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Each Art of Problem Solving class is held in the AoPS online classroom. To attend each class, students log in to the Art of Problem Solving Community up to 10 minutes before class begins, then they click the Classroom button on the left sidebar. The classroom then opens automatically. The classroom consists of a main window in which classroom discussion takes place, an entry window into which students type their questions and answers, and a class list/options panel in which students can alter classroom appearance settings.
Each class consists of an experienced instructor leading students through a series of related problems of increasing complexity. The classes are highly interactive. Students are not simply told mathematical facts and shown solutions to problems. They are challenged to answer questions throughout their study of each problem. Students are also able to ask questions of their own, and work one-on-one with instructors if they need more personal attention.
We are able to achieve this high degree of interactivity by holding our classes in a text-only, moderated classroom. By holding our classes in a text-only environment, all students are able to continually share their ideas or ask questions. When the instructor asks a question, all the students can answer. The classroom is moderated, which means that all these responses come to the instructor, rather than being shared with the whole room. This way, the instructor can quickly review students' comments, and choose to share only those comments that contribute to the discussion. This structure has many enormous benefits over a typical classroom, such as:
| Typical Classroom | AoPS classroom |
|---|---|
| Students fear being embarrassed by speaking up in class, either for getting a question wrong or for asking a question that others (incorrectly!) think is stupid. | All student comments initially go only to the instructors, and these are only shared with the room if they fit the flow of the class. Questions are often answered privately, and students aren't embarrassed by having their wrong answers consistently shared with the whole class. So, students are less afraid to answer questions, and less afraid to ask them. |
| In a typical classroom, a teacher can only invite one student at a time to participate, and once a student is called on, it is easy for the other students to stop thinking about the problem at hand and await the called-on student's response. | In the AoPS classroom, all students can respond to all questions. Therefore, students stay engaged and are constantly able to communicate their ideas. They don't stop thinking when other students are called on, because single students are never called on. |
| Students have to wait their turn to ask a question, and may not have a chance to ask the question until well after the most opportune time. | Students can ask questions at any time, so they can ask their question right at the moment the answer would be most helpful to them. |
| Students either have to rely on memory or very good note-taking skills to capture everything that happens in class. The note-takers often have to spend far more time writing notes than thinking about the concepts presented in class. | The AoPS classroom allows us to make full transcripts of every class, including all the discussion in the general classroom. Students are able to review this transcript on their own time later, so they can spend class time focusing on the problems rather than worrying about taking notes. The transcript consists of text and images, so students can print it, or scan it for the parts they're most interested in. (As opposed to a video transcript, which is very hard to scan!) |
| Most classrooms only have one teacher, and it's very hard for most teachers in a typical classroom to work closely with more than one student at a time. | The AoPS classroom allows for multiple instructors. Most AoPS classes have assistants, who take care of some student questions, or correct student errors privately. Also, our technology allows our instructors to communicate privately with multiple students at once. |
| Students may be stuck, or have a misconception, in ways that the teachers never see or hear. | Because many students are constantly speaking up and sharing their ideas, teachers can quickly see when a student misunderstands something, and correct the misunderstanding. |
| One or two aggressive students, or one or two conduct problems, can dominate or disrupt a classroom. | The moderated nature of the classroom makes it impossible for one student to disrupt other students, or to dominate the discussion. |
Moreover, most of the benefits listed above for the AoPS classroom are not possible even in most online classes. Many other online classes use complicated video and audio technology, which both increases the chance of having software or hardware problems and eliminates many of the advantages that the AoPS classroom offers over a typical non-virtual school classroom. The AoPS classroom quickly loads automatically, and there is no special additional software or hardware students have to buy. While it may be rare for an online company to suggest that "more is not necessarily better" when it comes to technology, we find that this is definitely the case for our classes - we have just the right amount of technology to reap the benefits above, but not so much technology that we lose them.
Our classroom is also specially equipped to handle mathematics by being able to render mathematics with the LaTeX typesetting system, which is used by professional mathematicians to write papers. Our instructors (and many of our students!) are therefore able to use a text message that appears on students' screen as fully typeset mathematics. So, instead of writing the following,
| (a^2+b^2)/[(1/a^2) + (1/b^2)] = (a^2+b^2)/[(b^2/(a^2b^2)) + (a^2/(a^2b^2))] = (a^2+b^2)/[(a^2+b^2)/(a^2b^2)] = [(a^2+b^2)(a^2b^2)]/(a^2+b^2)=a^2b^2 |
our instructors can send a message to students that renders easy to read mathematics, like
Please note: Students are not required to use or know LaTeX for our classes.
Students can try out our online classroom by attending one of our free Math Jams. Click here for more information about the Math Jams. Click here for more information about how AoPS online classes work.
