By Jane Murphy Wilburne
The classroom practice of assigning homework is a necessity to reinforce the topic of the day's lesson, review skills and practice them in a variety of problems, or challenge students' thinking and application of the skills. Effective mathematics teachers know how to choose worthwhile assignments that can significantly impact students' learning and understanding of the mathematics. The challenge, however, is how to manage and review the assignments in a manner that will benefit students' learning, and use classroom time effectively.
Over the years, I have tried various approaches to reviewing and assessing students' homework. Collecting and grading every students' homework can be very time consuming, especially when you have large classes and no graduate assistants to help review students' work. On the other hand, while it is important to provide students with immediate feedback on their homework, it does not benefit them much to have the professor work out each problem in front of the class.
I believe it is important for college students to take responsibility for their learning. By promoting opportunities for them to communicate with and learn from each other, we can help students come to rely less on the professor to provide them with all the answers, and teach them to pose questions that enhance each others' understanding.
One technique that has been effective in my classes is to assign homework problems that vary in concept application and level of difficulty. The students were instructed to solve each problem and place a check (’) next to any problem they could not solve. As the students entered class the next day, they would list the page number and problem number of the problems they could not solve, on the front board in a designated area. If the problem was already listed, they placed a check (’) next to it. Once the class started, they were not allowed to record problem numbers at the board. Other students, who were successful in solving these problems, immediately went to the board when they entered the class, indicated that they would solve one of the listed problems, and worked it out in detail. When they finished they signed their name to the problem.
By the time I entered the classroom, students were busy solving problems at the board while others were checking their homework at their seats. If there were any questions about the problems, the student who solved the problem at the board would explain his work to the class. If there was a problem in which no one was able to solve, I would provide a few details about the problem and reassign it for the next class. In a short period of time, all homework was reviewed, and I recorded notes as to which students posted solutions on the board. Rather than collecting every student's homework, I noted the problems that gave most students difficulty and would assign similar problems in a future assignment. Students who listed the problems they had difficulty with were not penalized. Instead, those who solved the problems would receive a plus (+) in my grade book. A series of five pluses (+) would earn them a bonus point on a future exam.
My classroom quizzes would always include several homework problems to help keep students accountable for completing their assignments and motivate them to review problems they had difficulty with. Those who did typically received an A!
Time spent in class: approximately 5-12 minutes reviewing the homework. Time saved: about 30 minutes per class
Jane M. Wilburne is assistant professor of mathematics at Penn State Harrisburg.
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