Before we decide which problems we want to assign and how many, we have to establish why we assign homework. What do we want students to gain from it?
What is the purpose of homework?
Homework is a self-assessment tool. It allows students to see where they are in their progression toward the learning targets. The primary benefactor must be the student.
Homework is not graded. Grading homework negates messages about the value of making mistakes and learning over time, encourages cheating, and actually decreases effort and motivation by relying on an extrinsic reward system of points.
Quality over quantity. Assigning multiple questions that address the same skill increases mimicking (rather than thinking) among students who can solve the problem, and unnecessary frustration for those who can’t. When we talk about quality problems, we mean problems that use different representations (graphical, verbal, algebraic, numerical) and assess conceptual understanding, not just skills. Although it is harder to find and write these questions, we need to see what students understand and not just what they know and can do. For example, a student could correctly find a midpoint of a segment using the algebraic formula, without any understanding of what a midpoint is and the importance of it being equidistant from both endpoints. Depending on the course and topic, we might assign about 3-10 homework problems a night. Only assign what will truly aid student learning. Read more about how we balance conceptual and procedural questions.
What should we have students do for homework?
Homework can stem directly from work done in class that day. “For homework tonight, I’d like you to think about the 423rd figure and use Jamirea’s method to find the total number of squares in that figure.”
Homework can be reflective and metacognitive and does not always have to include solving problems. Students could respond to prompts like “What are the 2-3 most important take-aways from today’s lesson?” or “Write about 3 things you understand after today’s lesson, 2 things you still have questions about, and 1 connection you can make between today’s lesson and other work we’ve done in this class or outside of school.” Having students write (or make a video/audio file) explaining a concept is one of the most useful tools for both building and demonstrating understanding.
Homework should align to the learning targets. We generally give 1-2 questions per learning target (if 2, then the second is slightly more complex or often times asks the question in reverse), 1-2 questions that connect ideas from multiple learning targets, and one extension question. You could also add a review question or a looking ahead question.
Where do we get problems from?
After years of being disappointed with the mostly procedural questions we found in textbooks, we decided to start writing our own questions. We wanted questions that further develop the ideas students explored in class, and build students' conceptual understanding. These are now available in the Math Medic Assessment Platform.
Further Resources
Read Dan Meyer’s blog post about why he doesn’t assign homework.
What’s the Right Amount of Homework? Edutopia
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