Journal ofResearch in Rural Education, Fall, 2003, Vol. 18, No.2, 86-95

Research About Mathematics Achievementin the Rural Circumstance

Craig B. Howley and Erik GunnACCLA IM Research Initiative

Rural education scholars have noted that many educators presume rural schooling suffers when compared to nationalnorms. This rel'iell' rakes a closer look at this common presumption by placing the issue in historical con text and thenfocusing attention 011 mathematics achievement. Because mathematics is arguably the mas t teachable ofsubjects, determin­ing the comparative status ofrural students .achievement ill this subject seems a good tes t ojthe pres ump tion The reviewshows that available evidencefalsifies the presumption. hut a more critical issue persists: What is the place ofmeaning inmathematics education, and what role docs "place" occupy in such meaning! An unpacking ofthis issue. together with alist ofsalient research topics. concludes the discussion.

Interest in the achievement of rural students is under­standable as, in part, an issue of equi ty. Rural educationscholars (e .g.. Herzog & Pillman, 1995) have poin ted outthat rural schooling typically has been viewed as deficient.Raymond Williams, professor of literature at CambridgeUniversity and au thor of perhaps the finest book on thetopic of the cultural rela tionshi p of country and city (Wil­Iiams. 1973), observed tha t this prejudice is difficult tounseat because me tropolitan norms have been establishedas universal norm s. "The World City," he later wrote. be­came the . tandard of cultural propriety (Williams. 1989)' .Cultural deficiency, of course, translates rather directly intopresumed educational deficiency (sec Johnson & Howley.2000, for a review of Williams's work addressed to ruraleducators), For many such reasons, rural education. on thewhole. i. pre umed to be nationally deficient. The politicsof poverty rely on con tinued propagation of the impressionof deficiency as a route to continued assistance and atten­tion (and sources of local power: sec, e.g .. Gaventa, 1980;Whisnant. 1980).

Does the presumption sta nd up to evidence-and tocurrent evidence abou t mathematics achievemen t, in par­ticular? And what if it docs not'? These questions matter.first . because the rate of poverty in nonmetropoli tan coun-

A previous draft of this material appeared as Working PaperI o. 4 of the Appalachian Collaborative Center for Learning,Assessment. and Instruction in Mathematics (ACCLAIM). Thismaterial IS based upon the work supported by the rational ScienceFoundation under grant no. 0119679. Any opinions. findings. andconclusions or recommendations expressed in this material arcthose of the authorts) and do not necessarily reflec t the views ofthe National cicncc Foundation.

Correspondence concerning this article should be addressedto Craig Howley, McCmeken Hall, College of Education, OhioUniversity, Athens. 01-145701. (howlcyc@ohio.edu)

ties exceeds that in metropolitan counties, and poverty ofcourse carries s trong achievement costs. On one hand, then,observers have an empirical reason, no t directly related tocultural and ideo logica l arguments, to presume deficiency.On the other hand. the observed differences in nonrnetro

and metro poverty rates are modest-I 3,4% as compared to10.8% (U nited State' Department o f Ag riculrure [USDA].2002). Insofar as achievement i concerned, empirical testof the presumption of rural deficiency ac tually arc po. sible:one need no t res t with inferences based on overall povertyrates in metro and nonmetro counties. This article reports theevi dence on rural differences in mathematics achievement,setting the synthesis first in historical co ntext.

The pres umption is shown no t actua lly to be warrantedby the available evidence. This "discovery" relates to theimportance of the second question. In light of the bad habitof'claiming rural deficiency as a warrant for resources and at­tention, one must address wha t other significance being ruralmight actually possess. For this reason, the discussion close 'with a consideration ofthe place ofmeaning and the practicalmean ing of place to rural mathematics education.

Historical Background

Hi torica l data on mathemati c ' achievemen t are notavailab le. but literacy rates and educational attainment dataillus tra te hi torical trends related to rural educa tional ac­compl ishment from the mid-20 th ce ntury to now. Illiteracyand educationa l attainment were regarded as dis tinctive ruralprob lems as sho rt a time ago as 50 years.'

I The World City is the standard to which all other eulementsarc compared. with London being the first world city. followedrapidly by others-Paris. cw York. Singapore. and Hong Kongamo ng many others. Cosmopolitan sta ndards. of course, prevailtoday and are embedded in thc phrase "world-cia s."

RESEARCH A BOU T MATl IEMATICS AC llIEVEMENT 87

Illiteracy wa.. somewhat more prevalent in rural areasthan elsewhere. and within rura l areas . it was mo re prevalentamong fanu rather than non farm populations.' In 194 7. theBurea u of the Census es timated the national ill iteracy rate at2.7% (among the population aged 14 ye ars or old er : Bureauof the Census. 194X), For the " rura l-farm" populati on therate was 5,3%; the "ru ral-nonfarm" rate was 2.4 % . In otherwords. the illite racy rate lo r fanners was about twice thenational average.

This seem.. to be a wide gap . but it is important to ob­serve tha t ill ite rates cons tituted a vel')' sma ll proportion ofthe population whatever the loc ale (nat ion . rura l-farm, orrural-non farm]. The failure in man y d iscu ssions to make that

distinction reinforces the prevai lin g mi scon cep tion of rura lcultura l. intellectual. and edu cati onal inadequ acy.

