Cooperative Learning Techniques Are Being

Cooperative learning techniques are being used extensively in many educational classrooms, although such methods are more likely to be found in the arts, science and literature than they are in mathematic courses. The reasons behind this are varied and can include the fact that math is perceived more as a cut and dried discipline than the other areas of education.

One early study on cooperative learning showed that "the emphasis on fluency and flexibility, two important elements of mathematical discourse, has several implications. First, students tend to conceive of mathematics as a rigid subject based on arbitrary rules that allow only one correct answer and one correct argument to explain the answer" (Schoenfeld, 1985).

That student's perceptions of mathematics tends to be concrete in nature should not be surprising since many times teachers of mathematics also see mathematic pedagogy in the same manner. According to one researcher, "in a 2000 survey of economic instruction, the median time devoted to student discussion in the economics classroom was just over 5% (Becker and Watts 2001a; 2001b).

Since cooperative learning is widely accepted and used in educational arenas throughout the U.S. And the world, it is interesting that teachers of mathematics would perceive these methods as lacking in the capability to help in a mathematics classroom.

Cooperative learning is an effective way to develop the ability to communicate with others. However, some mathematicians (e.g., Wu, 1997) doubt whether cooperative learning could be used in mathematics classrooms without considering the major purpose of mathematics instruction, which is to help students learn to think mathematically" (Schoenfeld, 1988). Teaching is considering by many to be the epitome of efficient and effective communication, and since mathematics is also considered to be an area that needs to have that type of communication between the teacher(s) and the student(s) it would seem that teachers of mathematics would be the first to embrace such teaching methods in order to more effectively teach. As evidenced by the above studies, such an embrace has not been readily discernable.

This paper will take a look at the reasons behind such blase attitudes and discuss how cooperative learning, and other pedagogical techniques can be employed in educational mathematic environments in order to facilitate learning. Cooperative learning encompasses many areas of pedagogy with discussions and small group activities being paramount in usage.

Many experts and teachers feel that test scores, comprehension of the material and knowledge all improve when cooperative learning is used in the classroom.

According to Felder and Brent (1994), "Studies show that students taught with cooperative learning methods exhibit higher academic achievement, greater persistence through graduation, better high-level reasoning and critical thinking skills, deeper understanding of learned material, more on-task and less disruptive behavior in class, lower levels of anxiety and stress, greater intrinsic motivation to learn and achieve, greater ability to view situations from other's perspectives, more positive and supportive relationships with peers, more positive attitudes towards subject areas, and higher self-esteem."

Implementing techniques in the mathematics classroom can be relatively simple in nature. One study suggests that cooperative learning is best enhanced when, "students are assigned to work in teams of four. Introductory in-class, team-building activities in which teams discuss rules and expectations can foster a positive learning experience" (Doyle, Beatty, Shaw, 1999, p. 73). Fostering a positive learning environment in a mathematics classroom (that is likely perceived as not the most exciting of courses) is likely a key factor in learning in that classroom. In many regards mathematics as it is taught today may not have that positive learning environment. By allowing the students to interact, working together in small groups to discover answers and the step-by-step process of doing so could be very positive in nature, and would surely add to the positive classroom environment being sought.

Another factor that can be introduced in a mathematics classroom in order to facilitate the positive environment being sought is listing the lesson objectives and then describing what the students will be able to accomplish once those objectives have been reached.

By doing this, the students understand exactly what is needed to reach the goal that is being sought and, maybe even more importantly, the students will understand why they are seeking that goal.

Many students in today's educational society seem to be more interested in knowing why homework is being assigned, why they have to complete certain projects and why certain subjects are being taught and required at their school.

One recent study showed that the impact of using cooperative learning to teach heterogeneous students in a classroom would likely have very positive results, especially in regards to test scores. The study's researcher "using multivariate regression analysis, found that students taught by cooperative learning achieved greater academic performance in the form of higher exam scores" (Yamarik, 2007, p. 259). This is an extremely important factor when considering adding cooperative learning to a mathematic classroom. The educational environment has changed mightily during the last decade, now the focus is on ensuring that every child receive an equal opportunity to receive an education and that every student achieve at an equally high level of education.

School districts and schools are now required to educate students who before 1997 were considered too disabled for such an attempt. To comply with the requirements schools have had to make fundamental changes in the approach to providing education to students, not just in a physical sense but in the basic method used by teachers, administrators and parents in teaching their children, and not only with the students that are now being included into the general educational society, but those children that were previously included as well.

For the most part, these changes that have taken place, as well as the changes that are taking place currently, have meant an awakening for all involved, educators as well as students and their parents.

Some of these changes have been implemented in conjunction with the use of technology. According to Roblyer (2003), there are a number of technological advances in the classroom including these three technology resources: 1) use of interactive books for those students with mild mental deficits, 2) alternate keyboards and input software for those students who might be suffering from a disease that has impaired their fine-motor skills, and 3) speech development software for those students who might have hearing loss or deafness.

