Dive Brief:
- Math logic puzzles can prompt students to work together in a way that incorporates play and critical thinking while easing the usual pressures and daily routine of solving standard math problems, math education experts say.
- Deductive reasoning is a step-by-step process for using information to find a unique solution to such puzzles. But students often don't exercise that skill in traditional math curriculum until students take geometry in high school and are required to use it to solve proofs, said Jeff Wanko, dean of the College of Education and Health Sciences and a math education professor at Bradley University in Peoria, Ill..
- Organizations such as the National Council of Teachers of Mathematics, as well as other educators, say waiting that long does students a disservice, Wanko said. “I see these puzzles as one way we can develop what I call ‘proof-readiness.’”
Dive Insight:
Sudoku, invented in the U.S. in the late 1970s but renamed and popularized by the Japanese puzzle magazine Nikoli, is probably the most well-known of these math puzzle games. But there are others — many of which originated in Japan — including Shikaku, Kakuro and Hashiwokakero, said Wanko.
“One of the coolest things is, for every puzzle I have ever seen, there’s not just one way to get to that unique solution," Wanko, who taught at Miami University of Ohio for 25 years before working at Bradley this school year, said. "There are a lot of problem-solving strategies.”
For example, Shikaku, one of Wanko’s go-to puzzles, involves numbers on a grid similar to Sudoku, except the puzzle-solver needs to draw a rectangle around each set of numbers with a surface area that corresponds to the numbers inside — and on top of that, the rectangles need to fit together like a puzzle.
“All the spaces in the grid get used,” he said. “It’s not just guess-and-check, put a ‘2’ in this box. That’s not deductive reasoning. With real deductive reasoning, I’ve eliminated the other possibilities, and only a ‘2’ can go in this box.”
Wanko recommends that educators start with Sudoku and other math logic puzzles in later elementary grades, although there are simpler versions — like Sudoku puzzles on 4x4 or 6x6 grids instead of the usual 9x9 — if you want to start earlier than high school. Reputable puzzle-makers typically provide a rating system to provide an indication of how difficult a certain puzzle might be, he said.
Before introducing students to the different puzzles, teachers should get comfortable with the games' rules and with the idea that there might be more than one way to get to a correct answer, the latter of which Wanko said wasn’t necessarily a strength of math teachers he encountered while growing up.
“We have to recognize the importance of having more than one way to solve problems, and that different students think differently,” he said. “It’s important to validate different ways to think through something, if it is still mathematically correct.”
And don’t judge a puzzle itself at first glance, either, he added. “Sometimes you get into it, and you think, ‘Wow, there were advanced strategies I didn’t realize [at first].’”
One of the many things Wanko likes about math logic puzzles is that students who don’t necessarily score the highest on traditional tests can find a way to shine.
“These can often excite kids who have not been turned on to mathematics yet,” he said. “Oftentimes, it’s not your best math student who might have insight into a puzzle.”
