or an äracle-rhat can check rhe corre4ness of students, solution proposals, they lack .... n. h *t" colnoo"irion tinaenon, t'Seo, l9a9), which can be based on the ...
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Prblished by Association for the Advancement ol Computing in Education (AACE) P.O Box 2966 Chadotewille, VA 22902 USA Prinled in the USA
tsBN 1-880094-16-9
Towards an Epistemology of Intelligent Problem Solving Environments: The Hypothesis Testing Approach Claus Möbus D eP artme nt of I nfo rmat i c s
I'eaming and Teachinq S)stems C.v.O. Unirersitj, 261t 1 OuenbutS' Gemanr E - M ail : C la u s M o e b us @ info rnati k uni' o Ae nb w 8. de -
Absträct Tbe main purpose ofintetligent lmblem lolving gnvironments @SEs) is
to offer students the oppoauniry lo acquire knowledge whi le working on a sequence of problems chosen ftorn the domain Up to now we have developed IPSES for various cunicula and aPplications (computer science, hy&aulics' chemistry' economic simulation games and causal modeling). On lhe surface being very differen. all IPSES follow a corrunon d€sign lheorv: the student shoüld acquire knowledge by testing hj' o\rn hypolheses First 1'e want to show thal hlpothesis l€sting plays a tundamental role m a cognitive science oient^tEd theory oi knowledge acquisiton 0sP-Dl-_theory) This th;ry is the basis of our IPSES ln a case studv dree IPSES and lheü relationshrp to hypoihesis testi g are discussed. Then we define the concept of hyPothesis testing learning we describe knowledge acqusition erentsin'a logic -It isftarnöwork. IPSES is based stimulated by acquisition knowledge that argued effects. fundanentally on selfexplaining the responses of the IPSE to the student's
{d
hypotheses.
Introduction It
difficult questions, lile: fiov a,ra ins*ucrioinal naterial ro be deirgned? When should remedial information be suppli€d? Why is ltre
has been well recognized thar the development of intelligent help systems Iaises
i" r,.io
sameinfocmduonuselesstoonepersonandhelpfulroanother]ExisrlnginlelligenttutorialandbelD'51t0ü have not always Fovided satisfaciory answers o such quesrions. For example. rhe rnformation delivered loüe
Äume too tirtle or too ;uch knowtedge. the user interartion is _too reslnctive, or nrtoring and hl! unprincipled and ad hoc. These shon€omings are basicallv stiil rrue (Sef, 1990) To mak€ lome äe itrategies teamer rnay
p-g.;"i t *.!ti*t i."-"work seems ro be necessary. h should b€ sufficiendy. detailed. r,o enable sp€cjft " and oredicrions. Ar the same rime ir should be so general rhat ir is appticabl€ !o diffeßd ä."i_ a""isron" domäns. This paper is-a fißI steP in that direction: we trv to desüibe üe epistemologv of IPsEsiron our pätit or view 1ncll'igenr problem solving Environments (IpsEs) seem to be rhe most
cosr efle.li$
inlellisentsvs.emsfCJrthecommunicadonofproblemsolvingknowledge.Thoughtheycontainanexpensysen or an äracle-rhat can check rhe corre4ness of students, solution proposals, they lack other expensive cornpo'!ß üke a teactring or a stuaent model. The curricular component in form of a teaching model is abandoned in hv0i i***" of task-relevad problerns. The student model which should be responsible for lh "i" "i."1. inatuiauii"uCotiof.yrt m responses is nissing, too- Inst€ad of that individüalization is achieved by the abiliry oitfr" ry.t"- to t".päna intelligently to student hypotheses ln IPsEs an expert system (or an oracle) adlh cürrent student hypothesis are sufficient to generate adaptive help. ro avoia deiign errors the design of IPSES should be guided by a psvchological r\@ry o'f k]idvhJ{l acquisition. Our ;Ark is based on ISP-DL-Theory, an acronvm for "Impasse-Success-Problem$olvingDiiwn' te;ing". ISP-DL is influenceal by .he cognjtive theories of ANDERSoN (Anderson. 1986, 1989), NEWEII
