One compromise that I like is slides for complicated figures (that would take forever for you to draw, poorly, on the board) and handouts of those slides so that the students don't have to try to recreate them (again, poorly).
Indeed. I would even go so far as to say that this is not a compromise, but the actual, honest-to-goodness, correct use of slides in a presentation, and has been since the dawn of the slide projector. Complicated figures, photographs (of, say, an archaeological excavation or Civil War soldier), or the hypotheses of a theorem that you are planning to prove on the board are reasonable things to put on a slide, and are things that should be put up on the screen for reference. Lacking a projector, handouts are a good alternative (and, perhaps, might be preferable, except for the time that it takes to pass them out and the fact that most of them will end up on the trash).
The material wasn't an issue. I had taken the equivelent of two years of university physics and one year of university calculus in a program from a private university. And, as your incredulity goes, the person in charge of accepting that credit as a transfer, refused to accept the credit and apply it. If I didn't have a math, I couldn't graduate, and I don't remember if science was also required. My senior year of Calculus, I spent no time in my class, until the principal found out, and grounded me to class. After which I brought jigsaw puzzles from home and worked them in the back of the class. After that was discovered by the principal, I was "ordered" to sit at my desk. The room had Pi to 50 digits. I still remember the first 50 digits of Pi. I never scored less than a perfect score on any Calculous test, and slept as much as possible. Near the end of the year, the class was nearing the half-way point of my previous class.
I've been smarter than most of my teachers since about the 2nd grade. The class was told to draw "a man with two orange heads" for a halloween display for an upcoming open house. Everyone in the class drew a man with one head on each shoulder, both orange. I drew a man (normal man) with a jack-o-lantern in each hand - a man, with two orange heads. I was sent to the principal's office and beaten for failure to follow directions (a violation of the law, parents must be notified before any beatings). That's also about when I started getting locked in a closet every day for lunch. That teacher had many accolades, and my mother lied about my address to get me in her class.
With that as my benchmark, I was never worse than my second grade teacher.
As for FERPA, the teacher of record was still the other teacher, and I don't think there was anything in the arrangement that would violate FERPA. The "real" teacher gave the topics, and some minimum mandatory work, and I created a class to fill in the other 90% of the time. I don't know what the grades were derived from, but evaluations of the students were passed to the "real" teacher for her to do with as she wished.
I'm sorry if I wasn't clear, but I accept that you taught a high school class as a high school student. I expressed my concerns about the arrangement, but I accept that you did it.
Having been brought up with standardized tests, I preferred to give them. Doesn't hurt that for IT training, most people were seeking a certification, almost all of which were multiple choice. So it's a common format, with well known rules. It doesn't hurt that it's almost entirely objective (though many times tests will contain poor questions, whether poor wording in the question, or multiple correct answers, of which the "best" is expected, but often hard to determine).
I don't mean to put words in your mouth, but the basic gist of the above seems to be that standardized tests are objective, and this objectivity is an advantage. I agree that standardized, multiple choice tests are about as objective as possible, and that this is a point in their favor. There is one right answer to any given question, assuming that the question is well written. However, as I said way up the thread, such assessments are not very good at measuring anything except rote memorization. I expect my students to be able to do more than memorize the values of trig functions for a subset of angles or the first 50 digits of pi. I want them to be able to analyze and synthesize. Multiple choice questions do a poor job of assessing a student's ability to to this.
Though in college, in smaller classes, the grades were almost divined by the teachers. Twice I feel I did inferior work, but received a passing grade or better because the teacher felt I "tried". I would have felt robbed if it went the other way, but was happy to have the boost the other way. When I got my master's, it was hard to get anything other than an A. That was great. Why? Because it meant that the people learned, without regard to tests, assignments, and such. You got from it what you put in to it. There were no worries about the freeloaders dragging down the group projects, or the annoying people who slow things down asking questions that were answered in the reading they didn't do. Some people are externally motivated, but the internally motivated ones do worse in a graded environment.
I'm not sure of the relevance of this bit. You have repeatedly said that you want to understand my grading scheme. You are exploring the way in which I do things. I don't see how your experience is relevant to that exploration. Can you clarify?
I have been known to remove questions after the fact, usualy with giving the best score from the two scores, so someone who got it right wouldn't get a deduction for it going away. Nobody has ever complained about that. Weights change as well. To help approximate a curve. I'm generous with grades. But not afraid to fail someone that deserves it.
Is there anything that I have said that in any way indicates that my approach is significantly different from the outline you have just provided?
(1) I am not "tip toeing" around any particular term. It is clear to me that grading on a curve means something different to each of us, and that the particular phrase is causing confusion. To prevent as much confusion as possible, I am attempting to explain how I actually grade, rather than relying on a term whose definition we clearly cannot agree on.
