Reflection 3: Cooperative Learning
Cooperative learning groups are not simply lessons in which students work together. Johnson and Johnson (1999) defined it as instruction that involves students working in teams to accomplish a common goal that include interdependence, individual accountability, face-to-face interaction, appropriate use of collaborative skills, and group processing. Throughout my experience in the classroom I have structured cooperative learning activities with these elements. Though student interdependence, discussions, and self-regulation within the group, and the use of these five key elements, cooperative learning shows itself in the following activities/lessons.
Interdependence
One aspect of cooperative learning groups is interdependence among the group (Green, 2006). It is essential that the teacher includes certain characteristics of the assignment so the students are required to work together. If they could accomplish the goals by working independently, then the task would be lacking many of the benefits of cooperative learning groups. By having each student in the group take on a different role, then the students are required to work together in order to be successful. When interdependence is structured appropriately students understand that each member’s efforts are required and indispensable for group success and each group member has a unique contribution because of their skill set or role within the group (Green, 2006).
While teaching Introduction to Calculus at Cornwall Central High School, I informed the students at the beginning of the unit that their end of unit test would be a group test. They would be divided into teams of four, be given problems that would need to be completed during the single class period, and were receiving a group grade. The students immediately felt a responsibility to take good notes, ask questions, and participate throughout the unit because they did not want to let down their team. I noticed an immediate change in how the students acted throughout the unit knowing there would be a group test. Students who were not participating, and struggling to pay attention, were suddenly asking questions and seeking help as soon as they came across a topic they did not understand. In addition, those students who were doing exceptionally well in the class were approaching the other members of their group and asking if they needed clarification on anything. These normally high achieving students did not want the others in their groups to bring them down, so they made an effort to help them if needed. One aspect of this cooperative group assignment that unexpectedly changed the dynamic of the class was the comradery and willingness to help and talk with peers who they normally had not associated with. Students were now engaging in conversations with someone new, and as a result the classroom environment felt more warm and welcoming throughout the unit.
The way that I set up the assignment required the students to work together, and each had to participate for the group to be successful. By telling the class at the beginning of the unit that they would be taking a team test, I ensured that all group members felt responsible for understanding each day’s lesson so it wasn’t crunch time right before the test, and everyone could help get a good test grade. When test day came, the students were given more questions than they would be able to finish if done independently. This required the students to divide and conquer, then reconvene to discuss any potential issues.
This activity is a prime example of a cooperative learning activity because the students were working towards a common goal, each with a responsibility to be prepared the day of the test, and work together to complete the test within the class period. As I walked around the room I could see students developing a plan, dividing up the work, and agreeing to check with one another once they were done. The way the students split up the work varied, but most groups went through all the questions, and students volunteered to complete certain questions based on their level of comfort and skills in that area. Those groups who did not successfully rely on interdependence were unsuccessful in completing their goal of completing the test in time.
If I could make any changes to the assignment, I would change the group sizes to two or three students max. Although the groups of four worked well together, I noticed that a lot of time was spent discussing how each person wanted to approach the problem rather than actually doing the work. Although it was wonderful to see them using teamwork and checking the understanding of each team member, I had to give them multiple problems to assess all the topics covered in the unit, and they had to complete it within class time because I did not want them discussing the test with other groups. By limiting it to two people per team, accountability is higher for each person yet they can still work as a team to accomplish the task.
An activity that I have not had the opportunity to implement in the classroom, but have created a lesson for is surrounding the book The Greedy Triangle by Marilyn Burns. The group work of this lesson will require students to collaborate to try to figure out the relationship between the angles inside of a polygon. From the book the students will learn that the sum of all angles in a triangle are 180 degrees, however this number increases as a polygon has more sides. Together students will need to guess and check, and share their ideas to come up with a general formula to determine the degrees of a polygon with n number of sides. Because the groups will have very little help from the teacher, they will need to rely on their interdependence, and share their thinking with the group. Alone, this is a difficult relationship to discover, therefore working together and trying various problems is essential.
