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AUTHOR Problem Solving DOCUMENT RESUME ED 068 340 SE 014 918 AUTHOR Aiken, Lewis R., Jr. TITLE Language Factors in Learning Mathematics. INSTITUTION ERIC Information Analysis Center for Science, Mathematics, and Environmental Education, Columbus, Ohio. PUB DATE Oct 72 NOTE 47p. EDRS PRICE MF-$0.65 HC-$3.29 DESCRIPTORS Achievement; Learning; *Mathematical Linguistics; Mathematical Vocabulary; *Mathematics Education; Problem Solving; *Readability; *Research Reviews (Publications); *Verbal Ability ABSTRACT This paper focuses on the relationship of verbal factors to mathematics achievement and reviews research from 1930 to the present. The effects of verbalization in the mathematics learning process are considered; mathematics functioning as a unique language in its own right is analyzed. Research on the readability of mathematics materials and research relating problem-solving abilities to verbal abilities are reviewed. An extensive bibliography is included. (Editor/DT) 440 'clt 44. e CZ) '4 4447'Ws'7`. 4t,.? S Of PAN TN't NT OF41 At T14 IDUCATION h WI IF AFil Of FICI OF IDUCATION SMEAC/SCIENCE, MATHEMATICS, AND ENVIRONMENTAL EDUCATION INFORMATION ANALYSIS CENTER . an information center to organize and disseminate information and materials on science, mathematics, Cep and environmental education to teachers, administrators, supervisors. researchers, and the public. A joint project of The Ohio State University and the Educational Resources Information Center of USOE. FILMED FROM BEST AVAILABLE COPY 4-3 C) MATHEMATICS EDUCATION REPORTS LANGUAGE FACTORS IN LEARNING MATHEMATICS by Lewis R. Aiken, Jr. ERIC Information Analysis Center for Science, Mathematics, and Environmental Education 1460 West Lane Avenue Columbus, Ohio43216 October, 1972 Mathematics Education Reports Mathematics Education Reports are being developedto disseminate information concerning mathematics education documentsanalysed at the ERIC Information Analysis Center for Science,Mathematics, and Environmental Education. These reports fall into, three broad categories. Research reviews summarize and ana]yze recent researchin specific areas of mathematics education. Resource guides identify and analyze materials and references for use by mathematics teachersat all levels. Special bibliographies announce the availability of documents and review the literature in selected interestareas of mathematics education. Reports in each of these categories may also be targeted for specific sub-populations of the mathematics education community. Priorities for the development of future Mathematics Education Reports are established by the advisory board of the Center, in cooperation with the National Council of Teachers of Mathematics, the Special Interest Group for Research in Mathematics Education of the American Educational Research Association, the Conference Board of the Mat;tematical Sciences, and other professionalgroups in mathematics education. Individual comments on past Reports and suggestions for future Reports are always welcomed by the editor. Foreword The nature of the interaction between mathematical,verbal, and general intellectual abilities with achievement inmathematics has long been a primary research concern of mathematicseducators. This paper focuses on the relationship of verbalfactors to math ematics achievement, and reviews relevant research from 1930to the present. The paper considers the effects of verbalization in the mathematics learning process, and analyses mathematicsas a unique language in its own right. Research on the readability of mathematics materials is also reviewed. Because problems in mathematics are so often presented verbally, a separate section details the research which rel/ates problemsolving abilitiesto verbal abilities. The extensive bibliography which is attachedto this review should help guide the reader to documents in thisarea which are available through the ERIC system. Jon L. Higgins Editor This publication was prepared pursuant to a contract with the Office of Education, U.S. Department of Health, Education and Welfare. Contractors undertaking such projects under Government sponsorship are encouraged to express freely their judgment in professional and technical matters. Points of view or opinions do not, therefore, necessarily represent official Office of Education positionor policy. 