The Search forMethods ofGroup Instructionas Effective asOne-to-OneTutoringBENJAMIN S. BLOOM

Schools cannotprovide tutoring forevery student, butthe use of masterylearning incombination withother practicalmethods mayenable students tolearn almost aswell.

dents and I have been searchingfor solutions to what we call the

"2 sigma problem": can researchers andteachers devise teaching-learning condi-tions that will enable the majority ofstudents under group instruction to at-tain levels of achievement that can, atpresent, be reached only under goodtutoring conditions?

Two University of Chicago doctoralstudents in education, Anania andBurke, began in 1980 to compare stu-dent learning under one-to-one tutor-ing, mastery learning, and conventionalgroup instruction. As the results of theseseparate studies at different grade levelsand in differing school subjects began tounfold, we were astonished at the con-sistency of the findings and at the greatdifferences in student cognitive achieve-ment, attitudes, and self-concept undertutoring as compared with group meth-ods of instruction.

Anania (1981) and Burke (1983) de-fined the three methods of instruction asfollows:

* Conventional: Students learn thesubject matter in a class with about 30students per teacher. Tests are givenperiodically only for purposes of deter-mining students' marks.

* Mastery Learning: Students learnthe subject matter in a class with about30 students per teacher. The instructionis the same as in the conventional classand is usually with the same teacher.Formative tests (the same tests used withthe conventional group) are given forpurposes of feedback followed by correc-tive procedures and by parallel forma-tive tests to determine the extent towhich the students have mastered thesubject matter.

* Tutoring: Students learn the sub-ject matter with a good tutor for eachstudent, or for two or three studentssimultaneously. This tutoring instruc-tion is followed periodically by forma-tive tests, feedback-corrective proce-dures, and parallel formative tests as inthe mastery learning classes. The needfor corrective work under tutoring isvery small.

The students were randomly assignedto these three learning conditions, andtheir initial aptitude test scores, previous

Benjamin S. Bloom is Professor of Edu-cation, the University of Chicago andNorthwestern University, Chicago, Illi-nois. Copyright 1984, Benjamin S.Bloom.

4 EDUCATIONAL LEADERSHiP4 EDUCATIONAL LEADERSHIP

achievement in thile subject, and initialattitudes and interests in the subjectwere similar. The amount of time forinstruction was the same in all threegroups except for the corrective work inthe mastery learning and tutoring

groups. Burke and Anania replicatedthis study with four different samples ofstudents at different grade levels andwith two different subiect fields.

Most striking were the differences infinal achievement measures under the

three conditions. Using the standarddeviation (sigma) of the control class.which was taught under conventionalconditions, it was found that the averagestudent under tutoring was about twostandard deviations above the average ofthe control class. Put another way, theaverage tutored student outperformed98 percent of the students in the controlclass. The average student under mas-ter- learning was above one standarddeviation above the average of the con-trol class, or above 84 percent of thestudents in the control class.

The variation of the students' achieve-ment also changed under these learningconditions such that about 90 percent ofthe tutored students and 70 percent ofthe mastery learning students attainedthe level of summative achievementreached by only the highest 20 percentof the students under conventional in-structional conditions (Figure I).

There were corresponding changes instudents' time-on-task in the classroom(65 percent under conventional instruc-tion, 75 percent under masters learn-ing, and 90+ percent under tutoring)and students' attitudes and interests(least positive under conentional in-struction and most positive under tutor-ing). There were great reductions in the

MAY 1984 5;MAY 1984

relations betseen prior measures ofaptitude or achievement and the sum-mative achiesemcnt measures. T'pi-calls, the aptitudc-achiceminent cor-relations changed from +.60 tinderconventional instruction, to +.35 un-

der mastery learning, and + 2 uindertutoring.

Howevser, the most striking of thefindings is that under the best learningconditions xce can dc-ise-4tutoring-the average student is 2 sigmas abo e theaserage control student taught tinderconventional group methods of instruc-tion.

The tutoring process demonstratesthat most of the students do have thepotential to reach this high lecel oflearning. An important task of researchand instruction is to seek twats of accom-plishing this under more practical andrealistic conditions than one-to-one tu-

toring, Mtich is too costly for mostsocieties to hear on a large scale This,then, is the "2 sigmaia problem.

It has taken almost a decade and ahalf to dexclop the tlastery learningstrategs to a point hcere large numbersof teachers at cscr Icesel of instructionand in man- countries cain use thefeedhack-correctisc procedures to getthe I sigma effect. 'Ihat is, the averagemasters learning student is abose 84percent of the students under consen-tional instruction, eCen w ith the sameteacher teaching both the mastcry Iearnm-ing and the conventional classes. ) If theresearch on the 2 sigma prohlem yicldspractical methods--which the averageteacher or school facultv can learn in abrief period of time and use *with littlemore cost or time than coinicltirnalinstructior--it xontlcl he an educationalcontribution of the greatest magnitude.

Figure 2. Effect of Selected Alterable Variables on Stu

DDAD

(A) D

AA

(D) CDDA

C

D

DD

(D) B

DCB

Tutorial instructionReinforcementFeedback-corrective (ML)Cues & explanationsStudent classroomparticipationStudent time-on-taskImproved reading/studyskillsCooperative learningHomework (graded)Classroom moraleInitial cognitiveprerequisitesHome environmentinterventionPeer and cross-ageremedial tutoringHomewor': (assigned)Higher order questionsNew science & mathcurriculaTeacher expectancyPeer group influenceAdvance organizers

Socioeconomic status(for contrast)

udent Achievement

PercentileEffect size equivalent

2.00 981.201.00 841.001.00

1.00+1.00

.80

.80

.60+

.60

.50+

.40

.30

.30

.30+

.30

.20

.20

79

73

69

66

62

58

.25 60

+ = Averaged or estimated from correlational data or from several effect sizes

Object of change process: A- Learnert- Instructional MaterialC- Home environment or peer groupD- Teacher

Adapted from Walberg (1984)

It wouldl charnge popular notions ahouthuman potential and w ould have signif-icant effects in w hat the schools can andshoulnd do wsith the educatiorial yearseach society requires of its young pco-pie.

