The following is a true story.
I am an advisor at my school. There are five students who make up my advisee group. One of my primary functions as Advisor is to monitor their academic progress (aka grades) and communicate to their parents how the advisees are doing. This means I send emails every two weeks to my advisee parents in which I write their current grades and my spin on those grades. You know, progress reports. Mostly, the parents care about the grades.
One of my advisees, let's call her Chris, is in AP Chemistry. Her parents have emailed me all of two times in the year and a half that I have been her advisor. So, you can see they are not the most hands-on parents. Thus, when Chris came to me with a question about her AP Chem grade, I figured it was from her, and not from her parents. Before Christmas break, Chris had a B+ in AP Chem. Since that report, Chris had earned an A for Participation and an A on the alternative assessment (a substitute for a final exams which were cancelled due to school being closed early... but that's a different story). So, essentially, she had a B+ in the class, and then two more grades were added to her AP Chem gradebook that were both higher. Her final grade for the semester? B.
So, Chris emailed me and asked me about this. I had not yet had a chance to notice the change in grades. I was happy she brought it to my attention. I looked into it and discovered that her grade had gone down despite her last grades being better. The reason? When the teacher had initially set up his computer gradebook, she had not set it up properly, or it had been changed on her, and the weighting was off. So, she had readjusted her weighting and that had changed grades a lot and resulted in Chris's grade dropping.
Do you know what a weighted average is? Google it. Teachers use it all the time. A grade may be on a 100-point scale, but those points are not distributed equally among the different kinds of assessments. Teachers usually calculate averages for each category, and then weight them according to their significance. For example, tests could be worth 60%, quizzes worth 25%, and homework worth 15%.
Anyway, the AP Chem teacher, let's call her Amy, weighted her assignments this way: tests 25%, quizzes 25%, labs 25%, homework 20%, and participation 5%. On the surface, there is nothing terrible with this distribution of weights. It is perhaps odd that tests and quizzes have the same weight, but I can imagine how this might be appropriate. Dig a little deeper, and an interesting fact emerges: there were only two quizzes while there were four tests. This means that each quiz was worth 12.5% (25% divided among two quizzes) of the course grade while each test was worth 6.25% (25% divided among four tests). Or, to put it another way, the teacher's weighting meant that a quiz was worth twice as much as a test in the course grade.
Now, I did not know how Amy viewed tests and quizzes for her AP Chem class, so I asked Chris about what her AP Chem teacher had said regarding the importance of quizzes. Chris remembered that her teacher had said quizzes were worth less than tests. Unfortunately, Amy's weighting did not make that a reality in the calculation of the course average.
I sat down with Chris and we looked at her averages and calculated her course average using a variety of weight distributions. In the end, it did not change Chris's letter grade. It certainly changed her numeric average, but it did not take her from a B to a B+.
However, it would be very possible that a change in the weighting could change the letter grade of a student whose numeric course average was on the cusp of the next letter grade.
For example, suppose Cory had a 92 test average, an 84 quiz average, a 90 lab average, a 90 homework average, and a 93 for participation. Using Amy's weights, Cory's numeric course average would be 89.2, which would be a B+. If the weighting were changed so that tests were 40% and quizzes were 10%, then Cory's average rises more than a full point to 90.4, an A-.
For those of you who know, the difference between a B+ and an A- to the University of California is huge. A B+ gets a score of three while an A- gets a score of four in Grade Point Average (GPA) calculations. Thus, this teacher's seemingly arbitrary designation of grade weights could have a very real consequence to a student in the college admissions process.
Do you still believe in grades?
Wednesday, January 16, 2013
Tuesday, November 13, 2012
Striving for the "acceptable" grade (Part 2)
When I last left you, Jolene had been wanting to switch math courses because she wanted to be able to get an A in math and spend less time achieving that grade. Our plan was for Jolene to take the next test and see how it went and she would decide based on that result.
Jolene earned an A- on the Unit 2 Test. She decided to stay in the honors course.