By including these technological advances into the mathematics classroom the environment will be enhanced and more importantly learning will improve. A key in introducing these advances as well as in implementing cooperative learning procedures is how well the teacher accomplishes those feats. Introducing new procedures or practices oftentimes takes a certain amount of skill and teachers who do not exhibit such skills will likely have a difficult time in the classroom. It is important therefore to ensure that the teachers understand cooperative learning and technology, and further understand how to effectively introduce it into the classroom. Recent studies have shown how the many facets of teacher's roles, including organizing classrooms, metacognitive guidance and the selection and use of worthwhile mathematical tasks are of ultimate importance in the classroom.

One recent study suggests, "Such tasks should include complex situations that present quantitative information in different contexts, allow multiple representations, or afford students opportunities to resolve mathematical conflicts" (Mevarech, Kramarski, 1997, p. 366).

Using 'mathematical conflicts' in a cooperative learning environment is a simple matter of forming discussion groups, informing the groups of a mathematical equation needing to be solved, and allowing the groups to not only seek the correct answer, but to discuss along the way the steps it takes to reach the correct conclusion. Wittrock (1986) conducted a study in cognitive psychology that studied whether students learn better if they are engaged in education activities especially in regards to elaboration (discussions) or restructuring and discovered that, "research in cognitive psychology has shown that learning occurs when the learner is engaged in some sort of cognitive restructuring or elaboration" (Wittrock, 1986).

Though many studies have shown that a cooperative learning environment is an excellent way of improving test scores, student comprehension and more, there are other methods that might work just as well and should be considered. One such method that produced some very favorable results was developed and tested by Z.R. Mevarech and B. Kramarski. The program's acronym IMPROVE stands for all the teaching stages.

Those stages are: "Introducing the new concepts, Metacognitive questioning, Practicing, Reviewing and reducing difficulties, Obtaining mastery, Verification, and Enrichment" (Mevarech, Kramarski, 1997, p. 365).

The two researchers suggested that using these steps would enhance the learning environment, with little or no difference between those students who used IMPROVE individually, or those who used it in small groups. What Mevarech and Kramarski reported was "that IMPROVE students who studied in heterogeneous classrooms without tracking or grouping outperformed their counterparts in nontreatment control groups who studied in small groups. In particular, observation showed that IMPROVE had positive effects on students' mathematical achievement and ability to explain their reasoning" (Mevarech, 1997, p. 390). It seems likely that components of IMPROVE assists the students in learning especially in a mathematical classroom. If this is true, then implementing some or all of the components may be a good choice for educators. Learning how to integrate those components along with the other aspects of cooperative learning will enhance all classrooms and especially "have positive effects on students' mathematical achievement'. Positive achievements is what should be sought on every level and those teaching methods that assist in accomplishing this goal should be integrated.

One recent article touted the fact that a variety of teaching methods should be sought out in order to allow all students to benefit from the variety and creativity it takes to implement such methods.

Are we concerned with developing creativity in relevant teachers, students, processes, and/or curricula; with pedagogic practice and/or theory; with institutional practice and/or public policy? The answer turns out to be "all of them and more" (Elton, 2007, p. 373). Elton's study seems to say that the answer to an improved classroom experience is the creativity exhibited by the educators as well as those being educated.

Another consideration might be to include a certain percentage of research in the student's work. One researcher is "convinced that applied research findings could significantly improve student learning and attitudes" (Battersby, 2007, p. 377). By having the students research the fundamentals of mathematics, and perhaps the founders of the different areas of mathematics could lead to student's having a far greater understanding of the practical applications of mathematics as well as the mathematical why's and wherefores. Battersby also "makes the point that new and old teaching interventions cannot be directly compared as they do not have the same objectives" (Battersby, 2007, p. 378).

Battersby's statement begs the question(s), what are the current objectives of education and have they really changed over the past couple of decades? Is the objective of education to allow the student to learn, or as many experts now believe, is the objective to ensure the student is prepared for life after schooling? One study shows that "recent research suggests that work-based learning is complex, cognitive, and context dependent, and involves initiation into a community of practice (Billett, 2000; Wenger, 1998)" (Chin, Bell, Munby, Hutchinson, 2004, p. 401).

What Chin et al. concludes is that the objective of modern educational system(s) should be to train students concerning what comes after school is finished, and that it takes an entire community to do that training. One could assume that the entire community would most likely be effective in teaching as long as there was a large amount of communication between students and students, students and teachers, teachers and administrators, administrators and parents and that the way to accomplish this communication, especially in the classroom, would be to have discussion groups. Teachers could still monitor these groups to keep them on track and to offer advice and wisdom in the subject area. Studies have shown that such teacher intervention methods work in the classroom arena, even if it is in a mathematical classroom.

One study that showed the effectiveness of such interventions showed that "Teacher interventions (TIs) involved groups of ninth-grade students working on an algebra problem; videotaped lessons were transcribed and analyzed. Results showed that teachers initiated most TIs and typically did so when students were off-task or showed little progress. After TIs, students' TOT and problem solving often improved" (Chiu, 2004, p 365). This improvement should come as no surprise, it makes sense to most people that when a student is corrected the result can be that the student learns the correct answer or method.