Cooperative Learning and Individualized Instruction

Cooperative Learning and Individualized InstructionAuthor(s): Robert E. SlavinSource: The Arithmetic Teacher, Vol. 35, No. 3 (November 1987), pp. 14-16Published by: National Council of Teachers of MathematicsStable URL: http://www.jstor.org/stable/41194251 .

Accessed: 17/06/2014 20:03

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

National Council of Teachers of Mathematics is collaborating with JSTOR to digitize, preserve and extendaccess to The Arithmetic Teacher.

http://www.jstor.org

This content downloaded from 185.44.77.55 on Tue, 17 Jun 2014 20:03:03 PMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=nctm

http://www.jstor.org/stable/41194251?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Cooperative Learning and

Individualized Instruction

14 Arithmetic Teacher

If you have been involved in education since the early 1970s, you have witnessed a dramatic turn of events: the rise and fall of individualized mathematics instruction (Rothrock 1982).

Individualization has long been ad- vocated as a way to meet the needs of diverse groups of students, especially in mathematics because so many mathematical concepts build on ear- lier concepts. For example, if students do not understand common fractions, they will have great diffi- culty understanding decimals. In a class containing students with diverse skills, a teacher using one pace of instruction would either have to review common fractions, wasting the time of those who do not need the review, or to go ahead to teach decimals knowing that many students do not have the conceptual basis to understand this topic.

Individualized instruction offers a way out of this dilemma by offering instruction appropriate to each student's needs. Individualization was the wave of the future in the 1960s. This wave crested in the 1970s as many schools adopted such programs as Individually Prescribed Instruction (IPI) and other programmed ap- proaches.

Today, however, one encounters

Robert Slavin is director of the elementary school program at the Center for Research on Elementary and Middle Schools, Johns Hop- kins University, Baltimore, MD 21218. His research has focused on classroom organization, especially cooperative learning, mastery learning, individualized instruction, and ability grouping.

little enthusiasm for individualized instruction. This wane can be attributed to many factors. Perhaps most impor- tant, individualized programs can be so complex to manage that they re- quire heavy investments in aides or platoons of volunteers. One study of individualized instruction (Broussard 1976) evaluated a program for 344 fourth-grade students that involved (in addition to the students' regular teachers) "a mathematics coordinator . . . five instructional specialists, seven mathematics specialists, sixty- three instructional aides, five materials clerks, and special mathematics supplies, materials and equipment" (p. 235).

Because of the great need for checking students' papers, many teachers felt that they were being turned into clerks. Worse, students in individualized programs typically re- ceived little direct instruction from the teacher. Yet we know that mathematical ideas must be explained, shown, and experienced - things that programmed booklets cannot do. For this reason and others, research on the individualized mathematics programs of the 1960s and 1970s gener- ally failed to find consistent benefits for students' achievement (Hartley 1977; Horak 1981; Schoen 1976; Schoen 1986; Miller 1976). ч Given the disappointing history of individualized instruction in mathematics, one might imagine that this innovation should be shelved and for- gotten. But the problems individualization was designed to solve are still with us. If anything, students in schools are becoming even more di-

verse, Elementary mathematics teachers still experience frustration in teaching groups of students who vary widely in prior knowledge.

Team Assisted Individualization In 1980, we began a program of research into the delivery of elementary mathematics instruction to diverse classes. Our original interest was in improving the achievement of mainstreamed learning disabled students, but we soon realized that mainstreaming was only one part of the problem. Almost all elementary mathematics classes contain students with a wide range of skills, and teachers often feel unable to ensure that low achievers are getting the assistance they need without holding back the progress of more able students.

We set out to see if we could make individualized instruction succeed by working from a new direction. Our idea was very simple. We had been working for years on instructional methods in which students cooperate in small teams to learn material ini- tially presented by the teacher (see Slavin [1980, 1983]). Our research established that, if properly organized and motivated, students could take a great deal of responsibility for their own learning, for their teammates' learning, and for classroom management. Many studies have shown that students in cooperative learning groups learn more than do students in traditional programs (e.g., Huber, Bogatzki, and Winter [1981]; Hulten and DeVries [1976]; Madden and

By Robert E. Slavin



students may skip checkout В and go straight to the final test. No student may take the final test until he or she has been passed by a teammate on a checkout.

6. When a student has "checked out," he or she takes the checkout to a student monitor from a different team to get the appropriate final test. The student then completes the final test, and the monitor scores it. Two or three different students serve as mon- itors each day.

Team scores and team recognition. At the end of each week, the teacher computes a team score. This score is based on the average number of units covered by each team member and the accuracy of the final tests. Criteria are established for team performance. A high criterion is set for a team to be a "super team," a moderate criterion is established for a team to be a "great team," and a minimum criterion is set for a team to be a "good team." The teams meeting the "super team" and "great team" criteria receive attract- ive certificates (table 1).