I know, this is kind of a quick ending to a long story, but it was really as easy as that. Why? Because there was only one important thing - her grade. There was no discussion as to how long she spent preparing for the test.
A few weeks later, she remains in the class and her grade is at an A-. But there's been no discussion involving me about whether her other classes are suffering or if she has, in fact, reduced the amount of time she devotes to her math homework.
Today, we had our Unit 3 Test. I have no idea how Jolene did and I probably won't look at the tests until Thanksgiving break. (Yes, I do school work during my "break". In fact, most teachers I know use their breaks to do work. Often a significant amount of work.) At the end of today's test, Jolene commented that the test was difficult. But, she didn't leave my room crying.
No, today it was Brenda who left crying. Brenda, my superstar. Brenda, like Jolene, is a new student at my school. She considered trying to move on to the third-year honors course. In the end, she opted to stay in my second-year honors course, and this has proven to be a pretty good fit for her. Her grades have often been near or at the very top of my class. But, she has been learning a lot and the class has not been as simple as she had thought it might.
Today, Brenda melted down at the end of the test. Time was up and just as Brenda was about to hand her test to me, she noticed that there was a page 6. She looked at me and asked for time to complete page 6. I told her no, that I had not been able to give students in the other period extra time, so it would not be fair to give her additional time. Moreover, the last page had one problem that was worth 2 of a possible 34 marks. There is absolutely no way that 2 marks will have any impact on her semester grade. Brenda has already demonstrated to me remarkable mathematical skills. She readily recognizes pattern and is proficient at explaining how the ideas connect. Despite all of this, Brenda broke down crying over not having gotten to do anything on page 6.
I'm not sure about this, but I'm guessing Brenda's breakdown has many more reasons behind it other than the math test she just took. Regardless, not finishing the test ignited her feelings and brought them to the surface. Since I don't know what's going on with her beyond my math class, it's not fair to say that the almighty letter grade is the main culprit here. But, the letter grade certainly has played a major role. It's as simple as this. If the test had no grade associated with it, would Brenda have left my class sobbing today?
Jolene earned an A- on the Unit 2 Test. She decided to stay in the honors course.
I know, this is kind of a quick ending to a long story, but it was really as easy as that. Why? Because there was only one important thing - her grade. There was no discussion as to how long she spent preparing for the test.
A few weeks later, she remains in the class and her grade is at an A-. But there's been no discussion involving me about whether her other classes are suffering or if she has, in fact, reduced the amount of time she devotes to her math homework.
Today, we had our Unit 3 Test. I have no idea how Jolene did and I probably won't look at the tests until Thanksgiving break. (Yes, I do school work during my "break". In fact, most teachers I know use their breaks to do work. Often a significant amount of work.) At the end of today's test, Jolene commented that the test was difficult. But, she didn't leave my room crying.
No, today it was Brenda who left crying. Brenda, my superstar. Brenda, like Jolene, is a new student at my school. She considered trying to move on to the third-year honors course. In the end, she opted to stay in my second-year honors course, and this has proven to be a pretty good fit for her. Her grades have often been near or at the very top of my class. But, she has been learning a lot and the class has not been as simple as she had thought it might.
Today, Brenda melted down at the end of the test. Time was up and just as Brenda was about to hand her test to me, she noticed that there was a page 6. She looked at me and asked for time to complete page 6. I told her no, that I had not been able to give students in the other period extra time, so it would not be fair to give her additional time. Moreover, the last page had one problem that was worth 2 of a possible 34 marks. There is absolutely no way that 2 marks will have any impact on her semester grade. Brenda has already demonstrated to me remarkable mathematical skills. She readily recognizes pattern and is proficient at explaining how the ideas connect. Despite all of this, Brenda broke down crying over not having gotten to do anything on page 6.
