Homework and Grades in a Math Class

I am trying to reconcile two recent conversations, and I suspect that most of us have had similar discussions.

First, a student (after missing a passing grade by 5%):

I have worked hard, and did extra homework. The instructor set up the class to fail. Very unreasonable.

Second, a potential faculty member in response to a question about classroom assessment techniques:

I am really in favor of homework. I don’t grade it, but it shows what students do not know.

The potential faculty member was reacting to the practice of some colleagues who assign significant points in a class for the completion of homework. Their institution also suggested that they use the publisher’s homework system for the tests in online sections (My Math Lab, Connect Math, or Web Asssign). The sad part of this candidates response was that they never mentioned any other assessment technique.

In the student’s situation, she was mostly responded out of frustration. She is trying to overcome a false start in college a few years ago resulting in a very low GPA, and was dealing with a family health situation; a failing grade in our math class meant that she would not be able to continue in college.

The question is this: What is the primary purpose of homework? We know that students do not learn if they do not apply significant effort. This leads many of my colleagues to give credit for completing homework, sometimes up to 10% of the course grade. They either give all points regardless of ‘score’ on the homework, or they prorate the points based on the performance level. The ‘all points’ approach tells students that the main goal of homework is to complete the problems regardless of learning; the prorated method tells students that mistakes in homework can cost them points.

Doing assignments (reading, studying, practice, checking answers, etc) is the critical learning activity in any mathematics class.

With good intentions, we award points for homework; however, that’s pretty much a no-win situation: Awarding points will encourage students to get it done. However, getting it done does not mean that students are learning anything. As a sports metaphor, points for homework is a bit like telling a batter in baseball to swing at anything close to the plate: you need to swing to hit the ball. The problem is that swinging at anything means hitting the ball is mostly a coincidence — just like learning when points are awarded for homework. I would prefer to not settle for accidental learning.

My own conclusion is that doing homework should not be connected directly to a grade in a math class. Without a learning attitude, the homework will not help; with a learning attitude, the work will get done. If I can build a learning attitude with my students, they are better prepared for success in any math class they take.

The current media treatment of this concept uses words like ‘grit’ and ‘perseverance’; these phrases reflect the infatuation with educational outsiders creating solutions for educational problems. Two weeks ago, I sat through a day-long professional development session featuring a psychologist who tried to tell us how to flip our classrooms. This was a practicing therapist with great expertise in generational issues, but with no particular understanding of learning in a classroom. [He suggested awarding 25% of the course grade for completing the preparation for class, and another 25% for the assessment activities in class dealing with that preparation.]

The problem I have with this media approach is that grit and perseverance have strong cultural components reflecting the student’s history (especially familial). I much prefer to focus on a learning attitude; this concept is accessible to students, and we have some tools to build a learning attitude.

A quick list of ingredients for a learning attitude in a mathematics classroom:

All students involved in conversations about mathematics (I use directed small group work for this)
Cold-calling on students (expecting every student to be engaged, understanding that “I don’t get it yet” is an acceptable answer)
Encouraging discussion and reasonable disagreement in class (an initial step is to ask “is there a different way to do this?” … and then waiting 15 seconds or more)
Quizzes at the start of class (I do a quiz in about half of the non-test days)
Spending class time working with individual students on something they are struggling with (I do ‘test drives’ for students after doing examples, and worksheets with challenging problems)

This particular list is a practitioner’s list, not entirely founded in learning theory. However, I can say that my reading of cognitive psychology leads me to believe that the critical necessary condition for learning is the brain engaged with significant and accessible material — this is reflected in most of the items above.

Homework is a poor assessment; homework points is a weak motivator for learning. How do you build a learning attitude for your students?

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cognition | Jack Rotman | May 24, 2014 1:55 pm

1 Comment

By schremmer, May 27, 2014 @ 11:22 pm

“Homework is a poor assessment; homework points is a weak motivator for learning.”

I agree very much.
“How do you build a learning attitude for your students?”

A necessary condition is that the contents be *mathematics* rather than the usual “applicable”
stuff, or the usual “factual” stuff, or the usual whatever currently “sells” stuff.

Regards
–schremmer

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