Using Structured & Flexible Collaborative Learning Groups
Classroom Examples of Using Structured & Flexible Collaborative Learning Groups
Numerous studies show that students working in cooperative groups achieve at a higher level than students working individually. Students working together cooperatively are able to generate more problem-solving strategies than students working competitively (Qin, et al., 1995, cited in Johnson, J., 2000). As with whole-class discussions, it is important to establish expectations up front about behaviors that encourage students to work productively in groups and behaviors that discourage students. Post lists of agreed-on desired and undesired behaviors and use them for reflection, with the teacher asking groups to identify what they did working as a group that helped them solve the problem. Also, select tasks that are appropriate for group work, including those that encourage multiple approaches, are cognitively challenging, use manipulatives, and permit the possibility of more than one solution or effective strategy. Give students time to work individually before they engage as a group. Assigning roles such as team captain, resource monitor, facilitator and recorder/reporter, and delineating expectations for each role on a math task card, gives each student responsibility in accomplishing the task.
[Johnson, J. (2000). Teaching and learning mathematics: Using research to shift from the “Yesterday” mind to the “Tomorrow” mind. Olympia, WA: Office of Superintendent of Public Instruction.]
1. Word problems (elementary)
Structure a lesson(s) with time for students to explore a word problem in pairs or small groups (no more than four students in a group). Identify roles such as facilitator, recorder, and spokesperson; provide clear expectations for the assigned task (i.e., read the problem out loud, paraphrase it as a group, make a list of data provided and the data that is missing, identify two ways of solving the problem, represent at least one of those solutions through a drawing). When all teams have completed the majority of the expectations, and have the spokespersons for each group share out their group’s methods and solutions with the rest of the class. For success with this method, you will likely need to model group roles, processes, and expectations prior to implementing it with the class as a whole.
2. Clues (elementary)
Divide students into groups of three to five. Each group member is given a clue. Together the group finds the answer, recording not only the answer but how they know they are right. For example, the clues might be: I am a not a prime number; I am a multiple of 11; I am less than 8 times 7; I am divisible by 5
3. Triangles (elementary)
Use three examples of equilateral triangles: the first made up of one triangle, the second made up of four of the same-sized triangles as the first with three triangles at the base and one on top, and the third made up of 7 triangles at the base, 5 at the next level, 3 at the next and one at the top. The first diagram is made up of three line segments of equal length, the second diagram is made up of nine segments of that same length, and so on.
- Find the number of segments of the given length that would be needed for the tenth diagram in this sequence.
- Explain how you would find the number of segments of the given length that would be needed for the 100th diagram in this sequence.
- How would you find the number of segments of the given length for any diagram in this sequence?
Adapted from the “Interactive Mathematics Program, Year 1” (Emeryville, CA: Key Curriculum Press). In Mark Driscoll, Fostering Algebraic Thinking: A Guide for Teachers Grades 6-10. 1999. Portsmouth, NH: Heinemann Press.
4. Creating a Guide (high school)
In a high school geometry classroom, students in groups of four create a beginners guide to developing proofs (or guide to developing mathematical arguments, develop and use of justifications, etc.). Each student is assigned, or selects a role: Researcher (identifies required properties, theorems, etc.), Writer (develops drafts and final version of group’s product), Quality Control (edits both mathematical work and written work for consistency, accuracy and clarity), and Communicator (problem solver—works with teacher as needed and communicates information back to group).