Question: What are Prof. Mário’s teaching principles?
Answer: A statement of my teaching principles can be found in the syllabus of every course I teach. Here’s a summary:
Principle 1: “Everything should be made as simple as possible, but not simpler.” I approach each topic as clearly and directly as possible, but with proper balance not to avoid its intrinsic complexity. I believe that it is part of a student’s path of development to be properly challenged intellectually.
Principle 2: Good learning = mastering the theory + interpreting the results. Most of my courses are of a mathematical and fundamental nature, and I boldly work to develop students’ both mathematical and pragmatic skills. I detect that some students present highly developed mathematical ability, while others present a great talent for identifying problems in the real world that need a solution, but often some students are not able to present both capabilities at the same time. I design my lectures and activities to help develop in every student their best in both skills since success in the real world involves mastering both.
Principle 3: Talent alone does not necessarily lead to good results – hard work is essential. However talented one is, they can always do better when they work hard. Reading the basic bibliography is essential, as is doing homework, and such habits will improve anyone’s results. Understanding everything covered in a lecture does not automatically mean one will master the subject. Reading and practicing are essential, and irreplaceable.
Principle 4: Students’ development involves teamwork between students and teachers. It’s clear to me that students and teachers share the same goal in striving for the former’s best development, and so I see my students and myself as a team working together to achieve this objective. As in any team, each member has to do their best, and I certainly strive to do mine as a teacher. Similarly, I expect students to offer their best in their particular context.
Question: I believe that a question in my exam was given an unfair grade. What should I do?
Answer: If you believe one or more questions in an exam were unfairly graded, please write a clear and concise justification of why you think that is the case. You must:
I will analyze your request and respond in writing in the exam itself.
Be aware that the burden of proof is on you: you have to convince me that your answer is correct, and I do not have to convince you your answer is wrong.
Here there are some examples of invalid justifications:
Question: Why in true/false questions does each wrong answer cancel out a correct answer?
Answer: This rule is just a natural application of a field of study called decision theory (if you are interested in it, you can take my course on information theory, where we discuss the subject). Let me try to briefly explain here the rationale behind this rule.
Suppose that in an ordinary exam, 50% of the true/false questions are true and 50% are false. An unprepared student who blindly guesses the answer to each question is expected to get 50% of the answers correctly (by simply, say, guessing all answers to be “true”). In case I don’t use the rule that a wrong answer cancels out a correct answer, such a student is expected to get 50% of the marks for this question, even if they know nothing about the subject of the exam!
Now suppose that I adopt the rule that every wrong answer cancels out a correct answer. An unprepared student facing a question whose answer they don’t know still has to choose between leaving the answer blank or making a blind guess. If the question is left blank, the grade for the question will be 0 marks. If the student blindly guesses an answer, they respond correctly with a probability of 50%. In case the answer is correct, they will get full marks for the question (say, N marks), and in case it’s wrong they will have the marks for another correctly answered question canceled out (which means they’ll lose N marks). Hence, the student’s expected grade in this case will be
50% * (N marks) + 50% * (-N marks) = 0 marks.
Now you can probably understand why I adopt this policy. It discourages an unprepared student from blindly guessing, and brings the expected grade of such a student back to zero – since the expected gain of guessing and that of leaving the question blank is the same. On the other hand, a prepared student still has an incentive to answer the question, as their expected gain will be positive (but the derivation of this result is left for you as an exercise 😉).
Question: Still regarding the grading system for true/false questions… I just read your explanation, but I still think that’s unfair: you are discouraging students from providing an answer if they are not certain of their answer!
Answer: Well, discouraging students from providing an answer if they are not certain of their answer is the exact purpose of this grading scheme: that’s a feature, not a bug!
Question: I missed an exam. What should I do?
Answer: If you missed an exam, for any reason, you can take the make-up (substitute) exam at the end of the semester. No justification is needed.
Question: Who can take the make-up (substitute) exam?
Answer: Every student who missed an exam, for any reason, can take the make-up (substitute) exam at the end of the semester. No justification is needed.
Students who did not miss any exam, however, are NOT allowed to take the make-up exam, for two reasons. First, the end of the semester is a very hasty period, and there’s usually barely enough time to grade all finals, seminar papers, make-up exams, problem sets, etc., to provide students with their final grades within a reasonable time frame; opening up the make-up exam to all students would only further delay this process. Second, if I did open the make-up exam to all, I wouldn’t be giving students who did miss an exam the same opportunities as those who didn’t, as they would be taking one fewer exam than all others (and that isn’t fair).
If you do not qualify to take the make-up exam but still want to improve your final grade, see the section “improving your final grade” below.
Question: How does the make-up (substitute) exam work?
Answer: The make-up (substitute) takes place at the end of the semester, and it covers all subjects seen during the whole semester. It does not matter which exam you missed or the exam’s grades you want to have replaced, all students will take the same make-up (substitute) exam on the same date.
Question: The semester is over and I need only 0.1 marks to pass the course. What can I do to get these 0.1 extra marks?
Answer: If you have failed the course, but attended 75% of the classes and obtained a final grade between 40 and 59 marks, you can take the special exam (“exame especial”) at the end of the semester. If you pass the special exam, you’ll pass the course.
Question: The semester is over and, although I did not miss any exam, I still want to improve my final grade. What can I do?
Answer: If you have passed the course (final grade >=60 marks), but still want to improve your final grade, I will allow you, in an act of grace, to take the special exam to replace your worst grade on an exam during the semester.
Question: Do I really have to take the special exam if I want to pass/improve my final grade? I only need 0.1 extra marks!
Answer: To get the 0.1 marks you need/want at the end of the semester, you have two options:
Note, however, that the following are NOT available options: