Why Make The Problems So Challenging?

AoPS courses are rooted in the belief that students learn best by working through very challenging problems that ask them to think in new ways. Everyone is challenged at some point in our courses. The homework in AoPS classes requires complex thought. It requires creativity. You need to struggle with deep and difficult problems in order to learn most effectively. By providing problems you'll struggle with—and even fail at sometimes—we are presenting you with an opportunity to develop deep problem-solving and critical reasoning skills.

Real Challenge Can Be Frustrating

It's not unusual for students accustomed to getting 100% on every assignment before AoPS to start answering just 50-60% (or even less!) of AoPS problems correctly. That can be really, really frustrating.

We Understand

When you get stuck, you aren't alone! We understand that feeling - we've spent hours, days, weeks, even years working on some problems. We've shed tears and had other outbursts of frustration when something just isn't working out.

As one AoPS staff member puts it, "... I can paint a picture that may be comforting. I work in an office of people with incredible mathematical minds. These people have studied math for many years and have won prestigious math contests and even started their own mathematical contests. They have written the book [you are] using and many others with more advanced content. I see these people get frustrated and stumped by math problems almost every day. They sigh and pace and growl (really), but they persist and come back to the problems that challenge them because they are patient and they know that the only way they'll grow is to challenge themselves. They have grown so much because they are used to making mistakes and getting problems wrong and they have struggled many times. I know I always like to remind myself that every mathematician, even the best ones, struggles like this."

We've been there, and we want to help you work through the difficulty to overcome the most challenging problems.

What If I Get Something Wrong?

Great! Mistakes provide an opportunity to learn. Answering the problem incorrectly tells you that you might have an incorrect assumption or approach, or a mistake in calculation. Carefully review your work. Can you identify where the error occurred? Try the problem again. Do you still feel stuck? Is there another resource (such as the textbook or class transcript) that you need to review a bit more before continuing with these problems?

Once you have answered the problem correctly, or if you choose to "give up" on the problem after some careful thought, be sure to read the solution! We always recommend that you read through the solutions presented to every problem, but this is especially important for problems you've answered incorrectly. Take a good look at the solution, and compare it to your work. Do you understand the given solution? How might you apply the ideas from this solution to a similar problem in the future?

Strategies for Success

Below are some general strategies we recommend to set yourself up for success. We also recommend AoPS founder Richard Rusczyk's article on Dealing with Hard Problems and the When You Get Stuck guide for more tips.

• Ask for help when needed.

  Ask questions at any time during the live class sessions, or let us know if something just isn't making sense. The course staff can then address your question or confusion right away!

  Outside of class time, you have a dedicated course message board on which you can look over questions from others and ask your own questions at any time! You have the ability to post your question "anonymously" if you prefer—your username will be hidden from everyone except the teacher.

  The When You Get Stuck guide outlines some suggestions for how to ask good questions.

• Start early and give yourself enough time.

  The challenging homework you're faced with requires complex and difficult thought. It is not designed to be completed all at once, in one evening, or even in one day. Our most successful students start the homework soon after the related class. This allows sufficient time to think through problems, take breaks, and ask questions. If your course homepage has a "My Goals" tab, look over the scheduling options it offers.

  You should expect to spend around 5-7 hours per week in a Subject course and 2.5-3.5 hours per week in a Contest Preparation course. This can vary by course, and it can even vary by week. Some weeks may require even more time!

• Work on the course material in increasing order of difficulty.

  Depending on what materials and assignments your course has, we generally recommend that you read the textbook or handouts before class, then attend class or read the transcripts, then complete the homework (Alcumus first, then Short-Answer Challenge Problems, then Writing Problems). The Working Through Course Material page outlines more details about this recommended order.

A Special Note for Parents

For many of our students, our courses are the first time they've enountered problems that truly challenge them—they don't see the answer right away, they get a problem wrong, they don't get a "perfect" score. This can come as quite a shock to students who are accustomed to getting 100% on tests without much effort, and it can often become a source of great frustration. This leads us, as parents and educators, to two major questions: How can we help students cope? and When is it too much?

How can we help students cope?

• Acknowledge the difficulty.

  We refer to the weekly homework as "Challenge Problems" to acknowledge the difficulty from the start. Remind students that they aren't expected to get everything correct right away, and we intentionally include some problems meant to challenge even the very best students. In fact, we believe that if a student is getting a lot of the problems right on the first try, that probably means the course is too easy.

• Normalize struggling and making mistakes.

  Struggle doesn't have to mean misery, being stuck isn't the end of the world, and making a mistake doesn't mean you can't ultimately be successful.

  Problems that we don't know how to solve right away are those that provide an opportunity to think outside the box, get creative, and try something new. When a student answers something incorrectly, keep things positive and encouraging. Remind them that mistakes are normal, even if they're frustrating. Acknowledge the effort the student put into the problem. Help the student re-frame the mistake as an opportunity to learn. At the end of the day, they can always try the problem over again!

  Have you tried helping your student with a problem only to end up stumped yourself? That's often a great time to share your own struggle and "dealing with getting stuck" process with your student!

• Try, try, and try again.

  All short-answer Challenge Problems and all Alcumus problems allow students multiple tries. Furthermore, all of these problems reward an eventual correct answer over the choice to "give up" on the problem. A student should not be discouraged if they aren't able to solve all of these questions on the first (or second, or third) try, and a couple of mistakes won't ruin a student's progress.

• Encourage the use of available resources.

  We've developed, revised, and continue to develop new resources to help students in their quest for success, including the Course Message Board, Transcripts, "My Goals" tab, Student Progress Tracking, and Parent Tools for Tracking Student Progress.

When is it too much?

Above, we've discussed why we find it best to really challenge our students in novel ways and provided some guidance for how to navigate this difficulty. However, there is also a point at which it can be too much. If you find that your child is struggling too much, to the point of extreme frustration, endless hours of work, and/or a refusal to do any work, it may be that the course is too difficult for your child at this time.

Students new to AoPS may consider taking the AoPS class whose material overlaps a little with the class they have most recently completed elsewhere. This can give them the opportunity to develop problem-solving skills while more deeply exploring material they have already learned.

You ultimately know your child best. If your child is in a class that is challenging them too much, please email classes@aops.com or click here to contact us—we want to work with you to make sure your child is being challenged at the right level.