafterwards. From their point of view, itwas having to teach and explain fractionsto someone else that caused them to em-brace it so thoroughly because, as theysaid, "how can you teach it if you don'tknow it yourself?" Much like professionaleducational-software producers, who gaindeeper understanding of the topics in-volved in their software by thinking of waysto build explanations and graphical repre-sentations for their future software users—the experimental children, through teach-ing and explaining, also gained an aware-ness of what fractions were or of what theyknew and did not know about fractions. Togive some examples of students' metacog-nitive expressions, here are four relatedquotes from the post-interviews.

Andy: "It's supposed to be for littlerkids, right? But to program it so they canunderstand it, you have to be sure that youknow what you are talking about. 'Causethe teacher has to know more . . . Youdon't know how the other kid will react to itand all of that . . . It was really hard to get itso they will like it . . . Always to think aboutand imagine that you are small, right, andhow would you like it?!"

Naomi: "It is hard to teach. You haveto have a pretty good understanding ofsomething, so you'll be able to explain itwell to others . . . and a lot of times it'sreally hard to understand what's happen-ing with these fractions . . . "

Debbie: "You have to show them frac-tions and explain, little by little. To pro-gram the scenes, so they will learn how todo fractions, and what they did wrong . . .then, someone can listen to you, to thecomputer, I mean, and understand."

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Paul: "It's hard to tell someone elsethat doesn't know about fractions how todo these things. So I program this soft-ware for them, to help them understand it. . . But I have to think a lot about what Ireally know and how to show it on thecomputer, and how to explain it. And atthe end, how to test them about it."

DISCUSSION: WHY DID THEYLEARN?

The simplest description of the ISD ex-periment reads like a "treatment" type ofexperiment: These subjects did somethingparticular (made instructional software) forso many hours (close to 70 hours of work).In fact, the situation is vastly more complexthan anything that could be sensibly de-scribed as "changing one variable whilekeeping the everything else constant" be-cause there were too many particulars in-volved. To make their pieces of software,the students used particular computers(IBM PCjrs) and a particular programminglanguage (LogoWriter). The project includ-ed focus sessions where the specific con-tent of fractions was discussed in a particu-lar way—informally and compared withschool classes, briefly. The project tookplace in a particular part of the school witha particular "computer culture." And dur-ing the ISDP the culture developed furtherin a particular way, with particular customsof interaction, attention, mutual help, se-crecy, humor, and so on. The students andtheir teacher were aware of having aunique relationship with the experimentalstaff. They reacted in particular ways to thepresence of video cameras, question-askers, and note-takers.

One can raise innumerable conjecturesabout the "real" source of their learningabout fractions, for example. Did the simplefact of spending some 70 hours program-ming representations in Logo contribute tothe results? Was the "moral climate" in theproject largely responsible? Or the fact thatthe teacher felt she was part of somethingimportant or simply different? Some suchconjectures, or aspects of such conjectures,

we can, and do, try to check by studyingcontrol groups. But there are far too manyof them to treat in a rigorous way.

What can be said with some certainty isthat we created a total learning environ-ment in which some impressive learningtook place. Teasing out the contributions ofparticular aspects of the environment is nota reasonable goal for any single well-defined experiment. Understanding willcome through a process of gradual accu-mulation of many projects and of a greatdeal of theory building (e.g., Kafai & Harel,1990; Jackson, 1990; Resnick, 1989). Whatwe can do here is to share our own intu-itions and, as part of the larger scientificenterprise, to formulate and discuss someconjectures concerning these intuitions ofours.

In the following sections we speculatethat improvement in performance might beaffected by factors related to the affectiveside of cognition and learning; to the chil-dren's process of personal appropriation ofknowledge; to the children's use of Logo-Writer, to the children's constructivistinvolvement with the deep structure offractions knowledge (namely, constructionof multiple representations) to the "inte-grated-learning" principle; to the "learningby teaching" principle; to the power of de-sign as a learning activity.

However, the main point we would liketo make here is that each one of these con-jectures, when considered alone, wouldonly give very partial information aboutwhy ISDP took the form and yielded theresults that it did. Only by considering themtogether, and by speculating about their in-terrelations, can we take a step towards un-derstanding the holistic character of Con-structionism in general and of ISDP inparticular.

The Affects of AffectFrom certain Instructionist points of

view (e.g., Papert, 1990) one could see aparadox in the results obtained here. Here

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are a few examples from the ISDP students'test scores: Debbie scored 51% correct onthe fractions pre-test and 84% on the post(33% difference); Casey scored 55% on pre-and 83% on post (28% difference); Rachel,55% on pre- and 87% on post (32% differ-ence); or Oai, 55% on pre- and 97% on post(42% difference). Debbie's, Oai's, Casey'sand other children's ability to work withfractions, improved considerably fromworking on a project that was entirely self-directed, gave them no "feedback" in theform of marking responses right or wrong,gave them very little guidance or informa-tion about fractions. How could worryingabout whether "fractions are everywhere,"to take Debbie's concern as an example,lead to greater ability to do school prob-lems in manipulating fractions?

