Homework can be a useful tool to support and deepen the learning done during class, but it must be used intentionally in order for it to have its desired effects. Students must know why they are doing homework and buy into that purpose, otherwise it will be an exercise in compliance, mimicking, or finding creative ways to cheat. Let's dive into the "why" of homework before we discuss some of the practical considerations.
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. Motivation to complete homework should come from close alignment between the learning targets, homework, and assessments. Students should understand that deep understanding is fostered through intentional practice.
Less is more with homework. While it is tempting to think sheer quantity will produce fluency, this is often not the case. We carefully select about 3-10 homework problems a night and only assign what we believe will truly aid student learning.
What does homework entail?
Homework should align to the learning targets. We generally give 1-2 questions per learning target, then 1-2 questions that connect ideas from multiple learning targets, and one extension question. We vary the types of representation so that students aren’t always solving analytically but reasoning using graphs, tables, and equations. You could also add a review question from previous content.
Homework can include reflection and be metacognitive. 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.
Where do we get problems from?
AP Classroom—this is our #1 resource for getting quality AP style questions. The Calc Medic lessons align to the CED, so simply search by lesson number to find relevant questions for that topic.
Textbook—While Calc Medic lessons are not aligned to any particular textbook, most Calculus textbooks will offer a fine selection of practice problems. Our school adopted the Demana, Waits, Kennedy, et al. Calculus for AP text (6th edition), that we sometimes use for homework problems.
Create our own—We also create our own homework assignments by writing questions or modifying questions from various sources. (The “Check Your Understanding” questions at the end of each lesson provide a good template for writing your own questions)
Online resources—Sites like Delta Math offer practice questions by topic.
How do we go over homework?
Instead of taking time every day in class to go over homework, we post answer keys for students to review, either at the beginning of class as a warm-up or on their own time. It can be helpful to provide numerical solutions when you assign the homework so students can get instant feedback, and then provide worked out solutions about 1-2 days after assigning the homework. On review days, we may choose to go over specific questions, but more likely we will discuss the topic or style of problem students struggled with, instead of the specifics of one particular question.