Research on routine problem solving (e.g. the typical story ,. problem) was reviewed to facilitate the identification and dissemination of promising practices for teaching routine problem solving, and to provide suggestions and directions for further research in the area. Promising teaching practices which were identified included giving attention to processes involved in solving routine problems (e.g., write an equation, make a chart) and devoting time to developing the meanings of mathematical vocabulary and symbols. Areas identitied as warranting further research included studies that examine the role of language variables (both syntactic and semantic) in the odecodingn pbase of solving a routine problem. Appendix C contains a coded bibliography which may be of great value to researchers in problem solving. (
DOCUMENT RESUME SE 029 968 ED 182 175 AUTHOg TITLE INSTITUTION SPONS AGENCY PUB DATE Sowder, Larry: And Others A Review of Research on Solving Routine Problems in Pre-College Mathematics Northern Illinois Univ., De Kalb National Science Foundation, Washingtnn, 79 GRANT NOTE NSP-SED-77-19157 99p.: Not available in hard copy due to marginal legibility of original document EDRS PRICE DESCRIPTORS MF01 Plus Postage PC Not Available from EDRS Algebra: *Bibliographies: *Educational Research; Elementary Secondary Education: Information Dissemination: Mathematical Vocabulary; Mathematics Curriculum: *Mathematics Education; *Mathematics Instruction: Memory: *Problem Solving; *Research Reviews (Publications): Symbols (Mathematics) ABSTRACT Research on routine problem solving (e.g the typical facilitate the identification and "story , problem) was reviewed to dissemination of promising practices for teaching routine problem solving, and to provide suggestions and directions for further research in the area Promising teaching practices which were identified included giving attention to processes involved in solving routine problems (e.g., write an equation, make a chart) and devoting time to developing the meanings of mathematical vocabulary and symbols Areas identitied as warranting further research included studies that examine the role of language variables (both syntactic and semantic) in the odecodingn pbase of solving a routine problem Appendix C contains a coded bibliography which may be of great value to researchers in problem solving (MK) *********************************************************************** Reproductions suppl3ed by EDPS are the best that can be made from the original document *********************************************************************** S DEPARTMENT OF HEALTH EDUCATION & WELFARE NATIONAL INSTITUTE OF EDUCATION pets DOCUMENT HAS BEEN PERRO- T.- DUCED EXACTLY AS RECEIvED FROM THE PERSON OR ORGANIZATION ORIGIN AT:Nc IT POINTS OF VIEW OR OPINIONS STATED DO NOT NECESSARILY REPRE SENT OFFICIAL NATIONAL INSTITUTE OF EDuCTtON POSITION OR POLICY (NI A REVIEW OF RESEARCH ON SOLVING ROUTINE PRdBLEMS IN PRE-COLLEGE MATHEMATICS Larry Sowder Jeffrey C Barnett Kenneth E Vos 1979 $ UMMARY This project reviewed the research on routine problem solving (e.g., the typica- "story" problem) with an aim toward (a) identifying and disseminating promising practices for teaching routine problem solving and (b) sug3esting dftections for further research in the area The investigators surveyed relevant dissertations, journal articles, and files of research studies Products of the work include a chapter in a National Council of Teachers of Mathematics yearbook oriented toward teachers, and chapters in two monographs oriented toward educational researchers Various talks at meetings for teachers and researchers have also been scheduled Practices which might improve the teaching of routine problem solving include these; Give attention to processes involved in solving routine problems (e.g.) write an equatlon, make a chart) Devote time to developing the meanings of mathematical vocabulary and symbols Teach that reading of a mathematical problem is different from reading less technical prose, and requires multiple readings with attention to vocabulary and relationships among variables Have the learners make up, and solve, their own word problems Ar2as in which further research and development seem warranted include these: Instrumentation is needed for process-analysis studies, both for protocol coding and process measurement Studies that examine the role of language variables (both syntactic and semantic) in the "decoding" phase of solving a routine problem should contribute to our knowledge of teaching problem solving Whether different ways of presenting problemsobjects, pictures, words help children of different ages and mental characteristics needs examiaation INDEX page I Summary page Narrative Appendix A: A Review of Selected Literature on the Role of Memory in Arithmetic and Algebra Word Problem Solving Appendix B: Publications Based on the Project Appendix C: Bibliography Appendix D: Project Collaboratore 0" A Review of Research on Solving Routine Problems in Pre-College Mathematics ObitctIm The aims of the project were as follows: "0; Review and evaluate research on routine problem solving in precollege mathematics To identify directions for further research on routine problem solving in mathematics To make the findings about routine problei solving available to classroom teachers and researchers eL Lee terms in the objectives not have standard meanings Here are explanations of how the terms were used in the project: Problem A problem is a task which does not immediately suggest to the solver a systematic procedure for resolving the task (i.e., an algorithm) Thus, a person's kriowledge of algorithms determines whether a given task is a problem for that person Multiplying with multi-digit numerals would be a problem for third graders but not a problem for most seventh graders rough Routine vs nonroutine The routineness of a problem mays in a The solution way, be defined by the nature of its solution of a now7outine pmblem requires considerable analysis, synthesis, and perhaps some novelty of approach On the other hand, the solution of a routine problem requires only a relatively small amount of analysis and no unusual insights The typical verbal problem in pre-college mathematics books is an example of a routine problem Such problems usually require only the selection of an appropriate computation In elementary school book, protlems described as "challenges" or "brainbusters," are ueually nonroutine problems Rationale The ratanale for the project was based on four things to routine problems in mathematics is important First, attention Effective citizenship as a consumer, as a wage earner, as a taxpayer, requires an ability to solve a myr.Lad of routine problems Checking purchases, calculating interest costs, these are evaluating budgets, determining best buys, planning meals all sample routine problems The Second, unfortunately many students.do not solve problems well availability of handheld calculators is of no value if