Our view of people like Debbie isstrongly colored by the sense that whenthey allow themselves to tap into personalknowledge, they allow knowledge aboutfractions to become connected with thepersonal sides of themselves. We conjec-ture that improvement in performance isrelated to the extent to which the studentsrespond to a problem about fractions by"digging around" in their own stocks ofknowledge as opposed to trying to followset procedures. We note that this pointcould be formulated in Scribner's (1984)language by saying that their thinkingabout fractions shifts from scholastic intel-ligence, characterized by rigid, inflexible,externally imposed methods, to practicalintelligence characterized by the use ofmultiple, flexible, and personal methods.

The "obvious" explanation, which nev-ertheless surely has more than a little truth,is that the students developed a better atti-tude towards fractions, perhaps even cameto like fractions. We recall that Debbie wasinitially reluctant to have anything to dowith such stuff but ended up with enthusi-astic missionary zeal. One does not needany complex theory of affectivity to conjec-ture that she might therefore be more likelyto engage her mind with fractions both inthe regular math class, so that she wouldlearn more of what she wanted to teach,and in test situations, so that she wouldscore more.

Pursuing the idea that Debbie changedher "relationship with fractions" leads intoan area where the line between the affec-tive and the cognitive becomes hard tomaintain (e.g., Turkle, 1984; Turkle & Pa-pert, 1990). We see something happeningthat is analogous to the development of agreater intimacy in relationships with peo-ple. Debbie becomes willing to take morerisks, to allow herself to be more vulner-able, in her dealings with fractions. As longas fractions-knowledge was teacher'sknowledge regurgitated, she was emo-tionally safe; the risk of poor grades is lessthreatening than the risk of exposing one'sown ideas.

The Importance ofSituatedness

The idea, though not the word, is animportant theme in the development ofLogo-based Constructionism (Ackermann,1990; Papert 1980, 1984a-b, 1987). In thisspirit we attribute the fluency with whichour subjects work with fractions to the factthat this knowledge is situated in computa-tional microworlds, much as Jean Lave'sweight watchers benefit from the suppor-tive consequences of the fact that fractionsare situated in the micro-world of the kitch-en. A similar example is how Michaela wasable to grasp fractions' significance in thecontext of using cooking tools for repre-senting fractions. An even more striking ex-ample is provided by Sherifa, who got agrasp on the fractional nature of timethrough support from an overlap betweenthe way the clock face represents fractionsas angles, and the way in which the Logoturtle (which by then was familiar to her)does something very similar.

In that sense, our observations are con-sistent with those of Lucy Suchman, JeanLave, and John Seeley Brown about "situ-ated knowledge." Like these researchers,we are strongly committed to the idea thatno piece of knowledge stands and grows by

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itself. Its meaning and its efficacy dependon its being situated in a relation to sup-porting structures. However, we attachmore weight than we think those writers doto the Society of Mind metaphor (e.g.,Lawler, 1985; Minksy, 1986; Papert, 1980)which would allow the situating of knowl-edge in internalized, mental environmentsto act in much the same way as situated inexternal, physical environments. Looking atthe performance of Sherifa from this pointof view we would say that her work with thecomputer enabled her to bring together inher thinking mutually supportive internalmicroworlds, in this particular case, micro-worlds of clock-time and of simple frac-tions.

The Contribution of LogoThere is a body of literature that ad-

dresses the question whether "program-ming" in general or "Logo" in particularcan induce cognitive effects, and if so towhat extent. In this sense, Logo would beseen as a causal factor in the improvementof fractions-knowledge or cognitive skillsseen in our study.

But Papert (1987) has used the term"Technocentrism" to warn against simplis-tic forms of this question. In different con-texts the import of the phrase "learningLogo" can differ so greatly that the ques-tion borders on meaninglessness. Nev-ertheless, in the particular context of theISD Project, where Logo was not isolatedfrom a total context, and where studentsprogrammed intensively and extensively,one can meaningfully begin to ask how var-ious features of Logo contributed to thesuccess of the children's work.

At least one important contribution ofLogo in this study was indirect—havingless to do with acquiring cognitive skillsthan with mastering a subject domain-learning how to program and using Logoenabled these students to become more in-volved in thinking about fractions knowl-edge.

But we do think that Logo, because ofits structure (or ISDP, because of the uniqueway it used the structure of Logo), had adirect affect. Sherifa's ability to see theanalogy between the clock and the turtle isone example of these affects. Our conjec-ture here, stated in its most general form, isthat the structure of Logo brings studentsinto direct and concrete contact with issuesof representation—in the case of ISDP, rep-resentation of the specific object of study,fractions; and more generally, with the rep-resentation of objects, projects, structures,and processes in terms of subprocedures,LogoWriter pages, and other computation-al structures.

