“My student does all their homework, but they’re not doing well on the tests.”
Math students get math homework; it’s just how the math world is. It’s not bad in any way—the standard homework assignments help students practice what they just learned, reinforce steps, and increase knowledge retention. However, sometimes homework isn’t enough on its own to truly prepare students for exams or help them really understand concepts.
The Copycat Trap
One of the biggest unintentional pitfalls of homework is that it can turn into a “copycat” exercise. Students may be given 30 problems to complete, but there really are only 3 unique problems for them to solve: the rest of the problems are just tweaked slightly. A student can look at an example from class for guidance on how to solve the first problem, and then it’s a matter of repeating the same steps for the other problems, just with different numbers. This can leave out the development of conceptual understanding of why the steps work.
Practice Isn’t the Same as Problem-Solving
Homework assignments are usually fairly straightforward and routine: plug numbers into the formulas, follow the steps, and get an answer. It’s fine when the problems are similar and repetitive, but this process sometimes doesn’t develop problem-solving skills required to recognize why to do certain steps in the first place or what to do when the format of the problem changes. “The test had problems that were completely different from what we had for homework” students often say.
The Solution
What do we do then? Students obviously shouldn’t stop doing their homework. The real solution is supplementing the homework with two additional areas: conceptual questions prompting critical thinking skills and a variety of “harder” problems targeting development of those problem-solving skills.
Most students groan at the words “explain your reasoning” or “justify your answer” and understandably so. It requires more effort and a deeper understanding, and while many teachers are transitioning to more test-questions requiring a “why”, their homework assignments haven’t caught up. This means students aren’t getting the practice they need. Students need to get more exposure to these types of problems to feel more comfortable and confident when they see those on tests.
Finding problems that prepare students for the difficulty level of tests can be, well, difficult. Many easy-to-find materials a Google search away are too cookie-cutter and standard, similar to the homework assignments they already have. Extremely difficult “challenge” problems—borderline riddles—are also sometimes too niche for many students. The real gem is finding Goldilocks “harder” test-difficulty problems—more complex than homework assignments but not nearly as frustrating or convoluted as those aforementioned challenge problems—which should best match their test problems and benefit most students, especially at an honors-level.
Finding these problems that match a more complex exam structure and prepare students for the difficulty level of tests can be, well, difficult. It becomes much easier when you have experience working with these students, recognizing the criteria needed, and building up an arsenal of tools and resources to best support students, and we at AJ Tutoring pride ourselves on being able to offer this to our students!
