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As I prepare to instruct an online Mathematics course next year, I'm currently writing the syllabus. Right now, I'm writing about student participation in the Learning Management System, which takes about 20% of the total grade, involving the exchange of ideas through discussion posts to earn credit. However, I'm considering what can be considered common knowledge for our course, and I am prompted to reflect on the role of class materials, including lecture slides, textbooks, past homework assignments, and exams. How do I define common knowledge in my syllabus to warn students of unethical scholarly conduct in student postings on platforms?

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    $\begingroup$ "How do I define common knowledge in my syllabus to warn students of unethical scholarly conduct in student postings on platforms?" What exactly is the issue, i.e., what exactly do you want one to be allowed to do with "common knowledge" that wouldn't be allowed to do with all other sorts of information? The definition to choose heavily depends on that, IMHO. If it is just "free sharing", then I second Justin's opinion in general (though the legal definition of "information giving away an answer" may be quite a headache). Otherwise, I would prefer to see the question clarified a bit first :-) $\endgroup$
    – fedja
    Sep 27 at 21:45
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    $\begingroup$ Are you seeking to prevent plagiarism? These posts are to be considered formal writing? With due research as far as citations go? (It's not the only way to frame discussion groups. Hallway conversations often have no better citation than "I remember reading somewhere, I think,...," if you don't have time to dash back to your office and look up the citation. Perhaps the formal expectations can be similarly relaxed in online discussion boards?) $\endgroup$
    – Raciquel
    Sep 27 at 23:26
  • $\begingroup$ Yep, I'm trying to prevent the plagiarism in the student discussion post, and I'm trying to find out $\endgroup$ Sep 28 at 5:49

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Unless you're specifically asking about college/superior degrees (which I have none), as posed right now, this question has no possible answer.

It depends way too much on your public, their background, their goals and their interests.

E.g., in Brazil, there are something like the SATs. I don't know much about US's higher education logistics, but that's not the point. The key differences here are 1) anyone can take the tests/exams however many times they'd like (although they're applied only once or twice a year, in order to properly size classes); 2) only federal universities are required to use the same default exam, elaborated by the ministry of education, although they are somewhat free to define how the results will be calculated (weighting averages). State universities and private universities are almost free to elaborate their own exams. And 3) Some courses and universities will have more competition: Medicine or Law will require higher grades, as well as any course at USP, a world top-100 university. Public vs. private also play a big role.

I've seen people who, after graduating from high school, spent 6 to 8 years (which means they took 6 to 8 exams (per non-federal institutions)) in order to get into a Medical school.

This means they're likely to have parents/relatives capable of paying all of their expenses and paying for top-grade "prep-schools" (most of those are located in the state's capital, have some of the country's absolutely best teachers, and are progressively expensive).

Getting into higher education is a big deal (and an enormous business). At least for those born in wealthy families who could afford the best education from kindergarten to prep-school, which means they'll be fighting for the absolute best courses.


(I'm circling a lot, but bear with me). These prep-school will have the most meticulously designed classes, textbooks written by their very teachers and highly per course directed schedules/curriculums/timetables (couldn't translate this one, haha): those applying to engineering will have way more Math and Physics classes and so on.

Competing against this top-tier education is where most high school graduates are, minus the money. They tend to have had a worse elementary education, they rarely apply for the highly competitive "slots"(?), etc. Still, they focus on the federal universities. Their exams tend to take the whole country's general education and also implement way more inclusion policies.


That's where I actually start my answer: I happened to be lucky enough to have had an excellent education. During 2020, we had the idea to create an online social prep-school. We had over a hundred volunteers and about 40 students, for whom we had personal lessons (no big classroom problems, such as being afraid to ask, etc.). I managed to make available for all teachers, on every school subject the whole exercise/textbook set, 1 through 8, of a top-tier prep-school.

For some subjects, there were also "book 0s", for actually creating and checking the common grounds before starting.

I still recall my first class (in this project) for my student, Lyon. I intended to assess his knowledge and how we would progress the lessons through the year. Lyon had a lot of trouble with book 0 already. So that's what I focused on for months, the proper grounding. I made a big effort to have him master the basics. I actually started with multiplication and how potentiating related to it, I delved deep into how fractions are always divisions or ratios, I also focused on averages and medians, which were common topics for that exam.

As such, I knew I'd never have the time to get into analytical geometry, matrixes or polynomial equations, so I tried to create a good foundation, so he could actually know and understand the questions, instead of throwing some poorly memorized formula and hoping for the best.


This means I understood where my student was coming from, whether he had actual interest in learning or not, his goal, and, e.g., he would engage his homework or not.

I'm very happy to say he got in the federal university he desired (in his own city, so he could keep living with his parents), and the course he chose.


I believe the students shape the teaching as much as the educator, you'll surely not put the same effort if you were to teach a bunch of stupid kids pranking each other and not paying attention at all.

As Paulo Freire's (whose workings are a must in Pedagogy, used even in Harvard and the likes) words, teaching is not a full jar filling an empty glass. Teaching is a trade of knowledge and experience, and I'm sure I learned a lot by teaching Lyon during those days!

Oh, and BTW, there is no such thing as enforcing ethical practices for online teaching. Netflix, HBO, Disney+ etc. are not able to attain immunity against piracy, you'll certainly not be able to enforce it yourself. Once again, the students goals will shape the teaching.

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I would consider common knowledge to be any information that does not give away the answer to a question on a pending assignment or test.

  • A piece of information "gives away" an answer if it is the answer itself, a formula (or any sort of template) that can be filled in to obtain the answer, a generality for which the answer is a special case, or a special case from which the answer can be inferred as an obvious generalization. (This is just off the top of my head -- there may be more conditions I'm not thinking about.)

  • An assignment or test is "pending" if it is accepting submissions or will be accepting submissions at any point in the future.

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