Finding exactly where algebra gets hard

Now that thousands of students have gone through the 88 interactive lessons of AlgebraX (not to mention the 92 lessons of GeometryX), we're starting to see trends emerge. We previously found how engaging our interactive lessons are (compared to plain video lessons), and in this post we'll dive into the content itself.

One thing we hear over and over again is how hard algebra is. It's true -- learning algebra can be quite challenging. But it's also important: every subsequent math subject (geometry, trigonometry, calculus, statistics, and so on) builds on the foundations of prior ones, starting at algebra.

With AlgebraX, we're trying to make it easier (and more fun!) to pick up algebra. So are we accomplishing this? Where should we be improving our lessons? (That's something we ask ourselves all our time, because our authoring platform is uniquely suited toward iteration and improvement.)

One way to measure the difficulty of different topics is to look at how many students completed review questions (the assessments in AlgebraX) vs. how many students attempted those questions. If a topic is hard to learn (and/or our lesson on that topic could use improvement), we'd expect to see fewer students complete the corresponding review. Now this differs from how advanced a topic might be. For example, factoring quadratic polynomials is pretty advanced stuff for Algebra I, but students zipped right through those review questions in the course.

Here's a bar graph showing the completion of all the reviews in AlgebraX. Each topic has its own bar, and the vertical axis shows the percentage of students who started a review who finished it (meaning they mastered the topic).

The first thing to notice is that it's mostly green. In fact, the average completion rate for AlgebraX reviews is 96.1%. Once a students starts a review, it's highly likely that he/she will finish it. So what about those red and yellow areas? Well, here's a list of the hardest topics in algebra -- a "hit-list," if you will, where we'll focus on improving our lessons:

1. Two equations, two unknowns (78.3% completion)
2. Fractional exponents (82.0%)
3. Two equations, with no solution (84.1%)
4. Solving for intercepts (85.0%)
5. Point-slope form (86.7%)
6. Discriminants and roots (87.5%)
7. The quadratic formula (87.9%)
8. Solving multi-step equations (88.1%)
9. Multi-variable equations (90.5%)
10. Distributing roots (91.0%)
11. Perpendicular slopes (91.3%)
12. Calculating averages (91.4%)

And what's the "easiest" topic? You might think it's something early on in the course, but then you'd be wrong. It's simplifying expressions by combining like terms, a topic that 99.8% of students have mastered.

We're already underway improving the more challenging topics in the course, both by improving the lessons themselves, as well as by adding new hints to review questions. Our goal is to turn this entire chart green. Yes, algebra will still have advanced topics, but nothing will be too hard for students to conquer!