Th e Ce nsus Bureau itscl f. however. observed tha t illi t ­e racy at mid -cen tury was co ntinu ing 10 decli ne for the nation

as a whole. and tha t econ om ic cond ition s accou nted for thesma ll (an d sh rin king) rural-urban dispari ties. The ano ny­mous bureau analyst (Bureau of the Census. 1953 )attributedrura l illiteracy to three possible ca uses: (a) ourmigration o find ividu als wit h more schooling; (b ) the exige nc ies ofopcr­at ing a fami ly farm : and (c) the remoteness ofschools. xoncof these hypotheses rei nfo rce d the longsta nd ing message ofcultural defic ien cy identifi ed by Wi lliam s (19731.

Data on ed ucational atta inment in the 1953 report paral­lc l tho sc tor literacy: The medi an yea rs of fo rmal sc hoolingwas R,5 yea rs in rural farm areas. 9.7 in rura l non farm areas,

and 10.8 in urb an area s. Comparable data on educa tional at­

tainment from 1950 to 2000 in ru ral \'CTS US othe r areas doe snot appear to he available. Table I. the res ult o f library andInternet res earch, assembles so me wh at inconsistent data:changes in the way the Census Bureau has reported educa­tiona l uuai mucnt data re flect the changes tha t trans formedrura l areas in the 20'hcentury.

About 1950. grad uation fro m high sch oo l was hardlythe nonn among the adult poputation. and abou t tw ice asma ny urba n as rura l farm adults had gra duated fro m highschool (42% ve rsus 23%). By the end of this time period(1950-2 000; sec Table I ), the Census had g ive n up report­ing far m an d nonfarm d ist inct ions. replacin g rural wi thnanmetropolitan, Educa tiona l at tainment in metropoli tanand nonrnctropolitan are as was nearl y ide ntica l. As farrn­ing decli ned as a rural way of life. high sch oo l graduationbeca me the expec ted norm for all Americans, The slig htdifference in rates ma y be the joint resu lt o f co ntinuingourmigrarion among you nger res ide nts and the concurre ntdis proportionately older po pulat ion in rural areas.

Information abo ut illit era cy und educational a ttai nme ntsho w that for mu ch of the :W'hce ntu ry. rural Americans weresome whatless schooled than other Americans. I Iowever, the

compa rison is cl ouded by seve ra l ongo ing circ ums tanc es.Unt il about 1950 or so. fan ning di d not requ ire a largecapua l investment: it was widel y understood. moreover. tha t

one could fann suc cessfu lly w ithout graduating from highschool. Second. tho se who did co mplete high schoo l we remor e like ly to ah andon rural area s for urban areas see kingindustr ia l employme nt or. after receiving univers ity creden­tial s . 10 take up metropol itan careers (e.g.. Berry. I 97R/ I990;Gruchow, 1995). Th ird. and as a res ult of the prev ious fac t.acad emic tale nt was ex po rted to the metro poli s . Rur alareas were a major con tributor o f human resources to thecons truct ion of an ind ust r ia lized and burea ucratized 20'"century America . and rural m igrants to urban are as sharedin the acco mpli shm ents there of nonmigrants. Indeed, it isa wonder that rural area s no lon ger exhibit "d eficie ncies" inlitera cy and atta inment . We m ight expec t. then. that . overall.rura l achievement levels in ma them atics sho uld app roxima tethose prevailing elsewhere.

Ntlliunal Assessment of Educational /'IlW,J'(',H Reports 01Rural ,\!<llh£'ffwlics Achievement

T he National Assessment of Ed uc atio nal Pro gresstNA EP) ma kes it fIlolss ib le to assemble co nsistent in for­

ma tion on the co ntemporary mathematics ach ievem ent ofrura l students . :-.lA EP has pro vided com parable reports ofma thematic s achievemen t nati ona lly since 197x! and at thestate level since 199 2. beginning w ith a sta te-level " trialasse ssment" tha t year.

In the firs t pa rt of the d iscuss ion , we examine na tionalaggregations based on official NA EP reports . These reportsprovide only descrip tiv e data , but tes t no theories or hy ­potheses and ca nnot by themselves provide mu ch insightinto fhc ca uses of any observed differences or vari ations.~AEP nonetheless ha s been wry careful to d istingui shs tat istica lly non significant from statistically significan t d if­fere nces among s ta tes an d 10 provide the ba sis lo r ma king

" Illiteracy in Census reports of this time was self-reportedinabrhty to read or ....me among Ihat pon i.m of the populauonwith fewer than 5 years of formal scbcolmg: those with at least5 years of schooling were pres umed 10 be literate. a presumptionapplied by the U.s Army .... hen ;1screened draftees during theSecond World War.

1 Rural areas for the 19"'and 20-' centuries .... ere divided bythe Census Bureau into two segments due to the prevalence ofagriculture as a way of hfe: "rural- farm" areas and "rurat-ooefarm"areas. The "rural-farm" population included people hving on farms(defined as such according 10 a low annual sales threshold. e,g..S1.000 in 19!':9); "rural-nonfarm" was the residual rural population.During the course of the 20'" century. the rural-farm populationshrank from about M%ofthe ruralpopulalloo to about 6% by \990.the last decennial census for which the distinction was made.