As my students complete this assignment I will look for signs of progress in terms of cooperative learning through their discussions with one another. Its important that students learn how to communicate their mathematical and problem solving ideas with one another verbally. This project is a wonderful way for them to begin to explain thought processes, test hypotheses, and question outcomes with their peers before working on more challenging problems.
Another cooperative learning activity that I created that stressed the aspect of interdependence was “Area- Piecing the Puzzle Together.” When learning how to find the area of irregular polygons, my 6th grade, self-contained special education class worked together to break up the polygons, take the necessary measurements, and solve for the area of the whole shape. Each team member was a critical component of the assignment, and they were seeking each other for help in seeing how the irregular polygon could be divided.
As the girls worked on this activity they discussed various strategies towards accomplishing their goal. One girl stated “why don’t we each do a job. I’ll be the measurer.” Their interdependence was clear to me because they relied on each other to be responsible for their task in order to be successful as a group. At one points the measurer made an error in her measurement and the “calculator” stated “hey if you do your job wrong then mine will be wrong too!” It was clear that the girls understood their importance within the group, and the need to work together in order to complete the task.
If I were to change this assignment, I would set specific roles or responsibilities for each student. Although they worked well by helping one another for with each task, it would have been better if they were each responsible for a specific task.
Discussion
When developing a cooperative learning structured assignment it is essential that the teacher asks questions or includes aspects that require the students to engage in group discussion. Within the group students should ask each other questions about the procedure, concepts, and requirements for the task. Groups discuss task goals, problem solving techniques, check for understanding, the concepts being learned, and connections to prior knowledge (Green, 2006). Through these discussions, students are reaching higher levels of thinking and developing an understanding of the topic that they wouldn’t have had if they were working independently.
In my Introduction to Calculus class, I had the students work in a “reciprocal teaching” type of set up during our unit on various functions. The students were broken up into groups of four and given a list of new types of functions (contiguous, one to one, onto etc.) and had to use their textbooks, and as resources to learn what each type of function was. Within each group there was a predictor, researcher, clarifier, and questioner. As the students took on their roles, they discussed the functions they were learning about. By working together and engaging in a discussion, the group was gaining an understanding of the material, and challenging each other to learn more about the concepts. By listening to the groups, I could clearly see the students taking on their roles, challenging the thinking of the group, and making connections to prior lessons. In addition, when we later reconvened as a whole class, many students shared the input other group members had. Kyle for example, stated “our questioner Dave brought up a good point about inverse functions!” It was clear that the students’ discussions and questioning was encouraging them to take their thinking to the next level. When this class took the test on this topic, I also noticed a lot of similar verbatim that they used within their group discussion to explain their answers on the exam. The students remembered what their peers discussed, and used it to express their knowledge on the exam.
If I were to change anything about this cooperative learning group, I would have created a list of possible questions, or sentence starters for the questioners to use. I had seen sentence starters used for younger students, but I had assumed that since these were high school students, they could come up with questions on their own. I hadn’t considered that they were not familiar with reciprocal learning groups, and weren’t used to thinking of questions to ask their peers. Typically, teachers pose the questions to the students, however in cooperative learning groups the students need to work together and rely on one another to accomplish the task.
Another cooperative group activity I created for my class included my 8th grade, self-contained math class at Cornwall Middle School, and a Translations Activity. At the end, the students from each team would have to present to the rest of the class and myself how they solved the problem, and their final answer. I informed the students that they should ask each other questions because “getting supplies for a party, and meeting Justin Bieber are very big deals!” While the two teams worked on their task, I listened to the discussions within the groups. I noticed certain students taking leadership roles, and other students questioning their decision making. Because of their inquiry as to why they were doing each step, it was clear that the group members were challenging each other’s thinking. In addition, I heard one high achieving student ask another student if they understood what they just did. The student was honest and explained that he had not; therefore she took the time to explain her thought process to him. As the teams presented their work, they verbalized their thinking, and had broke down their steps to show the rest of the class how they completed the problem. This improved the students’ understanding of the math, and gave me valuable information about the children’s knowledge of translations.