a person does not know which buttons to press It is well known that students are not usually fond of "story" problems, and the firdt National Assessment of Educational Progress (1975) offered evidence that people are not very proficient in solving routitie problems If existing research evidence suggests that certain procedures for teaching routine problem solving are promising, these should he identified and disseminated Third, at least a few such promising practices are identified in the literature but not appear to be widely known For example, VanderLinde (1.964, found a positive effect on problem solving from spending time on developing meanings for symbols and on studying quantitative vocabulary -Finally, directions for further research on routine problem solving in mathematics might be identified by an analysis and critique of the existing research Procedures The investigators Barnett, Vos, and Sowder identified as many studies of routine Problem solving in pre-college mathematics as they could, through searches of dissertation abntracts and ERIC files and through examination of journals deemed most likely to contain such studies The studies were categorized with an adaptation of Kilpatrick's taxonomy of variables in problem solving research (1978) The most promising dissertations, reports, and articles were studied in full On the basis of this wo-A, manuscripts were prepared (see Products below) In addition, Dr Edward Silver agreed to consult with the project and prepared a project paper on memory aspects of routine problem solving (see Appendix A) RP Limitations Which journals The project was necessarily limited in scope shouli be conceutrated on? llow far afield from routine problems in mathematics should we explore? The homely when-do-we-stop-reading-and-start-writing question demanded an answer, dictated by manuscript deadlines in our case Hence, we cannot claim to have accomplished a comprehensive search For example, the information-processing approach to routine problem solving was slighted Work along these lines is currently popular, perhaps too current for a dispassionate critique or for an even moderately thorough survey Silver's project paper (Appendix A) does draw on work in information processing, however Anotherattractive but unexplored body of work was in problem solving in fields other than mathematics e.g., science, therapy, busineas It may well be that important implications fcr mathematics education lie in studies in such domains Products Serendipitously, the dissemination objective of the project was realized through the post-proposal appearance of plans for two works on problem solving-a monograph on "applied" problem solving (R Lesh & D Mierkiewicz, Eds.) and a National Council of Teachers of Mathematics yearbook on problem solving (S Krulik, Ed.) Proposals and drafts of chapters for these two forthcoming works were prepared and accepted In addition, Barnett prepared a chapter for a mono6rupn on task variables in mathematical problem solving (G Goldin & E McClintock, Eds.), soon to appear publications are summarized in Appendix B Citations for these The intent to reach the teacher audience through the Arithmetic Teacher was abandoned on the appearance in the November, 1977, issue of an excellent problem-solving article al3ng the lines planned (Suydam & Weaver); the yearbook chapter served oriented article as a teacher- Presentations based on the project have aided, or will aid, in the dissemination of the major findings: Barnett (state meeting of the Illinois Council of Teachers of Mathematics, October, 1978); Sowder (regional Illinois meeting, March, 1979; National (ouncil of Teachers of Mathematics regional meeting, March, 1980); Vos (California Mathematics Council, Southern Section, Novembei, 1979); Barnett, Vos, and Sowder (National Council of Teachers of Mathematics national meetinc April, 1980) Finally, one product of the*project was not planned in the original project but may be of great value to researchers'in problem solving: coded bibliography (see Appendix C) the This bibliography will be made available to interested researchers through contacts in the Special Interest Group on Research in Mathematics Education of the American Educational Research Association, and through ERIC Selected research recommendations The following condensed excerpts from the manuscript for the Lesh monograph represent the flavor of our recommendations for further research in routine problem solving in mathematics: For studies of the processes involved in routine problem solving, test instruments that emphasize such process variables must be developed, as well as a protocol scoring-coding scheme that is both elegant and efficient Studies that attempt to determine the role of syntax and semantic variables in the decoding process in the first stage of problem solving are of particular importunce Another area of needed research is that concerned with the improvement of instruction in reading and its relationship to improved problem solving ability Although the linear regression model has shown some promise as a research technique in the area of language variables and routine problem solving, it is clear that in its present form it falls short Improvements in of being able to predict problem solving success the model might include different criteria of importance; it would be helpful for studies to provide data on several dependent measures used with several measures of importance The relative effects of different formats words, pictures, objects-for problems should be investigated, particularly as they relate to learner characteristics What within-format variations make a difference? Studies with positive results should be replicatedfor example, Keil's 1964 study, in which student-generated and student-solved problemi apparently led to improved problem solving e Would concentrated attention'to routine problems give the same striking results as in Bramhall's 1939 study (8 months growth in 2.5 months)? 