Relearning math as an adult: Why starting from scratch is a trap

If you’ve decided to brush up on mathematics as an adult, or maybe even expand your knowledge further, you’re likely to run into a frustrating wall.

Let's say you want to transition into a new career or maybe you just want to conquer a subject that made you feel lost in high school. Before you know it you’re registering for a popular online math course.

The first few modules tell you to start from the beginning. This seems logical, and so you spend three days manually calculating fractions and doing basic long division. This isn't what you wanted to learn but it's an essential part of the process, right? Before long you’re getting bored and your drive fizzles out. Between work, family, and other obligations your time is limited. Inevitably you get busy, your bookmarked course starts to get buried, and you become part of the staggering statistic: 73% of online learners quit halfway.

Your first thought might be that you’re the problem. Maybe you aren’t sharp enough for it or maybe you just don’t have the dedication to stay at it. Meanwhile, the most likely problem is that traditional education treats mathematics like a ladder, forcing you to reclimb every single rung from scratch.

But human knowledge doesn’t work that way. Those years you spent in Algebra or learning all of the basics before that don’t entirely wash away. When we’re kids, linear learning is necessary. We have to learn to count before we can add. This is why, on the surface, the same approach seems logical when we circle back to math.

However, as an adult, your brain is already a complex web of mental models. You might not remember the exact formula for the quadratic equation, but you understand the concept of optimization. You might have forgotten how to manually compute a matrix, but you intuitively understand systems of moving parts.

When an online course forces you to sit through a two-week module on concepts you already subconsciously grasp, it creates friction and stifles your drive. You likely dove back into learning because you craved a new frontier of knowledge, and this light is dimmed by focusing your energy on things you already have a solid grasp on.

To put it simply: if you start too far behind, you get bored. If you jump too far ahead, you get frustrated. To successfully learn math as an adult, you don't need to start from scratch. You need to map your specific gaps in knowledge.

In the 1980s, cognitive scientists developed a framework called Knowledge Space Theory. It posits that a massive domain of knowledge (like all of undergraduate mathematics) isn't a straight line, but a complex web of interconnected states.

Every mathematical concept has prerequisites. If you understand Concept C, you likely understand Concepts A and B. Leveraging this logic, we’re able to completely redesign the flow of online courses.

Instead of testing you on 500 concepts individually, an adaptive algorithm can ask you specific questions to probe your knowledge. If you get a question right, it instantly deduces that you’ve mastered any of the foundational concepts behind it. If you get it wrong, it adjusts to narrow down exactly what stage your existing knowledge fell short.

This is how the 15 minute test on Consiliae can replace weeks of tedious review. It respects your time by identifying where your existing knowledge is strong and quickly figuring out where you’re best suited to begin learning.

So, if you are ready to give mathematics a second chance, drop the "back to basics" mindset. Instead, register on Consiliae and follow a framework designed to save you time and help you direct your energy wisely.

Tuan, Cofounder