For students, it's hip to do squares

The lights dimmed, and a grid strewn with numbers splashed across a projection screen, transfixing Tish Mency's sixth-grade math class like a summer blockbuster. It was Sudoku time.

The students at Belmont Street Elementary School in Brockton quickly scanned the puzzle on the screen for patterns, and within moments hurled their hands into the air to volunteer. Handed a wooden pointer, young George Holyoke-Spencer took the first crack.

"Eight can't be here, or here," he said, pointing to two cells in the top left corner, "because of this," tapping an 8 already in that row. "And it can't be here or here, either, because of this 8 down here," tapping a square in the bottom left corner. By George, he'd got it: "The 8 has to go here," he said, conclusively.

It was a mind-bending sight: students hooked on a box of numbers like it was an Xbox game. But as legions of addicts know, Sudoku is no ordinary puzzle. A fixture on subway cars, Internet sites, and best-seller lists, the brainteasers are now inexorably finding their way into the classroom.

Mency uses the logic-based puzzles once a week, joining a growing number of math teachers mining the games to hone problem-solving skills, powers of deduction, and mental patience and focus. Though they are number-based, the puzzles involve no arithmetic but help students recognize patterns, follow logical progressions, and solve complex problems systematically, educators say.

"There's no actual math, but there's a lot of strategizing," Mency said. "And a lot of math is strategizing."

Using George's 8, Patricia St. Martin was able to find another in the top right, and the puzzlers were on their way. Mency urged her students to use the process of elimination to find solutions, and justify their answers by explaining their reasoning, kind of a grade-school version of a geometric proof.

"They have to show how they know it," she said. "They have to justify each move."

Sudoku is a simple yet endlessly variable puzzle. The goal is to fill the empty grid with the numbers 1 through 9 without repeating a number in any row or column.

The game became popular in Japan in the 1980s before taking the rest of the world by storm last year when a New Zealander named Wayne Gould wrote a computer program to produce the puzzles and persuaded a London newspaper to print them. A pop-culture craze was born.

Sudoku and math are a natural fit, said James Rubillo , executive director of the National Council of Teachers of Mathematics , because the puzzles require students to develop logical strategies and techniques.

"It forces you to ask the 'What if?' questions, and it teaches cause-and-effect in a relatively simple way," he said. "Students have to take all the facts and draw a conclusion."

An informal survey of area schools found that many math teachers are using the puzzles in class, either as an entertaining supplement to the regular curriculum, or as extra credit or a fun diversion after a long week. And many of the students, even as young as third and fourth grade, had already worked on the puzzles at home.

Kate McAlarney, who assigns the puzzles to her Cohasset sixth-graders, said the puzzles help promote abstract thought and teach students to think on several levels at once.

For Deborah Anderson , who just began incorporating Sudoko into her sixth-grade math class at Norwell Middle School, the puzzles are excellent problem-solving exercises, particularly since many students are unaccustomed to breaking down complex, multipart questions.

"It's the one area I find they really need strengthening," she said. Like many areas of math, Sudoku involves "trying to find an unknown," she said.

Duxbury High School math teacher Karen Hendrickson hands the puzzles out as extra credit, and praises them for helping students learn to tackle tough algebraic equations.

"It's the same kind of logic," she said. "Nothing has more variables than Sudoku."

Educators don't know for sure whether Sudoku is improving students' math skills, but many believe it is sharpening reasoning skills that will pay off on standardized tests.

Sudoku puzzles range widely in difficulty, and while the version Mency's sixth-graders are tackling isn't diabolical, it's not the easiest, either.

Kevin Gomes-Viera thought he had found the spot for the 3 in the bottom right square, then realized a 3 was already there. A common mistake, and he rebounded nicely, noticing there was only one square for the 3, in the lower left section.

"It has to go there," he said. His teacher wanted to know why. "The other 3 blocks the others."

"Right. Nice recovery," Mency said.

She introduced the puzzles to her math class last year, and found the students were not only thinking more logically, they also enjoyed solving them and would be racking their brains to finish them long after they would have punted on fractions or word problems. Top finishers in her class win prizes, and the competition seems to sharpen their focus.

Mency said that while arithmetic problems are fairly cut-and-dried, Sudoku puzzles can be tackled from many angles, forcing students to think creatively and try new approaches when initial attempts fail.

"They are so used to getting the answer one way," she said. "This forces them to be creative."

In a classroom with many foreign-born students who haven't mastered English, Sudoku is even more useful, helping them learn logic without word problems they might not understand.

"There's no language to get in the way," Mency said.

Peter Schworm can be reached at schworm@globe.com.