The SearchIn a nurber of articles mv graduatestudernts and I hase attempted to con-trast alterable cducationial sariables w ithmore stable or static variables (Bloom,1980(). In our treatment of this topic wesummarized the literature on such alter-able variables as thie quality of teaching,the use of time by teachers and students,cognitive and affective entry characteris-tics of students, formative testing, rate oflearning, and the home environment. Ineach case wsc contrasted these alterablevariables w ith the more stable variables,such as personal characteristics of teach-ers, intelligence measures, achievementtests for gradiing purposes, socioccolnom-ic status of the faimils, a(ld so oil. Wealso intlicated some of the asys inwhich the alterable -ariables influencelearning, and the processes by whichthese variables have been altered.

But not all alterable variables arelikely to have equal effects on learningOur research summaries were inrtendecto emphasize those alterable variablcsthat have had the strongest effects onschool learning. Within the last threeyears, this search has been aided bis thlerapid growth of the meta analysis litera-ture. In this literature, each writer hassummarized the research on a particularset of alterable variables to indicate theeffect size between control and experi-mental groups of students. They havestandardized the results in terms of thedifference between the experimental andcontrol groups divided by the standarddeviation of the control group.' In eachstudy, the reviewer also analyzed theeffect size under different conditions,level of school, sex of student, schoolsubject, size of sample, and so on. Suchreviews are very useful in selecting alter-able variables which are most likely tocontribute significantly to the 2 sigmasolution.

Figure 2 is adapted from Walberg's(1984) summary of effect sizes of keyvariables. Walberg listed the selectedvariables in order of magnitude. We

EDUCATIONAL LEADERSHIP

................

.........

.........

.........

.........

........

........

6

have added additional variables and in-dicated the equivalent percentile foreach effect size. Thus, in the first entry,tutorial instruction, we have indicatedthe effect size, 2 sigma, and the findingthat under tutorial instruction, the aver-age student is above 98 percent of thestudents under the control teachingconditions. The average student underthe control conditions would be above50 percent of the students under theseteaching conditions.

In our own attempts to solve the 2sigma problem, we assume that two orthree alterable variables used togethercontribute more to learning than anyone of them alone. Having used masterylearning for more than 15 years at differ-ent levels of education and in differentcountries, we have come to rely onmastery learning as one of the possiblevariables to be combined with selectedother variables. Under good conditions,

the feedback-corrective process of mas-tery learning yields approximately aI sigma effect. We have systematicallytried other variables, which, combinedwith mastery learning, might approachthe 2 sigma effect size. So far, we havenot found any two-variable combinationthat has exceeded the 2 sigma effect.Thus, our present research approachesthe 2 sigma effect but does not gobevond it.

We have classified the variables inFigure 2 in terms of the direct object ofthe change process:

A. The learnerB. The instructional materialC. The home environment or peer

groupD. The teacher and the teaching

processWe believe that two variables involvingdifferent objects of the change processare likely to be additive, while two

variables involving the same obiect ofthe change process are less likelv to beadditive-unless they occur at differenttimes in the teaching-leaming process.Thus the mastery learning process.which affects the learner most direcdtlyv,when combined with changes in theteaching process. which affects theteacher most directlv, vield additirv re-sults (Tenenbaum, 1982; XMevarech.1980). While we do not believe theserules are more than suggestive at pre-sent, future research on this problemwill undoubtedhl ield a stronger set ofgeneralizations about how the effects ofseparate alterable variables may be bestcombined.

ImPOSEi SnttLe-r PRocGssim orCONvEN-rONAL ISt un1oIn this section we are concerned withwavs students can learn more effectivelvwithout basically changing the teach-ing. If students develop good study hab-its, devote more time to the learning,improve their reading skills, and so on.thev will be better able to learn from aparticular teacher and course eventhough neither the course nor the teach-ing has been changed.

For example, the mastery learningfeedback-corrective approach, is primar-ily addressed to providing students withthe cognitive and affective prerequisitesfor each new learning task. When themastery learning procedures are donesystematicallyv and well. the schoolachievement of the average student un-der mastery learning is approximatelyI sigma (84th percentile) above the aver-

age student in the control class evenwhen both classes are taught by thesame teacher with much the same in-struction and instructional material.We view the mastery learning process asa method of improving the students'learning from the same teaching over aseries of learning tasks.

The more students possess the cogni-tive prerequisites for each new learningtask, the more positive they are abouttheir ability to learn the subject; andthey put in more active learning timethan do control students. As we observethe students' learning and the test resultsin both the mastery learning and theconventional class. we note the im-

MAY 1984

'x v e believe thisW solution is

relevant at all levels ofeducation includingelementary-secondary,college, and even at thegraduate and professionalschool level."

provements in student learning undermastery learning and the lack of suchimprovement in the conventional class-es. The main point is that the masterylearning students improve their process-ing of the instruction, although the in-struction is much the same in both typesof classes.

Leyton (1983) suggested that one ap-proach to the 2 sigma problem would beto use mastery learning during an ad-vanced course in a sequence, but inaddition attempt to enhance the stu-dents' initial cognitive entry prerequi-sites at the beginning of the course. Heworked with high school teachers inAlgebra 2 and French 2 to develop aninitial test of the prerequisites for each ofthese courses. The procedure in devel-oping the initial test was to take the finalexamination in the prior course (Alge-bra I or French 1) and have a commit-tee of four to six teachers in the subjectindependently check each test item theybelieved measured an idea or skill thatwas a necessary prerequisite for the nextcourse in the subject. There was veryhigh agreement on most of the selecteditems, and discussion among the teach-ers led to consensus about some of theremaining items.

