Interim Summary: Cooperative learning for mathematics education

Cooperative learning is the name given to a range of educational instruction methods in which students work in groups with defined goals (Nattiv, 1994). Cooperative learning has been described as “one of the greatest success stories in the history of educational innovation” (Slavin, 1999, 74) and has been found to improve student learning.

An important part of cooperative learning is that students are individually accountable for their own learning, quite often with individual goals within the group goal. Individual accountability and goals are very important components, as without them a single student in the group may do all the work, dictate roles to the other group members or group members may ostracise a group member, ignoring any contributions they may make (Slavin, 1999). Antil, Jenkins, Wayne, & Vadasy (1998) report that in six schools in a single region of the United States of America, 81% of the teachers used cooperative learning activities daily, however only 24% of those teachers used any form of individual accountability within those activities.

There are a range of different structures which can be applied for different educational exercise. The term structure is used because an activity has a “specific content-bound objective” (Kagan, 1989, p. 12), whereas a structure can be modified for any specific learning task. As there are a range of structures, it is important to consider the type of cognitive, academic and social development desired by the activity. Where the activity occurs in the lesson plan and the resources required also needs to be considered. Some structures encourage inductive reasoning, review of knowledge, equal participation, debate, role-taking and team building. The social interaction component of the structure has equal time with the cognitive and academic components.

Numbered Heads Together is a cooperative learning structure which Kagan (1989) suggest can replace the traditional Whole-Class Question-Answer structure. In the Numbered Heads Together structure, the teacher numbers off students who form groups based upon the number they are given. The teacher asks a question and the groups then discuss the question and how it should be answered. Finally, the teacher picks a number and that group answers the question. In this structure the students are group tutoring for knowledge and comprehension, where the Whole-Class Question-Answer structure had individual students competing for the teacher's attention.

A different cooperative learning structure is the Jigsaw method, in which a group assigned learning task is divided into distinctive components and given to individual members of a group (Sharan, 1980). The completion of the learning task is dependant on each member finishing their component and teaching it to the other group members, as each member is required to learn the content for assessment. The task components are structured so that one member of each group in the class is doing the same component, but for different group tasks. When combined with communication and tutoring training, the Jigsaw method has been observed to improve academic achievement as well as self-esteem and student cooperation (Sharan, 1980).

A cooperative learning structure used in the cooperative learning in mathematics studies is Student Teams and Achievement Divisions (STAD) (Nattiv, 1994; Slavin, 1999). In this structure students are split into small groups, usually of mixed gender, ability, ethnicity, for group problem solving and peer tutoring. The teacher instructs the class in a new topic and instead of traditional individual exercises the students split into their groups to do the exercise. The execution of the group work can vary, some groups may form problem solver and solution checker pairs, who then check their solution with the whole group, or a whole group approach may be taken with the problems. Nattiv (1994) performed a study where primary students were taught how to give explanations to other students when they encountered difficulty with problems. Using the STAD structure and this training, it was found that there was a strong, statistical correlation between giving or receiving explanations and improvement in student achievement. Not surprisingly, high achieving students gave more explanations, while low achieving students received more explanations from group members.

Currently, cooperative learning appears to be an excellent technique at improving student achievement. Of interest for further research are additional structures and studies identifying structures for mathematical learning.



References

Antil, L.R., Jenkins, J.R., Wayne, S.K., and Vadasy, P.F. (1998). Cooperative learning: Prevalence, conceptualizations, and the relation between research and practice. American Educational Research Journal, 35, 419-454. doi:10.3102/00028312035003419

Kagan, S. (1989). The structural approach to cooperative learning. Educational Leadership, 47(4), 12-15. Retrieved from MasterFILE Premier database.

Nattiv, A. (1994). Helping behaviors and math achievement gain of students using cooperative learning. Elementary School Journal, 94(3), 285-297. Retrieved from Education Research Complete database.

Sharan, S. (1980). Cooperative learning in small groups: Recent methods and effects on achievement, attitudes, and ethnic relations. Review of Educational Research, 50, 241-271. doi:10.3102/00346543050002241

Slavin, R. (1999). Comprehensive approaches to cooperative learning. Theory Into Practice, 38(2), 74-79. Retrieved from Business Source Premier database.

Contains maths

Nattiv, A. (1994). Helping behaviors and math achievement gain of students using cooperative learning. Elementary School Journal, 94(3), 285. Retrieved from Education Research Complete database.

This paper starts by saying that cooperative learning is a name given to a wide range of education strategies based on the idea that students are placed into small groups, where each member works towards a group goal while being an accountable individual. Teams may contain a mix of genders, ethnicity and student ability level. Students instructed through cooperative learning learn more than students instructed through individual or competitive methods. It has been found that students who give and receive explanations relevant to the topic learn more than those that are given the answer without explanation.