• NAEP began operations in 1969and produced us first math­ematics as..essment in \976 . The 1976 data are not comparable tothose provided in later years. especially as the U.s. Department ofEduca tion assumed management of the program. which had begununder the auspices of the Education Commission of the States.

1I0WLEY AND GUNN

Table IEducat ional Attainment in the United Stutes f or Rural Arell.~. Urban Areas, lind the Nation

Year' Rural Farm" Rural Nonfarm" Ncnmctro' UrbaniMetro~ Nation- --

1952 (YRS) ".5 9 .7 io.s 10,1(IIS +) (23.2'\!o) 135.9"10 ) (42 .1% ) (3k .-l%)

1960 (YRS) R.R 9.5 9,2 11.1 10.6(HS+) (29.5% ) 0 4.4%) (33.2%) (4.1.3%) (4L1%)

1970 (YRS j 10.0 II. S I l. fl 12,3 12.2H{S+) (34. Q%) (4K.9% ) (47.9% ) (59 .3%) (55.3% )

19K! ( 11 5 +) 63.5% 66 .1% 65.9% 73.4 % 71%

1991 (II S+ ) 76.g% 71. K~~ 10:0.1'% 710:.4%

l OOt) (HS+) lolO.O% R3.8% 83.1%- - - - --

.\101<'.'. Census Reports P-:W, No. 45, reere 12 u l}51 ); PetS 1)-10. Table 76 (ll}()OI: 1'-10, No. 207, Tabh: 2 41970 ): 1'-20. :\0. 390, Table7 (I ',llll ); 1' · 20, 1'\0. 46 2, Tahle 10 i 1991 ); and p·2l1, ~o. 536. Table I I (2000 ).• " YRS" indicates media n years o r schcolmg. Alier the 1970 report, ed uca tional atta inment was not repon ed as median years of scbcol­ing. hut on ly as perc entage of persons complet ing a specified nu mbe rs Ilf years . "11$+" indicate'S the percentage of pe rsons com pleting atlea' l 4 years o f high school For I ',l52, 1l}M1, and 1l}70, this figu re IS the sum of the percentage' for the rele vant categories: pa renthesesmdscate these sums, For IQ81-20<Xl. apparently cqmvalenttotnls wen: supplied in the ca ptioned tab les For the 1952, 1960 , and 1970data. the statistics pert arn to the populauon III yean; and olde r. whereas lo r the ]',lll i . 1Q91 . and 200(J data . the stali, tics pertain 10 thepopu latio n 25 yea n; and older· " Rural-Fann" and "Rural-Nonfarm" catego ries were elimina ted ... ith the 200t) decen nia l census.' '' Nunmctro''- II county-level des igmll ion-appears liT'it in thi s se ries uf reports in the 1970 Table. The still istlO: f(>r 1960 is for "ruraltotal," a de-agnanon that does not ap pear in the ca ptioned 1952 Table.' The "urban/metro" column gives statistics for al l UrOOn areas through the 1960 report, and metropolitan sta tistics (a county-level des­

ignauonj thcrcaft cr.

the di suncuons among variously constituted population

su bgrou ps .Interp retin g NA EI' data requires appreciation of the

changes in NAEP administ rat ion and design . From IQ7Rthrough I'}t}2 , NAEP "s rural category was "extreme rural"(contrasting "extreme rura l: ' for instance. with "advantag edurban" and "disadvanta ged urban" loca les) . "Extreme rural"was portrayed in NAEP report s from about ! lJ70 as home10 farm families and agricultural wo rkers-s-e ven as thi scharacterization was becoming less apt. Worse still. thefu nction o tlocalc in this conce ption was essentially 10 drawa geographic line around disadvantaged groups: a defi citmod el of loc ale .

Starting in 1996, Ih is shortco m ing wa s corrected .For 1996 and 21100, loca le breakouts of NA EP data wereinclusive of all students. nOI JUSI an cxcepnonat fractionunderstood as disad vantaged or somehow defi cien t Th e newcat egories were "c entral city" (central cities of MetropolitanStatisncal Ar cas): "urba n fringe/large town" [me tro areasadja cent to the ce ntral cit ies of 250 .000 or more population

and towns ofpopulation 25,000 to 50.000): and "rural/sma lltown" (non rnctru towns uf'nu more tha n 25 ,000 plus outsidetowns or villages of 2.500 or less and the open countrysidein both metro a nd nonmctro areas ).'

In 1992. NAE r began to rep lace its previous aSSeSSIIll'll1sys tem, which provided only nat ional estimates ofachieve­menl owith a system thai now incorporates sla te-level esti­mates. Thi s change provides researchers the opportunity toinvestigate variability among sta te sys tems. incl uding rura lwithin-state compar isons. (~AEr itself reports mean diffe r­enc es but docs no t usually auemptto sort out rela tionshipsamong contributing influcnccs.)

