General Strategies

We strongly encourage you to read over the Dealing with Hard Problems article written by AoPS founder Richard Rusczyk, which outlines some strategies for handling difficult problems and the frustrations that come with them.

There are two powerful techniques in particular mentioned in that article: asking for help and taking a break. It's often a good idea to take a break both before asking for help and after asking for help. This could mean moving on to a different problem or taking a break from the homework altogether for a brief time. Returning to a problem later with a fresh mind, as well as with any advice or guidance received after asking for help, can make a huge difference.

Your class message board is the best place to ask questions during the course. The section below on How To Ask A Good Question outlines some ways to ask specific and direct questions that will help you get un-stuck as soon as possible.

One final strategy for AoPS courses is to start the homework early. Unlike some assignments that you may be accustomed to, our homework is not designed to be completed in one sitting, in one evening, or even in one day. Start the homework early and allow time to think through problems, take breaks, and ask questions. This is essential for true learning to occur (and ultimately for success in the course). Most courses also have a My Goals tab on the course homepage to help you set up a schedule for completing work between classes. You can request an extension if you need another couple of days to work on a writing problem.

Questions You Can Ask Yourself

It may help to consider some of the following things if you're stuck.

• What makes the problem hard? A good first step may be to do something that gets rid of the thing that makes it hard.
• What information haven't you used yet? When you're stuck, incorporating unused information is often the key to getting unstuck.
• Can you simplify the problem? Explore the problem with smaller numbers or a simpler version of the problem and see if a pattern emerges.
• Can you work backwards? Start from the goal and ask yourself what you need to get there.
• Does this remind you of anything? If this problem resembles one you've seen before, a similar approach may help here.
• What does the problem have to do with this week's class? This is cheating a bit, since the problems you'll meet in the real world won't tell you which week they are in, but your homework problems are often related to that week's material.

How To Ask A Good Question

Most often, we ask others questions to get answers. But at AoPS, we won't just tell you what the next step is or what you need to do in order to get a perfect score. Instead, we'll help you understand the material and ask questions that help you develop your own critical thinking skills. This will allow you to solve the problem on your own.

Some students may find this frustrating because the homework is due that day, and they just want to be told what to do. Please understand that you will not learn as much this way, and we will not just give you the answer or solution.

Moderate Level Question-Asking: Be Specific

Statements like "Please help" or "I'm stuck" are very hard to answer. After all, there aren't any details there! These statements will generally get a response of "What do you need help with?" or "What are you stuck on?" or "What don't you understand?"

In order to get help, think carefully about what you're are stuck on and try to tell us about it in your question. Some examples are:

"I don't understand what the question means when it says ____."
"Can someone explain how (some property) applies to this problem?"

Expert Level Question-Asking: Providing Background

In addition to asking specific questions, great questions include some background. If we know about what you have already tried or how you're thinking about the problem, it will help us give better, more relevant tips. Expert-level questions look like this:

"I tried (some approach), but now I'm stuck. Can someone give me a hint?"
"It seems like we can use (some property) on this problem. I can tell how it applies ____ but I'm stuck on how it works with ____. Any tips?"

Knowing what you are having trouble with is an important skill to develop. To help us assist you in the best way, try to figure out specifically what is stopping you from moving forward. Try to make your question as specific as possible. We are here to help you, but we need some information to directly respond to your inquiry.

Getting Started

Regarding homework questions, AoPS has a general policy that students should get the discussion started. If you tell us you have no idea how to start, we will prompt you to come up with an idea to get the ball rolling. It doesn't even have to be a good idea, but looking at a problem and coming up with ideas is an important problem-solving skill that we want you to practice. After you get in the habit of coming up with ideas, then you can sort out the good ones.

A Special Note For Teachers and Families: How To Be A Good Tutor

Below are some general guidelines we use when helping students in our classes, and we welcome you to incorporate any of these when helping your student.

We wish to be a guide, a coach, a facilitator of practice, and not an omniscient being who fills passive minds with facts and formulas. In this spirit, you'll notice that most of the examples given below are questions aimed at getting the students do the "heavy lifting" and deep thinking, rather than statements that provide an answer or give away the "right" next step.

• Listen to the student. Your goal is to help the student discover the answer in their own way. A good tutor begins by finding out exactly how the student is thinking about the problem. When a student tells us, "I don't know how to solve this problem," we always respond with something like, "Where did you start? What did you try? Where did you get stuck?"

• Point out any misconceptions or broken assumptions. "Explain this part to me a little more." "Does this part work for odd numbers, too?" "Let's try to draw a picture of this part." "How does this step compare to the problems from the book?"

• Help the student find strategies that will help him or her explore the current set of ideas. "How about we try some small cases of this?" "Is there anything useful you can add to this diagram?" "Are there any assumptions in the problem you haven't used?" "Did you try a simpler version of the problem?"

• Help the student track down new ideas. "How about putting this problem down for a while and going back to the textbook?" "Did you solve any similar problems in class? Look back over the transcript again."

• It's OK if you're stuck too. Most of the ideas above work even if you don't see the solution. Sometimes you can even help your student learn more if you don't see where to go. And don't forget that we have your back. Encourage your student to post a question on the message board.