Two of the classes were helped toreview and relearn the specific prerequi-

sites they lacked. This was not done forthe students in the other two classes.The method of enhancing the prerequi-sites was much like the mastery learningfeedback-corrective process in which theteacher retaught the items the majorityof students had missed; small groups ofstudents helped each other over itemsthat had been missed; and the studentsreviewed items they were not sure aboutby referring to the designated pages inthe instructional material. The correc-tive process involved about three to fourhours of time during the first week of thecourse. After the students completed thecorrective process, they were given aparallel test. As a result of the correctiveprocess most of the students reached themastery standard (80 percent) on theparallel test given at the end of the firstweek of the course. In a few cases,students who didn't reach this standardwere given further help.

More important was the improvedperformance of the enhanced classesover the other two classes on the firstformative test in the advanced course(French 2 or Algebra 2). The enhancedclasses, which had been helped on theinitial prerequisites, were approximately.7 sigma higher than the other twoclasses on the first formative test given atthe end of a two-week period of learningin the advanced course.

When one of the enhanced classeswas also provided with mastery learningfeedback-corrective procedures over aseries of learning tasks, the final resultafter a ten- to 1 2-week period of instruc-tion was that this experimental groupwas approximately 1.6 sigmas above thecontrol group on the summative exami-nation. In other words, the averageexperimental student was above 95 per-cent of the control students on thisexamination. There were also attitudi-nal and other affective differences instudents related to these achievementdifferences. These included positive ac-ademic self-concept, interest in the sub-ject, and desire to learn more in thesubject field.

Leyton found that the average effectof initial enhancement of prerequisitesalone is about .6 sigma. (See Figure 3for differences between conventionaland conventional plus enhanced prereq-

uisites and between mastery learningand mastery learning plus enhancedprerequisite.) That is, we have two pro-cesses, mastery learning and initial en-hancement of cognitive prerequisites,which have sizable but separate effects.When they are combined, their separateeffects tend to be additive. We believethese two variables are additive becausethey occur at different times. The en-hancement of the initial prerequisites iscompleted during the first week of thenew course, while the mastery learningfeedback-corrective process takes placeevery two or three weeks during thecourse, and after the initial enhance-ment.

This solution to the 2 sigma problemis likely to be applicable to sequentialcourses in most school subjects. (In theUnited States over two-thirds of theacademic courses in elementary-sec-ondary schools are sequential.) This so-lution, of course, applies most clearly tothe second course in a sequence. Itprobably will not work as well withthird, fourth, or later courses in a se-quence if there has been no earlier useof initial enhancement of prerequisitesor mastery learning procedures. Wehope these ideas will be further exploredin the United States as well as in othercountries. We believe this solution isrelevant at all levels of education in-cluding elementary-secondary, college,and even at the graduate and profession-al school level.

We also regard this approach as wide-ly applicable within a country becausethe prerequisites for a particular sequen-tial subject or course are likely to be verysimilar even though different textbooksand teachers may be involved. Thus, awell-made test of the initial prerequisitesfor a particular sequential course, suchas 5th grade arithmetic, French 2, andso on, may with only minor changesapply to other versions of the samecourse within a particular country.Also, the procedures that work well inenhancing these prerequisites in oneschool should work equally well in otherschools. Much further research is need-ed to establish which sequential coursesfor this approach are most effective.

Finally, the time cost of the initialenhancement procedures is limited tothe class hours of the course during thefirst week of the sequential course, while

S EDUCATIONAL LFADERSHIP

l

8 EDUCATIONAL LEADERSHIP

the time or other costs of the masterylearning procedures have usually beenvery small. We hope that this approachto the 2 sigma problem will be found tobe a widely applicable and economicalsolution for teachers who wish to im-prove student learning, student academ-ic self-concept, and student attitudesand interest in the subject matter.

Our graduate students have proposedseveral other approaches for improvingstudent processing of conventional in-struction.

i. Help students develop a studentsupport system in which groups of twoor three students study together, helpeach other when thcv encounter diffi-cultics in the course, review in advanceof taking tests, and review their learningperiodically. A student support systemthat provides support, encouragement,and even help when needed can domuch to raise the level of learning of theparticipants. There is evidence thatthese and other cooperative learningefforts are almost as effective as mastery

learning procedures. (The effect size ofcooperative learning [Slavin, 1980] isestimated at .80 or the 79th percentile.See Figure 2.)

2. There is evidence that studentswho take special programs to improvetheir reading and/or their study andlearning methods tend to learn moreeffectively. Ideally, such special pro-grams should be available at the begin-ning of each new school level; that is,junior high school, high school. Onewould hope that the special programswould be closely related to the academiccourses the student is taking currently.(The effect size of improved reading/study [Pflaum and others, 1980] is esti-mated at 1.00 or 84th percentile.)

IMPROVE INSTRUCIONAL MATERIALS ANDEDUCATIONAL TECHNOLOGYThe textbook in the United States andin most advanced countries in the worldis an almost universal part of schoolinstruction. Authors and publishershave worked very hard to improve text-

books for reading and to some extentarithmetic, mathematics, and scienceby changing the sequential nature oftopics, attempting to find importantideas or schema that interrelate diferentparts of the subject, and improving illus-trations and exercises. However, as faras we can find these have not had vervsignificant efects on student achieve-ment unless teachers were provided withmuch inservice education for the newcumcula or the new textbooks.

Our graduate students have been in-trigued by the possibility that the organu-zation of a particular section (or chapter)of the textbook might be better integrat-ed or the parts of the section moreclearly related to each other. The, havefound that pre-organizers or advanceorganizers (Ausubel, 196I%) have beenmoderately effective when provided inthe textbook or provided ny the teacherat the beginning of each new unit of thecourse. These may be provided in theform of objectives, some ideas aboutwhat will be learned in the unit, or a

MAY 1984

9

aure 3. Ava Slmt Acewmenl Soramn Unde Dommt Lru CeisCompe of tonql mdies, m Ietav/_ml, and enhkaONd A _:=qn."

