# What is more valuable to learn, math or English?

In our last post, we looked broadly at the value of an education by analyzing income data for different degree types. Here we’ll take a deeper look at the value of different types of *educational content*, specifically math and English, with the goal of quantitatively measuring how they affect students’ long-term outcomes in Washington state.

We will start by looking at the impact of various factors (including math and English SBA scores) on postsecondary *enrollment.*

# Data sources and model

We’ll start with data from Washington’s Educational Research Data Center (ERDC), which provides detailed postsecondary enrollment data broken out by a large number of factors, such as high school and demographic group. We then connect this up to K-12 enrollment and assessment data from OSPI, and see how well we can predict college enrollment.

How well does it work? It turns out that with the information we have, *we can predict college enrollment pretty accurately at the student-group level*. As an example of our accuracy metrics, our “Bachelor’s enrollment” model has an R² of 0.84 and a mean absolute error (MAE) of 4.1%. What does this mean? If we take a specific group, such as “low-income students at Roosevelt High School”, it means that on average we can predict the percent of students enrolling in a Bachelor’s degree to within 4%. Not bad! This level of accuracy is important for us to have confidence in the rest of our model outputs.

Finally, we can connect up our enrollment model with some relatively simple completion models (how likely students are to graduate) and our long-term earnings to data to quantify things like the impact of math scores on earnings.

At a high level, our final model looks like this:

# What factors impact college enrollment?

Before diving into earnings, let’s take a quick look at some of the factors that predict college enrollment. Below I show a few plots that show how college enrollment into Bachelor’s programs varies as a function of a few important variables (while holding everything else constant).

We can quickly see a few things from this chart. The first is that math proficiency is a **much** larger predictor of college enrollment than English proficiency. Surprisingly, it is even a stronger prediction than high school graduation rates! Finally, we see that the percentage of low-income students at a school has a big negative impact on college enrollment, even after controlling for all of our other variables. This is consistent with a lot of our previous analyses, which showed that schools with a lot of low-income students tend to have lower academic outcomes for *all* enrolled students.

To put this data in context, let’s take a quick look a specific student group (low-income students) across all schools in Washington and see how taking them from completely “not proficient” to “fully proficient” (as measured by their 11th grade SBA results) would affect their odds of enrolling in a Bachelor’s program:

Before moving on, it is worth checking if our results match previous research on this topic. It turns out the US Dept. of Education performed a very thorough, large scale study on what drives college completion, and found that high school math was the biggest factor. In fact, they did a detailed course analysis and concluded that going “*one step beyond Algebra 2 doubles the odds that you will earn a bachelor’s degree.*” This aligns very well with our results.

# What does this mean for long-term outcomes?

After measuring how standardized test scores improve the odds of getting a college degree, we can combine it with a lifetime earnings dataset we recently analyzed to estimate the impact of subject matter knowledge on long-term incomes. To calculate the total impact, we simply add up the effects of subject matter knowledge on each level of educational attainment (Associate’s, Bachelors, Baster’s, etc.) The summary is shown below, where we’ve specifically analyzed data for the “low-income” student group. The key result:

*Taking a low-income student from completely “not proficient” to “fully proficient” on their math exams is worth over $650k in lifetime earnings.*

# Comparisons to previous research

At a first glance, these results seem pretty surprising. $660k is a lot of money! Given that, it is worth stepping back and comparing our results to previous research on this topic. In particular, there are two very relevant studies. In 2014 Raj Chetty’s group at Harvard connected up academic records of over 2.5M students with their adult tax records and estimated the impact of test scores on earnings; the full details are here. The Washington Institute for Public Policy (WSIPP) did a similar study focused on Washington state and it is covered in their 2019 technical documentation. A comparison of all three results is shown below. **In short, our results very closely match the results from the two other analyses. **The agreement between the three studies is impressive, especially given that all three used completely different data sources.

# What does it all mean?

The size of the impact of math knowledge raises a few important points:

*Even though math is far more important for later success than English, Washington does a far worse job of teaching it.*In 2018, only 42% of 10th graders tested as proficient in math, as opposed to 73% in English. Even worse, only 23% of low-income students passed the math test.- Despite the above point, it is possible to dramatically boost math learning. We recently analyzed the effects of repeated interventions in elementary school, and estimated that moving an elementary student from not-proficient to proficient in math would cost between $1k–$4k per student. This isn’t the same as keeping them proficient until graduation,
*but clearly the benefits will far outweigh the costs!*

**To summarize,** we’ve used our “end-to-end” model of the Washington education system to estimate the benefits of improving test scores in both math and English. We find that math proficiency is far more important, with a lifetime benefit of over $650k in making a low-income student proficient in math. *This highlights that fact we should looking a lot more deeply at ways to make that happen!*