December Brainteaser Solution, And "No Such Thing As A Bad Math Student"
01/21/2020
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I've posted a worked solution to the brainteaser in my December Diary here.

Meanwhile, a friend has passed on this bit of math news from three years ago. It's about a Canadian named John Mighton who claimed to have discovered the secret to making all kids good at math.

Mighton thinks—and offers brain research (pdf) to support it—that kids succeed more with math when it is broken down into small components which are explained carefully and then practiced continually. [A mathematician has created a teaching method that's proving there's no such thing as a bad math student by Jenny Anderson; qz.com, February 15 2017.]

Uh-huh. Excuse my skepticism. If you think the diet business is the galactic-core concentration of wacky fads, you have never undergone a teacher-training course.

Back in my own days of training to be a math teacher, the fad was for "exploratory" math, in which kids were supposed to discover principles for themselves. The following joke was current in the student lounge.

An Inspector of Schools is observing a math class in progress. He watches one little girl carefully assembling a 6-by-7 rectangle out of colored bricks. When she's through the inspector nods approvingly and asks the child: "Now, can you tell me what is six times seven?"

The little girl scrunches up her face in concentration and, with eyes closed tight, recites her multiplication table: "One seven is seven two sevens are fourteen three sevens are twenty-one four sevens are twenty-eight five sevens are thirty-five six sevens are forty-two. So …" [opening her eyes] "… it's forty-two."

The inspector frowns. "Well … yes. That is the right answer. But … why were you laying out those blocks like that?"

"Because Teacher told me to!"

However, Mr Mighton offered historical support for his position:

Mathematicians "have big egos, so they haven't told anyone that math is easy," he said at the World Economic Forum in Davos last month. "Logicians proved more than 100 years ago it can be broken into simple steps."

I assume that's a reference to Whitehead and Russell's Principia Mathematica, sample page here