138
t-
van LEHN (1988) as well as by the motrvational "Rubikon" theory of mCKIIAUSEN (1987' 1989) part 2 and design principles for IPSES which can be and GOLLWTTZER (1990). The rheory is sketched in are discLrssed in pan hronnatlv ) derived irom 'r (derivation of To deironstrate the feasibili ry of rhesa ideas rhree case studies from different domains 11990)and
I
'
functionalprogTans'modelingtime-discretedistnbutedsystemqroomconfigumtiontasks)withverydiffefent *-nL*;" anä nonmonotoniil oroblem spaces are presented in pan 4 ll is shown how ciose one can sticl lo a phjtotopt'l despiie differenie. in knöwledge domarns and desprre lhe use of v€ry diilerenr AJ-
$"iJa.rien ,i.hnr*r r-inföttn.a siar.t',
rule-based grarnmars. modelchecking and inductive leaming) and abstraci the results of the case studies. we define formallv the concept of a into tlteor) lvnorlr'esis in a fnowledee revision framework W€ show thal bpothesis testing can be integrated qnation wft?' we discuss the probl€m solver' abstract processes of an r'iisw ana *,o-leaee2cq4r"rirrotr
- i; ;;; i ;"
""r'-*r.
r-"r"a* -o-sltioi
evena will ha;Den and
trdt
kind of knowtedge is acquired when worklng with
'hese hypothesii that knowtedge acquisirion stimulated by IPSES is based tundämentaUy to his hvpoüeses ot the IPSE lhe responsec F) to selfeiplain mrelfe\pl;alion: the sludeniahould
mrr. lü" or"i.n, ou,
,"n
ISP-DL: A Theory of Knowledge Acquisition Fomourownempiricalinvestigationsotöbus&scht'del'1993)weconcludedthatitisfruitfultodescribe iÄi,,g us an int"rptay or irnpaie- and success-driven leaming. tn particular. we d€vetop€d a model based on ii". .i"".,t, *f,ii,f, ifo*tv;imutares üe conlinuous stream of actions and verbalizations of a single subject of Droblems (Möbus, Schtkler & Thole, 1995) Further development led to the .i r" '"iti'" - " ."o*"ie Schröd;r & Thole, 994) which is intended to describe the str€am of acdons and isp or n'""ä rMöb;. 1
,"-irive nrocisses occurrinq in Droblem solvrng siluauons tSP DL Theory has thre€ aspecß: "";
1990) In the n.'a*ri*,i." of diereit probten sofuing phases (Heckhausen, 1989; coltwitzer' pl" a solurron one ln the goals finalb chooses and problem severäl Phase solveiconsiden ftLDzrarp ohase rhe plan or is erecured Then the sequenced cr€äkd and are Subgoals the t; obrdn ir'" ;. a.i,.too"a eoal. 'iDtenz&ed.
'".-lin"
iinallv
rhe prcblem lolver e'al"zter the resuh
new knowLedge (Laird et 41., 198?; van Lehn, 1988; Newell, 1990) üe goal an impasse occuß In resPonse to an impasse' the imPlement vlen tnowielge is not sufficient to weak heuristics, like asking questions and lookng for help Thus theory to the u"coraing oolt"r sorr".äpple" l*iÄer ottairii new inrormaäon. As a rasult of this, .he leamer may overcome tbe impasse and acquire new may cause a mo*leage. ttrus impasses Figger the acElßition of knowledge But &e new information secondary problem. imFoved: iuccess driuen improrement of eristing ho"/edSe Successfully used knowledge will be (Möbus' method on the resotution be based which can l9a9), t'Seo, ,.n. h *t" colnoo"irion tinaenon, reduced' a fr'ot., t Sel l. Thus the number of control dec isions and subgoals can be iirnoü.r '' wiJo*ai""i ISp-iI- tft"ory with higher order Petri nets (Huber et al . 1990) A sketch of th€ theory is ,no*in ngu." r. L""-lng has iwo aspects: the process of knowtedgeoprimzarion occuJs afur a solurion has knowledge is a logical consequence of urr" i"""a.T,f" p-1"" t"zrarctivd i;the s€nse that the new opÜmized
iiriu" äa*i
*nuistiott of
--',#
old
knowledge:
ba€kground knowledge !-, €vid€nce l= optimized knowl€dge help llß nore interesting knowledge acquisition Focess occuß after solutions have been found witb the heuristics.