100 - ------------------------- -_2 SIGMA -

95%90 - 1.6o

80 .I0c

.60 a

30 1 I i20

10 I I-l o- 90 Tuftft Sd_

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MAY 1984 9

brief discussion of the relation betweenwhat has already been learned and whatwill be learned in the unit. Such ad-vance organizers (Luiten and others,1980) appear to have an average effectsize on achievement of about .2 sigma. 2While this effect is rather consistent, byitself it is not enough to contributesignificantly to the 2 sigma effect. How-ever, the students have suggested that acombination of advance organizers atthe beginning of a new topic, furtherorganizational aids during the chapteror unit, and appropriate questions, sum-maries, or other organizational aids atthe end of the unit are likely to have asubstantial effect on the student's learn-ing of that chapter.

In ProcessOne of our students, Avalos, is workingon a study of the effect of organizationalaids in the instructional material com-bined with the initial enhancement ofcognitive perrequisites and the masterylearning feedback-corrective procedures.Avalos is planning a research design thatwill enable him to determine the sepa-rate effects of each of the three process-es, the effect of any two of the processes,and the combined effect of all threeprocesses. At least, it is anticipated thatthe combination of any two of the pro-cesses will be greater than the effects ofany one of the same processes. Hopeful-ly, the effect of any two will be above1.3 sigmas (90th percentile). If this isfound, it will provide several new solu-tions to the 2 sigma problem, some ofwhich can be done with very little costor effort by the teachers or the schoolsystem.

Avalos expects the results noted abovebecause the organizational aids can bebuilt into new textbooks and can be usedby students with a minimum of empha-sis from teachers. The initial enhance-ment of the prerequisites is completedbefore students begin to study newcourse subject matter, while the masterylearning feedback-corrective procedurestake place every two or three weeksduring the course. We believe that eachof these processes is somewhat indepen-dent of the other processes.

My students have suggested ways toimprove instructional materials andeducational technology.

1. Some computer learning courses,such as the Plato system, appear to workvery well for highly motivated students.It should be possible to determine whichcomputer courses enable sizable propor-tions of students to attain the 2 sigmaachievement effect. The effectiveness ofcomputer courses can be determined interms of the time required, completionrates, student performance on achieve-ment tests, and student retention of thelearned material. Hopefully, the moreeffective computer courses will also havepositive effects on such affective charac-teristics as academic self-concept, inter-est in the subject, and desire to learnfurther with computer learning meth-ods.

2. While the average effect size fornew science and math curricula is only.3 sigma, some of tl - new curricula inthese and other subjects may be muchmore effective than others. A carefulsearch of new curricula may determinewhich ones are more effective and whatit is about these new curricula thatmakes them more effective than theothers.

3. Many countries have developednew science and math curricula. Somehave permanent curriculum centers thatare responsible for the planning anddevelopment of new curricula, teachertraining, and use of the new curricula.The students have proposed that cross-national studies be made to determinewhere new curricula in other countrieshave been far more effective than othersand what made them more effective.Hopefully, some of the new curriculamay also show the 2 sigma effect inthese other countries.

Home Environment and the PeerGroupIn this section, we are primarily con-cerned with out-of-school support fromthe home or peer group-specificallythe ways in which the student's achieve-ment, academic aspirations and goals,and progress in learning are influencedby this support. We know that the homeenvironment has a great influence onthe pupil's school learning and that thisinfluence is especially effective at theelementary level or earlier. The peergroup's influence is likely to be strongest(both positively and negatively) at thesecondary level.

Home Environment Processes. Manystudies have focused on the home envi-ronment processes that affect learning.These studies involve interviews andobservations to determine the relevantinteractions between parents and theirchildren. The studies find correlationsof +.70 to +.801 between an index ofthe home environment processes andthe children's school achievement.Some of the home environment pro-cesses that appear to have high relation-ships with school achievement include:

1. Work habits of the family: thedegree of routine in the home, theemphasis on regularity in the use ofspace and time, and the priority given toschoolwork over other activities.

2. Academic guidance and support:the availability and quality of the helpand encouragement parents give thechild for his or her schoolwork and theconditions they provide to support thechild's schoolwork.

p' arent encouragement and supportthroughout the elementary years

would have very great consequences forchildren over the many years theyattend schools and colleges."

10 EDUCATIONAL LEADF.RSHIPo10 EDUCATIONAL LFADERSHIP

3. Stimulation: the opportuniht pro-vided bs the home to explore ideas,events, and the larger environment.

4. Language development: opportuni-ties in the home for developing correctand cffcctive usc of language.

5. Academic aspirations and expecta-tions: thce parents' aspirations for thechild. the standards thev set for thechild's school achievement, and theirinterests in and knowlcdge of the child'sschool experiences.

1These studies of the home environ-ment processes began w-ith thile ork ofDave (1963) and Wolf (1964. 1966),and have since been replicated in otherstudies done in the U S. and othercountries (Marjoribanks, 1974; Kalin-owski and Sloanc, 1980).

While these pres ions studies suggest astrong effect of home environments onschool learning of children. they do notprbvide ce-idence on the extent to whichhome environmenlets can be altered andthe effect of such alteration on changesin children's school achicenmeiut.

A recent studv done in Thailand byJanhom (1983) involved a control groupand three experimental groups of par-ents and their children. In this study,the most effective treatment of the par-ents w-as for the group of parents to meetwithl a parent educator for about twohours twice a month for six months. Inthese meetings the parcnts discussedways in swhich thes could support theirchildren's Icarning in the school. Usual-Iv, the parent educator made an initialpresentation on one of the topics listedabove (work habits of the family, and soon) and then the parents discussed whatthev did as *well as what they hoped to doto support their children's school learnm-ing.

Another approach included visits toeach home separately bs a parent educa-tor twicc a month for six months. Athird approach \was one in which news-letters about the same topics were sent tothe home htice a month for six months.