9, Cooperation among researchers interested in routine problem solving must increase so that common problemst similar instruments, and shared data analysiq can be more easily facilitated References Bramhall, k, W An experimental study of two types of arithmetic problems The alOUrnal of Experimental Education, 1939, 8, 36-38 Goldin, G A & McClintock, C E (Eds.) Task variables in mathematical Columbus, Ohio: ERICISMEAC, 1979 (in press) _problem solving Keil, G E Writing and solving original problems as a means of improving verbal arithmetic problem solving ability (Doctoral dissertation, Indiana University, 1964) Dtusrl,asjoruatuttii, 1965, 25, 7109-7110 (University Microfilms No 65-2376) Kilpatrick, J Variables and methodologies in research on problem solving In L Hatfield (Ed.), liathettobler, Columbus, Ohio: ERIC/SMEAC, 1978 Problem solving Reston, Virginia: Krulik, S of Mathematics, in press National Council of Tc:achers Lesh, R., & Mierkiewicz, D Applied problem solving SMEAC, 1979 (in press) Columbus, Ohio: ERIC/ Consumer math, selected results National Assessment of Educational Progress from the First National Assessment of Mathematics Mathematics Report No 04-MA-02 June, 1975 Suydam, M N., & Weaver, J F Research on problem solving: Implications Arithmetic Teacher, 1977, 25(2), for elementary school classroon,s 40-42 Does the study of quantitative vocabulary improve problemVanderLinde, L F solving? Elementary School Journal, 1964, 65, 143-152 Appendix A Project Paper A Review of Selected Literature on the Role of Memory in Arithmetic and Algebra Word Problem Solving by Edward A Silver San Diego State University - assembly in protlem solving and development using Wertheimer$3 area of a Parallelogram problem (Doctoral dissertation, University of Pittsburgh, 1975) Dissertation (University Abstracts International, June, 1976, 36, 7957A Microfilms No .76-1(4, 155) S 000 Journal An analysis of geometric ability Surrey, John E of Educational Esychology, 1949, 40, 118-124 /000 The prevention and correction of errors Nyers, Garry C Chicago: Plymouth Press, c1925 in arithmetic 000 P A study of the performance of third Neil, Mrilyn S grad* children cr two types of verbal arithmetic problems (Doctoral dissertation, University of Alatama, 1968) Dissertation Abstracts Inter(University Micronational, 1965, 29, 3337A films No 6J-6559) Not math Information-gathering in diagnostic Neitark, Edi*h D Psychological' a preliminary report problem-solving: Record, 1961, 11, 243-248 Not math The development of logical Neimark, Edith J., Lewis, Nan Child Development, March, rroblem-3olving strategies 1967, 38(1), 1C7-117 000 The effects of diagram drawing and translation Nelern, Glenn T problem-solving performance (Doctoron pupi1.0 mathenatical al dissertation, University of Iowa, 1974) Dissertation (Universit Abstracts /nternationa), Jan., 1975, 35, 4149A Microfilms No 75-1234) J 000 Thrce determinants of difficulty in verbal Nesher, Perla Educational Studies in Plathearithmetic oroolems matic3, Decamltr, 1976, 7(4) , 369-d13 J 000 NewccU, R S Texching pupils how to solve protlems in 1922, Elementary School Journal, November, arithmetic (3), 183-1s9 Englewood Newell, A., 3imon, a A Human problem solving Prentice-Hall, 1972 Lliffl, N.J.: J 100 A study of the relaiionshins bctwecn socioculNewstat, Stevtn solving performances tural variables and geometric problem or disadvantaged children (Doctoral diss(.rtation, Michigan State university, 1972) Dissertation Abstracts Interna(Univorsi.ty nicrofilms ticnal mAV, 1.172, 33, 6069A 73-12, 733) 000 A multi-expc.rience approach to conceptnalizaNickel, Anton d tica tor the PUIPOSO of improv(.:dent of verbal problem solving in arithretic (Dectural disbortation, University of Dissertation Abstracts international, Dec., Oregon, 1971) No 72-960) (University iictoEilin 1971, 32, 2)17A-2918A SA000 Pelationship3 between problem-solving abLiit y NOVIld14, Philip U arwunt of training in ccz,putationll skill, inteliigenck, and mathLmatics ()ectoral dissertation, Columbia University, (Uni Dissrtation Abstracts, 1950, 10(4), 156-157 195j) verli'y Microtilzs No 50-J33) Ihe develo;.cental significance of pictorial IJ 100 O'Flahettv, fielen T rerres,ntition in ploviem s)lving (Doctoral dissertation, Fordham University, 1971) DI,Lsertation Abstracts InteUnd(University Microfilms No ticAtt, Oct., 1571, 32, 23829 71-26, 9d9) variables on the arith- 13 100 ylion, LaCc1le ThE effects of selected performance of educable metical vezbal problem solving dissertation, Univermentally retarded children (Doctoral 000V 000 000000S 010 durray 1949 100R 000 000000S 010 Ayers 1925 001R 000 CCOOOOS 010 NEIL 1969 Neimark 1961 treimark & Lewis1967 001R 000 -ma 111 000N 100000 011 Nelson 1975 C000005 010 Kosher 1976 011 Newcomb -1922 000 100000 -Nevell t.Simon 1972 000G 000 C00000 110 Newstat 1973 001R 000 IC0000 010 Nickel 197 100R 000 CCOOOOS 010 Norman 19 50 001R 000 CC0000C 010 Wriaherty 1971 10011 000 CCOOOOS 111 Olion 197 Dissertation Abstracts Internasity of Connecticut,' 197 3) (University Microfilms ho 57281t 1974, 34, tional, March, 74-7 130) olson, Gary it.; Miller, ,keon K.; Bale, Gordon A ; & Long-term correlates of ohildren°S._ Stevenson, llarold W learning and problem-solving behavior Journal; of Educational Psyctelogy, Aggust, 1968, 59(4) , 227-232 Pace, Angela Understanding and the ability to solve problems Arithmetic Teacher, May, 1961, 8(5), 6-233 The effect of mode of computer-operation on Pack, Elbert C learninn a computer language and on problem solving effici- 010 Olson et al 1968 100 000L 000 0000005 000 000R goo top000 011_ Pace 196 run din mood 110 _Pack 197 s000 ency of college bound high school students (Doctoral dissertation, University of California, Los'Angeles, 1970) Diesertatioh Abstracts International, June, 1911, 31, 6477A. - (University ftiorcfilms No 1-16, 348) Cognitive processes raige, Jeffrey M., & Simon, Ileruert In D Kleinmuntz in solvini algetra word problems Research, Method, and Theory (Ed.), Problem Solving: Wiley, 1966 New York: An -analysis o f the ef recta of verbalization Palzere, Dor.11.1 40 and acnverhalization in the learning of mathematics (DocDistcral dissertation, Univer tity of Connecticut, 1967) 28, 3034Aa, 196 sert at ion Anstracts International, (University Microfilms No 68-1386) 3035A Teaching children to be mathematicians Parert, Seymour versus teaching buut mathematics Inte rna tional Journal ot mathematical Education in Scit nee and Technology, July-September, 1572, 3(3) , 249-262 eading skills incorporated into mathematical Parli-?r, Jane U ruct ion,s effect on ability to solve mat hematical word inst problems (Doctoral dissertat ion, University of South Caro- Paige & Sinan 6000 000A 000 0000005 Papert 1972 I Di:6aertation Abstr cts Interne ional, 1974) (University 4icrof ilLs No 75-8686) 1975, 35, 6579A Ft Cects o L 'x t ended effort in Parries, slum; y Journal of Educat ional crea rive nzoblem solving 1968 1.1 Palzere,- Gen inf 1966 100 000R 110 100000 110 Parler 1975 000 00.0L 000 0000005 001 Parnes 1961 A000 000L 000 100000 001 Parnes & Meadow1959 A000 000L 000 100000 011 Parnes & S000 0004 000 000000S 011 Paull 1972 I 100 0001I 110 000 000S 10 Penner 1973 000 0:1011 000 100000 010 Penn ington 1970 lina , Psychology, June, 1961, 52 (3) , 117- 122 Effects of Parni=s, ;idtw.y 3., & t!c.tdo d, Arnold "bra instorming" instructions on creat Ira d sub jvct i :Journal lv ing 1.y t dined and nutra ycnolog y, August, 1959, or Fducational 171-171 Parnes, Sidne y J., & Meadow, Arnold 50 (4), F.valua tion of eadow1960 rsistcnce ur et te cts produced by a creative Psychological ate por: ts, problem-.;olv ink) course 1Sn.), , 3'4-361 Paull, Duane I ThE ,tLility tu esti,;kite in Ina dis.se rtation, Columbia Univer sit Abst facts Inter rat iona l, Jan., Microfilms No y, 1971) 1972, 32, tie J (Doctoral Dissertation (University 3567A 7s-4173) Effecr of cue word for m class on th oivinq w erd ptoblcnis by the menta Ily handicapped pectoral dissertation , Universit y of Connecticut, 1973) Dissertation Abstracts I nter