of
This process is irdxctive:
backgrcünd knovl€dge
u
new knowledge l= evidence
be seen as inductive inference .ules. "" lha! heuristics can r,yp"lhesis testing activirie"s? we assume that tbe problem sotver has a solurion proposal wr,"" Jo "ip."t ii ävaluated by ;enut of rcal rime sinulation or asking an oracle (eg. the IPSE). when r* rr," aven rast. so
*"
ir*
lr-"""",i* f*aS""*,r,e studeni realizrs an impasse. The reacrion to tbat is planning and use of weak ir*i*.t. ö". *t" ;. t€sting a hlpoüesrs: that means askjng the IPsE-system questrons conceming the part of mv solution Proposal emheddäble in a ,rf"tlon .t"t* of"fp"te ot the orilinl äifective proposat: "Is this ,l."
=-
lr}I/SDL-Ner
Figure
I
: ISP-DL Ituowl€dg€ Acquisition Th€orv
Principles of Design for IPSES Based on ISP'DL Theory The ISPDL Theory motivates the followirg
princiPles:
,
constrain and inteftupt the problem solver but offer information only on dernand js eccoiding to ttre ttreory, information is onty helpful al impasse time. Tfus principle in contrast to active help jmponant develoP her/hjs o$n to let rhe leamtr firsl systems ;ith irunediite feedback. We think thar it is generating unusual "creative" in are rathd As novices his solutions s;lüion ideas and then later optimize powerful. be sufticiently the systems should solutions (2) The student should have the opPotunity to obtain delailed fe€dback and infonnadon a'y ttme Since a simplified sketch of rhe impa;ses are possible at diferent phases ol ptoblem solling (figure I gives
(1) The IPSE ;hould
thäry withoüt any
,'rt
recursibns;, the
-only sy"t"- rrust offer support in the problem solving
phases Piar'?rng
inDle n ?ntation. and evaluaio^ ' (3) The leame. should b e enableÄ ro Mke use of har/his pre'kno\9ledge as much as possible when asking fol
help.Thustheinfornationprovidedshouldbeconditionaltohishypothesesandpreknowledgetoavoidfolio{'
-
uP impasses.
(4t Tbe information provided should in 8rarrrtze and arnount be tailared to the bowledge stote of the oroltem solver. ff rhe erainsze ot the infomation is too fine or too coarse and the amount not synchrcnized to ihe knowledee deficii üen rhe problem solver has to filter or genemte new information which can hare undesirable
;otionat
eff€cts prevanting any progress An (expensive) rt iden, n odel is needed only
iff
there is
a
set ofhelp altematives to choose ftom. (5) It is necessary rhat ihe learner is free in the choice of his o'oblem solving operators and her/his inteßction modality. W€ shoutd offer ar.IPSE for free and unconstrained prcblen solving-
140
Case Studies
I
Now rve wart to describe thre€ systerns (figures 2-4) which are designed according to ISP-DL theory and u/hich oable hypothesis testing for the student. The first two IPsEs were developed for computer science and the third for health care curicula. The idea of a hypoth€sis testing environment was first develoPed for the ABSYNT system (Möbus. Thole & Schdjder, 1993a). Figure 2 shows a typical problen solving state: the reversal of a list. The solution proposal contains opemtors and planning/goal nodes. The nexa system is PETRI-HELP- The sysaem suppo(s the modeling of distributed time discrete systems (€g. taffrc lights, production plants. libraries, telePhone nets) with simple condition-event nets. The transilion of nets can be c;mpared to productions in a production systeüt (Zsrnan, 1978). Figure 3 shows ä solution Foposal to nodel the photosynthesis process.