I'm not sure about this, but I'm guessing Brenda's breakdown has many more reasons behind it other than the math test she just took. Regardless, not finishing the test ignited her feelings and brought them to the surface. Since I don't know what's going on with her beyond my math class, it's not fair to say that the almighty letter grade is the main culprit here. But, the letter grade certainly has played a major role. It's as simple as this. If the test had no grade associated with it, would Brenda have left my class sobbing today?
Thursday, November 1, 2012
Striving for the "acceptable" grade (Part 1)
I had an experience recently in my honors math class that reminded me of this blog. So here I am again. But only for 15 minutes. Go.
I got an email a few weeks ago from our registrar saying that Jolene (not her real name, of course) was dropping the honors course and changing to the Algebra 2 course. "Wow," I thought. What was this all about? My gut feeling was that Jolene was doing just fine. Maybe not at the very top of the class, but certainly in the top half. (And I suppose it's contradictory of me to have used my grades as a way to think this through. Do I contradict myself? Okay, then I contradict myself.) From my observations of Jolene in class, I certainly did not notice her struggling to the point of giving up. So, to check on my gut feeling, I checked my online grading program (my school requires me to use one to my revulsion) and discovered that her grade at the time was an A-.
I immediately emailed Jolene's advisor writing that this was not a good idea, that Jolene was doing very well from a grade standpoint and according to my observations and impression of her in class. (As I only had 12 students in that particular section at the time, I very much trust my classroom impression.) Jolene's advisor, Liz (not her real name), wrote back saying that Jolene was spending so much time on her math homework that she wanted to drop the honors course so she could devote more time to her other classes. Jolene had been relying on other students, it turns out, for a lot of help, and always worked to get a perfect homework assignment.
This, on the surface, sounded like a very good reason to change courses, but, I replied back and suggested that she could likely spend less time and still earn a B. Furthermore, homework assignments in my class are not graded and I have no expectation that a student get every question correct by the day it is due. Rather, my expectation is that the student do as much as they can on each problem and get help as needed. (I had other discussions with honors students around the same time that made me realize I had not adequately communicated these expectations to my student.)
Of course, the main sticking point was the grade. I found out that Jolene's preference was to switch courses so that they could get an A in math and have more time to spend on other subjects. She mainly wanted to switch because she was concerned she might not be able to get an A in the honors course.
Jolene, Liz, and I met to talk this over. I emphasized to her that she seemed to have a very good grasp of the ideas, that her results were indicative of this, but that it was certainly possible her grade could be a B. I did my best to emphasize that I did not think her getting an A was paramount. My opinion was that the Algebra 2 course would be too easy and she would be bored and that, in the end, this would lead her to a less rich education. Liz, her advisor, supported me on all of this, and we devised a plan: she would take the next test before switching and use that to make her ultimate decision. (Again, something that was grade-dependent, but at least something the student would identify as tangible.)
What happened? You'll have to wait for my next post as my 15 minutes are up.
I got an email a few weeks ago from our registrar saying that Jolene (not her real name, of course) was dropping the honors course and changing to the Algebra 2 course. "Wow," I thought. What was this all about? My gut feeling was that Jolene was doing just fine. Maybe not at the very top of the class, but certainly in the top half. (And I suppose it's contradictory of me to have used my grades as a way to think this through. Do I contradict myself? Okay, then I contradict myself.) From my observations of Jolene in class, I certainly did not notice her struggling to the point of giving up. So, to check on my gut feeling, I checked my online grading program (my school requires me to use one to my revulsion) and discovered that her grade at the time was an A-.
I immediately emailed Jolene's advisor writing that this was not a good idea, that Jolene was doing very well from a grade standpoint and according to my observations and impression of her in class. (As I only had 12 students in that particular section at the time, I very much trust my classroom impression.) Jolene's advisor, Liz (not her real name), wrote back saying that Jolene was spending so much time on her math homework that she wanted to drop the honors course so she could devote more time to her other classes. Jolene had been relying on other students, it turns out, for a lot of help, and always worked to get a perfect homework assignment.