Teaching groups. Every day, the teacher works for ten to fifteen min- utes with small groups of students drawn from the heterogeneous teams who are at the same point in the curriculum. Teachers use specific concept lessons supplied as part of the program. The purpose of these ses- sions is to introduce major concepts

November 1987 15

Slavin [1983]; Slavin and Karweit [1984]). We reasoned that if we could apply principles of cooperative learning to an individualized program, the students themselves could take care of the checking and management, help one another with problems, and en- courage one another to achieve. Then we could free the teacher to do what only a teacher can do well: teach the fundamental concepts of mathematics.

The program we developed is called Team Assisted Individualization, or Τ ΑΙ. Τ AI is primarily designed for grades 3-6, but it has also been used at higher grade levels. It is almost always used without aides, volunteers, or other assistance. The princi- pal elements of TAI are as follows (from Slavin [1985]):

Teams. Students are assigned to four- to five-member teams. Each team consists of a mix of high, average, and low achievers, boys and girls, and students of any ethnic groups in the class. Every four weeks, students are reassigned to new teams.

Placement test. Students are pre- tested at the beginning of the program on mathematics operations. They are placed at the appropriate point in the individualized program on the basis of their performance on the placement test.

Curriculum materials. For most of their mathematics instruction, students work on individualized curriculum materials covering addition, sub- traction, multiplication, division, numeration, decimals, fractions, word problems, statistics, and algebra. Word problems are emphasized throughout the materials. The units are in the form of books or booklets. Each unit has the following subparts:

• An instruction sheet explaining the skill to be mastered and giving a step-by-step method of solving the problems

• Several skill sheets, each consisting of twenty problems and introducing a subskill that leads to a final mastery of the entire skill

• A checkout, which consists of two

parallel sets of ten items • A final test • Answer sheets for the skill sheets,

the checkouts, and the final tests

Team-study method. Following the placement test, the students are given a starting place in the individualized mathematics units. They work on their units in their teams, using the following steps:

1. The students form into pairs or triads within their teams. They locate the unit that they are working on and bring it to the team area.

2. In pairs, the students exchange answer sheets with their partners. In triads, they pass their answer sheets to the student on their left.

3. Each student reads his or her instruction sheet, asking teammates or the teacher for help if necessary.

Then, the students begin with the first skill sheet in their unit.

4. Each student works the first four problems on his or her own skill sheet and then has his or her partner check the answers against the answer sheet. If all four are correct, the student may go on to the next skill sheet. If any are wrong, the student must try the next four problems, and so on, until he or she gets one block of four problems correct. If they run into difficulties at this stage, the students are encour- aged to ask for help within their teams before asking the teacher for help.

5. When a student gets four in a row on the last skill sheet, he or she takes checkout A, a ten-item quiz that resembles the last skill sheet. On the checkout, the students work alone until they are finished. A teammate scores the checkout. If the student gets eight or more of the ten problems correct, the teammate signs the checkout to indicate that the student is certified by the team to take the final test. If the student does not get eight correct, the teacher is called in to respond to any problems the student is having. The teacher might ask the student to work again on certain skill-sheet items. The student then takes checkout B, a second ten-item test comparable in content and diffi- culty to checkout A. Otherwise, the

Table 1



to the students. Teachers make exten- sive use of manipulatives, diagrams, and demonstrations. The lessons are designed to help students understand the connection between the mathematics they are doing and familiar, real-life problems. In general, the students have concepts introduced to them in the teaching groups before they work on them in their individualized units. While the teacher works with a teaching group, the other students continue to work in their teams on their individualized units. This direct instruction to teaching groups is made possible in an individualized program by the fact that students take responsibility for almost all checking, materials handling, and routing.

Facts tests. Twice each week, the students are given three-minute facts tests (usually multiplication or division facts). The students are given fact sheets to study at home to pre- pare for these tests.

Whole-class units. After every three weeks, the teacher stops the individualized program and spends a week teaching lessons to the entire class, covering such skills as geome- try, measurement, sets, and problem- solving strategies.

Research on TAI

Research on TAI has amply justified our expectation that if the management, motivational, and direct instructional problems of individualized instruction could be solved, this approach could considerably improve students' mathematics achievement. In six carefully controlled studies in grades 3-6, TAI classes gained an average of twice as many grade equivalents as control classes on standard- ized tests of mathematics computa- tions (Slavin, Leavey, and Madden 1984; Slavin, Madden, and Leavey 1984; Slavin and Karweit 1985). For example, in the most recent study in Wilmington, Delaware (Slaviit and Karweit 1985), TAI classes gained 1.63 grade equivalents in computa- tions in only eighteen weeks, while control classes gained 0.61.

