kitchen table math, the sequel: Math students in other countries can do, plus a brain teaser

Sunday, April 26, 2015

Math students in other countries can do, plus a brain teaser

From Nicholas Kristoff's column in the Times today:

What is the sum of the three consecutive whole numbers with 2n as the middle number?

A. 6n+3

B. 6n

C. 6n-1

D. 6n-3

More than three-quarters of South Korean kids answered correctly (it is B). Only 37 percent of American kids were correct, lagging their peers from Iran, Indonesia and Ghana.


A piece of wood was 40 centimeters long. It was cut into 3 pieces. The lengths in centimeters are 2x -5, x +7 and x +6. What is the length of the longest piece?

Only 7 percent of American eighth graders got that one right (the answer is 15 centimeters). In contrast, 53 percent of Singaporean eighth graders answered correctly.


How many degrees does a minute hand of a clock turn through from 6:20 a.m. to 8 a.m. on the same day?

A. 680 degrees

B. 600 degrees

C. 540 degrees

D. 420 degrees

Only 22 percent of American eighth-graders correctly answered B, below Palestinians, Turks and Armenians.


Correlation isn't causation, but the absence of correlation is meaningful.

Fifteen years of constructivist mathematics programs adopted in virtually every public school in the country, fifteen years of teacher-training in authentic problem solving and guide-on-the-sidery, and here we are.

At a minimum, we can say that constructivist math has not been a blinding success.


Back to Kristoff, I love this brain teaser for some reason:

You’re in a dungeon with two doors. One leads to escape, the other to execution. There are only two other people in the room, one of whom always tells the truth, while the other always lies. You don’t know which is which, but they know that the other always lies or tells the truth. You can ask one of them one question, but, of course, you don’t know whether you’ll be speaking to the truth-teller or the liar. So what single question can you ask one of them that will enable you to figure out which door is which and make your escape?
Are You Smarter Than an 8th Grader?


kcab said...

For more like the brain teaser, try "What is the Name of this Book?" by Raymond Smullyan. Or look for "knights and knaves" puzzles, seems likely that other people have published them as well.

We love that type of logic puzzle in my house!

Glen said...

Ask either guy (I'll assume 2 guys): "Which door will he [pointing at the other guy] say is the escape door?"

Whatever the answer, take the other door.

If you ask the truth-teller what the liar will say, you'll get the lie. If you ask the liar what the truth-teller will say, you'll get the lie.

You can therefore be confident that the answer is a lie, regardless of who you ask.

lgm said...

It doesnt matter what technique is used for teaching, if the student is not attending enough to benefit (in body and mind) or the amount of material has been reduced by eliminating topics such as problem solving, clock arithmetic, etc. The material needed to solve those problems described wasnt offered to either of my children at their public school after nclb and full inclusion started. It was offered before, when students were grouped by instructional need. Now, it is left for the parent to afterschool.