Mathematics Professional Series|
Cooperative Learning Algebra
What Is Cooperative Learning?
Cooperative Learning IS . . .
- Group members understanding that they are part of a team and all members of the team are working toward a common goal.
- Group members understanding that the successes or failures of the group will be shared by all members. Therefore, each member must contribute as much as he or she can to the group goal.
- All students learning to talk and discuss problems with each other in order to accomplish the group goal.
- Group success being dependent on, and being a direct effect of, the individual work of each member of the group.
- A process that capitalizes on the presence of student peers, encourages interaction among students, and establishes positive relationships among team members.
- A process that requires the guidance of a teacher who can help students develop the cooperative learning skills they need, understand group dynamics, and learn mathematics by working in groups.
- Students asking for help only after each one in the group has considered the question.
- Helping students to be individually accountable for their learning. This is discussed in detail by Spencer Kagan in his book Cooperative Learning.
Cooperative Learning IS NOT . . .
- Separating students into small groups to work on a problem or a group of problems without direction or individual responsibility.
- Students sitting together in groups and working on problems individually without conversation or interaction regarding the method or process being used for problem solving.
- Students sitting together in groups and letting one student do all of the work while the others watch or listen.
Learning to Work Together
Checking homework daily is an excellent and efficient method to help teams learn to work together. It can be done in this way.
This method will reduce the number of problems addressed by the teacher and thus allow for better use of class time. Students will have more peer pressure to complete homework fully and on time. Teachers may choose to have students keep their own weekly homework records by team, individually, or both.
- The teacher displays correct answers on the overhead projector.
- Students in cooperative groups check their homework and discuss any differences with their team members. Many will find answers to their questions from members of their team.
- Each team must agree upon the problems that they cannot solve.
- The teacher then asks each team to indicate which problems they would like discussed. The teacher then guides students through a solution of those problems.
The teacher may choose to select a problem or two for discussion based on information gathered by circulating around the room while students are checking and talking about their homework. Calling on a random person in a random group can add responsibility to this method.
Structures to Deliver Instruction to Students
There are a variety of structures that can be used to deliver instruction to students via cooperative learning.
One structure is called Think-Pair-Share. It offers each student an opportunity to respond to a question. In a typical classroom, the teacher asks a question, and students raise their hands to answer. Using Think-Pair-Share, the teacher asks a question, the students think about the answer for a specified amount of time, and then they share their answers with a partner or the entire team. The teacher then asks students to share their answers with the rest of the class. A time limit is usually set for each step in the process. The teacher may use cuing devices such as hand signals, a bell, a timer, and so on.
Methods for Sharing with the Whole Class
This structure allows the teacher to call on students who feel that they have something important to share with the rest of the class.
- Students write responses at the same time on the chalkboard.
- Do a quick check through the class. Students respond rapidly one after another.
- All students stand up. After each student gives his or her response, he or she sits down. Anyone who has a similar response also sits down. This process is continued until everyone is seated. This allows several different ideas to be heard by all students in a short amount of time.
- Each student shares a response with a student in another group.
Spencer Kagan states the following benefits to teachers.
The following example problems could be used to practice using the structure Think-Pair-Share in an algebra classroom.
- Students have been found to spend more time on the task and to listen to each other more when involved in Think-Pair-Share activities. More students raise their hands to respond after rehearsing in pairs. Students may have better recall due to increased wait time, and the quality of the responses may be better.
- Teachers may also have more time to think when using Think-Pair-Share. They can concentrate on listening to student responses, observing student reactions, and asking higher-order questions. Class discussion can be a much more relaxing experience for both students and teachers.
Algebra 1 Examples
- Explain the meaning of area and perimeter. Describe how to calculate the area and perimeter of a rectangle.
- A linear equation is written in the form y = mx + b. Explain the meaning of the values of m and b.
- Is it possible to choose any two points on a line and calculate its slope? Illustrate by examples. Is the slope always the same for a given line no matter what two points you choose?
- Explain how to simplify the following expression .
3 + (4 + 2 · 5) - 8 · 3 + 4 ÷ 2 - 72
Describe, in general, the rules for order of operations.
Algebra 2 Examples
- Given a system of two linear equations in two variables, describe how to determine if the graphs intersect, coincide, or are parallel.
- Explain how you determine from the equation if the graph of a parabola opens upward or downward.
Algebra 1 Answers
- The perimeter of a figure is the distance around the figure. The area of a figure is the number of square units contained in the interior of the figure.
P = 2w + 2l ; A = lw
- m is the slope of the graph of the equation. b is the y-intercept of the graph of the equation.
- yes; See students' work; yes
- 3 + (4 + 2 · 5) - 8 · 3 + 4 ÷ 2 - 72
= 3 + (4 + 1 0) - 24 + 2 - 49
= 3 + 14 - 24 + 2 - 49
Rules for the order of operations:
- Simplify the expressions inside grouping symbols.
- Evaluate all powers.
- Then do all multiplications and divisions from left to right.
- Then do all additions and subtractions from left to right.
Algebra 2 Answers
- If the graphs of the two equations have different slopes, the graphs will intersect. If the graphs of the two equations have the same slope and the same y-intercept, the graphs will coincide. If the graphs of the two equations have the same slope and different y-intercepts, the graphs will be parallel.
- For y = ax2 + bx + c, if a > 0, the graph opens upward.
If a < 0, the graph opens downward.
For more information on cooperative learning, see "Cooperative Learning in the Mathematics Classroom", part of the Glencoe Professional Mathematics Series.