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ED 055 457 Goldberg, Adele a Generalized Instructional System DOCUMENT RESUME ED 055 457 EM 009 308 AUTHOR Goldberg, Adele TITLE A Generalized Instructional Systemfor Elementary Mathematical Logic. INSTITUTION Stanford Univ., Calif. Inst. for MathematicalStudies in Social Science. SPONS AGENCY National Science Foundation, Washington, D.C. REPORT NO TR-179 PuB DATE 11 Oct 71 NOTE 96p.; Psychology and Education Series EDRS PR/CE MF-$0.65 HC-$3.29 DESCRIPTORS Calculus; *Computer Assisted Instruction; *Computer Programs; *Mathematical Logic;*Mathematics Instruction ABSTRACT A computer-based instructionalsystem for teaching the notion of mathematical proofis described. The system is capable of handling formalizations of the fullpredicate calculus with identity and, with minor work, definitedescription. Designed as an instructional device, the program is also thebasis for a number of research projects involving the useof mechanical theorem-provers for teaching theorem-proving. The entire systemis presented here in detail: the program as written in the LISPprograming language for a PDP-10 computer. Instructions on how to usethe system for research and teaching, block diagrams of key programroutines, and example curriculums are included. Enough detailis provided so that versions in other languages for other computer systems maybe programed from the information presented here. (Author/JY) A GENERALIZED INSTRUCT I ONALSYSTEM FOR ELEMENTARY MATHEMAT I CAL LOG I C SCOPE OF INTEREST NOTICE The ERIC Facility has assigned BY this document for.gocessing to: In our judgement, this document is alsc of interest to the clearing- houses noted to the right. Index- ADELE GOLDBERG ing should reflect their special points of view. TECHNICAL REPORT NO. 179 OCTOBER 11, 1971 PSYCHOLOGY & EDUCATION SERIES INSTITUTE FOR MATHEMATICAL STUDIES, IN THE .SqC,tAL SC IENCES STANFORD UNIVER'SI Tlr cri STANFORD,CALIFORN IC) v..11 TECHNICAL REPORTS PSYCHOLOGY SERIES INSTITUTE FOR MATHEMATICAL STUDIES IN THE SOCIAL SCIENCES (Place of publication shown in parenthes.sipublished title is different from title of Technical Report, this Is also shown in parentheses.) (For reports no. 1.- 44, see Technical Report' no. 125.) 50 R. C. Atkinson and R. C. Geffee. Mathematical learning theory. January 2,1963. Or. B. B. Wo !man (Ed.), Scientific Psycho !eel,. New York: Basic Books, Inc., 1965. Pp. 254-275). 51 P. Suppe3, E. Crothers, and-R. Weir. Application of mathematical learning theory and linguistic analysis to vowel phoneme matching In Russian words. December 28,1962. 52 R. C. Atkinson, R. Ca Hee, G. Sommer, W. Jeffrey and R. Shoemaker. A test of three models for stimulus compounding with children. January 29,4963. U. tate. Psychol., 1964, 67, 52-58) 53 E. Crothers. General Markov modals for learning with Inter-trial forgeUing. April 8,19113. 54 J. L. Myers and R. C. Atkinson. Choice behavior and reward structure. May 24,1963. (Journal math. Psychol., 1964,1,170-203) 55 R. E. Robinson'. A setrtheoretical approach to empirical Meaningfulness of measurement statements. JUneI0, 1963. 56 E. Crothers, R. Weir and P. Palmer. The role of transcription in the learning of the orthowaphic representations of Russian sounds. June17,. 