If I were to change this assignment, I would have given them more complex problems, and challenged them to make connections other areas of mathematics that include transformational geometry. I wasn’t sure how well these students would work together. My fear was that the low-achieving students would fall behind or not actively participates in group discussion, however these students all worked together and were good at clarifying challenging concepts to one another.
While working with the students of the Math Club at Bishop Dunn Memorial, I had them play Math Dodge Ball one day. After having the students play the game a few times, switching their roles, I asked them to consider if there are strategies to guaranteeing a win as the Matcher or Dodger. As I walked around the room, I heard students sharing their ideas with their partner. I remember one student in particular who felt as though they came up with a solution in order to guarantee a win for the Dodger. While his partner was happy that they could have potentially found a solution, he expressed his concern over whether or not the strategy was guaranteed to work. I listened to the students discuss various issues or theories as to why their idea seems like it would work, but may not. They challenged each other’s thinking and motivated one another to consider other options. Like this pair of students, others in the classroom were very expressive with their partners, checking for solutions, sharing hypothesis, and taking time to reevaluate their plans. It was clear that they had adopted the essence of discussions within a cooperative group, and bounced ideas off one another in order to determine a correct answer.
A lesson that I have created but have not implemented was an example of Reciprocal Teaching in Action using a possible reading passage in a social studies classroom. While the focus of this lesson is on the Expedition of Lewis and Clarke, it can be adapted to be used for any reading assignment. Because I have observed and implemented a reciprocal teaching lesson in the past, I know what to look for in my students to determine whether or not they are properly using the characteristics of cooperative learning. When listing to the discussions, I will hear all students correctly fulfilling their roles within the group. Reciprocal teaching requires the students to maintain their specific roles to ensure group comprehension and development to higher levels of thinking. The students will challenge one another to think about the passage deeper, consider the feelings of the historical characters, as well as remember factual information stated in the text. True evidence of this lesson working as planned will present itself when students work independently, and carry out the four reciprocal teaching roles themselves to improve their own reading comprehension.
Self-Regulation within the Group
The third aspect of cooperative learning groups is self-regulation, but of the group as a whole rather than individually. Very often group assignments involve more parts, a deeper analysis of the topic, and more challenging questions. Because it is more thought-provoking, some self-regulation strategies that students use individually may not be appropriate for the group. Therefore new ones may need to be created, or old ones altered. By keeping in mind the goal of the task and time frame the students are given to complete it, they will need to develop strategies of how they can complete all components of the assignment.
While teaching my 7th grade, self-contained special education math class, I gave the three girls in my class a cooperative group assignment requiring them to find how many candy bars it would take to fill the classroom. Since they had been learning about various forms of measurement, volume of three-dimensional objects, and incessantly telling me about their love of candy, I figured it would be an appropriate assessment for them. Because these students were classified as learning disabled and autistic, the planning aspect of this assignment was a major part for them. Coming up with a set of procedures to get them from the task to the final answer, and then checking to see if it was effective as they worked through the problem was a major accomplishment for this set of students. Stephanie, the dominant group member, went to the board and wrote down a list of steps they agreed upon as a procedure to complete the task. As they completed each step, Stephanie asked the others “do you think we can move on?” If they agreed, she put a check on the board next to that step. If they didn’t, they discussed what more needed to be done. As the girls completed this activity, the repeatedly checked on their progress to ensure they were working towards their goal. Had they not created this plan and regulated the progress of the group, they would not be successful on the assignment.
If I were to make any changes on this cooperative group assignment, I would have created a blank table or chart to give the students more structure when coming up with a plan to solve the problem. Although they had worked well together, and exceeded my expectations, I wish I had given them a blank outline, or sentence starters to help they come up with steps. I gave them a lot of hints, and guided them in the right direction, but by including the basic structure, they would have felt like they accomplished more on their own, independent of my help.