~ Sec Johnso n ( 19:'19) and N{' ES (2002 ) for further details onthe development and UM: of "locale code-s." Johnson provi des theorigi nal de velopment and the latte r CItat ion the current overview,as well 3~ links 10 numbers of sc hools, districts. and students bylocale. Betw ee n 1996 and 2f10(l. however, the methods for assign.meru of locale codes were altered slighlly. 10 tak e better accountof the " more informauon about the exact phy sicullocanon of the

Sl"hool" , Braswell et al ., 20()1, p. 223)

RESEAR CH ABOUT MATII EM..\ TICS AC HIEVEMENT

Table 2.VAEP St.·ule Scorrsfor 1978_/991, Nanonat MC(/I/s /'t'r.m.1 "Extreme Rural " '\/1'.11/.1

Year

Grade

4

,

12

Locale 197~ 19S2 19l'i6 1990 1992

nation 2 1S 219 22 1 230 21~

extreme rural 212 211 219 231 2 16difference ·6 ." -2 +1 -2

nation 2M 26S 269 270 268extreme rural 255 258 270 265 267difference ·9' - 10 · +1 · 5 · 1

nation 301 299 302 305 299extreme rural 295 293 305 304 2Q3difference -6' -6' +3 ·1 -6

Join' l'. Source for 197~ _ 199lJ : Stern (1 'N4 . p. 110); Source for 1991: (~lulli ~. Dossey, Owen. &: Phillips. 19'13)• - drtference significance at p :::; .05 (197~- J990 per Stern: 19'12 drrterence computed by author as stanJ3rJ error difference based on

reported SEMs (SEM. f - SQRT[(SEM/ + (5L\1)rl .

Finally. it is important to recog nize that scores generatedby the NAEI' testing and reporting sys tem arc. for eachstudent tested. predicted and not actual scores . Each studenttakes a frac tion of the entire assessment. and proced uresbased on Item Response Theory predict the score a studen twould have received had the whole tea been administered.None theless. there seems to be little doubt that agg regationsat the state and nationa llevel pro vide valid and relia ble as­sessmcnts of aggregate achieve ment level s.

Table 2 reports :"AEP data about the ma the maticsachievement of'rural students from the national assessmentsfrom 1978 through 1992 , Table 3 reports data about rura lstudent achieveme nt from the 1996 and 2000 assessments.

As suggested previously. the 1992 and 1996 "rural "data are by no means comparable. sinc e they represent theperformance o f subs tantially di(Iercn t national populations(data in Table 3 for 1996 and 21:HJO represe nt, by compa rison .slightly different national populations). Obse rved differencesfor 1992 and 1996 (+6 , +9, and +7, respectiv ely. for grades4. S. and 12) arc starisncally significant at the X'" and 10'"grade s. These reported differences. however, doubtless areexplained by the prob lematic d ifferences in the two pop u­lations (part icu larly soc ioeconomic status).

However. two infe rences about trends seem evi dent.First. across 25 yea rs of testing, there has bee n little changein the mathema tics performance of rural students. Seco nd.the performance of rural students differs litt le from thenational average in all th is time .

The second clai m need.. some justification. since Tables2. and 3 show negative differences in abo ut two th ird...o f rbe

cases. and this fact might appear to ind ica te a defici t. Butmos t ofthe given diffe rences are not statistically significant.For those that are . we can calc ulate effec t sizes. Effect size sgive the cha nge in standard devia tion units associated witha treatment or a condition. Moderate effect sizes are in therange o f +1- 0 .20 to +1- 0 ,50, with strong effect sizes rangingfrom - t, 0.50 and up.·

w hat effect sizes do the differences provid ed in Tables2 and 3 yield? The largest difference in both Tables is for theIl)X2 eighth grade (-10, P < .05 ). II represen ts an e ffect sizeof roughly -.25 <based on an appro ximate standard deviationo f 40) . For the las t 14 years (1 9~6-2000). however. none ofthe diff erences atta ined statistical sign ificance.

On the basis o f nearl y 25 ye,lTs nfNAE P dna, there islittle evidence fo r the cla im that rura l mathematics achieve­ment is deficient. The observed diff erenc es between ruralareas and the nation as a whole are small; the practical importo fpre- 19X6statisucully signi ficant differences is doubtful;and observed po sitive differences are almost as frequent a...

• Compare to Cohen (l 9~S l. who quite reluctantly offeredJ - .1tl a.. ....mall.·· ,1 - 5 0 as "medium," and ,/ - .sOas "[urge."Ili ~ reluctance ..rcmmcd from h IS appreciation of the very diverseresearch contexts in which the ruleofthumb might be applied. Withrespect to influences on achievement, the authors believe that aneffect SIZC of one-half standard deviation merits charactcrizauonas "large" and one tenth (d - .10) as "small." Roughly speaking,adifference of a full ..tnndard deviation on measures of compositeachievement is tantamount 10 a year's difference in learning (burthis too is a rulc-ol: thumh). and an effect of that magnitude (d "1.0) would be Olll "large" but very nearly mtrncu lous.

90 HOWLEY A D GU

Year

Current Research 0 11 Math Achievement in Rural Areas

observed negative differences (though none of the positivedifferences proves statistically significant).

Table 3NA£P Mathematics Scores/or Rural/Small Town Students,1996 and 2000

ic scores of 10,h grade students on tests administered bythe Longitudinal Study of American Youth (LSAY), a panelstudy of mathematic. and science achievemen t funded bythe ational Science Foundation. Previous studies. ba edlargely on different tests and samples among state- levelstudies. hewed no significant difference in test scores forstudents in small, rural communities compared with nationalaverage . Haller et al. sough t to test the hypothesis thatthose earlier findings were principally the result of norm­referenced tests that lacked items a'. cssing "higher-orderthinking." The LSAY tests were constructed using AEPitems and were thus notably different from nann-referencedmeasures used in the previous literature at that time. Halleretal. detail the way in which the NAEP-developed items moreclosely refl ect achievement related to higher-order thinking.The sample was nationally representative (including nearly2.300 12th grade students from 51 schools). Test includedboth mathematics and science.

