## Mathematics instruction as a fish

Imagine that the theory of some branch of mathematics is a fish; say a halibut. Imagine that teaching that theory to someone is like giving that person that fish.

These are the alternatives.

• Old-time pedagogic — You are slapped with the fish. Repeatedly. Then there is a quiz.
• New-time pedagogic — You are never shown the fish. Instead, there is a lot of singing and holding of hands. Then everyone does a mind map about pleuronectidae. (“Sounds like my cousin Bob swearing.” — “Bob has a car.” — “It is a very nice car.” — “It has wonky taillights.”)
• Very old-time pedagogic — You are informed that there are two of you and only one fish. Two men (plus a halibut) enter, one man (plus a halibut) leaves.
• New-new time pedagogic — “I wonder… where that fish has gone. It is a most elusive fish.” (etc.)
• Neurotic Precise — You get the fish and all seems fine. Then when you try to fry the fish in butter, not margarine, someone hits you in the head with a chisel.
• Full-immersion — The instructor slits open the fish, and makes you wear it as a hat. Or a mask. Or, in the case of function theory, a big floppy body suit. With tentacles. And Poisson glands. (This is the grad student way.)
• Cramming — Do I need to spell this out? Fish, orifice, definitely no long-term benefits.
• Enhanced presentation — The fish — or rather the cloud of particles that until one tenth of a second ago was a fish — is shot at you from a cannon. This will leave a high-definition outline of you on the fish-gutted wall behind yourself. There are also about 16 mil colors — mainly variants blood red and innard pink. Oh, and you might see a Flash, or a Shockwave.
• Diploma mill method — You want some cheap fish, but you get bull instead.
• Short, what-you-need-to-know, partly imprecise executive overview: You flounder.