This, on the surface, sounded like a very good reason to change courses, but, I replied back and suggested that she could likely spend less time and still earn a B. Furthermore, homework assignments in my class are not graded and I have no expectation that a student get every question correct by the day it is due. Rather, my expectation is that the student do as much as they can on each problem and get help as needed. (I had other discussions with honors students around the same time that made me realize I had not adequately communicated these expectations to my student.)
Of course, the main sticking point was the grade. I found out that Jolene's preference was to switch courses so that they could get an A in math and have more time to spend on other subjects. She mainly wanted to switch because she was concerned she might not be able to get an A in the honors course.
Jolene, Liz, and I met to talk this over. I emphasized to her that she seemed to have a very good grasp of the ideas, that her results were indicative of this, but that it was certainly possible her grade could be a B. I did my best to emphasize that I did not think her getting an A was paramount. My opinion was that the Algebra 2 course would be too easy and she would be bored and that, in the end, this would lead her to a less rich education. Liz, her advisor, supported me on all of this, and we devised a plan: she would take the next test before switching and use that to make her ultimate decision. (Again, something that was grade-dependent, but at least something the student would identify as tangible.)
What happened? You'll have to wait for my next post as my 15 minutes are up.
Monday, May 21, 2012
This is a test. This is only a test.
Grades. Yuck. I don't like them. My students don't like them. Alfie Kohn doesn't like them.
Here I am sitting in my classroom while my Algebra 2 students are taking a "unit test". Why? Because I am supposed to assign each student a letter grade that is meant to represent their... what? Math ability? Feats of memorization? The ability to regurgitate what I told them? Their understanding of certain math problems on this particular day?
A test is a pretty easy way for a teacher to defend a letter grade. Compared to other forms of assessment, they do not take too long to create, correct, and grade. Math tests in particular tend to be easier since there is (normally) one correct answer and only a few different ways to arrive at that answer. It will probably take me two hours of work to correct and grade the test my students are taking right now.
But how valuable is it really? And I am in fact harming the love of learning that I want to instill in my students by giving this test? And if I think that I am, why on earth don't I stand up and say, "Stop! Put your pencils down and let's get something meaningful done."?
One, because I'm tired. Last night, when I sat down to write the test, I had a pretty good idea how long it would take me and by what time I would be able to let my head hit the pillow. As I said before, tests are easy. I want to spend time with my two-year-old and with my wife and I know how to write a test and how evaluate a test. It's a known quantity and is not scary for me. I feel pretty certain that after I finish this test, it will be a decent tool to help me assign semester grades to my students.
Two, I prefer to follow the paths of those who have gone before me. And all of my colleagues from all of my schools, as far as I know, depend on tests to determine grades as much, if not more, than I do. Frankly, it's a bit daunting to jump off the diving board if I've never seen someone else do it before me. If I try something totally new, something that no one I know has tried, then I run a greater risk of the experience not being meaningful or effective. I only have so many teaching days and if I lose a week, I don't get it back. If I know someone has tried a particular project, then I feel more confident. I have been searching for alternatives to tests, but so far, I lack the necessary gurus. And don't send me a web link. A web link is not going to help. I need someone to sit down with me, and explain what they did and how it worked and why they liked it.
Three, I don't know that my school would look very favorably on me not giving tests. I do that with my Advanced Mathematics class, but that is not a pre-AP class. In fact, the typical student in there is likely never taking a math class again. So nobody can tell me that tests are necessary to get them ready for some big standardized test to come. I believe, but am not sure, that if I did not give tests in my Algebra 2 class, that I would get a "talking to" by some one. I know for certain that I must give a final exam (which I was planning to write during this period, but, hey, this blog is better for my soul, right?). It may be that I have sufficient flexibility in the format of that exam that I could design something that is not so test-like. But, I have a fear that would not go over so well. Hopefully, my fears are irrational.
I am sure there are other reasons I continue to give tests. But, I don't want my posts to be too long. So, now I shall stop. The testing, however, will continue...