(2) You are conflating the idea of grading on a curve with objective assessment. The most objective assessment that I can imagine is a multiple choice or true/false question (or a quiz or exam made up of such questions). One could very easily give such an assessment, then assign grades to raw scores (measured objectively) based on a curve. Conversely, a subjective assessment can be assigned grades on an absolute scale. The marking of individual questions may have some subjectivity in it, but the grade that a student is ultimately given on the assessment will not depend on the grades of other students. These are two distinct concepts, and I believe that I have addressed them both (yes, my assessments are subjective, because it is impossible to create a truly objective assessment; the system that I use to assign grades to assessments combines the extremes of grading on a curve and grading on an absolute scale, as described above). Is there something else that requires clarification in that respect?
(3) I apologize if I was incredulous regarding your high school teaching duties. I find that the idea of a high school students being given teaching duties over his peers strains belief. Frankly, if I learned that my daughter were in a class where another student was responsible for writing the exams, grading work, and assigning grades, I would immediately ask that she be transfered to another class. I don't believe that a high school student has the necessary knowledge base to teach a class (ideally, the teacher should be far in advance of the students), I don't think that the power imbalance created by such a situation is appropriate, and I wouldn't trust a high school student to maintain the privacy rights outlined by FERPA. If you really had that kind of power, the econ teacher you mentioned probably saved your school from a lawsuit.
(4) I asked about your experience writing assessments because knowing about your experience allows me to provide explanations and ask questions that are better tailored to your experience. If you had years of experience, I would ask how you write your assessments---your questions and comments imply that you believe that it is possible to write entirely objective assessments, and I would be curious to know how you write such assessments. Since you seem to lack that experience, let me again refocus on the questions that are important when writing an assessment: how do you eliminate as much subjectivity as possible? how will you know if a student has demonstrated mastery of the material? what will you do if, after giving your assessment, you discover that you wrote one or more questions that didn't measure what you thought they measured?
The first two questions go into assessment design, but the last is important for determining how to assign grades. If your design is flawless, you don't need to consider the final question. However, no one is perfect (though some are better than others), and a small post hoc rescaling (a curve, if you like) can mitigate problems with the design of an assessment. Another approach is to remove certain questions from the assessment after the fact, or to change the weight of certain questions. I sometimes use these techniques, as well.
I'm not trying to pigeongole you. I'm trying to understand. You imply things, then clarify to the opposite of the initial implication, but when I try to drill down to figure out what you are trying to say (or what you did, if you are deliberately trying to give a different impression), is pigeonholing you. Why, because you prefer to perform drive by assertions, without question or explanation?
You are the one making fine distinctions between the words "assign" and "mark," and you are the one that wants to declare that my grading system either is or is not "grading on a curve". When I attempt to actually explain what it is that I do, you accuse me of "performing drive by assertions, without question or explanation." Maybe you really are curious, but it feels to me like you are not making an honest intellectual effort to understand what I have written, and that you are trying to rely on easily understood pigeonholes.
Let me reiterate and attempt to clarify: I mark assessments (exams, quizzes, etc.). The marks that I make on those assessments are used to assign a grade, but marking an assessment and assigning a grade to that assessment are distinct activities, and the distinction is not between objective and subjective methodologies. The assignment of grades is as objective as I can make it, but complete objectivity is impossible. It should also be noted that even if the marking of an exam is done entirely objectively (by a Scantron device, for instance), a grade still has to be assigned to that assessment. This can be based on an a priori scale, a curve, or something in between. I do not grade on a curve in the sense that I do not determine ahead of time how many people will get a given grade. I do, on occasion, adjust the cutoffs for grade assignments in order to give all scores in a cluster the same letter grade. This is to take into account my own inability to write an assessment that is 100% objective, consistent, and reliable, and to acknowledge that there is likely very little difference between the demonstrated mastery of the material that similar scores on an assessment represent.
As an example, suppose that I have a pile of exams. Generally speaking, I grade on a 4 point scale, and assign anything greater than 3.5 an A. However, on a given exam, I might have a group of five or six students who all score in a range from 3.4 to 3.6 points, with the next highest score a 3.1. In this case, I do not see a meaningful distinction between a score of 3.4 and 3.6---all of the students in this group have demonstrated a similar level of mastery, and deserve the same letter grade. Hence, I will adjust the cutoff down to 3.4 out of 4, and assign As to all of these students.
Personally, I would not call this "grading on a curve," because, as I said above, "grading on a curve" usually implies that the number of grades at each level is determined a priori. However, if you feel it is necessary to label such a grading system, and you feel that the appropriate label is "grading on a curve," I have no objection to that label, as long as you recognize that this is not grading on a curve the way that most people mean it.
I have no answers.
You declared without justification or evidence that most instructors use entirely objective exams consisting of multiple choice exams, and implied that this is a solution to the subjectivity built into all human systems. That seems like an answer to me.
I just have more questions. Why do questions make you so uncomfortable?
