Just how imperfect is it?

  • Published in MyView

By Peter Kulis

Anyone with a student at Harwood is familiar with the student progress report that provides grades with 0.1 precision. The 0.1 precise grades appear highly accurate and readymade for class ranking and the mathematical analysis to determine such things as National Honor Society, insurance discounts, college admissions and potential merit aid awards in excess of $100K. And this year the Sugarbush pass, which was provided to the top 12 ranked students from each class after the grades were calculated to a further razor-thin 0.01 precision.

Unfortunately, what few understand is that hidden behind the veneer of 0.1 numeric precision is an inaccurate grading system which the Harwood leadership team admits uses numbers that are not mathematically accurate and does not follow basic mathematical accuracy rules. A system that college mathematicians say misleads and misrepresents with one professor describing the Harwood system as a "misuse of statistical thinking." A system that college admissions say lacks important detail, denies students their best admission and merit aid opportunities, and forces Harwood students to take and submit SAT/ACT scores to all colleges including those that are test-optional. A system that greatly overstates achievement for some and greatly understates for others making decisions based on class ranking and mathematical analysis little more than a roll of the dice – an invisible problem for which Harwood's school profile will be impossible to help regardless of how detailed it might be.

NEVER MEANT TO BE NUMERIC

To understand how these inaccuracies came to be, it is important to understand that Harwood's proficiency grades were never meant to be numeric, which is why two years ago student progress was reported as nonnumeric descriptive categories: Beginning, Emerging, Proficient, Advanced. However due to new software system requirements last year, the grades were provided the numeric aliases (1, 2, 3, 4), not because they were accurate but it was easy to do. The leadership team concedes they are not accurate stating that the amount of achievement in a 4 is not twice a 2. Similarly, the amount of achievement in a 3 is not midway between a 2 and a 4 as the numbers indicate. Consequently, math on these aliases is impossible but casually dismissed by the leadership team, "It is not a perfect fit, but this is how the data base is utilized."

Just how imperfect is it? Based on Harwood's grading documentation, which converts the limited 1-4 system into a granular 100-point achievement scale (1 = 64, 2 = 79, 3 = 95, 4 = 100), one can see that actual achievement in the 1-4 aliases does not increment in equal steps as required for accurate math. Consider student Amy with grades of (3, 3) and student Bobby with grades of (2, 4). In the current 1-4 system, Bobby would have the higher summary grade, but using the more accurate 100-point scale, the grades and ranking are turned upside down with Amy having the higher summary grade. An error of 13 percent, which for college admissions is quite significant.

ADDITIONAL PROBLEMS

Unfortunately, there are several additional problems. The first is that Harwood subjectively weights assignments based on timing versus assignment rigor. At Harwood, all assignments purposely have the same rigor and therefore a score of 4 on the first assignment demonstrates the same exact achievement as a 4 on the last. However, due to Harwood's time-based weighting, the effect is that Amy with grades of (3, 4, 2) and Bobby with grades of (2, 3, 4), both with the same scores but in a different sequence, will have final grades differing by 18 percent. Even though their academic achievement is identical, Amy with the high early grades but lower late grades, due to sickness or other, will be unfairly penalized making her potential $100K merit scholarship far less likely.

The second is that Harwood uses full-year proficiency expectations (as opposed to the commonly used semester expectations) where students in full-year courses are expected to reach Proficient but students in single-semester courses are expected to only reach a score of Emerging due to the reduced time. These disparate grades are then illogically equally weighted and averaged to arrive at a cumulative grade used for ranking and mathematical analysis. The effect of this is that Amy, who took two single-semester courses, as opposed to Bobby, who took the credit equivalent one full-year course, is in essence penalized 33 percent per class, bringing down her final grade and class ranking thus making the Sugarbush pass an impossibility.

The third and perhaps most significant issue is the fact that the grading system is ignoring basic mathematical accuracy rules and providing grades to an unjustified level of precision. Harwood's limited 1-4 grading system naturally has a very high potential of error (±25 percent as compared to nearly ±1 percent in a 100-point scale). This fact coupled with the reality that students are only graded three to five times per year, means that even a single error, which occurs more than anyone wishes, greatly impacts a student's summary grade but is hidden behind an implausible 0.1 accuracy. Mathematicians agree that ignoring these rules and providing grades with 0.1 precision is dishonest, misleading the end-user as to how uncertain the grades truly are. Incredibly, the leadership team understands this problem but has stated in essence that mathematical accuracy rules do not apply to the Harwood system. In other words, accuracy is not important.

To be clear, unlike the Harwood community who is perhaps reading about these problems for the first time, the HUUSD central office and leadership team are fully aware and have been for quite some time. The only thing more surprising than the overwhelming verifiable evidence is the disinterest of the leadership team to discuss or to explain why. To paraphrase one leadership team member, "[He's] not interested in the mathematical accuracy of the system but rather the philosophy of learning." Given the critical decisions at stake that require highly accurate grades, let's hope they all change their minds, become interested and provide an opportunity to discuss. Our students deserve it.

Kulis lives in Waterbury.