Teaching teachers 

 Andrew Gelman has some  good comments  on the great Elizabeth Green  article  about teaching in the  New York Times  Magazine. The article is about how to improve both classroom management and subject instruction for K-12 teachers, but Gelman correctly points out that many of these the struggles resonate with those of us teaching statistics at the undergraduate and graduate levels.  

 I used to be of the opinion that the teaching of children and the teaching of adults were two fundamentally different beasts and comparisons between the two were missing the point. The more I teach, though, the more I see teaching as a kind of a skill which is  separated from the material being taught. Knowing a topic well does not imply being able to teach a topic well. This should have been obvious to me given the chasm between good research and good presentations.  1   The article nails this as it talks about math instruction: 
 Mathematicians need to understand a problem only for themselves; math teachers need both to know the math and to know how 30 different minds might understand (or misunderstand) it. Then they need to take each mind from not getting it to mastery. And they need to do this in 45 minutes or less. This was neither pure content knowledge nor what educators call pedagogical knowledge, a set of facts independent of subject matter, like Lemov's techniques. It was a different animal altogether.  

 If this is true, how can we improve teaching? I think that Gelman is right in identifying student participation as important to teaching statistics. Most instructors would agree that statistics is all about learning by  doing , but many of us struggle to identify how to actually implement this, especially in lectures. Cold-calling is extremely popular with law and business schools, but rare in the social sciences. Breaking off to do group work is another useful technique. In addition to giving up control of the class (which Gelman mentions), instructors have to really build the class around these breaks.  

 Reflecting on my own experience, both as a student and an instructor, I am starting to believe in three (related) fundamentals of statistics teaching: 
  
	  Repetition.  If we really do learn by doing, then we should pony up and have students do  many  simple problems that involve the same fundamental skill or concept.   
  Mantras.  We are often trying to give students intuitions about the way statistics "works," but many students just need a simple, compact definition of the concept. Before I understood the Central Limit Theorem, I could tell you what it was ( "The sums and means of random variables tend to be Normal as we get more data" ) because of the mantra that my first methods instructor taught me. As a friend told me, statistics is a foreign language and in order to write sentences you first need to know some vocabulary.   
  Maps.  It is so easy to feel lost in a statistics course and not understand how one week relates to the next.  A huge help is to give students a diagram that represents where they are (specific topic) and where they are going (goals). The whole class should be focused around the path to the goals and they should always be able to locate themselves on the path.  
  

 There are probably more fundamentals that I am missing, but I think each of these is important and overlooked. Often this is simply because they are hard implement, instructors have other commitments, and the value-added of improving instruction can be very low. In spite of these concerns and the usual red herrings  2  , I think that there are simple changes we can make to improve our teaching.  
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   1  Perhaps a more subtle point is that being a good presenter does not imply being a good instructor. They are related, though. Good public speakers have an advantage as teachers, since they are presumably more comfortable in front of crowds. The goal of presenting (persuasion) and the goal of instruction (training people in a skill) are very different. People confuse the two because the medium is often so similar (lecture halls, podiums, etc). ↑   
   2  Teaching evaluations are important, but they are often very coarse. Students know if they didn't understand something, but rarely know why. Furthermore, improving evaluations need not come from improving instruction.  ↑