As far as I can tell, you have asked two questions: you questioned my use of---and drew great meaning from---the verb "to assign", and used that to launch into an implied question about objective vs subjective grades. I have done everything I can in order to clarify. I'm sorry that such clarification cannot be made into a nice, one-word summary.
I taught high school physics for one year. While I was in high school. The teacher noticed that 1/2 of the class was "above" the other (teaching physics is different whether you use algebra or calculus - reflected by when I went to college, there were seperate classes for each, and half the class had already had calculus, so many of the "complex" algebra physics were trivial if you just figured out one aspect and integrated over time, or such). So I was given the "calculus" half, and sent to another room. one semester later, another teacher complained about the arangement and the class was merged. "My" half had already completed the year's material in that one semester. I'd have kept going, if there hadn't been the complaints about us. By the stodgey economics teacher.
I have no degree in education, but was a trained tutor through college (even tutoring people in classes I've never taken, one need not know to be able to teach, though it helps), and worked a few years as an IT trainer.
So, stripping away the anecdotes and personal anger, you lead a high school study group and have done some non-academic training. Did you write the exams for your high school physics class? Did you assign grades based on those exams? Do you grade your trainees in your IT training seminars? Do you write assessments for those seminars? If yes to any of these, how do you use objective assessments to distinguish between rote memorization and the ability to abstract and synthesize? How do you deal with your own subjectivity in the selection of questions to ask?
Seriously? Your answer is to make everything multiple choice? Multiple choice questions are decent for measuring rote memorization and recall of facts. They are not so great for determining if a student can abstract from their base of knowledge and synthesize. And, frankly, most professors that I know don't give tests that look like that. In my department, there are consistently multiple choice sections on most of the exams for lower division classes (precalculus, calculus, linear algebra, and differential equations), but we have been moving away from those forms of assessment as they do a poor job of measuring student ability. Beyond these lower division classes, there are diminishingly few multiple choice or true false questions, and most of these allow for work shown and partial credit (which cannot be anything but subjectively graded).
Making everything multiple choice also does not address the subjectivity inherent in the selection of questions to ask, and manner in which material is emphasized in lecture or in the text, hence it does not solve those problems.
I find it funny that you feel the need to pigeonhole me. I don't grade on a curve in the sense that I do not determine ahead of time that a certain number of students will get an A. It is theoretically possible that every student in a class will earn an A, or that every every student will fail. I've never had it happen, but there is no reason that it couldn't. However, I acknowledge that people are imperfect (including myself) and that I might make mistakes in how I assess my students (I might make an exam too difficult, or fail to perfectly teach a particular topic). While I have cutoffs for particular letter grades established a priori, I am more than willing to adjust those cutoffs up or down a little to make them fall between clusters of raw scores, or to adjust for assessments that are too easy or difficult. I suppose that you would call this curving, but I don't see it as being nearly so black-and-white.
I am now honestly curious: what experience do you have teaching and assigning grades? You seem to think that you have solved all of these problems. How may I subscribe to your newsletter?
As you say, you didn't ask the question. You only implied it. I answered the question that you actually asked. There's no reason to be so passive aggressive about it.
The answer to the question that you have asked now is that instructors do their best to assign objective assessments, but a truly objective assessment is impossible. The instructors, like everyone else, are human. They make mistakes: in the emphasis of material in lecture, in the construction of assessment questions, and in the grading of assessments. Students also have an uncanny ability to screw up questions in unexpected ways---such mistakes may imply some understanding of the material, and deserve credit for that, but no objective rubric built before grading can possibly anticipate all possible errors. Not to mention the fact that grading papers is very different from grading computations or proofs. It is also impossible to write an assessment that can be done in a reasonable amount of time that will completely determine how well a student has mastered the material required, hence the selection of material for emphasis on an exam is somewhat subjective. For all of these reasons, and more, any assessment is going to be somewhat subjective, even if the design goal was to make it as objective as possible.
Suppose you have two candidates that are apparently equal on paper, except that one has excelled in their non-major classes, and they other has performed only marginally. This tells me that one of the two candidates is capable of tackling tasks that are outside of their wheelhouse, which is an indication that they might be able to think through situations in more than one way. The other either was incapable of performing a task outside of their chosen major, or chose not to. One of the candidates has displayed some intellectual flexibility, which I consider to be an important trait in any profession.
It should be pointed out that universities are not meant to train anyone for a job working in crypto. Most math majors have probably some calculus, linear algebra, and differential equations. Depending on the emphasis of the program, they have also taken some abstract algebra, real analysis, topology, number theory, and/or numerical methods. It is unlikely that many people with a bachelor's degree in mathematics has the mathematical knowledge or ability to tackle crypto sytems without further training. It will probably be easier to train someone with some intellectual flexibility than someone without, and good performance in areas outside of a student's major indicate some of that flexibility.