The issue for Haller et al. was the possible handicap thatrural status and small school size-especially the associationof smaller rural high school with fewer advanced mathemat­ics and science courses-might impose on higher-orderlearning. Control. included in the study's regression analysiincluded school size, rurality, poverty. advanced course of­ferings. and enrollment rates in the advanced courses .

either rurality nor school size correla ted significantlywith the outcome measures, including higher-order learningin mathematics. The number of advanced course offeringsshowed no relationship with either outcome measure, butthe degree of student participation in these courses didshow such a relationship (I' = + .38 for mathematics). Inregression analysis, the only significant predictor variablewa prior achievement. Haller et al. ( 1993, p. 71)conclude,"While large schools offer more advanced courses than dosmall ones. those offerings appear to have no influence onaverage levels of student achievement." As it relates to theoften more narrow mathematics curriculum of rural schools.this conclusion is quite provocative, particularly when oneremembers that "achievement" included the demonstrationof higher-order skills. which Haller ct al. (p. 68) define as"identifying and u ing a problem-solving strategy.screeningrelevant information, formulating a problem or electing amodel of a problem situation, determining what informationwould be needed to solve a problem, and organizing giveninformation to represent a problem."

One possible shortcoming of this study is its use of anationally representa tive dataset. Regional and state-levelconditions (economics , politics, history. culture of educa­tion policymaking, and so forth) exert strong influenceon schooling. These influences arc sufficient to structuresharp differences in student performance and in the condi­tions of schooling at state and regional levels (e.g.. Bee on& Strange. 2000). ational data-as in the AEP reportsand in Haller et al. ( 1993)-answer an important question

Locale 1996 2000

nation 224 22~

central city 218 222urban fringe 229 232rural/small town 222 227difference -2 -I

nation 272 275central city 265 268urban fringe 275 280rural/small town 276 276diffcrcncc +4 -d

nation 304 301central city 301 298urban fringe 309 304ruml/srna II town 301 300difference -3 - I

8

4

Note I. Because NCES changed slig htly the method for assign ingtype of locale codes between J996 and 2000. data for 1996 and2000 arc no t stric tly comparable, though the ove rall influenc e ofthe changes might we ll be random (as compared to the 1992-1996chan ge. which was clearly systematic). The comparisons reportedhere should be regarded cautiously with this complexity in view.

12

Grade

Note 2. Locale means from NCES (2002). National means fromBraswell et al. (200 I). Di fferences listed arc tho e prevailingbetween rura l/small town mean s and national means. None of thedifferences is statist ically significant . Since standard deviationsequal about 35 scaled score points. the (nonsignificant) effec t sizescan be estimated to vary between .029 and . II . The national samplecontains approx ima tely 15.000 students at each grade level. withapproximately 25% of the samp le at each grade level reported 10

have attended rural or small -town schools.

We tum now to empirical studies with an explici t basein theory. The extant litera ture is indeed thin, but threeexcellent recent studies nonetheless provide a surprising lycomprehensive picture of mathematics achievement amongrural uudents

Haller; Monk. and Tien (/993). Emil Haller, DavidMonk, and Lydia Tien examined the 1987-1989 mathcmat-

RESEARCH ABOUT MATHEMATIC ACHIEVEMENT 91

at the same time that they mise additional questio ns aboutvariability at levels closer to real experience: regions. states.districts. and schools. In additio n. the number of schoolsinvolved (N = 5 1) may embed a restriction-of-range prob­lem for rurality and size. although the authors state thatschools-not students-were selected in a random sampleproportiona l to enrollment size in 12sampling strata. one­theless, 51 schools seem a size unlike ly to capture well thelocale or size variab ility of 25.000 high schools.

Fan and Chell (/999). Xitao Fan and Michael Chenpublished an assessment of the academic achievement ofrural students as compared to uburban and urban studen ts.Thei r assessment included regio nal comparisons. Thcyexamined test sco res for reading, mathematics. science.and ocial studies using the ational Educational Longitu­dinal Survey ( ELS:88) data set. Separate analyses wereconducted for 8'\ IO~·. and 12th grade students. As with thepreviously considered study, mathematics was one amongseveral achievement outcomes . These researchers sough tprimari ly to test the hypothesis that rural studen ts in the

.S. received an inferior education compared with theirmetropolitan counterparts, with parity of achievement thecriterion. Methodo logically, Fan and Chen aimed to over­come fiveshortcomings ofprevious studies: sampling issues;inconsistent definitions of locale: and socioeconomic status.ethniciry, and sector as potentia lly confou nding variables .

