Point deduction

A2) Complications for the student Pro offers the following in refutation : 1) It is not much more complicated to evaluate with the proposed scenario 2) Not all students have a problem with time 3) Students who would need to can not calculate the percentages anyway In response, as both a teacher and student I would offer the following : In a normal marking scheme all a student has to do is consider the mark of a question and multiply that by the chance they think they are right and this is the expected return. Example, you look at a question which has a mark of 10, you estimate you have a 60% shot at being correct and thus it is worth 10*60% or 6 marks to attempt. You then think how much time it will take and decide if you want to try for those 6 marks. Now under the proposed scheme by Pro the student has to do the following calculation; 2.5*rank*certainty-2.5*rank*(certainty-1) and they have to see if this expected value is greater than -rank which is what happens if they just leave it out. Thus instead of one simple multiplication they are doing six operations and then a comparison. With an actual example; in the same scenario as noted in the above but using the marking scheme proposed by Pro the student would calculate 2.5*10*60%-2.5*10*40% which comes out to a mark of 5 (out of a possible 25) which is greater than -10 (if they left it out) so they should attempt the question if the time return is sensible. Note however there are two further issues which come out of this calculation. Issue #1) There are some scenarios where the expected value is negative, i.e., the average score the student will get is a loss and the are better off not attempting it. The demarcation point is actually 30%, if the student has less certainty that this they should not in general answer the question. Just think of what that means in general and is it a good thing to teach students that 30% certainty is useless and even more so consider than anything above 30% but less than 100 is *seriously* devalued. Issue #2) Because of the imbalance of the marking scheme it does very odd things to the expected value. As an example, if the student knew 60% of the material and attempted all the questions they would get a score of 20% on the exam. It is hardly the case that they could know which 60% they will get right on and leave the rest out. To show the full imbalance of Pro's system, in order to achieve the passing grade you have to be on average 85% or more certain on the questions! As for students not doing the calculations, Pro is right, due to the complexity few will do it unless they learn a few shortcuts (for example if you play with the equations a little you will realize that you need a 30% probability of being certain to break even, if you are less certain than that you should not [in general] answer the question). Thus students are being encouraged not to make careful decisions but instead just make wild guesses about what they should or should not do. A1) Marking Imbalance Pro returns with : 1) Pass marks are not everything to a test. 2) Student answers will still provide feedback. 3) Tests are also assessed based on the range of scores of students 4) Just dodging questions isn't smart in point deduction either. Now here is where I must cry foul and cry as long and hard as askbob when he spots a multi/sock account. In the comments section before I accepted this debate I asked specific questions to clarify the resolution. Among other clarifications Pro noted that the passing grade was 65%, clarified the total score and how it was calculated. When in rebuttal he was shown that this leads in very imbalanced testing Pro then attempts to change the resolution to something much more general akin to "Point deductions should be used on multiple choice questions." Again I cry foul! Pro has to defend the exact marking scheme proposed or concede the debate, they can not simply change the resolution. If they want Pro can defend a general claim of attempt penalty vs zero for incorrect answers but that has to be another debate - here they have to defend the resolution given. However, if Pro is going to propose such a grading scheme to transform the marks, which is possible, it is not sufficient simply to say it could be done, but rather the translation formula should be given. This should be able to deal with for example the one student who attempts all questions but gets them all wrong vs the one student who just leaves everything blank. If you have the second student get zero the first student actually gets a negative mark. A3) Teacher workload Pro makes the following arguments : 1) there would likely be a much higher number of blank answers. 2) What he doesn't note is that teachers already weigh questions based upon difficulty 3) Furthermore, teachers actually wouldn't have to multiply ranks. Pro fails to realize that developing a fair and balanced test is more demanding that marking it and in the developing of the test the teacher has to look at each question and then perform the same rank calculation that the student does and determine a fair mark based on the total score of the test. With even a trivial consideration it should be obvious this is not easy as while you are developing the test the total score is not known which means that the teacher could be constantly revising past ranks. Note further that Pro argues that his method reduces marking as teachers do not have to add up marks for correct answers because his scheme starts off with full marks and only subtracts, this of course can be done with the current marking scheme as well and in fact anyone who marks a lot of papers does just that - they just record all the negative marks and add them up and subtract off the total score. "Unanswered points" Pro makes the following arguments : 1) my system discourages guessing, which is not advised to be used on serious, real life situations (R1 example). 2) Con also did not attack the point about feedback. As noted, the scheme is severely imbalanced I was going to let the point stand on its own but added two more commentaries as it looked like Pro was attempting to formulate a marking scheme and I just wished to share my experience as a teacher. If it is wished to refute the latter two points then that can be done as well. First, guessing is a part of life as nothing can be known with absolute certainty and thus it is always the case that you are using expected gain calculations. In the case that Pro raised, many investments are worth investing if you only have a slight chance. If for example you have a 20% chance to win a million dollars and it only costs you $10 do you do it? Of course. It would be a horrible message to send to students that guessing is a bad thing and you should only act when certainty is 100%, they would be unable to function in the real world. Second, if Pro wanted to encourage feedback then they can do two simple things to change marking schemes. Stop taking off marks, grade all questions only positively, reward all attempts, even reward multiple attempts. When I was grading I would encourage students to try multiple approaches if they were uncertain because in the real world it is not the case that you either know something for certain or you are useless, it is often the case that you have to attempt several times and succeeding after a few attempts obviously has value. Even for multiple choice, I would encourage students if they were not certain to give multiple answers because it is obviously worth something if a student knew that it was either one of the two answers but unsure which one vs not knowing anything. I used a gradual marking scheme based on the number of attempts used. I would have to revisit my notes but it was something like (total marks/# attempts) per question and then then entire class was normalized based on the inflation.