Here I am sitting in my classroom while my Algebra 2 students are taking a "unit test". Why? Because I am supposed to assign each student a letter grade that is meant to represent their... what? Math ability? Feats of memorization? The ability to regurgitate what I told them? Their understanding of certain math problems on this particular day?
A test is a pretty easy way for a teacher to defend a letter grade. Compared to other forms of assessment, they do not take too long to create, correct, and grade. Math tests in particular tend to be easier since there is (normally) one correct answer and only a few different ways to arrive at that answer. It will probably take me two hours of work to correct and grade the test my students are taking right now.
But how valuable is it really? And I am in fact harming the love of learning that I want to instill in my students by giving this test? And if I think that I am, why on earth don't I stand up and say, "Stop! Put your pencils down and let's get something meaningful done."?
One, because I'm tired. Last night, when I sat down to write the test, I had a pretty good idea how long it would take me and by what time I would be able to let my head hit the pillow. As I said before, tests are easy. I want to spend time with my two-year-old and with my wife and I know how to write a test and how evaluate a test. It's a known quantity and is not scary for me. I feel pretty certain that after I finish this test, it will be a decent tool to help me assign semester grades to my students.
Two, I prefer to follow the paths of those who have gone before me. And all of my colleagues from all of my schools, as far as I know, depend on tests to determine grades as much, if not more, than I do. Frankly, it's a bit daunting to jump off the diving board if I've never seen someone else do it before me. If I try something totally new, something that no one I know has tried, then I run a greater risk of the experience not being meaningful or effective. I only have so many teaching days and if I lose a week, I don't get it back. If I know someone has tried a particular project, then I feel more confident. I have been searching for alternatives to tests, but so far, I lack the necessary gurus. And don't send me a web link. A web link is not going to help. I need someone to sit down with me, and explain what they did and how it worked and why they liked it.
Three, I don't know that my school would look very favorably on me not giving tests. I do that with my Advanced Mathematics class, but that is not a pre-AP class. In fact, the typical student in there is likely never taking a math class again. So nobody can tell me that tests are necessary to get them ready for some big standardized test to come. I believe, but am not sure, that if I did not give tests in my Algebra 2 class, that I would get a "talking to" by some one. I know for certain that I must give a final exam (which I was planning to write during this period, but, hey, this blog is better for my soul, right?). It may be that I have sufficient flexibility in the format of that exam that I could design something that is not so test-like. But, I have a fear that would not go over so well. Hopefully, my fears are irrational.
I am sure there are other reasons I continue to give tests. But, I don't want my posts to be too long. So, now I shall stop. The testing, however, will continue...
Thursday, March 10, 2011
The Scoreboard
I recently came across this table. It is a table generated by a secondary school that the school sends to all colleges and universities to which the school's students apply. These are the cumulative GPAs for the Class of 2012 at this school. This is an actual thing, that is, I did not make this up.Why would a secondary school do this? Does this advantage students? What might a college admissions officer make of this?
What about the students? This is accessible on the school's web site (that's where I got it). If I'm a 12th grader at this school, then I'm in that list somewhere. What does that make me think? Is school a competition? Is this the scoreboard? Am I a winner? A loser?
I have no idea if other schools do this, but my guess would be that they do.
What do you think?
Thursday, February 17, 2011
I am the Gatekeeper.... are you the Keymaster?
The role of the letter grade as gatekeeper is yet another reason I am looking for something better.
At the end of my honors 9th grade math class today, one of my students asked me about moving up next year to the accelerated 10th grade math course (yes, we have a level above "honors"). This student, let's call him Ricardo, is a new 9th grader, that is, he was not in my school's 8th grade last year (my school is an independent K-12 school). He spoke of how when the year began, he felt mostly lost because the math curriculum at his last school was far behind ours. So, he explained, though he began the year in the C+/B- realm, his grades have steadily improved and so has his confidence and understanding of the material.
