Microprep
Footwork in tennis and test prep
If you get a chance, watch Novak Djokovic’s feet for a minute during the French Open this year. Though firmly planted during the shot itself, his feet are constantly moving at all other times: crossing over each other back to the middle of the court after the shot, hopping slightly when the opponent starts to hit, darting towards where the ball will be, then tap-tap-tap-ing with both feet just before he starts the swing.
It’s the tap-tap-tap I’m interested in today, the microprep he and other pros do just before they swing. These players are so skilled, they could still hit a good shot without these little steps most of the time, but the steps help them move from a good position into a great one. And that great position leads to great shots a very high percentage of the time.
This microprep exists in test prep, but it’s almost impossible to teach it to the point of mastery.
Consider this math question:
“The 6 kids in Mr. Zeck’s class took a test. Their average score was 90. The 4 kids in Mr. Spectre’s class took the same test. Their average score was 60. What is the average score of all 10 students?”
Here’s how a student might process it for the first time:
It’s an average question. Can I average the 60 and 90? No, because the classes have different numbers of students. So it’s a weighted average. Which way do I want to do it, with algebra or arithmetic? I messed up the algebra last time, so arithmetic. I’m thinking “total points divided by total students.” Total points: 90*6 + 60*4 = 780. Total students: 10. Answer: 78.
Notice all the little steps involved here – identifying the question type, specifying the variation, choosing the solving strategy, recalling the general shape of the answer, then executing. You might ask, “How is that not teachable? Just teach those steps to everyone!” But this is just one of many, many possible average questions. Here are a few others:
If the average of x and 6 is equal to the average of 1, 10, and x, what is the value of x?
Five students take a test. Two of the students are 3 points above the average (arithmetic mean). One student is 4 points below the average. Another is 11 below the average. How many points above the average was the fifth student’s test?
Barry’s first three test scores were 85, 93 and 91. He can’t remember his fourth test score, but he knows that his average for all four tests was 88. What was his fourth test score?
My “weighted average” process wouldn’t work for any of these questions, nor could I construct a magical skeleton key that would work for all averages.
In fact, that process wouldn’t even work for all students answering that exact question! What if the algebraic solving strategy I dismissed was better for that student? What if the thing the student had “messed up last time” was mental math? No student’s thought process will be exactly the same as another’s, even if the general response shapes and individual steps are similar.
This is quite similar to tennis shots. In a real game, no shot is exactly the same as any you’ve hit before. You can classify the shot (forehand) and you can identify the specific type (running forehand, aiming down the line), but the speed, spin, height, location, and angle of the ball will never quite be the same. Furthermore, no tennis player is exactly the same. Each one has a different body, with different swing mechanics, and different favorite shots. As a result, the players approach shots differently. On a given ball, one player might run around it so that he can hit his forehand. Another might hit a deep backhand slice to extend the rally. A third might attempt a drop shot.
Unique players attempting unique shots – what can coaches do? Sometimes, a shot comes up so frequently that it’s worth practicing a model version of it, sort of like Bernard King’s process I described in 22 Spots. But it often makes sense to focus on elements that will help the player on many shots, things like fitness, swing mechanics, target selection…and footwork.
If you watch an amateur’s feet, you can pretty easily predict when he’ll miss a shot. If he’s tired and responds with a lazy lunge, you can tell the shot will fail. The same is true in test prep – a student who is rushed or not thinking carefully will often make mistakes. And as in tennis, students are not eager to make this footwork habitual. It adds a little bit of extra work to every question, and many questions can be solved without it. But when students are fighting for two or three additional questions right (“I just need 30 more points!”), this microprep is often the most likely path to success.
But here we’re at a disadvantage in test prep. We don’t have full access to the student’s microprep, because it’s mostly in her mind. When a student stares at the paper for thirty seconds, she might be following a detailed, logical process…or she may be zoning out. Furthermore, just as a tennis player may not recall what steps he took before his shot, the student may not recall the exact thought sequence. The tennis coach can see the steps for himself; we can’t. Even worse, the student can’t see the correct process either.
And that’s one reason tutors ask questions like “How far did you get with this one?” and “How were you approaching this?” It’s also why we so often model our own solving method in an interactive way, both thinking out loud and frequently allowing the student to drive (“and then what would you do next?”). These methods help us see the footwork, and they help students learn it…or at least one version of it. Adapting it to their next shot is up to them.