Fractious Fractions and Recalcitrant Radicals: The Straits of Algebraltar
Be careful, Witty!
After a year of smooth sailing in the placid waters of Pre-Algebra, amid an enticing blend of the familiar and the exotic, daring to brave the straits of Algebra I heaves you into icy waters and leaden skies, slapping waves and stinging spray, howling tempests and tortuous maelstroms. You aren’t in middle school anymore, Dorothy.
You’re passing through the straits of Algebraltar, where calm waters give way to the trials of the real voyage.
Let me say it plainly: Algebra I is the single biggest academic chokepoint in U.S. education. Multiple studies show that success in Algebra I strongly predicts high school graduation and college enrollment.
The U.S. Department of Education has repeatedly identified Algebra I as a “gateway course” linked to long‑term academic outcomes.
The National Center for Education Statistics (NCES) reports that students who complete Algebra I by 9th grade are more likely to take advanced math and graduate on time.
The Education Trust has published analyses showing that Algebra I failure disproportionately affects students from under‑resourced schools.
None of this would be a problem if our students were battening down the hatches and powering through. They aren’t. Algebra I failure rates are high and consistent across states, with many districts reporting 20–40% failure rates in 8th and 9th grade Algebra I.
The Brookings Institution has written extensively about Algebra I as a “structural bottleneck” that derails students early.
The Civil Rights Data Collection (CRDC) shows that Algebra I repeat rates are among the highest of any high school course.
What is so difficult about Algebra I? The problem, it appears, is not students’ intelligence but missing foundations. Research consistently shows the following:
Students enter Algebra I with gaps in fractions, ratios, and integers
These gaps are often years old
Algebra I exposes them brutally and immediately
All sources agree–you don’t get to say that often–fraction mastery is the single strongest predictor of Algebra success. Fractions! That’s 3rd grade math. I say this not to denigrate our students but to impress upon you, dear readers, the importance of staying on top of math skills. If you can’t handle fractions, then ratios, exponents, radicals, and rational expressions, just to name a few Algebra basics, will be nightmares from which you will never awake. Trust me.
In my thirty years of teaching standardized test math–mostly Algebra and Geomtery—the two must-review topics for nearly every student regardless of math level are fractions and exponents. I have seen innumerable calculus students throw away test points because they fumble problems with rational exponents (that’s the offspring of fractions and exponents; yes, such an abomination really exists).
As if all this weren’t disheartening enough, fractions aren’t the only bugbear of the beleaguered Algebra I student: Executive function plays a major role in success–or failure. Studies from Harvard’s Center on the Developing Child, The Learning Sciences Institute, and The University of Chicago’s Consortium on School Research all determined that Algebra I performance is strongly dependent upon the following:
working memory
cognitive load
task initiation
error monitoring
sustained attention
For many students, Algebra I is the first course where executive function weaknesses become academically visible.These are not math skills per se; they are thinking skills–in other words, the first thing most overworked teachers jettison in order to get through the curriculum. Algebra I peels back the curtain, revealing all the topics crammed for the test and quickly forgotten. And therein lies the rub: What students fail to understand, they memorize; and even if they retain the memory, it’s rote, an inflexible template useless for any variation of the problem to which it was originally applied.
Case in point: (x^2 )(x^3) = ? vs. (x^2)^3= ? Most students know the answers are x^5 and x^6, but they’re not always sure which goes with which equation. After a beat, they assign the answers correctly. But why? I ask, is the answer to the first equation x^5 and the second x^6? They respond, Because that’s the rule. When I push just a little bit more–But how does it work?--I lose 90% of the students. How does it work? You could be forgiven for not knowing how fuel injectors work, but not if your job is to build and repair engines. How matters.
This isn’t just about failing or repeating a course. Research from the National Science Foundation (NSF), ACT’s College Readiness Benchmarks, and the American Institutes for Research (AIR) early Algebra success predicts STEM access to all of the following disciplines:
chemistry
physics
computer science
engineering
calculus
The stakes are high. A deficiency in any of these shuts doors, many doors. Algebra I is an academic cascade point–what happened here ramifies not only through students’ educations but potentially through their lives.
Students don’t fail Algebra I because they’re not “math people.” They fail because the system lets foundational cracks widen until they become chasms. Our work at Wit’s End is to seal those gaps before they become life‑shaping detours.
If you know students already in these waters — or about to set sail — they don’t need a louder captain. They need a navigator. Someone who knows the currents, the hidden shoals, the places where the map is useless. That’s the work we do at Wit’s End—guide students through the straits before the storm hits.
Sources
ACT. College Readiness Benchmarks data linking Algebra I performance to STEM readiness.
American Institutes for Research. Studies showing that early Algebra success predicts access to chemistry, physics, engineering, computer science, and calculus.
Brookings Institution. Research describing Algebra I as a “structural bottleneck” that derails students early.
Civil Rights Data Collection. Data indicating that Algebra I repeat rates are among the highest of any high school course.
Education Trust. Analyses demonstrating that Algebra I failure disproportionately affects students in under‑resourced schools.
Harvard Center on the Developing Child. Studies linking Algebra I performance to working memory, cognitive load, task initiation, error monitoring, and sustained attention.
Learning Sciences Institute. Research identifying executive function as a major factor in Algebra I success.
National Center for Education Statistics. Findings showing that completing Algebra I by 9th grade increases the likelihood of advanced math enrollment and on‑time graduation.
National Science Foundation. Research connecting early Algebra success to later access to STEM fields.
U.S. Department of Education. Reports identifying Algebra I as a “gateway course” connected to long‑term academic outcomes.
University of Chicago Consortium on School Research. Findings showing that Algebra I performance depends heavily on executive function skills.
