Dr. Theodore Panitz was a popular educator whose courses filled with eager students, but he had a problem. When the time came to test the students' understanding of mathematical concepts, they struggled. His own investigation led Panitz to the discovery that his teaching method was building up his own powers of problem solving -- not his students'. What was the answer to this baffling problem? Cooperative learning! Included: Three of Panitz's favorite cooperative-learning activities and links to his cooperative-learning resources on the Web!
"I used to be a very good lecturer," Dr. Theodore Panitz told Education World. "Being an engineering and mathematics teacher, I was well organized and, without knowing it, followed the 'advanced organizer' model of teaching. I established the day's class goals, provided an overview of the concept(s) under study, and then led the class through a series of problems and questions that demonstrated the concept or mathematical procedure."
IT'S GREEK TO THEM ...
"I developed concepts by starting with simpler questions and then proceeding to more-complex structures," said Panitz. "It made a lot of sense to everyone -- during the lecture. I also used a lecture-discussion format to try to engage students and asked students to work individually on problems and then present their solutions on the board for additional class discussion. I tended to be very enthusiastic about my subject matter and teaching, and I am sure this was somewhat contagious for my students."
The approach seemed to work well until test time arrived. The students did not perform as well as they or Panitz had expected. When they discussed this phenomenon as a group, the students expressed frustration. They felt that they understood the material in class, but when they went home and tried to solve the problems on their own, the material "looked like Greek."
"Looking back, based upon the research I have since read, I am not surprised," stated Panitz. "I was doing all the critical thinking by writing and explaining the concepts, strengthening my own brain synapses -- not the students'!"
FROM DICTATION TO COOPERATION
The realization that his teaching technique reinforced his own knowledge but did not build his students' understanding caused Panitz to seek another method. At that time, he also began a doctoral program in education at Boston University. The program introduced Panitz to the benefits of cooperative learning.
"The underlying premise for cooperative learning is founded in constructivist epistemology," Panitz explained. "Knowledge is discovered by students and transformed into concepts students can relate to. It is then reconstructed and expanded through new learning experiences. Learning consists of active participation by the student versus passive acceptance of information presented by an expert lecturer. Learning comes about through transactions among students and between faculty and students, in a social setting, as they construct a knowledge base."
The key to cooperative learning, not surprisingly, is cooperation. According to Panitz, " Cooperation is a structure of interaction designed to facilitate the accomplishment of a specific end product or goal achieved through people working together in groups. Cooperative learning is defined by a set of processes that help people interact in order to accomplish a specific goal or develop an end product that is usually content specific."
COOPERATIVE LEARNING TECHNIQUES
Pairs of students work together on this exercise. First, both students read the same section from text or instructor-provided materials. One student explains a single paragraph or short section of the text to his or her partner. The partner listens and then asks questions if he or she does not understand the explanation. The listener then rephrases the explanation. The students alternate roles of explainer and listener until they complete all the material. When the entire class has completed the exercise, groups of students are asked at random to explain the material to the whole class. This serves as a check to make sure the students do indeed understand the material they are reading.
This activity goes well with any content that involves multiple problems. It is especially useful for chapter reviews or section practice. Panitz uses this activity to introduce solving equations in elementary algebra classes.
Organize students into groups of four. Use existing groups, or form new ones. Place five questions on the board, or use one more question than there are students in the groups. Using one extra problem keeps the groups from simply dividing up the problems, one for each student. After five to ten minutes, depending on the complexity of the problems, ask each group to send one student to the board to record the group's answers on a pre-drawn grid. Check students' answers.
Repeat the process for the duration of the class, or use for a set period of time. If Panitz notices that groups are having trouble with a set of problems, he stops the activity and facilitates a whole-class discussion or gives a mini-lecture on the material.
Students are actively involved in solving many problems in a short period of time during class. Groups are encouraged to work out their own processes for solving each set of problems. Thus, the students assume some of the responsibility for the class process. Panitz takes the opportunity to observe the students solve problems individually and in groups.
Use this activity wherever material can be segmented into separate components. Each group member becomes an expert on a different concept or procedure and teaches his or her concept to the group. Panitz uses this activity when covering factoring of polynomials, where the coefficient of the first term is 1. There are four unique cases. He forms base groups of four students. Students count off from one to four, and the Panitz distributes a work sheet for each case. The work sheets have five sample polynomials that he has made up for the students to factor, plus a space for each student to make up five problems. Students form new groups by combining with other students who have been assigned the same case number, again four to a group. The students work together to determine what is unique about their cases. They are, in effect, becoming experts in the case to which they have been assigned.
In the next step, students develop a teaching strategy to take back to their base groups. At this stage, they make up their own problems. Each student practices his or her explanation with the case group.
Finally, the students return to their base groups and teach the case they have been studying. There is no set way in which students must teach their material, so the results are quite varied. This activity helps students understand what teaching mathematics involves. It also leads to interesting, often entertaining, classes. Students learn how to work with different partners and begin to see that they can indeed assume responsibility for their own learning.
'DIPPING INTO THE POOL' OF COOPERATIVE LEARNING
Panitz completed a minor in business as a part of his master's degree in chemical engineering at the Illinois Institute of Technology. Through that work, he used cooperative techniques in case studies and group processing, trust building, and group work.
Because the focus was exclusively on building working groups in companies, it did not occur to Panitz to adapt the techniques to teaching. Until he experienced the cooperative learning approach and practiced it, he didn't understand its implications for teaching. Panitz became convinced that hands-on, interactive learning is very important for the individual learner.
Clearly, it also serves to prepare students for the work environment of the "real world"!
"This was quite an eye-opener for me and started a turnaround in my teaching philosophy from a teacher-centered lecture approach to one that is student-centered and cooperative," said Panitz. "There is a lot of flexibility, and I have learned to use many techniques rather than adopt a single approach for every course.
"When I began incorporating student-centered techniques in my classes, I started slowly," said Panitz. "I used in-class group work with pairs followed by whole-class discussion. I added only one or two new cooperative activities each semester in response to my students' performance on assessments or their expressed needs and interests."
If teachers are interested in bringing cooperative learning into their classrooms, Panitz recommends that they experiment with a few group activities before they make a total shift into the method. Educators can "get their feet wet" with the cooperative writing assignments found on Pantiz's Web page, Ted's WAC (Writing Across the Curriculum) E-Book.
WEB OFFERINGS FROM DR. THEODORE PANITZ
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