I agree with Ricardo's assessment 100%. However, his semester grade was a B and he earned a B on the semester exam. Our criteria for a student moving from the honors course to the accelerated course is a 95% and a student ought to have earned that without extraordinary effort. Essentially, for the student who wants to move up, the honors course should be easy.
At this point, it does seem like Ricardo is understanding the newer topics with more ease than was the case in the first quarter. In fact, his level of performance at the moment might be at the necessary level for the move he wants to make. But, is that enough? From a pedagogical point of view, if he shows a mastery of the course throughout the second semester, should that make up for his difficulties in the first semester? As the topics in the course build off of each other, should he show such a mastery in the second semester, it would show that he has now mastered the first semester topics, too.
However, from the grade's perspective, it may be too little too late (to use a boring cliche). His semester "average" was an 85. Thus, even if his average in the second semester is 100, he would average 92.5 for the year. He would fall short of the 95 benchmark. And, from his own admission, the first semester was not easy for him.
How much importance should really be put on that grade?
I do think our school is flexible enough to look beyond the letter grade and take the student's full performance into consideration. Also, the student could potentially make the move from honors to accelerated between the 10th and 11th grade year.
That's only one small example of how letter grades serve as keys to opening doors in education. The "best" example of this role of the letter grade is college admissions. Ricardo probably sees getting an A in honors math as not enough. Instead, he wants to get an A in accelerated math so that he can say he took the most rigorous courses at our school to impress colleges.
Do you see what I see? If this is Ricardo's thinking (or his parents' thinking), Ricardo is treating his math courses as steps on the way to college. The content of the courses is of no relevance. All that matters is that he does well in the hardest classes. Does he enjoy math? Does it spark his imagination? Does he explore topics in math in greater depth in ways that are not graded? Maybe, but the system does nothing... NOTHING... to promote this love of learning.
At the end of my honors 9th grade math class today, one of my students asked me about moving up next year to the accelerated 10th grade math course (yes, we have a level above "honors"). This student, let's call him Ricardo, is a new 9th grader, that is, he was not in my school's 8th grade last year (my school is an independent K-12 school). He spoke of how when the year began, he felt mostly lost because the math curriculum at his last school was far behind ours. So, he explained, though he began the year in the C+/B- realm, his grades have steadily improved and so has his confidence and understanding of the material.
I agree with Ricardo's assessment 100%. However, his semester grade was a B and he earned a B on the semester exam. Our criteria for a student moving from the honors course to the accelerated course is a 95% and a student ought to have earned that without extraordinary effort. Essentially, for the student who wants to move up, the honors course should be easy.
At this point, it does seem like Ricardo is understanding the newer topics with more ease than was the case in the first quarter. In fact, his level of performance at the moment might be at the necessary level for the move he wants to make. But, is that enough? From a pedagogical point of view, if he shows a mastery of the course throughout the second semester, should that make up for his difficulties in the first semester? As the topics in the course build off of each other, should he show such a mastery in the second semester, it would show that he has now mastered the first semester topics, too.
However, from the grade's perspective, it may be too little too late (to use a boring cliche). His semester "average" was an 85. Thus, even if his average in the second semester is 100, he would average 92.5 for the year. He would fall short of the 95 benchmark. And, from his own admission, the first semester was not easy for him.
How much importance should really be put on that grade?
I do think our school is flexible enough to look beyond the letter grade and take the student's full performance into consideration. Also, the student could potentially make the move from honors to accelerated between the 10th and 11th grade year.
That's only one small example of how letter grades serve as keys to opening doors in education. The "best" example of this role of the letter grade is college admissions. Ricardo probably sees getting an A in honors math as not enough. Instead, he wants to get an A in accelerated math so that he can say he took the most rigorous courses at our school to impress colleges.
