Rachel McAnallen, known nationwide as "Ms. Math," starts her lecture about teaching math with a lesson in punctuation.
Seems odd until you see what she's driving at. The exercise involves two "Dear John" letters written by a woman named Gloria. Both letters contain the same words in the same order, but the punctuation is changed.
In the first letter, Gloria opens like this: "John, I want a man who knows what love is all about. You are generous, kind and thoughtful. People who are not like you admit to being useless and inferior."
Shine on, John!
But watch what happens in Gloria's second letter, where only the punctuation changes: "I want a man who knows what love is. All about you are generous, kind and thoughtful people who are not like you. Admit to being useless and inferior."
Tough day to be John.
What does this have to do with math and what does it mean for the teachers gathered at the MEA-MFT teachers conference in Missoula on Thursday?
"Respect the decimal point," said McAnallen, noting the tiny dot's ability to change everything, in both language and math.
Math, she told the teachers, is just another gorgeous language, but it's easy to teach it poorly by refusing to be flexible.
"I'm really a language arts teacher, I just came in through the math door," McAnallen said. "So today, I'm going to tell you how we screw up kids."
That drew a bit of tense laughter, which McAnallen quickly defused with a relentless bombardment of humor.
But McAnallen had serious points to make. Namely, that American math teachers have been stuck in the same mode of instruction since she was a student. Little, if anything, has changed, other than the textbooks.
"We get a new textbook every single year, but it turns out the Pythagorean theorem is the same as it always was," she said in an interview.
The problem with most mathematics instruction in America, McAnallen said, is that it's become hidebound. Math has to be done a certain way or it's wrong. That, she said, is part of the reason American children are falling distantly behind their peers in other developed countries.
"We need to be open to other ways of doing things," she said.
She used simple problems to make her point, about both teaching and the decimal point. Take this equation - 148 divided by four.
After a quick and hilarious disquisition on "long" division - why is there no long multiplication, for instance? - the 72-year-old McAnallen asked the teachers what they'd first ask the student.
"First step is four into one, right? Well, four doesn't go into one, am I right?" she said to the nodding teachers. "Well, that's wrong on two counts."
First, four does go into one and the answer is .25. But more importantly, the one is not really a one. It's 100, and four goes into 100 just fine.
Remember the decimal.
The problem is that teachers too often tell children that there's only one way to get the answer. That doesn't account for the differences in the way kids learn, but it also discounts the fact that there's more than one way to get the answer.
McAnallen, who has been a math teacher, an administrator and a department chairwoman in nearly 50 years in education, then returned to her problem, noting the division of one by four.
"OK, so that answer is a fraction, but we don't teach fractions during the chapter about division," she said. "And then we have another chapter about fractions. And then, to make it worse, we do ratios in yet another chapter. But guess what? It's all division."
That, she said, is why kids in other developed countries carry around a slim math book while American students haul around a behemoth that's so heavy that it requires its own backpack.
It's also why some children lose their way - they're being taught a language that isn't embracing its common tenets.
"We teach kids all these algorithms but we're not real good at making sure they understand them," she said.
But that's a problem teachers can fix McAnallen said.
A bigger problem is the standards imposed by the federal "No Child Left Behind Act." That law imposed certain standards that students and schools must meet if their schools are to continue receiving federal money.
"That's been very bad for math teaching," McAnallen said. "What's happened is that we're teaching to a test and that means we've left the best students on their own."
While the worst math students have made some progress, advanced math students have been left in a twilight zone.
"The unfortunate thing is those are the students we are going to depend on in the future to solve the problems that our generations have made," she said. "And now we've just left them hanging."
Reporter Michael Moore can be reached at 523-5252 or by e-mail at firstname.lastname@example.org