Do you have perfect math homework but bad test scores? Here are three things that might be going wrong.
Why do homework?
During homework, you should gain more independence, work a wider variety of problems, and get to move at your own pace. As you work, try to self-assess. Figure out where you are confused BEFORE you fall too far behind in class.
When you work from a math textbook or have a homework sheet, there are often learning aids. You might have written explanations, videos, example problems, and answers (or even full solutions) for the homework. This is great! These are all wonderful helpers as you learn. BUT, they can turn into crutches that give you a false sense of confidence about what you genuinely know and understand.
Three ways *NOT* to do homework:
1) Avoid looking back.
ASK YOURSELF: Can I solve this myself without looking up information I need to have memorized?
Many students rely on looking back for information they should be trying to master and memorize. This includes definitions such as "What is a similar triangle?" or formulas such as the area of a triangle.
AVOID BECAUSE: You need to have these in your brain, not just your book. Once you understand, take steps to truly memorize necessary formulas and definitions.
INSTEAD: Use your homework as a chance to figure out what you need to memorize and to begin memorizing. Start a list of definitions and formulas you needed to look up. As you work, try to remember and write it down or say out loud before you look back.
2) Avoid mimicking.
ASK YOURSELF: Can I solve this myself using my understanding, and without following an example?
Some students skim the text looking for example problems. They try to follow along and imitate that problem to solve their homework problems.
AVOID BECAUSE: You may be following an example without actually understanding the concepts. Also, there are many variations on every problem. Following an example will lead you wrong.
INSTEAD: Read the text AND the examples until you feel like you are understanding both. Then, keep any examples covered up while you do your homework.
3) Avoid working back from solutions.
ASK YOURSELF: Can I solve this myself without reading a solution, or knowing the final answer?
AVOID BECAUSE: The solutions and final answers will not be there when you are solving problems in other contexts, or on a quiz or test.
INSTEAD: Solve the problem completely yourself. Then check your work. Then check it again. THEN check the answers in the back. You will develop skills in catching your own mistakes.
Just remember that even when it is graded, the TRUE purpose of homework is helping you gain understanding.
Avoid distractions while you work.
If you use the internet to help you, remember that your goal is to UNDERSTAND, not just solve that one problem.
Consider forming a study group for a challenging class. My very best understanding comes from talking ideas out with other people!
Use homework time as a chance to figure out where you are confused, so you can ask questions the next day.