nationa 1, Nov., 1973, 34, 2424A(Uni versity Microfilms No 73-26, 581) 2425A Behavior al and conce ptual strategies as Perningtou, Uarbara A decision models for solving problems (Doctoral University of California, Los Angeles,1970) Dissertation Permit., 6illiao J ot ar ie i'mct ic dissertation, I 7G (UniAbstracts International, Oct., 1970, 31, 1630A-16.31A versity Microfilms No 70-19, 879) Pereira-Mendoza, Licnel The effect of teaching heuristics on of grade ten students to solve novel mathematical problems (Dectoral dissertetion, University of British Columbia, 1975) Dissertation Abstracts international, (University Microfilms No sone) 1976, 36, 8014A June, Peterson, Margaret ".1., Aller, Setae Arithmetic problem solving Journal of Experimental - 100 011 fieletra:itiltdoia1976 000AG-000 100000 the ability £000 Psychclogy, November, 119 71, 91(1), 93-97 solutions of problems Petty, Olen Non-pencil-end-paper Arithmetic Teacher, December, 1956, 3(6), 22 9-2 35 Au analysis of the performance Fortis, Theodore it of fourth, fifth and sixth grade students on I atm 000R _000 110000 I 000 001R 000 100R lj 011 Peterson A11e197 010 000000S 010AR 000 010. petty 1956 000 0000005 011 PORTIS 1973 00 C000 005 011 Post , R 1958 000R 000 1000 00 -010 *Post, T 196 000 000G 00 O 100000 010 £100 000L 000 Problems involving proportions, three lvels of m ow aids and three I O levels (Doctoral dissertation, Indiana University, 19 72) Dissertation Atstracts Interrational, 1973, 33, 5981A-5982A (University Microfilms No 73-10, 858) Post, Richard A study of certain factors affecting the understanding of vertal problems in arithmetic (Doctoral dissertaticn, Columbia University, 1956) Dissertation Abstracts, July, 1958, 19, 90-9 (University Microfilms No 58-2242) Post, Thomas R The effects of the presentation of a structure cf the prublem-sclving process upon problem-solving ability in seventh grade mathematics (Doctoral dissertation, Indiana Abstracts International, University, 1967), Dissertation (University Microfilms No 68-4746) nay, 196d, 28, 4545A experimental Post, Thomes R., t bicunan, Michael I An 1/EA's113 an study ot the effectiveness ot a formal general heuristic a informal presentatioe of rtocess On problem solvititi in tenth-grade geometry Journal for Research in mathematics Education, Januiry, 1976, 7(1) , 59-64 Priest, hobert F., Uunsaker, Phillip L Compensating for a female disa#4vantage in problem solving Journal of Experimental Research in Personality, 1969, Lif 57-64 011 Priest: Hunsac196 0000005 PIJS 000 00011 000 0000 00s xperiment &2 stexly of the development Jouinal of of cer7ain aspects of reasouing Edle:aticnal Psycl.ology, Cctober, 1935, 6(7), 549-546 Not sath Search strategy and pioblem Pylyshyn, Zenon W Canadian structuie in heuristic problee-I-Iolving .1 tncil of Psychclugy, 1963, 17(a), 291-301 100000 I T 100 00 1R 00 Rarkin, Jeanne S The deyelopne nt and testieg ot indigenous %furl PLChIC als for grades tour-six in Litcria, 111st Africa poctoral d1S6erta ion, Dissrtation University of Fichigan, 1977) Abstracts International, 1977, 3, 1272A-1273A (University micrefilma No 77-18, 101) Review of gen prob tasks complex tasks tor use in hunan Ray, iiiltert S problem-solving resedich Psycho.logieal Bulletin, March, 1955, 52 (2) , 134-149 The reflective-impulsive dimension and mathe- PI 010 000R 000 000000S Pyle, w If Post & Brennan 197 010 Pyle 1935- PYshyn 1963 RANKIN 1977 kit genius, Albert M 010 to 110 Ray 1955 hebhun 197 matical performance in the elementary school (Doctoral dimsertaticn, University of Califoreia, Los Angeles,' 1973) Dissertation Abstracts International, Dec., 1973, 34, 30 39A- ' '77 - - 78 (Universit), aicroilms No 13-28, 970) 3040.A Success and speed aestla, Izank, & bavis, Jamos E of problem solving by individuals and groups Psychological Review, November, 1962, 69 (6) , Restle & Davis 1962 Math sodel !20-536 Riban 1970 010 Richardson 1974 1C0000 011 Ridbardsou 1975 S 000 000A 000 100000.- 010 JST000 00011 000 100010 JST000 000401 000 Aitan, David M An investigation of the relationship of Gagne's hierarchical sequence model in mathematics to the learning of high school physics (Doctoral dissertation, Purdue UniDissertation Abstracts International, May, versity, 19(,9) (University Microfilms No 70-8957) 1970, 30, 4845A Richardson, Lloyd 1., Jr Student achievement in solviag verbal rtoblems as related to teacher preparation (Doctoral dissertation, George Peabody College for Teachers, 1973) Dissertaticn Abstracts International, Feb., 1974, 34, 39278 (University Microfilms Nc 74-462d) Richardson, Lloyd I The role of strategies for teaching pupils to solve verbal problems Arithmetic Teacher, Mal?, 1975, 22(5) , 414-421 Procedures for improving verbal Riedesel, Clark A problem-solving ability in arithmetic (Doctoral dissertation, State Uriiversity Of Iowa, 1902) Di Esc rtati on Abstracts International, 1963, 23, (Universit y Microfilms No 63-956) 2d19-2H20 An invest igat ion of the efft:cts of Riley, J a mes D reading guides and a directed reading method upon word problem comprehension, problem solving_ ability, dila ittittlae towara mathematics (Doctoral dissertaticn, Syracuse University, 1976) Dif.s«Irtatioa AbEtracts International, 1977, 37, (University Microfilms No 77-9897) 7587A Riaoldi, H J A A technique for the study of roolern solving Educational and Psychological Mcasureacnt, 19!!, 15, 450-461 G SOME diacldi, J A.; Aghi, :I.; 3urger, language, and age effects of logical structure, in croblcm ::;olving in children Journal of J in the Schools, 1967, 4, 24:) -245 An investication of problem solving behavior 000R 000 100000 011 RIEDESEL 1963 000 000R 000 100000 010 RILEY 1977 Rimoldi 1955 Scoring technique PI Gene tic Psychology, March, 196U, 112( 1) , 127- 143 & Dacey, John The facilitation Ripple, Richard of problem solving and verbal creativity by expo3iire to program.:Na instruotioL Psychology Robinson, Mary L 000 ct al 1968 000 000L 110 000000S 011 Rimoldi 000 0001 000 100000 011 nipple 000 0002 '000 000000C 111 Robinson.