The parents of all four groups wereobserved and intcnriewed at the begin-ning and end of the six-month periodusing the Dave intenricw and observa-tional methods. While the three experi-mental approaches sho\w significantlygreater changes in the parents' homeenvironment index than the control

MAY 1984

group, the most cffectivc method \-asthe series of mectings behveen groups ofparents and the parent educator. Thechanges in the home environment ofthis group wecre highly significant whencompared with the changes in the otherthree groups of parents.

The 4th grade children of all theseparents were giscn a national standard-ized test on reading and mother tongueas well as arithmetic at the beginningand end of the six-month period. Here.it was found that the children of themeeting group of parents had changedby I sigma in achievement, as contrast-ed with the change in the control groupof children. In contrast, the parent edu-cators' visits to each of the homes evernother week had only a .5 sigma effect onthe childrcn's school achievement.

Other methods of changing the homeenvironment hace been reported by Do-lan (1980), Bronfenbrclnner (1974), andKalinowski and Sloane (1980). Hereagain, the most cffective approaches to

changing the home en-ironment pro-cesses result in changes in the children'sschool achiesement. (The effect size ofhome environment Iserson and Wal-berg, 19791 is estimated at .50 or 69thpercentile. )

While methods for changing thehome ens-ironment are relativelv costldvin terms of parent educators meetingwith groups of parents over a series ofsemi-monthly meetings. the payoff ofthis approach is likely to be y-en great.Parent encouragement and supportthroughout the elementanry ears wouldhave syen- great consequences for chil-dren over the many years they attendschools and colleges_

While such research has not beendone as yet. our graduate students hasesuggested an approach to the 2 sigmaproblem of combining effective parenteducation with mastern learning. Sinceparent support takes place in the homeand mastery learning takes place in theschool, we expect that these two effets

II

' The averageI student in the

enhanced groupwas above 93percent of thestudents in thecontrol classes."

will be additive. The result should beclose to a 2 sigma improvement instudent learning.

Ideally, if both methods began withIst or 2nd grade children, the combina-tion should result in consistently goodlearning at least through the elementaryschool vears with less and less effortexpended by the parents or by the use ofmastery learning procedures in theschool.

Peer Group. During the adolescentyears it is likely that the peer group willhave considerable influence on the stu-dent's activities, behavior, attitudes, andacademic expectations. The peer groupto which the individual "belongs" alsohas some effect on the student's highschool achievement level as well asfurther academic aspirations. These ef-fects appear to be greatest in urbansettings. While it is difficult to influencethe student's choice of friends and peergroups, the availability of a variety ofextracurricular activities and clubs inthe school enables students to be moreselective in their peer choices. (Theeffect size of peer group influence [Wal-berg, 1984] is estimated at .20 or 58thpercentile.)

IMPROS EMIENT OI TEACHINCGApproximately 20 percent of the stu-dents learning under conventional in-struction do about as well as the tutoredstudents (Figure I). That is, tutoringprobably would not enable these topstudents to perform any better than un-der conventional instruction. In con-trast, about 80 percent of the students dorelatively poorly under conventional in-struction as compared with what theymight do under tutoring. We believethis results in part from the unequaltreatment of students in most class-rooms.

Observations of teacher interactionwith students in the classroom revealthat teachers frequently direct theirteaching and explanations to some stu-dents and ignore others. They givemuch positive reinforcement and en-couragement to some students but notto others, and they encourage activeparticipation in the classroom interac-tion from some students and discourageit from others. The studies find thattypically the students in the top third ofthe class are given the greatest attentionby teachers, while the students in thebottom third of the class receive the leastattention and support. These differencesin the interaction between teachers andstudents provide some students withmuch greater opportunity and encour-agement for learning than is providedother students in the same classroom(Brophy and Good, 1970).

It is very different in a one-to-onetutoring situation where there is con-stant feedback and correction betweenthe tutor and tutee. If the explanation isnot understood by the tutee, the tutorsoon becomes aware of it and explainsfurther. There is much reinforcementand encouragement in the tutoring situ-ation, and the tutee must be activelyparticipating in the learning if the tutor-ing process is to continue. In contrast,there is less feedback from each studentin the group situation. Frequently theteacher gets most of the feedback on theclarity of his or her explanations, theeffect of reinforcements, and the degreeof active involvement in learning from asmall number of high achieving stu-dents in the typical class of 30 students.

Teachers are often unaware of thefact that they provide more favorable

conditions of learning for some studentsthan others. Generallyv, thev arc underthe impression that all students in theirclasses are given equal opportunity tolearn. One basic assumption of ourwork on teaching is that teachers whoare helped to secure a more accuratepicture of their own teaching methodsand styles of interaction with their stu-dents are increasingly able to providemore favorable learning conditions formore of their students, rather than justfor the top fraction of the class.

In some of our research on the 2sigma problem we have viewed the taskof teaching as providing more equaltreatment of students, and have there-fore been trying to give teachers feed-back on their differential treatment ofstudents. We attempt to provide teach-ers with a mirror of what they are nowdoing and have them develop tech-niques for equalizing their interactionswith students. These include such tech-niques as calling on students in randomorder, finding something positive andencouraging in each student's response,involving more students in active en-gagement in the learning process, secur-ing feedback from a small random sam-ple of students to determine when theycomprehend the explanations and illus-trations, and supplying additional clari-fication and illustrations as needed. Themajor emphasis in this work has notbeen to change the teachers' methods ofinstruction, but to have teachers be-come more aware of ways they couldmore directly teach to a cross section ofthe students during each class session.

The first of our studies on improvinginstruction was done by Nordin (1979),who found wavs of improving the cuesand explanations for students as well asincreasing active participation. Nordinfound it helpful to meet frequently withteachers to explain these ideas and toobserve the teachers and help themdetermine when they still needed toimprove these qualities of the instruc-tion. He also had independent observersnoting the frequency with which theexperimental teachers were using theseideas well or poorly. Similarly, he hadthe students note the frequency withwhich they were actively participating inthe learning and any problems they had

12 EDUCATIONAL LEArn.Rswp

.

