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The Four Stages of Competence: Math Edition


We all like to think of ourselves as active participants in our lives. We make decisions from sun-up to sun-down: when to wake up, what to eat for breakfast, what email to answer first, what podcast to listen to on the drive home.

However, the uncomfortable truth is that our behavior is more mindless and automatic than we like to think. As Charles Duhigg noted in his book, The Power of Habit, somewhere around 40% of what we do each day is dictated by habit.

We receive a cue from our environment―for example, we walk into the kitchen and see the coffeemaker―and then the routine of the habit starts. We make coffee, drink it, and experience the “reward” of a warm, delicious beverage―and a hit of caffeine. Thus the habit is reinforced one more time.

Often our habits reside very far below the surface of consciousness. The next time you brush your teeth, pay attention to which part of your teeth you brush first. You’ve probably brushed them the same way since you were young. Or think about driving: when was the last time you really thought through the sequence of steps? You most likely turn the car on, put on your seat belt, check mirrors and put the car in reverse with very little thought. All of these routines have become muscle memory, deeply ingrained habits that require little to no conscious attention to execute.

Now, let’s consider how habits and unconscious behaviors relate to learning.

Most students have had the frustrating experience of being sure that they got a problem correct on a test, only to miss getting credit because of a careless mistake. Often the careless mistake is as simple as not distributing a negative sign correctly or solving for the wrong value. For some students, careless mistakes are pervasive in their work and a real barrier to improving their grade in a class or their SAT score. So what’s happening there?

There’s a model in psychology known as the four stages of competence (or the four stages of learning). The four stages are:

  1. Unconscious incompetence
  2. Conscious incompetence
  3. Conscious competence
  4. Unconscious competence

As we discussed before, much of what we do in our daily lives happens below the level of consciousness. We’ve been driving for years, so we can operate a two-ton SUV hurtling down the highway at 70 mph without too much active thought.

When a student’s math work is riddled with careless mistakes, they’re living in the first stage―the world of unconscious incompetence. To sum it up, they don’t know that they’re doing anything wrong, or they don’t know what they don’t know.

Our goal as tutors and educators is to move our students through all four stages of competence, hopefully arriving for good at the level of “flow,” or unconscious competence. The million dollar question, however, is how to move from one stage of competence to the next. Let’s explore the stages and how these play out for our tutors and their students.

Moving Through the Four Stages of Competence

1. Unconscious Incompetence

As we said before, this stage is characterized by unthinking, careless mistakes or an incorrect understanding of a concept that a student assumes they know. The giveaway that a student is in the first stage of competence is surprise at an incorrect answer or a bad test score. The student had no idea they were on the wrong track.

2. Conscious Incompetence

A student usually moves into conscious incompetence when prompted by someone else―a parent, teacher,  tutor, or by their own systematic review of their work. At this stage, students are aware of what they’re doing, and they’ve made the important move from “unthinking” to “thinking.” This should be praised!

Here’s a typical scenario: a student just got back an algebra test on solving systems of equations, and he received a much lower score than he was anticipating. He reviews his test with his tutor at the next session. The tutor points out that the student failed to correctly multiply equations all the way through by the appropriate constant.

The next time a student tries to solve a system of equations, he’s operating at the level of conscious incompetence. Now he knows that he doesn’t know how to do this correctly (or without careless errors), and he might get the problem wrong.

Conscious incompetence is a really uncomfortable place to be. No one likes to know that they’re doing a problem wrong! Thus, our goal as math tutors is to not let our students stay here for long. We try to channel our students’ discouragement into productive motivation to get the problem down cold. Which brings us to our next stage…

3. Conscious Competence 

Okay, this is better. When you work at this level, you’re getting things right. You still have to actively think about how to do a problem or how to avoid a careless mistake, but you have the satisfaction of getting a correct answer and a good test score.

So, how does a student move from level 2 to level 3, or from conscious incompetence to conscious competence? After all, this is the jump that makes the big difference in performance and confidence.

Unfortunately, I have to be the bearer of bad news here. There’s no magic pill that lets you jump levels. Moving from conscious incompetence to conscious competence takes a great deal of focused practice targeted on your weak areas. It also takes a willingness to relentlessly confront your mistakes, over and over, until you start consistently getting things right. This process hopefully won’t take 10,000 hours, but it does take time.

Our math tutors help students move to conscious competence by drawing on their experience to quickly diagnose students’ mistakes. We tailor effective problem sets that get students quickly on the path to competence.

4. Unconscious Competence 

Finally, we’ve returned to the unconscious level. To recap, this is the level most people operate on when they drive their car, make coffee, or do other routine daily tasks.

Unconscious competence―“being in the zone” or “experiencing flow”―allows you to efficiently and accurately get problems right without too much active thought. For routine math work and standardized tests like the SAT and ACT, this is a great place to be.

Cultivating Good Habits

Let’s return to our discussion of habits for a moment. Habits take place on the subconscious level and consist of a cue, routine, and a reward. Fitting habits into the levels of competence model shows us that math habits can be good or bad, competent or incompetent.

If your student is struggling with careless mistakes, their goal and their tutor’s goal should be to interrupt the routine of unthinking errors. This can be accomplished by reviewing math work with an eye toward identifying types of problems or behaviors that trigger mistakes. Does the student always miss questions with fractions? Do they miss more questions at the end of a test because they’re rushing to finish?

Once we identify those triggers, our tutors can move students through the levels of competence via targeted practice. And once a student is “consciously competent,” we’ll work to build new cues, routines and rewards that lead to the virtuous cycles of good math habits. Good math habits lead to greater success in school and on standardized tests. Even better, good math habits lead to a lifetime of self-confidence in one’s mathematical ability.


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