- 1973 Rogers 1975 & Dacey 1967 ard ccgnitive and affective characteristics cf good anl poor rtoblem solvers in sixth grade mathematics (Doctoral dissertation, State nniveraity of New York at buffalo, 1973) DiElA rtattoa Abs4ractq International, April, 1973, 33, 562JA (Unit/Qrs.:Ay aicrufilms No 73-9145) A ditterent look dt word Mathematics Teacher, April, 1975, ttcblems 68(4), 28E-288 The relationship of the ahility to conserve Rohr, Judith A G on Piagktian tAks to achievemcnt in mathematics (Doctoral Dissertation univ er:;it y of Tennk ssee, 1973) (Univer1473, 34, 2396A Abstracts International, Nov., Rogers, Aargaret Anne Textbook review 010 000R 000 C00000S 010 Rohr 1973 disseration, sity Microfilms tio 73-27, 143) Sohwer, W L., Mat2, R D Improving aural comprehension in white and in black children Journal of Experimental Child Psychology, 1975, 19, 23-26 S4 , I Children's Rosenthal, Daniel J., Resnick, Lauren B selution processes in arithmetic word problems Journal of Sducational Psychology, December, 1974, 66(6) , F17-J25 (loth, Bernard The effects cf overt verbalization on problem solving (Doctoral dissertation, new York University, 1965) Dissertation Abstracts International, Sept., 1966, 27, (University Microfilms No 65-9321) 9570 David H., Holmes, F Melville An Russell, experimentil comparison of algebraic reading practice and the :relying of additional verbal problems in tenth grade algebra Mathematics Teacher, December, 1941, 4(8), 347-352 Safzen, Miriam h Associations, sets, and the solution of word problems Journ,a1 of Experimental Psychology, January, 1962, 64(1), 40-45 Arithmetic problem solving strategies of sanders, Violet A fourth grade children (Dectural dissertation, Wayne State University, 1972) Dissertation Abstracts international, (University Microfilms No 73-._ May, 1973, 33, 59133A-5984A 33 (2) , 144-159 American a lathematical problem solving mathematical Mont hly, mdrch, 1974, 81 (3) , 273-2d0 Scanditra, Joseph m 1977 Schall, William E Problem solving 000 000 000 000000C _0 11 Roth 000h 000 100000 Safren 1962 Sanders 197 Scandura 196 I 10 000R 000 C.0000 000 l0000p 011 Scandura - 1964 000 100000 011 Gem exptl inf New York: Academic Press, Scandura 1964 Scandura 197 Scandura 197 000 000R 000 10000 010- Schall 100 001G 000 000000S 10 3F.9-otb The interrclationship of sex, visual spatial Schonberger, Ann K problem solving ability in grade aathematieal and abilitic3, seven (noctoral dissertation, University of WisconsinNadi- ilitc 1966 010 -Russell Uoime194 'Not bath word probs ccmparinq mental D rosei:t at Aon A ids t Rosenthal & Res197 '110 S -000 arithawtio modes of presa.ntition in elementary sclool mathematics School Seicac t and dat huwatir.'s, ns y, 1973, 73(5) , :len, 197u) 010 000R 12, 590) 000 000R an exploraThe teaching-harming process: Scandura, Jonvph N tory invcstigaticn of exposition dud discovery modes of problem solving instruction (Doctoral disseitation, Syracuse Dissertation Abstracts, Feb., 1963, 23, Unive rsity, 1962) (University Microfilms No 63-2874) 2798 Geizinf -:. -Scandura, JOSE: Pit a Abstract card tusks for use in Journal of Experimental rrchlom solvin4 research Elucation, Winter, 1'364, 33(2), 145-148 000 COOL An analysis of exposition and Scandurd, Joseph M discovery modes of problem solving instruction Journal of Experimental Education, Winter, 1964, Scauddra, Joacmh 0000005 000 J 197 Schouberger 1976 Schulz 196 Schw iegcr 197 nationdl, Dec, (University Microfilms No 7b-20, 132) 197i,, 21, Review kro tdcni JolvIng behavior and Schulz, ludcLuh Feview, Winter, 1960, Harvard Educational 30(1) , t1-77 A componnt analysis of crathema*.ical problem JSA000 Schwiecier, is,utn:ii D 35.1bA transfer 000AGR000 000000C 11 000 CC0000S 010 1974) ion, Purdue University, solving ( )octoral dit;.;crtat 1974, 35, 3300/.International, Dt:c , Dissertation Abstracts (University 8icrotilms No 74-26, 777) 330A Scott, Ralph ani Lichthall, Frederick, F Relationship between content, sex, grade, and degree uf disadvantage in arithmetic problem solving of School Paychology, Fall, 1967, 6(1), 61-67 I 100 100R Scott & Lightha196 to poor problem Sedlak, Robert it Eerformance of goe4 and sclyers on arittmetic word prcblems presented in a moditied cleft tormat Journal or Educational Research, July/August, 1974, 67(10), 461-47 ERR arithmetic Robert A A comparison of.good and poor problem solvers en modified cloze problems (Doctoral dissertation, Pennsylvania State dniversity; 1973) Dis.lertation Sedlak, Abstracts International, Dec., 1974, 35, 3557A (Dniver-_ _ sity dicrofms No 74-28, 934) Seqalla, A Using structural variables to predict wordprcblem solving difficulty for -junior college American arithmetic students Paper presented at the Meeting, New Edwational Research Association Annual Orleans, 1973 on Sekyra, Francis, III The effects ut taped instruction problem-solving skills of seventh grade children (Doctoral dissertation, University of Alabama, 1968) Dissertation, Abstracts International, April, 1969, 29, 3473A-3474A (University Microfilms No 69-65e9) Shaun, Mary H Evaluation of an interdisciplinary, problem solving curricUlum in elementary science and mathematics Science Education, W inter, 1977, 61 (4), 49 1-502 Shaw, J Reading problems in matlematics texts Columbus, Ohio, 1967 (E.iIC Document Iteproductiou Service No Et Olt E87) in Sheehan, 'I Joseph Patterns of sex differences learning mathematical prcblem-solving Journal of Experimental Educatiun, Summer, 1968, 3b(4) , 64-37 Sherard, Wade H., In The effect of arithmetical operatiens on disrertathe difficulty levels of verbal problc.ms (Doctoral Dissrta Teachers, 1974) tion, Georg.) Peabody College for tier' Abstracts International, Dtc., 1974, 5, 89 (Univer::ity Microfilms No 74-29, 189) presenta+ions of Sherrill, James h The effects of differing mathematical word problems upon the achievement of tenth grade students (Doctoral dissertation, University of Texas Abstracts International; at Austin, 1970) Dissertation Jan., 1971, 1, 3427A., (University Microfillis No 71-191) Jame3 M The effects of diffetent presentations 1974 010 0008 101 000R 110 0000005 100_ apogoc 111 Sediak _ j- 000 000E 000 4976) A Student perceptions or: relatedness among mathematical word problems (Doctoral dissertation, Shann 000 000RI, 000 100000S 010 100 000k 000 100000 010- Sheeha-s J 000 000R 111 C000005 PI J 011 5000 00 lAG 00C 000000S 10 S 000 0 1.AG 000 CC0000S 27, 149) of provisions for imagery through.-J Shceeraf t, Paul J The effects matptials and drawinq : on translating algebra word problems, (Irade-t evett an4 nine (Dectoral disser ration, University of Michigan, 197 1) Dissertation Abstracts international, Silver, E 3ekyia -196 0100 00 000 000000C 000 00011 000 001AR 000 gra It studqnts (Doctor ii dissert ition, Abstracts International, Dec., versity, 1976) Dissertation 1976, 37, 348 1A-4482A (University microfilms No 76- (University Microfilms No 72- 1974 Sedlak N ct oathematical word problems upon thc achievement of t enth grade students School Science and Mathematics, April, 1973, 73(4) , 277-282 of compre Shields, Joseph J The detection and identification by selected tOurth hensive problem solving utratcgies usedMichigan St4te Uni- Jan., 1972, 32, 3874A-3875A 010 100000 10 197 1968 Sherard 1914 Sherrill 197 Sherrill 197 110 Shoecra ft 1976 1972 - Teachers College, Columbia University, 1977) A100 000A 000 000000C 011 Smith, Charlotw E C The structure of intellect pro'ocol and analysis system: a technique to:: the investigation quantification of problem solving processes (Doctoral dissertaticn, University of bouston, 1971) Dissertation Abstracts International, Feb., 1972, 2, 42551 (University Microfilms No 72-7745) I T110 000R 000 0000005 teacher sex to Smith, Dan F A study of the relationship of general self concept, fifth grade boys sex role pref rence, and mathematics (Docand scholastic achievement in science toral dissertaticn, University of Miami, 1970): Dissertaticn Abstracts International, March, 1971, 31, 4563A (university Mictcfilms