12 EDUCATIONAL LEADERSHIP

with understanding the ideas or expla-nations.

Nordin also compared student learn-ing under conventional instruction, un-der masterv learning, and under en-hanced cues (explanations), andparticipation conditions. During the ex-periment, observers noted that studentparticipation and the explanations anddirections were positive in about 57percent of the observations in the con-trol class as compared with about 67percent in the enhanced cues plus par-ticipation classes. The students in thecontrol classes noted that the cues andparticipation were positive for themabout 50 percent of the time as com-pared with about 80 percent of the timefor students in the enhanced participa-tion classes.

In terms of final achievement, theaverage student in the enhanced cueand participation group was 1.5 sigmashigher than the average student in thecontrol classes. (The average student in

the enhanced group was above 93 per-cent of the students in the control class-es. See Figure 4.) Nordin also used themastery learning procedures in otherclasses and found that they worked evenbetter than the enhanced cues plus par-ticipation procedures. Unfortunately,he did not use mastery learning incombination with the enhanced cuesplus participation methods.

In any case, Nordin did demonstratethat teachers could be taught to be moreresponsive to most of the students in theclass, to increase student participation,and to ensure that most of the studentsunderstood the explanations and illus-trations provided. He found that thestudents in the enhanced participationand cues classes were actively engagedin learning about 75 percent of theclassroom time while the control stu-dents were actively learning only about57 percent of the time.

In a later study, Tenenbaum (1982)compared control groups, mastery

learning groups, and enhaned cues,participation, and reinforement incombination with mastery eamming(CPR+ML). Tenenbaum studied theethree methods of teaching with random-ly assigned students in two differentcourses, 6th grade science and 9th gradealgebra.

Tenenbaum also used students' ob-servations of their own classroom pro-cesses on cues, participation, and rein-forcement. He found that underCPR+ML students responded positivelyabout their own participation about 86percent of the time as contrasted with 67percent in the control classes. He alsohad the classes monitored by an obsenr-er who found large differences in theseteaching processes in the CPR+MLclasses as contrasted with the controlclasses.

The results of this studv demonstratedlarge differences between the threemethods of instruction with the finalachievement scores of the CPR+ML

MAY t984 I'

Figre 4 Avem Sumnaive Adchlevemui Saco Un D rw Lemmi C. a ._Comparion of t..s.bg -I.., nmi eIn _IG and .e.nced _m.d.

100 2 SIGMA-%93% .

90 1.56 1.7r~~~84% 6b84%

80 ol 1.

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50 50% 50%%

~40

It 301 1

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Nordin (1979) Tenenbaum (19182) TVaef ShldA _ar (rt). 8 11 (1l

MAY 1984 13

" ur teaching methods,instructional materials, and

testing methods rarely rise above thelowest category of the taxonomy:knowledge."

group about 1.7 sigmas above the con-trol students. (The average student inthis group was above 96 percent of thestudents in the control group.) Theaverage student in the mastery learninggroups was the usual 1 sigma above thecontrol students. (See Figure 4.)

This research makes it clear thatteachers in both the Nordin and Tenen-baum studies could, at least temporar-ily, change their teaching methods toprovide more equal treatment of thestudents in their classes. When thismore equal treatment is provided andsupplemented with the masters learningfeedback and corrective procedures, theaverage student approaches the level oflearning found under tutoring methodsof instruction.

There are several methods for givingfeedback to teachers on the extent towhich they provide equality of interac-tion with their students. The tactic ofproviding a "mirror" to the teacherseems to be an excellent approach. Thismay be in the form of an observer'snotes on what the teacher and studentsdid, or mav come from student observa-tions of their own interactions with theteaching (preferably anonymous, butcoded as to whether the students are inthe top third, middle third, or the bot-tom third of the class in achievement-.such as their understanding of the cues

and explanations, the extent of theirovert and covert participation, and theamount of reinforcement thev receive.A videotape or audiotape recording ofthe class could serve the same purpose ifthe teacher is trained in ways of summa-rizing the classroom interaction be-tween the teacher and students.

We hope that when teachers arehelped to secure a more accurate pictureof their own teaching methods andstyles of interaction with their students,they will be better able to provide favor-able learning conditions for most oftheir students.

IMPROVE THE TEACHING OF HIGHER

MENTAL PROCESSES

While there is much of rote learning inschools throughout the world, in someof the national curriculum centers indifferent countries I find great emphasison problem solving, application of prin-ciples, analytical skills, and creativity.Such higher mental processes are em-phasized because these centers believethey enable students to relate theirlearning to the many problems encoun-tered in day-to-day living. These abili-ties, which are retained and used longafter the individual has forgotten thedetailed specifics of the subject mattertaught in schools, are regarded as essen-

tial characteristics needed to continuelearning and to cope with a rapidlychanging world. Some curriculum cen-ters also believe that higher mental pro-cesses arc important because they makelearning exciting and constantly newand playful.

In these countries, subjects are taughtas methods of inquiry into the nature ofscience, mathematics, the arts, and thesocial studies. The subjects are taught asmuch for the ways of thinking theyrepresent as for their traditional content.Much of this learning makes use ofobservations. reflections on observa-tions, experimentation with phenome-na, and the use of firsthand lata anddaily experiences as well as primaryprinted sources. All of this is reflected inthe materials of instruction, the learningand teaching processes used, the ques-tions and problems used in quizzes,formative testing, and final summativeexaminations.

In sharp contrast with some of theseother countries, teachers in the U.S.typically use textbooks that rarely posereal problems. Instead, U.S. textbooksemphasize specific content to be re-membered and give students little op-portunity to discover underlying con-cepts and principles and even lessopportunity to attack real problems inthe environments in which they live.Both teacher-made and standardizedtests are largely tests of rememberedinformation. Even after the sale of overone million copies of the Taxonomy ofEducational Objectives-Cognitive Do-main (Bloom and others, 1956) andover a quarter of a century of using thisdomain in prservice and inscrviceteacher training, still over 95 percent oftest questions that U.S. students are nowexpected to answer deal with little morethan information. Our instructionalmaterials, our classroom teaching meth-ods, and our testing methods rarely riseabove the lowest category of the taxono-my: knowledge.