It is relevant to note that much of whatthe ISDP students did could in principle bedone by other methods, such as using pen-cil and paper to draw representations, orusing physical manipulatives of variouskinds (for representation construction).This might seem to make the contributionof Logo quite incidental. But in practice, wefind it implausible that traditional mediacould equal the ease with which Logo al-lows students to save and connect con-cepts and their different representations,and especially how it allows them to devel-op and modify such representations overlong periods of time. Even more important,working in Logo on one's own machine, ina culture where that's what everybody elseis doing, reinforces the learner's contactwith his or her personal knowledge that isexpressed in a real product—a piece ofsoftware—that can be used and re-used byoneself or others, changed, modified, andgrow with the knowledge of the learner andof the culture. Logo facilitated this ongoingpersonal engagement and gradual changeof knowledge; and at the same time, it alsofacilitates the sharing of the knowledgewith other members of the design studio,and it allowed learners to continue andbuild upon their and others' ideas and com-ments very easily. Logo facilitated commu-nications about the processes and acts ofcognition and learning.

Of course we do not maintain that onlyLogo could do this. Surely, many new me-

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dia will develop that can do it better. Butlooking carefully at the features of Logothat contribute here, and the ways it wasused in the ISDP context, will be of use inguiding such developments (e.g., Harel &Papert, 1990). Pursuing such issues re-quires much further research. However theresearch that will elucidate them is not wellguided by the kind of questions that haveoften been posed in the literature, such as"Does Logo have such and such a cognitiveeffect" but rather "Can Logo be used toamplify and support such and such a direc-tion of children's intellectual development,or such and such a change in a learningculture."

The Deep Structure of Rational-Number Knowledge

Whereas most school work touchesonly on the surface structure of rational-number knowledge, we believe ISDP putsstudents in touch with the deep structure.

Elementary-school children's pro-cesses as well as difficulties in learningfractions and understanding their represen-tations have been well documented. Unlikewhole numbers, the meaning of which stu-dents largely come to grasp informally andintuitively out of school, learning therational-number system is confined almostexclusively to school. Because rational-number concepts and algorithms are so dif-ficult for so many pupils, they figure promi-nently in school curricula from the secondgrade on, mainly in the form of algorithmictasks and the working out of specific well-defined mathematical problems. Even so,several national assessments have foundthat children's performance on fraction-ordering and computation was low and ac-companied by little understanding (see thediscussion of this topic in Harel, 1988;1989b,d, 1990a). This is particularly unfor-tunate because fractions are ideal tools forlearning about number systems and repre-sentational systems in mathematics.

We see the understanding of therational-number representational systemas a privileged piece of knowledge amongthe other pieces of rational-number knowl-edge. Representations form part of thedeep structure of rational-number knowl-edge, whereas algorithms put students intouch with only the surface structure (e.g.,Janvier, 1987; Lesh & Landau, 1983).

Logo can be a direct route to this en-counter with the deep structure, enablingstudents to explore the concept of fractionsthrough various on-screen representationsof their own devising. In ISDP, this processwas catalyzed by setting students the taskof creating good pedagogical aids for otherstudents, in the course of which theythought to create fractions representationsin such forms as money, food, or clocks, aswell as geometric shapes, and to accom-pany them with symbolic or verbal expla-nations, they thought would be helpful totheir target audience.

By becoming designers of instructionalsoftware, the students gained distance andperspective in two senses. In the first place,they were dealing not with the representa-tions themselves, but with a Logo represen-tation of the representations. Moving be-tween representations was subordinated toprogramming good examples of represen-tations. Secondly, the students pro-grammed, not for themselves, but for oth-ers. They had to step outside and thinkabout other children's reactions. The depthand creativity of such an experience con-trasts with the rote, superficial quality ofwhat typically occurs when a student is putthrough the paces of an externally-conceived sequence of learning.

In summary, ISDP recast fractionslearning in essentially three ways:

(1) it emphasized more involvementwith the deep structure (represen-tations) over the surface structure(algorithms) of rational-numberknowledge;

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(2) it made fractions learning simul-taneously incidental and instrumen-tal to a larger intellectual and socialgoal, that is, having students thinkabout and explain what they thinkand learn, in an interactive lessonfor younger children; and

(3) it encouraged both personal ex-pression and social communicationof rational-number knowledge andideas.

The "Integrated Learning"Principle: Learning More CanBe Easier Than Learning Less

It must be admitted that there are cer-tain problems with integrating instructionalsoftware design activity into a school'scurriculum. Software design is a time-consuming and complex enterprise for ateacher to handle, and it is not yet clearhow it can fit into the average class sched-ule. Also, at the present time, it is not veryclear which school subjects would lendthemselves best to this process of learning(e.g., Jackson, 1990; Kafai & Harel, 1990).

But knowledge about computation(such as programming) and the sciences ofinformation (involving control over one'sown processing, metacognition, and infor-mation construction) has a special charac-ter in this respect because it has a reflexivesynergistic quality—it facilitates otherknowledge. In ISDP, the learning of frac-tions and the learning of the complex ofskills (programming, design, etc.) encom-passed in the phrase "software design" didnot compete for time; rather we maintainthat each took place more effectively thanwould have been the case had they beentaught separately.

