A friend of mine asked me to help her son Kenny, a six-grader, with his math homework. Kenny's assignment sheet was filled with mathematical puzzles such as:
Solve (A3B)+(B2C)=(1268), where A, B, and C are digits of the numbers.
In fact, my friend was asking for advice rather than solutions: She had spent a whole night, tried all possible options, and had come up with the answer: A=3, B=C=9. Her question is: Is there an easy way for her and her kid to solve such problems?
The answer to her question is yes and no.
Yes, there is an easy way to solve this problem. Kenny's classmate Billy, the know-it-all kid, figured that B+C has to be 18 so that 1 can be advanced to the 10's place. Therefore B=C=9, and it follows immediately that A=3. Problem solved. (See [solution 1].)
Yet no, the MATHEMATICAL way to solve this kind of problems is no easy. Using algebra, one would have to set up several equations and inequalities that A, B, and C satisfy, and then solve for A, B, and C. (See [solution 2].) This is the math behind the puzzle, and the kind of math that should be taught at school: It deals with problems in a systematic approach, is reliable, and is of great importance for students' future development in other math skills. This method, however, is too hard for six-graders.
A few days later, I learned that Kenny's teacher gave the class answers without much explanation. He did comment that math puzzles are tricky, and he showed the class some tricks they may use. Kenny, with all the help he could get from a diligent mom and her mathematician friend, got all the correct answers, of course. Now, as Kenny stares at his next assignment, another collection of more difficult math puzzles, he cannot help but feel helpless: He would never be as smart as his teacher or Billy, who solves these puzzles with ideas coming out of nowhere.
He thinks that he is so stupid that he could never do math on his own.
Puzzles for math homework: What is it good for?
Absolutely nothing. The kind of puzzles Kenny solved for homework are "bad" math or hardly math: They are tricky and only those who know the tricks can do them. They are shallow and do not undermine important concepts of mathematics. In the name of fun math and the so-called creative thinking, these puzzles intimidate those who are not good at solving them.
Let me tell you this: Mathematics is not about having fun playing little number games. It is not about learning or creating your own tricks to do some useless puzzles. It is not even about making students feel good after they manage to do these little tricks (and extremely dumb if they don't).
Math is about being capable of analyzing problems and performing calculations, at least arithmetic, successfully and constantly. It is about developing skills that allow students to intellectually grow further so that they deal with more complicated problems.
When I teach financial math, I expect students to be able to do the arithmetic, and to use their calculators (or Excel spreadsheets) properly. And when I teach combinatorics, I want them to be able to do elementary algebra with ease, and not to ask questions like: Should I simplify 1x1x1x9?
Our current education system, however, has failed to produce students that meet these expectations.
So, forget about those math puzzles, games, or whatever. There is a lot of good math yet to be taught to our kids. Puzzles are not mathematics, just like crosswords are not literature. Kenny should be doing 20 arithmetic exercises per day, not 20 math puzzles.
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[solution 1]
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[solution 2]