Many years ago, when I was theCollege Examiner of the University ofChicago, the college faculty was verymuch concerned that the students wereonly learning to remember informationin the different courses in science, socialscience, and the humanities-in spite ofthe fact that their stated objectives em-

14 EDUCA~~~~~~~~~~~~~~~~~~iONAL LEADF.RSHIP~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

14 EDUCATIONAL LEADERSHIP

phasized problem solving and the high-er mental processes. After much obser-vation and data collection it becameclear that lectures to large groups ofstudents (300 to 400), supplemented bytextbooks that included facts but notproblems, and quizzes and final exami-nations that included only questions ofremembered information, could not en-able students to learn the higher mentalprocesses emphasized in the faculty'seducational objectives.

After much debate and further study,the facultv and administration decidedto replace lecture classes with smalldiscussion classes (28 students per class).They discarded the textbooks (whichsome of the faculty had authored) andmade greater use of primary sourcereadings, firsthand experiences, and lab-oratory situations. They developed testsand quizzes that included higher mentalprocess questions. T'he final compre-hensive examinations for the different

subjects largely became open-book ex-aminations during which students couldrefer to their notes or other materialsbecause most of the questions dealt withnew problems that required students todo more than remember detailed infor-mation. After several years of intensivework on these matters, the improve-ments in students' higher mental proc-ess learning and achievement becamevery pronounced. These and other ap-pro. cs made it clear that most stu-dents could learn the higher mentalprocesses if they became more central inthe teaching-learning process.

In the tutoring studies reported at thebeginning of this article, it was foundthat the tutored students' higher mentalprocess achievement was 2 sigmas abovethe control students (Figure 5). (Theaverage tutored student was above 98percent of the control students on thehigher mental processes part of the sum-mative examination.) In these studies,

"After severaly.t.years of

intensive work ...the improvementsin students' highermental processlearning andachievementbecame verypronounced."

Figure . Average Higher Mental Prom_ Achevement Under _DeI Lem- . C ai m.Comnpalson of tutoring tudles, malery leaunq, and higher menilmir Pu hubeucdeall nebads.

2 SIGMA100

90

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MAY 198415

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60

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40

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Lin

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.

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Levin (1979)

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1

15MAY 1984

lower mental processes as well as highermental process questions were includedin the formative tests used in the feed-back-corrective processes for both themastery learning and tutored groups.Once again, the point is that moststudents can learn the higher mentalprocesses if they become more central inthe teaching-learning process.

Several studies have sought to im-prove higher as well as lower mentalprocesses. In the Tenenbaum (1982)study, which emphasized changingteacher-student interaction, the cue-participation-reinforcement + masterylearning student group was 1.7 sigmashigher than the control students on thehigher mental process part of the sum-mative examination. (The averageCPR+ML student was above 96 percentof the control students on the highermental processes. See Figure 5.) Thus,this approach to the 2 sigma problemimproved both the students' lower andhigher mental processes.

Levin (1979) focused on improvinghigher mental processes by emphasizingthe mastery of lower mental processesand providing learning experiences inwhich the students applied principles ina variety of different problem situations.On the summative examinations, stu-dents scored very high on both theknowledge of principles and facts and intheir ability to apply the principles tonew problems. These experimental stu-dents were compared with a controlgroup that was taught only the princi-ples and not their application. On thehigher mental processes, the experi-mental group was 2 sigmas above thecontrol students (the average experi-mental student was above 98 percent ofthe control students) in the ability toapply the principles to new problemsituations.

A third study by Mevarech (1980) wasdirected to improving higher mentalprocesses by emphasizing heuristicproblem solving and including higherand lower mental process questions inthe formative testing and in the feed-back-corrective processes. On the high-er mental process part of the summativetests, the group using the heuristicmethods plus mastery learning was 1. 3sigmas above the control group taughtprimarily by learning algorithms-a set

of rules and procedures for solving par-ticular math problems. (The averageexperimental group student was above90 percent of the control students.)

In all of these studies, whether groupinstruction or tutoring, both the instruc-tion and the feedhack-correctives em-phasized higher mental processes. It wasevident in all of the studies that in theformative feedback and corrective pro-cesses the students needed and receivedmore corrective help on the highermental processes questions and prob-lems than they did on the lower mentalprocess questions.

In ProcessOne of the studies currently being con-ducted by Wegner-Soled compares con-trol and experimental groups on higherand lower mental process achievementin mathematics and social sciences. Inthe maximum experimental group, theteachers will be trained to use as muchas 33 percent of classroom questions

emphasizing higher mental processes;the formative tests will include at least33 percent higher mental process ques-tions; and the instructional material willemphasize both higher and lower men-tal processes. Wegner-Soled believesthat the combination of all three--class-room higher mental process questions,formative tests with feedback and correc-tives on higher mental process questions,and instructional material includinghigher mental process emphasis--shouldlead to something approaching the 2sigma solutions as compared with con-ventional instruction and materialswhere higher mental process is almostcompletely lacking. This study will at-tempt to determine the separate contri-butions of each of these three elementsas they affect both higher and lowermental processes.

In SummaryWhile all of us at first thought thatsolving the 2 sigma problem would be

EDUCATIONAL LEADERSHIP16

an impossible task, we agreed that if wesucceeded in finding one solution therewould soon be a great many solutions.In this article, I have reported on sixsolutions to the 2 sigma problem. Inspite of the difficulties, our graduatestudents found the problem to be mostintriguing because the goal was so clearand specific-find methods of groupinstruction as effective as one-to-onetutoring.