The reflexive quality of information sci-ence offers a solution to the apparent im-possibility of adding another component toan already full school day. If some knowl-edge facilitates other knowledge, then, in abeautifully paradoxical way, more canmean less!

The idea that learning more scienceand math necessarily means learning lessof something else shows a wrong concep-tion. If these domains are properly inte-grated into individuals' knowledge and intolearning cultures, they will be supportive,not competitive with other learning. We be-lieve in the possibility of integrating sci-ence, mathematical concepts, art, writing,and other subjects and making them mutu-ally supportive. We also believe that inISDP this principle of integration—whichmeant that young students learned frac-tions, Logo programming, instructional de-signing, planning, story-boarding, reflec-tion, self-management, etc. all at the sametime and in a synergistic fashion—greatlycontributed to the results.

Special Merits to Learning ByTeaching and Explaining

As educators or teachers, producers,computer programmers, software devel-opers, or professional people in general,we are rarely encouraged to draw on ourown learning experiences in order to betterunderstand the reasons, purposes, and pro-cesses of learning and teaching our subjectmatter. Too often we tend to forget whatwas really difficult for us to understand, orwhy one learning experience was more orless valuable for us than others in thecourse of our own intellectual and profes-sional development.

It has been observed by students andeducators in our group as well as by many"experts" that the best way to learn a sub-ject is to teach it. Let us consider for a mo-ment, experiences that are common to pro-fessional people in all fields in the course oftheir everyday work or professional train-ing. Teachers, for example, often remarkthat they "finally understood something to-day for the first time" when a student askedfor an explanation of something he did notunderstand. Some of our friends (profes-sional computer programmers) at MIT havetold us that they "really" learned how toprogram when they had to teach it to some-

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one else—or when they were involved in areal, complex, long, and meaningful pro-gramming job. Many university professorschoose to teach a course on the theory oftopic of their research while they are actu-ally working on it; so that the process ofteaching and discussing their work withstudents, will enable them to clarify andrefine their own ideas and theories. And itcertainly seems to be the case in the educa-tional software field, that the people whoare having the most fun, and are learningthe most, are the software designers andprogrammers. With most educational soft-ware today, especially the drill-and-practicekind, the users rarely gain deep under-standing of the concepts taught, unless thesoftware is supplemented by instructionand explanations from a good teacher. Butthe designer, who spent a long and inten-sive period of time designing, learning, andthinking of ways to build explanations andgraphical representations for given con-cepts (even for the simplest form of educa-tional software), has probably masteredthese concepts and gained a much deeperunderstanding of them than they were ableto convey in the software product itself.

The intellectual benefit of generatingone's own explanations have been stressedby a number of theorists. Piaget, for exam-ple, has argued that higher level reasoningoccurs in a children's group in the form ofarguments. These arguments, according toPiaget, help children construct and internal-ize ideas in the form of thought. Such ob-servations prompted Piaget to concludethat the very act of communication pro-duces the need for checking and confirmingone's own thoughts (e.g., Piaget, 1953).Furthermore, in the Child's Conception ofSpace (1967), Piaget emphasizes how diffi-cult it is for young children to decenter—that is, to move freely from their own pointof view to that of another, in either literal ormetaphorical senses. Increasing communi-cation develops the child's ability to decen-ter, and to come closer to an objective viewof the whole. The process of decentering,says Piaget, is fundamental to knowledgein all its forms.

Among contemporary researchers,Brown, for example, has done many stud-ies to elucidate the ways in which explana-tory processes, as part of reciprocal teach-ing activities, motivate learners andencourage the search for deeper levels ofunderstanding and subject mastery. Browncharacterizes these explanatory-based in-teractive learning environments as onesthat push the learners to explain and repre-sent knowledge in multiple ways and there-fore, in the process, to comprehend it morefully themselves. The interactions could besupported by computers, teachers, or otherlearners (e.g., Brown, 1988).

Hatano and Inagaki (1987) also arguethat comprehension and interest is en-hanced where students have to explaintheir views and clarify their positions toothers. In the process of trying to convinceor teach other students, they explain, "onehas to verbalize or make explicit that whichis known only implicitly. One must examineone's own comprehension in detail andthus become aware of any inadequacies,thus far unnoticed, in the coordinationamong those pieces of knowledge." Theirstudies demonstrate how persuasion orteaching requires the orderly presentationof ideas, and better intra-individual organi-zation of what one knows. It also invitesstudents to "commit" themselves to someideas, thereby placing the issue in questionin their personal domains of interest (Hata-no & Inagaki, 1987, p. 40).

Fourth-grade children seldom havesuch opportunities. Peer teaching or recip-rocal teaching can be used to take a smallstep in that direction. We feel that ISDP tooka much larger step.