The analyses were carefully executed and comparativelysophisticated. and the resu lts are simply stated : With care­ful controls in place. no practically significant differencesbetween test scores existed by locale (rura l, suburban. andurban).This includes locale comparisons by ethnicity, regionof the nation, grade level, sector. and even for Caucas ianstudents by locale by region. Small. statistically significantdifferences were found. but with large sample sizes. theeffect sizes of these small differences (generally hoveringaround 0) were judged to be of no practical importancewhatever, Marginal means (adjusted for the influence ofSES) were higher in private than in public schools, thoughthe authors did not compute A COVA statistics for thiscomparison since between-sector comparison. were nota focus of tudy. Within sector. though. there were nomeaningful differences by locale (e.g.. rural private-schoolstudent performed comparably to their urban and suburbancounterparts ).

The Fan and Chen data exhibit the familiar achievementdifferences regarding ethnicity and socioeconomic status.but within comparison groups they found few significantdifferences by locale and none that would be judged aspractically important. In sum, looking systematically fordifferences between rura l studen ts and other students, Fanand Chen (1999) found none.

Lee and Mcintire (2000) . Jaekyung Lee and WalterMcintire used A' P eighth grade data for 1992 and 1996to investigate state-level variabi lity in rural versus nonrural

mathematics achievement, as well as to investigate the po­tential influence ofsix schooling conditions on that variabil­ity. Information from 35 states was available for comparison .The study also exam ined state-level changes for rural andnonrural studen t segments from 1992 to 1996.

Lee and Mclntirc's six schooling condit ions were de­rived from perceptions elf-reported to AEP by teachersand principals: (a) instructional resources (percentage ofteachers responding all or most to a question about provi­'ion ofresources for teaching mathemat ics); (b) professionaltraining (based on I I AEP items having to do with trainingor course-taking); (c) eighth grade algebra offering (oneNAEP item: ye or no); (d) progressive instruction (10 itemsconcerning small-groups, calcu lator usc, and so forth); (e)safe/orderly climate (7 items relating to school-level disor­der); and (I) collective support (7 items about school-levelrelationships). This study. among the two others cited. isnotable for its specificconsideration of mathematics achieve­mcnt, which allowed the researchers to make hypothesesabout, and investigate the variation in. the conditions ofmathematics instruction that might influence rural mathemat­ics achievement at the state and national levels,

Lee and Mcin tire first reported national averages forrural/nonrura l comparisons. For 1992. the national-leveldifference is 265 (rural) versus 267 (nonrural), which wasnot statistically significant. For 1996, the rural mean was 276and the nonruralmean was 268. With tandard errors of 1.92and 1.80. the standard error of the difference (5.26) indicatesa stati .tically significant difference in 1996 favoring ruraltuden ts. The difference equates to an effect size of +0.23.

This positive di fference (favor ing rural students) is equalin magnitude 10 the largest pre- 1986 negative differencebetween disadva ntaged "extreme rural" and the nationalaverage. noted previously in the discussion of historical

AEP reports .Results for the 1992 and 1996 assessments. predictably.

varied a great deal at the state level. In some states. the nonru­raj portion of the population performed better or worse thanthe rural portion. but in other states there wa no significantdifference . In fact. in 21 of the 35 states with data for bothyears. a tatistically significant rural vs. nonrural gap did notexist. In the 14states with such gaps, however, the directionof the difference varied . In half these states. in fact. nonruralstudent aggregate scores were higher than those of ruralstudent (Georgia. Kentucky, Mary land. North Caro lina.South Carolina, Virginia. and West Virginia).

Such state-level differences can be accounted for, atleast in part. by differences in the conditions of schooling.These condi tions themselves arc linked to state-level poli­cies regulating or shaping the way districts, school • andclas rooms operate. In thi study, those conditions werelimited to the six schooling conditions previously described .Across the 35 state cases, these six conditions account forfully 84% of the variation in state-level AEP eighth grade

92 HOWLEY AND GU

mathematics achievement among the rural portions of therespective states' populations; the comparable statistic forthe nonrural segment was 69 % . According to the Lee andMcintire,

Rural students in states where they have accessto instructional support, safe/orderly climate. andcollective support tend to perform better than theircounterparts in states where they don't. (emphasisadded. p. 171)

However, it is important to ob .erve that the magnitudeof correlation. (of achievement) with the conditions ofschooling across the 2 years changed substantially. Progres­sive instruction. in fact. was moderately related (r = .52) to1992 achievement for nonrural, but not for rural students.Among rural students in 1992. the correlation was r == .70.accounting for nearly 50% of the variance in state-levelachievement. but in 1996. the correlation was a more moder­ate r = .50 . accounting for just 25% of the variance in state­level rural achievement (the same as for nonrural students in1992). The analysis. comparatively fine-grained as it maybe. does not permit generalization to future years. Instead.these data provide substantial material for hypotheses insubsequent studies.

Lee and Mcintire also correlated state-level differencesin rural vs. nonrural achievement with state-level rural vs.nonrural differences in the six condition of schooling forboth 1992 and 1996. The strength of the association ofthese measures and rural /nonrural difference varies acrossthe years, but the researchers report that the six conditionsaccount for about 45 % of the variance in the achievementgap . On this basi . they conclude that parity of schoolingconditions is associated with minimizing or eliminating thestate-level rural/nonrural achievement gap in sta tes wheresuch gaps exist. The researchers illustrated their conclusionwith a contrast of schooling conditions in Connecticut andVirginia: Favorable rural learning conditions existed in Con­necticut. where rural students exhibited higher scores thannonrural students. In Virginia. the opposite case prevailed.Of course. rural populations differ significantly by region(USDA, 2000). and the Lee and Mclntire analysis did nottake such differences into consideration.

