8 Failure Modes to Watch Out for in Math Learning Resources
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8 failure modes to watch out for in math learning resources, that will tank your learning efficiency:
Failure Mode #1: Not enough scaffolding.
You periodically run into situations where you bang your head on a wall thinking “how the heck did they get from here to there?” and it takes a long time to figure out what kind of logical leap is happening (if you figure it out at all).
Failure Mode #2: Doesn’t track your knowledge and make sure you’ve mastered the prerequisites for anything new you’re supposed to learn.
You often feel a large gap between your level of knowledge and the new material, which leads to more banging your head on a wall trying to figure out what prerequisite knowledge you’re missing and how to learn it.
Failure Mode #3: No spaced review.
You quickly get rusty on a lot of what you learn, which not only means you come out of the course having forgotten a lot of content, but even during the course, you’re constantly forgetting prerequisites.
Failure Mode #4: Doesn’t adapt to your level of performance.
You waste a lot of your time doing the wrong amount of work. Sometimes you grasp a topic quickly and end up doing way more practice problems than you need; other times you struggle with a topic and don’t do enough practice problems to reach mastery.
Failure Mode #5: Leaves the definition of “mastery” open to interpretation by the learner.
As a learner, it’s hard to know when you’ve mastered something well enough to continue moving forward.
You often think you’ve learned something well enough, when you actually haven’t – but you won’t know unless there’s an expert who is evaluating your knowledge.
On the flipside, you can also take things too far being a perfectionist, spinning your wheels on the same topic for a week over some minor point that doesn’t make perfect intuitive sense to you, when it would be more productive to just keep moving forward and solidify your understanding by building on top of it.
Failure Mode #6: Not enough successful problem-solving experiences.
In a typical college course, you might solve 50-100 homework problems all semester. There’s so much educational friction that it takes you 20+ minutes to struggle through each problem, often not even getting it right until you give up and look at a solution or get help at a TA session.
But if the problems were broken down and presented in a more finely scaffolded sequence, and each problem only presented once you’ve mastered the prerequisites, then you could get through problems much faster, say, just a couple minutes per problem on average.
That’s what a good tutor would do: scaffold your learning experience so that you’re solving a problem every couple minutes. They would build up your learning in bite-size increments. You could get through 10x as many problems that way, with a much higher success rate.
Failure Mode #7: Not enough knowledge audits.
Most college courses have only a handful of exams throughout the entire semester (and even grade school classes seldom have more than one quiz per several weeks).
But quick, frequent timed quizzes – say, 15 minutes every couple days – are a powerful way to engage in retrieval practice and build automaticity while simultaneously identifying weaker areas in need of additional practice.
Failure Mode #8: Not enough targeted remediation.
It’s rare to find a resource that gives you additional practice after you miss a question on an assessment. At best, you might take it upon yourself to review the questions you missed.
But it would be far better to complete a battery of additional problems like each one you missed, until you’re able to successfully and consistently solve those problems – and then you’d want to evidence that knowledge on a quiz retake (with different problems of the same types).
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