Designing For Learning

In Knowledge as Design, Perkins (1986)discusses in detail the instructional philoso-phy that supports the creation of a designenvironment for learning, arguing that theact of designing promotes the active andcreative use of knowledge by the learner—

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the designer. In the designing process,Perkins says, the problem's meaning is notgiven by the problem itself; rather, the de-signer imposes his own meanings and de-fines his own goals before and during theprocess. The goals and the sub-goals maychange over that period of time, and keep-ing track of these changes is a central inter-est when the design task is not for the pur-pose of "getting it right," but is insteadaimed at producing something usefulthrough the use of creative and criticalthinking.

Schon's work (1987) is also relevant tothis theme. He is interested in how differentdesigners (e.g., architects) impose theirown meaning on a given open-ended prob-lem, and how they overcome constraints(created by themselves, or given as part ofthe problem they solve) and take advantageof unexpected outcomes. This interactiveprocess requires high-levels of reflectionand develops the ability to "negotiate" withsituations in "as needed," and creativeways.

What is the difference between pro-gramming as such and designing a piece ofinstructional software? How does it relateto the "knowledge as design" framework?

A "computer program" is an indepen-dent entity consisting of a logically ar-ranged set of programming statements,commands or instructions, that defines theoperations to be performed by a computerso that it will achieve specific and desiredresults. We use the term "instructional soft-ware design" to refer to the building of acomputer program that has a specific in-structional purpose and format—muchmore is involved than mere programming.In this context, the lessons constructed bychildren were composed of many computerprocedures or routines (i.e., isolated units)that were connected to each other for thepurpose of teaching or explaining fractionsto younger children. A unit of instructionalsoftware is a collection of programs thatevolve through consideration of the inter-face between product and user. The in-

structional software must facilitate thelearning of something by someone.

Designing and creating instructionalsoftware on the computer requires morethan merely programming it, more thanmerely presenting content in static picturesor written words, more than managingtechnical matters. When composing les-sons on the computer, the designer com-bines knowledge of the computer, knowl-edge of programming, knowledge ofcomputer programs and routines, knowl-edge of the content, knowledge of commu-nication, human interface, and instructionaldesign. The communication between thesoftware producers and their medium is dy-namic. It requires constant goal-definingand redefining, planning and replanning,representing, building and rebuilding,blending, reorganizing, evaluating, modify-ing, and reflecting in similar senses to thatdescribed by Perkins and Schon in theirwork.

In terms of the programming end of it,software designers must constantly moveback and forth between the whole lessonand each of its parts, between the overallpiece and its subsections and individualscreens (e.g., Adelson & Soloway, 1984; At-wood, Jefferies, & Poison, 1980; Jeffries,Turner, Poison, & Atwood, 1981). Becauseof the computer's branching capabilities,the designer has to consider the multipleroutes a user might take, with the resultthat the nonlinear relationship between thelesson's parts can grow very complex.Moreover, the producer needs to design in-teractions between learner and computer:designing questions, anticipating users' re-sponses, and providing explanations andfeedback—which require sophisticated pro-gramming techniques. Finally, the child-producer who wants to design a lesson onthe computer must learn about the content,become a tutor, a lesson designer, a ped-agogical decision-maker, an evaluator, agraphic artist, and so on. The environmentwe created in ISDP encouraged and facili-tated these various processes, and there-fore we believe, contributed to the results.

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SUMMARY ANDCONCLUSIONS

This paper had a double intention: todescribe ISDP, and to situate this particularproject in a general theoretical frameworkcalled Constructionism. ISDP offered a real-istic and comprehensive model for our con-structionist vision of education in general,and for the use of computers in educationin particular. It also offered a model for thekinds of research that we find insightful andbeneficial to our understanding of learningand development, thinking, teaching, edu-cation, and the use of computers to facili-tate these processes.

We described how the participant ISDPclass, comprised of 17 fourth-grade stu-dents, integratively learned mathematics,design, and programming, etc. in thecourse of using LogoWriter to developpieces of instructional software for teach-ing third-graders. We illustrated various as-pects of our evaluation—quantitative andcomparative results, as well as qualitativeones. Our evaluation showed that the ISDPstudents achieved greater mastery of bothLogo and fractions as well as improvedmetacognitive skills than did either controlclass. The ISDP approach of using Logoprogramming as a tool for reformulatingfractions knowledge was compared withother approaches to using Logo, in particu-lar the traditional learning of programmingper se in isolation from a content domain,and was also compared with other ap-proaches of learning fractions. The ISDP ex-periment showed that simultaneouslylearning programming and fractions wasmore effective than learning them in isola-tion from each other.

The ISD Project recast fractions learn-ing in essentially three ways:

(1) it emphasized more involvementwith the deep structure (represen-tations) over the surface structureof rational-number knowledge (al-gorithms);

(2) it made fractions learning instru-mental to a larger intellectual andsocial goal, that is, having studentsthink about and explain what theythink and learn, in an interactive les-son designed for younger children;and

(3) it encouraged both personal ex-pression and social communicationof rational-number knowledge andideas.