ho 1-4312) Textbook analysis word problems Smith, Frank The readability of sixth grade 1971, 71(6) 559-562 Scheel Science and Mathematics, dune, 11 A000 000A01.000 100000 specific heuristics 'Smith, James P The effect of general versus in mathematical pzokaerr-solving tasks (Doctoral dissertation, Celeabia university, 1973) Dissertation Abstracts Interuational, Nov., 1973, 34, 2400A (University Microfilms Nc 73-2E, E37) Snethen, Charlos C Peer support in the teaching of verbal prob=0I 000 000R 000 001000 010 dissertation, University ler, solving in arithmetic (Doctoral Dissertation Abstracts Interof misscuriColumbia, 1975) national, oct., 1976 37, 1980A (University Micron/ma No 76-21, 977) I T 000 0008 000 1000 10 10 Sparks, Billie R Pupil achievement in solving verbal probleas in matheraties as related to teacher preparation and experince (Ccctoral dissertation, Jeorge Peabody College, for Teachers, 1976) Dissertation Abstracts Interrational, 1977, 37, 5058A (University iiiercfilits No 77-3119) Heading in ar it halo ic uszt,,11 , D Spencer, P., National Council or Teachers of Mathebatics Yearbook, 1960, 2, 202- z Textbook analysis, examples of ps Spitzer, Herbert F., & Flournoy, Francis Developing facility in solving verbal problems Arithmetic Teacher, Ncvsmber, 1956, 3(7), 177-182 S000 000AGT000 0000005 110 Stanionis, Victor A Au examination of the re/ationshipinbetween sathelitobitini the ability of s tudents to solve al:wiled of the students, their mitics and certain characteristics teachers, and zichools (1)cctotal dissertation, coluinvia UniAbstracts international, May, versity, 1975) oissortation 197i, 36, 25 12A-2513A (University Microfilms No 7525, 72) 10 000 0001 000 100000 P in Stet n , Carolyn Acquisition of problcul-3olv jug str at egic young CI:ilurin and its relatien *(s vOthaliZation Journal 245-252 of Educational rsychology, August, 19n7, 5a(4), 0.10 000 0001 000 100000 P of problemStern, Carolyn, & Keisiar, Ev1n1 ie Acquisition solving strategic:3 by young children, and its relation to ma-ntal lie American Educational lieseatch Journal, January, 1967, 411), 1-12 LI 000 00014 000 C00000S 010 Journal of Stevens, B A Problen solving in arithmetic 253-260 Educatioaal hesearca, April/May, 1932, 25(4/5),arithme'-ic I 000 00014 000 100000 11 Incrvasing the ability to so:ve Stevenson, P R Ptcblems Educatiosal Research Bullet in, October, 1924, 3, 267-270 ST000 0000 010 0001105 011 ntilvell, Merle E ihe development and analysis of a category Smith, C 1972 SaithD 1971 Smit h 1971 Smith, J 1973 Snethen 1976 SPARKS 1977 _ P, Spitzer Plour1956 Stanionis 1975 Stern 1967 Ster n & teislar 1967 Stevens 1932 Stevenson 1924 Stilwell 1968 ; at system for systematic observation of teacher-pupil interaction during gecrectry problem-solving activity (Doctoral sertati)n, Cornell University, 1967) Dibsertation (University Abstracts Iuteruational, Feb., 1968, 28, 3083A Microfilms No 68-d93) The relation of reading comprehension and Stright, Isaac L efficient methods of study to skill in solving algebraic aathematics Teacher, December, 1938, 31(8), problems 000 000A 000 1000 00 010 Stright 1938 I 000 Effects upon pupil performance in arithmetic of emphasis upon instructional programs differing in amounts of * :-ccreputational structure and verbal problem solving (Doctoral Dissertation : dissertation, uhio University, 19e5) (University_ Abstracts International, June, 1967, 7, 058A Microfilms No 66-4335) I 000 Auditory assistance of 'reading as d fact.or in Stull, Lorten L verbal arithintermediate-grade purlilsi interpretation of metic problems (Doctoral dissertation, Pennsylvania State Dissertation Abstracts, June, 1965, 25, University, 19(34) (University Microfilms No 65-4424) 7113 The efrects of varying practice exercises 000 Sumac:al/say, Logrdes S and relating methods of solution in mathematics problem solving (Doctoral dissertatioa, University of Toronto, Dissertation Abstracts International, June, 1972, 1970) (Microfilm National Library of Canada at Ottawa) 32, 6751A Suppes, P., :Lyman, I., & Jorman, M Linear modeis for response and latency performance in arithmetic Technical Report mu 100, Psychology series Ti;;;titute for mathematical Stanford, California: Studies in the Social Sciences, stanrord University, 0008 000 100000 010 Stuart 1967 00 1R 100 010000 010 Stull 1965 1008 000 1C0000 010 Sumagaisiy 1970 0008 111 0000005 11 Stinnes et al 1969 100000 010 Swart 1970 1973 J :4.t6-372 Stuart , Alvin J 1960 Computcr-Assisted Suppes, P., Jerman, M., & Brian, D The 1565-66 Stanford Arithmetic Instruction: Academic Press, 19s8 New York: Pro4tim ProblemSuppes, Patrick, Loftus, Elizabeth Jorm1it4 Max Educational teletype sclving on a computer-based Studies in Mathematics, 1969, 2(1), 1-15 Swart, William L A comparative stuuy of the effects of highapproaches to developing problem-solving and ici aliiliy in fourth grade children (Doctoral dissertatiou, Dissertation Abstracts Univcrsity of Michigan, 1969) _ (University Micror.:Ams International, Aug , 1970, 31, 669A No 70-14, 451) An investigation of selected mental, matheTaltcn, Circlyn F matieal, reading, and personality assessments as predictors or hilh CnitO/Vrs in iixth 4rady mathematical verbal problem solv ing (Doctoral 'dissertation, Northwestern State University or Louisiana, 197 3) Dissertation Abstracts interna(University Microtioaal, Sept., 1973, 4, 1008A-1009A films No 73-i1, 255) Dealing improvemEnt in mathematics, Taechow, U G Beading Improvemcnt, 1969, 6, 63-0 LI ror s in ludgmcut of late, Merit' W., & Stauier, Barbara Journal ot Experimental tiocii and poor prosier.' solvers 371-37 Education, Summer, 1964, 32(4), Manipulation of numerical presentaticn Thibodeau, Gerard P in vertal problems and its effect on verbal problem-among WI childreu :ducation and Training of the 000 000_ 01080 000 I J 000 0008 000 000000S 011 Talton 000 0008 000 CCOOOOS 011 Tate & Staniar 1964_ 0018 000 1C0000 010 Thibodeau 1974 Mentally Retarded, 1974, 9, 9-111 Readability and accessory remarks: factors (Des:toral dissertation, in proLlem solving in arithmetic Stanford University, 1967) Dissertation Abstracts International, Jsn., 1963, 28, 2464A-2465A (University Microfilms Nc 67-17, 547) Travers, Kenneth J D., Forced-choice preference for problemsolving situaticts in mathematics (Doctoral dissertation University of Illinois, 1965) Dissertstion Abstracts, Thompson, Elton N 000 000R 110 000000S 010 Thompson 1968 J 000 100R 00fs 0000005 110 Travers 1966 J 010 1008 000 000000S 011 Travers 1967 J 000 000R 000 000000S 010 Treacy 13 000 000R 000 100000 011 Treffinqer 1969 I 000 000R 000 0000005 010 Tucker 1975 5000 0000 000 100000 010 Tupesis 1973 Underwood 1977 Van Wie 1977 I June, 1966, 26, 7161-7162 (University Microfilms No 66-4310) Travers, Kenneth J A test of pupil preference for preblemsolving situaticts in -junior high school mathematics Journal of Experimental Education, Summer, 1967, 35(4), 9-18 skills to the Treacy, John P The relationship of reading of ability to 301ve arithmetic problems