1963. 57 P. Suppes. Fsoblems of optimization in learning a list of simple items. July 22,1963. (In Maynard W. Shelly; 11 and Glenn L. Bryan (Ed.), Human Judgments and Optimality. New York: Wiley. 1964. Pp. 116-126) 58 R. C. Atkinson and E. J. Crothers. Theoretiwi note: all-or-none learning and intertrial forgetting. July 24, 1963. 59 R. C. °Wee. Long-term behavior of rats under probabilistic reinfertement schedulei. October 1, 1963. 60 R. C. Atkinson and E. J. Crothers. Tests of acquisition and retention, axioms for paired-assoclate learning. October 25,1963. (A comparison of paired-associate learning models having different acquisition and retention axioms, J. meth. Psychot., 1964,1, 285-315) 61 W. J. McGill and J. Gibbon.. The.generalmiamma distribution and reaction time's: November 20,1963. W. math. Psychol., 1965, 11-18) 62 M. F. Norman. Incremental learning on random trials. December 9,1963. U. math. Psychol., 1964., f2336-351) 63 P. Suppes.The development Of mathematical concepts in children. February-25,1964. (On the behavioral foundations of mathematical cOncepto Moemphs of the Society far Research in Child Development, 1965, 30,. 60-96) 64 P. Suppes. MaThematical concept formation in children. April 10,1964. (Arer. Etset2.9,1ist 1966, 21,139-150) 65 R. C. Calf**, R. C. Atkinson, and T. Shelton, Jr. MathemitiCal models for verbal !earning. August 21,T964. (In N. Wiener and J.-P. Schad:: (Eds.); Cybernetics of tne Nervous Systenn Prowess In Brain Research. Anesten'.....m, The Netherlands: Elsevier Publishing Co.;1965. Pp. 333-349) 66 L. Keller, 11.. Cole, C. J. Bake, and W. K. Estes. Paired associate learning with differential rewards. August 20,1964. (Reward and information values of trial mitcomes in piked associate learning. (PsychOl. Monogr., 1965, 79,1-21) 67 Id..F. Norman. A probabilistic model for free-responding. Decomber 14, 1964. 68 W. K. Estes and H. A. Taylor. Visual detection In relatinc to display size and redundancy of critical elements. January 25,1965, Revlsed 7-1-65. (Percecon and Psychophysics, 1966, L, 9-16) ..- 69 P. Suppes and J. Donio. Foundatione of stimulus-sampii,ig.therry For oontinueus-time processes. Februarr 9,1965. U. r.th. Psyche.. 1967, 4,'202-225) 70 R.I. Atkinsen and R. A. Kinchla. A learning model for forced-choice.detection experiments. February 10;1965. (Br. J.- math stet. Psychol , 1965,18,184-206) 71 E. J. Crothers. Preseniation orders for items from different categories. March 10,1965. 72 P. Suppes, G. Groan, and Id. Schlag-Rey. Some models for response latency In paired-associates learning. May 5,1965. 1966, 3, 99-128). 73 11. V. 6'avine. The -generalization fenction In the proballIty leaning experiment. June3;,1965.-. 74 D. 'Hansen and T. S. Rodgers. An exploration of psycholIngtristic.unita In-Initial reading.. July6,1965. 75 B. C. Arnold. A correlated urn-scheme for A Oontinuum ofresponeas.. July 20,1965. 76 C. Iowa and W. K. Estes. Reinforce:none-test sequences In paired-asanciatelearning.' August 1,1965. (Psythol... lisarte,1966, 18, 879-919) .77 S. L.. Blehert. Pattern dIserheination learninfwIth 2hiMus monkeys-. September 1,1965. (Psichol. tem,.1966;.19,'311-324) 78 J. L. Phillips and R. C. Atkinson. The effeats of dielday size On ehort-term memory.. August31 1965 .. 