We emphasized the fact that ISDP hadlittle to do with the idea that learning Logois in itself either easy or beneficial. We as-serted that in different contexts the importof the phrase "learning Logo" can differ sogreatly, that the question borders on mean-inglessness. Nevertheless, in the particularcontext of the ISD Project, where Logo wasintegrated into a total context, and wherestudents programmed intensively and ex-tensively, one can meaningfully begin toinvestigate the question of how various fea-tures of Logo contributed to the success ofthe children's work.

We found that Logo facilitated the on-going personal engagement and gradualevolution of different kinds of knowledge;and at the same time, it also facilitated thesharing of that knowledge with other mem-bers of the community, which in turn en-couraged the learners to continue and buildupon their own and other people's ideas. Inshort, Logo facilitated communicationsabout the processes and acts of cognitionand learning. We do not maintain that onlyLogo could do this. But looking carefully atwhat specific features of Logo enhancedindividual cognition and social learningcan help guide us in future technologicaldevelopments. And indeed, ISDP providedus with many insights—cognitive/develop-mental as well as technological—into whatkinds of learning tools we want to developfor constructionist learning.

We mentioned that the ISDP should notbe viewed as a "very controlled treatment"type of experiment. The pedagogical situa-tion was quite complex, and one could for-mulate innumerable conjectures about the

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"real" source of the experimental chil-dren's learning. We concluded that ISDPallowed us to create a total learning envi-ronment in which some impressive inte-grated learning took place.

It was beyond the scope of this study tosingle out the contribution of the individualaspects of that environment. In our view, amore complete understanding of this learn-ing process can come through an integra-tive and accumulative process of experi-mentation and theory-building (and thereare several projects of this kind within ourGroup at the Media Laboratory, e.g., Harel,1990c). This article is also intended as acontribution to that process, in which weshared our conjectures and the bases onwhich we formulated them. We hypothe-sized, for example, that improvements inperformance among ISDP students couldhave been affected by factors related to:the affective side of cognition and learning;the children's process of personal appro-priation of knowledge; the children's use ofLogoWriter; the children's constructivist in-volvement with the deep structure of frac-tions knowledge; the integrated-learningprinciple; the learning-by-teaching princi-ple; and the power of design as a learningactivity.

supported by the IBM Corporation (Grant #OSP95952), the National Science Founda-tion (Grant # 851031-0195), the McArthurFoundation (Grant # 874304), the LEGOSystems A/S, and the Apple Computer Inc.The preparation of this paper was sup-ported by the National Science Foundation(Grant # MDR 8751190). The ideas ex-pressed here do not necessarily reflect thepositions of the supporting agencies.

We are deeply grateful to Linda Moriar-ty, who made an essential contribution tothe Project and to the research ideas report-ed here. Over the years, many other teach-ers in Project Headlight at the HenniganSchool contributed indirectly, but very im-portantly, to the work. We thank all the stu-dents and teachers of Headlight—withoutwhom this project would not have beenpossible.

We thank Aaron Falbel and BethRashbaum for their editorial assistance,and other members of our Epistemologyand Learning Group for their contributionin their inspiring discussions of the ideaspresented in this paper. We thank YasminKafai for her help in the preparations of thestatistical tables.

However, the main point we wanted tomake here was that each one of those con-jectures, when considered alone, wouldgive only very partial information about themeaning of the results. By consideringthem together, and by speculating abouttheir interrelations, we are endeavoring tomake use of the very kind of holisticapproach—to knowledge and cognition,and to the development of learningtechnologies—that we believe informs andcharacterizes Constructionism in general,and ISDP in particular.

Acknowledgements: The researchreported here was conducted at ProjectHeadlight's Model School of the Future dur-ing 1987-88 as part of Idit Harel's Ph.D The-sis at the MIT's Media Laboratory; and was

REFERENCES

Ackermann, E. (1990). From decontextualized to situ-ated knowledge. In I. Harel (Ed.). Constructionistlearning: A 5th anniversary collection of papers.Cambridge, MA: MIT Media Laboratory.

Adelson, B., & Soloway, E. (1984a). A cognitive modelof software design. Cognition and ProgrammingProject, (Research Report No. 342). New Haven, CT:Yale University.

Adelson, B. & Soloway, E. (1984)b. The role of domainexperience in software design. Cognition and Pro-gramming Project, (Research Report No. 25). NewHaven, CT: Yale University.

Atwood, M.E., Jefferies, R., & Poison, P.G. (1980,March). Studies in plan construction I and II. (Tech.Report No SAI-80-028-DEN). Englewood, CO: Sci-ence Applications Inc.

Behr, M.J., Lesh, R., T.R., & Silver, E.A. (1983). Rationalnumber concepts. In R. Lesh & M. Landau (Eds.),Acquisition of Mathematics Concepts and Pro-cesses. New York: Academic.