Results in mathematics concepts

and applications have been less dramatic but are still positive. In one twenty-four- week study (Slavin, Mad- den, and Leavey 1984), TAI students gained 0.24 grade equivalents more than control students in concepts and applications, but in two additional studies (Slavin and Karweit 1985) TAI students gained slightly (but not sig- nificantly) more than control students on this measure. Positive effects have been found on such varied outcomes as students' self-esteem in mathematics, liking of mathematics, acceptance of mainstreamed classmates, and race relations (see Slavin [1985]). On the basis of its achievement effects, TAI has been designated an exemplary program by the U. S . Department of Education's National Diffusion Net- work.

Conclusion

Research and development of TAI are still continuing. However, our experience so far has convinced us that the proponents of individualized instruction were on the right track. They failed because they overlooked students' needs for conceptual instruction from the teacher and their capac- ity to take responsibility for the management of the individualized programs. Teamed up with cooperative learning, individualized instruction may yet fulfill its once-bright promise.

The research summarized here was done in collaboration with Marshall Leavey, Nancy Madden, Nancy Karweit, Sabine Ois hi, Reva Bryant, and Barbara Cavanagh. It was funded by the National Institute of Education (Grant No. NIE-G-80-0113) and the Office of Special Education and Rehabilitative Services (Grant No. G-80-1494). However, the opinions ex- pressed are those of the author and do not represent Department of Education policy.

References

Mathematics." Journal of Educational Re- search 74(1981):249-53.

Huber, Gunter, Werner Bogatzki, and Manfred Winter. Kooperation als Ziel schulischen Lehr ens und Lernens. Tubingen, West Ger- many: Arbeitsbereich Pädagogische Psycho- logie der Universität Tubingen, 1982.

Hulten, Burma, and David DeVries. "Team Competition and Group Practice: Effects on Student Achievement and Attitudes." Balti- more, Md.: Center for Social Organization of Schools, Johns Hopkins University, Report No. 212, 1976.

Madden, Nancy, and Robert Slavin. "Effects of Cooperative Learning on the Social Accept- ance of Mainstreamed Academically Handi- capped Students." Journal of Special Educa- tion 17(1983): 171-82.

Miller, Richard. "Individualized Instruction in Mathematics: A Review of Research." Math- ematics Teacher 69(May 1976):345-51.

Rothrock, Dayton. "The Rise and Decline of Individualized Instruction." Educational Leadership 39(1982):528-31.

Schoen, Harold. "Research Report: Individu- alizing Mathematics Instruction." Arithmetic Teacher 33(April 1986):44-45.

."Self-pâced Instruction: How Effective Has It Been in Secondary and Postsecondary Schools?" Mathematics Teacher 69(May 1976): 352-57.

Slavin, Robert. Cooperative Learning. New York: Longman, 1983.

. "Cooperative Learning." Review of Educational Research 50(1980):315-42.

. 4 'Team-Assisted Individualization: Combining Cooperative Learning and Indi- vidualized Instruction in Mathematics." In Robert Slavin, Shlomo Sharan, Spencer Kagan, Rachel Hertz-Lazarowitz, Clark Webb, and Richard Schmuck (eds.), Learn- ing to Cooperate, Cooperating to Learn. New York: Plenum, 1985.

Slavin, Robert, and Nancy Karweit. "Effects of Whole-Class, Ability Grouped, and Individu- alized Instruction on Mathematics Achieve- ment." American Educational Research Journal 22(1985):351-67.

. "Mastery Learning and Student Teams: A Factorial Experiment in Urban General Mathematics Classes." American Educational Research Journal 21(1984): 725-36.

Slavin, Robert, Marshall Leavey, and Nancy Madden. "Combining Cooperative Learning and Individualized Instruction: Effects on Student Mathematics Achievement, Atti- tudes, and Behaviors." Elementary School Journal 84(1984):409^-22.

Slavin, Robert, Nancy Madden, and Marshall Leavey. "Effects of Team Assisted Individ- ualization on the Mathematics Achievement of Academically Handicapped and Nonhandicapped Students." Journal of Edu- cational Psychology 76(1984):813-19. Щ

Bfcoussard, Vernon. "A Personahzed-individ- ualfžed Tubtoiction Approach to Achieve- ment in Mathematics," California Journal of Educational Research 26(1976):233-37.

Hartley, Susan. "Meta-analysis <£ the Effects of Individually-paced Instruction in Mathe- matics." Unpublished doctoral dissertation, University of Colorado, 1977.

Horak, Virginia. "A Meta-analysis of Research Findings on Individualized Instruction in

TAI is currently being distributed under the name Team Accelerated Instruction by Mastery Education, 85 Main Street, Watertown, MA 02172, Information on materials, training, or visits to schools using TAI can be obtained from Marshall Leavey, 301/363-1948.

16 Arithmetic Teacher



Documents

Cooperative Learning and Individualized Instruction