The third system
IKEA was developed as an IPSE within a classical CBT-couße for the catholic
care
mganisation CARITAS. The CBT-couße should tsain service personal for elderly handicapped peoPle. One of üa lasks in the tsaining course consisted in communicating knowledge how to configure a rcom for a Peßon who needs help in every day live. Figure 4 shows draught) and some fumiture already placed
the room witb some regions (door, sun, window, washing'
'Ihe tlüee knowledge domains differ eg. with respect to the availability of expe( knowtedge. In functional Vosiarll'mine expen knowl?dge is in pnncjple available to derive correct solutions fiom a formal specification ihough rhe programmer may nol use i(. ln Peh-net modeling ,?o €?en knowledge is availab\e for the correct deduction of nets liom temporal logic specificalions, though it is possible to check the correctness of a students' solution proposal: model checking. Students solve &e problem only with rules of thumb or with heuristics. In co0figuring rooms a subset of the expens knowledge belongs to commonsense kn rledS€ (eg.: a hed should nol positioned in the draught region: a tv-set should not face the wall, etc). This knowledge is sometimes intuitively available to the student-
ABSYNT ABSYNT ("Abstract SynEx Trees") supports programming novices with help and proposals while thev acquirc functional progtamming concepts including rclu1sion. ABSYNT was designed to encourage explomtive Ierming. The ABSYNT system consists of four main Pafls. (l) a tisual editor for constructing programs. ABSYNT programs consist of tsees built {iom connected Primitive and self-defined operator nodes, parameters, and constints. ln addition progran plans can b€ constnrcled usltt9 Soal nodes.. (2) A visual trace makes ea.h comDurational step of the A.BSYNT interpreter visible. (3) h a diaenosis', hrpotheses' and hzlp em'itu nent (or part of üal proposal, to a progammrng rire üamer may siare Lhe h)pothesrs lhal her/his solutron proPosal task is corec!. The system then analys€s the pan of the solution Foposai chosen by the student as a hlTothesis-
the sysleh gives help and eror feedback on the imPlementution a\d plarüing lelel by synthesizing complete solutions for the given Fogramning tasks, staning ftom the leamer's hyPothesis lf the
As the result,
enbeddable within a complere solution, lhe leamer may ask for completion proposalsFiglre 2 shows the program "lisl-reversal". Programs arc a tree repres€ntation of mixed tems. Tems arc
ftypoth€sis is
nixed when they contain runnable opemtors (round shaped nod€s) and not runnable specification terms (cloüd shaped nodes). The figur€ shows a hypofEsis stated by the leamer Oold Pani of the proposal in the uPper willdow) The hypothesis means: "Is the bold marked part of the solütion proposal embeddable in a corr€ca solution?" The system generates a complete solution but to offer minimal help information only one node is shown to the learner to stimulate self explanation (Chi et al., 1994) How-, ffiy-, and WhynolExplanations are available on demand, too.
PETRI-IIELP PETRI-HELP project (Pitschke, 1994, Schöder et at. 1995). a system is developed for supporting probtem in the domain of modelling with condition-event Petri nets. Like in ABSYNT, the svstem will provide help sensitive to the actual knowledge stale of üe leamer. But there are differences to ABSYNT or IKEA due to rhe sp€cial demands of the Petsi n€t donain: (l) specification of dle task, (2) the analvsis of the leämer's solution proposals (3) the generation of "episodic" rules on which belp information in the form of completion
In the
solvers
Foposal is based. a
specificanon of tasks. For Petri net modeling task we use temporal logic specifications (Kröger, 1987) These üe verification of leamers' Petri net proposals by model checking (Clarke et al.. 1986).