The study was of 101 students in grades 3-5 in a elementary school in northern Utah, with "exemplary" teachers who were positive about and enjoyed teaching maths. The students were split into groups of six, mixed gender and ethnicity and containing two students of high, medium, and low ability (based on data from a standardised test three months prior). Students were instructed in helping behaviours for three weeks prior to the study, practised with daily feedback. Instruction methods included direct instruction, role playing, modelling, singling out correct behaviours, team points and feedback regarding effectiveness. Students were taught and shown methods of asking questions and explaining how to do things. The students and teachers had not previously been trained in cooperative learning or helping behaviours.

The cooperative learning system was one based on class wide direct instruction followed by student tutoring groups on the content. The students take a test on the concept and the team earned points based upon improvement over previous test results. Some of the tutoring took place by the group splitting into pairs which worked as solver/checker and the whole group coming together frequently to check progress and answers. They working in these groups for three weeks prior to the study.

The maths topics while the study was progressing were multiplication (3rd), measurement of distance, area and volume (4th) and complex fractions(5th), all involving comprehension, computation, application and some problem solving and use of manipulatives. Each team was video taped an average of twice a week for 5 minutes, with only on team taped at a time. The behaviours targeted were 'gives explanation', receives explanation', 'asks for help (receiving)', 'gives help other than explanation', 'receives help other than explanation', 'gives answer only', 'receives answer only' and 'receives no help after asking'.
When a behaviour was observed it was recorded for that student, with behaviours recorded again if went for longer than 30 seconds.

The results found that giving and receiving explanations or other help were positively related to achievement. High ability students gave more help, low ability students received more help and medium ability students giving and receiving help. Giving and receiving answer only was not significantly (statistically speaking) related to achievement.  There was no dependence on helping behaviours and gender observed. 5th grade students gave/received only answers half as often as 3rd and 4th grade students, however giving and receiving answers only occurred infrequently. Not receiving help after asking had the lowest mean observation frequency. They reported that sometimes team helping, one helping many and helping without being asked was observed. The author questions if students would engage in helping behaviours if they had not been taught them.

Cooperative Learning for Maths: References

Kramarski, B. and Mevarech, Z.R. (2003). Enhancing Mathematical Reasoning in the Classroom: The Effects of Cooperative Learning and Metacognitive Training. American Educational Research Journal, 40, 281-310. doi:10.3102/00028312040001281

Slavin, R.E., Lake, C., and Groff, C. (2009). Effective Programs in Middle and High School Mathematics: A Best-Evidence Synthesis. Review of Educational Research, 79, 839-911. doi:10.3102/0034654308330968

Armstrong, N., Chang, S.-M., Brickman, M. (2007). Cooperative Learning in Industrial-sized Biology Classes.
CBE Life Sciences Education, 6, 163-171. Retrieved from http://www.lifescied.org/cgi/reprint/6/2/163

Sharan, S. (1980). Cooperative Learning in Small Groups: Recent Methods and Effects on Achievement, Attitudes, and Ethnic Relations. Review of Educational Research, 50, 241-271. doi:10.3102/00346543050002241

Slavin, R. (1999). Comprehensive Approaches to Cooperative Learning. Theory Into Practice, 38(2), 74. Retrieved from Business Source Premier database.

Ross, J. (1995). Effects of feedback on student behavior in cooperative learning groups in a grade 7 math class. Elementary School Journal, 96(2), 125. Retrieved from Education Research Complete database.

Slavin, R. (1991). Synthesis of Research on Cooperative Learning. Educational Leadership, 48(5), 71. Retrieved from MasterFILE Premier database.

Nattiv, A. (1994). Helping behaviors and math achievement gain of students using cooperative learning. Elementary School Journal, 94(3), 285. Retrieved from Education Research Complete database.

Jones, E., Wilson, R., & Bhojwani, S. (1997). Mathematics instruction for secondary students with learning disabilities. Journal of Learning Disabilities, 30(2), 151-163. Retrieved from CINAHL Plus with Full Text database.

Slavin, R. (1996). Cooperative learning in middle and secondary schools. Clearing House, 69(4), 200. Retrieved from MasterFILE Premier database.

Springer, L., Stanne, M.E., and Donovan, S.S. (1999) Effects of Small-Group Learning on Undergraduates in Science, Mathematics, Engineering, and Technology: A Meta-Analysis. Review of Educational Research, 69, 21-51. doi:10.3102/00346543069001021

Slavin, R. (1983). When does cooperative learning increase student achievement?. Psychological Bulletin, 94(3), 429-445. doi:10.1037/0033-2909.94.3.429.

Webb, N.M., and Farivar, S. (1994). Promoting Helping Behavior in Cooperative Small Groups in Middle School Mathematics. American Educational Research Journal, 31, 369-395. doi:10.3102/00028312031002369

Antil, L.R., Jenkins, J.R., Wayne, S.K., and Vadasy, P.F. (1998). Cooperative Learning: Prevalence, Conceptualizations, and the Relation Between Research and Practice. American Educational Research Journal, 35, 419-454. doi:10.3102/00028312035003419

Kagan, S. (1989). The Structural Approach to Cooperative Learning. Educational Leadership, 47(4), 12. Retrieved from MasterFILE Premier database.