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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.
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 the classroom subject might be.
Although experience is important for a teacher, it is also imperative that the research substantiate any findings so that the teacher might be assured that the direction being followed in the classroom is the correct one. 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.
Battersby, D., (2007) Improving subject teaching, British Journal of Educational Technology, Vol. 38, No. 2, pp. 377-378
Becker, W.E., and M. Watts. 2001a. Teaching methods in U.S. undergraduate economics courses. Journal of Economic Education, Vol 32, pp. 269-80.
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
Doyle, E.I., Beatty, C.F., Shaw, M.W. (1999) Using cooperative learning groups to develop health-related cultural awareness, the Journal of School Health, Vol. 69, No 2, pp. 73-76
Elton, L., (2007) Developing creativity in higher education, British Journal of Educational Technology, Vol. 38, No. 2, pp. 373-374
Felder, R.M., Brent, R., (1994) Cooperative learning in technical courses: Procedures, pitfalls, and payoffs, (ERIC) Document Reproduction Service Report, No. ED 377038, Accessed November 20, 2007
Mevarech, Z.R., & Kramarski, B., (1997a). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, Vol. 34, pp. 365-394
Mevarech, Z.R., & Kramarski, B., (2003) Enhancing Mathematical Reasoning in the classroom: The effects of cooperative learning and metacognitive training, American Educational Research Journal, Vol. 40, No. 1, pp. 281-310
Roblyer, MD., (2003) Integrating Educational Technology into Teaching (3rd Ed), Upper Saddle River, NJ: Merrill Prentice Hall
Schoenfeld, a.H. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, Vol. 23, pp. 145-166
Schoenfeld, a.H. (1985). Mathematical Problem Solving. San Diego, CA: Academic Press
Veenman, S., Denessen, E., van den Akker, a., van der Rijt, J. (2005) Effects of a cooperative learning program on the elaborations of students during help seeking and help giving, American Educational Research Journal, Vol. 42, No. 1, pp. 115-151
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The main concentration of this study was on the various approaches that were adopted in numerous educational institutes and universities and how their incorporation of cooperative learning strategies proved constructive. The demographics or spectrum of this study was very vast and carried out analyses and comparisons of universities from Australia, UK and the U.S.A. This particular study highlighted the CL strategies employed in the RMIT Graduate School of Business
Size/Cooperative Learning & it's effects on participation Action Research Question Will cooperative learning have a significantly positive impact on smaller or larger classes? The purpose of this study was to investigate if cooperative learning will have a significantly positive impact on smaller or larger classes. In order to have valid results, I used both my largest and smallest classes as my sampling. I also incorporated a variety of teaching styles with cooperative
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Methods for evaluating and monitoring the effectiveness of peer-assisted learning programs are discussed as well, followed by a summary of the literature review. Background and Overview. The growing body of scholarly evidence concerning peer tutoring has been consistent in emphasizing the powerful effects that children can exert on the academic and interpersonal development of their classmates and/or other students (Ehly & Topping, 1998). For example, Bloom (1984) reported early on that
A behavior resulting from injury or disease behavior resulting from experience behavior resulting from disease or drugs biologically determined behavior Evidence that learning has occurred is seen in published research studies changes in thinking changes in behavior emotional stability Change in performance is preceded by bad reviews scientific research the behavior of others change in disposition If-then statements may also be referred to as principles generalization hypothesis laws Statements which summarize relationships are restricted