Journal 86-96 Educational Research, October, 1944, 38(2), instruction in Treffinger, Donald J The effects of programmedproblem solving productive thinking on verbal creativity and among punils in gradeS four, five, six, and seven (Doctoral dissertation, Cornell University, 196:9) Dissertation Atstracts Inteerational, Sept., 1969, 30, 1031A sity Microfilni No b9-10, 473) of three primary skills Tucker, Denny F A correlation study problem-solving ability among which contribute to arithmetic forrth-grado/ students (Doctoral dissertation, University of Illinois at Urtana-Champaigu, 1975) Dissertation Abstracts Internationil, Nov., 1175, 36, 2620A (University hicrofilms Re,' 75-24, 41b) a consequence of the Tupesis, Janis A Mathematical learning as problem-solving tasks learner's involvement in interactive Wisconsin, 1974) (LoCtoral lisscrtation, University of July, 1973, 34, 126ADissertation Abstracts Inns:national, 1944 (University Microfilms No 73-9295) An exploratory study of the problems:sly:4ns procedures ust-d by 6electcd college freshmen on cer127A Underwood, Jacqueline _N A000 -000R -000 -0000001- 011 (Doctoral diylettatain basic consurur mathematics problems Dissert aS ion versi ty Jf Tennessee, 1976) tion, (Uni- Atstracts interrsticnal, Feb., 1577, 37, 4905A-4910A versity Miororilms No 77-3b94) A000 and appraisal of a unit on Van ;:i.e, Joseph L The deveiopment technology students (Docprollem solviag tor engineering Northern Colorado, 1976) toral dissertstion, University of Jan., 1977, 37, 4196A Disse rtation Abstracts international, 789) (University siorofilms NO 76-29, I 000 quantitative Vander Linde, Louis k Dues thc Stutiy ofElementary School vocatulary imptcve nroblem-solving? Jeurnal, Decemter, 1964, 65(3), 143-152 j 100 inrormation on the Velez-Serra, Damisn Effect:3 of extraneous by the Spanish-speaking solving sf arithretic word prol.ilems mentally htndicaPned (Doctoral dissertation, University of Abstracts International, Connocticus, 1975) Dissertation (University sicrofilms No 75Aug., 1975, 36, 622A 16, 25) The value of pictoral illustration, British Journal-of Educational Psychology, Vernon, maydalen D .1 160-187 SJ 000A 000 100000s 011 000R 000 100000 010 Vander Linda 1964 ODOR 110 CC0000S 010 Velez-Serra 1975 F 4111211111611119.44*.=011 41114 60.or of three variables on the solulate llo, Stanley J The effept requiring quantitative class inclu- I Lien of verbal ptcblems sicns amona educable mentally retarded children (Doctoral dissertation, University of Connecticut, 1972) Dissortaticn Abstracts International, Dec., 1972, 33, 2795A (University Microfilms No, 2-32, 194) of throe VCs, Kenneth E A cemparison study of the effects behaviors (Docinstructional strategies or problem solving _ DisserMinnesota, 1973) toral dissortaricn, University of _ tation Abstracts International, nov., 1973, 34, 2283A (University Mictailms No 73-25, 88) Vos, Kenneth E The effects of three instructional strategies on' Prcblem-solving behaviors in secondary school mathematics Journal for Research in Eathe _ matics Education November, 1976, 7(5), 264-275 Walek, Bruce P A study of the relationship between conceptual I caildren trope and nroblem-solving abilities of fourth-grade (Dectoral dissertation, University of Florida, 1972) Dissertation Abstracts International., July, 1973, 34, 215A(University Microfilms No 73-15, 55 0) 16A Washburne, Carleton h Comparison of two methods of teaching pepils to apply the mechanics of arithmetic to the solution of problems Elementary School Journal, June, 1927, 7(10), 758-767 Washburne, Carleton W., & Morphett, Mabel V Unfamiliar situaticns as a difficulty in solving atithmetic problems Journal of Educational Research, Cctober, - _ 100 ilmormewmpl .~ 101R 000000S 010 Vitello 1972 S 000 000AR 000 100000 011 Vos 1973 S 000 00011R 000 100000 011 Vos 1976 0005 000 0000005 011 Walek 1973 000- 100000 011 Washburae 000 C00000S 010 000 100000 011 Washburne & 0sb1926 000 100000 011 011 000 000R 000 100R 1918, 1i(3) 120-224 PIJ 000 000R Washburne, (arleton W., & Osborne, Raymond Solving Elementary School Journal, arithmetic problems I Ncvember, 1926, 2?(3), 219-226 PIJ two cam Washburne, Carleton W.; & Osborne, Raymond Solving arithmetic 4.) roblLins II Elemet.tary School Journal, Dezvinher, 1926 27(9), 296-304 of d telit of mat ematical problem Test Wearne, Ciana C Deveicpment selvin g which yields conurchfnsion, application, and probWislem solving score (Doctoral dissertation, University ofApril, DissettatiOn Abstracts International, consin, 1976) 1177, 37, 6328A-6329A (Univernity Microfilms No 7629, 945) A000 00 1G Webb, Lvland F., shorrill, Janes A 2he ctfects of diffeting presentations of mathematical word prollems upon the achievement of preservice elementary teacher.s Schocl Science aneMathematics, November, 1974, 74 (7), 559-565 000A S 110 Webb, Norman L An cxpluration of mattr matical prublem-solviny rtccuEsua ()octoral dissertation, Stanford Univcrsitv, 19'15) Dissertaticu A Lstracts laterhational, Nov., 1975, 3b, 268SA-2690A (Univetsity Microfilms ho 75-25, 625) PIJSA000 0001 Develcpmental changes in problem-solving Weir, , Morton W November, 1964, stratEciies Osychelogical Review, 71(6) , 473-490 Welch, Ronald c Tke relative merits of two types of arithmetic rtoblecis Umputlished master's thesis, University of Icva , 1350 J 000 0105 Welker, Latney C., Jr A study of interrelationships in arith _ 000 Vashbuine & Nor1928 Washburne & 0sb1926 Wearne 000 CO4000S 010 000 CC0000C '1927 1977 Webb & Shetrill1974 dissertation, University.-aetical proble4Aolving (Doctoral Dissertation Abstrocts, of Southernyssissippi, - -c-'en 196 2) 011 Webb 1975 h.) 000 000000S 11 Weir 19 64 000 000000S 1.0 we.lker 19 63 April, 1963, :c3, 37 50-3751 (Univeraitv Iiicrofilms No 63- 1780) Westmoreland 1975 First grade entrants' arithmetic problem- P 110 solving behavior as influenced by Ling:rage variation and sex (Dectoral dissertation, Indiana Universi4y, 1974) Dissertation Abstracts International, Narch 17%5, 354 5196A (University Microfilms No 75-5562) IJ 010 Wheat., harry (4 The relative merits or conventional and Contribuimaginative types cf problems irvarithmetic ticns tc Education, No 359 New York: Teachers College, 1929 Wheatley, Grayson h., Frankland, hobeit L., Mitchell, R., Krat t, Rosemarie ilemispheric specialization and cognitive develcpment: implications for mathematics elucaticn do!;rnal tor Besearch in Mathemacics Education, 1578, 9, 20-3 I T000 Whitaker, Douild H A study of the relationships between selected noncoquitive factors and the pioblem solving performance ot fourth grade children (Doctoral dissertation, University of Wisconsin, 1976) Dissertation Abstracts Internanational, April, 1977, 37, 6379A (University Microfilms No 76-29, 947) 000 Whit*, liclen i DocE experience in the situation involved duc ati5n, April, affect the solving of a proplem? 