Do you see what I see? If this is Ricardo's thinking (or his parents' thinking), Ricardo is treating his math courses as steps on the way to college. The content of the courses is of no relevance. All that matters is that he does well in the hardest classes. Does he enjoy math? Does it spark his imagination? Does he explore topics in math in greater depth in ways that are not graded? Maybe, but the system does nothing... NOTHING... to promote this love of learning.
Monday, February 7, 2011
Keeping up with the Joneses
In math, we say that 45 > 42 because 45 represents a larger quantity than 42. So, it seems fair to say that if Peter gets 42 points on a test and Claire gets 45 points on the same test then Claire did better than Peter. Right?
Hmmm... Suppose there were 50 points possible on my test. Suppose there are 10 questions and each is worth 5 points. Then perhaps Claire got 9 problems completely correct and 1 problem completely incorrect, and Peter got 1 point off of 8 problems. So, who did better? Is one large error better than several smaller errors? What seemed so clear now becomes murky.
In the "safe" world of adding up points earned and dividing by the points possible, Claire gets an A- (90%) and Peter gets a B (84%). But, if the above were true, it seems challenging to me to try to decide who did "better".
Keeping with the above scenario, Peter would have two "perfect" problems and 8 "imperfect" problems. What if Peter got full points on the problem on which Claire earned zero points? So, he understands that idea way better than Claire. That would also mean that Claire understands 8 questions better than Peter, but only in a small way on each.
Suppose, instead, the test were out of 214 points? How much of a difference is 3 points?
Comparing students to students is the real issue here. We, as teachers, do this all the time. The SAT does it. Colleges do it. Students do it. Why? To see who is better, or worse, or the same as us? How does that help my learning?
Let us keep Peter with his 84% and Claire with her 90%. What do these scores tell us about how they are doing overall? Not much. Those scores provide us only some measurement of how they did on one individual test. Perhaps Peter has never scored as high before. Perhaps Claire has never scored as low before. Now what? Does that diminish the value of Claire's score? Does that augment Peter's? Might we now say that Peter has, in a way, done "better" than Claire?
No, I go for Option Q2. With such scores on a test, do not be concerned with such questions as "Who did better on this test: Peter or Claire?" Rather, ask the question "What does Peter's performance on this test tell us about how Peter is doing at learning the ideas being tested?" Ask the same question of Claire. But don't bother with trying to make sense of comparing the two.
Hmmm... Suppose there were 50 points possible on my test. Suppose there are 10 questions and each is worth 5 points. Then perhaps Claire got 9 problems completely correct and 1 problem completely incorrect, and Peter got 1 point off of 8 problems. So, who did better? Is one large error better than several smaller errors? What seemed so clear now becomes murky.
In the "safe" world of adding up points earned and dividing by the points possible, Claire gets an A- (90%) and Peter gets a B (84%). But, if the above were true, it seems challenging to me to try to decide who did "better".
Keeping with the above scenario, Peter would have two "perfect" problems and 8 "imperfect" problems. What if Peter got full points on the problem on which Claire earned zero points? So, he understands that idea way better than Claire. That would also mean that Claire understands 8 questions better than Peter, but only in a small way on each.
Suppose, instead, the test were out of 214 points? How much of a difference is 3 points?
Comparing students to students is the real issue here. We, as teachers, do this all the time. The SAT does it. Colleges do it. Students do it. Why? To see who is better, or worse, or the same as us? How does that help my learning?
Let us keep Peter with his 84% and Claire with her 90%. What do these scores tell us about how they are doing overall? Not much. Those scores provide us only some measurement of how they did on one individual test. Perhaps Peter has never scored as high before. Perhaps Claire has never scored as low before. Now what? Does that diminish the value of Claire's score? Does that augment Peter's? Might we now say that Peter has, in a way, done "better" than Claire?
No, I go for Option Q2. With such scores on a test, do not be concerned with such questions as "Who did better on this test: Peter or Claire?" Rather, ask the question "What does Peter's performance on this test tell us about how Peter is doing at learning the ideas being tested?" Ask the same question of Claire. But don't bother with trying to make sense of comparing the two.
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