Math Homework

Creating homework problems can seem like the most straightforward thing in the world - just ask students to demonstrate the skills they have learned. But when a student misinterprets the question or continues to struggle after the skills have been taught, it's less clear what to do next. At that point, it makes sense to take a step back and explore what other options you might have to address your current dilemma.

Complex problems are often vague, and that means they have many possible solutions. Following the Meta-Problem Method may lead you to a distant dilemma from the one that started your quest. A key part of the method's value is that it forces you to clarify what you really want and what you are willing to give up. It also enables you to compare objectively the possible pathways and their trade-offs. It prevents you locking into solutions mode too early, and then doubling down on solving a low-yield problem that does not serve your goals as well as the alternatives. At the end of this process, you will have a better understanding of your priorities and how to achieve them.

Step in the Meta-Problem Method	Illustrative Example
Dilemma The high-level issue you are trying to address	How should we design math homework?
Goal The changes you would like to make to address the dilemma. There are usually many options. Selecting the best set comes after you learn what is possible.	Supporting Goals Improve student math fluency Validate specific math skills Reduce student math anxiety High homework completion
Problem Space While goals tell us what we want, our next step is to understand what is holding us back from making progress on them. This approach is borrowed from calculus as we explore the neighborhood of the current dilemma.	For each goal that you are considering, ask yourself: How much progress is possible? How much effort would it take to make progress? What methods might help to make progress? What might the positive or negative effects be on the other goals as you make progress towards the current one? Example Problems: How could we use homework problems to increase general math fluency? Do students need to practice specific techniques, checking their work, or something else?  For example, maybe students do well with simple questions, but struggle with word problems. How can we ensure students learn the specific skills they are supposed to? Are the problems designed in a way to test the required skills?  For example, fraction problems should not be neatly divisible or they will instead be division questions. How could we help the student reduce their math anxiety a little? Is this part of a larger challenge for the student, or is it math-specific?  For example, if the student seems to have anxiety around school in general, they may need mental health support to perform their best in math. How could we help the student improve their homework completion a little? Are the assignments the right length and structure to maximize completion?  For example, very long assignments may be discouraging to students. Similarly, ungraded problems may not be done at all.
High-Yield Problems Sometimes solving one problem helps make progress towards several goals. In this step, we identify these “two-for-the-price-of-one” problems.	Which Options Will Advance More Than One Goal? Design the assignments and grading to support learning, skill growth, and completion. This will ensure students get the intended benefit from the homework assignments. Allow time in class to discuss homework. If there are any hidden issues with the assignments or specific problems, this will allow those issues to be addressed and improve completion and learning. Focus homework questions on challenging or crucial skills. This ensures completing the homework will help as much as possible with math fluency and skill learning. Et cetera.
Problem Selection Which of the many possible options in the high-yield problem step is the best set to address the dilemma?	Selection Criteria Which solutions will best address the dilemma? Which solutions will deliver the best outcome for the least amount of time, effort and money? Which solutions is the student most excited to take on? By this point in the Meta-Problem process, you have clarified your goals, identified some options you could take, weighed the trade-offs that come with each of those options, rejected some options because they will take more time, effort or money than the results are worth, and you have identified a set of high-yield problems that will advance several of your goals at once. Now you are ready to start solving a problem knowing what you expect to achieve.
Implement, Learn and Adapt	Observe and learn as you go. New information may reveal itself as you implement your chosen solution, so check continuously that you’re still solving the right problem.