enable
141
Testing H1?otheses in ABSYNT IPSE for functional programming
Knoy,ledge Heüristics Itttzntians
Tran sformatio n
hv RDles
Analysis
of
t\
Solurions/ Diagnosis
of
Intention s
F€edback to Hypotheses
Fisur€ 2: Th€ Int€llis€nt Prcblem Solving Environm€nt ABSYNT
. Anabzinq the kamers'solution proposaß. We developed
. simple model checker (Clarke et a1.. 1986) for tie diagnosis of the user's solutions in PETRI-HELP. The diagnosis is based on .he case graph of the Peai net.In dlat graph, which describes all possible shtes of the system, the temporallogic fo.mulae of tie specification are verified. Thus it is possible to detect the set of formulae which is fulfilled by a user-created net. . Testine hypotheses. The student may state hypotbeses aboüt which temporal logic fomulae sÄle consideß fulfilled by the cunent state of the solution proposal. The system analyzes the hypotheses and gives f€edback accordingly. The model checker may be used after every editing saep. If the formula contains not the temporallogic operators O ("next tine"), 0 ("eventually"), U ("always"), then it is a propositional-logic formula rnd will be evaluat€d inside the cMent node of the case graph. ff tbe formula has the pan€m O F (F is a formula), tlen F must hold in ev€ry immediate successor of the curent state in the case-gäph. 0 F is irue iff in every patl leaving the current node F will be true at leas. in one node. Finally, [] F holds iff F holds in every state on €very path leaving the current state. . Epßodic rules and help infommtion. T\ese rules will be leamt by the system when th€ model-ch€cker finds that a net-fragement is a model ofa specification subset. Completion proposals will be created r) lfte.rrrten on the basis otthe learnr episodic rule.. ' Explanations: Why and mynot-explanations can be given witb the case graph. This is similar to the lrace ir ABSYNT.
IKEA IKEA was developed, because a classical CBT program presenting configrra.ion rules and multiple choicc configumtion tasks caused motivational problens. Parts of the configuration knowledge betongs to
commonsense knowledge so that their presentadon fi replicadon is mther dull for the saudent. So we were askei to develop an IPSE. The students' task is to configure a room for a handicapped peßon. The sysrem can lest hypolheses (like: "Is my proposal embeddable into a correct solution?"), offer conpletion proposals and Wb. /Whynot-explanations. Explanations show tulfilled and üolated rules.
142
-
Taskspecification
& 4" Analysis
o .
Knowledge
Heuistics Intenlitns
of Student Proposal New
hsign-
e)
loowledge
Figur€ 3r The Inte[igent Problcm Solving Environment PETRJ-mLP
Theory Revision, Hypotheses, Knowledge Acquisition and Selfexplanations /,s we srated
before the fomulation and testing of hypotheses is an impoiant concept in the development of
IPSB. Though we may have an intuitive idea what a hypothesis is we try to give a forrnal definition. The dcfinition is €mbedded in the concept of theory revision (De Raedl, 1992). we try to be as absiract as possible so üat hypolhesis testing in various IPSES can be subsumed as special cases. The main poinls are summärized in Fisure 5. Accordins to ISP-DL tbeory therc are several steps whet acquiring knowledge with IPSES. (1) The problem $lver generätes with his subjective theory S evidence E, which may a solution proposal. From the viewpoint of an ideal expert this proposal may be wrong. (2) This Foposal E is submitted to the IPSE. If the proposal is in
it cannot be explained by the domain tüeory T. So the problem soiver can genemte a h'?othesis and Foposal E into two parts Efix and Emod. The student has the hypothesis that Efix can be embedded inro a conecr solurion. According to this partition th€re is a corresponding panition of the domain theory büt this
efior
partition his is
nol under
hypothesis.
conEol of the student. (3) Now, üe IPSE generates witti a revised tbeory T' a system response to the E is a system generated solution proposal, which contains Efix. Emod is help information for the
which in our IPSES is shown to the stüdent on demänd. (4) After these events (hopetully) we have some acquisition events. Th€ s.udent tries to explain E with its parts Efix and E mod to himselt According js an inductive infercnce and when we compare (1) with (4) it is at the same trme a theory revision to(4)this studeni
hrowl€dge
from S to S'.
