How Many Math Problems For Homework

Homework battles have raged for decades. For as long as kids have been whining about doing their homework, parents and education reformers have complained that homework's benefits are dubious. Meanwhile many teachers argue that take-home lessons are key to helping students learn. Now, as schools are shifting to the new (and hotly debated) Common Core curriculum standards, educators, administrators and researchers are turning a fresh eye toward the question of homework's value.

In a recent study of Spanish students, Rubén Fernández-Alonso, PhD, and colleagues found that students who were regularly assigned math and science homework scored higher on standardized tests. But when kids reported having more than 90 to 100 minutes of homework per day, scores declined (Journal of Educational Psychology, 2015).

One point researchers agree on is that for all students, homework quality matters. But too many kids are feeling a lack of engagement with their take-home assignments, many experts say. In Pope and Galloway's research, only 20 percent to 30 percent of students said they felt their homework was useful or meaningful.

But critics say those skills can be developed with many fewer hours of homework each week. Why assign 50 math problems, Pope asks, when 10 would be just as constructive? One Advanced Placement biology teacher she worked with through Challenge Success experimented with cutting his homework assignments by a third, and then by half. "Test scores didn't go down," she says. "You can have a rigorous course and not have a crazy homework load."

Still, changing the culture of homework won't be easy. Teachers-to-be get little instruction in homework during their training, Pope says. And despite some vocal parents arguing that kids bring home too much homework, many others get nervous if they think their child doesn't have enough. "Teachers feel pressured to give homework because parents expect it to come home," says Galloway. "When it doesn't, there's this idea that the school might not be doing its job."

An event in George Dantzig's life became the origin of a famous story in 1939 while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.

One of the most interesting aspects of using unsolved problems in my classes has been to see how my students respond. I typically ask students to write a three-page reflective essay about their experience with the homework in the course, and almost all of the students talk about working on the open problems. Some of them describe feelings of relief and joy to have the opportunity to be as creative as they wish on a problem with no expectation of finding the right answer, while others describe feelings of frustration and immediate defeat in the face of a hopeless task. Either way, many students tell me that working on an unsolved problem is one of the noteworthy moments in the course. For this reason, as much as I enjoy witnessing mathematics develop and progress, I hope that some of my favorite problems remain tantalizingly unsolved for many years to come.

Some researchers say that the question isn't whether kids should have homework. It's more about what kind of homework students have and how much. To be effective, homework has to meet students' needs. For example, some middle school teachers have found success with online math homework that's adapted to each student's level of understanding. But when middle school students were assigned more than an hour and a half of homework, their math and science test scores went down.

Researchers at Indiana University discovered that math and science homework may improve standardized test grades, but they found no difference in course grades between students who did homework and those who didn't. These researchers theorize that homework doesn't result in more content mastery, but in greater familiarity with the kinds of questions that appear on standardized tests. According to Professor Adam Maltese, one of the study's authors, "Our results hint that maybe homework is not being used as well as it could be."

In an article in Education Week Teacher, teacher Samantha Hulsman said she's frequently heard parents complain that a 30-minute homework assignment turns into a three-hour battle with their kids. Now, she's facing the same problem with her own kids, which has her rethinking her former beliefs about homework. "I think parents expect their children to have homework nightly, and teachers assign daily homework because it's what we've always done," she explained. Today, Hulsman said, it's more important to know how to collaborate and solve problems than it is to know specific facts.

But while many elementary schools are considering no-homework policies, middle schools and high schools have been reluctant to abandon homework. Schools say parents support homework and teachers know it can be helpful when it is specific and follows certain guidelines. For example, practicing solving word problems can be helpful, but there's no reason to assign 50 problems when 10 will do. Recognizing that not all kids have the time, space, and home support to do homework is important, so it shouldn't be counted as part of a student's grade.

The issue of assigning homework is controversial in terms of its purpose, what to assign, the amount of time needed to complete it, parental involvement, its actual affect on learning and achievement, and impact on family life and other valuable activities that occur outside of school hours. I have encountered all of those controversies in my years of teaching mathematics. Math homework is usually a daily event. Unfortunately, many teachers assign most homework from problem sets following the section of the text that was addressed that day. There is little differentiation. For the most part the entire class gets the same assignment. (In fairness, teachers do take into consideration the nature of those problems, which are often grouped by difficulty, deciding which to assign based on the general ability level of students in the class: below average, average, above average, or mixed.)

Often teaching involves a "one size fits all" strategy. Elaborating on Joseph Simplicio's (2005) thoughts, the student who "didn't get it"--that basic understanding of how to solve the problems--can't complete one homework problem, let alone 20. The better or gifted student gets it after a couple of problems and doesn't need to complete 20. Then there is the student who completes all 20 to build confidence that he/she does get it. The first gets frustrated and quits, the second gets bored and quits, and the third might get frustrated and bored by all the time it takes to get done or hastily complete the work with errors. Some might copy each other's work along the way, too. These scenarios are not all-encompassing, and you might be thinking, "You exaggerate." But homework has and most likely will continue to pose a dilemma.

I recall in my early years as an educator moving to a new state and one particular interview for a middle school teaching position. The principal asked for my views on homework, and I responded that, yes, I believed in the concept. He was adamant, however, that no homework be given at his school because students' home situations and expectations after school meant that, for the most part, they would not do it. All assigned work needed to be completed during class time. It was a lesson learned about the importance of knowing about the home-school relationship in the learning process. Today, given the hectic and often overfilled schedules that are part of so many students' daily lives, I'd consider Simplicio's (2005) solution to the dilemma, which "lies in setting aside time at the end of the school day to coordinate and supervise homework activities in school" (p. 141).

Without accommodating learner differences, we set students up for failure or boredom when, in fact, we can do something about that in the design of experiences outside of school that are meant to reinforce learning. As educators, we can also recall the many reasons a particular assignment was not turned in even by our best students. One of the more original I received was from a high school student who accidentally spilled soda on the homework paper. She said it burned it up when she put it into the microwave to dry.

What I also suggest is taking a closer look at current literature on teaching and learning, which calls for differentiated instruction and attention to learning styles, thinking styles, and multiple intelligence theory. When it comes to math homework, differentiation does not seem to carry over, and it should be considered beyond assigning the problems out of a text by level of difficulty.

So where does homework fit into this? Each of these styles tends toward one of four dimensions of mathematical learning: procedural, conceptual, contextual, and investigative. "If teachers incorporate all four styles into a math unit, they will build in computation skills (Mastery), explanations and proofs (Understanding), collaboration and real-world application (Interpersonal), and nonroutine problem solving (Self-Expressive)" (Strong et al., 2004, p. 74). If you have ever solved Sudoku puzzles, you can appreciate the motivational value of options. Everyone might be solving a puzzle of the same size but has selected an easy, medium, hard, or evil challenge based on his/her understanding of how such puzzles are solved and a self-determined ability to do so. But, I'd soon lose motivation, if that was the only puzzle type I ever attempted. By providing options, adding variety, and differentiating homework into those categories, as well as in instruction, learning math might be better achieved for all. 2b1af7f3a8