79 R. C. Atkinson. and.R. 141.- Shiffrin. Miihematical modele for memory and. learning; September 20 ;1965.: 80 P. Suppei. The psychologleal foundations .or Mathematles.-. Octets:v.25,1965. '(Colingeee hitonnitionaux du-Centre National de Ia Recherche SclentifIgue. Editions *du donee National de la Recherche ScientifIget..Faris:196?... Pp. 213,242). 81 P. Suppes.. Computer-assisted instruction'in the- Sehoola: potenilalities, prohleme, prospects Oc.ieber.29; 1965.- 82- R. A...Kir:chit, J Townsend J Vellott Jrand-R. 6. Atkinson kiflueeie of correlated vistial cuei on auditory:nicer:II detection. November 2,1965., (Perception end Psychophysies,:1966, 83 P. Suppes, -M. Airman, and'S.1 Green.' ,Aritheietie &illa rind:review:On a Computer-based teletyPe. -November-5, .1965: (Arithmetic Teacher ripri1.1966;`303309..' 84 P. &aloes and L.-Nyman... ConeePt learning Mithnon-yerhalgamiaufleal srimuli.November 15 1968*, (J;rnith. 1:ychol.,1967-,.3; 377413): . Avitiation on the MiniMulh chlinuire test.: . 85 P HoIleee . 66 13.-Surepee. Aceelerited preemie In elemontary.ithool mathernatice--1. seCond year., Novemben 22,1965: (Esisholoag hi the Scheele, 1966, . 87 P. LarenienaMd: F. BInfOrd. Logic' an a dialogical game; NOredese. 29, 1945;. .., releforcement'interVal ton the imgelsielon of'patied-eaSeelate: L. Keller, W. J. TSomson, J.:R. Tweady,.and R. C. AtkInion.' The effeets Or . r . .. 88 . , . .:,.. ,. -: responses. Decembnr 10 1965(A m fhgeliel1967 73' 268-2771 ..-: 1 ' J. I. YMIOtti:Jr. '. Some affects -on neneaattagent,etrairmialiamen UrObokiiitsi learning. Deoemher 15, 1965.-, ,...,. 89 , . 90 P. Sepia* and G...Grolin. :, SOO eiainlee Made1*. far'firet4aMide lerfornumee:dehi:OnsInipte addition'. feat's'. Jannaii'14 ,1966. (In j..".M.-Seindiea (Ed.),, Riseircii.Iii Metheiiihm Edateithin.lWaigingtneD.0.2.RCT44,. ... .. 1967. rip.;. 357--43-........-'.. .. ' -, . 91 P. Supties;, Inf,reatIon pretreisIng Ind Choice Rehlelor, '. jenuety.31,. 1966. , . .. .. .,,. .. .. .... ,.. ... ... Fehruay II, 1966. (Pliehol. Bulletin,: 1966; 66 e 30-320),... 92 G. Green and.R.O., Sakinton. Madele for optinitstretlieleetninePreeest.,:. Inetractien fkinitill,reldiag:' 5tanfard prOject, :March 17,1966: (ReadlneRitelith '.. 93 R. C. .Aicinsim and.6. waton.- Gdarpidar7eMeIeried . ..,,,....-,:.: --.,,, .,, Rweleily, 1966, 2; 5725) -:''..,..' - ... .. 94 P. SuPpie. ProbablIlstIO'Infirenie and thl'oencept:Oftete( evidenia'. *Mimi!, 25, 1966. (In J. 'HIntIkkik and 'F,'.. Suppes (Eciii.); Aspeetir:Of 'Indiiethea'1,...41_e.' kiieterdinh 'itirth4leiiiincil,ebliiiiiina Co.:..f.96.4.:...Pii..:496......1;-':.-..':::',... '''' --. ' Thlincloraitisimetherilith/9646hi101, t6lit6lialittif.: L'Ai711',1;,.1966. Cili -12silli 4 Axleinitleitind kiibleM 5Cleing 6i ,Maifiernatihs: 95, P. SuPPes. 5clerietre;-Washington; D. C. Glen Mid Co.; Iii-66. Pp. 6976: The Canfeariem:Board Of the kitheinitieel . : ,: : (Continued on-inside baik cover). 2 U.S. DEPARTMENT OF HEALTH. EDUCATION & WELFARE OFFICE OF EDUCATION THIS DOCUMENT HAS BEEN REPRO- IN- DUCH) EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATIONORIG- '," INATING IT POINTS OF VIEW OROPIN-
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