Assigning Middle School Grades and Occam’s Razor: A Grading Exercise
In the Middle Ages, William of Occam made a claim that has come to be known as Occam’s Razor: pluralitas non est ponenda sine necessitate. It means that one should not resort to complexity unless it is necessary, and it is a warning against making anything unnecessarily complicated. I thought about Occam’s Razor as I approached writing this blog, and I wonder if it applies to assigning letter grades to students in a mastery-based school. I would be interested to know your thoughts on that. Perhaps after this exercise in assigning grades you will be able to speak to it.
But more immediately, and more concretely, I have an exercise in assigning letter grades to seventh grade students in a variety of academic situations, and I would like your input and thoughts to help us make grading in middle school better. For each of these students, who are fictional but resemble actual students, please assign the grade A, B, C, D, or F and explain why. The rationale behind determining grades is important because in order to formulate a grading policy for middle school, there must be a rationale that can be articulated and can apply to every student. A clearly stated and defensible rationale ensures that assigning grades is neither arbitrary nor capricious.
Please provide the grades and the rationale you use to assign them in the blog so everyone can see your thinking and anyone can comment on it. When we set out to make sense of assigning grades in middle school, we believed we had a rational plan that could apply to everyone and represent accurately middle school students’ academic attainment. There may be other ways of thinking about grades for middle school students, however, and I am interested in seeing them.
There are three rules for this exercise. First, in some way, math grades for seventh graders must incorporate what Illinois says seventh grade students must know and be able to do in math. Secondly, every student must have a grade, but simply assigning grades without providing the rationale behind the assignment will not further this discussion and probably cannot be considered. You can approach the rationale from the individual cases or you can approach assigning grades by using an articulated rationale, but to be considered in our internal deliberations, there must be a clearly stated rationale that articulates to each grade assigned. Moreover, not having a formula for calculating grades is unfortunately not an option because it puts at a disadvantage our students who want to apply to selective enrollment high schools. When our counselor fills out those applications, the only representation of school work the prospective high school wants to see is a letter grade. Thus every student in this exercise needs a grade. Finally, the data below are all the data given and no other considerations can be made. It seems reasonable to allow teachers to consider, for example, how hard a student tried. Of course effort matters, but grades are a reasonable proxy for effort. That is, if a student works very hard at learning, the outcomes of that learning should show up in results, and by measuring results we are measuring effective effort.
For the purpose of this exercise we will assume that none of these students qualifies for special education. So what grades would you give each of these students at the end of the school year? The first one is easy.
Seventh Grade Student 1
Mastered 90% of seventh grade math in the OLS
Mastered 95% of Illinois Math 7 Standards
Seventh Grade Student 2
Mastered 90% of fifth grade math in the OLS
Mastered 40% of Illinois Math 7 Standards
Seventh Grade Student 3
Mastered 90% of fifth grade math in the OLS after working two years at fifth grade level
Mastered 40% of Illinois Math 7 Standards
Seventh Grade Student 4
Mastered 90% of sixth grade math in the OLS
Mastered 75% of Illinois Math 7 Standards
Seventh Grade Student 5
Mastered 90% of eighth grade math in the OLS
Mastered 80% of Illinois Math 7 Standards
When I try to complete this exercise, articulating a rationale that could be evenly applied to all of these students resulting in a grade is complex. The question to answer is given that there is value in OLS math, and given that seventh grade letter grades must reflect what Illinois says all seventh graders should know and be able to do, how can that value and grade level attainment be captured in a single letter grade? Our solution to this problem was an Occam Razor solution, holding that middle school grades reflect grade level skills and ability, but I am eager to consider other ways of thinking that are parsimonious but at the same time sufficiently complex to cover all the students in this exercise. There could be a rationale that accounts for the various academic situations represented above that is as sharp as Occam’s Razor. I look forward to your solutions to the problem of assigning middle school grades in a mastery based program.
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Seventh Grade Student 1
ReplyDeleteMastered 90% of seventh grade math in the OLS
Mastered 95% of Illinois Math 7 Standards
"A"
Seventh Grade Student 2
Mastered 90% of fifth grade math in the OLS
Mastered 40% of Illinois Math 7 Standards
"F"
Seventh Grade Student 3
Mastered 90% of fifth grade math in the OLS after working two years at fifth grade level
Mastered 40% of Illinois Math 7 Standards
"F"
Seventh Grade Student 4
Mastered 90% of sixth grade math in the OLS
Mastered 75% of Illinois Math 7 Standards
"C"
Seventh Grade Student 5
Mastered 90% of eighth grade math in the OLS
Mastered 80% of Illinois Math 7 Standards
"B"
For students 2,3,4,5: it does not really matter how much below grade material they have completed - this is a grade for 7th grade material, so it has to be based on 7th grade OLS and Illinois Math 7 Standards.
Student 4 probably should have been promoted to grade 7 math earlier.
Student 5 probably was promoted too early or has some problems with test taking.
Thanks so much. I appreciate your taking the time to share your thoughts.
ReplyDeleteIt's an important observation that students' grade level attainment could be affected by previous placement and promotion decisions. That's why when students enroll at CVCS now, we place them on grade level and remediate any deficiencies they might have.