Dow

nloa

ded

by [

Idit

Har

el]

at 1

0:34

08

Sept

embe

r 20

14


Behr, M.J., Wachsmuth, I., Post, T.R., & Lesh, R. (1984).Order and equivalence: A clinical teaching experi-ment. Journal of Research in Mathematics Educa-tion, 15 (5), 323-341.

Brown, A.L., Bransford, J.D., Ferrara, R.A., & Cam-pione, J.C. (1983). Learning, remembering, and un-derstanding. Handbook of Child Psychology: Cog-nitive Development, 3, New York: Wiley.

Brown, A.L. (1984). Reciprocal teaching:Comprehension-fostering and comprehension-monitoring activities. Cognition and Instruction,7(2), 117-175.

Brown, A.L. (1988). Motivation to learn and under-stand: On taking charge of one's own learning.Cognition and Instruction, 5(4), 311-322. Hillsdale,NJ: Erlbaum.

Brown, J.S., Collins, A., & Duguid, P. (1989). Situatedcognition and the culture of learning. EducationalResearcher, 18(1), 32-42. AERA.

Carver, S.M. (1987). Transfer of LOGO debugging skill:Analysis, instruction, and assessment. Un-published doctoral dissertation, Carnegie-MellonUniversity: Pittsburgh, PA.

Chipman, S.F., Segal, J.W., & Glaser, R. (1985). Think-ing and learning Skills. Vol. 1 & 2, Hillsdale, NJ:Erlbaum.

Collins, A. & Brown, J.S. (1987, April). The new ap-prenticeship. Paper presented at the American Edu-cational Research Association, Washington, DC.

Falbel, A. (1990). The computer as a convivial tool. In I.Harel (Ed.). Constructionist learning: A Sth anniver-sary collection of papers. Cambridge, MA: MIT Me-dia Laboratory.

Golman Segall, R. (1989a, February). Videodisc tech-nology as a conceptual research tool for the studyof human theory making. Unpublished manuscript.Cambridge MA: Media Laboratory, MIT.

Golman Segall, R. (1989b, November). Learning con-stellations: A multimedia ethnographic descriptionof children's theories in a logo culture. Un-published Ph.D Thesis Proposal. Cambridge MA:Media Laboratory, MIT.

Harel, I. (1986, July). Children as software designers:An exploratory study in project headlight. Paperpresented at the LOGO '86 International Confer-ence, Cambridge, MA: MIT.

Harel, I. (1988, June). Software design for learning:Children's construction of meaning for fractionsand logo programming. Unpublished doctoral dis-sertation, Cambridge, MA: Media Laboratory, MIT.

Harel, I. (1989a, April). Tools for young software de-signers. Proceedings of the Third Workshop ofEmpirical Studies of Programmers (ESP Society).Austin, TX.

Harel, I. (1989b, June). Software design for learning. InW.C. Ryan (Ed.). Proceedings book of the nationaleducational computer conference (NECC). The In-ternational Council of Computers in Education,Boston, MA.

Harel, I. (1989c, September). Software designing in alearning environment for young learners: Cogni-tive processes and cognitive tools. Proceedings ofthe FRIEND21 international symposium on next

generation human interface technologies. Tokyo,Japan.

Harel, I. (1989d, September). Software design forlearning mathematics. In C. Maher, G. Goldin, & R.Davis (Eds.), Proceedings book of the eleventh an-nual meeting of psychology of mathematics educa-tion. Rutgers University, New Brunswick, NJ: Cen-ter for Mathematics, Science, and ComputerEducation.

Harel, I. (1990a). Children as software designers: Aconstructionist approach to learning mathematics.Journal of Mathematical Behavior, 9(1), 3-00.

Harel, I. (1990b). The silent observer and holistic note-taker: Using video for documenting a research pro-ject. In I. Harel (Ed.) Constructionist learning: A 5thanniversary collection of papers. Cambridge, MA:MIT Media Laboratory.

Harel, I. (1990c). (Ed.). Constructionist learning: A 5thanniversary collection of papers. Cambridge, MA:MIT Media Laboratory.

Harel, I. & Papert, S. (1990). Instructionalist productsvs. constructionist tools: The role of technology-based multimedia in children's learning. Cam-bridge, MA: MIT Media Laboratory. (Paper in pro-gress).

Hatano & Inagaki (1987). A theory of motivation forcomprehension and its applications to mathema-tics instruction. In T.A. Romberg & D.M. Steward(Eds.), The monitoring of school mathematics:Background papers. (Vol 2.): Implications frompsychology, outcomes from instruction. Madison,Wl: Center for Educational Research.

Jackson, I. (1990). Children's software design as a col-laborative process: An experiment with fifthgraders at project headlight. In I. Harel (Ed.). Con-structionist learning: A 5th anniversary collectionof papers. Cambridge, MA: MIT Media Laboratory.

Janvier, C. (Ed.) (1987). Problems in representation inthe teaching and learning of mathematics. Hills-dale, NJ: Erlbaum.

Jefferies, R., Turner, A.A., Poison, P.G., & Atwood,M.E. (1981). The processes involved in designingsoftware. In J.R. Anderson (Ed.), Cognitive skillsand their acquisition. Hillsdale, NJ: Erlbaum.