$unmary to show how a cognitive theory of knowledge acquisition (ISP-DL) motivates the IPSE concept and hw the hypothesis testing capability can be described on a metalevel and implemented in vmious domains. Similar system for hydraulics, economic simulation games and causal modelling are under constsuction. we tried
143
Testing Hlpotheses in IKEA lnEractir€ Xno*l€dge aüd Dduc.tion'Applic.tion
Svslem
Knowledge Heuristics Intenti(ms
Amlysis of Student-
uinräted
9\
Btrr€s *u
cor.e.t
93J
Feedback
Completion-/Conectionproposals
Figrr€ 4: Th€ Intetligent Problem Solving En'ironmert IKEA
(1)
Problem
(2)
Testing
Solving:
ofHypothesis:
S l=
E
T = TfixU Tmod
where:
and: (3)
Revision of
Theory:
l*E
E= EfrxU Emod
Tftx
l= EfDr
T' = T6 U T'666 l= E where: Ei = EIix U E,moal
(4) Self€xplanation:
S' l= E'
Figure 5 : Prcblem SoIviDg, Hypoth€sis Testing and SeHexplanation
144
i
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& Thole, H.J. (1994). Diagnosing and Eväluating the Acquisition Process of in J.E. Creer, C. Mccalla (eds), Sludent Modelling: The Key to lndividualized Knowledge-Based lnstsuction (Proceedings of the NATO Advanced Research Workshop on Stualent Modelling, in St.Adel€, Quebec, Canada), Berlin: Springer (NATO ASI Series F: ComPuter and Systems
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Schröder, O. (1993a). Iüteractive Suppon of Planning in a Functional' Visual H Pain (eds), hoceedings AI-ED 93, world confereDce on Artificial ln.elligence and Education, Edinburgh. 362 - 369 Möbus, C., Thole, H.-J. & Sctuöder, O. (1993b). Diagnosis of Intentions and Interactive Support of Planning in rFünctioral, Visual Programming Language, in D.M. Towne, T de Jong, H Spada (eds), Simulation_Based E4eriential Learning, Berlin: Springer (NATO ASI Series F: Computer and Systems Sciences, vol. 122), 61 Möbus,
C., Thole, H. J.
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16
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for domains without explicit design theories, in: Proceedings of the Founh Int€mational Confererce on User Modeling (UM '94), Hyannis, MA.: The Mire Corporation. 191-195 Schritd€r, O., Möbus, C. & Pitschke, K. (1995). A Cognitive model of Desigt hocesses for Modelling Disrributei Systems, paper presented on AI-ED 95 (this volume) Self, J.A. (1990). Bypassing tbe Intmctable Problem of Student Modelling, in C Frasson, G. Gautbier (eds)' IrrelligentTutoring Systems, Norwood: Ablex, 107-123 K. (1988). Toward a Theory of lmpasse-Driven Iraming, in H Mandl, A- Lesgold (eds)' Leaming hsu€s for Intelligent Tutoring Systems, Berlin: Springer, 1941 Zisman, M.D.(1978). Use of Production Systems for Modeling Asynchronous Concurrent Processes' ini Waternan D.H. (et al.), Pattem Directed lnference Systems, New York Academic Press, 53-68 Vanl-€hn,
Aclnowt€dgements:
I
want to thank
ahe
following researcheß ftom our unit on "I-eaming and Teaching
Slstems" without lheir contribution this paPer would have been only dr"): Jing Folcke$, Knut Pitschke, Olaf Sctuöder, Heinz-Jijtgen Thole.
a dream: "Lufischloß" ("castle rnade of
145
