The Math Death Spiral: How Knowledge Gaps Lead to Student Failure

Accumulating mathematical knowledge gaps can lead students to reach a tipping point where further learning becomes overwhelming, ultimately causing them to abandon math entirely.

When people age, they accumulate biological damage that eventually reaches a tipping point and leads to a cascade of catastrophic health issues.

The same thing happens to students learning mathematics.

Students accumulate knowledge gaps as they progress through math, and they stop taking math classes once the number of gaps reaches a tipping point and spirals out of control.

Knowledge gaps can form in a variety of ways. To name a few:

• A student may get stuck on foundational topics yet still be required to complete homework on more advanced topics, leading them to scrape by without really understanding the subject matter. Even a grade of B+ or A- means that there are things in the course that the student never completely grasped, much less mastered.
• Students typically do not review material learned in previous years (unless it just happens to be practiced implicitly while attempting to learn new content), and they often do not even review material from their current year unless they are preparing for a test. This leads them to forget what they’ve learned -- often so severely that they need to re-learn it from scratch when it shows up again in the future.
• Gaps can also be created if a student takes a course that is watered down or otherwise not comprehensive. When a future course assumes prior knowledge that the student never actually learned, that’s a gap.

Now here’s the real kicker: gaps beget more gaps.

Once you have a gap, you are unable to fully understand any new information further down that learning path. The gap proliferates.

Consequently, once a student amasses a critical number of gaps, things spiral out of control and a vicious cycle kicks off.

1. The cycle begins with a student trying to imitate procedures cookbook-style, without really understanding what’s going on, because they can’t intuitively grasp any of the new material that they’re being taught.
2. Soon after that, they find themselves unable to solve any problems that involve critical thinking or many steps.
3. Finally, they stop taking math classes because they feel it’s impossible to succeed no matter how hard they try.

The student may interpret this situation as “I’m not smart enough to learn more math” – when in fact, their mathematical lifespan could have been extended simply by having their knowledge gaps detected and repaired.