Lee and Mcintire also examined conditions associ­ated with rural achievement gains from 1992 to 1996 . Theresearchers contra ted 12 states with statistically signifi­cant gains for their rural populations with 23 states wheresuch gains were not evident; they concluded that the gainswere associated with the conditions of schooling. Such anexhibit (sec Lee & Mcintire, Figures 2 and 3. pp . 175-76)supplies some warrant for the claim. but a comparativelyweak one.

Although not conclusive. the Lee and Mclntire analysesillustrate the complexity ofthe landscape of rural mathemat-

ics achievement at state and national levels . In particular.they point out that the most interesting and useful work tobe done lies below the national level and ought particularlyto address issues of state context.

Conclusions and Extensions

A number of conclusions seem reasonable in view ofthe foregoing discussion. Together they point to an historicalconvergence. with prevailing national norms, ofeducationaloutcomes in rural places. It seems clear that . ince about1975, this national convergence is reflected in levels ofmathematics achievement, whether statistically controlledfor the effects of poverty and other influences or not.

Four specific conclusions seem evident. First. over thecourse of the 20 <b century. as fanning declined as an oc­cupational choice for Americans. gaps in literacy rates andeducational attainment rates among rural-farm, rural-non­farm, and metropolitan areas narrowed. until metropolitanand nonmetropolitan rates of educational attainment hadconverged by the close of the 20 th century. while a nationalrural vs . urban mathematics achievement gap existed atthe start of the last quarter of the 20 th century. Second. anational rural vs , nonrural mathematics achievement gapdoc . not now exist. either in the form of a national rural vs,suburban gap nor a national rural vs . urban gap. Third. atthe state level. a rural /nonrural achievement gap exist injust 40 % of the states. favoring nonrural students in 20 % ofstates and favoring rural students in the other 20 % of state .Fourth. conditions of schooling account for about 70% ofthe variance associated with the rural /nonrural, state-levelachievement gap .

These conclusions falsify common assumptions aboutrural deficiency in mathematics achievement. At least incomparison to national averages. the common assumptionsprove to be unwarranted . Of course. if national averagesreflect sharp deficiencies in teaching and learning as. say.Stigler and Hiebert (1999) insist. then rural achievementmust al 0 be considered deficient-but such a "deficiency"cannot be singled out for special scorn. Additionally. vari­ability is at least as characteristic of rural and small-townschools as it is of schools in other locales. These secondthoughts about the meaning of the evidence developed inthis review demonstrate that perhaps the sign ificant workis not the repudiation of deficiency but the elaboration ofsignificance that touche. on the place ofmeaning in school­ing (including the learning ofmathematics) and the meaningof plac e with respect to rural schooling. In other words.now that we can dispense with misconstructions of ruralperformance that damage rural places. what con tructionof mathematics leaching and learning arc needed 10 benefitrural places? The answers are not simple-and maybe noteven forthcoming-but the que tions must be asked .

RESEARCH ABOUT MATHEMATICS ACHIEVEM E T 93

Rural Mathematics Education: The Place 0/ Meaning andthe Practical Meaning ofPlace

Rural people have struggled under the burden of cosmo­politan portrayals that render them as ill-in formed, unedu­cated. and stupid (e.g .. Williams. 1973; Herzog & Pittman.1995). Jim Goad (1997). in particular. points out that anyonecan ridicule rural Appalachians without suffering criticismfor unfair discrimination-except from Appalachians. ofcour e. who e complaint need not be regarded seriouslyby those sponsoring the ridicule. The basis of such safetyis cultural power. not (of course) j ustice.

One semi nal . ociologica l study of educational. occu­pational. and economic attain ment among adults with ruralorigins (Howell, Tung, & Wade-Harper, 1996) found that.hi torical ly, the effect of rural origins has been mediatedby educational attainment. which in tum was shaped by theexpecta tion of parents and peers for less schooling: "theinfluences of parents and friends serve to transmit the Iion 's'hare of the negative effec t ofrural origins" (p. 82). In otherword. across the entire 20th century. fanning cul ture andlimited access to schooling may have been responsible forthe observed differences in the educational. occupational.and economic standing of rural vers us urban citizens.

Howe ll et a l. (1996) also found tha t rural-to-urbanmigra tion prod uced a predicted increase of about $3 ,200in adu lt fami ly income ( 1985 constant dollars). whereasurban-to-rural migration produced a similar decrease inpredicted adult family income. This finding, combined withthe aforementioned convergence in educational attainmentand performance in rural as compared to other area . suggeststhat rural residence alone exerts a negative effect on adu lt oc­cupational status and income. ' As Howell et al. conclude.

One inference from the NLS-72 data is that it seemsto be rural areas [per se] that prod uce lower famil yincomes rather than the socioeconomic origins orhuman capital characteristics of persons choos­ing to remai n there or to move there from urbanorig ins. (p. 83)

Allegation s of inferiority derive from cultural andideological dominance. as well as from a long line of mis­interpre tat ions of available evidence.