4 LANGUAGE FACTORS TN LEARNINGMATHEMATICS Lewis R. Aiken, Jr. Guilford College It is generally recognized that not only do linguisticabilities affect performance in mathematics but that mathematics itself isa specialized language. Monroe and Englehart (1931) summarized some of the earlierresearch )n the relationship of reading ability to problem solving. More recently, the writer (Aiken 1971 b) briefly reviewed research concernedwith verbal factors in mathematics learning and teaching conductedduring the past four decades. As one reader of that paper pointed out, however,a review of studies pertaining to the effects of all language factors wouldhe more useful. This is the intention of thepresent paper. Although many of these studiesin- volve only a few variables, are not clearly tied to otherinvestigations, and frequently pose more questions than they answer, a number ofimplications and suggestions for further researchare embedded in them. Mathematical, Verbal, and GeneralIntellective Abilities Reading Ability It is not difficult to ttnderstand how rending ability couldaffect per- formance on verbal arithmetic problems, and supporting dataare plentiful. Table 1 summarizes the results of a representative sampleof studies in which various measures of general and specific reading abilitieshave been found to be correlated positively with scores on arithmetic and mathematic:;tests. These investigations, the majority of which have been basedon children in the intermediate grades, yielded correlations between readingability and mathe- matics achievement ranging between .40 and 186 (see column 3of Table 1). 5 Correlations of Mathematics AchievementTable 1with ReadingAbility and Ge.teral Intelligence Reference and Sample Variables Zero-orderr = .46 r rPartial= r.13a Balow (1964), 368 California 2.1. ArithmeticStanford Achievement Reasoning TestTest-- 12 12,3 3. MentalCaliforniaReading Maturity Short-Form Test of sixthChase graders(1960), 119 California 2.1. VerbalGatesPrimary Reading Mental toAbilities- Note Details - r2414= .34.40 r24.1314.23= .21.27 4.3. IowaNumberPrimary Every Mental Pupil Abilities- Test- - - Cleland & Toussaint (1962), 1. GatesArithmetic Reading (problems Survey--Form section) 2 r14= .49 r14.5= .45 Pennsylvaniapupils172 intermediate-grade in Western 2. STEP Listening Comprehension r24= .41.46 r14.6= .36.46 4.3. AmericanCapacityDurrell-Sullivan School Arithmetic Reading 34 r24.624.5= .37 6.5. ScaleStanford-BinetPrimary Mental Abilities--Intelligence Total rr34.534.6= .42.45 Table 1(cont'd) r,, =.85 ,z3; underachieversthird-grade(LoS), arithmetic 18 New York 2.1. StanfordArithmetic AchievementAchievement Lest- Test- -- Reading r =.62 EricksonIndiana (1958),sixth graders 269 2.1. Iowasection)ITBS Silent(sixth-grade Reading arithmetic Test r1312=.67 3. Vocabulary)(ReadingIowa Silent Comprehension) Reading Test Ivanoff,(1965), DeWane286 Wisconsin & Praem 1. HighIQ Rating School Placement Test-- r12=.69 r12.6=.56 malesalgebrain general in andninth-grade mathematics162 males 2. ReadingHigh School Placement Test-- rr13 =.61.59 rr13.2=.37 3. ArithmeticHigh School Placement Test-- r25r.14 =.50.52 :24613.4:.41 4. LanguageHigh School Placement Test-- r26=.59 r25.1=.41.22 6.5. markSuccessfulEighth-grade Completion mathematics of r,_-34 =.55 r34.1r26.1=.31 algebrageneral mathematics vs. r46 =.53 rr45.146.1=.32.34 Table 1 (cont'd) Muscio (1962), 206 1. California Vocabulary Tests, r boysCalifornia and girls sixth-grade 2. MathematicsStanford Reading Tests, r27r17 =.78 r27.617.6=.48.50 3. StanfordParagraph Reading Meaning Tests. rr3747 =.68.78 rr37.647.6=.34.47 4. TestGatesWord C MeaningBasic Reading Tests, r57=.55 r57.6 .27 6.5. CaliforniaTestGates D Basic TestReading of MentalTests, 7. QuantitativeMathematics,MaturityFunctional (mental Evaluation TestUnderstanding ages)1: in Pittseleventh-grade (1952), 210 Negr- Georgia g4rls 1. CompetenceDavis Test inof MathematicsFunctional r13r12 =.46.53 r13.2r12.3=.12.31 3.2. Otis(readingIowa GammaSilenc grad IQs Reading Tests resultsreportedaIn of manyin different the of papersthe investigations.papers, but were the computedzero-order by and/orthe present first-order writer partialto serve correlation as a basis coefficientsfor comparing were the not 5. Obviously, as Monroe and Englehart (1911)concluded some 40 yearsago about related investigations, thesefindinv are open to variousinterpretations One recommendation made in thatclassic paper was that furtherresearch on the relationships between reading abilities and mathematics achievonent shouldhe directed toward specific reading skillsrather than general reading In response to this recommendation,a number of studies have been concerned with specific reading skills in mathematics (e.g., .John' on, 1949;lh 1969). Unfortunately, the results have notconsistently demonstrated superiorpre- dictive validity formeasures of specific reading abilities, either singly or in combination, when compared to measures of general reading ability. For example, Henney (1969) reported that specificreading abilities were nomore highly correlated than general readingability wit arithmetic problem solving in a large sample of fourth graders. Perhaps what is required isan extensive cross-sectional
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