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Dear Matt, One area of discussion during the beginning of the school year has been homework – how and when to deal with it, and how to grade it outside of class. Usually the teacher will go over any questions students might have at the beginning of class before collecting the homework to grade. Grading is done on a scale of 0 to 10, with 0 indicating the student did not turn it in or turned in a blank, and 10 indicating the student showed thoroughness and accuracy throughout the assignment. I question whether going over the homework in class is beneficial, since some students are simply copying down the answers. However, I also don’t believe it is fair to leave legitimate student questions unanswered. This dilemma makes me wonder, what is the point of homework? For me, the point of homework is not to punish students for getting answers wrong, but rather to help them learn. This being said, I think there is a fine line between giving the answers in class and simply collecting the homework right away. Currently, I feel that perhaps the best was to administer homework help as a teacher is before or after school. Response: Dear Student Teacher,: You already have a great start to becoming a reflective professional! You have also raised a question that has provoked discussions among teachers for a long time, and will probably continue to do so. Your italicized question is a good place to start. As you suggest, the primary purpose of math homework should be to help students learn mathematics. A secondary purpose is to provide feedback, both to the teacher and to the students. This might include clarifying concepts for students, while alerting the teacher to concepts that are not clear for a few or many students. One problem with answering student questions in class is that the teacher does not know if only the student asking has that question, or if many have the same question. A strategy some teachers use is to have students record on a board as they enter problems they would like clarified, with tallies for multiple students with the same question. The teacher can determine quickly whether s/he should talk to individuals later, or address the whole class. Your idea of using time before or after class, or during other times when students are not engaged in whole class activities is good. Individualized feedback is usually the most effective. A third homework purpose can be providing practice and opportunities to extend learning and connect to prior lessons. Depending on the type of assignment, however, this will be more or less effective. We know that practice is most effective when it happens over time. That is, when many practice problems are assigned immediately after teaching a skill or procedure, retention after a day or so is minimal. On the other hand, when homework addresses not only recent skills, procedures and concepts, but earlier ones, the retention is much better. Since what we want for our students is long term understanding and continuing flexibility in applying skills and procedures to new situations, the so-called “distributed practice” can yield much stronger results. The idea of revisiting material from last week, month, or term can be incorporated not only into homework but into daily warm ups, which can help students know they have mastered ideas, reawaken prior knowledge that will be used in the day’s lesson, and review earlier material, addressing multiple math strands and skills. The first 5-10 minutes of class represent prime learning time for students. It seems like a waste of this rich opportunity to fill it by reading out a list of answers, with students passively listening (or filling in answers, as you have observed). Even a short warm up (maximum 5 minutes) can be a more engaging and active learning time for students, while still providing feedback for students and teacher. Another strategy some teachers find effective and manageable is the Homework Quiz. Students have daily or regular assignments, have opportunities to check their work, possibly with a posted key, and take responsibility for asking questions on problems they do not fully understand. After several days or a week, the teacher identifies a small number of key problems from the homework. For this quiz, students use their completed (or incomplete) homework to answer the identified questions on a new sheet, including showing all work, handing the paper in to be graded as a quiz. Among the advantages of this are that students can clearly see the primary purpose of homework as a tool for learning; teachers can more easily manage the “paper tiger” of piles of homework to correct each day by reducing it to a single sheet; and students who do a careful and thorough job of doing homework regularly and asking questions as needed will do well on the Homework Quiz. It also allows the teacher to focus on those essential problems that best represent the small number of core concepts s/he wishes to be sure all students understand. As you progress and grow in your career, you may want to try various strategies – these and others - for addressing homework, based on the class, students, school policy, and your own preferences and needs. There is no one right answer for all occasions, and this issue will no doubt continue to offer material for discussions in Mathematics Departments for years to come! Good luck to you, and keep up the good thinking! Matt |
Matt Mentor, a wise and experienced teacher, offers advice about teaching mathematics topics to beginning teachers. Of course, experienced teachers can join in as well. Here’s how it works: Send your answers to MattMentorMCTM@aol.com and Matt will post as many different solutions that adequately address the question as are received. Have a Question for Matt? |
