I remember math class as a child. As soon as we walked in the door, we would get our homework out and grade it as a class, usually trading papers to keep us honest. The teacher would read the answers, and we would simply mark each item that was incorrect, total the number of correct answers, and write that number at the top. And then we would give the papers back to the original owners.
As a good math student, I remember both the pride and fear associated with this practice. I was proud when my paper came back with 100% written at the top. However, anything less than 100% resulted in silent shame, the certain knowledge that everyone in the class realized I was a fraud, clearly unworthy of the reputation I had built. (And I felt even worse for my friends who struggled in math, knowing the humiliation they felt when they received their papers back.)
More importantly, we were unaware that our scores were not the feedback we needed. With no opportunity to understand why each answer was correct or incorrect and to self-correct, as needed, we simply looked at our score, proud with a good score and ashamed with a bad score. End-of-story.
Let’s take it a step further – even now, math homework often includes practicing the same skill 20-30 times. Although students need to develop automaticity, if they already know how to do long division, for example, they need only practice a few times before the practice becomes tedious. And, of course, if they don’t already know how, then practicing 20-30 times incorrectly is only going to reinforce bad habits.
If the point of homework is to see if students “get it,” then 5 practice problems is enough. If kids get it after 5 problems, and you ask them to do another 35, you’re just being mean. And if kids don’t get it after 5 problems, and you ask them to do another 35, you’re really being mean. – Matt Cwalina, Discovery Education
So, what can we do to improve students’ homework experiences?
The 2-4-2 Homework Policy
Steve Leinwand, the author of Accessible Mathematics: Ten Instructional Shifts That Raise Student Achievement and Sensible Mathematics: A Guide for School Leaders, suggests a new way of thinking about homework. Rather than assigning 20-30 problems, assign students 8 well-crafted, engaging problems using the 2-4-2 homework policy.
- 2 problems on the new skill (This is usually enough to determine understanding and, at the same time, avoids practicing and reinforcing) mistakes);
- 4 cumulative review problems roughly drawn from content developed the day before, the week before, the month before (think about being strategic with prerequisite skills for the current content); and
- 2 problems that require showing work or including explanation that supports problem solving, reasoning, and justification.
A Feedback Process That Promotes Learning
And then comes the most important part…feedback time. At the beginning of math class the next day, rather than asking students to trade papers to “grade,” the teacher posts the answers to these eight problems on the board. S/he provides students with five minutes to review their work in pairs or triads with particular attention to the last two problems. After five minutes of small-group discussion, s/he leads a group discussion of any problems that are still causing trouble. And here’s the kicker: homework is only to be recorded as completed.
This practice sure would have been helpful to me as a young scholar. As a matter of fact, as a middle-school student, I would meet with two of my friends before school to “compare answers.” For me, this self-created practice was especially about knowing that I know – going into class confident of my ability to do and understand the math. What I didn’t know then was that, someday, this would be the exact practice I would encourage in my own students.
Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.
After reading this post, please join in on the conversation using the comments box below! What homework practices do you currently employ? How might you reframe your practices to make them meaningful and useful for students?
Interested in learning more about KP Ten-Frame Tiles? Please check out Peggy’s latest Beyond Base Ten Blocks journal entry, Manipulatives First.