Get All Students to do All Homework All the time... Homework basically contributes to a situation where students see learning as just an unpleasant means to an end, “a way to accrue points.” We should ask whether the primary purpose of homework is to help children become more enthusiastic and proficient learners, or to set up a situation where we can judge how good students are at doing things alone – and, perhaps to teach the value of solitary effort. As a rule, the point of homework generally isn’t to learn, much less to derive real pleasure from learning. It’s something to be finished. And until it is, it looms large in conversations, an unwelcome guest at the table every night. We are discouraged from asking whether an adult’s specific “academic goals” and priorities – or a given homework assignment – is of any value. That doesn’t matter. The task is to get students to summon the will to do whatever they’re assigned. I have been huffily informed that life isn’t always interesting and kids had better learn to deal with that fact. The implication of this response seems to be that the goal of education is not to nourish children’s excitement about learning but to get them acclimated to doing mind-numbing, if not downright unpleasant, chores. As students, we’re trained to sit still, listen to what the teacher says, run our highlighters across whatever words in the book we’ll be required to commit to memory. Pretty soon, we become less likely to ask (or even wonder) whether what we’re being taught really makes sense. We just want to know whether it’s going to be on the test. In math, too, even the new and improved concept of “engaged” ToT is directly correlated to achievement only if both the activities and the measure of achievement are focused on rote recall. By contrast, there is no “linear positive relationship for higher level mathematics activities, including mathematical applications and problem solving.”

Thus, to justify sending students home with a worksheet full of practice problems on the grounds that it reinforces skills is to say that what matters is not understanding but behavior. William Brownell – “If one is to be successful in quantitative thinking, one needs a fund of meanings, not a myriad of ‘automatic response, ‘” he wrote. “Drill does not develop meanings. Repetition does not lead to understandings.” In fact, if “arithmetic becomes meaningful, it becomes so in spite of drill.” In reality, it’s the children who don’t understand the underlying concepts who most need an approach to teaching that’s geared to deep understanding. The more they’re given algorithms and told exactly what to do, the farther behind they fall in terms of grasping these concepts. The best classrooms not only are characterized by more thinking than remembering they also have students doing much of the thinking. Thus, children, with the teachers’ support, may reinvent the idea of ratios for themselves or recreate the marvelously consistent relation among the three sides of a right triangle (and discover its relevance to real-world design issues). Practice often leads to habit – which is, by definition, a mindless repetition of behavior – but not to understanding. And when understanding is absent, the ability to reuse and apply the skill is very limited. Those students who didn’t understand it (the content contained in the homework assignment) made up their own ways to do things which were often wrong and repeated the practice, making it that much harder to get them to see it another way in class. The fact that so many children regard homework as something to finish as quickly as possible – or even as a significant source of stress – helps to explain why there’s so little evidence that it offers any academic advantage even for those who obediently sit down and complete the tasks they’ve been assigned. In the mid-1980’s, an educator named Bill Barber commented that “to include ‘more homework’ on an agenda for educational reform is embarrassing; it implies that we are nothing but amateurs if the best we can muster up for students who are dropping out at alarming rates, students who can’t read or write, is a recommendation that they ought to get more of the same thing.” Even good teachers end up routinely engaging in bad instruction lest their kids be unprepared when more bad instruction comes their way. An international comparison by two Penn State professors has concluded that junior high students who scored highest in math tended to come from countries where teachers assign relatively little homework -- including Denmark, the Czech Republic and (take note) Japan. Conversely, the lowest-scoring students came from countries where teachers assign tons of homework, such as Iran, Lebanon and South Africa . At present, the default policy in almost all schools is to assign homework on a regular basis. Giving kids something to take home is the rule; the absence of homework is the exception. What this means, as I pointed out earlier, is that the primary commitment, both logically and chronologically, is to make sure students usually have schoolwork to do at home. Only secondarily do teachers figure out what to make them do on a give night. This default only makes sense if homework itself – the very fact of having to do it, irrespective of its content – is beneficial. Have students read the textbook.

Homework can involve reading the textbook. Give short assignments when focusing on concepts

Homework assignments can be short. By keeping the homework assignments short, students know that they have the time to dig deep and make sense of the mathematical ideas. Instead of spending an hour repeating a memorized procedure, students may spend an hour working to make sense of just a couple of problems. Give longer assignments when practicing procedures

When students have made sense of the underlying ideas of a particular concept, it is appropriate to have them practice procedures. Assign challenging exercises to stretch learner understanding.

Homework assignments can be challenging. Use "Show You Know" assignments to provide students the opportunity to write, explain, describe, and explore core concepts. Find or create other homework exercises designed to challenge the strongest students. These exercises may be assigned to some students and not to others based on the student’s current mathematical understanding and learning needs. All students should not be treated the same. Be flexible in determining due dates

Homework assignments may take time to complete. If the purpose of the assignment is to have students develop convincing arguments or well articulated explanations, allow additional time for students to produce their best work. For example, an end-of-chapter "make it real" project may require students to collect and analyze data from an area of personal interest. An instructor may choose to allow up to a week or more for students to complete these projects. Don’t grade homework assignments

Homework assignments do not need to be graded. Research has shown that homework in the best classrooms is not checked – it is shared. In fact, some educators argue that to grade homework is especially destructive because this tells students that the point of the exercise isn’t to help them learn: it’s to evaluate them on whether or not they’ve already succeeded. Consider having students present selected homework problems on the board and give them homework credit for presenting regardless of the accuracy of the mathematical work, recognizing that the students may learn more from learning how to correct a common mistake than from watching a student present a perfectly executed problem. In a supportive classroom environment, the instructor and students can discuss on-board errors comfortably without causing the presenter to feel inferior to his classmates. Alternatively, have the students discuss the homework exercises in small groups and reach consensus on strategies that worked. Assign homework to be done as a group

Homework does not have to be done individually. Once a classroom culture of collaboration and teamwork has been created, it may be helpful to continue this culture outside of the classroom through the assignment of group homework. Admittedly, there are difficulties in assembling teams of students outside of class; however, the benefits of a fully functioning team working together to complete a meaningful task are great. Be flexible in considering student needs and schedules while simultaneously seeking ways to help students build effective teams. Use a variety of strategies to assess homework Classroom conversation. Ask students to share their ideas in small groups. Students may then be randomly selected to share and explain something that was discussed in the small group Collect and grade. Homework should only be collected and graded if students will receive meaningful feedback from the instructor. This may be done a handful of times during the semester. Paired board work. Students may work together with a partner to write solutions to problems on the board for discussion with the whole class. Check for effort . Depending on the purpose of the assignment, an instructor may check only to see if students have worked on making sense of the ideas. Homework Ideas Guaranteed Keep this in mind:

We should all want to help students become more enthusiastic and proficient learners. We should all want to help students become persistent problem solvers and improve their mathematical reasoning. Will the homework we assign help to accomplish this goal?

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