When creating an activity for Temple Hill Academy’s Math Day, I decided to create a challenging, teambuilding project that would allow students to use problem solving skills while working together. The Magic Squares activity I adapted from multiple online worksheets, required students to fill a box with numbers in which all rows, columns, and diagonals had the same sum. When introducing the activity to the students I had not told them why these boxes were magical. I simply told them that they were magic and it was up to them to determine why, then complete the worksheet.
As I left the students to work in small groups, I circulated the area and listed to their discussions. It was clear that self-regulation became an important issue within the groups. The first task was to determine why the boxes were magical. I remember hearing some students make guesses and wanting to rush to fill in the boxes without determining whether or not their guess was right. In some groups, there were students who expressed their concern over jumping to conclusion and suggested they test their theory before moving on. Other groups however, did not waste time checking their work and ended up getting the worksheet wrong when they asked for me to check it. The beauty about this assignment is students realized that they had to consider the thoughts of the group. Initially they felt like they could come up with an idea on their own and run with it, but they soon realized that creating a plan, testing it, and discussing the progress of the group was the only way to be successful. Approximately 15 minutes into the exercise, I noticed the eager students who were initially rushing, had now slowed down, and were sharing their ideas with their peers before moving on.
As I reflect on my work in the classroom, it is clear that I have had a lot of wonderful opportunities to implement effective cooperative learning lessons. These lessons have allowed students to utilize interdependence, discussions with peers, and self-regulation within the group to achieve common goals. I look forward to using these lessons again as well as creating new ones with similar characteristics for my classes in the future.
Appendix
Standard 3- Knowledge of the Students |
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Aspect |
Explanation |
Ways I Met the Standard |
Commitment to knowing the individual needs of each student and the process of human development |
Accomplished teachers are committed to getting to know students’ backgrounds, past experiences, learning styles, and personal needs. Teachers motivate and challenge students when it’s appropriate as needed and offer additional support as needed. |
-In order for the group test to work properly, I had to know my students abilities, and what they could accomplish in the time allotted to them. -The reciprocal teaching in action activity requires students to have mastered the reciprocal teaching process. Unless they have shown signs of being able to control the thinking of the group, I as the teacher need to continue to guide thinking until they are ready to do so without my help. -Because the students who completed the irregular polygons activity were low achieving math students, it was important that I as the teacher was there to offer guidance when necessary so they did not get frustrated, or off track. |
Standard 6- Ways to Think Mathematically |
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Aspect |
Explanation |
Ways I Met the Standard |
Accomplished mathematics teachers develop their own ability to think and use it to effectively teach their students concrete and abstract mathematical concepts. |
Accomplished mathematics teachers develop their own and their student’ abilities to reason and think mathematically- to investigate and explore patterns, to discover structures and establish mathematical relationships, to formulate and solve problems, to justify and communicate conclusions, and to question and extend those conclusions. |
-Translations can be a challenging concept for many students, therefore it was important that I created an activity such as this one that incorporated cooperative learning and kinesthetic characteristics. -The dodge ball activity was a problem solving puzzle that required the students to think deeper about the strategies for winning and losing the game. -The Magic Squares activity was a cooperative lesson that got students thinking critically about how to solve the puzzle. A great component of this activity is that the level of difficulty can be changed easily as the students progress through the problems. -The Room Full of Candy got the students thinking about candy in a mathematical sense. -The Greedy Triangle Lesson required students to work together to come up with a formula on their own rather than having the teacher tell it to them. This provided them the opportunity to think critically as well as understand where the formula came from. |
Green, K. (2006). [Web log message]. Retrieved from http://cooperativelearning.nuvvo.com/lesson/216-5-basic-elements-of-cooperative-learning
Johnson, D. H., & Johnson, R. (1999, January 1). Cooperative Learning. Cooperative Learning. Retrieved , from http://www.cehd.umn.edu/research/highlights/coop-learning