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.

Chiu's study went on to explain that "Teacher evaluations of student actions had the largest positive effects, serving as gatekeepers for other teacher actions.

Higher levels of teacher help content tended to reduce post-TI TOT, while teacher commands reduced post-TI TOT only when a group grasped the problem situation. In summary, TIs can increase TOT and problem solving, especially if teachers evaluate students' work" (Chiu p. 366). The key, according to Chiu, is that teachers must evaluate the progress of the student.

This statement portrays the level of experience the teacher should have in order to affect efficient methods of teaching in the classroom. A study conducted by Veenman et al. states, "Dyads with experience in cooperative learning achieved more than dyads without such experience" (Veenman, 2005, pg. 118).

Therefore, the experienced teachers who implement cooperative teaching methods meet with more success, according to Veenman et al., than do teachers without such experience. Experience can come from actually doing, but it can also come from watching others experience as well. The point is that teachers who are taught in cooperative learning methods, will likely implement such methods in the classroom, no matter what...

One way of substantiating different pedagogy methods is to compare them with studies. One such study attempted to discern the difference between cooperative learning techniques and non-cooperative learning techniques.
The study compared "cooperative learning combined with metacognitive training (COOP+META), individualized learning combined with metacognitive training (IND+META), cooperative learning without metacognitive training (COOP), and individualized learning without metacognitive training (IND)" (Mevarech, 2003, pg 282). What Mevarech learned from the study was that, "Results showed that the COOP+META group significantly outperformed the IND+META group, which in turn significantly outperformed the COOP and IND groups on graph interpretation and various aspects of mathematical explanations. Furthermore, the metacognitive groups (COOP+META and IND+META) outperformed their counterparts (COOP and IND) on graph construction (transfer tasks) and metacognitive knowledge" (Mevarech, 2003, pg 283). The study provided evidence that using cooperative learning in a mathematical arena could enhance the student's learning capabilities.

It is important to remember that cooperative learning is just one more tool teachers can use to enhance the classroom setting, enhancement that (as shown above) is especially needed in many mathematical classrooms. By using this tool, the classroom can become an environment where students work in small groups, analyzing, discussing and discovering the joys and wonders of mathematics. No longer will students be left to wander through the pitfalls of wrong mathematical equations and answers, instead they will be able to interact with other students in small group settings that enhance their learning abilities and understanding.

Works Cited

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Becker, W.E., and M. Watts. 2001b. Teaching economics at the start of the 21st century: Still chalk-and-talk, American Economic Review Papers and Proceedings, Vol. 91, No. 2, pp. 446-51

Chin, P., Bell, K.S., Munby, H., Hutchinson, N.L., (2004) Epistemological appropriation in one high school student's learning in cooperative education, American Educational Research Journal, Vol. 41, No. 2, pp. 401-417

Chiu, M.M., (2004) Adapting teacher interventions to student needs during cooperative learning: How to improve student problem solving and time on-task, American Educational Research Journal, Vol. 41, No. 2, pp. 365-399

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