Unprepared students suffer comprehension gaps after skipping math levels

Graphic by Skyler Mao

Percentage comparisons for drop numbers of math levels in SHS between 2017-18 and 2022-23.

In the past decade, the number of students skipping to higher level math classes at the school has spiked dramatically — a trend that math teachers say has hurt overall understanding of the subject, especially when combined with pandemic-related learning loss. 

According to the Western Association of Schools and Colleges (WASC) — an accrediting commission which regularly reviews Saratoga High — between the 2005-2006 and the 2022-2023 school years, the percentage of students taking Algebra 1 has dropped from 12.7% to 4.9%, demonstrating a shift toward more students taking higher-level math courses earlier in their high school years. 

Math teacher P.J. Yim, who first started teaching here in 2008, recalls that prior to 2013, students almost never skipped math levels other than one or two exceptional freshmen taking Precalculus Honors.

“When I first saw sophomores in [AP Calculus] BC, it was almost certain that they were the best math students. However, that’s not the case anymore,” Yim said. “We have kids who don’t know basic algebra taking BC and I mean — what’s the purpose of that?”

To “skip” a math level, students can take a summer course that demonstrates math proficiency in the subject they want to skip. Alternatively, in 5th grade, students can take the Northwest Evaluation Association (NWEA) exam as a way of being placed in a higher math level, such as Algebra 1, at the start of middle school.

In his experience, Yim has seen that most students who skip even just one math level by taking a summer course (for example, by taking Algebra 2 during their freshman year, taking Precalculus over the following summer and then taking AP Calculus BC during their sophomore year) barely receive passing grades in his classes. Yim attributes the skipping of math levels mostly to peer or parental pressure. 

“You should only skip college and try to get into the NBA if you’re going to be a star player, not a benchwarmer,” Yim said. “So what I don’t understand is why students will just skip an entire year’s math class by taking a summer school and not obtaining complete mastery.”

When skipping classes such as Geometry and Algebra 2, students can miss critical concepts that teachers in later subjects — including Precalculus and Calculus — sometimes end up needing to reteach. By spending a significant amount of time tailoring information to students who need more review with foundational concepts in the general class, Yim finds he loses vital class time that could instead be used to teach new concepts to the students who are better prepared to learn Calculus. 

Yim argues that certain courses like Calculus should have stricter and enforced prerequisites, such as having to take Precalculus in person. Too often he has seen that an A from an online course is basically a “fake A,” and an in-person course is necessary to ensure that students are capable of handling the curriculum. By doing so, this requirement would prevent unprepared students from making bad decisions.

“I’m always rooting for my students to do their best every single time,” Yim said. “I want them to prove me wrong, to take the most challenging courses, and I want to trust that they will be prepared for that course. But being unprepared and making bad decisions is just irresponsible.”

Pandemic grade inflation encourages skipping and exacerbates learning gaps

Adding to these issues, the COVID-19 pandemic had a detrimental impact on math scores — and more broadly, math proficiency — nationwide. An article from NBC reports that math scores in the National Assessment of Educational Progress, conducted by the National Center for Education Statistics, dropped by 8 points over the pandemic; a 10-point drop is equivalent to being an entire year behind in material, showing just how far nationwide math proficiency declined in K-12 schools.

SHS is not exempt from this trend — many students have suffered greater gaps in comprehension as a result of the pandemic and yet continue skipping math levels after they returned to in-person learning two years ago. Yim has seen that many students falsely overestimate their mathematical abilities and skip to math courses that were unsuitable for them because online learning generally provided less rigorous coursework and inflated their grades.

Due to learning losses caused by the pandemic, many math teachers have had to modify their curriculum post-pandemic in order to fit in review material, leading to a less than sufficient scope and mastery of the material for students. 

Another major factor for the dropoff in students’ math abilities was online cheating, Yim said. He said that some students would struggle their way through math courses by using online tools and outside resources for homework and take-home tests, yet they still earned good grades due to cheating and less rigorous grading. 

“I had kids in AP Calculus BC who barely could do anything and could never answer any of my questions in class,” Yim said. 

Meanwhile, looking at the homework assignments, those same students produce work that “only people who have already taken Advanced Calculus would even think to do.” This substantial difference in performance implied that students cheated in order to complete assignments.

When students cheat or take significant shortcuts in math, he said, it undermines the solid foundations they should be building in the subject. He sees the result of this in his Calculus BC classes, where a substantial number of mistakes he sees on tests are not misunderstandings of advanced concepts, but rather, basic algebra mistakes that reveal incomplete mastery. Having a weak understanding of a single concept, such as quadratics from the middle school 7B/8 course, can hinder students’ ability to follow along with the rest of the curriculum, he said.