1934, 54(8), 451-455 selected factors that P 000 Whitloa, Prentice E An investigation or atical problems at the affect ability tc solve verLal mathem dissertation, Fordham University, Priallry level Groctotal 1974) Dr.rsertat ion Abstracts International, Sent., 1974, 000k 010 000000S 010 100E4 000 GC0000S 010 Wheat 1929 000R 000 010000 110 Whitaker 1977 10CL1 00 000000S 11 White 19.34 100R 01 0000005 10 Whitlock 197 I '1000 ODOR 000 100110 10 Williams 19 73 Westmorelanc4 John S (University M.crofilms No 74-19, 713) Williams, Ann w Teaching mathematical verbal problems to anilityl, sixth giade readers with an ingui, y mothod (Doctoral issertation, Fnnsylvania State Univeisity, 197 35, 1:437A Dissertation Abstracts International, Sept., 1973, 34, 114 4A (univ(rsity 4icrefilas No 73-21, 20) S 000 000A 000 100000 ability gained Wills, Herbert, Ili Transfer ot problem solving through learning by ulscovery (Doctoral dissertation, UniverAbstracts Internationsity or Illinois, 19 67) Disseitation al, Oct., 1967, 28, 13 19A-1320A (Univt rsity Microfilms 14o 67-1 1, 937) Review Improving the ability to read arithmetic wilscn, hstaline.Mleccutary School Journal, January, 1922, problems i;(5) , 3J0-386 000 000A 000 100000 S Wilson, James W Generality of hLuristios as an instructional University, 1967) variable ()octoral dissertaficn, stanioid fljs rtatioa Abstract.F Intk.rnational, Jan., 1946, 28, 25751t (University Niercfili,i3 Nc 67-17, 52b) 000 100000 000 000R Jchn W The role of structure in verhal problem solving I a.n analytical and experimental comparison of in a rithar three problem-sclving programs (Doctoral dissertation, SyraAbstracts Infernacu:,e University, 196 4) Dissertation (University Microrillas 442-64143 tionai, :lay, 14o5, 25, hc 65-3445) V ' 000 000R 000 100000 wilsen, John W The role of structure in verbal proilen solving Arithaetic Teacher, October, 1967, 14(6), 4E6-497 000 0001 000.100000 enlacement strategies P wittrock, ri C Replacement and nontJournal of Educational in children' s picblem solving _ 010 Wills Wilson 1967 1922 011 Wilson, James 1968 011 Wilson, John 1965 11 Wilson -.010 1967 Wittrock 1967 Psychology, April, 1967, 58(2) , 69-74 IJ 000 woody, Clifforl Som investigations resulting from the c1:1 investigation to t est ino program in dr itnntetiC: detr rmine the influence of specialized drill in reading upon the solution of verbal prcblems Indiana University School of Education Bulletin, April, 1930, (4), 30- 39 I 010 Wright, Jone P A study of childrttils performance on word clues and verbally stated problems containing of Alabama, omitting them (Doctoral dissertaion, UniversityNovember, 1968 Dissertation Abstracts International, 1S68) 29, 17703 ((Jniversity Microfilms Nu 68-15,518) Review young, Robert 1/., mcIsaac, John S The sequence of interpretation of processes aftects the pupil's verbal proulems in arithmetic Education, April, 1941, 61(8), 488-491 two perfor- J 000 Zalewski, rcnald L An exploratory study to compare of mathematical an interview-coding scheme mance measures: rroblem solving and a written test (Doctoral dissertation, University of Wisconsin, 1974) Dissertation Abstracts International, parch; 1975, 35, 5797A-5798A (University Microfilms Ng 74-27, 77 1) ODOR 000 100000 010 Woody 1930 000R 010 0000005 011 Wright 1968 Young & ticIsaac1941 000W 000 000000C 011 Zalewski 1975 ' ci APPENDIX D NATIDNALSCIENCEFOUNDATION WaslAnston, D.0 20550 Institution and Address FINAL PROJECT REPORT NSF FORM 98A PLEASE READ !NSTRUCT:ONS ON REVERSE BEFORE COMPILING PART IPROJECT IDENTIFICATION INFORMATION NSF Award Number NSF Program Northern Illinois University DeKalb, IL 60115 SED 77-19157 RISE S CumulAtive Award Amount Award Period From 9/1/77 To10/31/79 $35.000 Project Title A Review of Research on Solving Routine Problems in Pre-College Mathematics PART IISUMMARY OF COMPLETED PROJECT (FOR PUBLIC USE) This project reviewed the research on routine problem solving (e.g., the typical "story" problem) with an aim toward (a) identifying and disseminating promising practices for teaching routine problem solving and (b) suggesting directions for further research in the area Practices which might improve the teaching of routine problem solving include these: Give attention to processes involved in solving routine problems (e.g., write an equation, make a chart) Devote time to developing the meanir of mathematical vocabulary and symbols Teach that reading of a mathematical problem is different from reading less technical prose, and requires multiple readings with actention to vocabulary and relationships among variables I the Learners make up, and solve, their own word problems Areas in which further research and development seem warranted include these: Instrumentation is needed for process-analysis studier, both 'or protocol coding and process meesurement Studies that examine, the role of language variables (both Lintactic and semantic) in the "decoding" phase of solving a routine problem should contribute to our knowledge of teaching problem solving Whether different ways of presenting problemsobjects, pictures, words-help children of different ages and mental characteristics needs examination PART IIITECIINICAL INFORMA HON (F)R PRof;RAM 31.-1;40EMEN1 USES! F0 131 ITEM (Check appropriate blocks) NONE ArrAcHED PRP/Mt:SLY I URNISHED l RNISH1 1) SUPARA II I Y 10 Pi4.06}(Aki cheek (i, ) Approx Dafi a Abstracts of Theses b Puhlic.ition Citations c Data on Scientific Collaborators d Information un Inventions c Technical Descoutzon ot Prill'l Ond Results C Other(speNy; Prink ipal Invest igatoT 'Pi ject Director Nme (r.,,,:.0 Larry Sowder I X X(App I X \\V\\ \77v VVOr:\ X Printipal lnvestivator P:e;t ' irc;tot _ Signatuiv 4.11.1W 4.7 CYLAA-1 orrri 98A (D/8) Supersedes All Previuus E dawns , 1.14:.-1, Appri%ctl 14 tt 'go 90 X11 Appendix D Project Collaborators Co-investigator" Jeffrey C Barnett, Associate Professor, Fort Hays State University, Hays, Kansas Larry K Sowder, Associate Professor, Northern Illinois University, DeKalb, Illinois Kenneth E Vos, Associate Professor, College of St Catherine, St Paul, Minnesota Consultant Edward A Silver, Assistant Professon, San Diego State University, San Diego, California ERIC Reedy Reference 11 ERIC Accession Number Ranges (By Year) Resources in Education (RIE) PRE-1966 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 ED ED ED ED ED ED ED ED ED ED ED ED ED ED ED ED - 003 960 010 093 010 094 - 012 348 021 151 012 349 021 152 - 031 604 031 605 - 042 060 054 390 042 061 066 620 054 391 066 621 - 080 787 080 788 - 095 253 095 254 - 110 594 127 413 110 595 127 414 - 142 684 157 987 142 685 174 743 157 988 174 744 001 001 010 WO Current Index to Journals in Education (CIJE) 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 EJ EJ EJ EJ EJ EJ EJ EJ EJ EJ EJ EJ 000 001 011 708 027 600 045 272 062 752 082 165 101 873 121 927 142 253 163 352 186 218 207 485 99 011 707 027 599 045 271 062 751 082 164 1^1 872 121 926 142 252 163 351 186217 207 484 ... with highly capable mathematics students The findings of the studies reported in this section strongly suggest that future tesearch pay specific attention to the mechanisms of schema construction