Struggles with math homework
When a student misinterprets the question or continues to struggle after the skills have been taught, it makes sense to take a step back and explore what options you might have to address your current dilemma.
Complex problems are often vague and have many possible solutions. The Meta-Problem Method may lead you far away from the dilemma that started your quest. That’s because the method forces you to clarify what you really want and what you are willing to give up. It 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.
Steps in the Meta-Problem Method
Dilemma
The high-level issue you are trying to address
Better designed math homework.
Goal
The changes you want to make to address the dilemma. There are usually many options.
Supporting goals
- Validate specific math skills
- Increase homework completion
Other goals could include improving student math fluency or reducing student math anxiety.
Problem Space
The set of problems you could chose to solve to advance your goals, plus the constraints that hold you back.
Example Problems
- How can we test specific math skills with homework? Maybe the problem to solve is “What kinds of questions test each skill?”
- How could we help students complete more of their homework? Maybe the problem to solve is “What is the right length and structure for homework assignments?”
There are many other potential problems to solve related to designing homework. Each goal has many possible problems we could link to it. Are there other problems linked to these first two goals? Which options come to mind for the other goals?
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?
- Customizing homework assignments based on which kinds of questions students are getting wrong would strengthen the specific knowledge that they are missing, which also increases fluency. However, it may decrease homework completion if the assignments are too challenging.
- Harshly graded homework with multiple attempts will validate specific math skills and increase homework completion. However, it may increase student math anxiety if they focus too much on the initial low grade.
There are many potential solutions that will have varying effects on the set of goals. Which alternatives improve the most important goals? How might the unknown change the right path forward? What other possible solutions are there to address the dilemma?
Problem Selection
Which of the many possible options in the high-yield problem step is the best set to address the dilemma?
- Which solutions make the most sense as an educator?
- Which solutions will best address the dilemma?
- Which solutions will deliver the best outcome for the least amount of time, effort and money?
Implement, Learn and Adapt
Check continuously that you are still solving the best problem, as new information emerges.
Observe and learn as you go. As new information reveals itself, check continuously that you’re still solving the right problem.