Kafai, Y., & Harel, I. (1990). The instructional softwaredesign project: Phase II. In I. Harel (Ed.). Construc-tionist learning: A 5th anniversary collection of pa-pers. Cambridge, MA: MIT Media Laboratory.

Lammer, S. (1987). Programmers at work. Redmond,WA: Microsoft Corp Press.

Latour, B. (1987). Science in action: How to followscientists and engineers through society. Cam-bridge MA: Harvard University Press.

Lawler, R. W. (1985). Computer experience and cogni-tive development: A child learning in a computerculture. West Sussex, England: Ellis Horwood Lim-ited.

Lesh, R., & Landau, M. (1983). Acquisition of mathe-matics concepts and processes. New York: Aca-demic.

Minsky, M. (1986). Society of mind. New York: Simonand Schuster.

Motherwell, L. (1988). Gender and style differences in

Dow

nloa

ded

by [

Idit

Har

el]

at 1

0:34

08

Sept

embe

r 20

14


a logo-based environment. Unpublished doctoraldissertation, Cambridge MA: Media Laboratory,MIT.

Papert, S. (1971a). Teaching children thinking. (AlMemo No. 247, and Logo Memo No. 2). Cambridge,MA: MIT.

Papert, S. (1971b). Teaching children to be mathemati-cians vs. teaching about mathematics. (Al MemoNo. 249 and Logo Memo No. 4). Cambridge MA:MIT.

Papert, S., Watt, D., diSessa, A., & Weir, S. (1979). Finalreport of the brookline logo projects. Part I and II.(Logo Memo No. 53). Cambridge MA: MIT.

Papert, S. (1980). Mindstorms: Children, computers,and powerful ideas. New York: Basic Books.

Papert, S. (1984a). Microworlds transforming educa-tion. Paper presented at the ITT Key Issues Confer-ence, Annenberg School of Communications, Uni-versity of Southern California, Los Angeles.

Papert, S. (1984b). New theories for new learnings.Paper presented at the National Association forSchool Psychologists' Conference.

Papert, S. (1987). Computer criticism vs. technocentricthinking. Educational Researcher, 76(1), 22-30.AERA.

Papert, S. (1990). An introduction to the 5th anniversa-ry collection. In Harel, I. (Ed.). Constructionist learn-ing: A 5th anniversary collection of papers. Cam-bridge, MA: MIT Media Laboratory.

Pea, R.D. & Sheingold, K. (Eds.) (1987). Mirrors ofmind: Patterns of experience in educational com-puting. Norwood, NJ: Ablex.

Perkins, D.N. (1986). Knowledge as design. Hillsdale,NJ: Erlbaum.

Piaget, J. (1955). The language and thought of thechild. New York: New American Library.

Piaget, J. & Inhelder, B. (1967). The child's conceptionof space. New York: W.W. Norton.

Resnik, M., Ocko, S., & Papert, S. (1988). Lego, LOGO,and design. Children's Environments Quarterly,

5(4), New York: Children's Environments ResearchGroup, The City University of New York.

Resnick, M. (1989, April). Lego Logo: Learning throughand about design. Paper presented at the AmericanEducational Research Association. San Francisco,CA. Appeared in Harel, I. (1990). (Ed.). Construc-tionalist learning: A 5th anniversary collection ofpapers. Cambridge, MA: MIT Media Laboratory.

Sachter, J.E. (1989). Kids in space: Exploration intochildren's cognitive styles and understanding ofspace in 3-D computer graphics. Unpublished Ph.DThesis Proposal. Cambridge, MA: Media Labora-tory, MIT. A short version of this proposal appearedin Harel, I. (1990). (Ed.). Constructionalist learning:A 5th anniversary collection of papers. Cambridge,MA: MIT Media Laboratory.

Schon, D.A., (1987). Educating the reflective practi-tioner. San Francisco: Jossey-Bass.

Scribner, S. (1984). Practical intelligence. In B. Rogoff& J. Lave (Eds.), Everyday cognition: Its develop-ment in social context. Cambridge, MA: HarvardUniversity Press.

Soloway, E. (1984). Why kids should learn to program?(Cognition and Programming Knowledge ResearchReport No. 29). New Haven, CT: Yale University.

Suchman, L. (1987). Plans and situated actions: Theproblem of human machine communication. Cam-bridge, MA: Cambridge University Press.

Turkle, S. (1989). The second self: Computer powerand the human spirit. New York: Simon & Schus-ter.

Turkle, S., & Papert, S. (1990, in press). Epistemologi-cal pluralism: styles and voices within the comput-er culture. Signs Journal. Chicago, IL: The Univer-sity of Chicago Press. Also appeared in Harel, I.(1990). (Ed.). Constructionalist learning: A 5th anni-versary collection of papers. Cambridge, MA: MITMedia Laboratory.

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nloa

ded

by [

Idit

Har

el]

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