Homework Should Support the SMP’s
While all homework is up for discussion these days, and many argue it impinges on time for more worthy activities, I am a firm believer, for reasons Daniel Willingham (2009) describes, that most students need a considerable amount of practice outside the school day to develop and retain basic math skills. So like many others, I have put a lot of thought into finding a way to give students short-term accountability without investing an unreasonable amount of time grading homework. If we are going to achieve the Standards for Mathematical Practice of the Common Core State Standards (SMP’s), our practices surrounding homework should support those standards. Of all the grading methods I have heard of and/or tried, I believe “completion grading,” whereby a teacher awards homework grades based only on appearance of completion, is second from the top for sabotaging the SMPs. I rank “completion grading” one notch below the “no zeros” policy.
I think it is safe to say that when most parents see a 10/10 in the grade book, regardless of whether there is a comment about accuracy, they tend to believe all is well. Students are, likewise, satisfied with 100% whether they invested 5 minutes or 35 minutes. Poor test scores that follow are often attributed to anxiety when the real cause is insufficient, high-quality practice.
Writing homework grades in the grade book may inspire students to produce it; but once the word is out that accuracy doesn’t matter, human nature is likely to kick in. Since our students’ brains are not yet completely formed, and Friday night fun sounds a lot better than thinking about math, one can only wonder how often the primary goal becomes making it look “done.” Smart students can game the system by guessing what the teacher will be looking for. As a result, we may inadvertently re-frame the mathematical practices in the students’ minds like this:
1. Make sense of problems and persevere in solving them
Student thinks: Number the paper to match the assignment.
2. Reason abstractly and quantitatively
Student thinks: Would it be a big number or small?
3. Construct viable arguments and critique the reasoning of others
Student thinks: Write down words and numbers I see in the problems.
4. Model with mathematics
Student thinks: Write down an equation.
5. Use appropriate tools strategically
Student thinks: Mechanical pencils don’t have to be sharpened.
6. Attend to precision
Student thinks: Copy the answer from the back of the book.
7. Look for and make use of structure
Student thinks: Is the teacher looking for a lot of work to be shown here?
8. Look for and express regularity in repeated reasoning
Student thinks: The rest of the answers will look similar
Students who actually try to work out the problems but stop short of verifying their answers may be worse off as they practice mistake-making over and over. Surely this kind of homework is working against our goals. Instead, I propose a random sampling system that not only supports the SMPs, but can also support the “4 C’s” of creativity, communication, collaboration, and critical thinking. The random sampling system takes no classroom time (other than collecting assignments) and grading can be done as little as semi-weekly to be highly effective. Grades in the grade book become meaningful and motivating.
Let’s use what we know about random sampling…
I don’t have time to grade 150 homework papers very often. I collect it every day and file it. I can fire an email to a parent in about 45 seconds if someone doesn’t turn one in. Parents are some of my biggest fans because, for the first time in their student’s academic life, they know immediately when their student is off track. My older students hate that, “You emailed my mom!” I say, Yes, thanks for putting more work on my plate. If you are unhappy about it, please do your homework. But the real secret is an application of statistics: random sampling. The students never know what will end up in the grade book. My grade book represents a sample of each student’s work and tons of comments. It looks more like a journal. “Excellent representation of concepts.” “Much of the work did not lead to the answers provided.” “Did not check answers with those provided.” The parents understand, then, why test grades are what they are. The truth is, I might not grade any homework for two solid weeks.
To add a little fun to the endeavor, and encourage creativity, I often award 11/10 for a homework that shows effort beyond my expectations. The students notice, and many start using color to tie concepts together or make grading easier. They start comparing each other’s homework feedback and develop an understanding of what excellence looks like. They know who to collaborate with when they are getting wrong answers and find ways to communicate. (Snapchat isn’t always bad.) That is one of many reasons I don’t have to waste time in class answering homework questions.
Often parents request that I accept late work (not due to an absence) and I explain my system: Students would only do what they see ended up in the grade book . I also explain if there are anomalies that are adversely affecting a student’s grade, they can be deleted at the end of the semester. This also gives hope to the student who is late getting with the program. After all, it should never be for a grade, it should be for the learning.
Willingham, D.T. (2009). Why Don’t Students Like School? SanFrancisco, CA: Jossey-Bass.