I wrestled with this question over the weekend, and hoped that by Monday I would have a brilliant response! But this is still a difficult question to answer. Here are my decisions:
ReplyDeleteStudent 1- A, because the student is ready for 8th grade material
Student 2- C, because the student made a year's worth of growth in OLS course work and shouldn't be penalized with a grade lower than a C, for being behind from the get-go. If the child is going to be penalized with a grade lower than a C, we shouldn't put him in a level 5 class to begin with, setting him up for failure. But a higher grade also isn't accurate, since the child is not above average in his understanding of level 7 curriculum.
Student 3- F, because this student did not make a year's worth of growth, and should have been having regular discussions with his teacher about a plan to catch up.
Student 4- C, for the same reason as student #2. A year's worth of growth was made in OLS work.
Student 5- B. This student concerns me. If the child is ahead of grade level, and truly mastered 90% of his eighth grade material, then mastering the 7th grade material in achievement exercises should have been easy, especially considering the opportunity for remediation and make-up sesssions if a skill was difficult. The fact that this child did not master more than 80% of the 7th grade Achievement objectives with the opportunities for practice and review causes me to wonder if the child has really mastered 90% of the 8th grade OLS objectives.
School and grades...they seem to go hand-in-hand. What do grades actually represent though? When a teacher gives a student an A does it mean they know the material? Does it mean they completed all homework or are just savvy test takers? In addition, there's a certain subjectivity to the entire grading system. The student "on the fence" who has worked hard generally receives the higher grade. Grades just don't effectively measure what students know.
ReplyDeleteImagine the joy of finding a school that evaluates student work based on what they know. It seems a travesty to be forced to revert to a system that doesn't work in the first place. It's as if CPS is asking us to turn apples into oranges. In the future, I hope we will be able to send our students to selective enrollment High Schools without converting our grades into a letter grade.
Since we have not been granted that yet, the next best thing is to have sound criteria on which to make conversion decisions.
Grades should be based on 3 things:
1. the mastery of grade level math & Language Arts skills as determined by the Achievement Series exercises
2. progress through and mastery of their OLS program
3. student effort or even more radical, student character.
Character qualities that are important in our school would be things like perseverance, determination, cooperation, meeting deadlines, time management, responsibility, and more. Since students are at home 95% of the time with their Learning Coaches, it makes sense to allow the Coach to help determine that portion of their grade.
It seems reasonable that 40% of their grade be based on their Achievement Series exercises, 40% on their OLS progress, and the final 20% be based on character.
Assigning the first 40% would be easy because it's easy to see how a student performed on the Achievement Series exercises. The next 40% would be more challenging. Some sort of scale could be established for OLS completion. If students are at or above grade level and on track with their progress, they receive an A. Students would earn a B for being at grade level and within a certain % of the expected range. If the student is even further below or a grade level below but making steady progress than a C is fair. Those below grade level and not making great progress earn a D, and those significantly below grade level and whose progress is a serious issue earn an F. Those exact % would have to be determined.
Kim,
ReplyDeleteThank you for taking the time to post your solution to a problem I too find difficult.
It sounds like what you are saying is a logarithm is unnecessary, but each student is considered according to guidelines that would go something like, on target but below grade level results in a grade no lower than a "C;" above grade level but not mastering grade level content looks to grade level content rather than the OLS. Is that fair?
What is interesting to me is if we had a student above grade level in the OLS and mastering grade level content and a student at grade level in the OLS and mastering grade level content, we would only need to rely on mastering grade level content. That is borne out in the case of student 5, who was in 8th grade OLS but not mastering grade level content. Thus the buffer students had working below grade level is unavailable to the student working above and by extension would be unavailable to the student working at grade level in the OLS but not mastering grade level skills.
It's also interesting that a seventh grade student can use fifth grade curriculum to avoid a failing grade. Not using OLS work undervalues it, but at what point are undervaluing grade level work?
I see the argument for using student progress in the OLS to buffer their grades as a way to reflect the value of their OLS work. We would still need to think through what to do with a seventh grade student mastering 73% of fifth grade OLS content and 40% of seventh grade standards.
Thanks again for the post. It really made me think, and I think it advances our discussion.
Dear December 7 Anonymous,
ReplyDeleteI could not agree more that grades historically have been unreliable measures of what students have learned. Does an "A" in our eighth grade algebra mean that a student in another CPS eighth grade student earning an "A" in algebra has learned the same thing to the same extent? Probably not.
I would also gladly welcome the day when CVCS students are evaluated based on their accomplishments rather than on a single letter grade attempting to reflect those accomplishments. There's a larger societal issue here of reducing students to test scores and schools to test results. As I have written before, I appreciate the focus on what students have learned and holding schools accountable for teaching so that students learn, but we could have that focus and accountability without the reduction to a number or letter grade. But that's the world we currently live in.
One observation and one question to your solution. If we say that OLS counts as much as grade level performance, then potentially fifth grade OLS math is of equal value to seventh grade standards. Or if students are below grade level but making "steady progress," fifth grade OLS could count for more than grade level performance. Student 2 would get a "C" if we could use 40% OLS and 40% grade level performance and the student got 90% of the character grade. Less than 90% for the character portion would require that fifth grade OLS math count more than seventh grade standards for a seventh grader.
I worry that including a character grade issued by a Learning Coach as part of an academic grade would further erode the reliability of grades. A 90% for one student might be a failing grade in one family but 100% in another.
Yet you make a strong point about the importance of character, particularly in representing our students to selective enrollment high schools. What if we had a separate "Work Ethic" grade that included all the virtues you mentioned, assigned by the Learning Coach, that showed up on students' report cards?
Thanks so much for writing. You have introduced an important idea in the discussion.