Consequently, since many students base their sense of curriculum mastery on their grades during online learning, they acquire a false sense of their mathematical capability, further leading them to overreach in their course selections for the following years.

Not only is this overreach detrimental to students, but it also affects logistics for the school’s math department and the guidance department since a large number of students drop out of difficult classes early in the fall semester. For example, in the 2021-22 school year, many Algebra 2 Honors classes experienced a heavy drop rate, affecting the schedules of many students that didn’t even request a change. During the 2022-2023 school year, 14% of Algebra 2 Honors students dropped the class.

This trend can also be observed in other math classes as well. For instance, Calculus BC experienced an astonishing 22% drop rate in the 2022-2023 school year.

There were 124 students who initially signed up for Calculus BC that year. The usual number is anywhere from the high 70s to the high 80s. Yim said people were “dropping out left and right.”

Yim hopes that as time passes, the lingering effects of COVID-hampered math education will start to die down.

Peer pressure fuels long-term math level trends

Although Yim argues that the pandemic was a factor contributing to students skipping math levels in recent years, there is another cause that existed long before the pandemic and still remains today: peer and parental pressure.

Given the competitive culture in the school, many students feel that they are obligated to sign up for difficult classes. As a result, WASC reports that “students’ workload may be more stressful due to taking more AP classes, tests.”

Junior Neha Natu is one of many students who signed up for a challenging schedule during the 2022-2023 school year. She took Precalculus Honors during freshman year after taking Algebra 2 Honors over the previous summer, being partially influenced by peer pressure. Natu described her experience in Precalculus Honors as “a breeze,” though she partly attributed her success to her teacher’s tests being easier than expected.

“Initially, a friend of mine talked to me about taking Algebra 2H during the summer, and I decided to make this skip in order to fast forward through the levels of my math in high school,” Natu said. “I was confident in my intelligence, so I didn’t think too much about it.”

By skipping Algebra 2 Honors,  Natu found she didn’t have the needed foundation during her sophomore year when she was taking Calculus BC; the difficulty of the course material as well as the intensity of the workload was nothing like what she had experienced before. Natu recalls that she sometimes skipped her Chemistry Honors class in order to study for Calculus BC tests and generally felt overwhelmed and stressed. However, despite her struggles, Natu believes that she would still make the same decision if she could travel back in time.

“It was definitely challenging, especially adjusting to the course pace and level we were going at,” she said. “But these were all valuable because it taught me about overcoming challenges, which is really important. I don’t think peer pressure is good, as it may lead someone to further stress that they are not ready for. However, if an individual believes that they can succeed jumping forward, then they should take the challenge.”

For his part, Yim thinks certain students are capable of jumping a level as long as they are fully prepared for the workload and difficulty of the class. 

A prime example is junior Ian Kim, who has taken Multivariable Calculus at West Valley College in his first semester of junior year. He skipped Algebra 2 by studying asynchronously with his math tutor during the summer between eighth and ninth grade, which prepared him for Precalculus Honors during freshman year. To comprehensively learn the material in a short period of time, Kim worked extensively with his tutor to get as much practice as he needed — which he thinks is the primary difference between him and many other students who also took summer courses but struggled afterward.

Furthermore, while choosing courses for high school, Kim strategically planned the intensity and rigor of his freshman year courses. He compared the two math classes, Algebra 2 Honors and Precalculus Honors, using his older brother’s notes and syllabi to see if he would be missing any important concepts by skipping Algebra 2 Honors.

“When I was looking between the two, I realized that the concepts covered in Algebra 2 were also covered in Precalculus [such as trigonometry and series]. The main difference was the pace of the two classes,” Kim said. “Of course, Precalculus covered less of Algebra 2 and expanded more on additional concepts. I wanted to make a leap to challenge myself, so I enrolled in a course to help me with the jump.”

Kim emphasizes that his decision was made out of personal choice and not due to peer or parental pressure. 

When looking at students as a whole, Yim has seen a consistent stigma applied to those who sign up for a regular version of class.

“People make assumptions like: ‘You’re in a regular class, and therefore you must be XYZ,’” Yim said. “I don’t think like that. All I care about is how hard you’re working.”

Yim emphasizes the importance of listening to teachers when they recommend math courses for students, who even spend time talking to each student and advising them on courses to pursue in the future. He finds it frustrating that some students may ignore their teacher’s advice and take a class that they are underqualified for.

The ability to skip math classes was originally designed to challenge students who would benefit from the ability to engage with harder courses. However, throughout the past decade, this system has developed into a futile competition of selecting the highest level classes rather than the ones that help students actually learn, according to Yim.

“If you’re completely misplaced, I think signing up for classes appropriate for you is fine,” Yim said. “But when you begin to do it because other people are doing it, that’s the problem.”