FAQ about Mário’s teaching & grading principles
Question: What are 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 team work 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 in order to do mine as a teacher. Similarly, I expect students to offer their best within their particular situation.
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:
- write your justification on the side of each corresponding question in the exam itself,
- add to top of the front page of the exam: “Please, review questions 1a, 2, and 4c”, and
- return the exam to me.
I will analyze your request and respond in written 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:
- “I think I answered the question correctly. What did I do wrong?”
- “I see nothing wrong in my answer. I deserve full marks for it.”
- “Well, while I wrote ‘x’ as an answer, what I really meant was ‘y’. Would you please consider what I meant instead of what I actually wrote?”
- “Isn’t there anything at all you can do to give me a higher grade on this question?”
Question: Why in true/false questions does each wrong answer cancel a right 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 actually true and 50% are actually 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 a right 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 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 will correctly get it with probability 50%. In case it is correct, they will get full marks for the question (say, N marks), and in case it’s wrong they will cancel the marks for another correctly answered question (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.
You now can probably see why I adopt this rule. 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 the answer!
Answer: Well, discouraging students from providing and answer if they are not certain of the answer is the exact purpose of this grading scheme! That’s a feature, not a bug.
Missed exams and make-up (substitute) exam.
Question: I missed an exam. What should I do?
Answer: You can take the make-up (substitute) exam at the end of the semester.
Question: Who can take the make-up (substitute) exam?
Answer: Every student who missed any exam for any reason can take them make-up (substitute) exam at the end of the semester. No justification is needed.
As an act of grace, I may allow students who didn’t miss any exam to take the make-up (substitute) exam to try to improve their final grade in the course. However, it is by no means granted that I will be able to implement this act of grace at any given semester: the end of a semester is often a very busy period and there may simply not be enough time for me to grade the make-up (substitute) exam for (possibly) every student in the class.
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 replace, all students will take the same make-up (substitute) exam at the same date.
But be aware: if you take the make-up (substitute) exam, your grade in that exam will necessarily replace your lowest grade in exams in the semester.
Improving your final grade
Question: I did not miss any exam. Can I take the make-up (substitute) exam to try to improve my grade?
Answer: As I said in a previous question, as an act of grace, I may allow students who didn’t miss any exam to take the make-up (substitute) exam to try to improve their final grade in the course. However, it is by no means granted that I will be able to implement this act of grace at any given semester: the end of a semester is often a very busy period and there may simply not be enough time for me to grade the make-up (substitute) exam for (possibly) every student in the class.
But be aware: if you take the make-up (substitute) exam, your grade will necessarily replace your lowest grade in exams in the semester.
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: You have three options, in this order:
- Take the make-up exam (substitute) exam, if you qualify, and get a grade 0.1 marks higher than you had before.
- Take the special exam, if you qualify, and get a higher grade.
- Build a time machine, go back in time, and do better during the semester.
Note that are NOT options listed above:
- Have me give you 0.1 marks out of the blue.
- Do all homework you haven’t done during the whole semester in hopes of getting marks for that.
- Make some sort of special project to try to increase your grade.
Question: The semester is over and I need only 0.1 marks to get a grade I really want (e.g., change from concept B to A). What can I do to get these 0.1 extra marks?
Answer: See the answer to the previous question.