It soon became evident that morethan group instruction had to be consid-ered. We also needed to find ways ofimproving students' learning processes,the curriculum and instructional mate-rials, and the home environmental sup-port of the students' school learning.While this article is only a preliminaryreport on what has been accomplishedto date, it should be evident that muchcan now be done to improve studentlearning in the school. However, thesearch is far from complete. We look foradditional solutions to the 2 sigma prob-lem to be reported in the next few years.

In the meantime, I hope that teachersand the schools will make use of thefindings reported here. Each teachermight find one of the solutions moreuseful and practical than the others.Each school or school system might trysome combination of the following:

1. Improve the student processing ofinstruction by using the mastery learn-ing feedback-corrective process and/orthe enhancement of the initial cognitiveprerequisites for sequential courses.

2. Improve the tools of instruction byselecting a curriculum, textbook, orother instructional material that hasproven to be very effective.

3. Improve the home environmentalsupport of student learning by beginninga dialogue between the school and thehome.

4. Improve instruction in the schoolby providing favorable conditions oflearning for all the students in eachclassroom as well as by increasing theemphasis on higher mental processlearning for all the students. I

'Mean experimental-Mean controlStandard Deviation of the control

Mex-McSiMaof = controlEffect Size

Sigma of control

'Incidentally, such advance organizershave about a .4 sigma effect on retention ofthe leaming.

'When questionnaires rather than inter-views and observations have been used, thecorrelations are somewhat lower. with theaverage being between +.45 and +5.5

References

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Anania, J. "The Influence of InstructionalConditions on Student Learning andAchievement." Evaluation in Education:An International Review Series 7. 1 (1983).

Ausubel, D. "The Use of Advanced Orga-nizers in the Leamrning and Retention ofMeaningful Verbal Material." Joumal ofEducational Psychology 51 (1960): 267-272.

Bloom, B.S. "The New Direction in Edu-cational Research: Alterable Variables." PhiDelta Kappan 61, 6 (Februarv 1980): 382-385.

Bloom, B.S.; Krathwohl, D.; and others.Taxonomy of Educational Objectives: Hand-book 1, Cognitive Domain. New York: Long-man, 1956.

Bloom, B.S., and others. The State ofResearch on Selected Alterable Variables inEducation. Chicago: Department of Educa-tion, University of Chicago, 1980.

Bronfenbrenner, U. "Is Early Interven-tion Effective?" In The Family as Educator.Edited by H.J. Leichter. New York: Teach-ers College Press, 1974.

Brophy, .E., and Good, T. L. 'Teachers'Communication of Dilferential Expectationsfor Children's Classroom Performance:Some Behavioral Data." lournal of Educa-tional Psychology 61 (1970): 365-374.

Burke, A. J. "Students' Potential forLearning Contrasted Under Tutorial andGroup Approaches to Instruction." Ph.D.dissertation, University of Chicago, 1983.

Dave, P. H. "The Identification and Mea-surement of Environmental Process Varia-bles that are Related to EducationalAchievement." Ph.D. dissertation, Univer-sity of Chicago, 1963.

Dolan, L.. 'The Affective Correlates ofHome Concern and Support, InstructionalQuality., and Achievement." Ph.D. disserta-tion, University of Chicago, 1980.

Iverson, B.K., and Walberg, H.J. "HomeEnvironment and Learning: A QuantitativeSynthesis." Paper presented at the 1979 an-nual meeting of the American EducationalResearch Association.

Janhom, S. "Educating Parents to Edu-cate Their Children." Ph.D. dissertation,

University of Chicago, 1983.Kalinrowski. A.. and Sloane. K. "The

Home Environment and School Achiee-ment." In The State of Research on SeletedAlterable Variables in Education. B.S.Bloom and others. Chicago: Depaintment ofEducation, University of Chicago. 1980.

Levin. T. "Instruction Which EnablesStudents to Develop Higher Mental Prceres." Evaluation in Education: An Intema-tional Review Series 3. 3 (1979).

Le.ton. F.S. "The Extent to WhichGroup Instruction Supplemented bI- Mas-terv of the Initial Cognitive PreirequiitaApproximates the Learning Elctenea ofOne-to-One Tutorial Methods." Ph.D. dis-sertation. University of Chicago. 1983.

Luiten. J.; Ames. W.; and A.keison. G."A Meta-Analvsis of the Elets of AdKanceOrganizers on Learning and Reeuntion.-American Educational Researh Jourmal 17(1980): 211-218.

Maroribanks. K., ed. Environment forLearning. London: National Foundation forEducational Research Publishing Companm.Ltd., 1974.

Mevarech, A.R. '"The Role of Teaching-Leaming Strategies and Feedback-Couc-tive Procedures in Developing Higher Cog-nitive Achievement." Ph.D. dispeation.University of Chicago, 1980.

Nordin. A.B. "The Effecs of DirentQualities of Insmruction on Selected Cogni-tive, Affective. and Time Variables." Ph.D.dissertation, Unisvesitv of Chicago. 1979.

Nordin. A.B. "'lmproing Learning AnExperiment in Rural Primarn Schools inMalavsia." Evaluation in Education: AnInternational Review Series 4. 2 (1980).

Pflaum. S.W.; Walberg, H..; and others."Reading Instruction: A Quantitative Syn-thesis." Educational Resarcher 9 (1980f12-18.

Slavin, R.E. "Cooperative Leanming. Re-view of Educational Research 50 (1980)315-342.

Tenenbaum. G. "A Method of GrupInstruction Which is as Effeetive as One-t-One Tutorial Instruction." Ph.D. diserta-tion. Universihb of Chicago. 1982.

Walberg, H.I. "Improving the Prductivi-ty of America's Schools." Educational Lead-ership 41, 8 (1984): 19-27.

Wolf, R. M. 'The Identification and Mea-surement of Home Environmentd ProcesVariables that are Related to Intelligence."Ph.D. dissertation, Universihty of Chicago,1964.

Wolf, R. M. "The Measurement of Envi-ronments." In Testing Problems in Peric-tive. Edited by A. Anastasi. Washington.D.C.: American Council on Education,1966.

MAY 1984 17

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