Circumstances of likely interest. Given the finding ofapproximate achievement parity. it is time, as Kifer (200 I)advise. 10 examine more closely variability within rural

, Ironically. the GSS ana lyses suggest 110 systematic effects

of migration earl ier in the 20 th century: During the first three quar­tcrs of the century. rural youth moved in great numbers 10 urbanareas in the expectation of social and economic benefits. but thismigration is shown by lI owell et al. (19911) not 10 have yieldedthese benefits system atically .

contexts. As Lee and Mcin tire (2000) show, variab ilityexists at the sta te level. sometimes favoring rural studentsand sometimes not. We can be certain that conceptually andpractically interes ting variability is greater till at the di trier,school. and classroom levels. While some of this variabilitymight be random. much of it is probably not. Some of thatvariability. in tum, may be related to features of the ruralcircumstance over which humans migh t exert some influ­ence for the common good of more and better mathematicslearning. Those circumstances may include:

structural features of the educational system(e.g.. class size. school size . district size);

equity of local resources (e.g.. income dis tri­bution in the comm unity. pari ty of instruc tionalresources among di trict schools. patterns ofassignment of the be. t teacher among adistric t's schools) ;

the local culture of schooling (e .g.. the extentto whic h the school is embedded in the com­munity and vice versa. concep tions of educa­tional purposes and effects):

in tentions of teach er s and administra tors(e .g.. school climate. profes ional collegial­ity. rela tionships among students and be tweenstudents and educators) ;

adequacy o f resource. (e.g.. school fundinglevels in view of challenges. tax effort. staffturnover); and

degree of collect ive purpose (e .g.. student­cen tered focus. ex tent of tracking. equity ofeducational outcomes).

Many studies have considered these issues. but practi­cally no inves tigation of them has as yet been atte mptedwith respect to mathematics achievement in rural schoolsand districts.

Contradictions, dil emmas , and complexities. Somework relat ed to rural achievement (including mathematicsachievement) has been done with respect to the first of thesecircum tances: structural issues ofsize and scale (e.g .. Bickel& Howley. 2000). This circumstance is important to ruralcommunities because schools and dis tricts are smaller thanelsewhere. whi le state-level consolidation efforts continueto make both schools and districts larger. Interpreting therelated findings to policymakers is difficult enough. Suggest­ing practical courses for policymaking is even more difficu lt.and that difficulty means that even the mo. t thoughtful policyrecommendations will exhibit infidelity not merely to the

94 HOWLEY A D GUNN

research findings but to a proper (and respectful) researchagenda . The lip between cup and lip is not an accident : It isinevitable because the real world is unimaginably complexand contingent.

The relationship of rural lifeways to future research.The American preoccupation with excellence and its com­parative disregard for equity have produced a dilemmafor rural education. The United States, though perhaps thewealthiest nation on the planet. is al 0 one of the most in­equitable among developed nations. Despite this situation,and also because of it. liberal Americans have spent mucheffort to address the symptoms of inequity-among whichare educational outcomes. Thus, as part of the effort to callattention to the nation'. real inequities. journalists, practitio­ners, and researchers have dramatized rural inequities . Forthat reason, the findings summarized here would probablynot be considered good news by most rural practitioners,or by many researchers, as they would seem to threaten theestablished political economy of interest that secures atten­tion to rural issues.

Mean differences, of course. are not the point withrc earch into the conditions of rural education :

iducational research, unfortunately. often focuseson findings of statistical difference between overallmeans or averages. Most media reports of resultsof such research routinely give those differencesand little else: they report means and mean differ­ences as though that is all one needs to know inorder to under tand the findings of the researchand what the implications might be for practice.(Kifer.2001,p.44)

In fact, qual itative researchers-whose work is seldomconsidered by popular media-s-have a better understandingof the importance of locale than many quantitative re­searchers. Unlike most quantitative researchers. most quali­tative rescarchers arc interested to discover and articulatethe meanings attached to circumstances. places. and expe­riences . The meaningfulness of rural places (and of rurallyattuned educations) is more likely to exhibit itself in vari­ation, interaction. contradiction. dilemma. and even paradoxthan in simple measures of difference on conventionally(c.g., nationally) valued quantities.

Future research into rural mathematics education mustconsider. as it frames and pur 'ues salient questions (e.g.,about structural features. equity and adequacy, and collectivepurpose) . the meanings of rural lifeways. onsideration ofthese meanings is tantamount to valuing them, since theyare-as Raymond Williams (1973) insisted-so widelydevalued . In a recent essay on the topic of doing researchinto mathematics and science education in rural contexts.one observer claimed,

[fyou don't re pect something, you shouldn't studyit. Far from harboring a bias, a respectful stanceactively constitutes objectivity. The deficit viewis a hidden bias that fatal to the object of study.(Howley, 200 I, p. 19)

Respect does not mean approval, but unlike lack of respect,it harbors that possibility.

Quite narrow quantitative studie. must also be informedby such meanings. But rather than ecking simple differ­ences, future quantitative studies. hould eonsider variation,interactions. dilemmas. and contradictions, for the carethe challenges that make practice and improvement diffi­cult-and they make for interesting and valuable research.Such studies , however. are far less likely to unfold withoutan informative base of qualitative studies that articulaterural meanings in the context of mathematics knowledge atwork-in and out of rural schools. As yet. hardly any suchresearch exists. and. for that reason, it is no wonder theexisting quantitative research base i so thin.

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