The Achievement Gap, Part One

Are the top so-and-so percent really that much better?

America’s children are falling behind. There are scores of news reports, data dumps, and teacher complaints that students are slipping. The most recent Nation’s Report Card found that reading has declined seriously, where the median student in 4th and 8th grade today is doing worse than students in 1992. For math, the news is a bit better, but has rebuked an upward trend from the early 2000s. Even the 90th percentile barely slips past the old scores.

By almost every metric, students across the nation are struggling. Everything from COVID closures, to a mental health crisis, to TikTok brain rot is getting the blame. Fewer students are reading outside of class, administration is absorbing costs, and kids aren’t being challenged with abstract or critical thinking.

However, college enrollment rates have been flat over the last decade. Competition to get into Ivy League schools appears to be the greatest it has ever been. Anecdotally, you’ll find horror stories of people with perfect GPAs and test scores being confronted with rejection from so-called “mid” universities.

You also see a lot more ‘whiz kids’ coming into prominence. Maybe an effect of social media, maybe there are simply more. Whatever the case, you can find high school dropouts raising millions or current students publishing with OpenAI. In the past, I’ve gone over how Ivy Plus-level universities make up less than a percent of high schoolers. Yet, they’re a hotbed for academic competition and stacked extracurricular profiles. How is it that the average student is reading worse than three decades ago?

Before we get into questioning the how and why, let’s first see if the achievement gap is real or not. Those other questions will be answered with another blog post.

A Mirage or a Miracle?

Let’s try a few different tactics to see if there’s a gap in achievement between the top portion of students and the bottom portion. Previous achievement gaps have been well identified as stratified by income and race. Quite credibly, “family income [is as strong] as parental education in predicting children’s achievement” (Reardon 2011).

This income gap has only grown over time, and I don’t see a reason why the trend could be changed now. Middle-class and above parents are able to afford tutors, produce better environments conducive to academic accomplishment, and employ concerted cultivation to connect their children with extracurricular activities.

However, what if we standardize these results? In fact, what if we look at just a few schools and see if students who are already strong are doing better across cohorts? The first method I’ll be using is examining school profiles for data about an academic achievement gap.

School Profiles

School profiles are documents created by high schools by counselors to provide information about the school to college admissions offices. They often include details of the grading system, reports on average GPA/SAT, and demographic details about the graduating senior class. With these details, we might be able to see that even within the same school, the students already at the top have gotten better over time. With that said, I’ll analyze the following schools based on what I can find: Phillips Academy Andover, Canyon Crest Academy, and Sharpstown High School.

Andover is a nearly $80k elite-level boarding school in Massachusetts. That said, Andover brings in a good chunk of students on scholarship, about 30-50% in any given year. Canyon Crest Academy is a top-tier public school in San Diego. Sharpstown High School is a Title I school in Houston where 96% of its students are eligible for free lunch. These three schools should provide a decent picture to show whether the top students at each school are improving over time compared to their peers.

Starting with Andover, the gap between the median GPA and the top decile cutoff is shrinking! Furthermore, the gap between the bottom decile cutoff and the median has remained consistent over the last decade. The class of 2021 saw a shock because of the pandemic, though it looks like the top decile wasn’t affected as much compared to the other groups. At least at one of the best high schools in the nation, there’s no obvious academic evidence of an achievement gap.

In addition to GPA estimates, Canyon Crest also lets us look at National Merit Semifinalists, a scholarship program based on scoring in the top 1% of PSAT scorers in a given year. If the proportion of semifinalists is increasing, we know that more students are entering this top 1% bracket. CCA last reported GPA distributions in 2023, so I’ll be working off interpolations from that profile. The red highlight is when the profile reported a weighted GPA instead of an unweighted GPA. The gap seems fairly consistent, but the switch to an unweighted GPA may be masking the issue. The gap during the weighted portion of the graph looks to be increasing, with the median barely making progress on catching up in the unweighted portion. At the same time, the bottom decile had a slight peak in 2021 (pandemic grading, probably) but has been trending downward since, while the top decile and median are consistent. For National Merit Semifinalists, the percentage of the student body with this achievement seems to be slightly increasing. There’s a decent dip for the class of 2022 who would’ve taken the PSAT in 2021 during the pandemic, which makes sense to me. If you ignore that class, there are about 2% more people with that award, or roughly 13 more people on average per year, past 2018. Overall, there seems to be relatively weak but possible evidence of an achievement gap worsening since the pandemic.

Sharpstown High School has an interesting backstory. It was featured in a 2012 episode of Frontline titled “Dropout Nation”. It was also part of the Apollo 20 program where Houston ISD worked with Harvard University’s Education Innovation Laboratory to develop programs targeting at-risk youth and low-income schools. Despite some missing data from 2014-2020, the top quartile and top decile are pulling away from the median and bottom quartile. The top decile of students is the only group to have a better average GPA at the end of the period.

Based on these schools, there’s probably something going on where the top chunk of students maintain their strong performance or improve while the median and bottom portions stagnate or fall behind. Let’s tackle another way to see if there are simply more “high achieving” students. Academically talented high schoolers often compete in academic competitions (well, duh!). If the share of participants in these competitions is increasing heavily over time, while the Nation’s Report Card is reporting slowdowns or decreases, this could be further evidence that an elite group of students is getting bigger. Most of these competitions cover STEM subjects, so that’s something to consider. Also, these competitions alone are getting more popular. Whether that’s a result of more people who are high skill, more people who are interested in these subjects, or more people pursuing them for college admissions remains to be seen.

USACO

I will not be doing mathematics competitions like the AMC, AIME, or USAMO because they employ cutoff thresholds to determine AIME and above qualification. With a relatively fixed number of participants who can be awarded some qualification, it makes it difficult to see if there’s an increase in the number of people capable of being ‘high achieving’. Instead, I’ll look at USACO medal awards, as they do award qualifications solely based on competition threshold scores.

Participation in the open contest grew by 10 times from the minimum to the peak in 2023. While anyone can compete in the bronze division, silver and up require scoring well in the previous division to enter. The number of silver competitors nearly 20x-ed at the top while gold saw a moderate increase, and the platinum division, created in 2016, remained steady. The open contest is usually held in March, so it’s a bit interesting to see the height of participation come right after the decline of software development job postings in late 2022. From individual reports, competitors also claim that the competition has gotten more difficult in recent years.

According to the NCES, there were around 64k CS (and related) degrees conferred in 2016 and 108k in 2022. I think it’s safe to assume that people who are aware of USACO and compete in it are probably fairly good at computer science, part of the top portion of computer science students, even. With a four-year lag, 201 participants above bronze in 2012 would be ~0.3% of graduates in their respective year. For 2022 graduates, it would be ~1.3%.

Though it would be great to have more recent and more historical data, I do think it’s noteworthy that the percentage of promoted medalists over CS degree graduates has increased sharply over the limited timeframe available. It shows that a greater proportion of graduates had relatively strong computer science knowledge in high school, enough to be in the top so-and-so percent of that competition.

So, is it real?

If I had more time, I would’ve gone through more schools and looked at more extracurricular competitions to confirm my intuition. Based on what I have so far, it’s clear that there’s a greater proportion of young people with strong academic skills and top-level talent in certain fields than a decade ago. Contrasted with overall standardized test score averages being flat or even down, there’s solid evidence for an achievement gap. The next post in this series will address the causes and consequences of this gap. For now, I’ll just enjoy my intuition being correct.