This second article on math tracking in our high school shows how tracking impacts grading and how that relationship can yield unintended consequences, causing students – especially those worried about affording college – to take less rigorous classes than otherwise. This article also shows how the problem of demographic imbalance in advanced courses is being obscured, letting the district overlook this inequity and leaving little need for the issue to be addressed.
To present this issue, we must first cover how GPAs are computed at the high school. This GPA Math is documented in the high school’s Program Planning Guide, but not everyone is familiar with how this works.
GPA Math
The GPA formula used at MHS starts with a basic 4.0 scale. Every year-long class contributes a certain amount to a student’s GPA based upon the student’s grade: A=4, B=3, C=2, D=1. This sum of these values is then divided by the number of classes. For example, a student with grades A, A, B, B, C for a year will have a GPA of (4+4+3+3+2)/5 = 3.2. Semester long and quarter long courses are scaled accordingly.
However, we want to incentivize students to take more challenging classes and avoid effectively punishing them for doing so. To this end, many high schools – including ours – use a weighted GPA. This involves assigning to each class an Instruction Level based upon the class’s rigor, or degree of challenge, and then indexing what each class contributes to a student’s GPA based upon that level of rigor. That indexing is called a Quality Point Index (QPI).
At MHS, most classes fall into one of these three levels of rigor (taken from the Program Planning Guide):
- Academic (A) – These classes are for students with achievement test scores generally between the 30th and 70th percentile. Classroom work depends upon outside preparation each day with class reinforcement. These classes will afford students a solid foundation to build upon as they move through their high school experience.
- Honors (H) – These classes are for students of high academic achievement. Students recommended to these classes typically have high grades and high scores on standardized assessments usually above the 70th percentile. Classroom instruction assumes that all students have the skills and motivation enabling them to do special reports and projects, etc., in addition to mastering the regular basic test and materials.
- Advanced Placement (AP) and High Honors (HH) – Students recommended to these classes typically have high grades and very high-test scores – usually above 95th percentile on appropriate standardized achievement tests. These students have also demonstrated a great interest in the subject with skills commensurate with enthusiastic independent work and exploration.
Different schools use different forms of weighting, but MHS weights class grades based upon this table:
For example, let’s again consider the student who earned grades A, A, B, B, C. If one of the A grades was earned in an honors class and if one of the B grades were earned in an AP class, the GPA would be (4.5+4+4+3+2)/5 = 3.5.
Here is a spreadsheet which may be copied and used to compute a student’s weighted and unweighted GPAs.
History of Math Tracks
With GPA math understood, let’s look at the history of math tracks in the district. Before the 2016-2017 academic year, the math sequence looked like:
For the main math topics in the high school (eg, Geometry, Algebra 2, Precalculus, Calculus), a student would have a choice of three levels of rigor: Academic (A), Honors (H), and either High Honors (HH) or Advanced Placement (AP). As the Program Planning Guide notes, “High Honors and AP courses are equally rigorous. A course carries the AP designation if its course content corresponds to the content of an AP test offered by the College Board.” College Board provides AP classes for Calculus 1 and 2 but not for Algebra 2 or Calculus 3.
For students of the 2020 graduating class, starting when they were in 9th grade, most HH classes were relabeled or eliminated. In most cases, such as in Precalculus, the only actual change was to change the Instruction Level. Changing the Instruction Level also reduced the Quality Point Index for these classes. In some cases, such as Precalculus, this left us with three classes of different levels of rigor, but two of them had the same instruction level: Precalculus, Precalculus H, and Trig/Calc H.
As there was no change to the classes themselves, this did nothing but add a penalty for any student taking the more rigorous of the two honors classes. Taking the more rigorous class puts the student’s GPA at risk with no increase in Quality Point Index to counter that risk. Students seeking to maximize their GPA, perhaps in hopes of receiving more merit-based financial aid from colleges, are incentivized to take the easier – and less challenging – honors class.
The fact that the two honors-level classes are actually at different levels of rigor can be confirmed by reviewing the prerequisites of the two Honors-level Precalculus classes as well as how each of these two classes fulfills the prerequisites of subsequent courses. To be recommended for Precalculus H, a student must have received either an 80+ in Algebra 2H or a 75+ in Algebra 2/Trig H. To be recommended for Trig/Calc H, a student must have received either a 95+ in Algebra 2H or an 85+ in Algebra 2/Trig H. This shows that Trig/Calc H is more challenging than Precalc H.
Students who complete Precalculus H can move on to AP Calculus AB with a 90+. Students who complete Trig/Calc H can move on to AP Calculus AB with an 80+ or to AP Calculus BC with an 88+. This makes clear the expectation that students will cover more material, and be better prepared for more advanced work, taking the Trig/Calc H class in contrast to the Precalculus class, thus again documenting the more advanced nature of Trig/Calc H over Precalculus H.
This can be done for any pair of honors-level classes to determine which is the more rigorous.
Our district’s Vision Statement tells us that we must “support our students to become high academic achievers.” Having classes with markedly different levels of rigor and challenge and the same quality point index will motivate students to take the easier of the two courses. That this is more likely to be an issue for those worried about paying for college makes this an equity issue; students with less of a need for financial aid incur less risk taking the more advanced class.
Concerning why there continue to be three classes, consider the history of Algebra 2 at MHS.
For a year or two, Algebra 2 had only Academic and Honors level classes. This created problems for many students who found Academic insufficiently challenging, but Honors too much of a challenge. Eventually, this was corrected by adding Algebra 2/Trig H. This replaced the more rigorous course, and Algebra 2H became again a true honors-level course. Despite Algebra 2H and Algebra 2/Trig H both being honors-level, the prerequisites again show a clear difference in rigor.
Recent Changes Add to the Disincentive
In 2024, the situation became even worse. No longer did MHS merely have multiple classes with the same Quality Point Index but different levels of rigor: a new class was introduced with an AP-level Quality Point Index but where the prerequisites show that it is of less rigor than an honors-level class.
The new class is Advanced Placement (AP) Precalculus, a class provided by College Board. As an AP class, it has the maximum Quality Point Index. However, by comparing the prerequisites of the two classes again, we can see that this class is less rigorous than the Trig/Calc H class. Moreover, internal discussions within the math department (not yet reflected on the Program Planning guide) indicate that the prerequisites for AP Calculus BC require a student to take either Trig/Calc H or AP Calculus AB. That is, while Trig/Calc H prepares a student for the more advanced Calculus class, AP Precalculus does not.
Despite that, an A in the AP Precalculus class will be worth more to a student’s GPA than an A in the Trig/Calc H class.
Equity Requires a Fix
The current assignment of Instruction Levels offers an incentive for students to avoid more challenging classes. This incentive is stronger for students who are more worried about affording college, as a student’s GPA can play a large role in colleges’ determinations of financial aid and admissions. Our district’s Vision Statement does not state that we will “support only our financially comfortable students to become high academic achievers,” but that’s what our Instruction level assignments for our math classes achieve.
Having classes of different degrees of rigor all labeled with the same Instruction Level obscures – and avoids accountability for – the disparity in demographics of the students taking these classes. If more students of color are pushed into AP Precalculus instead of the more rigorous Trig/Calc H, for example, the district can claim a “win” in that these students are in a more rigorous class. That “win”, unfortunately, would be an illusion.
When it was determined that having only two Instruction Levels for Algebra 2 was a problem for many students, this was fixed. We must now go further and assign more fair and equitable Instruction Levels to our math classes that more honestly reflect their different degrees of rigor and challenge.